Subgroups — #37548291

Order 23168.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042033	C₂	1	2	yes	maximal, complemented
2	#26042023	C₂	1	2	yes	maximal, complemented
3	#26042002	C₂	1	2	yes	maximal, complemented
4	#26041952	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₃₆₂	C₂	1	2	yes	maximal, complemented
6	#26041938	C₂	1	2	yes	maximal, complemented
7	#26041925	C₂	1	2	yes	maximal, complemented
8	#26041904	C₂	1	2	yes	maximal, complemented
9	#26041900	C₂	1	2	yes	maximal, complemented
10	#26041895	C₂	1	4	yes	maximal, complemented
11	#26041866	C₂	1	2	yes	maximal, complemented
12	#26041855	C₂	1	2	yes	maximal, complemented
13	#26041836	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19153804	C₂	1	1	yes	maximal, characteristic, complemented
15	#529×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668449	C₂²	1	2	yes	—
17	C₂²×Dic₃₆₂	C₂²	1	1	yes	characteristic
18	C₂²×Dic₃₆₂	C₂²	1	2	yes	complemented
19	C₂²×D₇₂₄	C₂²	1	1	yes	characteristic
20	#19153816	C₂²	1	1	yes	characteristic, complemented
21	#19153816	C₂²	1	2	yes	complemented
22	#19153816	C₂²	1	1	yes	characteristic, complemented
23	#19153815	C₂²	1	4	yes	complemented
24	#19153811	C₂²	1	4	yes	complemented
25	#19153811	C₂²	1	4	yes	complemented
26	#19153811	C₂²	1	4	yes	complemented
27	#19153808	C₂²	1	2	yes	complemented
28	#19153804	C₂²	1	2	yes	—
29	#19153804	C₂²	1	2	yes	—
30	#19153804	C₂²	1	2	yes	—
31	#19153804	C₂²	1	2	yes	—
32	#19153804	C₂²	1	2	yes	—
33	#19153802	C₂²	1	4	yes	complemented
34	#19153802	C₂²	1	4	yes	complemented
35	#19153801	C₂²	1	4	yes	—
36	#19153800	C₂²	1	4	yes	complemented
37	#19153800	C₂²	1	4	yes	complemented
38	#19153798	C₂²	1	4	yes	complemented
39	#19153796	C₂²	1	4	yes	complemented
40	#19153796	C₂²	1	4	yes	complemented
41	#19153795	C₂²	1	2	yes	—
42	#19153795	C₂²	1	2	yes	—
43	#19153795	C₂²	1	2	yes	complemented
44	#19153794	C₂²	1	4	yes	complemented
45	#19153794	C₂²	1	4	yes	complemented
46	#19153793	C₂²	1	4	yes	—
47	#19153793	C₂²	1	4	yes	complemented
48	#19153792	C₂²	1	4	yes	complemented
49	#19153790	C₂²	1	2	yes	—
50	#19153789	C₂²	1	4	yes	—
51	#19153788	C₂²	1	4	yes	complemented
52	#19153784	C₂²	1	4	yes	—
53	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
54	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
55	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
56	C₄×D₇₂₄	C₂²	1	2	yes	—
57	D₄×Dic₁₈₁	C₂²	1	4	yes	—
58	#19153776	C₂²	1	4	yes	complemented
59	#19153775	C₂²	1	2	yes	—
60	#19153774	C₂²	1	4	yes	complemented
61	C₂×#15668426	C₂²	1	2	yes	—
62	C₂×#15668426	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₁₈₁	C₂²	1	4	yes	—
64	#126×C₁₈₁	C₂²	1	2	yes	complemented
65	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
66	#124×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
67	#123×C₁₈₁	C₂²	1	2	yes	—
68	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic
