Subgroups — #36539831

Order 22784.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031195	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030040	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029732	C₂	1	1	yes	maximal, characteristic
4	#26019668	C₂	1	2	yes	maximal, complemented
5	#26019661	C₂	1	2	yes	maximal, complemented
6	#26019600	C₂	1	2	yes	maximal, complemented
7	#26019593	C₂	1	2	yes	maximal, complemented
8	#26019023	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	C₂×#15668009	C₂²	1	1	yes	characteristic
15	#19151971	C₂²	1	2	yes	—
16	#19151945	C₂²	1	2	yes	—
17	#19151905	—	2	1	no	—
18	#19151898	—	2	1	no	—
19	#19151893	C₂²	1	1	yes	characteristic, complemented
20	#19151888	C₂²	1	1	yes	characteristic, complemented
21	#19151883	C₂²	1	1	yes	characteristic, complemented
22	#19151878	C₂²	1	1	yes	characteristic, complemented
23	#19151799	—	2	1	no	—
24	#19151799	—	2	1	no	—
25	#19151798	—	2	1	no	—
26	#19151798	C₂²	1	2	yes	—
27	#19151793	—	2	1	no	—
28	#19151793	C₂²	1	2	yes	—
29	#19151751	—	2	2	no	—
30	#19151634	—	2	1	no	—
31	#19151622	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
33	#19151602	—	2	1	no	—
34	#19151594	—	2	1	no	—
35	#19151349	C₂²	1	2	yes	complemented
36	#19151349	C₂²	1	2	yes	complemented
37	#19151346	C₂²	1	2	yes	complemented
38	#19151345	C₂²	1	2	yes	complemented
39	#19151341	C₂²	1	2	yes	—
40	#19151341	C₂²	1	2	yes	—
41	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
42	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
43	C₈×D₄×C₈₉	—	2	2	no	—
44	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
45	#431×C₈₉	—	2	1	no	—
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
48	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×D₃₅₆	—	2	1	no	—
50	C₂²×D₃₅₆	—	2	1	no	—
51	C₂²×D₃₅₆	—	2	1	no	—
52	#15668037	—	4	4	no	—
53	C₂×#13083563	—	2	2	no	—
54	C₂×#13083563	—	2	2	no	—
55	C₂×#13083561	—	2	2	no	—
56	C₂×#13083559	—	2	2	no	—
57	C₂×#13083558	—	2	1	no	—
58	C₂²×#10623494	—	2	1	no	—
59	#15668012	C₂³	1	1	yes	characteristic
60	#15668012	C₂³	1	1	yes	characteristic
61	#15668009	—	2	1	no	—
62	#15668009	—	2	1	no	—
63	#15668009	—	2	1	no	—
64	#15668009	C₂³	1	2	yes	—
65	#15668004	—	2	1	no	—
66	#15667991	—	2	1	no	—
67	#15667991	—	2	1	no	—
68	C₄×Dic₁₇₈	—	2	1	no	—
69	C₄×Dic₁₇₈	—	2	1	no	—
70	#15667971	—	2	1	no	—
71	#15667945	—	2	1	no	—
72	#15667945	—	2	1	no	—
73	#15667943	—	2	1	no	—
74	#15667943	—	2	1	no	—
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	C₄⋊#10623494	C₂³	1	2	yes	—
80	#15667936	—	2	1	no	—
81	#15667936	—	2	1	no	—
82	#15667934	—	2	2	no	—
83	#15667934	—	2	2	no	—
84	#15667933	—	2	1	no	—
85	#15667933	—	2	1	no	—
86	#15667932	—	2	2	no	—
87	#15667932	—	2	2	no	—
88	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	—	2	1	no	—
90	C₂²×C₈×C₈₉	—	2	2	no	—
91	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	—	2	1	no	—
95	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
96	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
97	#117×C₈₉	—	2	1	no	—
98	#117×C₈₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	—	2	2	no	—
102	C₄⋊C₈×C₈₉	—	2	1	no	—
103	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
106	C₂²⋊C₈×C₈₉	—	2	2	no	—
107	C₂²⋊C₈×C₈₉	D₄	1	2	yes	—
108	C₄×C₈×C₈₉	—	2	2	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	C₂³×D₈₉	—	4	1	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×D₃₅₆	—	2	2	no	—
114	C₂×D₃₅₆	—	2	2	no	—
115	C₂×D₃₅₆	—	2	2	no	—
116	C₂×D₃₅₆	—	4	2	no	—
117	C₂×D₃₅₆	—	4	2	no	—
118	C₂×D₃₅₆	—	4	1	no	—
119	C₂×D₃₅₆	—	4	1	no	—
120	C₂×D₃₅₆	—	4	1	no	—
121	C₂×D₃₅₆	—	8	1	no	—
122	C₂×D₃₅₆	—	8	1	no	—
123	C₂×D₃₅₆	—	8	2	no	—
124	#13083563	—	8	2	no	—
125	#13083563	—	8	2	no	—
126	#13083561	—	4	4	no	—
127	#13083559	—	4	4	no	—
128	#13083558	—	4	2	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	2	2	no	—
132	C₂×#10623494	—	4	2	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	#13083553	—	4	1	no	—
138	#13083553	—	4	1	no	—
139	C₂²⋊Dic₈₉	—	4	1	no	—
140	C₄×Dic₈₉	—	4	1	no	—
141	#41×C₈₉	—	2	2	no	—
142	#41×C₈₉	SD₁₆	1	4	yes	complemented
143	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₈₉	—	2	1	no	—
145	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	8	2	no	—
