Subgroups — C₈₉×#63024 #36440872

Order 22784.

7264 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3551	C₂	1	4	yes	maximal, complemented
2	C₈₉×#3549	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3547	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3545	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3544	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3542	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3519	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3514	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3511	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3500	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3496	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3494	C₂	1	8	yes	maximal, complemented
14	C₈₉×#3483	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3481	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3475	C₂	1	4	yes	maximal, complemented
17	C₂×#555×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	4	yes	complemented
20	#563×C₈₉	C₂²	1	8	yes	complemented
21	#562×C₈₉	C₂²	1	16	yes	complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	4	yes	complemented
23	#560×C₈₉	C₂²	1	8	yes	complemented
24	#559×C₈₉	C₂²	1	2	yes	complemented
25	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#556×C₈₉	C₂²	1	4	yes	complemented
27	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	#555×C₈₉	C₂²	1	8	yes	complemented
29	#555×C₈₉	C₂²	1	4	yes	complemented
30	#555×C₈₉	C₂²	1	8	yes	complemented
31	#555×C₈₉	C₂²	1	2	yes	complemented
32	#555×C₈₉	C₂²	1	8	yes	complemented
33	#555×C₈₉	C₂²	1	4	yes	complemented
34	#555×C₈₉	C₂²	1	4	yes	complemented
35	#555×C₈₉	C₂²	1	4	yes	complemented
36	#554×C₈₉	C₂²	1	2	yes	complemented
37	#554×C₈₉	C₂²	1	2	yes	complemented
38	#554×C₈₉	C₂²	1	4	yes	complemented
39	#553×C₈₉	C₂²	1	8	yes	complemented
40	#553×C₈₉	C₂²	1	4	yes	complemented
41	#553×C₈₉	C₂²	1	4	yes	complemented
42	#553×C₈₉	C₂²	1	8	yes	complemented
43	#553×C₈₉	C₂²	1	8	yes	complemented
44	#552×C₈₉	C₂²	1	8	yes	complemented
45	#552×C₈₉	C₂²	1	8	yes	complemented
46	#551×C₈₉	C₂²	1	16	yes	complemented
47	#551×C₈₉	C₂²	1	8	yes	complemented
48	#551×C₈₉	C₂²	1	8	yes	complemented
49	#551×C₈₉	C₂²	1	16	yes	complemented
50	#550×C₈₉	C₂²	1	2	yes	complemented
51	#550×C₈₉	C₂²	1	4	yes	complemented
52	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
53	#548×C₈₉	C₂²	1	8	yes	complemented
54	#548×C₈₉	C₂²	1	8	yes	complemented
55	#547×C₈₉	C₂²	1	4	yes	complemented
56	#547×C₈₉	C₂²	1	8	yes	complemented
57	#547×C₈₉	C₂²	1	8	yes	complemented
58	#547×C₈₉	C₂²	1	4	yes	complemented
59	#546×C₈₉	C₂²	1	8	yes	complemented
60	#546×C₈₉	C₂²	1	4	yes	complemented
61	#546×C₈₉	C₂²	1	4	yes	complemented
62	#546×C₈₉	C₂²	1	16	yes	complemented
63	#546×C₈₉	C₂²	1	16	yes	complemented
64	#546×C₈₉	C₂²	1	8	yes	complemented
65	#546×C₈₉	C₂²	1	16	yes	complemented
66	#546×C₈₉	C₂²	1	8	yes	complemented
67	D₄²×C₈₉	C₂²	1	2	yes	—
68	D₄²×C₈₉	C₂²	1	4	yes	complemented
69	D₄²×C₈₉	C₂²	1	8	yes	complemented
70	D₄²×C₈₉	C₂²	1	2	yes	complemented
71	#544×C₈₉	C₂²	1	8	yes	complemented
72	#542×C₈₉	C₂²	1	16	yes	complemented
73	#542×C₈₉	C₂²	1	8	yes	complemented
74	#542×C₈₉	C₂²	1	8	yes	complemented
75	#540×C₈₉	C₂²	1	16	yes	complemented
76	#540×C₈₉	C₂²	1	8	yes	complemented
77	#538×C₈₉	C₂²	1	16	yes	complemented
78	#538×C₈₉	C₂²	1	16	yes	complemented
79	#537×C₈₉	C₂²	1	8	yes	complemented
80	#537×C₈₉	C₂²	1	4	yes	complemented
81	#536×C₈₉	C₂²	1	4	yes	complemented
82	#536×C₈₉	C₂²	1	2	yes	complemented
83	#536×C₈₉	C₂²	1	8	yes	complemented
84	#536×C₈₉	C₂²	1	4	yes	complemented
85	#535×C₈₉	C₂²	1	8	yes	complemented
86	#535×C₈₉	C₂²	1	8	yes	complemented
87	#535×C₈₉	C₂²	1	4	yes	complemented
88	#534×C₈₉	C₂²	1	16	yes	complemented
89	#533×C₈₉	C₂²	1	4	yes	complemented
90	#532×C₈₉	C₂²	1	2	yes	complemented
91	#532×C₈₉	C₂²	1	4	yes	complemented
92	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#532×C₈₉	C₂²	1	4	yes	complemented
94	#532×C₈₉	C₂²	1	8	yes	complemented
95	#532×C₈₉	C₂²	1	4	yes	complemented
96	#532×C₈₉	C₂²	1	2	yes	complemented
97	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
98	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#529×C₈₉	C₂²	1	16	yes	complemented
100	#529×C₈₉	C₂²	1	8	yes	complemented
101	#529×C₈₉	C₂²	1	4	yes	complemented
102	#529×C₈₉	C₂²	1	4	yes	complemented
103	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
104	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
105	#525×C₈₉	C₂²	1	8	yes	complemented
106	#525×C₈₉	C₂²	1	8	yes	complemented
107	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
108	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
109	#520×C₈₉	C₂²	1	4	yes	complemented
110	#518×C₈₉	C₂²	1	8	yes	complemented
111	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
112	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
113	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
116	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
117	C₂×#117×C₈₉	C₂²	1	8	yes	complemented
118	2₋¹⁺⁴×C₈₉	—	4	8	no	—
119	H(5,𝔽₂)×C₈₉	—	4	16	no	—
120	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×#41×C₈₉	C₂³	1	4	yes	—
122	C₂×#41×C₈₉	C₂³	1	4	yes	—
123	C₂×#41×C₈₉	C₂³	1	2	yes	—
124	C₂×#41×C₈₉	C₂³	1	4	yes	—
125	C₂×#41×C₈₉	C₂³	1	2	yes	—
126	C₂×#41×C₈₉	C₂³	1	4	yes	—
127	C₂×#41×C₈₉	C₂³	1	8	yes	—
128	C₂×#41×C₈₉	C₂³	1	4	yes	—
129	C₂×#41×C₈₉	C₂³	1	8	yes	—
130	C₂×#41×C₈₉	C₂³	1	8	yes	—
131	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
132	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
133	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
