Subgroups — C₈₉×#62923 #36440771

Order 22784.

7300 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3558	C₂	1	6	yes	maximal, complemented
2	C₈₉×#3549	C₂	1	3	yes	maximal, complemented
3	C₈₉×#3547	C₂	1	3	yes	maximal, complemented
4	C₈₉×#3546	C₂	1	3	yes	maximal, complemented
5	C₈₉×#3546	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3543	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3542	C₂	1	6	yes	maximal, complemented
8	C₈₉×#3540	C₂	1	6	yes	maximal, complemented
9	C₈₉×#3524	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3519	C₂	1	3	yes	maximal, complemented
12	C₈₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3514	C₂	1	3	yes	maximal, complemented
14	C₈₉×#3508	C₂	1	3	yes	maximal, complemented
15	C₈₉×#3500	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3488	C₂	1	2	yes	maximal, complemented
19	C₈₉×#3487	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3483	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#3460	C₂	1	3	yes	maximal, complemented
24	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
25	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	2	yes	complemented
26	C₂²×#41×C₈₉	C₂²	1	2	yes	complemented
27	#562×C₈₉	C₂²	1	12	yes	complemented
28	H(3,𝔽₄)×C₈₉	C₂²	1	12	yes	complemented
29	#560×C₈₉	C₂²	1	12	yes	complemented
30	#560×C₈₉	C₂²	1	12	yes	complemented
31	#559×C₈₉	C₂²	1	3	yes	complemented
32	#559×C₈₉	C₂²	1	6	yes	complemented
33	#559×C₈₉	C₂²	1	6	yes	complemented
34	#559×C₈₉	C₂²	1	3	yes	complemented
35	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#556×C₈₉	C₂²	1	3	yes	complemented
38	#556×C₈₉	C₂²	1	3	yes	complemented
39	#556×C₈₉	C₂²	1	6	yes	complemented
40	#555×C₈₉	C₂²	1	6	yes	complemented
41	#555×C₈₉	C₂²	1	3	yes	complemented
42	#555×C₈₉	C₂²	1	6	yes	complemented
43	#555×C₈₉	C₂²	1	3	yes	complemented
44	#555×C₈₉	C₂²	1	6	yes	complemented
45	#554×C₈₉	C₂²	1	3	yes	complemented
46	#553×C₈₉	C₂²	1	3	yes	complemented
47	#553×C₈₉	C₂²	1	3	yes	complemented
48	#553×C₈₉	C₂²	1	6	yes	complemented
49	#553×C₈₉	C₂²	1	6	yes	complemented
50	#552×C₈₉	C₂²	1	6	yes	complemented
51	#551×C₈₉	C₂²	1	12	yes	complemented
52	#550×C₈₉	C₂²	1	1	yes	characteristic
53	#550×C₈₉	C₂²	1	1	yes	characteristic
54	#550×C₈₉	C₂²	1	2	yes	complemented
55	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#550×C₈₉	C₂²	1	3	yes	complemented
57	#550×C₈₉	C₂²	1	2	yes	complemented
58	#550×C₈₉	C₂²	1	6	yes	complemented
59	#550×C₈₉	C₂²	1	6	yes	complemented
60	#550×C₈₉	C₂²	1	3	yes	complemented
61	#550×C₈₉	C₂²	1	6	yes	complemented
62	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	D₄×Q₈×C₈₉	C₂²	1	3	yes	complemented
64	#548×C₈₉	C₂²	1	2	yes	complemented
65	#548×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#548×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#548×C₈₉	C₂²	1	2	yes	complemented
68	#548×C₈₉	C₂²	1	6	yes	complemented
69	#548×C₈₉	C₂²	1	6	yes	complemented
70	#548×C₈₉	C₂²	1	2	yes	complemented
71	#548×C₈₉	C₂²	1	2	yes	complemented
72	#548×C₈₉	C₂²	1	6	yes	complemented
73	#547×C₈₉	C₂²	1	3	yes	complemented
74	#547×C₈₉	C₂²	1	6	yes	complemented
75	#546×C₈₉	C₂²	1	6	yes	complemented
76	#546×C₈₉	C₂²	1	6	yes	complemented
77	#546×C₈₉	C₂²	1	6	yes	complemented
78	#546×C₈₉	C₂²	1	6	yes	complemented
79	#546×C₈₉	C₂²	1	6	yes	complemented
80	#546×C₈₉	C₂²	1	6	yes	complemented
81	#546×C₈₉	C₂²	1	6	yes	complemented
82	#546×C₈₉	C₂²	1	6	yes	complemented
83	#546×C₈₉	C₂²	1	6	yes	complemented
84	#546×C₈₉	C₂²	1	6	yes	complemented
85	#546×C₈₉	C₂²	1	12	yes	complemented
86	D₄²×C₈₉	C₂²	1	3	yes	complemented
87	D₄²×C₈₉	C₂²	1	6	yes	complemented
88	D₄²×C₈₉	C₂²	1	6	yes	complemented
89	D₄²×C₈₉	C₂²	1	3	yes	complemented
90	D₄²×C₈₉	C₂²	1	3	yes	complemented
91	D₄²×C₈₉	C₂²	1	6	yes	complemented
92	D₄²×C₈₉	C₂²	1	6	yes	complemented
93	#544×C₈₉	C₂²	1	3	yes	complemented
94	#542×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#542×C₈₉	C₂²	1	3	yes	complemented
96	#542×C₈₉	C₂²	1	6	yes	complemented
97	#542×C₈₉	C₂²	1	6	yes	complemented
98	#542×C₈₉	C₂²	1	6	yes	complemented
99	#542×C₈₉	C₂²	1	6	yes	complemented
100	#542×C₈₉	C₂²	1	12	yes	complemented
101	#540×C₈₉	C₂²	1	3	yes	complemented
102	#540×C₈₉	C₂²	1	3	yes	complemented
103	#540×C₈₉	C₂²	1	6	yes	complemented
104	#540×C₈₉	C₂²	1	6	yes	complemented
105	#540×C₈₉	C₂²	1	6	yes	complemented
106	#538×C₈₉	C₂²	1	6	yes	complemented
107	#538×C₈₉	C₂²	1	6	yes	complemented
108	#538×C₈₉	C₂²	1	12	yes	complemented
109	#538×C₈₉	C₂²	1	12	yes	complemented
110	#538×C₈₉	C₂²	1	12	yes	complemented
111	#537×C₈₉	C₂²	1	3	yes	complemented
112	#537×C₈₉	C₂²	1	6	yes	complemented
113	#537×C₈₉	C₂²	1	6	yes	complemented
114	#536×C₈₉	C₂²	1	6	yes	complemented
115	#535×C₈₉	C₂²	1	3	yes	complemented
116	#535×C₈₉	C₂²	1	3	yes	complemented
117	#535×C₈₉	C₂²	1	6	yes	complemented
118	#535×C₈₉	C₂²	1	6	yes	complemented
119	#535×C₈₉	C₂²	1	6	yes	complemented
120	#535×C₈₉	C₂²	1	6	yes	complemented
121	#535×C₈₉	C₂²	1	6	yes	complemented
122	#535×C₈₉	C₂²	1	6	yes	complemented
123	#535×C₈₉	C₂²	1	12	yes	complemented
124	#534×C₈₉	C₂²	1	12	yes	complemented
125	#533×C₈₉	C₂²	1	3	yes	complemented
126	#532×C₈₉	C₂²	1	3	yes	complemented
127	#532×C₈₉	C₂²	1	3	yes	complemented
128	#532×C₈₉	C₂²	1	6	yes	complemented
129	#532×C₈₉	C₂²	1	3	yes	complemented
130	#532×C₈₉	C₂²	1	3	yes	complemented
131	#532×C₈₉	C₂²	1	3	yes	complemented
132	#532×C₈₉	C₂²	1	6	yes	complemented
133	#532×C₈₉	C₂²	1	3	yes	complemented
134	#532×C₈₉	C₂²	1	3	yes	complemented
135	C₂×#127×C₈₉	C₂²	1	3	yes	complemented
136	#529×C₈₉	C₂²	1	3	yes	complemented
137	#529×C₈₉	C₂²	1	3	yes	complemented
138	#529×C₈₉	C₂²	1	6	yes	complemented
139	#529×C₈₉	C₂²	1	3	yes	complemented
140	#529×C₈₉	C₂²	1	3	yes	complemented
141	#529×C₈₉	C₂²	1	6	yes	complemented
142	C₂×#124×C₈₉	C₂²	1	6	yes	complemented
143	#525×C₈₉	C₂²	1	6	yes	complemented
144	#525×C₈₉	C₂²	1	6	yes	complemented
145	#525×C₈₉	C₂²	1	6	yes	complemented
146	#525×C₈₉	C₂²	1	6	yes	complemented
147	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
148	#520×C₈₉	C₂²	1	2	yes	complemented
149	#519×C₈₉	C₂²	1	2	yes	complemented
150	#518×C₈₉	C₂²	1	6	yes	complemented
151	C₄×#41×C₈₉	C₂²	1	3	yes	complemented
152	C₄×#41×C₈₉	C₂²	1	3	yes	complemented
153	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
154	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
155	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
156	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
157	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	complemented
158	2₋¹⁺⁴×C₈₉	—	4	8	no	—
159	H(5,𝔽₂)×C₈₉	—	4	8	no	—
160	C₂×#41×C₈₉	—	4	8	no	—
161	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×#41×C₈₉	C₂³	1	2	yes	—
164	C₂×#41×C₈₉	C₂³	1	2	yes	—
165	C₂×#41×C₈₉	C₂³	1	3	yes	—
166	C₂×#41×C₈₉	C₂³	1	3	yes	—
167	C₂×#41×C₈₉	C₂³	1	6	yes	—
168	C₂×#41×C₈₉	C₂³	1	6	yes	—
169	C₂×#41×C₈₉	C₂³	1	6	yes	—
170	C₂×#41×C₈₉	C₂³	1	6	yes	—
171	C₂×#41×C₈₉	C₂³	1	6	yes	—
172	C₂×#41×C₈₉	C₂³	1	6	yes	—
173	C₂×#41×C₈₉	C₂³	1	6	yes	—
174	C₂×#41×C₈₉	C₂³	1	6	yes	—
175	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
176	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
177	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
178	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
179	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
180	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
181	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
182	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
183	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
184	C₂²×D₄×C₈₉	C₂³	1	12	yes	—
185	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
186	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
187	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
188	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
189	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
190	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
191	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
192	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
193	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
194	#127×C₈₉	C₂³	1	3	yes	—
195	#127×C₈₉	C₂³	1	3	yes	—
196	#127×C₈₉	C₂³	1	3	yes	—
197	#127×C₈₉	C₂³	1	6	yes	—
