Subgroups — #36537875

Order 22784.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031578	C₂	1	2	yes	maximal, complemented
2	#26030831	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019780	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019775	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019736	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019731	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019668	C₂	1	2	yes	maximal, complemented
8	#26019661	C₂	1	2	yes	maximal, complemented
9	C₂×#19151349	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018948	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152148	C₂²	1	2	yes	—
13	#19152003	C₂²	1	1	yes	characteristic
14	#19151975	C₂²	1	1	yes	characteristic
15	#19151945	C₂²	1	2	yes	—
16	#19151895	—	2	2	no	—
17	#19151893	C₂²	1	2	yes	—
18	#19151888	C₂²	1	2	yes	—
19	#19151834	—	2	1	no	—
20	#19151834	—	2	1	no	—
21	#19151832	—	2	2	no	—
22	#19151829	—	2	2	no	—
23	#19151810	—	2	2	no	—
24	#19151798	C₂²	1	2	yes	—
25	#19151793	C₂²	1	2	yes	—
26	C₄×D₇₁₂	—	2	1	no	—
27	C₄×D₇₁₂	—	2	1	no	—
28	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
29	#19151349	C₂²	1	2	yes	—
30	#19151349	C₂²	1	1	yes	characteristic
31	#19151349	C₂²	1	1	yes	characteristic
32	#19151346	C₂²	1	2	yes	—
33	#19151346	C₂²	1	2	yes	—
34	#19151341	C₂²	1	2	yes	—
35	#19151341	C₂²	1	2	yes	—
36	#529×C₈₉	C₂²	1	1	yes	characteristic
37	#446×C₈₉	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#436×C₈₉	C₂²	1	1	yes	characteristic
40	#435×C₈₉	—	2	1	no	—
41	C₈×D₄×C₈₉	—	2	1	no	—
42	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
43	#433×C₈₉	—	2	1	no	—
44	#432×C₈₉	C₂²	1	1	yes	characteristic
45	#405×C₈₉	—	2	1	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	2	no	—
48	C₂×#13083561	—	2	2	no	—
49	C₂×D₇₁₂	—	2	1	no	—
50	C₂×D₇₁₂	—	2	1	no	—
51	C₂×#13083559	—	2	2	no	—
52	C₂²×#10623494	—	2	2	no	—
53	#15668012	C₂³	1	2	yes	—
54	#15668009	C₂³	1	2	yes	—
55	#15668000	—	2	2	no	—
56	#15667986	—	2	2	no	—
57	#15667986	—	2	2	no	—
58	C₄×D₃₅₆	—	2	2	no	—
59	C₄×D₃₅₆	—	2	2	no	—
60	#15667946	—	2	1	no	—
61	#15667946	—	2	1	no	—
62	#15667945	—	2	2	no	—
63	#15667943	—	2	2	no	—
64	C₄⋊#10623494	—	2	2	no	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	#15667936	—	2	2	no	—
68	#15667934	—	2	2	no	—
69	#15667934	—	2	2	no	—
70	#15667933	—	2	2	no	—
71	#15667932	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	C₂×M₁₆×C₈₉	—	2	1	no	—
74	C₂²×C₈×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
77	#126×C₈₉	—	2	1	no	—
78	#125×C₈₉	D₄	1	1	yes	characteristic
79	#124×C₈₉	D₄	1	1	yes	characteristic
80	#123×C₈₉	—	2	1	no	—
81	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
82	#121×C₈₉	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₈₉	—	2	1	no	—
85	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	#117×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₈₉	—	2	1	no	—
93	C₂²⋊C₈×C₈₉	—	2	1	no	—
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	#97×C₈₉	—	2	1	no	—
96	#97×C₈₉	—	2	1	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	#13083574	—	8	4	no	—
103	C₂×Dic₁₇₈	—	2	2	no	—
104	C₂×D₃₅₆	—	2	2	no	—
105	C₂×D₃₅₆	—	2	2	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×C₂²⋊D₈₉	—	4	2	no	—
108	C₂×C₄×D₈₉	—	4	2	no	—
109	#13083561	—	8	2	no	—
110	D₇₁₂	—	4	2	no	—
111	D₇₁₂	—	4	2	no	—
112	#13083559	—	8	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	8	2	no	—
116	C₄⋊Dic₈₉	—	2	2	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	#13083551	—	4	2	no	—
