Subgroups — C₈₉×#63044 #36440892

Order 22784.

6904 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3562	C₂	1	6	yes	maximal, complemented
2	C₈₉×#3554	C₂	1	6	yes	maximal, complemented
3	C₈₉×#3552	C₂	1	6	yes	maximal, complemented
4	C₈₉×#3551	C₂	1	3	yes	maximal, complemented
5	C₈₉×#3547	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3541	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3540	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3539	C₂	1	6	yes	maximal, complemented
9	C₈₉×#3538	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3529	C₂	1	3	yes	maximal, complemented
11	C₈₉×#3524	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3523	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3516	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3497	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3489	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3486	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3486	C₂	1	2	yes	maximal, complemented
20	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
22	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	#563×C₈₉	C₂²	1	3	yes	—
26	#563×C₈₉	C₂²	1	6	yes	complemented
27	#563×C₈₉	C₂²	1	6	yes	complemented
28	#563×C₈₉	C₂²	1	6	yes	complemented
29	#562×C₈₉	C₂²	1	6	yes	—
30	#562×C₈₉	C₂²	1	6	yes	complemented
31	#562×C₈₉	C₂²	1	6	yes	complemented
32	#562×C₈₉	C₂²	1	12	yes	complemented
33	H(3,𝔽₄)×C₈₉	C₂²	1	3	yes	—
34	#560×C₈₉	C₂²	1	1	yes	characteristic
35	#560×C₈₉	C₂²	1	3	yes	—
36	#560×C₈₉	C₂²	1	6	yes	—
37	#560×C₈₉	C₂²	1	6	yes	complemented
38	#560×C₈₉	C₂²	1	6	yes	complemented
39	#559×C₈₉	C₂²	1	6	yes	complemented
40	#559×C₈₉	C₂²	1	6	yes	complemented
41	#557×C₈₉	C₂²	1	2	yes	complemented
42	#557×C₈₉	C₂²	1	6	yes	complemented
43	#556×C₈₉	C₂²	1	6	yes	—
44	#556×C₈₉	C₂²	1	6	yes	complemented
45	#555×C₈₉	C₂²	1	6	yes	complemented
46	#555×C₈₉	C₂²	1	6	yes	complemented
47	#554×C₈₉	C₂²	1	6	yes	complemented
48	#554×C₈₉	C₂²	1	12	yes	complemented
49	#553×C₈₉	C₂²	1	6	yes	complemented
50	#553×C₈₉	C₂²	1	6	yes	complemented
51	#553×C₈₉	C₂²	1	12	yes	complemented
52	#553×C₈₉	C₂²	1	12	yes	complemented
53	#552×C₈₉	C₂²	1	6	yes	complemented
54	#552×C₈₉	C₂²	1	6	yes	complemented
55	#552×C₈₉	C₂²	1	6	yes	complemented
56	#552×C₈₉	C₂²	1	6	yes	complemented
57	#551×C₈₉	C₂²	1	6	yes	—
58	#551×C₈₉	C₂²	1	6	yes	complemented
59	#550×C₈₉	C₂²	1	6	yes	—
60	#550×C₈₉	C₂²	1	2	yes	complemented
61	#550×C₈₉	C₂²	1	6	yes	complemented
62	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
63	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
64	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
65	D₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
66	D₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
67	D₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
68	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
69	D₄×Q₈×C₈₉	C₂²	1	6	yes	complemented
70	#548×C₈₉	C₂²	1	2	yes	—
71	#548×C₈₉	C₂²	1	2	yes	—
72	#548×C₈₉	C₂²	1	6	yes	—
73	#548×C₈₉	C₂²	1	2	yes	complemented
74	#548×C₈₉	C₂²	1	6	yes	complemented
75	#548×C₈₉	C₂²	1	6	yes	complemented
76	#548×C₈₉	C₂²	1	6	yes	complemented
77	#548×C₈₉	C₂²	1	2	yes	complemented
78	#548×C₈₉	C₂²	1	6	yes	complemented
79	#548×C₈₉	C₂²	1	6	yes	complemented
80	#547×C₈₉	C₂²	1	6	yes	—
81	#547×C₈₉	C₂²	1	6	yes	complemented
82	#547×C₈₉	C₂²	1	6	yes	complemented
83	#547×C₈₉	C₂²	1	6	yes	complemented
84	#546×C₈₉	C₂²	1	6	yes	—
85	#546×C₈₉	C₂²	1	6	yes	complemented
86	#544×C₈₉	C₂²	1	12	yes	complemented
87	#542×C₈₉	C₂²	1	6	yes	complemented
88	#542×C₈₉	C₂²	1	6	yes	complemented
89	#542×C₈₉	C₂²	1	12	yes	complemented
90	#542×C₈₉	C₂²	1	12	yes	complemented
91	#541×C₈₉	C₂²	1	6	yes	complemented
92	#541×C₈₉	C₂²	1	6	yes	complemented
93	#541×C₈₉	C₂²	1	6	yes	complemented
94	#540×C₈₉	C₂²	1	6	yes	complemented
95	#540×C₈₉	C₂²	1	12	yes	complemented
96	#540×C₈₉	C₂²	1	12	yes	complemented
97	#539×C₈₉	C₂²	1	12	yes	complemented
98	#539×C₈₉	C₂²	1	12	yes	complemented
99	#539×C₈₉	C₂²	1	12	yes	complemented
100	#538×C₈₉	C₂²	1	12	yes	—
101	#538×C₈₉	C₂²	1	12	yes	complemented
102	#537×C₈₉	C₂²	1	6	yes	—
103	#537×C₈₉	C₂²	1	6	yes	complemented
104	#537×C₈₉	C₂²	1	6	yes	complemented
105	#536×C₈₉	C₂²	1	3	yes	—
106	#536×C₈₉	C₂²	1	3	yes	—
107	#536×C₈₉	C₂²	1	6	yes	complemented
108	#536×C₈₉	C₂²	1	6	yes	complemented
109	#536×C₈₉	C₂²	1	3	yes	complemented
110	#536×C₈₉	C₂²	1	6	yes	complemented
111	#536×C₈₉	C₂²	1	3	yes	complemented
112	#535×C₈₉	C₂²	1	3	yes	—
113	#535×C₈₉	C₂²	1	3	yes	complemented
114	#533×C₈₉	C₂²	1	6	yes	complemented
115	#532×C₈₉	C₂²	1	3	yes	—
116	#532×C₈₉	C₂²	1	6	yes	complemented
117	#532×C₈₉	C₂²	1	6	yes	complemented
118	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
119	#529×C₈₉	C₂²	1	6	yes	—
120	#529×C₈₉	C₂²	1	6	yes	complemented
121	#529×C₈₉	C₂²	1	6	yes	complemented
122	#529×C₈₉	C₂²	1	6	yes	complemented
123	#529×C₈₉	C₂²	1	6	yes	complemented
124	#525×C₈₉	C₂²	1	3	yes	—
125	#525×C₈₉	C₂²	1	3	yes	—
126	#525×C₈₉	C₂²	1	6	yes	—
127	#525×C₈₉	C₂²	1	6	yes	complemented
128	#525×C₈₉	C₂²	1	3	yes	complemented
129	#525×C₈₉	C₂²	1	6	yes	complemented
130	#525×C₈₉	C₂²	1	3	yes	complemented
131	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
132	#520×C₈₉	C₂²	1	2	yes	complemented
133	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
134	#519×C₈₉	C₂²	1	2	yes	complemented
135	#519×C₈₉	C₂²	1	1	yes	characteristic, complemented
136	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
138	2₋¹⁺⁴×C₈₉	—	4	4	no	—
139	2₋¹⁺⁴×C₈₉	—	4	8	no	—
140	2₋¹⁺⁴×C₈₉	—	4	4	no	—
141	C₂×#41×C₈₉	—	4	4	no	—
142	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₈₉	C₂³	1	2	yes	—
144	C₂×#41×C₈₉	C₂³	1	3	yes	—
145	C₂×#41×C₈₉	C₂³	1	6	yes	—
146	C₂×#41×C₈₉	C₂³	1	3	yes	—
147	C₂×#41×C₈₉	C₂³	1	6	yes	—
148	C₂×#41×C₈₉	C₂³	1	3	yes	—
149	C₂×#41×C₈₉	C₂³	1	3	yes	—
150	C₂×#41×C₈₉	C₂³	1	6	yes	—
151	C₂×#41×C₈₉	C₂³	1	6	yes	—
152	C₂×#41×C₈₉	C₂³	1	6	yes	—
153	C₂²×Q₈×C₈₉	—	4	4	no	—
154	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
155	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
156	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
157	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
159	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
160	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
161	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
162	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
163	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
164	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
165	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
166	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
167	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
168	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
169	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
170	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