135	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
136	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
137	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
138	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
139	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
140	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
145	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
147	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
148	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
149	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
150	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
151	#127×C₈₉	C₂³	1	2	yes	—
152	#127×C₈₉	C₂³	1	1	yes	characteristic
153	#127×C₈₉	C₂³	1	8	yes	—
154	#127×C₈₉	C₂³	1	4	yes	—
155	#127×C₈₉	C₂³	1	4	yes	—
156	#126×C₈₉	C₂³	1	8	yes	—
157	#126×C₈₉	C₂³	1	16	yes	—
158	#126×C₈₉	C₂³	1	16	yes	—
159	#126×C₈₉	C₂³	1	16	yes	—
160	#126×C₈₉	C₂³	1	8	yes	—
161	#125×C₈₉	C₂³	1	4	yes	—
162	#125×C₈₉	C₂³	1	16	yes	—
163	#125×C₈₉	C₂³	1	4	yes	—
164	#125×C₈₉	C₂³	1	8	yes	—
165	#124×C₈₉	C₂³	1	4	yes	—
166	#124×C₈₉	C₂³	1	8	yes	—
167	#124×C₈₉	C₂³	1	4	yes	—
168	#124×C₈₉	C₂³	1	8	yes	—
169	#124×C₈₉	C₂³	1	8	yes	—
170	#124×C₈₉	C₂³	1	8	yes	—
171	#124×C₈₉	C₂³	1	8	yes	—
172	#124×C₈₉	C₂³	1	16	yes	—
173	#124×C₈₉	C₂³	1	16	yes	—
174	#124×C₈₉	C₂³	1	16	yes	—
175	#124×C₈₉	C₂³	1	4	yes	—
176	#124×C₈₉	C₂³	1	4	yes	—
177	#124×C₈₉	C₂³	1	4	yes	—
178	#124×C₈₉	C₂³	1	2	yes	—
179	#124×C₈₉	C₂³	1	8	yes	—
180	#124×C₈₉	C₂³	1	4	yes	—
181	#123×C₈₉	C₂³	1	8	yes	—
182	#123×C₈₉	C₂³	1	16	yes	—
183	#123×C₈₉	C₂³	1	8	yes	—
184	#123×C₈₉	C₂³	1	16	yes	—
185	#123×C₈₉	C₂³	1	16	yes	—
186	#123×C₈₉	C₂³	1	8	yes	—
187	#123×C₈₉	C₂³	1	8	yes	—
188	#123×C₈₉	C₂³	1	16	yes	—
189	#123×C₈₉	C₂³	1	16	yes	—
190	#123×C₈₉	C₂³	1	16	yes	—
191	#123×C₈₉	C₂³	1	8	yes	—
192	#123×C₈₉	C₂³	1	16	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
205	#121×C₈₉	C₂³	1	4	yes	—
206	#121×C₈₉	C₂³	1	8	yes	—
207	#121×C₈₉	C₂³	1	4	yes	—
208	#121×C₈₉	C₂³	1	4	yes	—
209	#121×C₈₉	C₂³	1	8	yes	—
210	#121×C₈₉	C₂³	1	16	yes	—
211	#121×C₈₉	C₂³	1	16	yes	—
212	#121×C₈₉	C₂³	1	16	yes	—
213	#121×C₈₉	C₂³	1	8	yes	—
214	#121×C₈₉	C₂³	1	8	yes	—
215	#121×C₈₉	C₂³	1	16	yes	—
216	#121×C₈₉	C₂³	1	8	yes	—
217	#121×C₈₉	C₂³	1	8	yes	—
218	#121×C₈₉	C₂³	1	8	yes	—
219	#121×C₈₉	C₂³	1	8	yes	—
220	#121×C₈₉	C₂³	1	4	yes	—
221	#121×C₈₉	C₂³	1	8	yes	—
222	#121×C₈₉	C₂³	1	8	yes	—
223	#121×C₈₉	C₂³	1	4	yes	—
224	#121×C₈₉	C₂³	1	4	yes	—
225	#121×C₈₉	C₂³	1	4	yes	—
226	#121×C₈₉	C₂³	1	8	yes	—
227	#121×C₈₉	C₂³	1	8	yes	—
228	#121×C₈₉	C₂³	1	16	yes	—
229	#121×C₈₉	C₂³	1	16	yes	—
230	#121×C₈₉	C₂³	1	16	yes	—
231	#120×C₈₉	C₂³	1	8	yes	—
232	#120×C₈₉	C₂³	1	16	yes	—
233	#120×C₈₉	C₂³	1	8	yes	—
234	#120×C₈₉	C₂³	1	16	yes	—
235	#120×C₈₉	C₂³	1	16	yes	—
236	#120×C₈₉	C₂³	1	8	yes	—
237	#120×C₈₉	C₂³	1	8	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
241	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
242	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
243	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	4	yes	—
247	C₄×D₄×C₈₉	C₂³	1	4	yes	—
248	C₄×D₄×C₈₉	C₂³	1	8	yes	—
249	C₄×D₄×C₈₉	C₂³	1	8	yes	—
250	C₄×D₄×C₈₉	C₂³	1	8	yes	—
251	C₄×D₄×C₈₉	C₂³	1	4	yes	—
252	C₄×D₄×C₈₉	C₂³	1	4	yes	—
253	C₄×D₄×C₈₉	C₂³	1	4	yes	—
254	C₄×D₄×C₈₉	C₂³	1	8	yes	—
255	C₄×D₄×C₈₉	C₂³	1	4	yes	—
256	C₄×D₄×C₈₉	C₂³	1	4	yes	—
257	C₄×D₄×C₈₉	C₂³	1	4	yes	—
258	C₄×D₄×C₈₉	C₂³	1	4	yes	—
259	C₄×D₄×C₈₉	C₂³	1	16	yes	—
260	C₄×D₄×C₈₉	C₂³	1	2	yes	—
261	C₄×D₄×C₈₉	C₂³	1	4	yes	—
262	C₄×D₄×C₈₉	C₂³	1	8	yes	—
263	C₄×D₄×C₈₉	C₂³	1	4	yes	—
264	C₄×D₄×C₈₉	C₂³	1	8	yes	—
265	C₄×D₄×C₈₉	C₂³	1	16	yes	—
266	C₄×D₄×C₈₉	C₂³	1	8	yes	—
267	C₄×D₄×C₈₉	C₂³	1	8	yes	—
268	C₄×D₄×C₈₉	C₂³	1	16	yes	—
269	C₄×D₄×C₈₉	C₂³	1	16	yes	—
270	C₄×D₄×C₈₉	C₂³	1	8	yes	—
271	#117×C₈₉	C₂³	1	4	yes	—
272	#117×C₈₉	C₂³	1	8	yes	—
273	#117×C₈₉	C₂³	1	8	yes	—
274	#117×C₈₉	C₂³	1	16	yes	—
275	#117×C₈₉	C₂³	1	8	yes	—
276	#117×C₈₉	C₂³	1	16	yes	—
277	#117×C₈₉	C₂³	1	2	yes	—
278	#117×C₈₉	C₂³	1	8	yes	—
279	#117×C₈₉	C₂³	1	8	yes	—
280	#117×C₈₉	C₂³	1	4	yes	—
281	#117×C₈₉	C₂³	1	2	yes	—
282	#117×C₈₉	C₂³	1	1	yes	characteristic
283	#117×C₈₉	C₂³	1	4	yes	—
284	#117×C₈₉	C₂³	1	8	yes	—
285	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
286	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
287	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
289	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
290	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
291	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
292	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
294	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
295	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
296	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
297	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
298	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
299	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
300	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
301	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
302	#41×C₈₉	—	2	16	no	—
303	#41×C₈₉	—	2	4	no	—
304	#41×C₈₉	—	4	8	no	—
305	#41×C₈₉	—	4	8	no	—
306	#41×C₈₉	—	4	4	no	—
307	#41×C₈₉	—	4	16	no	—
308	#41×C₈₉	—	4	16	no	—
309	#41×C₈₉	—	4	8	no	—
310	#41×C₈₉	—	4	8	no	—
311	#41×C₈₉	—	4	4	no	—
312	#41×C₈₉	—	4	16	no	—
313	C₂×Q₈×C₈₉	—	4	8	no	—
314	C₂×Q₈×C₈₉	—	4	8	no	—
315	C₂×Q₈×C₈₉	—	4	4	no	—
316	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
317	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
319	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
320	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