69	#121×C₁₈₁	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₁₈₁	C₂²	1	2	yes	—
72	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
73	#117×C₁₈₁	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₁₈₁	C₂²	1	1	yes	characteristic
75	C₂³×D₁₈₁	C₂³	1	2	yes	—
76	#15668449	—	4	4	no	—
77	C₂×Dic₃₆₂	—	4	2	no	—
78	C₂×Dic₃₆₂	—	4	4	no	—
79	C₂×Dic₃₆₂	C₂³	1	2	yes	—
80	C₂×Dic₃₆₂	C₂³	1	2	yes	—
81	C₂×Dic₃₆₂	C₂³	1	2	yes	—
82	C₂×Dic₃₆₂	C₂³	1	4	yes	—
83	C₂×Dic₃₆₂	C₂³	1	2	yes	—
84	C₂×D₇₂₄	—	4	2	no	—
85	C₂×D₇₂₄	C₂³	1	2	yes	—
86	C₂×D₇₂₄	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₈₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₈₁	C₂³	1	4	yes	—
89	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
90	C₂²×Dic₁₈₁	C₂³	1	4	yes	—
91	C₂×C₄×D₁₈₁	C₂³	1	4	yes	—
92	C₂×C₄×D₁₈₁	C₂³	1	4	yes	—
93	C₄⋊Dic₁₈₁	C₂³	1	4	yes	—
94	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
95	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
96	C₄⋊Dic₁₈₁	C₂³	1	4	yes	—
97	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
98	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
99	#15668428	C₂³	1	4	yes	—
100	#15668428	C₂³	1	4	yes	—
101	#15668428	C₂³	1	4	yes	—
102	#15668428	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₈₁	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₈₁	C₂³	1	4	yes	—
105	#15668426	C₂³	1	4	yes	—
106	#15668426	C₂³	1	4	yes	—
107	#15668426	C₂³	1	4	yes	—
108	#15668426	C₂³	1	4	yes	—
109	#15668426	C₂³	1	4	yes	—
110	#15668426	C₂³	1	4	yes	—
111	#15668426	C₂³	1	4	yes	—
112	#15668426	C₂³	1	4	yes	—
113	C₄×Dic₁₈₁	C₂³	1	4	yes	—
114	C₄×Dic₁₈₁	C₂³	1	4	yes	—
115	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
117	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
123	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
124	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
126	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
127	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
133	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
134	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
135	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
136	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
137	C₄²×C₁₈₁	C₂³	1	2	yes	—
138	C₂²×D₁₈₁	—	2	4	no	—
139	C₂²×D₁₈₁	—	4	2	no	—
140	C₂²×D₁₈₁	—	4	2	no	—
141	C₂²×D₁₈₁	C₂⁴	1	4	yes	—
142	Dic₃₆₂	—	2	4	no	—
143	Dic₃₆₂	—	2	4	no	—
144	Dic₃₆₂	—	4	4	no	—
145	Dic₃₆₂	—	4	2	no	—
146	Dic₃₆₂	—	4	2	no	—
147	D₇₂₄	—	2	4	no	—
148	D₇₂₄	—	4	2	no	—
149	C₂²⋊D₁₈₁	—	4	4	no	—
150	C₂²⋊D₁₈₁	—	4	4	no	—
151	C₂×Dic₁₈₁	—	4	4	no	—
152	C₂×Dic₁₈₁	—	4	2	no	—
153	C₂×Dic₁₈₁	C₂⁴	1	4	yes	—
154	C₂×Dic₁₈₁	C₂⁴	1	4	yes	—
155	C₂×Dic₁₈₁	C₂⁴	1	4	yes	—
156	C₄×D₁₈₁	—	4	4	no	—
157	C₄×D₁₈₁	—	4	4	no	—
158	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
159	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₈₁	—	4	1	no	—
