Subgroups — #37548417

Order 23168.

958 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042033	C₂	1	1	yes	maximal, characteristic, complemented
2	#26042033	C₂	1	1	yes	maximal, characteristic, complemented
3	#26042029	C₂	1	1	yes	maximal, characteristic, complemented
4	#26042021	C₂	1	1	yes	maximal, characteristic, complemented
5	#26042001	C₂	1	2	yes	maximal, complemented
6	#26041997	C₂	1	2	yes	maximal, complemented
7	#26041996	C₂	1	2	yes	maximal, complemented
8	#26041958	C₂	1	2	yes	maximal, complemented
9	#26041954	C₂	1	2	yes	maximal, complemented
10	#26041953	C₂	1	2	yes	maximal, complemented
11	#26041899	C₂	1	2	yes	maximal, complemented
12	#26041897	C₂	1	2	yes	maximal, complemented
13	#26041894	C₂	1	2	yes	maximal, complemented
14	#26041865	C₂	1	2	yes	maximal, complemented
15	#26041862	C₂	1	2	yes	maximal, complemented
16	#26041861	C₂	1	2	yes	maximal, complemented
17	#26041813	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041813	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#19153815	C₂²	1	2	yes	complemented
21	#19153815	C₂²	1	2	yes	complemented
22	#19153814	C₂²	1	2	yes	complemented
23	#19153811	C₂²	1	2	yes	complemented
24	#19153811	C₂²	1	2	yes	complemented
25	#19153811	C₂²	1	2	yes	complemented
26	#19153811	C₂²	1	2	yes	complemented
27	#19153811	C₂²	1	2	yes	complemented
28	#19153810	C₂²	1	2	yes	complemented
29	#19153810	C₂²	1	2	yes	complemented
30	#19153810	C₂²	1	2	yes	complemented
31	#19153809	C₂²	1	2	yes	complemented
32	#19153809	C₂²	1	2	yes	complemented
33	#19153809	C₂²	1	2	yes	complemented
34	#19153809	C₂²	1	2	yes	complemented
35	#19153808	C₂²	1	1	yes	characteristic, complemented
36	#19153808	C₂²	1	1	yes	characteristic, complemented
37	#19153805	C₂²	1	2	yes	—
38	#19153804	C₂²	1	2	yes	—
39	#19153804	C₂²	1	1	yes	characteristic
40	#19153804	C₂²	1	1	yes	characteristic
41	#19153803	C₂²	1	2	yes	complemented
42	#19153802	C₂²	1	2	yes	—
43	#19153802	C₂²	1	2	yes	—
44	#19153802	C₂²	1	2	yes	—
45	#19153802	C₂²	1	2	yes	—
46	#19153802	C₂²	1	2	yes	complemented
47	#19153802	C₂²	1	2	yes	complemented
48	#19153801	C₂²	1	2	yes	—
49	#19153801	C₂²	1	2	yes	—
50	#19153801	C₂²	1	2	yes	—
51	#19153799	C₂²	1	2	yes	—
52	#19153799	C₂²	1	2	yes	complemented
53	#19153799	C₂²	1	2	yes	complemented
54	#19153798	C₂²	1	2	yes	—
55	#19153797	C₂²	1	2	yes	—
56	#19153796	C₂²	1	2	yes	complemented
57	#19153796	C₂²	1	2	yes	complemented
58	#19153795	C₂²	1	1	yes	characteristic, complemented
59	#19153795	C₂²	1	2	yes	complemented
60	#19153795	C₂²	1	1	yes	characteristic, complemented
61	#19153794	C₂²	1	2	yes	complemented
62	#19153794	C₂²	1	2	yes	complemented
63	#19153794	C₂²	1	2	yes	complemented
64	#19153794	C₂²	1	2	yes	complemented
65	#19153793	C₂²	1	2	yes	complemented
66	#19153793	C₂²	1	2	yes	complemented
67	#19153790	C₂²	1	1	yes	characteristic
68	#19153790	C₂²	1	1	yes	characteristic
69	#19153789	C₂²	1	2	yes	—
70	#19153788	C₂²	1	2	yes	—
71	#19153787	C₂²	1	2	yes	—
72	#19153786	C₂²	1	2	yes	—
73	#19153786	C₂²	1	2	yes	—
74	#19153784	C₂²	1	2	yes	—
75	#19153784	C₂²	1	2	yes	complemented
76	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
77	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
79	#19153781	C₂²	1	2	yes	complemented