171	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
172	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
173	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
174	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
175	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
176	#127×C₈₉	C₂³	1	1	yes	characteristic
177	#127×C₈₉	C₂³	1	6	yes	—
178	#127×C₈₉	C₂³	1	6	yes	—
179	#127×C₈₉	C₂³	1	6	yes	—
180	#126×C₈₉	C₂³	1	6	yes	—
181	#126×C₈₉	C₂³	1	6	yes	—
182	#126×C₈₉	C₂³	1	2	yes	—
183	#126×C₈₉	C₂³	1	6	yes	—
184	#126×C₈₉	C₂³	1	12	yes	—
185	#126×C₈₉	C₂³	1	6	yes	—
186	#126×C₈₉	C₂³	1	6	yes	—
187	#126×C₈₉	C₂³	1	12	yes	—
188	#126×C₈₉	C₂³	1	12	yes	—
189	#126×C₈₉	C₂³	1	12	yes	—
190	#126×C₈₉	C₂³	1	12	yes	—
191	#125×C₈₉	C₂³	1	6	yes	—
192	#125×C₈₉	C₂³	1	6	yes	—
193	#125×C₈₉	C₂³	1	6	yes	—
194	#125×C₈₉	C₂³	1	6	yes	—
195	#125×C₈₉	C₂³	1	6	yes	—
196	#125×C₈₉	C₂³	1	12	yes	—
197	#125×C₈₉	C₂³	1	12	yes	—
198	#125×C₈₉	C₂³	1	12	yes	—
199	#125×C₈₉	C₂³	1	12	yes	—
200	#124×C₈₉	C₂³	1	6	yes	—
201	#124×C₈₉	C₂³	1	6	yes	—
202	#124×C₈₉	C₂³	1	6	yes	—
203	#124×C₈₉	C₂³	1	6	yes	—
204	#124×C₈₉	C₂³	1	6	yes	—
205	#124×C₈₉	C₂³	1	3	yes	—
206	#124×C₈₉	C₂³	1	3	yes	—
207	#124×C₈₉	C₂³	1	6	yes	—
208	#124×C₈₉	C₂³	1	6	yes	—
209	#124×C₈₉	C₂³	1	6	yes	—
210	#124×C₈₉	C₂³	1	6	yes	—
211	#124×C₈₉	C₂³	1	6	yes	—
212	#124×C₈₉	C₂³	1	6	yes	—
213	#124×C₈₉	C₂³	1	12	yes	—
214	#124×C₈₉	C₂³	1	12	yes	—
215	#123×C₈₉	C₂³	1	1	yes	characteristic
216	#123×C₈₉	C₂³	1	3	yes	—
217	#123×C₈₉	C₂³	1	3	yes	—
218	#123×C₈₉	C₂³	1	3	yes	—
219	#123×C₈₉	C₂³	1	6	yes	—
220	#123×C₈₉	C₂³	1	6	yes	—
221	#123×C₈₉	C₂³	1	6	yes	—
222	#123×C₈₉	C₂³	1	12	yes	—
223	#123×C₈₉	C₂³	1	6	yes	—
224	#123×C₈₉	C₂³	1	6	yes	—
225	#123×C₈₉	C₂³	1	6	yes	—
226	#123×C₈₉	C₂³	1	6	yes	—
227	#123×C₈₉	C₂³	1	2	yes	—
228	#123×C₈₉	C₂³	1	6	yes	—
229	#123×C₈₉	C₂³	1	12	yes	—
230	#123×C₈₉	C₂³	1	6	yes	—
231	#123×C₈₉	C₂³	1	6	yes	—
232	#123×C₈₉	C₂³	1	6	yes	—
233	#123×C₈₉	C₂³	1	6	yes	—
234	#123×C₈₉	C₂³	1	12	yes	—
235	#123×C₈₉	C₂³	1	12	yes	—
236	#123×C₈₉	C₂³	1	12	yes	—
237	#123×C₈₉	C₂³	1	12	yes	—
238	#123×C₈₉	C₂³	1	12	yes	—
239	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
240	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
241	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
242	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
243	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
244	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
245	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
246	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
247	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
248	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
249	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
250	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
251	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
252	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
253	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
254	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
255	C₂²⋊Q₈×C₈₉	C₂³	1	6	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	12	yes	—
262	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
263	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
264	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
265	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
266	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
267	#121×C₈₉	C₂³	1	2	yes	—
268	#121×C₈₉	C₂³	1	6	yes	—
269	#121×C₈₉	C₂³	1	6	yes	—
270	#121×C₈₉	C₂³	1	6	yes	—
271	#121×C₈₉	C₂³	1	6	yes	—
272	#121×C₈₉	C₂³	1	6	yes	—
273	#121×C₈₉	C₂³	1	6	yes	—
274	#121×C₈₉	C₂³	1	6	yes	—
275	#121×C₈₉	C₂³	1	6	yes	—
276	#121×C₈₉	C₂³	1	6	yes	—
277	#121×C₈₉	C₂³	1	2	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	6	yes	—
284	#121×C₈₉	C₂³	1	6	yes	—
285	#121×C₈₉	C₂³	1	2	yes	—
286	#121×C₈₉	C₂³	1	12	yes	—
287	#121×C₈₉	C₂³	1	6	yes	—
288	#121×C₈₉	C₂³	1	6	yes	—
289	#121×C₈₉	C₂³	1	12	yes	—
290	#121×C₈₉	C₂³	1	12	yes	—
291	#121×C₈₉	C₂³	1	12	yes	—
292	#121×C₈₉	C₂³	1	12	yes	—
293	#121×C₈₉	C₂³	1	12	yes	—
294	#121×C₈₉	C₂³	1	12	yes	—
295	#120×C₈₉	C₂³	1	1	yes	characteristic
296	#120×C₈₉	C₂³	1	3	yes	—
297	#120×C₈₉	C₂³	1	3	yes	—
298	#120×C₈₉	C₂³	1	3	yes	—
299	#120×C₈₉	C₂³	1	6	yes	—
300	#120×C₈₉	C₂³	1	6	yes	—
301	#120×C₈₉	C₂³	1	2	yes	—
302	#120×C₈₉	C₂³	1	6	yes	—
303	#120×C₈₉	C₂³	1	6	yes	—
304	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
305	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
306	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
307	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
308	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
309	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
310	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
311	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
312	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
313	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
314	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
315	C₄×D₄×C₈₉	C₂³	1	6	yes	—
316	C₄×D₄×C₈₉	C₂³	1	6	yes	—
317	C₄×D₄×C₈₉	C₂³	1	6	yes	—
318	C₄×D₄×C₈₉	C₂³	1	6	yes	—
319	C₄×D₄×C₈₉	C₂³	1	6	yes	—
320	C₄×D₄×C₈₉	C₂³	1	6	yes	—
321	C₄×D₄×C₈₉	C₂³	1	6	yes	—
322	C₄×D₄×C₈₉	C₂³	1	6	yes	—
323	C₄×D₄×C₈₉	C₂³	1	6	yes	—
324	C₄×D₄×C₈₉	C₂³	1	6	yes	—
325	C₄×D₄×C₈₉	C₂³	1	6	yes	—
326	C₄×D₄×C₈₉	C₂³	1	6	yes	—
327	C₄×D₄×C₈₉	C₂³	1	12	yes	—
328	C₄×D₄×C₈₉	C₂³	1	12	yes	—
329	C₄×D₄×C₈₉	C₂³	1	12	yes	—
330	C₄×D₄×C₈₉	C₂³	1	12	yes	—
331	C₄×D₄×C₈₉	C₂³	1	12	yes	—
332	C₄×D₄×C₈₉	C₂³	1	12	yes	—
333	C₄×D₄×C₈₉	C₂³	1	12	yes	—
334	C₄×D₄×C₈₉	C₂³	1	12	yes	—
335	#117×C₈₉	C₂³	1	3	yes	—
336	#117×C₈₉	C₂³	1	3	yes	—
337	#117×C₈₉	C₂³	1	3	yes	—
338	#117×C₈₉	C₂³	1	6	yes	—
339	#117×C₈₉	C₂³	1	3	yes	—
340	#117×C₈₉	C₂³	1	3	yes	—
341	#117×C₈₉	C₂³	1	6	yes	—
342	#117×C₈₉	C₂³	1	6	yes	—
343	#117×C₈₉	C₂³	1	12	yes	—
344	#117×C₈₉	C₂³	1	12	yes	—
345	#117×C₈₉	C₂³	1	12	yes	—
346	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
347	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
348	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
349	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
350	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
351	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
352	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
353	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
354	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
355	#41×C₈₉	—	2	8	no	—
356	#41×C₈₉	—	2	4	no	—
357	#41×C₈₉	—	4	6	no	—
358	#41×C₈₉	—	4	12	no	—
359	#41×C₈₉	—	4	6	no	—
360	#41×C₈₉	—	4	12	no	—
361	#41×C₈₉	—	4	6	no	—
362	#41×C₈₉	—	4	12	no	—
363	#41×C₈₉	—	4	6	no	—
364	#41×C₈₉	—	4	12	no	—
365	#41×C₈₉	—	4	12	no	—
366	C₂×Q₈×C₈₉	—	2	4	no	—
367	C₂×Q₈×C₈₉	—	2	8	no	—
368	C₂×Q₈×C₈₉	—	2	4	no	—
369	C₂×Q₈×C₈₉	—	2	8	no	—
370	C₂×Q₈×C₈₉	—	4	6	no	—