321	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
322	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
323	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
324	C₂×D₄×C₈₉	—	2	16	no	—
325	C₂×D₄×C₈₉	—	4	8	no	—
326	C₂×D₄×C₈₉	—	4	16	no	—
327	C₂×D₄×C₈₉	—	4	8	no	—
328	C₂×D₄×C₈₉	—	4	16	no	—
329	C₂×D₄×C₈₉	—	4	32	no	—
330	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
331	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
332	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
333	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
334	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
335	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
336	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
337	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
338	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
339	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
340	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
341	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
342	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
343	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
344	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
345	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
346	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
347	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
348	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
349	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₈₉	—	4	16	no	—
351	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
360	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
361	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
363	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
365	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
366	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
367	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
374	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
376	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
377	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
379	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
384	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
385	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
388	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
389	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
391	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
393	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
397	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
398	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
403	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
404	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
405	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
406	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₈₉	C₂⁴	1	2	yes	—
409	C₄²×C₈₉	C₂⁴	1	4	yes	—
410	C₄²×C₈₉	C₂⁴	1	2	yes	—
411	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄²×C₈₉	C₂⁴	1	4	yes	—
413	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄²×C₈₉	C₂⁴	1	8	yes	—
415	C₄²×C₈₉	C₂⁴	1	4	yes	—
416	C₄²×C₈₉	C₂⁴	1	16	yes	—
417	C₄²×C₈₉	C₂⁴	1	4	yes	—
418	C₄²×C₈₉	C₂⁴	1	4	yes	—
419	C₄²×C₈₉	C₂⁴	1	2	yes	—
420	C₄²×C₈₉	C₂⁴	1	4	yes	—
421	C₂³×C₈₉	—	2	16	no	—
422	C₂³×C₈₉	—	4	8	no	—
423	C₂³×C₈₉	—	4	8	no	—
424	C₂³×C₈₉	—	4	8	no	—
425	C₂³×C₈₉	—	4	16	no	—
426	C₂³×C₈₉	C₂⁵	1	8	yes	—
427	C₂³×C₈₉	C₂⁵	1	4	yes	—
428	C₂³×C₈₉	C₂⁵	1	4	yes	—
429	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
430	C₂³×C₈₉	C₂⁵	1	2	yes	—
431	Q₈×C₈₉	—	2	2	no	—
432	Q₈×C₈₉	—	2	8	no	—
433	Q₈×C₈₉	—	2	4	no	—
434	Q₈×C₈₉	—	4	2	no	—
435	Q₈×C₈₉	—	4	8	no	—
436	Q₈×C₈₉	—	4	4	no	—
437	Q₈×C₈₉	—	4	4	no	—
438	Q₈×C₈₉	—	4	4	no	—
439	D₄×C₈₉	—	2	16	no	—
440	D₄×C₈₉	—	2	16	no	—
441	D₄×C₈₉	—	2	4	no	—
442	D₄×C₈₉	—	2	8	no	—
443	D₄×C₈₉	—	2	8	no	—
444	D₄×C₈₉	—	2	4	no	—
445	D₄×C₈₉	—	2	8	no	—
446	D₄×C₈₉	—	4	4	no	—
447	D₄×C₈₉	—	4	8	no	—
448	D₄×C₈₉	—	4	8	no	—
449	D₄×C₈₉	—	4	16	no	—
450	D₄×C₈₉	—	4	8	no	—
451	D₄×C₈₉	—	4	16	no	—
452	D₄×C₈₉	—	4	8	no	—
453	D₄×C₈₉	—	4	4	no	—
454	D₄×C₈₉	—	4	8	no	—
455	D₄×C₈₉	—	4	4	no	—
456	D₄×C₈₉	—	4	4	no	—
457	D₄×C₈₉	—	4	2	no	—
458	D₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
459	C₂×C₄×C₈₉	—	2	16	no	—
460	C₂×C₄×C₈₉	—	2	4	no	—
461	C₂×C₄×C₈₉	—	2	8	no	—
462	C₂×C₄×C₈₉	—	2	8	no	—
463	C₂×C₄×C₈₉	—	2	2	no	—
464	C₂×C₄×C₈₉	—	2	8	no	—
465	C₂×C₄×C₈₉	—	2	8	no	—
466	C₂×C₄×C₈₉	—	2	16	no	—
467	C₂×C₄×C₈₉	—	2	4	no	—
468	C₂×C₄×C₈₉	—	4	8	no	—
469	C₂×C₄×C₈₉	—	4	8	no	—
470	C₂×C₄×C₈₉	—	4	8	no	—
471	C₂×C₄×C₈₉	—	4	16	no	—
472	C₂×C₄×C₈₉	—	4	4	no	—
473	C₂×C₄×C₈₉	—	4	8	no	—
474	C₂×C₄×C₈₉	—	4	8	no	—
475	C₂×C₄×C₈₉	—	4	4	no	—
476	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
477	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
478	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
479	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
480	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
481	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
482	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
483	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
484	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
485	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
486	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
487	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
488	C₂²×C₈₉	—	2	4	no	—
489	C₂²×C₈₉	—	2	1	no	—
490	C₂²×C₈₉	—	2	4	no	—
491	C₂²×C₈₉	—	2	4	no	—
492	C₂²×C₈₉	—	2	8	no	—
493	C₂²×C₈₉	—	2	4	no	—
494	C₂²×C₈₉	—	2	8	no	—