198	#127×C₈₉	C₂³	1	6	yes	—
199	#127×C₈₉	C₂³	1	6	yes	—
200	#127×C₈₉	C₂³	1	3	yes	—
201	#127×C₈₉	C₂³	1	6	yes	—
202	#127×C₈₉	C₂³	1	3	yes	—
203	#127×C₈₉	C₂³	1	12	yes	—
204	#126×C₈₉	C₂³	1	2	yes	—
205	#126×C₈₉	C₂³	1	6	yes	—
206	#126×C₈₉	C₂³	1	6	yes	—
207	#126×C₈₉	C₂³	1	6	yes	—
208	#126×C₈₉	C₂³	1	6	yes	—
209	#126×C₈₉	C₂³	1	6	yes	—
210	#126×C₈₉	C₂³	1	12	yes	—
211	#126×C₈₉	C₂³	1	12	yes	—
212	#125×C₈₉	C₂³	1	3	yes	—
213	#125×C₈₉	C₂³	1	3	yes	—
214	#125×C₈₉	C₂³	1	3	yes	—
215	#125×C₈₉	C₂³	1	6	yes	—
216	#125×C₈₉	C₂³	1	3	yes	—
217	#124×C₈₉	C₂³	1	3	yes	—
218	#124×C₈₉	C₂³	1	6	yes	—
219	#124×C₈₉	C₂³	1	6	yes	—
220	#124×C₈₉	C₂³	1	12	yes	—
221	#124×C₈₉	C₂³	1	6	yes	—
222	#124×C₈₉	C₂³	1	6	yes	—
223	#124×C₈₉	C₂³	1	1	yes	characteristic
224	#124×C₈₉	C₂³	1	3	yes	—
225	#124×C₈₉	C₂³	1	3	yes	—
226	#124×C₈₉	C₂³	1	6	yes	—
227	#124×C₈₉	C₂³	1	2	yes	—
228	#124×C₈₉	C₂³	1	6	yes	—
229	#124×C₈₉	C₂³	1	6	yes	—
230	#124×C₈₉	C₂³	1	12	yes	—
231	#124×C₈₉	C₂³	1	6	yes	—
232	#124×C₈₉	C₂³	1	6	yes	—
233	#124×C₈₉	C₂³	1	6	yes	—
234	#124×C₈₉	C₂³	1	6	yes	—
235	#124×C₈₉	C₂³	1	12	yes	—
236	#124×C₈₉	C₂³	1	12	yes	—
237	#124×C₈₉	C₂³	1	12	yes	—
238	#123×C₈₉	C₂³	1	6	yes	—
239	#123×C₈₉	C₂³	1	2	yes	—
240	#123×C₈₉	C₂³	1	12	yes	—
241	#123×C₈₉	C₂³	1	6	yes	—
242	#123×C₈₉	C₂³	1	6	yes	—
243	#123×C₈₉	C₂³	1	6	yes	—
244	#123×C₈₉	C₂³	1	6	yes	—
245	#123×C₈₉	C₂³	1	6	yes	—
246	#123×C₈₉	C₂³	1	6	yes	—
247	#123×C₈₉	C₂³	1	6	yes	—
248	#123×C₈₉	C₂³	1	6	yes	—
249	#123×C₈₉	C₂³	1	12	yes	—
250	#123×C₈₉	C₂³	1	12	yes	—
251	#123×C₈₉	C₂³	1	12	yes	—
252	#123×C₈₉	C₂³	1	12	yes	—
253	#123×C₈₉	C₂³	1	12	yes	—
254	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
255	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
256	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
257	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
258	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
259	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
260	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
261	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
262	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
263	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
264	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
265	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
266	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
267	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
268	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
269	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
270	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
271	#121×C₈₉	C₂³	1	6	yes	—
272	#121×C₈₉	C₂³	1	3	yes	—
273	#121×C₈₉	C₂³	1	6	yes	—
274	#121×C₈₉	C₂³	1	12	yes	—
275	#121×C₈₉	C₂³	1	6	yes	—
276	#121×C₈₉	C₂³	1	6	yes	—
277	#121×C₈₉	C₂³	1	6	yes	—
278	#121×C₈₉	C₂³	1	6	yes	—
279	#121×C₈₉	C₂³	1	6	yes	—
280	#121×C₈₉	C₂³	1	6	yes	—
281	#121×C₈₉	C₂³	1	6	yes	—
282	#121×C₈₉	C₂³	1	6	yes	—
283	#121×C₈₉	C₂³	1	3	yes	—
284	#121×C₈₉	C₂³	1	6	yes	—
285	#121×C₈₉	C₂³	1	6	yes	—
286	#121×C₈₉	C₂³	1	3	yes	—
287	#121×C₈₉	C₂³	1	3	yes	—
288	#121×C₈₉	C₂³	1	1	yes	characteristic
289	#121×C₈₉	C₂³	1	3	yes	—
290	#121×C₈₉	C₂³	1	12	yes	—
291	#121×C₈₉	C₂³	1	6	yes	—
292	#121×C₈₉	C₂³	1	3	yes	—
293	#121×C₈₉	C₂³	1	6	yes	—
294	#121×C₈₉	C₂³	1	3	yes	—
295	#121×C₈₉	C₂³	1	6	yes	—
296	#121×C₈₉	C₂³	1	6	yes	—
297	#121×C₈₉	C₂³	1	6	yes	—
298	#121×C₈₉	C₂³	1	6	yes	—
299	#121×C₈₉	C₂³	1	6	yes	—
300	#121×C₈₉	C₂³	1	3	yes	—
301	#121×C₈₉	C₂³	1	6	yes	—
302	#121×C₈₉	C₂³	1	6	yes	—
303	#121×C₈₉	C₂³	1	3	yes	—
304	#121×C₈₉	C₂³	1	6	yes	—
305	#121×C₈₉	C₂³	1	6	yes	—
306	#121×C₈₉	C₂³	1	6	yes	—
307	#121×C₈₉	C₂³	1	6	yes	—
308	#121×C₈₉	C₂³	1	6	yes	—
309	#121×C₈₉	C₂³	1	12	yes	—
310	#121×C₈₉	C₂³	1	12	yes	—
311	#121×C₈₉	C₂³	1	12	yes	—
312	#121×C₈₉	C₂³	1	12	yes	—
313	#121×C₈₉	C₂³	1	12	yes	—
314	#121×C₈₉	C₂³	1	12	yes	—
315	#120×C₈₉	C₂³	1	6	yes	—
316	#120×C₈₉	C₂³	1	12	yes	—
317	#120×C₈₉	C₂³	1	6	yes	—
318	#120×C₈₉	C₂³	1	12	yes	—
319	#120×C₈₉	C₂³	1	6	yes	—
320	#120×C₈₉	C₂³	1	6	yes	—
321	#120×C₈₉	C₂³	1	12	yes	—
322	#120×C₈₉	C₂³	1	12	yes	—
323	#120×C₈₉	C₂³	1	12	yes	—
324	#120×C₈₉	C₂³	1	12	yes	—
325	#120×C₈₉	C₂³	1	12	yes	—
326	#120×C₈₉	C₂³	1	12	yes	—
327	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
328	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
329	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
330	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
331	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
332	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
333	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
334	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
335	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
336	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
337	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
338	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
339	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
340	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
341	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₄×D₄×C₈₉	C₂³	1	3	yes	—
343	C₄×D₄×C₈₉	C₂³	1	6	yes	—
344	C₄×D₄×C₈₉	C₂³	1	3	yes	—
345	C₄×D₄×C₈₉	C₂³	1	3	yes	—
346	C₄×D₄×C₈₉	C₂³	1	6	yes	—
347	C₄×D₄×C₈₉	C₂³	1	3	yes	—
348	C₄×D₄×C₈₉	C₂³	1	3	yes	—
349	C₄×D₄×C₈₉	C₂³	1	6	yes	—
350	C₄×D₄×C₈₉	C₂³	1	3	yes	—
351	C₄×D₄×C₈₉	C₂³	1	3	yes	—
352	C₄×D₄×C₈₉	C₂³	1	3	yes	—
353	C₄×D₄×C₈₉	C₂³	1	6	yes	—
354	C₄×D₄×C₈₉	C₂³	1	3	yes	—
355	C₄×D₄×C₈₉	C₂³	1	3	yes	—
356	C₄×D₄×C₈₉	C₂³	1	3	yes	—
357	C₄×D₄×C₈₉	C₂³	1	6	yes	—
358	C₄×D₄×C₈₉	C₂³	1	3	yes	—
359	C₄×D₄×C₈₉	C₂³	1	3	yes	—
360	C₄×D₄×C₈₉	C₂³	1	3	yes	—
361	C₄×D₄×C₈₉	C₂³	1	6	yes	—
362	C₄×D₄×C₈₉	C₂³	1	3	yes	—
363	C₄×D₄×C₈₉	C₂³	1	12	yes	—
364	C₄×D₄×C₈₉	C₂³	1	12	yes	—
365	C₄×D₄×C₈₉	C₂³	1	6	yes	—
366	C₄×D₄×C₈₉	C₂³	1	6	yes	—
367	C₄×D₄×C₈₉	C₂³	1	6	yes	—
368	C₄×D₄×C₈₉	C₂³	1	6	yes	—
369	C₄×D₄×C₈₉	C₂³	1	6	yes	—
370	C₄×D₄×C₈₉	C₂³	1	6	yes	—
371	C₄×D₄×C₈₉	C₂³	1	6	yes	—
372	C₄×D₄×C₈₉	C₂³	1	6	yes	—
373	C₄×D₄×C₈₉	C₂³	1	6	yes	—
374	C₄×D₄×C₈₉	C₂³	1	12	yes	—
375	C₄×D₄×C₈₉	C₂³	1	6	yes	—
376	C₄×D₄×C₈₉	C₂³	1	6	yes	—
377	#117×C₈₉	C₂³	1	1	yes	characteristic
378	#117×C₈₉	C₂³	1	3	yes	—
379	#117×C₈₉	C₂³	1	3	yes	—
380	#117×C₈₉	C₂³	1	3	yes	—
381	#117×C₈₉	C₂³	1	3	yes	—
382	#117×C₈₉	C₂³	1	6	yes	—
383	#117×C₈₉	C₂³	1	3	yes	—
384	#117×C₈₉	C₂³	1	6	yes	—
385	#117×C₈₉	C₂³	1	6	yes	—
386	#117×C₈₉	C₂³	1	6	yes	—
387	#117×C₈₉	C₂³	1	6	yes	—
388	#117×C₈₉	C₂³	1	6	yes	—
389	#117×C₈₉	C₂³	1	12	yes	—
390	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
391	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
392	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
393	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
394	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
395	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
396	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
397	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
398	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
399	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
400	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
401	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
402	C₂⁴×C₈₉	C₂⁴	1	6	yes	—
403	#41×C₈₉	—	2	4	no	—
404	#41×C₈₉	—	2	8	no	—
405	#41×C₈₉	—	2	4	no	—
406	#41×C₈₉	—	2	8	no	—
407	#41×C₈₉	—	4	6	no	—
408	#41×C₈₉	—	4	12	no	—
409	#41×C₈₉	—	4	12	no	—
410	#41×C₈₉	—	4	12	no	—
411	#41×C₈₉	—	4	12	no	—
412	#41×C₈₉	—	4	6	no	—
413	#41×C₈₉	—	4	12	no	—
414	#41×C₈₉	—	4	12	no	—
415	#41×C₈₉	—	8	6	no	—
416	#41×C₈₉	—	8	6	no	—
417	C₂×Q₈×C₈₉	—	2	8	no	—
418	C₂×Q₈×C₈₉	—	2	4	no	—
419	C₂×Q₈×C₈₉	—	4	12	no	—
420	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
421	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
422	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
423	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
424	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
425	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
426	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
427	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
428	C₂×D₄×C₈₉	—	4	12	no	—
429	C₂×D₄×C₈₉	—	4	6	no	—
430	C₂×D₄×C₈₉	—	4	12	no	—
431	C₂×D₄×C₈₉	—	4	12	no	—