371	C₂×Q₈×C₈₉	—	4	12	no	—
372	C₂×Q₈×C₈₉	—	4	12	no	—
373	C₂×Q₈×C₈₉	—	4	6	no	—
374	C₂×Q₈×C₈₉	—	4	6	no	—
375	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
376	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
377	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
378	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
379	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
380	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
381	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
382	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
383	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
384	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×D₄×C₈₉	—	4	6	no	—
386	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
387	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
388	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
389	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
390	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
391	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
392	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
393	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
394	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
395	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
396	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
397	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
398	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
399	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
400	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
401	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
402	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
403	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
404	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
405	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
406	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
407	C₂²×C₄×C₈₉	—	4	6	no	—
408	C₂²×C₄×C₈₉	—	4	6	no	—
409	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
410	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
411	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
412	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
413	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
414	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
415	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
417	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
418	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
419	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
420	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
421	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
422	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
423	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
424	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
425	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
427	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
428	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
429	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
430	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
431	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
432	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
433	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
434	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
435	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
436	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
437	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
438	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
440	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
441	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
442	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
443	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
444	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
445	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
446	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
448	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
449	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
450	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
451	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
452	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
453	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
454	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
455	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
456	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
457	C₂²⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
458	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
459	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
460	C₂²⋊C₄×C₈₉	C₂⁴	1	3	yes	—
461	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
462	C₂²⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
463	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
464	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
465	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
466	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
467	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
468	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
469	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
470	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
471	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
472	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
473	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
474	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
475	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
476	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
477	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
478	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
479	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
480	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
481	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
482	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
483	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
484	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
485	C₄²×C₈₉	C₂⁴	1	3	yes	—
486	C₄²×C₈₉	C₂⁴	1	6	yes	—
487	C₄²×C₈₉	C₂⁴	1	6	yes	—
488	C₄²×C₈₉	C₂⁴	1	6	yes	—
489	C₄²×C₈₉	C₂⁴	1	6	yes	—
490	C₄²×C₈₉	C₂⁴	1	6	yes	—
491	C₄²×C₈₉	C₂⁴	1	6	yes	—
492	C₄²×C₈₉	C₂⁴	1	12	yes	—
493	C₄²×C₈₉	C₂⁴	1	6	yes	—
494	C₂³×C₈₉	—	4	1	no	—
495	C₂³×C₈₉	—	4	2	no	—
496	C₂³×C₈₉	—	4	3	no	—
497	C₂³×C₈₉	—	4	6	no	—
498	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
499	C₂³×C₈₉	C₂⁵	1	2	yes	—
500	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
501	C₂³×C₈₉	C₂⁵	1	6	yes	—
502	C₂³×C₈₉	C₂⁵	1	2	yes	—
503	C₂³×C₈₉	C₂⁵	1	3	yes	—