80	#19153781	C₂²	1	2	yes	complemented
81	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
82	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
83	#19153778	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
87	#19153776	C₂²	1	2	yes	—
88	#19153774	C₂²	1	2	yes	complemented
89	#19153773	C₂²	1	2	yes	complemented
90	#19153773	C₂²	1	2	yes	complemented
91	#19153773	C₂²	1	2	yes	complemented
92	#19153772	C₂²	1	2	yes	complemented
93	C₂×#15668426	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
96	#126×C₁₈₁	C₂²	1	2	yes	complemented
97	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
98	#124×C₁₈₁	C₂²	1	1	yes	characteristic
99	#123×C₁₈₁	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
101	#121×C₁₈₁	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
105	#117×C₁₈₁	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₈₁	C₂³	1	2	yes	—
108	C₂×Dic₃₆₂	C₂³	1	2	yes	—
109	C₂×Dic₃₆₂	C₂³	1	2	yes	—
110	C₂×Dic₃₆₂	C₂³	1	2	yes	—
111	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
112	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
113	C₂×D₇₂₄	C₂³	1	2	yes	—
114	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
115	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
120	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
121	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
122	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
123	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
124	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
125	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
126	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
129	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
131	#15668428	C₂³	1	2	yes	—
132	#15668428	C₂³	1	2	yes	—
133	#15668428	C₂³	1	2	yes	—
134	#15668428	C₂³	1	2	yes	—
135	#15668428	C₂³	1	2	yes	—
136	#15668428	C₂³	1	2	yes	—
137	#15668428	C₂³	1	2	yes	—
138	#15668428	C₂³	1	2	yes	—
139	#15668428	C₂³	1	2	yes	—
140	#15668428	C₂³	1	2	yes	—
141	#15668428	C₂³	1	2	yes	—
142	#15668428	C₂³	1	2	yes	—
143	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
144	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
145	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
146	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
147	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
148	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
149	#15668426	C₂³	1	2	yes	—
150	#15668426	C₂³	1	2	yes	—
151	#15668426	C₂³	1	2	yes	—
152	#15668426	C₂³	1	2	yes	—
153	#15668426	C₂³	1	2	yes	—
154	#15668426	C₂³	1	2	yes	—
155	#15668426	C₂³	1	2	yes	—
156	#15668426	C₂³	1	2	yes	—
157	#15668426	C₂³	1	2	yes	—
158	#15668426	C₂³	1	2	yes	—
159	#15668426	C₂³	1	2	yes	—
160	#15668426	C₂³	1	2	yes	—
161	#15668426	C₂³	1	2	yes	—
162	#15668426	C₂³	1	2	yes	—
163	#15668426	C₂³	1	2	yes	—
164	#15668426	C₂³	1	2	yes	—
165	C₄×Dic₁₈₁	C₂³	1	2	yes	—
166	C₄×Dic₁₈₁	C₂³	1	2	yes	—
167	C₄×Dic₁₈₁	C₂³	1	2	yes	—
168	C₄×Dic₁₈₁	C₂³	1	2	yes	—
169	C₄×Dic₁₈₁	C₂³	1	2	yes	—
170	C₄×Dic₁₈₁	C₂³	1	2	yes	—
171	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
172	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
173	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
174	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