495	C₂²×C₈₉	—	2	2	no	—
496	C₂²×C₈₉	—	2	4	no	—
497	C₂²×C₈₉	—	2	8	no	—
498	C₂²×C₈₉	—	2	8	no	—
499	C₂²×C₈₉	—	8	16	no	—
500	C₂²×C₈₉	—	16	8	no	—
501	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
502	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
503	C₄×C₈₉	—	2	4	no	—
504	C₄×C₈₉	—	2	1	no	—
505	C₄×C₈₉	—	2	4	no	—
506	C₄×C₈₉	—	2	8	no	—
507	C₄×C₈₉	—	2	2	no	—
508	C₄×C₈₉	—	2	4	no	—
509	C₄×C₈₉	—	2	4	no	—
510	C₄×C₈₉	—	2	8	no	—
511	C₄×C₈₉	—	2	2	no	—
512	C₄×C₈₉	—	2	4	no	—
513	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
514	C₄×C₈₉	#585	1	4	yes	—
515	#63024	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₈₉	—	2	4	no	—
517	C₂×C₈₉	—	4	1	no	—
518	C₂×C₈₉	—	4	4	no	—
519	C₂×C₈₉	—	4	8	no	—
520	C₂×C₈₉	—	4	4	no	—
521	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂×C₈₉	C₂×#585	1	2	yes	—
523	#3551	C₂×C₈₉	1	4	yes	complemented
524	#3549	C₂×C₈₉	1	1	yes	characteristic, complemented
525	#3547	C₂×C₈₉	1	4	yes	complemented
526	#3545	C₂×C₈₉	1	8	yes	complemented
527	#3544	C₂×C₈₉	1	2	yes	complemented
528	#3542	C₂×C₈₉	1	8	yes	complemented
529	#3519	C₂×C₈₉	1	4	yes	complemented
530	#3514	C₂×C₈₉	1	4	yes	complemented
531	#3511	C₂×C₈₉	1	2	yes	complemented
532	#3500	C₂×C₈₉	1	4	yes	complemented
533	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
534	#3496	C₂×C₈₉	1	4	yes	complemented
535	#3494	C₂×C₈₉	1	8	yes	complemented
536	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
537	#3481	C₂×C₈₉	1	2	yes	complemented
538	#3475	C₂×C₈₉	1	4	yes	complemented
539	C₂×#555	C₂×C₈₉	1	2	yes	complemented
540	C₈₉	#63024	1	1	yes	characteristic, direct product factor, Sylow
541	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
542	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	4	yes	complemented
543	#563	C₂²×C₈₉	1	8	yes	complemented
544	#562	C₂²×C₈₉	1	16	yes	complemented
545	H(3,𝔽₄)	C₂²×C₈₉	1	4	yes	complemented
546	#560	C₂²×C₈₉	1	8	yes	complemented
547	#559	C₂²×C₈₉	1	2	yes	complemented
548	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
549	#556	C₂²×C₈₉	1	4	yes	complemented
550	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
551	#555	C₂²×C₈₉	1	8	yes	complemented
552	#555	C₂²×C₈₉	1	4	yes	complemented
553	#555	C₂²×C₈₉	1	8	yes	complemented
554	#555	C₂²×C₈₉	1	2	yes	complemented
555	#555	C₂²×C₈₉	1	8	yes	complemented
556	#555	C₂²×C₈₉	1	4	yes	complemented
557	#555	C₂²×C₈₉	1	4	yes	complemented
558	#555	C₂²×C₈₉	1	4	yes	complemented
559	#554	C₂²×C₈₉	1	2	yes	complemented
560	#554	C₂²×C₈₉	1	2	yes	complemented
561	#554	C₂²×C₈₉	1	4	yes	complemented
562	#553	C₂²×C₈₉	1	8	yes	complemented
563	#553	C₂²×C₈₉	1	4	yes	complemented
564	#553	C₂²×C₈₉	1	4	yes	complemented
565	#553	C₂²×C₈₉	1	8	yes	complemented
566	#553	C₂²×C₈₉	1	8	yes	complemented
567	#552	C₂²×C₈₉	1	8	yes	complemented
568	#552	C₂²×C₈₉	1	8	yes	complemented
569	#551	C₂²×C₈₉	1	16	yes	complemented
570	#551	C₂²×C₈₉	1	8	yes	complemented
571	#551	C₂²×C₈₉	1	8	yes	complemented
572	#551	C₂²×C₈₉	1	16	yes	complemented
573	#550	C₂²×C₈₉	1	2	yes	complemented
574	#550	C₂²×C₈₉	1	4	yes	complemented
575	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
576	#548	C₂²×C₈₉	1	8	yes	complemented
577	#548	C₂²×C₈₉	1	8	yes	complemented
578	#547	C₂²×C₈₉	1	4	yes	complemented
579	#547	C₂²×C₈₉	1	8	yes	complemented
580	#547	C₂²×C₈₉	1	8	yes	complemented
581	#547	C₂²×C₈₉	1	4	yes	complemented
582	#546	C₂²×C₈₉	1	8	yes	complemented
583	#546	C₂²×C₈₉	1	4	yes	complemented
584	#546	C₂²×C₈₉	1	4	yes	complemented
585	#546	C₂²×C₈₉	1	16	yes	complemented
586	#546	C₂²×C₈₉	1	16	yes	complemented
587	#546	C₂²×C₈₉	1	8	yes	complemented
588	#546	C₂²×C₈₉	1	16	yes	complemented
589	#546	C₂²×C₈₉	1	8	yes	complemented
590	D₄²	C₂²×C₈₉	1	2	yes	—
591	D₄²	C₂²×C₈₉	1	4	yes	complemented
592	D₄²	C₂²×C₈₉	1	8	yes	complemented
593	D₄²	C₂²×C₈₉	1	2	yes	complemented
594	#544	C₂²×C₈₉	1	8	yes	complemented
595	#542	C₂²×C₈₉	1	16	yes	complemented
596	#542	C₂²×C₈₉	1	8	yes	complemented
597	#542	C₂²×C₈₉	1	8	yes	complemented
598	#540	C₂²×C₈₉	1	16	yes	complemented
599	#540	C₂²×C₈₉	1	8	yes	complemented
600	#538	C₂²×C₈₉	1	16	yes	complemented
601	#538	C₂²×C₈₉	1	16	yes	complemented
602	#537	C₂²×C₈₉	1	8	yes	complemented
603	#537	C₂²×C₈₉	1	4	yes	complemented
604	#536	C₂²×C₈₉	1	4	yes	complemented
605	#536	C₂²×C₈₉	1	2	yes	complemented
606	#536	C₂²×C₈₉	1	8	yes	complemented
607	#536	C₂²×C₈₉	1	4	yes	complemented
608	#535	C₂²×C₈₉	1	8	yes	complemented
609	#535	C₂²×C₈₉	1	8	yes	complemented
610	#535	C₂²×C₈₉	1	4	yes	complemented
611	#534	C₂²×C₈₉	1	16	yes	complemented
612	#533	C₂²×C₈₉	1	4	yes	complemented
613	#532	C₂²×C₈₉	1	2	yes	complemented
614	#532	C₂²×C₈₉	1	4	yes	complemented
615	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
616	#532	C₂²×C₈₉	1	4	yes	complemented
617	#532	C₂²×C₈₉	1	8	yes	complemented
618	#532	C₂²×C₈₉	1	4	yes	complemented
619	#532	C₂²×C₈₉	1	2	yes	complemented
620	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
621	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#529	C₂²×C₈₉	1	16	yes	complemented
623	#529	C₂²×C₈₉	1	8	yes	complemented
624	#529	C₂²×C₈₉	1	4	yes	complemented
625	#529	C₂²×C₈₉	1	4	yes	complemented
626	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
627	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
628	#525	C₂²×C₈₉	1	8	yes	complemented
629	#525	C₂²×C₈₉	1	8	yes	complemented
630	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
631	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
632	#520	C₂²×C₈₉	1	4	yes	complemented
633	#518	C₂²×C₈₉	1	8	yes	complemented
634	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
635	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