161	D₄×C₁₈₁	—	2	4	no	—
162	D₄×C₁₈₁	—	4	1	no	—
163	C₂×C₄×C₁₈₁	—	2	2	no	—
164	C₂×C₄×C₁₈₁	—	2	2	no	—
165	C₂×C₄×C₁₈₁	—	2	4	no	—
166	C₂×C₄×C₁₈₁	—	4	1	no	—
167	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
176	C₂²×C₁₈₁	—	2	1	no	—
177	C₂²×C₁₈₁	—	2	1	no	—
178	C₂²×C₁₈₁	—	2	2	no	—
179	C₂²×C₁₈₁	—	2	2	no	—
180	C₂²×C₁₈₁	—	2	2	no	—
181	C₂²×C₁₈₁	2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
183	C₂×D₁₈₁	—	2	4	no	—
184	C₂×D₁₈₁	—	2	4	no	—
185	C₂×D₁₈₁	—	2	4	no	—
186	C₂×D₁₈₁	—	8	4	no	—
187	C₄×C₁₈₁	—	2	2	no	—
188	C₄×C₁₈₁	—	2	1	no	—
189	C₄×C₁₈₁	—	2	1	no	—
190	C₄×C₁₈₁	—	2	1	no	—
191	C₄×C₁₈₁	—	2	2	no	—
192	C₄×C₁₈₁	—	2	1	no	—
193	C₄×C₁₈₁	—	2	1	no	—
194	C₄×C₁₈₁	—	2	2	no	—
195	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
196	Dic₁₈₁	—	2	4	no	—
197	Dic₁₈₁	—	2	4	no	—
198	Dic₁₈₁	—	2	4	no	—
199	C₂×C₁₈₁	—	2	2	no	—
200	C₂×C₁₈₁	—	4	2	no	—
201	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₁₈₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₁₈₁	#585	1	1	yes	characteristic
204	D₁₈₁	—	4	4	no	—
205	C₁₈₁	#3561	1	1	yes	characteristic, complemented, Sylow
206	#3561	—	181	1	no	maximal, Sylow
207	#563	—	181	2	no	—
208	#562	—	181	2	no	—
209	#556	—	181	2	no	—
210	#551	—	181	4	no	—
211	D₄×Q₈	—	181	2	no	—
212	#548	—	181	2	no	—
213	#546	—	181	2	no	—
214	#543	—	181	2	no	—
215	#542	—	181	4	no	—
216	#542	—	181	2	no	—
217	#538	—	181	2	no	—
218	#536	—	181	2	no	—
219	#533	—	181	1	no	—
220	#529	D₁₈₁	1	1	yes	characteristic, complemented
221	C₂×#124	—	181	1	no	—
222	C₂×#41	—	181	2	no	—
223	C₂²×Q₈	—	181	1	no	—
224	C₂²×Q₈	—	181	2	no	—
225	C₂²×D₄	—	181	1	no	—
226	C₄⋊Q₈	—	181	4	no	—
227	C₄⋊Q₈	—	181	1	no	—
228	C₄⋊Q₈	—	181	1	no	—
229	C₄⋊Q₈	—	181	2	no	—
230	#126	—	181	4	no	—
231	#126	—	181	4	no	—
232	#126	—	181	4	no	—
233	#126	C₂×D₁₈₁	1	2	yes	complemented
234	#125	—	181	2	no	—
235	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
236	#124	—	181	4	no	—
237	#124	—	181	4	no	—
238	#124	—	181	2	no	—
239	#124	—	181	2	no	—
240	#124	—	181	2	no	—
241	#124	—	181	2	no	—
242	#124	—	181	2	no	—
243	#124	C₂×D₁₈₁	1	1	yes	characteristic, complemented
244	#123	—	181	4	no	—
245	#123	—	181	4	no	—
246	#123	—	181	4	no	—
247	#123	—	181	4	no	—
248	#123	C₂×D₁₈₁	1	2	yes	—
249	C₂²⋊Q₈	—	181	4	no	—
250	C₂²⋊Q₈	—	181	2	no	—
251	C₂²⋊Q₈	—	181	2	no	—
252	C₂²⋊Q₈	—	181	2	no	—
253	C₂²⋊Q₈	—	181	4	no	—
254	C₂²⋊Q₈	—	181	4	no	—
255	C₂²⋊Q₈	—	181	4	no	—
256	C₂²⋊Q₈	—	181	4	no	—
257	C₂²⋊Q₈	—	181	4	no	—
258	C₂²⋊Q₈	—	181	4	no	—
259	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic
260	#121	—	181	4	no	—
261	#121	—	181	2	no	—
262	#121	—	181	4	no	—
263	#121	C₂×D₁₈₁	1	1	yes	characteristic
264	#120	—	181	4	no	—
265	C₄×Q₈	—	181	2	no	—
266	C₄×Q₈	—	181	2	no	—
267	C₄×Q₈	—	181	2	no	—
268	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
269	C₄×D₄	—	181	4	no	—
270	C₄×D₄	—	181	4	no	—