178	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
179	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
189	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
190	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
191	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
192	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
193	C₄²×C₁₈₁	C₂³	1	2	yes	—
194	C₂²×D₁₈₁	—	4	2	no	—
195	C₂²×D₁₈₁	—	4	2	no	—
196	C₂²×D₁₈₁	—	4	2	no	—
197	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
198	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
199	Dic₃₆₂	—	4	2	no	—
200	Dic₃₆₂	—	4	2	no	—
201	Dic₃₆₂	—	4	2	no	—
202	Dic₃₆₂	—	4	1	no	—
203	Dic₃₆₂	—	4	1	no	—
204	D₇₂₄	—	4	1	no	—
205	D₇₂₄	—	4	1	no	—
206	D₇₂₄	—	4	2	no	—
207	C₂²⋊D₁₈₁	—	4	2	no	—
208	C₂²⋊D₁₈₁	—	4	2	no	—
209	C₂²⋊D₁₈₁	—	4	2	no	—
210	C₂²⋊D₁₈₁	—	4	2	no	—
211	C₂×Dic₁₈₁	—	4	2	no	—
212	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
213	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
214	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
215	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
216	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
217	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
218	C₄×D₁₈₁	—	4	2	no	—
219	C₄×D₁₈₁	—	4	2	no	—
220	C₄×D₁₈₁	—	4	2	no	—
221	C₄×D₁₈₁	—	4	2	no	—
222	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
223	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
224	Q₈×C₁₈₁	—	4	1	no	—
225	D₄×C₁₈₁	—	4	1	no	—
226	D₄×C₁₈₁	—	4	2	no	—
227	C₂×C₄×C₁₈₁	—	4	2	no	—
228	C₂×C₄×C₁₈₁	—	4	1	no	—
229	C₂×C₄×C₁₈₁	—	4	1	no	—
230	C₂×C₄×C₁₈₁	—	4	1	no	—
231	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
240	C₂²×C₁₈₁	—	2	1	no	—
241	C₂²×C₁₈₁	—	2	1	no	—
242	C₂²×C₁₈₁	—	2	1	no	—
243	C₂²×C₁₈₁	—	2	2	no	—
244	C₂²×C₁₈₁	—	2	2	no	—
245	C₂²×C₁₈₁	—	2	2	no	—
246	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
247	C₂×D₁₈₁	—	2	2	no	—
248	C₂×D₁₈₁	—	2	2	no	—
249	C₂×D₁₈₁	—	2	2	no	—
250	C₂×D₁₈₁	—	2	2	no	—
251	C₂×D₁₈₁	—	2	2	no	—
252	C₂×D₁₈₁	—	2	2	no	—
253	C₂×D₁₈₁	—	8	4	no	—
254	C₄×C₁₈₁	—	2	1	no	—
255	C₄×C₁₈₁	—	2	1	no	—
256	C₄×C₁₈₁	—	2	1	no	—
257	C₄×C₁₈₁	—	2	1	no	—
258	C₄×C₁₈₁	—	2	2	no	—
259	C₄×C₁₈₁	—	2	1	no	—
260	C₄×C₁₈₁	—	2	1	no	—
261	C₄×C₁₈₁	—	2	2	no	—
262	C₄×C₁₈₁	—	2	2	no	—
263	Dic₁₈₁	—	2	2	no	—
264	Dic₁₈₁	—	2	2	no	—
265	Dic₁₈₁	—	2	2	no	—
266	Dic₁₈₁	—	2	2	no	—
267	Dic₁₈₁	—	2	2	no	—
268	Dic₁₈₁	—	2	2	no	—
269	C₂×C₁₈₁	—	4	2	no	—
270	C₂×C₁₈₁	—	4	1	no	—
271	C₂×C₁₈₁	#585	1	1	yes	characteristic
272	C₂×C₁₈₁	#585	1	1	yes	characteristic
273	C₂×C₁₈₁	#585	1	1	yes	characteristic
274	D₁₈₁	—	4	2	no	—
275	D₁₈₁	—	4	2	no	—
276	C₁₈₁	#3568	1	1	yes	characteristic, complemented, Sylow
277	#3568	—	181	1	no	maximal, Sylow
278	#563	—	181	1	no	—
279	#563	—	181	1	no	—
280	#563	—	181	1	no	—
281	H(3,𝔽₄)	—	181	1	no	—
282	#556	—	181	2	no	—
283	#556	—	181	2	no	—
284	#556	—	181	2	no	—
285	#551	—	181	2	no	—
286	#551	—	181	2	no	—
287	#551	—	181	2	no	—
288	#542	—	181	2	no	—
289	#542	—	181	2	no	—
290	#542	—	181	2	no	—
291	#538	—	181	2	no	—
292	#538	—	181	2	no	—
293	#538	—	181	2	no	—
294	#529	—	181	1	no	—
295	#529	—	181	1	no	—
296	#529	D₁₈₁	1	1	yes	characteristic, complemented
297	C₄⋊Q₈	—	181	2	no	—
298	C₄⋊Q₈	—	181	2	no	—
299	C₄⋊Q₈	—	181	2	no	—