432	C₂×D₄×C₈₉	—	4	12	no	—
433	C₂×D₄×C₈₉	—	4	12	no	—
434	C₂×D₄×C₈₉	—	8	6	no	—
435	C₂×D₄×C₈₉	—	8	12	no	—
436	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
437	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
438	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
439	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
440	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
441	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
442	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
443	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
444	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
445	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
446	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
447	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
448	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
449	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
450	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
451	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
452	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
453	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
454	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
455	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
456	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
457	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
458	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
459	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
460	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
461	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
462	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
463	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
464	C₂²×C₄×C₈₉	—	4	12	no	—
465	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
467	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
468	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
469	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
470	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
471	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
472	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
473	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
474	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
475	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
476	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
477	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
478	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
479	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
480	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
481	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
482	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
483	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
484	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
485	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
486	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
487	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
488	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
489	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
490	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
491	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
492	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
493	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
494	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
495	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
496	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
497	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
498	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
499	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
500	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
501	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
502	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
503	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
504	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
505	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
506	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
507	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
508	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
509	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
510	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
511	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
512	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
513	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
514	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
515	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
516	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
517	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
518	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
519	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
520	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
521	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
522	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
523	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
524	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
525	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
526	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
527	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
528	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
529	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
530	C₂²⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
531	C₂²⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
532	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
533	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
534	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
535	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
536	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
537	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
538	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
539	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
540	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
541	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
542	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
543	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
544	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
545	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
546	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
547	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
548	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
549	C₄²×C₈₉	C₂⁴	1	3	yes	—
550	C₄²×C₈₉	C₂⁴	1	3	yes	—
551	C₄²×C₈₉	C₂⁴	1	2	yes	—
552	C₄²×C₈₉	C₂⁴	1	6	yes	—
553	C₄²×C₈₉	C₂⁴	1	3	yes	—
554	C₄²×C₈₉	C₂⁴	1	3	yes	—
555	C₄²×C₈₉	C₂⁴	1	3	yes	—
556	C₄²×C₈₉	C₂⁴	1	6	yes	—
557	C₄²×C₈₉	C₂⁴	1	3	yes	—
558	C₄²×C₈₉	C₂⁴	1	3	yes	—
559	C₄²×C₈₉	C₂⁴	1	3	yes	—
560	C₄²×C₈₉	C₂⁴	1	12	yes	—
561	C₂³×C₈₉	—	4	6	no	—
562	C₂³×C₈₉	—	4	6	no	—
563	C₂³×C₈₉	—	4	6	no	—
564	C₂³×C₈₉	—	4	12	no	—
565	C₂³×C₈₉	—	4	12	no	—
566	C₂³×C₈₉	—	4	12	no	—
567	C₂³×C₈₉	C₂⁵	1	3	yes	—
568	C₂³×C₈₉	C₂⁵	1	2	yes	—
569	C₂³×C₈₉	C₂⁵	1	6	yes	—
570	C₂³×C₈₉	C₂⁵	1	3	yes	—
571	C₂³×C₈₉	C₂⁵	1	6	yes	—
572	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
573	Q₈×C₈₉	—	2	6	no	—
574	Q₈×C₈₉	—	2	12	no	—
575	Q₈×C₈₉	—	2	2	no	—
576	Q₈×C₈₉	—	4	6	no	—
577	Q₈×C₈₉	—	4	3	no	—
578	Q₈×C₈₉	—	4	2	no	—
579	Q₈×C₈₉	—	4	6	no	—
580	Q₈×C₈₉	H(5,𝔽₂)	1	4	yes	—
581	D₄×C₈₉	—	2	6	no	—
582	D₄×C₈₉	—	2	12	no	—
583	D₄×C₈₉	—	2	6	no	—
584	D₄×C₈₉	—	2	12	no	—
585	D₄×C₈₉	—	2	2	no	—
586	D₄×C₈₉	—	2	6	no	—
587	D₄×C₈₉	—	2	6	no	—
588	D₄×C₈₉	—	4	6	no	—
589	D₄×C₈₉	—	4	6	no	—
590	D₄×C₈₉	—	4	6	no	—
591	D₄×C₈₉	—	4	6	no	—
592	D₄×C₈₉	—	4	12	no	—
593	D₄×C₈₉	—	4	12	no	—
594	D₄×C₈₉	—	4	6	no	—
595	D₄×C₈₉	—	4	6	no	—
596	D₄×C₈₉	—	4	6	no	—
597	D₄×C₈₉	—	4	6	no	—
598	D₄×C₈₉	—	4	6	no	—
599	D₄×C₈₉	—	4	6	no	—
600	D₄×C₈₉	—	4	12	no	—
601	D₄×C₈₉	—	4	3	no	—
602	D₄×C₈₉	—	4	3	no	—
603	D₄×C₈₉	—	4	3	no	—
604	D₄×C₈₉	—	4	6	no	—
605	D₄×C₈₉	—	4	2	no	—
606	D₄×C₈₉	—	4	6	no	—