271	C₄×D₄	—	181	2	no	—
272	C₄×D₄	C₂×D₁₈₁	1	2	yes	—
273	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
274	#117	—	181	2	no	—
275	#117	—	181	4	no	—
276	#117	C₂×D₁₈₁	1	2	yes	complemented
277	C₂×C₂²⋊C₄	—	181	2	no	—
278	C₂×C₂²⋊C₄	—	181	2	no	—
279	C₂×C₂²⋊C₄	—	181	4	no	—
280	C₂×C₄²	C₂×D₁₈₁	1	1	yes	characteristic
281	C₂⁴	—	181	2	no	—
282	#41	—	724	4	no	—
283	C₂×Q₈	—	181	2	no	—
284	C₂×Q₈	—	181	2	no	—
285	C₂×Q₈	—	181	2	no	—
286	C₂×Q₈	—	181	4	no	—
287	C₂×Q₈	—	181	2	no	—
288	C₂×Q₈	—	724	2	no	—
289	C₂×Q₈	—	724	4	no	—
290	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
291	C₂×D₄	—	181	4	no	—
292	C₂×D₄	—	181	4	no	—
293	C₂×D₄	—	181	2	no	—
294	C₂×D₄	—	181	2	no	—
295	C₂×D₄	—	724	2	no	—
296	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
297	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
298	C₂²×C₄	—	181	2	no	—
299	C₂²×C₄	—	181	4	no	—
300	C₂²×C₄	—	181	4	no	—
301	C₂²×C₄	—	181	4	no	—
302	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
305	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
306	C₄⋊C₄	—	181	4	no	—
307	C₄⋊C₄	—	181	2	no	—
308	C₄⋊C₄	—	181	2	no	—
309	C₄⋊C₄	—	181	2	no	—
310	C₄⋊C₄	—	181	4	no	—
311	C₄⋊C₄	—	181	4	no	—
312	C₄⋊C₄	—	181	4	no	—
313	C₄⋊C₄	—	181	4	no	—
314	C₄⋊C₄	—	181	4	no	—
315	C₄⋊C₄	—	181	2	no	—
316	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
317	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
318	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
319	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
320	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
321	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
322	C₂²⋊C₄	—	181	4	no	—
323	C₂²⋊C₄	—	181	4	no	—
324	C₂²⋊C₄	—	181	4	no	—
325	C₂²⋊C₄	—	181	4	no	—
326	C₂²⋊C₄	—	181	4	no	—
327	C₂²⋊C₄	—	181	4	no	—
328	C₂²⋊C₄	—	181	4	no	—
329	C₂²⋊C₄	—	181	4	no	—
330	C₂²⋊C₄	—	181	4	no	—
331	C₂²⋊C₄	—	181	4	no	—
332	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
334	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
335	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
336	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
337	C₄²	—	181	4	no	—
338	C₄²	—	181	4	no	—
339	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
340	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
341	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
342	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
343	C₄²	C₂²×D₁₈₁	1	2	yes	—
344	C₂³	—	362	4	no	—
345	C₂³	—	181	4	no	—
346	C₂³	—	724	2	no	—
347	C₂³	—	724	2	no	—
348	C₂³	C₂³×D₁₈₁	1	2	yes	—
349	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	362	4	no	—
352	Q₈	—	362	4	no	—
353	Q₈	—	724	4	no	—
354	Q₈	—	724	2	no	—
355	Q₈	—	724	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	362	4	no	—
359	D₄	—	724	2	no	—
360	D₄	—	724	4	no	—
361	D₄	—	724	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	181	4	no	—
