Subgroups — #36537174

Order 22784.

642 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	#26030831	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030312	C₂	1	2	yes	maximal, complemented
3	#26019792	C₂	1	2	yes	maximal, complemented
4	#26019785	C₂	1	2	yes	maximal, complemented
5	#26019780	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019775	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019736	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019731	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018912	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2965	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	#19151922	—	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	#19151798	C₂²	1	2	yes	—
22	#19151793	C₂²	1	2	yes	—
23	#19151743	—	2	2	no	—
24	C₄×#13083561	—	2	2	no	—
25	C₄×D₇₁₂	—	2	1	no	—
26	C₄×D₇₁₂	—	2	1	no	—
27	C₄×#13083559	—	2	2	no	—
28	#19151651	C₂²	1	2	yes	—
29	#19151351	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	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
37	#446×C₈₉	C₂²	1	1	yes	characteristic
38	#446×C₈₉	C₂²	1	1	yes	characteristic
39	#436×C₈₉	C₂²	1	1	yes	characteristic
40	#436×C₈₉	C₂²	1	1	yes	characteristic
41	#435×C₈₉	—	2	1	no	—
42	#435×C₈₉	—	2	1	no	—
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×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	#15668012	C₂³	1	2	yes	—
53	#15668009	C₂³	1	2	yes	—
54	#15668000	—	2	2	no	—
55	#15667986	—	2	2	no	—
56	#15667986	—	2	2	no	—
57	C₄×D₃₅₆	—	2	2	no	—
58	C₄×D₃₅₆	—	2	2	no	—
59	#15667946	—	2	1	no	—
60	#15667946	—	2	1	no	—
61	#15667945	—	2	2	no	—
62	#15667943	—	2	2	no	—
63	C₄⋊#10623494	C₂³	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	2	yes	—
65	#15667936	—	2	2	no	—
66	#15667934	—	2	2	no	—
67	#15667934	—	2	2	no	—
68	#15667933	—	2	2	no	—
69	#15667932	—	2	2	no	—
70	#15667932	—	2	2	no	—
71	C₂²⋊#10623494	—	2	2	no	—
72	C₄×#10623494	—	2	2	no	—
73	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₈₉	—	2	1	no	—
75	C₂×M₁₆×C₈₉	—	2	1	no	—
76	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	#117×C₈₉	—	2	1	no	—
85	#117×C₈₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×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	—	4	4	no	—
110	D₇₁₂	—	4	2	no	—
111	D₇₁₂	—	4	2	no	—
112	#13083559	—	4	4	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₄⋊Dic₈₉	—	2	2	no	—
116	C₄⋊Dic₈₉	—	2	2	no	—
117	#13083551	—	4	2	no	—
118	#13083551	—	4	2	no	—
119	#41×C₈₉	—	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	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	M₁₆×C₈₉	—	4	2	no	—
130	M₁₆×C₈₉	—	4	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	4	1	no	—
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₈₉	—	2	1	no	—
147	C₄²×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	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	2	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	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₈₉	—	8	4	no	—
177	C₂×Dic₈₉	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	—	4	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	4	2	no	—
182	D₃₅₆	—	8	2	no	—
183	C₄×D₈₉	—	8	4	no	—
184	Dic₁₇₈	—	8	2	no	—
185	C₈×C₈₉	—	2	1	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	—	4	1	no	—
189	C₈×C₈₉	—	4	1	no	—
190	C₈×C₈₉	#135	1	2	yes	—
191	#10623494	—	4	2	no	—
192	#10623494	—	4	2	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	4	1	no	—
197	C₂²×C₈₉	—	4	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
200	C₂×D₈₉	—	8	2	no	—
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	4	1	no	—
208	C₄×C₈₉	—	4	1	no	—
209	C₄×C₈₉	#472	1	2	yes	—
210	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
211	C₄×C₈₉	#575	1	1	yes	characteristic
212	C₄×C₈₉	#575	1	2	yes	—
213	Dic₈₉	—	8	2	no	—
214	#19160	—	89	1	no	maximal, Sylow
215	C₂×C₈₉	—	4	1	no	—
216	C₂×C₈₉	—	8	1	no	—
217	C₂×C₈₉	#3035	1	1	yes	characteristic
218	C₂×C₈₉	#3054	1	1	yes	characteristic
219	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
220	D₈₉	—	16	2	no	—
221	#3169	—	89	1	no	—
222	#3106	—	89	2	no	—
223	#2965	D₈₉	1	1	yes	characteristic, complemented
224	#1698	—	89	2	no	—
225	#1697	—	89	2	no	—
226	#1696	—	89	1	no	—
227	#1695	—	89	1	no	—
228	#1688	—	89	1	no	—
229	#1687	—	89	1	no	—
230	#1564	—	89	1	no	—
231	#1543	—	89	2	no	—
232	C₈₉	#19160	1	1	yes	characteristic, complemented, Sylow
233	#532	—	89	2	no	—
234	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
235	#500	—	89	1	no	—
236	#493	—	89	1	no	—
237	#486	—	89	2	no	—
238	#482	—	178	2	no	—
239	#477	—	89	2	no	—
240	#476	—	89	2	no	—
241	#466	—	178	1	no	—
242	#466	—	178	1	no	—