607	D₄×C₈₉	—	4	6	no	—
608	D₄×C₈₉	—	4	6	no	—
609	C₂×C₄×C₈₉	—	2	6	no	—
610	C₂×C₄×C₈₉	—	2	12	no	—
611	C₂×C₄×C₈₉	—	2	12	no	—
612	C₂×C₄×C₈₉	—	2	6	no	—
613	C₂×C₄×C₈₉	—	2	12	no	—
614	C₂×C₄×C₈₉	—	2	6	no	—
615	C₂×C₄×C₈₉	—	2	6	no	—
616	C₂×C₄×C₈₉	—	2	6	no	—
617	C₂×C₄×C₈₉	—	2	2	no	—
618	C₂×C₄×C₈₉	—	4	2	no	—
619	C₂×C₄×C₈₉	—	4	6	no	—
620	C₂×C₄×C₈₉	—	4	6	no	—
621	C₂×C₄×C₈₉	—	4	3	no	—
622	C₂×C₄×C₈₉	—	4	12	no	—
623	C₂×C₄×C₈₉	—	4	12	no	—
624	C₂×C₄×C₈₉	—	4	6	no	—
625	C₂×C₄×C₈₉	—	4	3	no	—
626	C₂×C₄×C₈₉	—	4	6	no	—
627	C₂×C₄×C₈₉	—	4	3	no	—
628	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
629	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
630	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
631	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
632	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
633	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
634	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
635	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
636	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
637	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
638	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
639	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
640	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
641	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
642	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
643	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
644	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
645	C₂²×C₈₉	—	2	2	no	—
646	C₂²×C₈₉	—	2	1	no	—
647	C₂²×C₈₉	—	2	3	no	—
648	C₂²×C₈₉	—	2	6	no	—
649	C₂²×C₈₉	—	2	6	no	—
650	C₂²×C₈₉	—	2	3	no	—
651	C₂²×C₈₉	—	2	1	no	—
652	C₂²×C₈₉	—	2	3	no	—
653	C₂²×C₈₉	—	2	3	no	—
654	C₂²×C₈₉	—	2	6	no	—
655	C₂²×C₈₉	—	2	2	no	—
656	C₂²×C₈₉	—	2	6	no	—
657	C₂²×C₈₉	—	2	1	no	—
658	C₂²×C₈₉	—	2	6	no	—
659	C₂²×C₈₉	—	2	3	no	—
660	C₂²×C₈₉	—	2	6	no	—
661	C₂²×C₈₉	—	2	3	no	—
662	C₂²×C₈₉	—	2	2	no	—
663	C₂²×C₈₉	—	8	12	no	—
664	C₂²×C₈₉	—	16	12	no	—
665	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
666	C₄×C₈₉	—	2	1	no	—
667	C₄×C₈₉	—	2	2	no	—
668	C₄×C₈₉	—	2	1	no	—
669	C₄×C₈₉	—	2	2	no	—
670	C₄×C₈₉	—	2	6	no	—
671	C₄×C₈₉	—	2	3	no	—
672	C₄×C₈₉	—	2	3	no	—
673	C₄×C₈₉	—	2	3	no	—
674	C₄×C₈₉	—	2	1	no	—
675	C₄×C₈₉	—	2	2	no	—
676	C₄×C₈₉	—	2	1	no	—
677	C₄×C₈₉	—	2	3	no	—
678	C₄×C₈₉	—	2	1	no	—
679	C₄×C₈₉	—	2	3	no	—
680	C₄×C₈₉	—	2	6	no	—
681	C₄×C₈₉	C₂×H(5,𝔽₂)	1	6	yes	—
682	C₄×C₈₉	#585	1	2	yes	—
683	#62923	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
684	C₂×C₈₉	—	4	1	no	—
685	C₂×C₈₉	—	4	3	no	—
686	C₂×C₈₉	—	4	2	no	—
687	C₂×C₈₉	—	4	6	no	—
688	C₂×C₈₉	—	4	6	no	—
689	C₂×C₈₉	—	4	3	no	—
690	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂×C₈₉	C₂×#585	1	1	yes	characteristic
692	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
693	#3558	C₂×C₈₉	1	6	yes	complemented
694	#3549	C₂×C₈₉	1	3	yes	complemented
695	#3547	C₂×C₈₉	1	3	yes	complemented
696	#3546	C₂×C₈₉	1	3	yes	complemented
697	#3546	C₂×C₈₉	1	6	yes	complemented
698	#3543	C₂×C₈₉	1	3	yes	complemented
699	#3542	C₂×C₈₉	1	6	yes	complemented
700	#3540	C₂×C₈₉	1	6	yes	complemented
701	#3524	C₂×C₈₉	1	2	yes	complemented
702	#3522	C₂×C₈₉	1	1	yes	characteristic, complemented
703	#3519	C₂×C₈₉	1	3	yes	complemented
704	#3518	C₂×C₈₉	1	1	yes	characteristic, complemented
705	#3514	C₂×C₈₉	1	3	yes	complemented
706	#3508	C₂×C₈₉	1	3	yes	complemented
707	#3500	C₂×C₈₉	1	2	yes	complemented
708	#3498	C₂×C₈₉	1	1	yes	characteristic, complemented
709	#3497	C₂×C₈₉	1	1	yes	characteristic, complemented
710	#3488	C₂×C₈₉	1	2	yes	complemented
711	#3487	C₂×C₈₉	1	2	yes	complemented
712	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
713	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
714	D₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
715	#3460	C₂×C₈₉	1	3	yes	complemented
716	C₈₉	#62923	1	1	yes	characteristic, direct product factor, Sylow
717	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
718	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	2	yes	complemented
719	C₂²×#41	C₂²×C₈₉	1	2	yes	complemented
720	#562	C₂²×C₈₉	1	12	yes	complemented
721	H(3,𝔽₄)	C₂²×C₈₉	1	12	yes	complemented
722	#560	C₂²×C₈₉	1	12	yes	complemented
723	#560	C₂²×C₈₉	1	12	yes	complemented
724	#559	C₂²×C₈₉	1	3	yes	complemented
725	#559	C₂²×C₈₉	1	6	yes	complemented
726	#559	C₂²×C₈₉	1	6	yes	complemented
727	#559	C₂²×C₈₉	1	3	yes	complemented
728	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
729	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
730	#556	C₂²×C₈₉	1	3	yes	complemented
731	#556	C₂²×C₈₉	1	3	yes	complemented
732	#556	C₂²×C₈₉	1	6	yes	complemented
733	#555	C₂²×C₈₉	1	6	yes	complemented
734	#555	C₂²×C₈₉	1	3	yes	complemented
735	#555	C₂²×C₈₉	1	6	yes	complemented
736	#555	C₂²×C₈₉	1	3	yes	complemented
737	#555	C₂²×C₈₉	1	6	yes	complemented
738	#554	C₂²×C₈₉	1	3	yes	complemented
739	#553	C₂²×C₈₉	1	3	yes	complemented
740	#553	C₂²×C₈₉	1	3	yes	complemented
741	#553	C₂²×C₈₉	1	6	yes	complemented
742	#553	C₂²×C₈₉	1	6	yes	complemented
743	#552	C₂²×C₈₉	1	6	yes	complemented
744	#551	C₂²×C₈₉	1	12	yes	complemented
745	#550	C₂²×C₈₉	1	1	yes	characteristic
746	#550	C₂²×C₈₉	1	1	yes	characteristic
747	#550	C₂²×C₈₉	1	2	yes	complemented
748	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
749	#550	C₂²×C₈₉	1	3	yes	complemented
750	#550	C₂²×C₈₉	1	2	yes	complemented
751	#550	C₂²×C₈₉	1	6	yes	complemented
752	#550	C₂²×C₈₉	1	6	yes	complemented
753	#550	C₂²×C₈₉	1	3	yes	complemented
754	#550	C₂²×C₈₉	1	6	yes	complemented
755	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
756	D₄×Q₈	C₂²×C₈₉	1	3	yes	complemented
757	#548	C₂²×C₈₉	1	2	yes	complemented
758	#548	C₂²×C₈₉	1	1	yes	characteristic, complemented
759	#548	C₂²×C₈₉	1	1	yes	characteristic, complemented
760	#548	C₂²×C₈₉	1	2	yes	complemented
761	#548	C₂²×C₈₉	1	6	yes	complemented
762	#548	C₂²×C₈₉	1	6	yes	complemented
763	#548	C₂²×C₈₉	1	2	yes	complemented
764	#548	C₂²×C₈₉	1	2	yes	complemented
765	#548	C₂²×C₈₉	1	6	yes	complemented
766	#547	C₂²×C₈₉	1	3	yes	complemented
767	#547	C₂²×C₈₉	1	6	yes	complemented
768	#546	C₂²×C₈₉	1	6	yes	complemented
769	#546	C₂²×C₈₉	1	6	yes	complemented
770	#546	C₂²×C₈₉	1	6	yes	complemented
771	#546	C₂²×C₈₉	1	6	yes	complemented
772	#546	C₂²×C₈₉	1	6	yes	complemented
773	#546	C₂²×C₈₉	1	6	yes	complemented
774	#546	C₂²×C₈₉	1	6	yes	complemented
775	#546	C₂²×C₈₉	1	6	yes	complemented
776	#546	C₂²×C₈₉	1	6	yes	complemented
777	#546	C₂²×C₈₉	1	6	yes	complemented
778	#546	C₂²×C₈₉	1	12	yes	complemented
779	D₄²	C₂²×C₈₉	1	3	yes	complemented
780	D₄²	C₂²×C₈₉	1	6	yes	complemented
781	D₄²	C₂²×C₈₉	1	6	yes	complemented
782	D₄²	C₂²×C₈₉	1	3	yes	complemented
783	D₄²	C₂²×C₈₉	1	3	yes	complemented
784	D₄²	C₂²×C₈₉	1	6	yes	complemented
785	D₄²	C₂²×C₈₉	1	6	yes	complemented
786	#544	C₂²×C₈₉	1	3	yes	complemented
787	#542	C₂²×C₈₉	1	1	yes	characteristic, complemented
788	#542	C₂²×C₈₉	1	3	yes	complemented
789	#542	C₂²×C₈₉	1	6	yes	complemented
790	#542	C₂²×C₈₉	1	6	yes	complemented
791	#542	C₂²×C₈₉	1	6	yes	complemented
792	#542	C₂²×C₈₉	1	6	yes	complemented
793	#542	C₂²×C₈₉	1	12	yes	complemented
794	#540	C₂²×C₈₉	1	3	yes	complemented
795	#540	C₂²×C₈₉	1	3	yes	complemented
796	#540	C₂²×C₈₉	1	6	yes	complemented
797	#540	C₂²×C₈₉	1	6	yes	complemented
798	#540	C₂²×C₈₉	1	6	yes	complemented
799	#538	C₂²×C₈₉	1	6	yes	complemented
800	#538	C₂²×C₈₉	1	6	yes	complemented
801	#538	C₂²×C₈₉	1	12	yes	complemented
802	#538	C₂²×C₈₉	1	12	yes	complemented
803	#538	C₂²×C₈₉	1	12	yes	complemented
804	#537	C₂²×C₈₉	1	3	yes	complemented
805	#537	C₂²×C₈₉	1	6	yes	complemented
806	#537	C₂²×C₈₉	1	6	yes	complemented
807	#536	C₂²×C₈₉	1	6	yes	complemented
808	#535	C₂²×C₈₉	1	3	yes	complemented
809	#535	C₂²×C₈₉	1	3	yes	complemented
810	#535	C₂²×C₈₉	1	6	yes	complemented
811	#535	C₂²×C₈₉	1	6	yes	complemented
812	#535	C₂²×C₈₉	1	6	yes	complemented
813	#535	C₂²×C₈₉	1	6	yes	complemented
814	#535	C₂²×C₈₉	1	6	yes	complemented
815	#535	C₂²×C₈₉	1	6	yes	complemented
816	#535	C₂²×C₈₉	1	12	yes	complemented
817	#534	C₂²×C₈₉	1	12	yes	complemented
818	#533	C₂²×C₈₉	1	3	yes	complemented
819	#532	C₂²×C₈₉	1	3	yes	complemented