119	#13083551	—	4	2	no	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
127	M₁₆×C₈₉	—	4	2	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	4	1	no	—
132	C₂×C₈×C₈₉	—	4	2	no	—
133	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₈₉	#41	1	1	yes	characteristic
152	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂³×C₈₉	—	2	1	no	—
154	C₂³×C₈₉	#121	1	1	yes	characteristic
155	C₂²×D₈₉	—	4	2	no	—
156	Q₈×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	2	2	no	—
158	D₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₈₉	—	8	4	no	—
175	C₂×Dic₈₉	—	4	2	no	—
176	D₃₅₆	—	4	2	no	—
177	D₃₅₆	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	8	2	no	—
181	C₄×D₈₉	—	8	4	no	—
182	Dic₁₇₈	—	8	2	no	—
183	C₈×C₈₉	—	2	1	no	—
184	C₈×C₈₉	—	2	1	no	—
185	C₈×C₈₉	—	2	1	no	—
186	C₈×C₈₉	—	4	1	no	—
187	C₈×C₈₉	—	4	1	no	—
188	C₈×C₈₉	#135	1	2	yes	—
189	#10623494	—	4	2	no	—
190	#10623494	—	4	2	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	1	no	—
195	C₂²×C₈₉	—	4	1	no	—
196	C₂²×C₈₉	#472	1	2	yes	—
197	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
198	C₂×D₈₉	—	8	2	no	—
199	C₂×D₈₉	—	8	2	no	—
200	C₂×D₈₉	—	8	2	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	4	1	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	4	1	no	—
208	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
209	C₄×C₈₉	#575	1	1	yes	characteristic
210	C₄×C₈₉	#577	1	2	yes	—
211	Dic₈₉	—	8	2	no	—
212	#19227	—	89	1	no	maximal, Sylow
213	C₂×C₈₉	—	2	2	no	—
214	C₂×C₈₉	—	8	1	no	—
215	C₂×C₈₉	#3035	1	1	yes	characteristic
216	C₂×C₈₉	#3060	1	1	yes	characteristic
217	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
218	D₈₉	—	16	2	no	—
219	#3247	—	89	2	no	—
220	#3169	—	89	1	no	—
221	#2966	D₈₉	1	1	yes	characteristic, complemented
222	#1696	—	89	1	no	—
223	#1695	—	89	1	no	—
224	#1688	—	89	1	no	—
225	#1687	—	89	1	no	—
226	#1678	—	89	2	no	—
227	#1677	—	89	2	no	—
228	C₂×#334	—	89	1	no	—
229	#1551	—	89	2	no	—
230	C₈₉	#19227	1	1	yes	characteristic, complemented, Sylow
231	#532	—	89	2	no	—
232	#529	C₂×D₈₉	1	1	yes	characteristic
233	#500	—	89	1	no	—
234	#493	—	89	1	no	—
235	#486	—	89	2	no	—
236	#478	—	178	2	no	—
237	#477	—	89	2	no	—
238	#476	—	89	2	no	—
239	#466	—	178	1	no	—
240	#466	—	178	1	no	—
241	#466	—	178	2	no	—
242	#465	—	178	2	no	—
243	#463	—	178	2	no	—
244	#460	—	89	2	no	—
245	#459	—	89	2	no	—
246	#446	C₂×D₈₉	1	1	yes	characteristic
247	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
248	C₄×D₈	—	178	1	no	—
249	C₄×D₈	—	178	1	no	—
250	#436	C₂×D₈₉	1	1	yes	characteristic
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
254	#433	—	2	1	no	—
255	#432	C₂×D₈₉	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	89	2	no	—
257	#405	—	2	1	no	—
258	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
259	#334	—	89	2	no	—
260	#334	—	89	1	no	—
261	#334	—	89	1	no	—
262	#333	—	89	2	no	—
263	#333	—	89	2	no	—
264	#331	—	89	2	no	—
265	#331	—	89	2	no	—
266	C₂×#41	—	178	2	no	—
267	C₂×SD₁₆	—	178	2	no	—
268	C₂×D₈	—	178	2	no	—
269	C₂×D₈	—	178	1	no	—
270	C₂×D₈	—	178	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	178	2	no	—
274	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
276	C₄⋊Q₈	—	89	2	no	—
277	#127	—	89	2	no	—
278	#126	—	2	1	no	—
279	#125	D₃₅₆	1	1	yes	characteristic
280	#124	—	178	2	no	—
281	#124	D₃₅₆	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	D₃₅₆	1	1	yes	characteristic
284	#121	—	178	2	no	—