300	#126	—	181	2	no	—
301	#126	—	181	2	no	—
302	#126	—	181	2	no	—
303	#126	—	181	2	no	—
304	#126	—	181	2	no	—
305	#126	—	181	2	no	—
306	#126	—	181	2	no	—
307	#126	—	181	2	no	—
308	#126	—	181	2	no	—
309	#126	—	181	2	no	—
310	#126	—	181	2	no	—
311	#126	—	181	2	no	—
312	#126	C₂×D₁₈₁	1	2	yes	complemented
313	#125	—	181	1	no	—
314	#125	—	181	1	no	—
315	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
316	#124	—	181	2	no	—
317	#124	—	181	2	no	—
318	#124	—	181	2	no	—
319	#124	—	181	2	no	—
320	#124	—	181	2	no	—
321	#124	—	181	2	no	—
322	#124	—	181	2	no	—
323	#124	—	181	2	no	—
324	#124	—	181	1	no	—
325	#124	—	181	1	no	—
326	#124	—	181	2	no	—
327	#124	C₂×D₁₈₁	1	1	yes	characteristic
328	#123	—	181	2	no	—
329	#123	—	181	2	no	—
330	#123	—	181	2	no	—
331	#123	—	181	2	no	—
332	#123	—	181	2	no	—
333	#123	—	181	2	no	—
334	#123	—	181	2	no	—
335	#123	—	181	2	no	—
336	#123	C₂×D₁₈₁	1	2	yes	complemented
337	C₂²⋊Q₈	—	181	1	no	—
338	C₂²⋊Q₈	—	181	1	no	—
339	C₂²⋊Q₈	—	181	2	no	—
340	C₂²⋊Q₈	—	181	2	no	—
341	C₂²⋊Q₈	—	181	2	no	—
342	C₂²⋊Q₈	—	181	2	no	—
343	C₂²⋊Q₈	—	181	2	no	—
344	C₂²⋊Q₈	—	181	2	no	—
345	C₂²⋊Q₈	—	181	2	no	—
346	C₂²⋊Q₈	—	181	2	no	—
347	C₂²⋊Q₈	—	181	2	no	—
348	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
349	#121	—	181	2	no	—
350	#121	—	181	2	no	—
351	#121	—	181	1	no	—
352	#121	—	181	1	no	—
353	#121	—	181	2	no	—
354	#121	C₂×D₁₈₁	1	1	yes	characteristic
355	#120	—	181	2	no	—
356	#120	—	181	2	no	—
357	#120	—	181	2	no	—
358	#120	—	181	2	no	—
359	C₄×Q₈	—	181	2	no	—
360	C₄×Q₈	—	181	2	no	—
361	C₄×Q₈	—	181	1	no	—
362	C₄×Q₈	—	181	1	no	—
363	C₄×Q₈	—	181	2	no	—
364	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
365	C₄×D₄	—	181	2	no	—
366	C₄×D₄	—	181	2	no	—
367	C₄×D₄	—	181	2	no	—
368	C₄×D₄	—	181	2	no	—
369	C₄×D₄	—	181	2	no	—
370	C₄×D₄	—	181	1	no	—
371	C₄×D₄	—	181	1	no	—
372	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
373	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
374	#117	—	181	2	no	—
375	#117	—	181	2	no	—
376	#117	—	181	2	no	—
377	#117	—	181	2	no	—
378	#117	—	181	2	no	—
379	#117	C₂×D₁₈₁	1	2	yes	complemented
380	C₂×C₂²⋊C₄	—	181	2	no	—
381	C₂×C₂²⋊C₄	—	181	2	no	—
382	C₂×C₂²⋊C₄	—	181	2	no	—
383	C₂×C₄²	C₂×D₁₈₁	1	1	yes	characteristic, complemented
384	C₂⁴	—	181	2	no	—
385	C₂×Q₈	—	181	2	no	—
386	C₂×Q₈	—	181	2	no	—
387	C₂×Q₈	—	181	2	no	—
388	C₂×Q₈	—	181	1	no	—
389	C₂×Q₈	—	181	1	no	—
390	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
391	C₂×D₄	—	181	2	no	—
392	C₂×D₄	—	181	2	no	—
393	C₂×D₄	—	181	2	no	—
394	C₂×D₄	—	181	2	no	—
395	C₂×D₄	—	181	1	no	—
396	C₂×D₄	—	181	1	no	—
397	C₂×D₄	—	181	2	no	—
398	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
399	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
400	C₂²×C₄	—	181	2	no	—
401	C₂²×C₄	—	181	2	no	—
402	C₂²×C₄	—	181	2	no	—
403	C₂²×C₄	—	181	2	no	—
404	C₂²×C₄	—	181	2	no	—
405	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
408	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
409	C₄⋊C₄	—	181	2	no	—
410	C₄⋊C₄	—	181	2	no	—
411	C₄⋊C₄	—	181	2	no	—
412	C₄⋊C₄	—	181	2	no	—
413	C₄⋊C₄	—	181	2	no	—
414	C₄⋊C₄	—	181	2	no	—
415	C₄⋊C₄	—	181	2	no	—
416	C₄⋊C₄	—	181	2	no	—
417	C₄⋊C₄	—	181	2	no	—
418	C₄⋊C₄	—	181	1	no	—
419	C₄⋊C₄	—	181	1	no	—
420	C₄⋊C₄	—	181	2	no	—