820	#532	C₂²×C₈₉	1	3	yes	complemented
821	#532	C₂²×C₈₉	1	6	yes	complemented
822	#532	C₂²×C₈₉	1	3	yes	complemented
823	#532	C₂²×C₈₉	1	3	yes	complemented
824	#532	C₂²×C₈₉	1	3	yes	complemented
825	#532	C₂²×C₈₉	1	6	yes	complemented
826	#532	C₂²×C₈₉	1	3	yes	complemented
827	#532	C₂²×C₈₉	1	3	yes	complemented
828	C₂×#127	C₂²×C₈₉	1	3	yes	complemented
829	#529	C₂²×C₈₉	1	3	yes	complemented
830	#529	C₂²×C₈₉	1	3	yes	complemented
831	#529	C₂²×C₈₉	1	6	yes	complemented
832	#529	C₂²×C₈₉	1	3	yes	complemented
833	#529	C₂²×C₈₉	1	3	yes	complemented
834	#529	C₂²×C₈₉	1	6	yes	complemented
835	C₂×#124	C₂²×C₈₉	1	6	yes	complemented
836	#525	C₂²×C₈₉	1	6	yes	complemented
837	#525	C₂²×C₈₉	1	6	yes	complemented
838	#525	C₂²×C₈₉	1	6	yes	complemented
839	#525	C₂²×C₈₉	1	6	yes	complemented
840	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
841	#520	C₂²×C₈₉	1	2	yes	complemented
842	#519	C₂²×C₈₉	1	2	yes	complemented
843	#518	C₂²×C₈₉	1	6	yes	complemented
844	C₄×#41	C₂²×C₈₉	1	3	yes	complemented
845	C₄×#41	C₂²×C₈₉	1	3	yes	complemented
846	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
847	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
848	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
849	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
850	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	complemented
851	2₋¹⁺⁴	—	4	8	no	—
852	H(5,𝔽₂)	—	4	8	no	—
853	C₂×#41	—	4	8	no	—
854	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
855	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
856	C₂×#41	C₂³×C₈₉	1	2	yes	—
857	C₂×#41	C₂³×C₈₉	1	2	yes	—
858	C₂×#41	C₂³×C₈₉	1	3	yes	—
859	C₂×#41	C₂³×C₈₉	1	3	yes	—
860	C₂×#41	C₂³×C₈₉	1	6	yes	—
861	C₂×#41	C₂³×C₈₉	1	6	yes	—
862	C₂×#41	C₂³×C₈₉	1	6	yes	—
863	C₂×#41	C₂³×C₈₉	1	6	yes	—
864	C₂×#41	C₂³×C₈₉	1	6	yes	—
865	C₂×#41	C₂³×C₈₉	1	6	yes	—
866	C₂×#41	C₂³×C₈₉	1	6	yes	—
867	C₂×#41	C₂³×C₈₉	1	6	yes	—
868	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
869	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
870	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
871	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
872	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
873	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
874	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
875	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
876	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
877	C₂²×D₄	C₂³×C₈₉	1	12	yes	—
878	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
879	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
880	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
881	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
882	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
883	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
884	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
885	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
886	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
887	#127	C₂³×C₈₉	1	3	yes	—
888	#127	C₂³×C₈₉	1	3	yes	—
889	#127	C₂³×C₈₉	1	3	yes	—
890	#127	C₂³×C₈₉	1	6	yes	—
891	#127	C₂³×C₈₉	1	6	yes	—
892	#127	C₂³×C₈₉	1	6	yes	—
893	#127	C₂³×C₈₉	1	3	yes	—
894	#127	C₂³×C₈₉	1	6	yes	—
895	#127	C₂³×C₈₉	1	3	yes	—
896	#127	C₂³×C₈₉	1	12	yes	—
897	#126	C₂³×C₈₉	1	2	yes	—
898	#126	C₂³×C₈₉	1	6	yes	—
899	#126	C₂³×C₈₉	1	6	yes	—
900	#126	C₂³×C₈₉	1	6	yes	—
901	#126	C₂³×C₈₉	1	6	yes	—
902	#126	C₂³×C₈₉	1	6	yes	—
903	#126	C₂³×C₈₉	1	12	yes	—
904	#126	C₂³×C₈₉	1	12	yes	—
905	#125	C₂³×C₈₉	1	3	yes	—
906	#125	C₂³×C₈₉	1	3	yes	—
907	#125	C₂³×C₈₉	1	3	yes	—
908	#125	C₂³×C₈₉	1	6	yes	—
909	#125	C₂³×C₈₉	1	3	yes	—
910	#124	C₂³×C₈₉	1	3	yes	—
911	#124	C₂³×C₈₉	1	6	yes	—
912	#124	C₂³×C₈₉	1	6	yes	—
913	#124	C₂³×C₈₉	1	12	yes	—
914	#124	C₂³×C₈₉	1	6	yes	—
915	#124	C₂³×C₈₉	1	6	yes	—
916	#124	C₂³×C₈₉	1	1	yes	characteristic
917	#124	C₂³×C₈₉	1	3	yes	—
918	#124	C₂³×C₈₉	1	3	yes	—
919	#124	C₂³×C₈₉	1	6	yes	—
920	#124	C₂³×C₈₉	1	2	yes	—
921	#124	C₂³×C₈₉	1	6	yes	—
922	#124	C₂³×C₈₉	1	6	yes	—
923	#124	C₂³×C₈₉	1	12	yes	—
924	#124	C₂³×C₈₉	1	6	yes	—
925	#124	C₂³×C₈₉	1	6	yes	—
926	#124	C₂³×C₈₉	1	6	yes	—
927	#124	C₂³×C₈₉	1	6	yes	—
928	#124	C₂³×C₈₉	1	12	yes	—
929	#124	C₂³×C₈₉	1	12	yes	—
930	#124	C₂³×C₈₉	1	12	yes	—
931	#123	C₂³×C₈₉	1	6	yes	—
932	#123	C₂³×C₈₉	1	2	yes	—
933	#123	C₂³×C₈₉	1	12	yes	—
934	#123	C₂³×C₈₉	1	6	yes	—
935	#123	C₂³×C₈₉	1	6	yes	—
936	#123	C₂³×C₈₉	1	6	yes	—
937	#123	C₂³×C₈₉	1	6	yes	—
938	#123	C₂³×C₈₉	1	6	yes	—
939	#123	C₂³×C₈₉	1	6	yes	—
940	#123	C₂³×C₈₉	1	6	yes	—
941	#123	C₂³×C₈₉	1	6	yes	—
942	#123	C₂³×C₈₉	1	12	yes	—
943	#123	C₂³×C₈₉	1	12	yes	—
944	#123	C₂³×C₈₉	1	12	yes	—
945	#123	C₂³×C₈₉	1	12	yes	—
946	#123	C₂³×C₈₉	1	12	yes	—
947	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
948	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
949	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
950	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
951	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
952	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
953	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
954	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
955	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
956	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
957	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
958	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
959	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
960	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
961	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
962	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
963	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
964	#121	C₂³×C₈₉	1	6	yes	—
965	#121	C₂³×C₈₉	1	3	yes	—
966	#121	C₂³×C₈₉	1	6	yes	—
967	#121	C₂³×C₈₉	1	12	yes	—
968	#121	C₂³×C₈₉	1	6	yes	—
969	#121	C₂³×C₈₉	1	6	yes	—
970	#121	C₂³×C₈₉	1	6	yes	—
971	#121	C₂³×C₈₉	1	6	yes	—
972	#121	C₂³×C₈₉	1	6	yes	—
973	#121	C₂³×C₈₉	1	6	yes	—
974	#121	C₂³×C₈₉	1	6	yes	—
975	#121	C₂³×C₈₉	1	6	yes	—
976	#121	C₂³×C₈₉	1	3	yes	—
977	#121	C₂³×C₈₉	1	6	yes	—
978	#121	C₂³×C₈₉	1	6	yes	—
979	#121	C₂³×C₈₉	1	3	yes	—
980	#121	C₂³×C₈₉	1	3	yes	—
981	#121	C₂³×C₈₉	1	1	yes	characteristic
982	#121	C₂³×C₈₉	1	3	yes	—
983	#121	C₂³×C₈₉	1	12	yes	—
984	#121	C₂³×C₈₉	1	6	yes	—
985	#121	C₂³×C₈₉	1	3	yes	—
986	#121	C₂³×C₈₉	1	6	yes	—
987	#121	C₂³×C₈₉	1	3	yes	—
988	#121	C₂³×C₈₉	1	6	yes	—
989	#121	C₂³×C₈₉	1	6	yes	—
990	#121	C₂³×C₈₉	1	6	yes	—
991	#121	C₂³×C₈₉	1	6	yes	—
992	#121	C₂³×C₈₉	1	6	yes	—
993	#121	C₂³×C₈₉	1	3	yes	—
994	#121	C₂³×C₈₉	1	6	yes	—
995	#121	C₂³×C₈₉	1	6	yes	—
996	#121	C₂³×C₈₉	1	3	yes	—
997	#121	C₂³×C₈₉	1	6	yes	—
998	#121	C₂³×C₈₉	1	6	yes	—
999	#121	C₂³×C₈₉	1	6	yes	—
1000	#121	C₂³×C₈₉	1	6	yes	—
1001	#121	C₂³×C₈₉	1	6	yes	—
1002	#121	C₂³×C₈₉	1	12	yes	—
1003	#121	C₂³×C₈₉	1	12	yes	—
1004	#121	C₂³×C₈₉	1	12	yes	—
1005	#121	C₂³×C₈₉	1	12	yes	—
1006	#121	C₂³×C₈₉	1	12	yes	—
1007	#121	C₂³×C₈₉	1	12	yes	—
1008	#120	C₂³×C₈₉	1	6	yes	—
1009	#120	C₂³×C₈₉	1	12	yes	—
1010	#120	C₂³×C₈₉	1	6	yes	—
1011	#120	C₂³×C₈₉	1	12	yes	—
1012	#120	C₂³×C₈₉	1	6	yes	—
1013	#120	C₂³×C₈₉	1	6	yes	—
1014	#120	C₂³×C₈₉	1	12	yes	—
1015	#120	C₂³×C₈₉	1	12	yes	—
1016	#120	C₂³×C₈₉	1	12	yes	—
1017	#120	C₂³×C₈₉	1	12	yes	—
1018	#120	C₂³×C₈₉	1	12	yes	—
1019	#120	C₂³×C₈₉	1	12	yes	—
1020	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
1021	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
1022	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
1023	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
1024	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
1025	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
1026	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
1027	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
1028	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
1029	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
1030	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
1031	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
1032	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
1033	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