504	Q₈×C₈₉	—	2	6	no	—
505	Q₈×C₈₉	—	2	12	no	—
506	Q₈×C₈₉	—	2	12	no	—
507	Q₈×C₈₉	—	2	6	no	—
508	Q₈×C₈₉	—	4	6	no	—
509	Q₈×C₈₉	—	4	6	no	—
510	Q₈×C₈₉	—	4	3	no	—
511	Q₈×C₈₉	—	4	3	no	—
512	Q₈×C₈₉	—	4	6	no	—
513	Q₈×C₈₉	H(5,𝔽₂)	1	4	yes	—
514	D₄×C₈₉	—	2	12	no	—
515	D₄×C₈₉	—	2	6	no	—
516	D₄×C₈₉	—	4	6	no	—
517	D₄×C₈₉	—	4	2	no	—
518	D₄×C₈₉	—	4	6	no	—
519	D₄×C₈₉	—	4	2	no	—
520	D₄×C₈₉	—	4	6	no	—
521	D₄×C₈₉	—	4	6	no	—
522	D₄×C₈₉	—	4	2	no	—
523	D₄×C₈₉	—	4	6	no	—
524	D₄×C₈₉	—	4	6	no	—
525	D₄×C₈₉	—	4	12	no	—
526	D₄×C₈₉	—	4	2	no	—
527	D₄×C₈₉	—	4	2	no	—
528	D₄×C₈₉	—	4	1	no	—
529	D₄×C₈₉	—	4	1	no	—
530	D₄×C₈₉	—	4	3	no	—
531	D₄×C₈₉	—	4	6	no	—
532	D₄×C₈₉	—	4	6	no	—
533	D₄×C₈₉	—	4	3	no	—
534	D₄×C₈₉	—	4	6	no	—
535	C₂×C₄×C₈₉	—	2	6	no	—
536	C₂×C₄×C₈₉	—	2	6	no	—
537	C₂×C₄×C₈₉	—	2	12	no	—
538	C₂×C₄×C₈₉	—	2	12	no	—
539	C₂×C₄×C₈₉	—	2	12	no	—
540	C₂×C₄×C₈₉	—	2	6	no	—
541	C₂×C₄×C₈₉	—	4	1	no	—
542	C₂×C₄×C₈₉	—	4	6	no	—
543	C₂×C₄×C₈₉	—	4	3	no	—
544	C₂×C₄×C₈₉	—	4	6	no	—
545	C₂×C₄×C₈₉	—	4	12	no	—
546	C₂×C₄×C₈₉	—	4	6	no	—
547	C₂×C₄×C₈₉	—	4	6	no	—
548	C₂×C₄×C₈₉	—	4	2	no	—
549	C₂×C₄×C₈₉	—	4	6	no	—
550	C₂×C₄×C₈₉	—	4	6	no	—
551	C₂×C₄×C₈₉	—	4	12	no	—
552	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
553	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
554	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
555	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
556	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
557	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
558	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
559	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
560	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
561	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
562	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
563	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
564	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
565	C₂²×C₈₉	—	2	2	no	—
566	C₂²×C₈₉	—	2	1	no	—
567	C₂²×C₈₉	—	2	1	no	—
568	C₂²×C₈₉	—	2	2	no	—
569	C₂²×C₈₉	—	2	3	no	—
570	C₂²×C₈₉	—	2	6	no	—
571	C₂²×C₈₉	—	2	2	no	—
572	C₂²×C₈₉	—	2	6	no	—
573	C₂²×C₈₉	—	2	2	no	—
574	C₂²×C₈₉	—	2	6	no	—
575	C₂²×C₈₉	—	2	2	no	—
576	C₂²×C₈₉	—	2	2	no	—
577	C₂²×C₈₉	—	2	2	no	—
578	C₂²×C₈₉	—	2	6	no	—
579	C₂²×C₈₉	—	2	2	no	—
580	C₂²×C₈₉	—	4	4	no	—
581	C₂²×C₈₉	—	8	6	no	—
582	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
583	C₄×C₈₉	—	2	2	no	—
584	C₄×C₈₉	—	2	1	no	—
585	C₄×C₈₉	—	2	3	no	—
586	C₄×C₈₉	—	2	6	no	—
587	C₄×C₈₉	—	2	3	no	—
588	C₄×C₈₉	—	2	6	no	—
589	C₄×C₈₉	—	2	6	no	—
590	C₄×C₈₉	—	2	2	no	—
591	C₄×C₈₉	—	2	6	no	—
592	C₄×C₈₉	—	2	2	no	—
593	C₄×C₈₉	—	2	6	no	—
594	C₄×C₈₉	—	2	2	no	—
595	C₄×C₈₉	C₂×H(5,𝔽₂)	1	6	yes	—
596	#63044	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
597	C₂×C₈₉	—	4	2	no	—
598	C₂×C₈₉	—	4	3	no	—
599	C₂×C₈₉	—	4	2	no	—
600	C₂×C₈₉	—	4	1	no	—
601	C₂×C₈₉	—	4	6	no	—
602	C₂×C₈₉	—	4	1	no	—
603	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
605	#3562	C₂×C₈₉	1	6	yes	complemented
606	#3554	C₂×C₈₉	1	6	yes	complemented
607	#3552	C₂×C₈₉	1	6	yes	complemented
608	#3551	C₂×C₈₉	1	3	yes	complemented
609	#3547	C₂×C₈₉	1	6	yes	complemented
610	#3541	C₂×C₈₉	1	6	yes	complemented
611	#3540	C₂×C₈₉	1	3	yes	complemented
612	#3539	C₂×C₈₉	1	6	yes	complemented
613	#3538	C₂×C₈₉	1	3	yes	complemented
614	#3529	C₂×C₈₉	1	3	yes	complemented
615	#3524	C₂×C₈₉	1	2	yes	complemented
616	#3523	C₂×C₈₉	1	2	yes	complemented
617	#3516	C₂×C₈₉	1	2	yes	complemented
618	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
619	#3497	C₂×C₈₉	1	2	yes	complemented
620	#3489	C₂×C₈₉	1	2	yes	complemented
621	#3487	C₂×C₈₉	1	1	yes	characteristic, complemented
622	#3486	C₂×C₈₉	1	1	yes	characteristic, complemented
623	#3486	C₂×C₈₉	1	2	yes	complemented
624	C₈₉	#63044	1	1	yes	characteristic, direct product factor, Sylow
625	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
626	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
627	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic, complemented
628	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
629	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
630	#563	C₂²×C₈₉	1	3	yes	—
631	#563	C₂²×C₈₉	1	6	yes	complemented
632	#563	C₂²×C₈₉	1	6	yes	complemented
633	#563	C₂²×C₈₉	1	6	yes	complemented
634	#562	C₂²×C₈₉	1	6	yes	—
635	#562	C₂²×C₈₉	1	6	yes	complemented
636	#562	C₂²×C₈₉	1	6	yes	complemented
637	#562	C₂²×C₈₉	1	12	yes	complemented
638	H(3,𝔽₄)	C₂²×C₈₉	1	3	yes	—
639	#560	C₂²×C₈₉	1	1	yes	characteristic
640	#560	C₂²×C₈₉	1	3	yes	—
641	#560	C₂²×C₈₉	1	6	yes	—
642	#560	C₂²×C₈₉	1	6	yes	complemented
643	#560	C₂²×C₈₉	1	6	yes	complemented
644	#559	C₂²×C₈₉	1	6	yes	complemented
645	#559	C₂²×C₈₉	1	6	yes	complemented
646	#557	C₂²×C₈₉	1	2	yes	complemented
647	#557	C₂²×C₈₉	1	6	yes	complemented
648	#556	C₂²×C₈₉	1	6	yes	—
649	#556	C₂²×C₈₉	1	6	yes	complemented
650	#555	C₂²×C₈₉	1	6	yes	complemented
651	#555	C₂²×C₈₉	1	6	yes	complemented
652	#554	C₂²×C₈₉	1	6	yes	complemented
653	#554	C₂²×C₈₉	1	12	yes	complemented
654	#553	C₂²×C₈₉	1	6	yes	complemented
655	#553	C₂²×C₈₉	1	6	yes	complemented
656	#553	C₂²×C₈₉	1	12	yes	complemented
657	#553	C₂²×C₈₉	1	12	yes	complemented
658	#552	C₂²×C₈₉	1	6	yes	complemented
659	#552	C₂²×C₈₉	1	6	yes	complemented
660	#552	C₂²×C₈₉	1	6	yes	complemented
661	#552	C₂²×C₈₉	1	6	yes	complemented
662	#551	C₂²×C₈₉	1	6	yes	—
663	#551	C₂²×C₈₉	1	6	yes	complemented
664	#550	C₂²×C₈₉	1	6	yes	—
665	#550	C₂²×C₈₉	1	2	yes	complemented
666	#550	C₂²×C₈₉	1	6	yes	complemented
667	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
668	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
669	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
670	D₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
671	D₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
672	D₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
673	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
674	D₄×Q₈	C₂²×C₈₉	1	6	yes	complemented
675	#548	C₂²×C₈₉	1	2	yes	—
676	#548	C₂²×C₈₉	1	2	yes	—
677	#548	C₂²×C₈₉	1	6	yes	—
678	#548	C₂²×C₈₉	1	2	yes	complemented
679	#548	C₂²×C₈₉	1	6	yes	complemented
680	#548	C₂²×C₈₉	1	6	yes	complemented
681	#548	C₂²×C₈₉	1	6	yes	complemented
682	#548	C₂²×C₈₉	1	2	yes	complemented
683	#548	C₂²×C₈₉	1	6	yes	complemented
684	#548	C₂²×C₈₉	1	6	yes	complemented
685	#547	C₂²×C₈₉	1	6	yes	—
686	#547	C₂²×C₈₉	1	6	yes	complemented
687	#547	C₂²×C₈₉	1	6	yes	complemented
688	#547	C₂²×C₈₉	1	6	yes	complemented
689	#546	C₂²×C₈₉	1	6	yes	—
690	#546	C₂²×C₈₉	1	6	yes	complemented
691	#544	C₂²×C₈₉	1	12	yes	complemented
692	#542	C₂²×C₈₉	1	6	yes	complemented
693	#542	C₂²×C₈₉	1	6	yes	complemented
694	#542	C₂²×C₈₉	1	12	yes	complemented
695	#542	C₂²×C₈₉	1	12	yes	complemented
696	#541	C₂²×C₈₉	1	6	yes	complemented
697	#541	C₂²×C₈₉	1	6	yes	complemented
698	#541	C₂²×C₈₉	1	6	yes	complemented