636	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
637	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
638	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
639	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
640	C₂×#117	C₂²×C₈₉	1	8	yes	complemented
641	2₋¹⁺⁴	—	4	8	no	—
642	H(5,𝔽₂)	—	4	16	no	—
643	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
644	C₂×#41	C₂³×C₈₉	1	4	yes	—
645	C₂×#41	C₂³×C₈₉	1	4	yes	—
646	C₂×#41	C₂³×C₈₉	1	2	yes	—
647	C₂×#41	C₂³×C₈₉	1	4	yes	—
648	C₂×#41	C₂³×C₈₉	1	2	yes	—
649	C₂×#41	C₂³×C₈₉	1	4	yes	—
650	C₂×#41	C₂³×C₈₉	1	8	yes	—
651	C₂×#41	C₂³×C₈₉	1	4	yes	—
652	C₂×#41	C₂³×C₈₉	1	8	yes	—
653	C₂×#41	C₂³×C₈₉	1	8	yes	—
654	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
655	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
656	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
657	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
658	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
659	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
660	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
661	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
662	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
663	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
664	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
665	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
666	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
667	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
668	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
669	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
670	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
671	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
672	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
673	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
674	#127	C₂³×C₈₉	1	2	yes	—
675	#127	C₂³×C₈₉	1	1	yes	characteristic
676	#127	C₂³×C₈₉	1	8	yes	—
677	#127	C₂³×C₈₉	1	4	yes	—
678	#127	C₂³×C₈₉	1	4	yes	—
679	#126	C₂³×C₈₉	1	8	yes	—
680	#126	C₂³×C₈₉	1	16	yes	—
681	#126	C₂³×C₈₉	1	16	yes	—
682	#126	C₂³×C₈₉	1	16	yes	—
683	#126	C₂³×C₈₉	1	8	yes	—
684	#125	C₂³×C₈₉	1	4	yes	—
685	#125	C₂³×C₈₉	1	16	yes	—
686	#125	C₂³×C₈₉	1	4	yes	—
687	#125	C₂³×C₈₉	1	8	yes	—
688	#124	C₂³×C₈₉	1	4	yes	—
689	#124	C₂³×C₈₉	1	8	yes	—
690	#124	C₂³×C₈₉	1	4	yes	—
691	#124	C₂³×C₈₉	1	8	yes	—
692	#124	C₂³×C₈₉	1	8	yes	—
693	#124	C₂³×C₈₉	1	8	yes	—
694	#124	C₂³×C₈₉	1	8	yes	—
695	#124	C₂³×C₈₉	1	16	yes	—
696	#124	C₂³×C₈₉	1	16	yes	—
697	#124	C₂³×C₈₉	1	16	yes	—
698	#124	C₂³×C₈₉	1	4	yes	—
699	#124	C₂³×C₈₉	1	4	yes	—
700	#124	C₂³×C₈₉	1	4	yes	—
701	#124	C₂³×C₈₉	1	2	yes	—
702	#124	C₂³×C₈₉	1	8	yes	—
703	#124	C₂³×C₈₉	1	4	yes	—
704	#123	C₂³×C₈₉	1	8	yes	—
705	#123	C₂³×C₈₉	1	16	yes	—
706	#123	C₂³×C₈₉	1	8	yes	—
707	#123	C₂³×C₈₉	1	16	yes	—
708	#123	C₂³×C₈₉	1	16	yes	—
709	#123	C₂³×C₈₉	1	8	yes	—
710	#123	C₂³×C₈₉	1	8	yes	—
711	#123	C₂³×C₈₉	1	16	yes	—
712	#123	C₂³×C₈₉	1	16	yes	—
713	#123	C₂³×C₈₉	1	16	yes	—
714	#123	C₂³×C₈₉	1	8	yes	—
715	#123	C₂³×C₈₉	1	16	yes	—
716	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
717	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
718	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
719	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
720	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
721	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
722	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
723	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
724	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
725	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
726	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
727	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
728	#121	C₂³×C₈₉	1	4	yes	—
729	#121	C₂³×C₈₉	1	8	yes	—
730	#121	C₂³×C₈₉	1	4	yes	—
731	#121	C₂³×C₈₉	1	4	yes	—
732	#121	C₂³×C₈₉	1	8	yes	—
733	#121	C₂³×C₈₉	1	16	yes	—
734	#121	C₂³×C₈₉	1	16	yes	—
735	#121	C₂³×C₈₉	1	16	yes	—
736	#121	C₂³×C₈₉	1	8	yes	—
737	#121	C₂³×C₈₉	1	8	yes	—
738	#121	C₂³×C₈₉	1	16	yes	—
739	#121	C₂³×C₈₉	1	8	yes	—
740	#121	C₂³×C₈₉	1	8	yes	—
741	#121	C₂³×C₈₉	1	8	yes	—
742	#121	C₂³×C₈₉	1	8	yes	—
743	#121	C₂³×C₈₉	1	4	yes	—
744	#121	C₂³×C₈₉	1	8	yes	—
745	#121	C₂³×C₈₉	1	8	yes	—
746	#121	C₂³×C₈₉	1	4	yes	—
747	#121	C₂³×C₈₉	1	4	yes	—
748	#121	C₂³×C₈₉	1	4	yes	—
749	#121	C₂³×C₈₉	1	8	yes	—
750	#121	C₂³×C₈₉	1	8	yes	—
751	#121	C₂³×C₈₉	1	16	yes	—
752	#121	C₂³×C₈₉	1	16	yes	—
753	#121	C₂³×C₈₉	1	16	yes	—
754	#120	C₂³×C₈₉	1	8	yes	—
755	#120	C₂³×C₈₉	1	16	yes	—
756	#120	C₂³×C₈₉	1	8	yes	—
757	#120	C₂³×C₈₉	1	16	yes	—
758	#120	C₂³×C₈₉	1	16	yes	—
759	#120	C₂³×C₈₉	1	8	yes	—
760	#120	C₂³×C₈₉	1	8	yes	—
761	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
762	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
763	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
764	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
765	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
766	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
767	C₄×D₄	C₂³×C₈₉	1	2	yes	—
768	C₄×D₄	C₂³×C₈₉	1	2	yes	—
769	C₄×D₄	C₂³×C₈₉	1	4	yes	—
770	C₄×D₄	C₂³×C₈₉	1	4	yes	—
771	C₄×D₄	C₂³×C₈₉	1	8	yes	—
772	C₄×D₄	C₂³×C₈₉	1	8	yes	—
773	C₄×D₄	C₂³×C₈₉	1	8	yes	—
774	C₄×D₄	C₂³×C₈₉	1	4	yes	—
775	C₄×D₄	C₂³×C₈₉	1	4	yes	—
776	C₄×D₄	C₂³×C₈₉	1	4	yes	—
777	C₄×D₄	C₂³×C₈₉	1	8	yes	—
778	C₄×D₄	C₂³×C₈₉	1	4	yes	—
779	C₄×D₄	C₂³×C₈₉	1	4	yes	—
780	C₄×D₄	C₂³×C₈₉	1	4	yes	—
781	C₄×D₄	C₂³×C₈₉	1	4	yes	—
782	C₄×D₄	C₂³×C₈₉	1	16	yes	—
783	C₄×D₄	C₂³×C₈₉	1	2	yes	—
784	C₄×D₄	C₂³×C₈₉	1	4	yes	—