421	C₄⋊C₄	—	181	2	no	—
422	C₄⋊C₄	—	181	1	no	—
423	C₄⋊C₄	—	181	1	no	—
424	C₄⋊C₄	—	181	2	no	—
425	C₄⋊C₄	—	181	2	no	—
426	C₄⋊C₄	—	181	2	no	—
427	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
428	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
429	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
430	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
432	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
433	C₂²⋊C₄	—	181	2	no	—
434	C₂²⋊C₄	—	181	2	no	—
435	C₂²⋊C₄	—	181	2	no	—
436	C₂²⋊C₄	—	181	2	no	—
437	C₂²⋊C₄	—	181	2	no	—
438	C₂²⋊C₄	—	181	2	no	—
439	C₂²⋊C₄	—	181	2	no	—
440	C₂²⋊C₄	—	181	2	no	—
441	C₂²⋊C₄	—	181	2	no	—
442	C₂²⋊C₄	—	181	2	no	—
443	C₂²⋊C₄	—	181	2	no	—
444	C₂²⋊C₄	—	181	2	no	—
445	C₂²⋊C₄	—	181	2	no	—
446	C₂²⋊C₄	—	181	2	no	—
447	C₂²⋊C₄	—	181	2	no	—
448	C₂²⋊C₄	—	181	2	no	—
449	C₂²⋊C₄	—	181	2	no	—
450	C₂²⋊C₄	—	181	2	no	—
451	C₂²⋊C₄	—	181	2	no	—
452	C₂²⋊C₄	—	181	2	no	—
453	C₂²⋊C₄	—	181	2	no	—
454	C₂²⋊C₄	—	181	2	no	—
455	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
456	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
457	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
458	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
459	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
460	C₄²	—	181	2	no	—
461	C₄²	—	181	2	no	—
462	C₄²	—	181	2	no	—
463	C₄²	—	181	2	no	—
464	C₄²	—	181	2	no	—
465	C₄²	—	181	2	no	—
466	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
467	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
468	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
469	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
470	C₄²	C₂²×D₁₈₁	1	2	yes	—
471	C₂³	—	181	2	no	—
472	C₂³	—	181	2	no	—
473	C₂³	—	724	2	no	—
474	C₂³	—	724	2	no	—
475	C₂³	—	724	2	no	—
476	C₂³	C₂³×D₁₈₁	1	2	yes	—
477	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	724	2	no	—
480	Q₈	—	724	1	no	—
481	Q₈	—	724	1	no	—
482	Q₈	—	724	2	no	—
483	Q₈	—	724	2	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	724	1	no	—
487	D₄	—	724	1	no	—
488	D₄	—	724	2	no	—
489	D₄	—	724	2	no	—
490	D₄	—	724	2	no	—
491	D₄	—	724	2	no	—
492	D₄	—	724	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	181	2	no	—
498	C₂×C₄	—	181	2	no	—
499	C₂×C₄	—	181	2	no	—
500	C₂×C₄	—	181	2	no	—
501	C₂×C₄	—	181	2	no	—
502	C₂×C₄	—	181	2	no	—
503	C₂×C₄	—	724	2	no	—
504	C₂×C₄	—	724	2	no	—
505	C₂×C₄	—	724	2	no	—
506	C₂×C₄	—	724	2	no	—
507	C₂×C₄	—	724	2	no	—
508	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
509	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
510	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
511	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
512	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
513	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
514	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
515	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
516	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	362	2	no	—
524	C₂²	—	362	2	no	—
525	C₂²	—	362	2	no	—
526	C₂²	—	362	2	no	—
527	C₂²	—	362	2	no	—
528	C₂²	—	362	2	no	—
529	C₂²	—	1448	4	no	—
530	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	362	2	no	—
541	C₄	—	362	2	no	—
542	C₄	—	362	2	no	—
543	C₄	—	362	2	no	—
544	C₄	—	362	2	no	—