699	#540	C₂²×C₈₉	1	6	yes	complemented
700	#540	C₂²×C₈₉	1	12	yes	complemented
701	#540	C₂²×C₈₉	1	12	yes	complemented
702	#539	C₂²×C₈₉	1	12	yes	complemented
703	#539	C₂²×C₈₉	1	12	yes	complemented
704	#539	C₂²×C₈₉	1	12	yes	complemented
705	#538	C₂²×C₈₉	1	12	yes	—
706	#538	C₂²×C₈₉	1	12	yes	complemented
707	#537	C₂²×C₈₉	1	6	yes	—
708	#537	C₂²×C₈₉	1	6	yes	complemented
709	#537	C₂²×C₈₉	1	6	yes	complemented
710	#536	C₂²×C₈₉	1	3	yes	—
711	#536	C₂²×C₈₉	1	3	yes	—
712	#536	C₂²×C₈₉	1	6	yes	complemented
713	#536	C₂²×C₈₉	1	6	yes	complemented
714	#536	C₂²×C₈₉	1	3	yes	complemented
715	#536	C₂²×C₈₉	1	6	yes	complemented
716	#536	C₂²×C₈₉	1	3	yes	complemented
717	#535	C₂²×C₈₉	1	3	yes	—
718	#535	C₂²×C₈₉	1	3	yes	complemented
719	#533	C₂²×C₈₉	1	6	yes	complemented
720	#532	C₂²×C₈₉	1	3	yes	—
721	#532	C₂²×C₈₉	1	6	yes	complemented
722	#532	C₂²×C₈₉	1	6	yes	complemented
723	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
724	#529	C₂²×C₈₉	1	6	yes	—
725	#529	C₂²×C₈₉	1	6	yes	complemented
726	#529	C₂²×C₈₉	1	6	yes	complemented
727	#529	C₂²×C₈₉	1	6	yes	complemented
728	#529	C₂²×C₈₉	1	6	yes	complemented
729	#525	C₂²×C₈₉	1	3	yes	—
730	#525	C₂²×C₈₉	1	3	yes	—
731	#525	C₂²×C₈₉	1	6	yes	—
732	#525	C₂²×C₈₉	1	6	yes	complemented
733	#525	C₂²×C₈₉	1	3	yes	complemented
734	#525	C₂²×C₈₉	1	6	yes	complemented
735	#525	C₂²×C₈₉	1	3	yes	complemented
736	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
737	#520	C₂²×C₈₉	1	2	yes	complemented
738	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
739	#519	C₂²×C₈₉	1	2	yes	complemented
740	#519	C₂²×C₈₉	1	1	yes	characteristic, complemented
741	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
742	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
743	2₋¹⁺⁴	—	4	4	no	—
744	2₋¹⁺⁴	—	4	8	no	—
745	2₋¹⁺⁴	—	4	4	no	—
746	C₂×#41	—	4	4	no	—
747	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
748	C₂×#41	C₂³×C₈₉	1	2	yes	—
749	C₂×#41	C₂³×C₈₉	1	3	yes	—
750	C₂×#41	C₂³×C₈₉	1	6	yes	—
751	C₂×#41	C₂³×C₈₉	1	3	yes	—
752	C₂×#41	C₂³×C₈₉	1	6	yes	—
753	C₂×#41	C₂³×C₈₉	1	3	yes	—
754	C₂×#41	C₂³×C₈₉	1	3	yes	—
755	C₂×#41	C₂³×C₈₉	1	6	yes	—
756	C₂×#41	C₂³×C₈₉	1	6	yes	—
757	C₂×#41	C₂³×C₈₉	1	6	yes	—
758	C₂²×Q₈	—	4	4	no	—
759	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
760	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
761	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
762	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
763	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
764	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
765	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
766	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
767	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
768	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
769	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
770	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
771	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
772	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
773	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
774	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
775	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
776	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
777	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
778	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
779	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
780	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
781	#127	C₂³×C₈₉	1	1	yes	characteristic
782	#127	C₂³×C₈₉	1	6	yes	—
783	#127	C₂³×C₈₉	1	6	yes	—
784	#127	C₂³×C₈₉	1	6	yes	—
785	#126	C₂³×C₈₉	1	6	yes	—
786	#126	C₂³×C₈₉	1	6	yes	—
787	#126	C₂³×C₈₉	1	2	yes	—
788	#126	C₂³×C₈₉	1	6	yes	—
789	#126	C₂³×C₈₉	1	12	yes	—
790	#126	C₂³×C₈₉	1	6	yes	—
791	#126	C₂³×C₈₉	1	6	yes	—
792	#126	C₂³×C₈₉	1	12	yes	—
793	#126	C₂³×C₈₉	1	12	yes	—
794	#126	C₂³×C₈₉	1	12	yes	—
795	#126	C₂³×C₈₉	1	12	yes	—
796	#125	C₂³×C₈₉	1	6	yes	—
797	#125	C₂³×C₈₉	1	6	yes	—
798	#125	C₂³×C₈₉	1	6	yes	—
799	#125	C₂³×C₈₉	1	6	yes	—
800	#125	C₂³×C₈₉	1	6	yes	—
801	#125	C₂³×C₈₉	1	12	yes	—
802	#125	C₂³×C₈₉	1	12	yes	—
803	#125	C₂³×C₈₉	1	12	yes	—
804	#125	C₂³×C₈₉	1	12	yes	—
805	#124	C₂³×C₈₉	1	6	yes	—
806	#124	C₂³×C₈₉	1	6	yes	—
807	#124	C₂³×C₈₉	1	6	yes	—
808	#124	C₂³×C₈₉	1	6	yes	—
809	#124	C₂³×C₈₉	1	6	yes	—
810	#124	C₂³×C₈₉	1	3	yes	—
811	#124	C₂³×C₈₉	1	3	yes	—
812	#124	C₂³×C₈₉	1	6	yes	—
813	#124	C₂³×C₈₉	1	6	yes	—
814	#124	C₂³×C₈₉	1	6	yes	—
815	#124	C₂³×C₈₉	1	6	yes	—
816	#124	C₂³×C₈₉	1	6	yes	—
817	#124	C₂³×C₈₉	1	6	yes	—
818	#124	C₂³×C₈₉	1	12	yes	—
819	#124	C₂³×C₈₉	1	12	yes	—
820	#123	C₂³×C₈₉	1	1	yes	characteristic
821	#123	C₂³×C₈₉	1	3	yes	—
822	#123	C₂³×C₈₉	1	3	yes	—
823	#123	C₂³×C₈₉	1	3	yes	—
824	#123	C₂³×C₈₉	1	6	yes	—
825	#123	C₂³×C₈₉	1	6	yes	—
826	#123	C₂³×C₈₉	1	6	yes	—
827	#123	C₂³×C₈₉	1	12	yes	—
828	#123	C₂³×C₈₉	1	6	yes	—
829	#123	C₂³×C₈₉	1	6	yes	—
830	#123	C₂³×C₈₉	1	6	yes	—
831	#123	C₂³×C₈₉	1	6	yes	—
832	#123	C₂³×C₈₉	1	2	yes	—
833	#123	C₂³×C₈₉	1	6	yes	—
834	#123	C₂³×C₈₉	1	12	yes	—
835	#123	C₂³×C₈₉	1	6	yes	—
836	#123	C₂³×C₈₉	1	6	yes	—
837	#123	C₂³×C₈₉	1	6	yes	—
838	#123	C₂³×C₈₉	1	6	yes	—
839	#123	C₂³×C₈₉	1	12	yes	—
840	#123	C₂³×C₈₉	1	12	yes	—
841	#123	C₂³×C₈₉	1	12	yes	—
842	#123	C₂³×C₈₉	1	12	yes	—
843	#123	C₂³×C₈₉	1	12	yes	—
844	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
845	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
846	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
847	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
848	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
849	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
850	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
851	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
852	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
853	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
854	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
855	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
856	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
857	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
858	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
859	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
860	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
861	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
862	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
863	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
864	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
865	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
866	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
867	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
868	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
869	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