1034	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
1035	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1036	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1037	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1038	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1039	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1040	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1041	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1042	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1043	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1044	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1045	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1046	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1047	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1048	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1049	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1050	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1051	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1052	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1053	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1054	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1055	C₄×D₄	C₂³×C₈₉	1	3	yes	—
1056	C₄×D₄	C₂³×C₈₉	1	12	yes	—
1057	C₄×D₄	C₂³×C₈₉	1	12	yes	—
1058	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1059	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1060	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1061	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1062	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1063	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1064	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1065	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1066	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1067	C₄×D₄	C₂³×C₈₉	1	12	yes	—
1068	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1069	C₄×D₄	C₂³×C₈₉	1	6	yes	—
1070	#117	C₂³×C₈₉	1	1	yes	characteristic
1071	#117	C₂³×C₈₉	1	3	yes	—
1072	#117	C₂³×C₈₉	1	3	yes	—
1073	#117	C₂³×C₈₉	1	3	yes	—
1074	#117	C₂³×C₈₉	1	3	yes	—
1075	#117	C₂³×C₈₉	1	6	yes	—
1076	#117	C₂³×C₈₉	1	3	yes	—
1077	#117	C₂³×C₈₉	1	6	yes	—
1078	#117	C₂³×C₈₉	1	6	yes	—
1079	#117	C₂³×C₈₉	1	6	yes	—
1080	#117	C₂³×C₈₉	1	6	yes	—
1081	#117	C₂³×C₈₉	1	6	yes	—
1082	#117	C₂³×C₈₉	1	12	yes	—
1083	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
1084	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
1085	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
1086	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
1087	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
1088	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
1089	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
1090	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
1091	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
1092	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
1093	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
1094	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
1095	C₂⁴	C₂⁴×C₈₉	1	6	yes	—
1096	#41	—	2	4	no	—
1097	#41	—	2	8	no	—
1098	#41	—	2	4	no	—
1099	#41	—	2	8	no	—
1100	#41	—	4	12	no	—
1101	#41	—	4	12	no	—
1102	#41	—	4	6	no	—
1103	#41	—	4	12	no	—
1104	#41	—	4	12	no	—
1105	#41	—	4	12	no	—
1106	#41	—	4	12	no	—
1107	#41	—	4	6	no	—
1108	#41	—	8	6	no	—
1109	#41	—	8	6	no	—
1110	C₂×Q₈	—	2	8	no	—
1111	C₂×Q₈	—	2	4	no	—
1112	C₂×Q₈	—	4	12	no	—
1113	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
1114	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
1115	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1116	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
1117	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1118	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
1119	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
1120	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
1121	C₂×D₄	—	4	12	no	—
1122	C₂×D₄	—	4	12	no	—
1123	C₂×D₄	—	4	12	no	—
1124	C₂×D₄	—	4	12	no	—
1125	C₂×D₄	—	4	12	no	—
1126	C₂×D₄	—	4	6	no	—
1127	C₂×D₄	—	8	6	no	—
1128	C₂×D₄	—	8	12	no	—
1129	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
1130	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1131	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1132	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1133	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1134	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1135	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1136	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1137	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1138	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1139	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1140	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
1141	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1142	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1143	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1144	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1145	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1146	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
1147	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1148	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1149	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1150	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1151	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
1152	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1153	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
1154	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1155	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1156	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1157	C₂²×C₄	—	4	12	no	—
1158	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1159	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1160	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1161	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1162	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1163	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1164	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1165	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1166	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1167	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1168	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1169	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1170	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1171	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1172	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1173	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
1174	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
1175	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1176	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