154	C₂×C₈×C₈₉	—	8	1	no	—
155	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₈₉	—	2	1	no	—
162	C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₂²⋊C₄×C₈₉	—	2	1	no	—
164	C₄²×C₈₉	—	2	1	no	—
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	—	2	1	no	—
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	#41	1	1	yes	characteristic
170	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₂³×C₈₉	—	2	1	no	—
172	C₂³×C₈₉	#121	1	1	yes	characteristic
173	C₂²×D₈₉	—	4	2	no	—
174	C₂²×D₈₉	—	8	2	no	—
175	C₂²×D₈₉	—	8	2	no	—
176	C₂²×D₈₉	—	8	2	no	—
177	Q₈×C₈₉	—	2	1	no	—
178	Q₈×C₈₉	C₂×SD₁₆	1	2	yes	—
179	D₄×C₈₉	—	2	4	no	—
180	D₄×C₈₉	—	2	1	no	—
181	D₄×C₈₉	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	8	1	no	—
192	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
196	C₂×C₄×C₈₉	#135	1	2	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₈₉	—	4	1	no	—
201	C₂×Dic₈₉	—	4	1	no	—
202	D₃₅₆	—	4	2	no	—
203	D₃₅₆	—	4	2	no	—
204	D₃₅₆	—	4	2	no	—
205	D₃₅₆	—	4	2	no	—
206	D₃₅₆	—	8	2	no	—
207	D₃₅₆	—	8	2	no	—
208	D₃₅₆	—	8	2	no	—
209	D₃₅₆	—	8	2	no	—
210	Dic₁₇₈	—	4	1	no	—
211	Dic₁₇₈	—	4	1	no	—
212	Dic₁₇₈	—	8	1	no	—
213	C₈×C₈₉	—	2	2	no	—
214	C₈×C₈₉	—	2	2	no	—
215	C₈×C₈₉	—	4	2	no	—
216	#10623494	—	4	2	no	—
217	#10623494	—	4	1	no	—
218	#10623494	—	4	1	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	2	no	—
222	C₂²×C₈₉	—	4	1	no	—
223	C₂²×C₈₉	—	4	1	no	—
224	C₂²×C₈₉	#465	1	2	yes	—
225	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
226	C₂×D₈₉	—	8	2	no	—
227	C₂×D₈₉	—	8	2	no	—
228	C₂×D₈₉	—	8	2	no	—
229	C₂×D₈₉	—	16	4	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	2	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	2	1	no	—
234	C₄×C₈₉	—	4	1	no	—
235	C₄×C₈₉	—	4	1	no	—
236	C₄×C₈₉	#465	1	2	yes	—
237	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
238	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
239	C₄×C₈₉	#576	1	1	yes	characteristic
240	C₄×C₈₉	#577	1	1	yes	characteristic
241	Dic₈₉	—	8	1	no	—
242	Dic₈₉	—	8	1	no	—
243	#19409	—	89	1	no	maximal, Sylow
244	C₂×C₈₉	—	2	2	no	—
245	C₂×C₈₉	—	4	2	no	—
246	C₂×C₈₉	#3045	1	1	yes	characteristic
247	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
248	C₂×C₈₉	#3068	1	1	yes	characteristic
249	D₈₉	—	16	2	no	—
250	#3208	—	89	1	no	—
251	#3076	—	89	1	no	—
252	#3038	—	89	1	no	—
253	#2988	D₈₉	1	1	yes	characteristic, complemented
254	#1678	—	89	2	no	—
255	#1677	—	89	2	no	—
256	#1666	—	89	2	no	—
257	#1665	—	89	2	no	—
258	#1570	—	89	1	no	—
259	#1550	—	89	1	no	—
260	C₂×#331	—	89	1	no	—
261	C₈₉	#19409	1	1	yes	characteristic, complemented, Sylow
262	C₂×AGL(1,ℤ/8)	—	178	1	no	—
263	#533	—	89	1	no	—
264	C₂×#127	—	89	1	no	—
265	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
266	#492	—	89	2	no	—
267	#486	—	89	2	no	—
268	#479	—	178	1	no	—
269	#478	—	178	1	no	—
270	#477	—	89	1	no	—
271	#476	—	89	1	no	—
272	#475	—	89	1	no	—
273	#474	—	89	1	no	—
274	#460	—	89	2	no	—
275	#460	—	178	1	no	—
276	#460	—	178	1	no	—
277	#460	—	178	1	no	—
278	#459	—	89	2	no	—
279	#459	—	178	1	no	—
280	#450	—	178	2	no	—
281	C₈×Q₈	C₂×D₈₉	1	2	yes	complemented
282	C₈×D₄	—	2	2	no	—
283	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
284	#431	—	2	1	no	—
285	#431	C₂×D₈₉	1	1	yes	characteristic
286	#427	—	178	1	no	—
287	#423	—	89	1	no	—
288	C₂×C₄⋊C₈	—	2	1	no	—
289	C₂×C₄⋊C₈	—	89	1	no	—
290	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
291	#418	—	178	1	no	—
292	#416	—	178	1	no	—
293	#334	—	89	2	no	—
294	#334	—	89	2	no	—
295	#333	—	89	2	no	—
296	#332	—	89	2	no	—
297	#331	—	89	2	no	—
298	#331	—	89	2	no	—
299	C₂×#41	D₃₅₆	1	1	yes	characteristic
300	C₂²×D₄	—	178	1	no	—
301	C₂²×D₄	—	178	1	no	—
302	C₂²×D₄	—	178	1	no	—
303	AGL(1,ℤ/8)	—	356	4	no	—
304	C₂×SD₁₆	—	178	2	no	—
305	C₂×SD₁₆	—	178	2	no	—
306	C₂×SD₁₆	—	178	2	no	—
307	C₂×D₈	—	178	2	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	178	1	no	—
312	C₄⋊Q₈	—	89	1	no	—
313	C₄⋊Q₈	—	89	1	no	—
314	#127	—	89	2	no	—
315	#127	—	178	1	no	—
316	#127	—	178	1	no	—
317	#127	—	178	1	no	—
318	#125	—	178	1	no	—
319	C₂²⋊Q₈	—	178	1	no	—
320	C₂²⋊Q₈	—	178	1	no	—
321	C₄×Q₈	—	178	1	no	—
322	C₄×Q₈	—	178	1	no	—
323	C₄×Q₈	D₃₅₆	1	1	yes	characteristic
324	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	D₃₅₆	1	1	yes	characteristic