870	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
871	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
872	#121	C₂³×C₈₉	1	2	yes	—
873	#121	C₂³×C₈₉	1	6	yes	—
874	#121	C₂³×C₈₉	1	6	yes	—
875	#121	C₂³×C₈₉	1	6	yes	—
876	#121	C₂³×C₈₉	1	6	yes	—
877	#121	C₂³×C₈₉	1	6	yes	—
878	#121	C₂³×C₈₉	1	6	yes	—
879	#121	C₂³×C₈₉	1	6	yes	—
880	#121	C₂³×C₈₉	1	6	yes	—
881	#121	C₂³×C₈₉	1	6	yes	—
882	#121	C₂³×C₈₉	1	2	yes	—
883	#121	C₂³×C₈₉	1	6	yes	—
884	#121	C₂³×C₈₉	1	6	yes	—
885	#121	C₂³×C₈₉	1	6	yes	—
886	#121	C₂³×C₈₉	1	6	yes	—
887	#121	C₂³×C₈₉	1	6	yes	—
888	#121	C₂³×C₈₉	1	6	yes	—
889	#121	C₂³×C₈₉	1	6	yes	—
890	#121	C₂³×C₈₉	1	2	yes	—
891	#121	C₂³×C₈₉	1	12	yes	—
892	#121	C₂³×C₈₉	1	6	yes	—
893	#121	C₂³×C₈₉	1	6	yes	—
894	#121	C₂³×C₈₉	1	12	yes	—
895	#121	C₂³×C₈₉	1	12	yes	—
896	#121	C₂³×C₈₉	1	12	yes	—
897	#121	C₂³×C₈₉	1	12	yes	—
898	#121	C₂³×C₈₉	1	12	yes	—
899	#121	C₂³×C₈₉	1	12	yes	—
900	#120	C₂³×C₈₉	1	1	yes	characteristic
901	#120	C₂³×C₈₉	1	3	yes	—
902	#120	C₂³×C₈₉	1	3	yes	—
903	#120	C₂³×C₈₉	1	3	yes	—
904	#120	C₂³×C₈₉	1	6	yes	—
905	#120	C₂³×C₈₉	1	6	yes	—
906	#120	C₂³×C₈₉	1	2	yes	—
907	#120	C₂³×C₈₉	1	6	yes	—
908	#120	C₂³×C₈₉	1	6	yes	—
909	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
910	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
911	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
912	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
913	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
914	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
915	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
916	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
917	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
918	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
919	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
920	C₄×D₄	C₂³×C₈₉	1	6	yes	—
921	C₄×D₄	C₂³×C₈₉	1	6	yes	—
922	C₄×D₄	C₂³×C₈₉	1	6	yes	—
923	C₄×D₄	C₂³×C₈₉	1	6	yes	—
924	C₄×D₄	C₂³×C₈₉	1	6	yes	—
925	C₄×D₄	C₂³×C₈₉	1	6	yes	—
926	C₄×D₄	C₂³×C₈₉	1	6	yes	—
927	C₄×D₄	C₂³×C₈₉	1	6	yes	—
928	C₄×D₄	C₂³×C₈₉	1	6	yes	—
929	C₄×D₄	C₂³×C₈₉	1	6	yes	—
930	C₄×D₄	C₂³×C₈₉	1	6	yes	—
931	C₄×D₄	C₂³×C₈₉	1	6	yes	—
932	C₄×D₄	C₂³×C₈₉	1	12	yes	—
933	C₄×D₄	C₂³×C₈₉	1	12	yes	—
934	C₄×D₄	C₂³×C₈₉	1	12	yes	—
935	C₄×D₄	C₂³×C₈₉	1	12	yes	—
936	C₄×D₄	C₂³×C₈₉	1	12	yes	—
937	C₄×D₄	C₂³×C₈₉	1	12	yes	—
938	C₄×D₄	C₂³×C₈₉	1	12	yes	—
939	C₄×D₄	C₂³×C₈₉	1	12	yes	—
940	#117	C₂³×C₈₉	1	3	yes	—
941	#117	C₂³×C₈₉	1	3	yes	—
942	#117	C₂³×C₈₉	1	3	yes	—
943	#117	C₂³×C₈₉	1	6	yes	—
944	#117	C₂³×C₈₉	1	3	yes	—
945	#117	C₂³×C₈₉	1	3	yes	—
946	#117	C₂³×C₈₉	1	6	yes	—
947	#117	C₂³×C₈₉	1	6	yes	—
948	#117	C₂³×C₈₉	1	12	yes	—
949	#117	C₂³×C₈₉	1	12	yes	—
950	#117	C₂³×C₈₉	1	12	yes	—
951	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
952	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
953	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
954	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
955	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
956	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
957	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
958	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
959	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
960	#41	—	2	8	no	—
961	#41	—	2	4	no	—
962	#41	—	4	6	no	—
963	#41	—	4	12	no	—
964	#41	—	4	6	no	—
965	#41	—	4	12	no	—
966	#41	—	4	6	no	—
967	#41	—	4	12	no	—
968	#41	—	4	6	no	—
969	#41	—	4	12	no	—
970	#41	—	4	12	no	—
971	C₂×Q₈	—	2	4	no	—
972	C₂×Q₈	—	2	8	no	—
973	C₂×Q₈	—	2	4	no	—
974	C₂×Q₈	—	2	8	no	—
975	C₂×Q₈	—	4	6	no	—
976	C₂×Q₈	—	4	12	no	—
977	C₂×Q₈	—	4	12	no	—
978	C₂×Q₈	—	4	6	no	—
979	C₂×Q₈	—	4	6	no	—
980	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
981	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
982	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
983	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
984	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
985	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
986	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
987	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
988	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
989	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
990	C₂×D₄	—	4	6	no	—
991	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
992	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
993	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
994	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
995	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
996	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
997	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
998	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
999	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
1000	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
1001	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1002	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
1003	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
1004	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1005	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1006	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
1007	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1008	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
1009	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1010	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
1011	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
1012	C₂²×C₄	—	4	6	no	—
1013	C₂²×C₄	—	4	6	no	—
1014	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1015	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1016	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1017	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1018	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1019	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1020	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
1021	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1022	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1023	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
1024	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
1025	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1026	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1027	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1028	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
1029	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