1177	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1178	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1179	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1180	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1181	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1182	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1183	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1184	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1185	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1186	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1187	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1188	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1189	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1190	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1191	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1192	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1193	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1194	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1195	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1196	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1198	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1199	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1200	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1201	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1202	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1203	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1204	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1205	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1206	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1207	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1208	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1209	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1210	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1211	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1212	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1213	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1214	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1215	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1216	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1217	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1218	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1219	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1220	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1221	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1222	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1223	C₂²⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1224	C₂²⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1225	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1226	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1227	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1228	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1229	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1230	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1231	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1232	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1233	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1234	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1235	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1236	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1237	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1238	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1239	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1240	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1241	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1242	C₄²	C₂⁴×C₈₉	1	3	yes	—
1243	C₄²	C₂⁴×C₈₉	1	3	yes	—
1244	C₄²	C₂⁴×C₈₉	1	2	yes	—
1245	C₄²	C₂⁴×C₈₉	1	6	yes	—
1246	C₄²	C₂⁴×C₈₉	1	3	yes	—
1247	C₄²	C₂⁴×C₈₉	1	3	yes	—
1248	C₄²	C₂⁴×C₈₉	1	3	yes	—
1249	C₄²	C₂⁴×C₈₉	1	6	yes	—
1250	C₄²	C₂⁴×C₈₉	1	3	yes	—
1251	C₄²	C₂⁴×C₈₉	1	3	yes	—
1252	C₄²	C₂⁴×C₈₉	1	3	yes	—
1253	C₄²	C₂⁴×C₈₉	1	12	yes	—
1254	C₂³	—	4	6	no	—
1255	C₂³	—	4	6	no	—
1256	C₂³	—	4	6	no	—
1257	C₂³	—	4	12	no	—
1258	C₂³	—	4	12	no	—
1259	C₂³	—	4	12	no	—
1260	C₂³	C₂⁵×C₈₉	1	3	yes	—
1261	C₂³	C₂⁵×C₈₉	1	2	yes	—
1262	C₂³	C₂⁵×C₈₉	1	6	yes	—
1263	C₂³	C₂⁵×C₈₉	1	3	yes	—
1264	C₂³	C₂⁵×C₈₉	1	6	yes	—
1265	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1266	Q₈	—	2	6	no	—
1267	Q₈	—	2	12	no	—
1268	Q₈	—	2	2	no	—
1269	Q₈	—	4	6	no	—
1270	Q₈	—	4	3	no	—
1271	Q₈	—	4	2	no	—
1272	Q₈	—	4	6	no	—
1273	Q₈	H(5,𝔽₂)×C₈₉	1	4	yes	—
1274	D₄	—	2	6	no	—
1275	D₄	—	2	12	no	—
1276	D₄	—	2	6	no	—
1277	D₄	—	2	12	no	—
1278	D₄	—	2	2	no	—
1279	D₄	—	2	6	no	—
1280	D₄	—	2	6	no	—
1281	D₄	—	4	6	no	—
1282	D₄	—	4	6	no	—
1283	D₄	—	4	6	no	—
1284	D₄	—	4	6	no	—
1285	D₄	—	4	12	no	—
1286	D₄	—	4	12	no	—
1287	D₄	—	4	6	no	—
1288	D₄	—	4	6	no	—
1289	D₄	—	4	6	no	—
1290	D₄	—	4	6	no	—
1291	D₄	—	4	6	no	—
1292	D₄	—	4	6	no	—
1293	D₄	—	4	12	no	—
1294	D₄	—	4	3	no	—
1295	D₄	—	4	3	no	—
1296	D₄	—	4	3	no	—
1297	D₄	—	4	6	no	—
1298	D₄	—	4	2	no	—
1299	D₄	—	4	6	no	—
1300	D₄	—	4	6	no	—
1301	D₄	—	4	6	no	—
1302	C₂×C₄	—	2	6	no	—
1303	C₂×C₄	—	2	12	no	—
1304	C₂×C₄	—	2	12	no	—
1305	C₂×C₄	—	2	6	no	—
1306	C₂×C₄	—	2	12	no	—
1307	C₂×C₄	—	2	6	no	—
1308	C₂×C₄	—	2	6	no	—
1309	C₂×C₄	—	2	6	no	—
1310	C₂×C₄	—	2	2	no	—
1311	C₂×C₄	—	4	2	no	—
1312	C₂×C₄	—	4	6	no	—
1313	C₂×C₄	—	4	6	no	—
1314	C₂×C₄	—	4	3	no	—
1315	C₂×C₄	—	4	12	no	—
1316	C₂×C₄	—	4	12	no	—
1317	C₂×C₄	—	4	6	no	—
1318	C₂×C₄	—	4	3	no	—
1319	C₂×C₄	—	4	6	no	—
1320	C₂×C₄	—	4	3	no	—
1321	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1322	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1323	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1324	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1325	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1326	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1327	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1328	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1329	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1330	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1331	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1332	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1333	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1334	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1335	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1336	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1337	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1338	C₂²	—	2	2	no	—
1339	C₂²	—	2	1	no	—
1340	C₂²	—	2	3	no	—
1341	C₂²	—	2	6	no	—
1342	C₂²	—	2	6	no	—
1343	C₂²	—	2	3	no	—
1344	C₂²	—	2	1	no	—
1345	C₂²	—	2	3	no	—
1346	C₂²	—	2	3	no	—
1347	C₂²	—	2	6	no	—
1348	C₂²	—	2	2	no	—
1349	C₂²	—	2	6	no	—
1350	C₂²	—	2	1	no	—
1351	C₂²	—	2	6	no	—
1352	C₂²	—	2	3	no	—
1353	C₂²	—	2	6	no	—
1354	C₂²	—	2	3	no	—
1355	C₂²	—	2	2	no	—
1356	C₂²	—	8	12	no	—
1357	C₂²	—	16	12	no	—
1358	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1359	C₄	—	2	1	no	—
1360	C₄	—	2	2	no	—
1361	C₄	—	2	1	no	—
1362	C₄	—	2	2	no	—
1363	C₄	—	2	6	no	—
1364	C₄	—	2	3	no	—
1365	C₄	—	2	3	no	—
1366	C₄	—	2	3	no	—
1367	C₄	—	2	1	no	—
1368	C₄	—	2	2	no	—
1369	C₄	—	2	1	no	—
1370	C₄	—	2	3	no	—
1371	C₄	—	2	1	no	—
1372	C₄	—	2	3	no	—
1373	C₄	—	2	6	no	—
1374	C₄	C₂×H(5,𝔽₂)×C₈₉	1	6	yes	—
1375	C₄	#585×C₈₉	1	2	yes	—
1376	C₂	—	4	1	no	—
1377	C₂	—	4	3	no	—
1378	C₂	—	4	2	no	—
1379	C₂	—	4	6	no	—
1380	C₂	—	4	6	no	—
1381	C₂	—	4	3	no	—
1382	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1383	C₂	C₂×#585×C₈₉	1	1	yes	characteristic
1384	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₉×#3558	C₂	semidirect
2. C₈₉×#3549	C₂	semidirect
3. C₈₉×#3547	C₂	semidirect
4. C₈₉×#3546	C₂	semidirect
5. C₈₉×#3546	C₂	semidirect
6. C₈₉×#3543	C₂	semidirect
7. C₈₉×#3542	C₂	semidirect
8. C₈₉×#3540	C₂	semidirect
9. C₈₉×#3524	C₂	semidirect
10. C₈₉×#3522	C₂	semidirect
11. C₈₉×#3519	C₂	semidirect
12. C₈₉×#3518	C₂	semidirect
13. C₈₉×#3514	C₂	semidirect
14. C₈₉×#3508	C₂	semidirect
15. C₈₉×#3500	C₂	semidirect
16. C₈₉×#3498	C₂	semidirect
17. C₈₉×#3497	C₂	semidirect
18. C₈₉×#3488	C₂	semidirect
19. C₈₉×#3487	C₂	semidirect
20. C₈₉×#3483	C₂	semidirect
21. C₈₉×#3480	C₂	semidirect
22. D₄×#41×C₈₉	C₂	semidirect
23. C₈₉×#3460	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
25. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
26. C₂²×#41×C₈₉	C₂²	semidirect
27. #562×C₈₉	C₂²	semidirect
28. H(3,𝔽₄)×C₈₉	C₂²	semidirect
29. #560×C₈₉	C₂²	semidirect
30. #560×C₈₉	C₂²	semidirect
31. #559×C₈₉	C₂²	semidirect
32. #559×C₈₉	C₂²	semidirect
33. #559×C₈₉	C₂²	semidirect
34. #559×C₈₉	C₂²	semidirect
35. Q₈²×C₈₉	C₂²	semidirect
36. #557×C₈₉	C₂²	semidirect
37. #556×C₈₉	C₂²	semidirect
38. #556×C₈₉	C₂²	semidirect
39. #556×C₈₉	C₂²	semidirect
40. #555×C₈₉	C₂²	semidirect
41. #555×C₈₉	C₂²	semidirect
42. #555×C₈₉	C₂²	semidirect
43. #555×C₈₉	C₂²	semidirect
44. #555×C₈₉	C₂²	semidirect
45. #554×C₈₉	C₂²	semidirect
46. #553×C₈₉	C₂²	semidirect
47. #553×C₈₉	C₂²	semidirect
48. #553×C₈₉	C₂²	semidirect
49. #553×C₈₉	C₂²	semidirect
50. #552×C₈₉	C₂²	semidirect
51. #551×C₈₉	C₂²	semidirect
54. #550×C₈₉	C₂²	semidirect
55. #550×C₈₉	C₂²	semidirect
56. #550×C₈₉	C₂²	semidirect
57. #550×C₈₉	C₂²	semidirect
58. #550×C₈₉	C₂²	semidirect