367	C₂×C₄	—	181	4	no	—
368	C₂×C₄	—	181	4	no	—
369	C₂×C₄	—	724	4	no	—
370	C₂×C₄	—	724	4	no	—
371	C₂×C₄	—	724	4	no	—
372	C₂×C₄	—	724	2	no	—
373	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
375	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
380	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
381	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	362	4	no	—
388	C₂²	—	362	4	no	—
389	C₂²	—	362	4	no	—
390	C₂²	—	1448	4	no	—
391	C₂²	#19153863	1	2	yes	—
392	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	1	no	—
401	C₄	—	362	4	no	—
402	C₄	—	362	4	no	—
403	C₄	—	362	4	no	—
404	C₄	#19153862	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	724	4	no	—
408	C₂	C₂×#19153862	1	1	yes	characteristic
409	C₂	C₂×#19153863	1	1	yes	characteristic
410	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#529×C₁₈₁	C₂
hypercenter	#529	D₁₈₁
hypocenter	C₁₈₁	#3561
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #26042033	C₂	semidirect
2. #26042023	C₂	semidirect
3. #26042002	C₂	semidirect
4. #26041952	C₂	semidirect
5. D₄×Dic₃₆₂	C₂	semidirect
6. #26041938	C₂	semidirect
7. #26041925	C₂	semidirect
8. #26041904	C₂	semidirect
9. #26041900	C₂	semidirect
10. #26041895	C₂	semidirect
11. #26041866	C₂	semidirect
12. #26041855	C₂	semidirect
13. #26041836	C₂	semidirect
14. C₂×#19153804	C₂	semidirect
15. #529×C₁₈₁	C₂	semidirect
18. C₂²×Dic₃₆₂	C₂²	semidirect
20. #19153816	C₂²	semidirect
21. #19153816	C₂²	semidirect
22. #19153816	C₂²	semidirect
23. #19153815	C₂²	semidirect
24. #19153811	C₂²	semidirect
25. #19153811	C₂²	semidirect
26. #19153811	C₂²	semidirect
27. #19153808	C₂²	semidirect
33. #19153802	C₂²	semidirect
34. #19153802	C₂²	semidirect
36. #19153800	C₂²	semidirect
37. #19153800	C₂²	semidirect
38. #19153798	C₂²	semidirect
39. #19153796	C₂²	semidirect
40. #19153796	C₂²	semidirect
43. #19153795	C₂²	semidirect
44. #19153794	C₂²	semidirect
45. #19153794	C₂²	semidirect
47. #19153793	C₂²	semidirect
48. #19153792	C₂²	semidirect
51. #19153788	C₂²	semidirect
53. C₄×Dic₃₆₂	C₂²	semidirect
54. C₄×Dic₃₆₂	C₂²	semidirect
55. C₄×Dic₃₆₂	C₂²	semidirect
58. #19153776	C₂²	semidirect
60. #19153774	C₂²	semidirect
64. #126×C₁₈₁	C₂²	semidirect
65. #125×C₁₈₁	C₂²	semidirect
66. #124×C₁₈₁	C₂²	semidirect
70. C₄×Q₈×C₁₈₁	C₂²	semidirect
72. C₄×D₄×C₁₈₁	C₂²	semidirect
73. #117×C₁₈₁	C₂²	semidirect
205. C₁₈₁	#3561	semidirect
220. #529	D₁₈₁	semidirect
233. #126	C₂×D₁₈₁	semidirect
235. #125	C₂×D₁₈₁	semidirect
243. #124	C₂×D₁₈₁	semidirect
268. C₄×Q₈	C₂×D₁₈₁	semidirect
273. C₄×D₄	C₂×D₁₈₁	semidirect
276. #117	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042033	2
#26042023	2
#26042002	2
#26041952	2
D₄×Dic₃₆₂	2
#26041938	2
#26041925	2
#26041904	2
#26041900	2
#26041895	2
#26041866	2
#26041855	2
#26041836	2
C₂×#19153804	2
#529×C₁₈₁	2
#3561	181