1030	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1032	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1033	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1034	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1035	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1036	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1037	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1038	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1039	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1040	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1041	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1042	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1043	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1044	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1045	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1046	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1047	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1048	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1049	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1050	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1051	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1053	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1054	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1055	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1056	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1057	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1058	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1059	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1060	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1061	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1062	C₂²⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1063	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1064	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1065	C₂²⋊C₄	C₂⁴×C₈₉	1	3	yes	—
1066	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1067	C₂²⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
1068	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1069	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1070	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1071	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1072	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1073	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1074	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1075	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1076	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1077	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1078	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1079	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1080	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1081	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1082	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1083	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1084	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1085	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
1086	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
1087	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1088	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
1089	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1090	C₄²	C₂⁴×C₈₉	1	3	yes	—
1091	C₄²	C₂⁴×C₈₉	1	6	yes	—
1092	C₄²	C₂⁴×C₈₉	1	6	yes	—
1093	C₄²	C₂⁴×C₈₉	1	6	yes	—
1094	C₄²	C₂⁴×C₈₉	1	6	yes	—
1095	C₄²	C₂⁴×C₈₉	1	6	yes	—
1096	C₄²	C₂⁴×C₈₉	1	6	yes	—
1097	C₄²	C₂⁴×C₈₉	1	12	yes	—
1098	C₄²	C₂⁴×C₈₉	1	6	yes	—
1099	C₂³	—	4	1	no	—
1100	C₂³	—	4	2	no	—
1101	C₂³	—	4	3	no	—
1102	C₂³	—	4	6	no	—
1103	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1104	C₂³	C₂⁵×C₈₉	1	2	yes	—
1105	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1106	C₂³	C₂⁵×C₈₉	1	6	yes	—
1107	C₂³	C₂⁵×C₈₉	1	2	yes	—
1108	C₂³	C₂⁵×C₈₉	1	3	yes	—
1109	Q₈	—	2	6	no	—
1110	Q₈	—	2	12	no	—
1111	Q₈	—	2	12	no	—
1112	Q₈	—	2	6	no	—
1113	Q₈	—	4	6	no	—
1114	Q₈	—	4	6	no	—
1115	Q₈	—	4	3	no	—
1116	Q₈	—	4	3	no	—
1117	Q₈	—	4	6	no	—
1118	Q₈	H(5,𝔽₂)×C₈₉	1	4	yes	—
1119	D₄	—	2	12	no	—
1120	D₄	—	2	6	no	—
1121	D₄	—	4	6	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	6	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	6	no	—
1126	D₄	—	4	6	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	6	no	—
1129	D₄	—	4	6	no	—
1130	D₄	—	4	12	no	—
1131	D₄	—	4	2	no	—
1132	D₄	—	4	2	no	—
1133	D₄	—	4	1	no	—
1134	D₄	—	4	1	no	—
1135	D₄	—	4	3	no	—
1136	D₄	—	4	6	no	—
1137	D₄	—	4	6	no	—
1138	D₄	—	4	3	no	—
1139	D₄	—	4	6	no	—
1140	C₂×C₄	—	2	6	no	—
1141	C₂×C₄	—	2	6	no	—
1142	C₂×C₄	—	2	12	no	—
1143	C₂×C₄	—	2	12	no	—
1144	C₂×C₄	—	2	12	no	—
1145	C₂×C₄	—	2	6	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	6	no	—
1148	C₂×C₄	—	4	3	no	—
1149	C₂×C₄	—	4	6	no	—
1150	C₂×C₄	—	4	12	no	—
1151	C₂×C₄	—	4	6	no	—
1152	C₂×C₄	—	4	6	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	6	no	—
1155	C₂×C₄	—	4	6	no	—
1156	C₂×C₄	—	4	12	no	—
1157	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1158	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1159	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1160	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1161	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1162	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1163	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1164	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1165	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1166	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
1167	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1168	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1169	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	1	no	—
1172	C₂²	—	2	1	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	3	no	—
1175	C₂²	—	2	6	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	6	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	6	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	6	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	4	4	no	—
1186	C₂²	—	8	6	no	—
1187	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1188	C₄	—	2	2	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	3	no	—
1191	C₄	—	2	6	no	—
1192	C₄	—	2	3	no	—
1193	C₄	—	2	6	no	—
1194	C₄	—	2	6	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	6	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	6	no	—
1199	C₄	—	2	2	no	—
1200	C₄	C₂×H(5,𝔽₂)×C₈₉	1	6	yes	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	3	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	4	1	no	—
1205	C₂	—	4	6	no	—
1206	C₂	—	4	1	no	—
1207	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1208	C₂	C₈₉×2₋¹⁺⁶	1	2	yes	—

	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×#3562	C₂	semidirect
2. C₈₉×#3554	C₂	semidirect
3. C₈₉×#3552	C₂	semidirect
4. C₈₉×#3551	C₂	semidirect
5. C₈₉×#3547	C₂	semidirect
6. C₈₉×#3541	C₂	semidirect
7. C₈₉×#3540	C₂	semidirect
8. C₈₉×#3539	C₂	semidirect
9. C₈₉×#3538	C₂	semidirect
10. C₈₉×#3529	C₂	semidirect