785	C₄×D₄	C₂³×C₈₉	1	8	yes	—
786	C₄×D₄	C₂³×C₈₉	1	4	yes	—
787	C₄×D₄	C₂³×C₈₉	1	8	yes	—
788	C₄×D₄	C₂³×C₈₉	1	16	yes	—
789	C₄×D₄	C₂³×C₈₉	1	8	yes	—
790	C₄×D₄	C₂³×C₈₉	1	8	yes	—
791	C₄×D₄	C₂³×C₈₉	1	16	yes	—
792	C₄×D₄	C₂³×C₈₉	1	16	yes	—
793	C₄×D₄	C₂³×C₈₉	1	8	yes	—
794	#117	C₂³×C₈₉	1	4	yes	—
795	#117	C₂³×C₈₉	1	8	yes	—
796	#117	C₂³×C₈₉	1	8	yes	—
797	#117	C₂³×C₈₉	1	16	yes	—
798	#117	C₂³×C₈₉	1	8	yes	—
799	#117	C₂³×C₈₉	1	16	yes	—
800	#117	C₂³×C₈₉	1	2	yes	—
801	#117	C₂³×C₈₉	1	8	yes	—
802	#117	C₂³×C₈₉	1	8	yes	—
803	#117	C₂³×C₈₉	1	4	yes	—
804	#117	C₂³×C₈₉	1	2	yes	—
805	#117	C₂³×C₈₉	1	1	yes	characteristic
806	#117	C₂³×C₈₉	1	4	yes	—
807	#117	C₂³×C₈₉	1	8	yes	—
808	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
809	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
810	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
811	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
812	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
818	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
819	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
820	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
821	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
822	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
823	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
824	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
825	#41	—	2	16	no	—
826	#41	—	2	4	no	—
827	#41	—	4	8	no	—
828	#41	—	4	4	no	—
829	#41	—	4	8	no	—
830	#41	—	4	16	no	—
831	#41	—	4	16	no	—
832	#41	—	4	8	no	—
833	#41	—	4	16	no	—
834	#41	—	4	8	no	—
835	#41	—	4	4	no	—
836	C₂×Q₈	—	4	8	no	—
837	C₂×Q₈	—	4	8	no	—
838	C₂×Q₈	—	4	4	no	—
839	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
840	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
841	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
842	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
843	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
844	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
845	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
846	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
847	C₂×D₄	—	2	16	no	—
848	C₂×D₄	—	4	8	no	—
849	C₂×D₄	—	4	8	no	—
850	C₂×D₄	—	4	16	no	—
851	C₂×D₄	—	4	16	no	—
852	C₂×D₄	—	4	32	no	—
853	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
854	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
855	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
856	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
857	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
858	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
859	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
860	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
861	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
862	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
863	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
864	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
865	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
866	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
867	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
868	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
869	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
870	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
871	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
872	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
873	C₂²×C₄	—	4	16	no	—
874	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
877	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
879	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
880	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
882	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
883	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
884	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
885	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
886	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
887	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
888	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
889	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
890	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
893	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
894	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
895	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
897	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
898	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
899	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
900	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
901	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
902	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
903	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
904	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
905	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
906	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
907	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
908	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
910	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
911	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
914	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
916	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
917	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
918	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
919	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