59. #550×C₈₉	C₂²	semidirect
60. #550×C₈₉	C₂²	semidirect
61. #550×C₈₉	C₂²	semidirect
62. D₄×Q₈×C₈₉	C₂²	semidirect
63. D₄×Q₈×C₈₉	C₂²	semidirect
64. #548×C₈₉	C₂²	semidirect
65. #548×C₈₉	C₂²	semidirect
66. #548×C₈₉	C₂²	semidirect
67. #548×C₈₉	C₂²	semidirect
68. #548×C₈₉	C₂²	semidirect
69. #548×C₈₉	C₂²	semidirect
70. #548×C₈₉	C₂²	semidirect
71. #548×C₈₉	C₂²	semidirect
72. #548×C₈₉	C₂²	semidirect
73. #547×C₈₉	C₂²	semidirect
74. #547×C₈₉	C₂²	semidirect
75. #546×C₈₉	C₂²	semidirect
76. #546×C₈₉	C₂²	semidirect
77. #546×C₈₉	C₂²	semidirect
78. #546×C₈₉	C₂²	semidirect
79. #546×C₈₉	C₂²	semidirect
80. #546×C₈₉	C₂²	semidirect
81. #546×C₈₉	C₂²	semidirect
82. #546×C₈₉	C₂²	semidirect
83. #546×C₈₉	C₂²	semidirect
84. #546×C₈₉	C₂²	semidirect
85. #546×C₈₉	C₂²	semidirect
86. D₄²×C₈₉	C₂²	semidirect
87. D₄²×C₈₉	C₂²	semidirect
88. D₄²×C₈₉	C₂²	semidirect
89. D₄²×C₈₉	C₂²	semidirect
90. D₄²×C₈₉	C₂²	semidirect
91. D₄²×C₈₉	C₂²	semidirect
92. D₄²×C₈₉	C₂²	semidirect
93. #544×C₈₉	C₂²	semidirect
94. #542×C₈₉	C₂²	semidirect
95. #542×C₈₉	C₂²	semidirect
96. #542×C₈₉	C₂²	semidirect
97. #542×C₈₉	C₂²	semidirect
98. #542×C₈₉	C₂²	semidirect
99. #542×C₈₉	C₂²	semidirect
100. #542×C₈₉	C₂²	semidirect
101. #540×C₈₉	C₂²	semidirect
102. #540×C₈₉	C₂²	semidirect
103. #540×C₈₉	C₂²	semidirect
104. #540×C₈₉	C₂²	semidirect
105. #540×C₈₉	C₂²	semidirect
106. #538×C₈₉	C₂²	semidirect
107. #538×C₈₉	C₂²	semidirect
108. #538×C₈₉	C₂²	semidirect
109. #538×C₈₉	C₂²	semidirect
110. #538×C₈₉	C₂²	semidirect
111. #537×C₈₉	C₂²	semidirect
112. #537×C₈₉	C₂²	semidirect
113. #537×C₈₉	C₂²	semidirect
114. #536×C₈₉	C₂²	semidirect
115. #535×C₈₉	C₂²	semidirect
116. #535×C₈₉	C₂²	semidirect
117. #535×C₈₉	C₂²	semidirect
118. #535×C₈₉	C₂²	semidirect
119. #535×C₈₉	C₂²	semidirect
120. #535×C₈₉	C₂²	semidirect
121. #535×C₈₉	C₂²	semidirect
122. #535×C₈₉	C₂²	semidirect
123. #535×C₈₉	C₂²	semidirect
124. #534×C₈₉	C₂²	semidirect
125. #533×C₈₉	C₂²	semidirect
126. #532×C₈₉	C₂²	semidirect
127. #532×C₈₉	C₂²	semidirect
128. #532×C₈₉	C₂²	semidirect
129. #532×C₈₉	C₂²	semidirect
130. #532×C₈₉	C₂²	semidirect
131. #532×C₈₉	C₂²	semidirect
132. #532×C₈₉	C₂²	semidirect
133. #532×C₈₉	C₂²	semidirect
134. #532×C₈₉	C₂²	semidirect
135. C₂×#127×C₈₉	C₂²	semidirect
136. #529×C₈₉	C₂²	semidirect
137. #529×C₈₉	C₂²	semidirect
138. #529×C₈₉	C₂²	semidirect
139. #529×C₈₉	C₂²	semidirect
140. #529×C₈₉	C₂²	semidirect
141. #529×C₈₉	C₂²	semidirect
142. C₂×#124×C₈₉	C₂²	semidirect
143. #525×C₈₉	C₂²	semidirect
144. #525×C₈₉	C₂²	semidirect
145. #525×C₈₉	C₂²	semidirect
146. #525×C₈₉	C₂²	semidirect
147. C₂×#121×C₈₉	C₂²	semidirect
148. #520×C₈₉	C₂²	semidirect
149. #519×C₈₉	C₂²	semidirect
150. #518×C₈₉	C₂²	semidirect
151. C₄×#41×C₈₉	C₂²	semidirect
152. C₄×#41×C₈₉	C₂²	semidirect
153. C₄×#41×C₈₉	C₂²	semidirect
154. C₄×#41×C₈₉	C₂²	semidirect
155. C₄×#41×C₈₉	C₂²	semidirect
156. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
157. C₂×C₄×D₄×C₈₉	C₂²	semidirect
683. #62923	C₈₉	direct (N × H)
693. #3558	C₂×C₈₉	semidirect
694. #3549	C₂×C₈₉	semidirect
695. #3547	C₂×C₈₉	semidirect
696. #3546	C₂×C₈₉	semidirect
697. #3546	C₂×C₈₉	semidirect
698. #3543	C₂×C₈₉	semidirect
699. #3542	C₂×C₈₉	semidirect
700. #3540	C₂×C₈₉	semidirect
701. #3524	C₂×C₈₉	semidirect
702. #3522	C₂×C₈₉	semidirect
703. #3519	C₂×C₈₉	semidirect
704. #3518	C₂×C₈₉	semidirect
705. #3514	C₂×C₈₉	semidirect
706. #3508	C₂×C₈₉	semidirect
707. #3500	C₂×C₈₉	semidirect
708. #3498	C₂×C₈₉	semidirect
709. #3497	C₂×C₈₉	semidirect
710. #3488	C₂×C₈₉	semidirect
711. #3487	C₂×C₈₉	semidirect
712. #3483	C₂×C₈₉	semidirect
713. #3480	C₂×C₈₉	semidirect
714. D₄×#41	C₂×C₈₉	semidirect
715. #3460	C₂×C₈₉	semidirect
716. C₈₉	#62923	direct (N × H)
717. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
718. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
719. C₂²×#41	C₂²×C₈₉	semidirect
720. #562	C₂²×C₈₉	semidirect
721. H(3,𝔽₄)	C₂²×C₈₉	semidirect
722. #560	C₂²×C₈₉	semidirect
723. #560	C₂²×C₈₉	semidirect
724. #559	C₂²×C₈₉	semidirect
725. #559	C₂²×C₈₉	semidirect
726. #559	C₂²×C₈₉	semidirect
727. #559	C₂²×C₈₉	semidirect
728. Q₈²	C₂²×C₈₉	semidirect
729. #557	C₂²×C₈₉	semidirect
730. #556	C₂²×C₈₉	semidirect
731. #556	C₂²×C₈₉	semidirect
732. #556	C₂²×C₈₉	semidirect
733. #555	C₂²×C₈₉	semidirect
734. #555	C₂²×C₈₉	semidirect
735. #555	C₂²×C₈₉	semidirect
736. #555	C₂²×C₈₉	semidirect
737. #555	C₂²×C₈₉	semidirect
738. #554	C₂²×C₈₉	semidirect
739. #553	C₂²×C₈₉	semidirect
740. #553	C₂²×C₈₉	semidirect
741. #553	C₂²×C₈₉	semidirect
742. #553	C₂²×C₈₉	semidirect
743. #552	C₂²×C₈₉	semidirect
744. #551	C₂²×C₈₉	semidirect
747. #550	C₂²×C₈₉	semidirect
748. #550	C₂²×C₈₉	semidirect
749. #550	C₂²×C₈₉	semidirect
750. #550	C₂²×C₈₉	semidirect
751. #550	C₂²×C₈₉	semidirect
752. #550	C₂²×C₈₉	semidirect
753. #550	C₂²×C₈₉	semidirect
754. #550	C₂²×C₈₉	semidirect
755. D₄×Q₈	C₂²×C₈₉	semidirect
756. D₄×Q₈	C₂²×C₈₉	semidirect
757. #548	C₂²×C₈₉	semidirect
758. #548	C₂²×C₈₉	semidirect
759. #548	C₂²×C₈₉	semidirect
760. #548	C₂²×C₈₉	semidirect
761. #548	C₂²×C₈₉	semidirect
762. #548	C₂²×C₈₉	semidirect
763. #548	C₂²×C₈₉	semidirect
764. #548	C₂²×C₈₉	semidirect
765. #548	C₂²×C₈₉	semidirect
766. #547	C₂²×C₈₉	semidirect
767. #547	C₂²×C₈₉	semidirect
768. #546	C₂²×C₈₉	semidirect
769. #546	C₂²×C₈₉	semidirect
770. #546	C₂²×C₈₉	semidirect
771. #546	C₂²×C₈₉	semidirect
772. #546	C₂²×C₈₉	semidirect
773. #546	C₂²×C₈₉	semidirect
774. #546	C₂²×C₈₉	semidirect
775. #546	C₂²×C₈₉	semidirect
776. #546	C₂²×C₈₉	semidirect
777. #546	C₂²×C₈₉	semidirect
778. #546	C₂²×C₈₉	semidirect
779. D₄²	C₂²×C₈₉	semidirect
780. D₄²	C₂²×C₈₉	semidirect
781. D₄²	C₂²×C₈₉	semidirect
782. D₄²	C₂²×C₈₉	semidirect
783. D₄²	C₂²×C₈₉	semidirect
784. D₄²	C₂²×C₈₉	semidirect
785. D₄²	C₂²×C₈₉	semidirect
786. #544	C₂²×C₈₉	semidirect
787. #542	C₂²×C₈₉	semidirect
788. #542	C₂²×C₈₉	semidirect
789. #542	C₂²×C₈₉	semidirect
790. #542	C₂²×C₈₉	semidirect
791. #542	C₂²×C₈₉	semidirect
792. #542	C₂²×C₈₉	semidirect
793. #542	C₂²×C₈₉	semidirect
794. #540	C₂²×C₈₉	semidirect
795. #540	C₂²×C₈₉	semidirect
796. #540	C₂²×C₈₉	semidirect
797. #540	C₂²×C₈₉	semidirect
798. #540	C₂²×C₈₉	semidirect
799. #538	C₂²×C₈₉	semidirect
800. #538	C₂²×C₈₉	semidirect
801. #538	C₂²×C₈₉	semidirect
802. #538	C₂²×C₈₉	semidirect
803. #538	C₂²×C₈₉	semidirect
804. #537	C₂²×C₈₉	semidirect
805. #537	C₂²×C₈₉	semidirect
806. #537	C₂²×C₈₉	semidirect
807. #536	C₂²×C₈₉	semidirect
808. #535	C₂²×C₈₉	semidirect
809. #535	C₂²×C₈₉	semidirect
810. #535	C₂²×C₈₉	semidirect
811. #535	C₂²×C₈₉	semidirect
812. #535	C₂²×C₈₉	semidirect
813. #535	C₂²×C₈₉	semidirect
814. #535	C₂²×C₈₉	semidirect
815. #535	C₂²×C₈₉	semidirect
816. #535	C₂²×C₈₉	semidirect
817. #534	C₂²×C₈₉	semidirect
818. #533	C₂²×C₈₉	semidirect
819. #532	C₂²×C₈₉	semidirect
820. #532	C₂²×C₈₉	semidirect
821. #532	C₂²×C₈₉	semidirect
822. #532	C₂²×C₈₉	semidirect
823. #532	C₂²×C₈₉	semidirect
824. #532	C₂²×C₈₉	semidirect
825. #532	C₂²×C₈₉	semidirect
826. #532	C₂²×C₈₉	semidirect
827. #532	C₂²×C₈₉	semidirect
828. C₂×#127	C₂²×C₈₉	semidirect
829. #529	C₂²×C₈₉	semidirect
830. #529	C₂²×C₈₉	semidirect
831. #529	C₂²×C₈₉	semidirect
832. #529	C₂²×C₈₉	semidirect
833. #529	C₂²×C₈₉	semidirect
834. #529	C₂²×C₈₉	semidirect
835. C₂×#124	C₂²×C₈₉	semidirect
836. #525	C₂²×C₈₉	semidirect
837. #525	C₂²×C₈₉	semidirect
838. #525	C₂²×C₈₉	semidirect
839. #525	C₂²×C₈₉	semidirect
840. C₂×#121	C₂²×C₈₉	semidirect
841. #520	C₂²×C₈₉	semidirect
842. #519	C₂²×C₈₉	semidirect
843. #518	C₂²×C₈₉	semidirect
844. C₄×#41	C₂²×C₈₉	semidirect
845. C₄×#41	C₂²×C₈₉	semidirect
846. C₄×#41	C₂²×C₈₉	semidirect
847. C₄×#41	C₂²×C₈₉	semidirect
848. C₄×#41	C₂²×C₈₉	semidirect
849. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
850. C₂×C₄×D₄	C₂²×C₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₉×#3558	2
C₈₉×#3549	2
C₈₉×#3547	2
C₈₉×#3546	2
C₈₉×#3543	2
C₈₉×#3542	2
C₈₉×#3540	2
C₈₉×#3524	2
C₈₉×#3522	2
C₈₉×#3519	2
C₈₉×#3518	2
C₈₉×#3514	2
C₈₉×#3508	2
C₈₉×#3500	2
C₈₉×#3498	2
C₈₉×#3497	2
C₈₉×#3488	2
C₈₉×#3487	2
C₈₉×#3483	2
C₈₉×#3480	2
D₄×#41×C₈₉	2
C₈₉×#3460	2
#62923	89

Subgroups — C89×#62923 #36440771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62923 #36440771