11. C₈₉×#3524	C₂	semidirect
12. C₈₉×#3523	C₂	semidirect
13. C₈₉×#3516	C₂	semidirect
14. C₈₉×#3499	C₂	semidirect
15. C₈₉×#3497	C₂	semidirect
16. C₈₉×#3489	C₂	semidirect
17. C₈₉×#3487	C₂	semidirect
18. C₈₉×#3486	C₂	semidirect
19. C₈₉×#3486	C₂	semidirect
22. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
23. C₂²×#41×C₈₉	C₂²	semidirect
24. C₂³×Q₈×C₈₉	C₂²	semidirect
26. #563×C₈₉	C₂²	semidirect
27. #563×C₈₉	C₂²	semidirect
28. #563×C₈₉	C₂²	semidirect
30. #562×C₈₉	C₂²	semidirect
31. #562×C₈₉	C₂²	semidirect
32. #562×C₈₉	C₂²	semidirect
37. #560×C₈₉	C₂²	semidirect
38. #560×C₈₉	C₂²	semidirect
39. #559×C₈₉	C₂²	semidirect
40. #559×C₈₉	C₂²	semidirect
41. #557×C₈₉	C₂²	semidirect
42. #557×C₈₉	C₂²	semidirect
44. #556×C₈₉	C₂²	semidirect
45. #555×C₈₉	C₂²	semidirect
46. #555×C₈₉	C₂²	semidirect
47. #554×C₈₉	C₂²	semidirect
48. #554×C₈₉	C₂²	semidirect
49. #553×C₈₉	C₂²	semidirect
50. #553×C₈₉	C₂²	semidirect
51. #553×C₈₉	C₂²	semidirect
52. #553×C₈₉	C₂²	semidirect
53. #552×C₈₉	C₂²	semidirect
54. #552×C₈₉	C₂²	semidirect
55. #552×C₈₉	C₂²	semidirect
56. #552×C₈₉	C₂²	semidirect
58. #551×C₈₉	C₂²	semidirect
60. #550×C₈₉	C₂²	semidirect
61. #550×C₈₉	C₂²	semidirect
63. D₄×Q₈×C₈₉	C₂²	semidirect
64. D₄×Q₈×C₈₉	C₂²	semidirect
65. D₄×Q₈×C₈₉	C₂²	semidirect
66. D₄×Q₈×C₈₉	C₂²	semidirect
67. D₄×Q₈×C₈₉	C₂²	semidirect
68. D₄×Q₈×C₈₉	C₂²	semidirect
69. D₄×Q₈×C₈₉	C₂²	semidirect
73. #548×C₈₉	C₂²	semidirect
74. #548×C₈₉	C₂²	semidirect
75. #548×C₈₉	C₂²	semidirect
76. #548×C₈₉	C₂²	semidirect
77. #548×C₈₉	C₂²	semidirect
78. #548×C₈₉	C₂²	semidirect
79. #548×C₈₉	C₂²	semidirect
81. #547×C₈₉	C₂²	semidirect
82. #547×C₈₉	C₂²	semidirect
83. #547×C₈₉	C₂²	semidirect
85. #546×C₈₉	C₂²	semidirect
86. #544×C₈₉	C₂²	semidirect
87. #542×C₈₉	C₂²	semidirect
88. #542×C₈₉	C₂²	semidirect
89. #542×C₈₉	C₂²	semidirect
90. #542×C₈₉	C₂²	semidirect
91. #541×C₈₉	C₂²	semidirect
92. #541×C₈₉	C₂²	semidirect
93. #541×C₈₉	C₂²	semidirect
94. #540×C₈₉	C₂²	semidirect
95. #540×C₈₉	C₂²	semidirect
96. #540×C₈₉	C₂²	semidirect
97. #539×C₈₉	C₂²	semidirect
98. #539×C₈₉	C₂²	semidirect
99. #539×C₈₉	C₂²	semidirect
101. #538×C₈₉	C₂²	semidirect
103. #537×C₈₉	C₂²	semidirect
104. #537×C₈₉	C₂²	semidirect
107. #536×C₈₉	C₂²	semidirect
108. #536×C₈₉	C₂²	semidirect
109. #536×C₈₉	C₂²	semidirect
110. #536×C₈₉	C₂²	semidirect
111. #536×C₈₉	C₂²	semidirect
113. #535×C₈₉	C₂²	semidirect
114. #533×C₈₉	C₂²	semidirect
116. #532×C₈₉	C₂²	semidirect
117. #532×C₈₉	C₂²	semidirect
118. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
120. #529×C₈₉	C₂²	semidirect
121. #529×C₈₉	C₂²	semidirect
122. #529×C₈₉	C₂²	semidirect
123. #529×C₈₉	C₂²	semidirect
127. #525×C₈₉	C₂²	semidirect
128. #525×C₈₉	C₂²	semidirect
129. #525×C₈₉	C₂²	semidirect
130. #525×C₈₉	C₂²	semidirect
131. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
132. #520×C₈₉	C₂²	semidirect
133. #519×C₈₉	C₂²	semidirect
134. #519×C₈₉	C₂²	semidirect
135. #519×C₈₉	C₂²	semidirect
136. C₄×#41×C₈₉	C₂²	semidirect
137. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
596. #63044	C₈₉	direct (N × H)
605. #3562	C₂×C₈₉	semidirect
606. #3554	C₂×C₈₉	semidirect
607. #3552	C₂×C₈₉	semidirect
608. #3551	C₂×C₈₉	semidirect
609. #3547	C₂×C₈₉	semidirect
610. #3541	C₂×C₈₉	semidirect
611. #3540	C₂×C₈₉	semidirect
612. #3539	C₂×C₈₉	semidirect
613. #3538	C₂×C₈₉	semidirect
614. #3529	C₂×C₈₉	semidirect
615. #3524	C₂×C₈₉	semidirect
616. #3523	C₂×C₈₉	semidirect
617. #3516	C₂×C₈₉	semidirect
618. #3499	C₂×C₈₉	semidirect
619. #3497	C₂×C₈₉	semidirect
620. #3489	C₂×C₈₉	semidirect
621. #3487	C₂×C₈₉	semidirect
622. #3486	C₂×C₈₉	semidirect
623. #3486	C₂×C₈₉	semidirect
624. C₈₉	#63044	direct (N × H)
627. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
628. C₂²×#41	C₂²×C₈₉	semidirect
629. C₂³×Q₈	C₂²×C₈₉	semidirect
631. #563	C₂²×C₈₉	semidirect
632. #563	C₂²×C₈₉	semidirect
633. #563	C₂²×C₈₉	semidirect
635. #562	C₂²×C₈₉	semidirect
636. #562	C₂²×C₈₉	semidirect
637. #562	C₂²×C₈₉	semidirect
642. #560	C₂²×C₈₉	semidirect
643. #560	C₂²×C₈₉	semidirect
644. #559	C₂²×C₈₉	semidirect
645. #559	C₂²×C₈₉	semidirect
646. #557	C₂²×C₈₉	semidirect
647. #557	C₂²×C₈₉	semidirect
649. #556	C₂²×C₈₉	semidirect
650. #555	C₂²×C₈₉	semidirect
651. #555	C₂²×C₈₉	semidirect
652. #554	C₂²×C₈₉	semidirect
653. #554	C₂²×C₈₉	semidirect
654. #553	C₂²×C₈₉	semidirect
655. #553	C₂²×C₈₉	semidirect
656. #553	C₂²×C₈₉	semidirect
657. #553	C₂²×C₈₉	semidirect
658. #552	C₂²×C₈₉	semidirect
659. #552	C₂²×C₈₉	semidirect
660. #552	C₂²×C₈₉	semidirect
661. #552	C₂²×C₈₉	semidirect
663. #551	C₂²×C₈₉	semidirect
665. #550	C₂²×C₈₉	semidirect
666. #550	C₂²×C₈₉	semidirect
668. D₄×Q₈	C₂²×C₈₉	semidirect
669. D₄×Q₈	C₂²×C₈₉	semidirect
670. D₄×Q₈	C₂²×C₈₉	semidirect
671. D₄×Q₈	C₂²×C₈₉	semidirect
672. D₄×Q₈	C₂²×C₈₉	semidirect
673. D₄×Q₈	C₂²×C₈₉	semidirect
674. D₄×Q₈	C₂²×C₈₉	semidirect
678. #548	C₂²×C₈₉	semidirect
679. #548	C₂²×C₈₉	semidirect
680. #548	C₂²×C₈₉	semidirect
681. #548	C₂²×C₈₉	semidirect
682. #548	C₂²×C₈₉	semidirect
683. #548	C₂²×C₈₉	semidirect
684. #548	C₂²×C₈₉	semidirect
686. #547	C₂²×C₈₉	semidirect
687. #547	C₂²×C₈₉	semidirect
688. #547	C₂²×C₈₉	semidirect
690. #546	C₂²×C₈₉	semidirect
691. #544	C₂²×C₈₉	semidirect
692. #542	C₂²×C₈₉	semidirect
693. #542	C₂²×C₈₉	semidirect
694. #542	C₂²×C₈₉	semidirect
695. #542	C₂²×C₈₉	semidirect
696. #541	C₂²×C₈₉	semidirect
697. #541	C₂²×C₈₉	semidirect
698. #541	C₂²×C₈₉	semidirect
699. #540	C₂²×C₈₉	semidirect
700. #540	C₂²×C₈₉	semidirect
701. #540	C₂²×C₈₉	semidirect
702. #539	C₂²×C₈₉	semidirect
703. #539	C₂²×C₈₉	semidirect
704. #539	C₂²×C₈₉	semidirect
706. #538	C₂²×C₈₉	semidirect
708. #537	C₂²×C₈₉	semidirect
709. #537	C₂²×C₈₉	semidirect
712. #536	C₂²×C₈₉	semidirect
713. #536	C₂²×C₈₉	semidirect
714. #536	C₂²×C₈₉	semidirect
715. #536	C₂²×C₈₉	semidirect
716. #536	C₂²×C₈₉	semidirect
718. #535	C₂²×C₈₉	semidirect
719. #533	C₂²×C₈₉	semidirect
721. #532	C₂²×C₈₉	semidirect
722. #532	C₂²×C₈₉	semidirect
723. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
725. #529	C₂²×C₈₉	semidirect
726. #529	C₂²×C₈₉	semidirect
727. #529	C₂²×C₈₉	semidirect
728. #529	C₂²×C₈₉	semidirect
732. #525	C₂²×C₈₉	semidirect
733. #525	C₂²×C₈₉	semidirect
734. #525	C₂²×C₈₉	semidirect
735. #525	C₂²×C₈₉	semidirect
736. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
737. #520	C₂²×C₈₉	semidirect
738. #519	C₂²×C₈₉	semidirect
739. #519	C₂²×C₈₉	semidirect
740. #519	C₂²×C₈₉	semidirect
741. C₄×#41	C₂²×C₈₉	semidirect
742. C₂×C₄×Q₈	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×#3562	2
C₈₉×#3554	2
C₈₉×#3552	2
C₈₉×#3551	2
C₈₉×#3547	2
C₈₉×#3541	2
C₈₉×#3540	2
C₈₉×#3539	2
C₈₉×#3538	2
C₈₉×#3529	2
C₈₉×#3524	2
C₈₉×#3523	2
C₈₉×#3516	2
C₈₉×#3499	2
C₈₉×#3497	2
C₈₉×#3489	2
C₈₉×#3487	2
C₈₉×#3486	2
#63044	89

Subgroups — C89×#63044 #36440892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63044 #36440892