Subgroups — #36537928

Order 22784.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031564	C₂	1	1	yes	maximal, characteristic
2	#26031177	C₂	1	1	yes	maximal, characteristic
3	#26028998	C₂	1	1	yes	maximal, characteristic
4	#26019762	C₂	1	2	yes	maximal, complemented
5	#26019748	C₂	1	2	yes	maximal, complemented
6	#26019638	C₂	1	2	yes	maximal, complemented
7	#26019624	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018909	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151344	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151972	—	2	1	no	—
15	#19151948	—	2	1	no	—
16	#19151885	C₂²	1	2	yes	—
17	#19151883	—	2	1	no	—
18	#19151829	—	2	2	no	—
19	#19151800	C₂²	1	2	yes	—
20	#19151800	C₂²	1	2	yes	—
21	#19151800	C₂²	1	2	yes	—
22	#19151798	—	2	1	no	—
23	#19151737	—	2	2	no	—
24	#19151677	C₂²	1	2	yes	—
25	#19151671	—	2	2	no	—
26	C₈×D₃₅₆	C₂²	1	2	yes	—
27	#19151651	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	#19151566	—	2	1	no	—
31	#19151351	C₂²	1	2	yes	—
32	#19151349	C₂²	1	2	yes	—
33	#19151347	C₂²	1	1	yes	characteristic
34	#19151347	C₂²	1	1	yes	characteristic
35	#19151344	C₂²	1	2	yes	—
36	#19151344	C₂²	1	1	yes	characteristic
37	#19151344	C₂²	1	2	yes	—
38	#19151344	C₂²	1	1	yes	characteristic
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#501×C₈₉	—	2	2	no	—
42	#500×C₈₉	C₂²	1	2	yes	—
43	#498×C₈₉	C₂²	1	2	yes	—
44	#428×C₈₉	—	2	1	no	—
45	#428×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083561	—	2	2	no	—
49	C₂×#13083561	—	2	2	no	—
50	C₂×#13083561	—	2	2	no	—
51	#15668020	—	4	4	no	—
52	C₂×#13083557	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	D₄	1	1	yes	characteristic
57	#15668009	D₄	1	1	yes	characteristic
58	#15668000	—	2	1	no	—
59	#15667986	—	2	1	no	—
60	#15667986	D₄	1	2	yes	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₄×D₃₅₆	C₂³	1	2	yes	—
63	#15667943	—	2	2	no	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667936	—	2	2	no	—
72	#15667936	—	2	2	no	—
73	#15667936	—	2	2	no	—
74	#15667932	—	2	2	no	—
75	C₂²⋊#10623494	—	2	1	no	—
76	#15667924	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	C₄×#10623494	—	2	1	no	—
79	C₂²×Q₈×C₈₉	—	2	1	no	—
80	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	—	2	1	no	—
83	C₄⋊Q₈×C₈₉	—	2	1	no	—
84	C₄⋊Q₈×C₈₉	—	2	1	no	—
85	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	#125×C₈₉	—	2	1	no	—
89	C₂²⋊Q₈×C₈₉	—	2	1	no	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	#117×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#107×C₈₉	—	2	2	no	—
98	#107×C₈₉	—	2	2	no	—
99	#106×C₈₉	—	2	2	no	—
100	#106×C₈₉	—	2	2	no	—
101	#97×C₈₉	D₄	1	2	yes	—
102	C₄×C₈×C₈₉	C₂³	1	2	yes	—
103	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×D₃₅₆	—	2	1	no	—
107	C₂×D₃₅₆	—	2	1	no	—
108	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	—	2	2	no	—
111	#13083561	—	8	2	no	—
112	#13083561	—	8	2	no	—
113	#13083561	—	8	2	no	—
114	#13083557	—	4	4	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	4	2	no	—
121	C₂×#10623494	—	8	1	no	—
122	C₈×D₈₉	—	4	4	no	—
123	C₄⋊Dic₈₉	—	2	1	no	—
124	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
125	#13083551	—	2	2	no	—
126	#13083551	—	2	2	no	—
127	C₂×Q₈×C₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	4	1	no	—
131	C₂×Q₈×C₈₉	—	8	1	no	—
132	C₂×Q₈×C₈₉	—	8	1	no	—
133	C₂²×C₄×C₈₉	—	4	1	no	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	2	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	4	1	no	—
148	C₄⋊C₄×C₈₉	—	4	1	no	—
149	C₄⋊C₄×C₈₉	—	4	1	no	—
150	C₄⋊C₄×C₈₉	—	4	1	no	—
151	C₂²⋊C₄×C₈₉	—	4	1	no	—
152	C₄²×C₈₉	—	4	1	no	—
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	#121	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	Q₈×C₈₉	—	4	1	no	—