920	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
921	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
922	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
923	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
924	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
925	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
926	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
927	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
928	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
929	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
930	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
931	C₂²⋊C₄	C₂⁴×C₈₉	1	2	yes	—
932	C₄²	C₂⁴×C₈₉	1	4	yes	—
933	C₄²	C₂⁴×C₈₉	1	2	yes	—
934	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
935	C₄²	C₂⁴×C₈₉	1	4	yes	—
936	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
937	C₄²	C₂⁴×C₈₉	1	8	yes	—
938	C₄²	C₂⁴×C₈₉	1	4	yes	—
939	C₄²	C₂⁴×C₈₉	1	16	yes	—
940	C₄²	C₂⁴×C₈₉	1	4	yes	—
941	C₄²	C₂⁴×C₈₉	1	4	yes	—
942	C₄²	C₂⁴×C₈₉	1	2	yes	—
943	C₄²	C₂⁴×C₈₉	1	4	yes	—
944	C₂³	—	2	16	no	—
945	C₂³	—	4	8	no	—
946	C₂³	—	4	8	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	4	16	no	—
949	C₂³	C₂⁵×C₈₉	1	8	yes	—
950	C₂³	C₂⁵×C₈₉	1	4	yes	—
951	C₂³	C₂⁵×C₈₉	1	4	yes	—
952	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
953	C₂³	C₂⁵×C₈₉	1	2	yes	—
954	Q₈	—	2	2	no	—
955	Q₈	—	2	8	no	—
956	Q₈	—	2	4	no	—
957	Q₈	—	4	2	no	—
958	Q₈	—	4	8	no	—
959	Q₈	—	4	4	no	—
960	Q₈	—	4	4	no	—
961	Q₈	—	4	4	no	—
962	D₄	—	2	16	no	—
963	D₄	—	2	16	no	—
964	D₄	—	2	4	no	—
965	D₄	—	2	8	no	—
966	D₄	—	2	8	no	—
967	D₄	—	2	4	no	—
968	D₄	—	2	8	no	—
969	D₄	—	4	4	no	—
970	D₄	—	4	8	no	—
971	D₄	—	4	8	no	—
972	D₄	—	4	16	no	—
973	D₄	—	4	8	no	—
974	D₄	—	4	16	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	2	no	—
981	D₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
982	C₂×C₄	—	2	16	no	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	8	no	—
985	C₂×C₄	—	2	8	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	8	no	—
988	C₂×C₄	—	2	8	no	—
989	C₂×C₄	—	2	16	no	—
990	C₂×C₄	—	2	4	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	4	16	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	4	8	no	—
997	C₂×C₄	—	4	8	no	—
998	C₂×C₄	—	4	4	no	—
999	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1000	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1001	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1002	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1003	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1004	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1005	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1006	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1007	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
1008	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
1009	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1010	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	4	no	—
1015	C₂²	—	2	8	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	8	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	4	no	—
1020	C₂²	—	2	8	no	—
1021	C₂²	—	2	8	no	—
1022	C₂²	—	8	16	no	—
1023	C₂²	—	16	8	no	—
1024	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
1025	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
1026	C₄	—	2	4	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	4	no	—
1032	C₄	—	2	4	no	—
1033	C₄	—	2	8	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
1037	C₄	#585×C₈₉	1	4	yes	—
1038	C₂	—	2	4	no	—
1039	C₂	—	4	1	no	—
1040	C₂	—	4	4	no	—
1041	C₂	—	4	8	no	—
1042	C₂	—	4	4	no	—
1043	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1044	C₂	C₂×#585×C₈₉	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×#3551	C₂	semidirect
2. C₈₉×#3549	C₂	semidirect
3. C₈₉×#3547	C₂	semidirect
4. C₈₉×#3545	C₂	semidirect
5. C₈₉×#3544	C₂	semidirect
6. C₈₉×#3542	C₂	semidirect
7. C₈₉×#3519	C₂	semidirect
8. C₈₉×#3514	C₂	semidirect
9. C₈₉×#3511	C₂	semidirect
10. C₈₉×#3500	C₂	semidirect
11. C₈₉×#3499	C₂	semidirect
12. C₈₉×#3496	C₂	semidirect
13. C₈₉×#3494	C₂	semidirect
14. C₈₉×#3483	C₂	semidirect
15. C₈₉×#3481	C₂	semidirect
16. C₈₉×#3475	C₂	semidirect
17. C₂×#555×C₈₉	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
19. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #562×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. #560×C₈₉	C₂²	semidirect
24. #559×C₈₉	C₂²	semidirect
25. Q₈²×C₈₉	C₂²	semidirect
26. #556×C₈₉	C₂²	semidirect
27. #555×C₈₉	C₂²	semidirect
28. #555×C₈₉	C₂²	semidirect
29. #555×C₈₉	C₂²	semidirect
30. #555×C₈₉	C₂²	semidirect
31. #555×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
33. #555×C₈₉	C₂²	semidirect
34. #555×C₈₉	C₂²	semidirect
35. #555×C₈₉	C₂²	semidirect
36. #554×C₈₉	C₂²	semidirect
37. #554×C₈₉	C₂²	semidirect
38. #554×C₈₉	C₂²	semidirect
39. #553×C₈₉	C₂²	semidirect
40. #553×C₈₉	C₂²	semidirect
41. #553×C₈₉	C₂²	semidirect
42. #553×C₈₉	C₂²	semidirect
43. #553×C₈₉	C₂²	semidirect
44. #552×C₈₉	C₂²	semidirect
45. #552×C₈₉	C₂²	semidirect
46. #551×C₈₉	C₂²	semidirect
47. #551×C₈₉	C₂²	semidirect
48. #551×C₈₉	C₂²	semidirect
49. #551×C₈₉	C₂²	semidirect
50. #550×C₈₉	C₂²	semidirect
51. #550×C₈₉	C₂²	semidirect
52. D₄×Q₈×C₈₉	C₂²	semidirect
53. #548×C₈₉	C₂²	semidirect
54. #548×C₈₉	C₂²	semidirect
55. #547×C₈₉	C₂²	semidirect
56. #547×C₈₉	C₂²	semidirect
57. #547×C₈₉	C₂²	semidirect
58. #547×C₈₉	C₂²	semidirect
59. #546×C₈₉	C₂²	semidirect
60. #546×C₈₉	C₂²	semidirect
61. #546×C₈₉	C₂²	semidirect
62. #546×C₈₉	C₂²	semidirect
63. #546×C₈₉	C₂²	semidirect
64. #546×C₈₉	C₂²	semidirect
65. #546×C₈₉	C₂²	semidirect