328	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
329	#117	—	2	1	no	—
330	#117	—	178	1	no	—
331	#117	D₃₅₆	1	1	yes	characteristic
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
334	#107	—	178	1	no	—
335	#107	—	178	1	no	—
336	#106	—	178	1	no	—
337	#106	—	178	1	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	89	1	no	—
341	C₄⋊C₈	—	89	1	no	—
342	C₄⋊C₈	—	89	2	no	—
343	C₄⋊C₈	—	178	1	no	—
344	C₄⋊C₈	—	178	1	no	—
345	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
346	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
347	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
348	#103	—	178	1	no	—
349	#103	—	178	1	no	—
350	#102	—	178	1	no	—
351	#102	—	178	1	no	—
352	#102	—	178	2	no	—
353	#102	—	178	2	no	—
354	#102	—	178	2	no	—
355	#102	—	178	2	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	C₂²⋊C₈	C₂²⋊D₈₉	1	2	yes	—
358	C₄×C₈	—	2	2	no	—
359	C₄×C₈	C₂²×D₈₉	1	2	yes	—
360	C₂⁴	—	356	1	no	—
361	#41	—	2	2	no	—
362	#41	#13083563	1	4	yes	complemented
363	C₂×Q₈	—	178	1	no	—
364	C₂×Q₈	—	178	1	no	—
365	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	356	1	no	—
368	C₂×D₄	—	356	1	no	—
369	C₂×D₄	—	356	1	no	—
370	C₂×D₄	—	356	2	no	—
371	C₂×D₄	—	356	2	no	—
372	C₂×D₄	—	178	2	no	—
373	C₂×D₄	—	178	2	no	—
374	C₂×D₄	—	178	2	no	—
375	C₂×D₄	—	712	1	no	—
376	C₂×D₄	—	712	1	no	—
377	C₂×D₄	—	712	2	no	—
378	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
384	C₂²×C₄	#13083574	1	1	yes	characteristic
385	SD₁₆	—	356	4	no	—
386	SD₁₆	—	712	2	no	—
387	SD₁₆	—	712	2	no	—
388	D₈	—	356	4	no	—
389	M₁₆	—	356	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	8	2	no	—
392	C₂×C₈	—	8	1	no	—
393	C₂×C₈	—	356	2	no	—
394	C₂×C₈	—	178	2	no	—
395	C₂×C₈	—	178	1	no	—
396	C₂×C₈	—	178	1	no	—
397	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
398	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	356	1	no	—
402	C₄⋊C₄	—	356	1	no	—
403	C₄⋊C₄	—	178	1	no	—
404	C₄⋊C₄	—	178	1	no	—
405	C₄⋊C₄	—	178	1	no	—
406	C₄⋊C₄	—	178	1	no	—
407	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₃₅₆	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	356	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	356	1	no	—
417	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
418	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
419	C₄²	#13083574	1	1	yes	characteristic
420	C₄²	C₂³×D₈₉	1	1	yes	characteristic
421	C₂³	—	2	1	no	—
422	C₂³	—	356	2	no	—
423	C₂³	—	712	2	no	—
424	C₂³	—	712	2	no	—
425	C₂³	—	712	2	no	—
426	C₂³	#15667986	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	356	1	no	—
429	Q₈	—	356	1	no	—
430	Q₈	—	712	1	no	—
431	Q₈	C₂×#13083563	1	2	yes	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	356	2	no	—
435	D₄	—	356	2	no	—
436	D₄	—	356	2	no	—
437	D₄	—	356	2	no	—
438	D₄	—	712	2	no	—
439	D₄	—	712	2	no	—
440	D₄	—	712	2	no	—
441	D₄	—	712	2	no	—
442	D₄	C₂×#13083563	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	356	1	no	—
454	C₂×C₄	—	356	1	no	—
455	C₂×C₄	#15667986	1	1	yes	characteristic
456	C₂×C₄	#15667986	1	1	yes	characteristic
457	C₂×C₄	#15667986	1	1	yes	characteristic
458	C₂×C₄	C₂×#13083563	1	2	yes	—
459	C₂×C₄	#15668034	1	2	yes	—
460	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
462	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	356	2	no	—
467	C₈	—	356	1	no	—
468	C₈	—	356	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	1424	4	no	—
475	C₂²	—	712	2	no	—
476	C₂²	—	712	2	no	—
477	C₂²	—	712	2	no	—
478	C₂²	#19151827	1	2	yes	—
479	C₂²	C₂×#15667986	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	712	1	no	—
487	C₄	—	712	1	no	—
488	C₄	#19151827	1	2	yes	—
489	C₄	C₂²×#13083563	1	1	yes	characteristic
490	C₄	C₂×#15668034	1	1	yes	characteristic
491	C₄	#19152401	1	1	yes	characteristic
492	C₄	#19152406	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	1424	2	no	—
496	C₂	#26029791	1	1	yes	characteristic
497	C₂	C₂×#19151827	1	1	yes	characteristic
498	C₂	#26029980	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2988	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26029732	C₂
hypercenter	#2988	D₈₉
hypocenter	C₈₉	#19409
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2988