161	Q₈×C₈₉	—	4	1	no	—
162	Q₈×C₈₉	—	4	2	no	—
163	Q₈×C₈₉	—	8	1	no	—
164	Q₈×C₈₉	—	8	2	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	—	8	2	no	—
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₈₉	#137	1	2	yes	—
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₈₉	—	4	4	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	D₃₅₆	—	2	2	no	—
183	D₃₅₆	—	2	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	8	1	no	—
186	C₄×D₈₉	—	4	2	no	—
187	C₄×D₈₉	—	4	2	no	—
188	Dic₁₇₈	—	4	2	no	—
189	C₈×C₈₉	—	2	2	no	—
190	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
191	#10623494	—	4	1	no	—
192	#10623494	—	4	1	no	—
193	#10623494	—	4	2	no	—
194	#10623494	—	4	1	no	—
195	#10623494	—	4	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	#461	1	2	yes	—
199	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
200	C₂×D₈₉	—	4	2	no	—
201	C₂×D₈₉	—	4	2	no	—
202	C₂×D₈₉	—	4	2	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	8	2	no	—
207	C₄×C₈₉	—	8	1	no	—
208	C₄×C₈₉	—	8	1	no	—
209	C₄×C₈₉	#461	1	2	yes	—
210	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
211	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
212	C₄×C₈₉	#576	1	1	yes	characteristic
213	C₄×C₈₉	#577	1	1	yes	characteristic
214	Dic₈₉	—	4	2	no	—
215	#19232	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	2	2	no	—
217	C₂×C₈₉	C₂×#461	1	1	yes	characteristic
218	C₂×C₈₉	#3062	1	1	yes	characteristic
219	C₂×C₈₉	#3069	1	1	yes	characteristic
220	D₈₉	—	8	2	no	—
221	#3246	—	89	1	no	—
222	#3206	—	89	1	no	—
223	#3165	D₈₉	1	1	yes	characteristic, complemented
224	#2935	—	89	1	no	—
225	#1693	—	89	2	no	—
226	#1691	—	89	2	no	—
227	#1673	—	89	2	no	—
228	#1671	—	89	2	no	—
229	#1565	—	89	1	no	—
230	#1542	—	89	1	no	—
231	C₂×#332	—	89	1	no	—
232	C₈₉	#19232	1	1	yes	characteristic, complemented, Sylow
233	C₂×#131	—	178	1	no	—
234	#533	C₂×D₈₉	1	1	yes	characteristic
235	#532	—	89	1	no	—
236	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
237	#501	—	2	2	no	—
238	#500	C₂×D₈₉	1	2	yes	—
239	#498	C₂×D₈₉	1	2	yes	—
240	#492	—	178	1	no	—
241	#487	—	178	1	no	—
242	#476	—	89	2	no	—
243	#475	—	178	1	no	—
244	#465	—	178	2	no	—
245	#461	—	89	2	no	—
246	#461	—	89	2	no	—
247	#461	—	89	2	no	—
248	#460	—	178	1	no	—
249	#448	—	178	2	no	—
250	#436	—	89	2	no	—
251	#435	—	178	2	no	—
252	C₈×D₄	—	89	2	no	—
253	#431	—	89	1	no	—
254	#428	—	2	1	no	—
255	#428	—	2	1	no	—
256	C₂×C₄⋊C₈	—	89	1	no	—
257	C₂×C₄⋊C₈	—	89	1	no	—
258	#408	—	178	1	no	—
259	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
260	#335	—	89	2	no	—
261	#334	—	89	2	no	—
262	#333	—	89	1	no	—
263	#333	—	89	1	no	—
264	#332	—	89	2	no	—
265	#332	—	89	2	no	—
266	#332	—	89	1	no	—
267	#332	—	89	1	no	—
268	C₂×#41	—	178	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂×SD₁₆	—	178	2	no	—
271	C₂×SD₁₆	—	178	2	no	—
272	C₂×SD₁₆	—	178	2	no	—
273	#131	—	356	4	no	—
274	C₂×M₁₆	—	178	2	no	—
275	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
276	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
277	C₂²×C₈	—	178	1	no	—
278	C₂²×C₈	—	178	2	no	—
279	C₂²×C₈	—	178	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	89	1	no	—
284	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
285	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
286	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
287	#127	—	89	1	no	—
288	#125	—	2	1	no	—
289	#124	—	178	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	89	2	no	—
293	#121	—	178	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	89	2	no	—
297	C₄×D₄	—	178	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	#106	—	178	2	no	—