66. #546×C₈₉	C₂²	semidirect
68. D₄²×C₈₉	C₂²	semidirect
69. D₄²×C₈₉	C₂²	semidirect
70. D₄²×C₈₉	C₂²	semidirect
71. #544×C₈₉	C₂²	semidirect
72. #542×C₈₉	C₂²	semidirect
73. #542×C₈₉	C₂²	semidirect
74. #542×C₈₉	C₂²	semidirect
75. #540×C₈₉	C₂²	semidirect
76. #540×C₈₉	C₂²	semidirect
77. #538×C₈₉	C₂²	semidirect
78. #538×C₈₉	C₂²	semidirect
79. #537×C₈₉	C₂²	semidirect
80. #537×C₈₉	C₂²	semidirect
81. #536×C₈₉	C₂²	semidirect
82. #536×C₈₉	C₂²	semidirect
83. #536×C₈₉	C₂²	semidirect
84. #536×C₈₉	C₂²	semidirect
85. #535×C₈₉	C₂²	semidirect
86. #535×C₈₉	C₂²	semidirect
87. #535×C₈₉	C₂²	semidirect
88. #534×C₈₉	C₂²	semidirect
89. #533×C₈₉	C₂²	semidirect
90. #532×C₈₉	C₂²	semidirect
91. #532×C₈₉	C₂²	semidirect
92. #532×C₈₉	C₂²	semidirect
93. #532×C₈₉	C₂²	semidirect
94. #532×C₈₉	C₂²	semidirect
95. #532×C₈₉	C₂²	semidirect
96. #532×C₈₉	C₂²	semidirect
97. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
98. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
99. #529×C₈₉	C₂²	semidirect
100. #529×C₈₉	C₂²	semidirect
101. #529×C₈₉	C₂²	semidirect
102. #529×C₈₉	C₂²	semidirect
103. C₂×#124×C₈₉	C₂²	semidirect
104. C₂×#124×C₈₉	C₂²	semidirect
105. #525×C₈₉	C₂²	semidirect
106. #525×C₈₉	C₂²	semidirect
107. C₂×#121×C₈₉	C₂²	semidirect
108. C₂×#121×C₈₉	C₂²	semidirect
109. #520×C₈₉	C₂²	semidirect
110. #518×C₈₉	C₂²	semidirect
111. C₄×#41×C₈₉	C₂²	semidirect
112. C₄×#41×C₈₉	C₂²	semidirect
113. C₄×#41×C₈₉	C₂²	semidirect
114. C₄×#41×C₈₉	C₂²	semidirect
115. C₂×C₄×D₄×C₈₉	C₂²	semidirect
116. C₂×C₄×D₄×C₈₉	C₂²	semidirect
117. C₂×#117×C₈₉	C₂²	semidirect
515. #63024	C₈₉	direct (N × H)
523. #3551	C₂×C₈₉	semidirect
524. #3549	C₂×C₈₉	semidirect
525. #3547	C₂×C₈₉	semidirect
526. #3545	C₂×C₈₉	semidirect
527. #3544	C₂×C₈₉	semidirect
528. #3542	C₂×C₈₉	semidirect
529. #3519	C₂×C₈₉	semidirect
530. #3514	C₂×C₈₉	semidirect
531. #3511	C₂×C₈₉	semidirect
532. #3500	C₂×C₈₉	semidirect
533. #3499	C₂×C₈₉	semidirect
534. #3496	C₂×C₈₉	semidirect
535. #3494	C₂×C₈₉	semidirect
536. #3483	C₂×C₈₉	semidirect
537. #3481	C₂×C₈₉	semidirect
538. #3475	C₂×C₈₉	semidirect
539. C₂×#555	C₂×C₈₉	semidirect
540. C₈₉	#63024	direct (N × H)
541. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
542. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
543. #563	C₂²×C₈₉	semidirect
544. #562	C₂²×C₈₉	semidirect
545. H(3,𝔽₄)	C₂²×C₈₉	semidirect
546. #560	C₂²×C₈₉	semidirect
547. #559	C₂²×C₈₉	semidirect
548. Q₈²	C₂²×C₈₉	semidirect
549. #556	C₂²×C₈₉	semidirect
550. #555	C₂²×C₈₉	semidirect
551. #555	C₂²×C₈₉	semidirect
552. #555	C₂²×C₈₉	semidirect
553. #555	C₂²×C₈₉	semidirect
554. #555	C₂²×C₈₉	semidirect
555. #555	C₂²×C₈₉	semidirect
556. #555	C₂²×C₈₉	semidirect
557. #555	C₂²×C₈₉	semidirect
558. #555	C₂²×C₈₉	semidirect
559. #554	C₂²×C₈₉	semidirect
560. #554	C₂²×C₈₉	semidirect
561. #554	C₂²×C₈₉	semidirect
562. #553	C₂²×C₈₉	semidirect
563. #553	C₂²×C₈₉	semidirect
564. #553	C₂²×C₈₉	semidirect
565. #553	C₂²×C₈₉	semidirect
566. #553	C₂²×C₈₉	semidirect
567. #552	C₂²×C₈₉	semidirect
568. #552	C₂²×C₈₉	semidirect
569. #551	C₂²×C₈₉	semidirect
570. #551	C₂²×C₈₉	semidirect
571. #551	C₂²×C₈₉	semidirect
572. #551	C₂²×C₈₉	semidirect
573. #550	C₂²×C₈₉	semidirect
574. #550	C₂²×C₈₉	semidirect
575. D₄×Q₈	C₂²×C₈₉	semidirect
576. #548	C₂²×C₈₉	semidirect
577. #548	C₂²×C₈₉	semidirect
578. #547	C₂²×C₈₉	semidirect
579. #547	C₂²×C₈₉	semidirect
580. #547	C₂²×C₈₉	semidirect
581. #547	C₂²×C₈₉	semidirect
582. #546	C₂²×C₈₉	semidirect
583. #546	C₂²×C₈₉	semidirect
584. #546	C₂²×C₈₉	semidirect
585. #546	C₂²×C₈₉	semidirect
586. #546	C₂²×C₈₉	semidirect
587. #546	C₂²×C₈₉	semidirect
588. #546	C₂²×C₈₉	semidirect
589. #546	C₂²×C₈₉	semidirect
591. D₄²	C₂²×C₈₉	semidirect
592. D₄²	C₂²×C₈₉	semidirect
593. D₄²	C₂²×C₈₉	semidirect
594. #544	C₂²×C₈₉	semidirect
595. #542	C₂²×C₈₉	semidirect
596. #542	C₂²×C₈₉	semidirect
597. #542	C₂²×C₈₉	semidirect
598. #540	C₂²×C₈₉	semidirect
599. #540	C₂²×C₈₉	semidirect
600. #538	C₂²×C₈₉	semidirect
601. #538	C₂²×C₈₉	semidirect
602. #537	C₂²×C₈₉	semidirect
603. #537	C₂²×C₈₉	semidirect
604. #536	C₂²×C₈₉	semidirect
605. #536	C₂²×C₈₉	semidirect
606. #536	C₂²×C₈₉	semidirect
607. #536	C₂²×C₈₉	semidirect
608. #535	C₂²×C₈₉	semidirect
609. #535	C₂²×C₈₉	semidirect
610. #535	C₂²×C₈₉	semidirect
611. #534	C₂²×C₈₉	semidirect
612. #533	C₂²×C₈₉	semidirect
613. #532	C₂²×C₈₉	semidirect
614. #532	C₂²×C₈₉	semidirect
615. #532	C₂²×C₈₉	semidirect
616. #532	C₂²×C₈₉	semidirect
617. #532	C₂²×C₈₉	semidirect
618. #532	C₂²×C₈₉	semidirect
619. #532	C₂²×C₈₉	semidirect
620. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
621. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
622. #529	C₂²×C₈₉	semidirect
623. #529	C₂²×C₈₉	semidirect
624. #529	C₂²×C₈₉	semidirect
625. #529	C₂²×C₈₉	semidirect
626. C₂×#124	C₂²×C₈₉	semidirect
627. C₂×#124	C₂²×C₈₉	semidirect
628. #525	C₂²×C₈₉	semidirect
629. #525	C₂²×C₈₉	semidirect
630. C₂×#121	C₂²×C₈₉	semidirect
631. C₂×#121	C₂²×C₈₉	semidirect
632. #520	C₂²×C₈₉	semidirect
633. #518	C₂²×C₈₉	semidirect
634. C₄×#41	C₂²×C₈₉	semidirect
635. C₄×#41	C₂²×C₈₉	semidirect
636. C₄×#41	C₂²×C₈₉	semidirect
637. C₄×#41	C₂²×C₈₉	semidirect
638. C₂×C₄×D₄	C₂²×C₈₉	semidirect
639. C₂×C₄×D₄	C₂²×C₈₉	semidirect
640. C₂×#117	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×#3551	2
C₈₉×#3549	2
C₈₉×#3547	2
C₈₉×#3545	2
C₈₉×#3544	2
C₈₉×#3542	2
C₈₉×#3519	2
C₈₉×#3514	2
C₈₉×#3511	2
C₈₉×#3500	2
C₈₉×#3499	2
C₈₉×#3496	2
C₈₉×#3494	2
C₈₉×#3483	2
C₈₉×#3481	2
C₈₉×#3475	2
C₂×#555×C₈₉	2
#63024	89

Subgroups — C89×#63024 #36440872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#63024 #36440872