Complements

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

N	H ≅ G/N	type
1. #26031195	C₂	semidirect
2. #26030040	C₂	semidirect
4. #26019668	C₂	semidirect
5. #26019661	C₂	semidirect
6. #26019600	C₂	semidirect
7. #26019593	C₂	semidirect
8. #26019023	C₂	semidirect
9. #26018940	C₂	semidirect
10. C₂×#19151341	C₂	semidirect
11. C₈₉×#2988	C₂	semidirect
19. #19151893	C₂²	semidirect
20. #19151888	C₂²	semidirect
21. #19151883	C₂²	semidirect
22. #19151878	C₂²	semidirect
35. #19151349	C₂²	semidirect
36. #19151349	C₂²	semidirect
37. #19151346	C₂²	semidirect
38. #19151345	C₂²	semidirect
42. C₈×Q₈×C₈₉	C₂²	semidirect
44. C₈×D₄×C₈₉	C₂²	semidirect
142. #41×C₈₉	SD₁₆	semidirect
253. #2988	D₈₉	semidirect
261. C₈₉	#19409	semidirect
281. C₈×Q₈	C₂×D₈₉	semidirect
283. C₈×D₄	C₂×D₈₉	semidirect
362. #41	#13083563	semidirect

Maximal subgroups

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

subgroup	index
#26031195	2
#26030040	2
#26029732	2
#26019668	2
#26019661	2
#26019600	2
#26019593	2
#26019023	2
#26018940	2
C₂×#19151341	2
C₈₉×#2988	2
#19409	89