285	#121	—	178	2	no	—
286	#121	D₃₅₆	1	1	yes	characteristic
287	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	178	2	no	—
290	C₄×D₄	—	178	2	no	—
291	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
294	#107	—	178	1	no	—
295	#107	—	178	1	no	—
296	#107	—	178	2	no	—
297	#106	—	178	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	89	2	no	—
302	C₄⋊C₈	—	178	2	no	—
303	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
305	#103	—	178	2	no	—
306	#102	—	178	2	no	—
307	#102	—	178	2	no	—
308	#102	—	178	2	no	—
309	#102	—	178	2	no	—
310	#102	—	178	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
318	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
321	#41	—	712	4	no	—
322	C₂×Q₈	—	178	2	no	—
323	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	356	2	no	—
326	C₂×D₄	—	178	2	no	—
327	C₂×D₄	—	178	2	no	—
328	C₂×D₄	—	178	2	no	—
329	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	356	2	no	—
332	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
334	C₂²×C₄	#13083574	1	1	yes	characteristic
335	SD₁₆	—	712	2	no	—
336	D₈	—	356	2	no	—
337	D₈	—	356	2	no	—
338	D₈	—	712	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	178	2	no	—
346	C₂×C₈	—	178	2	no	—
347	C₂×C₈	—	712	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	178	2	no	—
357	C₄⋊C₄	—	178	2	no	—
358	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	356	2	no	—
366	C₂²⋊C₄	—	356	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
370	C₄²	#13083574	1	1	yes	characteristic
371	C₄²	C₂³×D₈₉	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	356	2	no	—
374	C₂³	#15667986	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	712	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	356	2	no	—
380	D₄	—	356	2	no	—
381	D₄	—	356	2	no	—
382	D₄	—	356	2	no	—
383	D₄	—	712	2	no	—
384	D₄	—	712	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	712	4	no	—
396	C₂×C₄	#15667986	1	1	yes	characteristic
397	C₂×C₄	#15667986	1	1	yes	characteristic
398	C₂×C₄	#15667986	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
401	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	356	2	no	—
408	C₈	—	356	2	no	—
409	C₈	#15668032	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	712	2	no	—
416	C₂²	—	712	2	no	—
417	C₂²	—	712	2	no	—
418	C₂²	#19151868	1	2	yes	—
419	C₂²	C₂×#15667986	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	712	2	no	—
428	C₄	C₂×#15668032	1	1	yes	characteristic
429	C₄	#19152396	1	1	yes	characteristic
430	C₄	#19152410	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	1424	2	no	—
434	C₂	#26029707	1	1	yes	characteristic
435	C₂	#26029914	1	1	yes	characteristic
436	C₂	C₂×#19151868	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2966	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	#2966	D₈₉
hypocenter	C₈₉	#19227
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #26031578	C₂	semidirect
2. #26030831	C₂	semidirect
3. #26019780	C₂	semidirect
4. #26019775	C₂	semidirect
5. #26019736	C₂	semidirect
6. #26019731	C₂	semidirect
7. #26019668	C₂	semidirect
8. #26019661	C₂	semidirect
9. C₂×#19151349	C₂	semidirect
10. #26018948	C₂	semidirect
11. C₈₉×#2966	C₂	semidirect
221. #2966	D₈₉	semidirect
230. C₈₉	#19227	semidirect

Maximal subgroups

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

subgroup	index
#26031578	2
#26030831	2
#26019780	2
#26019775	2
#26019736	2
#26019731	2
#26019668	2
#26019661	2
C₂×#19151349	2
#26018948	2
C₈₉×#2966	2
#19227	89