307	C₄⋊C₈	—	89	1	no	—
308	C₄⋊C₈	—	89	1	no	—
309	C₄⋊C₈	—	89	2	no	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	178	1	no	—
313	C₄⋊C₈	—	178	1	no	—
314	#103	—	178	2	no	—
315	#103	—	178	2	no	—
316	#103	—	178	2	no	—
317	#102	—	178	2	no	—
318	C₂²⋊C₈	—	178	1	no	—
319	C₂²⋊C₈	—	178	2	no	—
320	C₂²⋊C₈	—	178	2	no	—
321	#97	C₂²⋊D₈₉	1	2	yes	—
322	C₄×C₈	—	178	1	no	—
323	C₄×C₈	C₂²×D₈₉	1	2	yes	—
324	#41	—	356	2	no	—
325	#41	—	356	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	—	8	1	no	—
331	C₂×Q₈	—	8	1	no	—
332	C₂×Q₈	—	178	1	no	—
333	C₂×D₄	—	89	2	no	—
334	C₂×D₄	—	178	2	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂×D₄	—	178	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	178	2	no	—
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083573	1	1	yes	characteristic
342	SD₁₆	—	712	2	no	—
343	SD₁₆	—	712	2	no	—
344	SD₁₆	—	712	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	356	4	no	—
347	M₁₆	#13083561	1	4	yes	complemented
348	C₂×C₈	—	356	2	no	—
349	C₂×C₈	—	356	4	no	—
350	C₂×C₈	—	178	1	no	—
351	C₂×C₈	—	178	1	no	—
352	C₂×C₈	—	178	2	no	—
353	C₂×C₈	—	178	1	no	—
354	C₂×C₈	—	178	1	no	—
355	C₂×C₈	—	712	1	no	—
356	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
357	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	89	2	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	178	2	no	—
372	C₂²⋊C₄	—	178	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	D₄×D₈₉	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
376	C₄²	#13083573	1	1	yes	characteristic
377	C₄²	C₂³×D₈₉	1	1	yes	characteristic
378	C₂³	—	178	2	no	—
379	C₂³	#15667983	1	1	yes	characteristic
380	Q₈	—	4	1	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	2	no	—
386	Q₈	—	356	2	no	—
387	D₄	—	356	4	no	—
388	D₄	—	356	2	no	—
389	D₄	—	178	2	no	—
390	D₄	—	178	2	no	—
391	D₄	—	712	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	356	2	no	—
400	C₂×C₄	—	356	2	no	—
401	C₂×C₄	—	178	2	no	—
402	C₂×C₄	#15667983	1	1	yes	characteristic
403	C₂×C₄	#15667983	1	1	yes	characteristic
404	C₂×C₄	#15667983	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083561	1	2	yes	—
406	C₂×C₄	#15668043	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	356	2	no	—
412	C₈	—	356	1	no	—
413	C₈	—	356	1	no	—
414	C₈	—	356	1	no	—
415	C₈	—	356	1	no	—
416	C₈	C₂×#13083561	1	4	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	356	2	no	—
420	C₂²	—	356	2	no	—
421	C₂²	—	356	2	no	—
422	C₂²	#19151800	1	2	yes	—
423	C₂²	C₂×#15667983	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	356	2	no	—
431	C₄	#19151800	1	2	yes	—
432	C₄	C₂²×#13083561	1	1	yes	characteristic
433	C₄	C₂×#15668043	1	1	yes	characteristic
434	C₄	#19152402	1	1	yes	characteristic
435	C₄	#19152408	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	712	2	no	—
438	C₂	C₂×#19151800	1	1	yes	characteristic
439	C₂	#26029926	1	1	yes	characteristic
440	C₂	#26029985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3165	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#3165	D₈₉
hypocenter	C₈₉	#19232
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
4. #26019762	C₂	semidirect
5. #26019748	C₂	semidirect
6. #26019638	C₂	semidirect
7. #26019624	C₂	semidirect
8. #26019004	C₂	semidirect
9. #26018909	C₂	semidirect
10. C₂×#19151344	C₂	semidirect
11. C₈₉×#3165	C₂	semidirect
138. M₁₆×C₈₉	SD₁₆	semidirect
223. #3165	D₈₉	semidirect
232. C₈₉	#19232	semidirect
347. M₁₆	#13083561	semidirect

Maximal subgroups

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

subgroup	index
#26031564	2
#26031177	2
#26028998	2
#26019762	2
#26019748	2
#26019638	2
#26019624	2
#26019004	2
#26018909	2
C₂×#19151344	2
C₈₉×#3165	2
#19232	89