Subgroups — #36537853

Order 22784.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031224	C₂	1	2	yes	maximal, complemented
2	#26030831	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019770	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019765	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	#26019696	C₂	1	2	yes	maximal, complemented
8	#26019689	C₂	1	2	yes	maximal, complemented
9	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018958	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	#19151980	—	2	2	no	—
15	#19151975	C₂²	1	1	yes	characteristic
16	#19151955	—	2	2	no	—
17	#19151945	C₂²	1	2	yes	—
18	#19151834	—	2	1	no	—
19	#19151834	—	2	1	no	—
20	#19151808	C₂²	1	2	yes	—
21	#19151803	C₂²	1	2	yes	—
22	#19151798	C₂²	1	2	yes	—
23	#19151793	C₂²	1	2	yes	—
24	#19151758	—	2	2	no	—
25	#19151741	—	2	2	no	—
26	C₄×D₇₁₂	—	2	1	no	—
27	C₄×D₇₁₂	—	2	1	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	#19151343	C₂²	1	2	yes	—
33	#19151343	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×#13083564	—	2	2	no	—
49	C₂×#13083562	—	2	2	no	—
50	C₂×#13083561	—	2	2	no	—
51	C₂×D₇₁₂	—	2	1	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×#13083559	—	2	2	no	—
54	#15668012	C₂³	1	2	yes	—
55	#15668009	C₂³	1	2	yes	—
56	#15668000	—	2	2	no	—
57	#15667986	—	2	2	no	—
58	#15667986	—	2	2	no	—
59	C₄×D₃₅₆	—	2	2	no	—
60	C₄×D₃₅₆	—	2	2	no	—
61	#15667946	—	2	1	no	—
62	#15667946	—	2	1	no	—
63	C₄⋊#10623494	C₂³	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	2	yes	—
65	#15667935	—	2	2	no	—
66	#15667935	—	2	2	no	—
67	#15667934	—	2	2	no	—
68	#15667934	—	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×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	2	no	—
103	#13083574	—	8	2	no	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×D₃₅₆	—	2	2	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×D₃₅₆	—	2	2	no	—
108	C₂×C₂²⋊D₈₉	—	4	2	no	—
109	C₂×C₄×D₈₉	—	4	2	no	—
110	#13083564	—	8	2	no	—
111	#13083562	—	8	2	no	—
112	#13083561	—	8	2	no	—
113	D₇₁₂	—	4	2	no	—
114	D₇₁₂	—	4	2	no	—
115	#13083559	—	8	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	—	2	2	no	—
120	#13083551	—	4	2	no	—
121	#13083551	—	4	2	no	—
122	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	4	1	no	—
134	C₂×C₈×C₈₉	—	4	2	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	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₂²⋊C₄×C₈₉	—	2	1	no	—
147	C₂²⋊C₄×C₈₉	—	2	1	no	—
148	C₂²⋊C₄×C₈₉	—	2	1	no	—
149	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	#41	1	1	yes	characteristic
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	#121	1	1	yes	characteristic
157	C₂²×D₈₉	—	4	2	no	—
158	Q₈×C₈₉	—	2	2	no	—
159	D₄×C₈₉	—	2	2	no	—
160	D₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	1	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	#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	—	4	2	no	—
185	Dic₁₇₈	—	4	2	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	—	2	1	no	—
189	C₈×C₈₉	—	4	1	no	—
190	C₈×C₈₉	—	4	1	no	—
191	C₈×C₈₉	#135	1	2	yes	—
192	#10623494	—	4	2	no	—
193	#10623494	—	4	2	no	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	4	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	—	8	2	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	—	4	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
212	C₄×C₈₉	#575	1	1	yes	characteristic
213	C₄×C₈₉	#576	1	2	yes	—
214	Dic₈₉	—	8	2	no	—
215	#19225	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	4	1	no	—
217	C₂×C₈₉	—	8	1	no	—
218	C₂×C₈₉	#3035	1	1	yes	characteristic
219	C₂×C₈₉	#3058	1	1	yes	characteristic
220	C₂×C₈₉	#3067	1	1	yes	characteristic
221	D₈₉	—	16	2	no	—
222	#3212	—	89	2	no	—
223	#3169	—	89	1	no	—
224	#2966	D₈₉	1	1	yes	characteristic, complemented
225	#1694	—	89	1	no	—
226	#1693	—	89	1	no	—
227	#1688	—	89	1	no	—
228	#1687	—	89	1	no	—
229	#1682	—	89	2	no	—
230	#1681	—	89	2	no	—
231	#1564	—	89	1	no	—
232	#1553	—	89	2	no	—
233	C₈₉	#19225	1	1	yes	characteristic, complemented, Sylow
234	#532	—	89	2	no	—
235	#529	C₂×D₈₉	1	1	yes	characteristic
236	#500	—	89	1	no	—
237	#495	—	178	2	no	—
238	#493	—	89	1	no	—
239	#488	—	178	2	no	—
240	#486	—	89	2	no	—
241	#466	—	178	1	no	—
242	#466	—	178	1	no	—
243	#462	—	89	2	no	—
244	#461	—	89	2	no	—
245	#460	—	89	2	no	—
246	#459	—	89	2	no	—
247	#452	—	178	2	no	—
248	#449	—	178	2	no	—
249	#446	C₂×D₈₉	1	1	yes	characteristic
250	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
251	C₄×D₈	—	178	1	no	—
252	C₄×D₈	—	178	1	no	—
253	#436	C₂×D₈₉	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	C₈×D₄	—	2	1	no	—