545	C₄	—	362	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	4	1	no	—
548	C₂	—	724	2	no	—
549	C₂	—	724	2	no	—
550	C₂	#26042115	1	1	yes	characteristic
551	C₂	#26042115	1	1	yes	characteristic
552	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	#3568
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. #26042033	C₂	semidirect
3. #26042029	C₂	semidirect
4. #26042021	C₂	semidirect
5. #26042001	C₂	semidirect
6. #26041997	C₂	semidirect
7. #26041996	C₂	semidirect
8. #26041958	C₂	semidirect
9. #26041954	C₂	semidirect
10. #26041953	C₂	semidirect
11. #26041899	C₂	semidirect
12. #26041897	C₂	semidirect
13. #26041894	C₂	semidirect
14. #26041865	C₂	semidirect
15. #26041862	C₂	semidirect
16. #26041861	C₂	semidirect
17. #26041813	C₂	semidirect
18. #26041813	C₂	semidirect
19. #529×C₁₈₁	C₂	semidirect
20. #19153815	C₂²	semidirect
21. #19153815	C₂²	semidirect
22. #19153814	C₂²	semidirect
23. #19153811	C₂²	semidirect
24. #19153811	C₂²	semidirect
25. #19153811	C₂²	semidirect
26. #19153811	C₂²	semidirect
27. #19153811	C₂²	semidirect
28. #19153810	C₂²	semidirect
29. #19153810	C₂²	semidirect
30. #19153810	C₂²	semidirect
31. #19153809	C₂²	semidirect
32. #19153809	C₂²	semidirect
33. #19153809	C₂²	semidirect
34. #19153809	C₂²	semidirect
35. #19153808	C₂²	semidirect
36. #19153808	C₂²	semidirect
41. #19153803	C₂²	semidirect
46. #19153802	C₂²	semidirect
47. #19153802	C₂²	semidirect
52. #19153799	C₂²	semidirect
53. #19153799	C₂²	semidirect
56. #19153796	C₂²	semidirect
57. #19153796	C₂²	semidirect
58. #19153795	C₂²	semidirect
59. #19153795	C₂²	semidirect
60. #19153795	C₂²	semidirect
61. #19153794	C₂²	semidirect
62. #19153794	C₂²	semidirect
63. #19153794	C₂²	semidirect
64. #19153794	C₂²	semidirect
65. #19153793	C₂²	semidirect
66. #19153793	C₂²	semidirect
75. #19153784	C₂²	semidirect
76. C₄×Dic₃₆₂	C₂²	semidirect
77. C₄×Dic₃₆₂	C₂²	semidirect
78. C₄×Dic₃₆₂	C₂²	semidirect
79. #19153781	C₂²	semidirect
80. #19153781	C₂²	semidirect
85. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
86. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
88. #19153774	C₂²	semidirect
89. #19153773	C₂²	semidirect
90. #19153773	C₂²	semidirect
91. #19153773	C₂²	semidirect
92. #19153772	C₂²	semidirect
93. C₂×#15668426	C₂²	semidirect
94. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
95. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
96. #126×C₁₈₁	C₂²	semidirect
97. #125×C₁₈₁	C₂²	semidirect
99. #123×C₁₈₁	C₂²	semidirect
100. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
102. C₄×Q₈×C₁₈₁	C₂²	semidirect
104. C₄×D₄×C₁₈₁	C₂²	semidirect
105. #117×C₁₈₁	C₂²	semidirect
106. C₂×C₄²×C₁₈₁	C₂²	semidirect
276. C₁₈₁	#3568	semidirect
296. #529	D₁₈₁	semidirect
312. #126	C₂×D₁₈₁	semidirect
315. #125	C₂×D₁₈₁	semidirect
336. #123	C₂×D₁₈₁	semidirect
348. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
364. C₄×Q₈	C₂×D₁₈₁	semidirect
373. C₄×D₄	C₂×D₁₈₁	semidirect
379. #117	C₂×D₁₈₁	semidirect
383. C₂×C₄²	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
#26042029	2
#26042021	2
#26042001	2
#26041997	2
#26041996	2
#26041958	2
#26041954	2
#26041953	2
#26041899	2
#26041897	2
#26041894	2
#26041865	2
#26041862	2
#26041861	2
#26041813	2
#529×C₁₈₁	2
#3568	181