243	#460	—	89	2	no	—
244	#459	—	89	2	no	—
245	#449	—	178	2	no	—
246	#446	C₂×D₈₉	1	1	yes	characteristic
247	#446	C₂×D₈₉	1	1	yes	characteristic
248	C₄×SD₁₆	—	178	2	no	—
249	C₄×D₈	—	178	2	no	—
250	C₄×D₈	—	178	1	no	—
251	C₄×D₈	—	178	1	no	—
252	#436	C₂×D₈₉	1	1	yes	characteristic
253	#436	C₂×D₈₉	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	#435	—	2	1	no	—
256	#431	—	2	1	no	—
257	#431	—	89	2	no	—
258	#431	C₂×D₈₉	1	1	yes	characteristic
259	C₄×M₁₆	—	2	1	no	—
260	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
261	#335	—	89	2	no	—
262	#334	—	89	1	no	—
263	#334	—	89	1	no	—
264	#333	—	89	2	no	—
265	#333	—	89	2	no	—
266	#331	—	89	2	no	—
267	#331	—	89	2	no	—
268	C₂×#41	—	178	2	no	—
269	C₂×#41	D₃₅₆	1	1	yes	characteristic
270	C₂×SD₁₆	—	178	2	no	—
271	C₂×D₈	—	178	2	no	—
272	C₂×D₈	—	178	1	no	—
273	C₂×D₈	—	178	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
277	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
278	C₄⋊Q₈	—	89	2	no	—
279	#127	—	89	2	no	—
280	#124	—	178	2	no	—
281	#121	—	178	2	no	—
282	#121	—	178	2	no	—
283	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
284	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	178	2	no	—
288	C₄×D₄	—	178	2	no	—
289	C₄×D₄	D₃₅₆	1	1	yes	characteristic
290	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	#117	D₃₅₆	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
295	#107	—	178	1	no	—
296	#107	—	178	1	no	—
297	#107	—	178	2	no	—
298	#106	—	178	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	89	2	no	—
302	C₄⋊C₈	—	89	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	C₂²⋊C₈	—	178	2	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	178	2	no	—
319	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
320	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
323	#41	—	4	2	no	—
324	#41	—	712	4	no	—
325	C₂×Q₈	—	178	2	no	—
326	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	356	2	no	—
329	C₂×D₄	—	178	2	no	—
330	C₂×D₄	—	178	2	no	—
331	C₂×D₄	—	178	2	no	—
332	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	356	2	no	—
337	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
339	C₂²×C₄	#13083574	1	1	yes	characteristic
340	SD₁₆	—	356	4	no	—
341	D₈	—	356	2	no	—
342	D₈	—	356	4	no	—
343	D₈	—	356	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	178	2	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	178	2	no	—
359	C₄⋊C₄	—	178	2	no	—
360	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
361	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
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	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
371	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
372	C₄²	#13083574	1	1	yes	characteristic
373	C₄²	C₂³×D₈₉	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	356	2	no	—
376	C₂³	#15667986	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	712	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	356	2	no	—
382	D₄	—	356	2	no	—
383	D₄	—	356	2	no	—
384	D₄	—	356	2	no	—
385	D₄	—	712	2	no	—
386	D₄	—	712	4	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	356	2	no	—
399	C₂×C₄	—	712	4	no	—
400	C₂×C₄	#15667986	1	1	yes	characteristic
401	C₂×C₄	#15667986	1	1	yes	characteristic
402	C₂×C₄	#15667986	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	356	2	no	—
412	C₈	—	356	2	no	—
413	C₈	#15668032	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	712	2	no	—
421	C₂²	—	712	2	no	—
422	C₂²	—	712	2	no	—
423	C₂²	C₂×#15667986	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	712	2	no	—
431	C₄	#19151868	1	2	yes	—
432	C₄	C₂×#15668032	1	1	yes	characteristic
433	C₄	#19152396	1	1	yes	characteristic
434	C₄	#19152398	1	2	yes	—
435	C₂	—	4	1	no	—
436	C₂	—	8	1	no	—
437	C₂	—	1424	2	no	—
438	C₂	#26029707	1	1	yes	characteristic
439	C₂	#26029861	1	1	yes	characteristic
440	C₂	C₂×#19151868	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2965	C₂
socle	C₂²×C₈₉	C₂×#121
hypercenter	#2965	D₈₉
hypocenter	C₈₉	#19160
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #26030831	C₂	semidirect
2. #26030312	C₂	semidirect
3. #26019792	C₂	semidirect
4. #26019785	C₂	semidirect
5. #26019780	C₂	semidirect
6. #26019775	C₂	semidirect
7. #26019736	C₂	semidirect
8. #26019731	C₂	semidirect
9. #26019000	C₂	semidirect
10. #26018912	C₂	semidirect
11. C₈₉×#2965	C₂	semidirect
223. #2965	D₈₉	semidirect
232. C₈₉	#19160	semidirect

Maximal subgroups

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

subgroup	index
#26030831	2
#26030312	2
#26019792	2
#26019785	2
#26019780	2
#26019775	2
#26019736	2
#26019731	2
#26019000	2
#26018912	2
C₈₉×#2965	2
#19160	89