256	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
257	#433	—	2	1	no	—
258	#432	C₂×D₈₉	1	1	yes	characteristic
259	#431	—	89	2	no	—
260	#405	—	2	1	no	—
261	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
262	#335	—	89	2	no	—
263	#334	—	89	1	no	—
264	#334	—	89	1	no	—
265	#332	—	89	2	no	—
266	#332	—	89	2	no	—
267	#331	—	89	2	no	—
268	#331	—	89	2	no	—
269	C₂×#41	—	178	2	no	—
270	C₂×Q₁₆	—	178	2	no	—
271	C₂×SD₁₆	—	178	2	no	—
272	C₂×SD₁₆	—	178	2	no	—
273	C₂×D₈	—	178	2	no	—
274	C₂×D₈	—	178	1	no	—
275	C₂×D₈	—	178	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
280	C₄⋊Q₈	—	89	2	no	—
281	#127	—	89	2	no	—
282	#126	—	2	1	no	—
283	#125	D₃₅₆	1	1	yes	characteristic
284	#124	—	178	2	no	—
285	#124	D₃₅₆	1	1	yes	characteristic
286	#123	—	2	1	no	—
287	C₂²⋊Q₈	D₃₅₆	1	1	yes	characteristic
288	#121	—	178	2	no	—
289	#121	—	178	2	no	—
290	#121	D₃₅₆	1	1	yes	characteristic
291	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	178	2	no	—
294	C₄×D₄	—	178	2	no	—
295	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
298	#107	—	178	1	no	—
299	#107	—	178	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	89	2	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
306	#103	—	178	2	no	—
307	#103	—	178	2	no	—
308	#102	—	178	2	no	—
309	#102	—	178	2	no	—
310	#102	—	178	2	no	—
311	#102	—	178	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	178	2	no	—
316	#97	—	2	1	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	178	2	no	—
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	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
324	#41	—	712	2	no	—
325	#41	—	712	2	no	—
326	C₂×Q₈	—	178	2	no	—
327	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	356	2	no	—
330	C₂×D₄	—	178	2	no	—
331	C₂×D₄	—	178	2	no	—
332	C₂×D₄	—	178	2	no	—
333	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	356	2	no	—
336	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
338	C₂²×C₄	#13083574	1	1	yes	characteristic
339	Q₁₆	—	712	2	no	—
340	SD₁₆	—	712	2	no	—
341	SD₁₆	—	712	2	no	—
342	D₈	—	356	2	no	—
343	D₈	—	356	2	no	—
344	D₈	—	712	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	—	4	2	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	—	178	2	no	—
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	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	178	2	no	—
362	C₄⋊C₄	—	178	2	no	—
363	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
364	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	356	2	no	—
371	C₂²⋊C₄	—	356	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
374	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
375	C₄²	#13083574	1	1	yes	characteristic
376	C₄²	C₂³×D₈₉	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	—	356	2	no	—
379	C₂³	#15667986	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	356	2	no	—
382	Q₈	—	356	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	356	2	no	—
386	D₄	—	356	2	no	—
387	D₄	—	356	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	712	2	no	—
390	D₄	—	712	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	356	2	no	—
401	C₂×C₄	—	712	4	no	—
402	C₂×C₄	#15667986	1	1	yes	characteristic
403	C₂×C₄	#15667986	1	1	yes	characteristic
404	C₂×C₄	#15667986	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
407	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	356	2	no	—
414	C₈	—	356	2	no	—
415	C₈	#15668032	1	2	yes	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	712	2	no	—
423	C₂²	—	712	2	no	—
424	C₂²	—	712	2	no	—
425	C₂²	C₂×#15667986	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	712	2	no	—
434	C₄	C₂×#15668032	1	1	yes	characteristic
435	C₄	#19152396	1	1	yes	characteristic
436	C₄	#19152403	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	1424	2	no	—
440	C₂	#26029707	1	1	yes	characteristic
441	C₂	#26029900	1	1	yes	characteristic
442	C₂	#26029972	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	#19225
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. #26031224	C₂	semidirect
2. #26030831	C₂	semidirect
3. #26019770	C₂	semidirect
4. #26019765	C₂	semidirect
5. #26019736	C₂	semidirect
6. #26019731	C₂	semidirect
7. #26019696	C₂	semidirect
8. #26019689	C₂	semidirect
9. #26019000	C₂	semidirect
10. #26018958	C₂	semidirect
11. C₈₉×#2966	C₂	semidirect
224. #2966	D₈₉	semidirect
233. C₈₉	#19225	semidirect

Maximal subgroups

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

subgroup	index
#26031224	2
#26030831	2
#26019770	2
#26019765	2
#26019736	2
#26019731	2
#26019696	2
#26019689	2
#26019000	2
#26018958	2
C₈₉×#2966	2
#19225	89