Subgroups — #37548088

Order 23168.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042018	C₂	1	2	yes	maximal, complemented
2	#26042017	C₂	1	2	yes	maximal, complemented
3	#26041998	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041974	C₂	1	2	yes	maximal, complemented
5	#26041950	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041950	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041948	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041931	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041926	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041919	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041902	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041894	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041867	C₂	1	2	yes	maximal, complemented
15	#26041865	C₂	1	2	yes	maximal, complemented
16	#26041858	C₂	1	2	yes	maximal, complemented
17	#26041847	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041846	C₂	1	1	yes	maximal, characteristic, complemented
19	#26041844	C₂	1	2	yes	maximal, complemented
20	#26041825	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041824	C₂	1	1	yes	maximal, characteristic, complemented
22	#26041809	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668450	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15668449	C₂²	1	2	yes	complemented
26	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
27	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
28	C₂×#15668448	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
30	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
31	#19153815	C₂²	1	1	yes	characteristic, complemented
32	#19153814	C₂²	1	1	yes	characteristic, complemented
33	#19153813	C₂²	1	1	yes	characteristic, complemented
34	#19153812	C₂²	1	1	yes	characteristic
35	#19153812	C₂²	1	1	yes	characteristic
36	#19153812	C₂²	1	1	yes	characteristic, complemented
37	#19153812	C₂²	1	2	yes	complemented
38	#19153812	C₂²	1	2	yes	complemented
39	#19153811	C₂²	1	1	yes	characteristic, complemented
40	#19153811	C₂²	1	2	yes	complemented
41	#19153809	C₂²	1	2	yes	complemented
42	#19153809	C₂²	1	1	yes	characteristic, complemented
43	#19153809	C₂²	1	2	yes	complemented
44	#19153809	C₂²	1	2	yes	complemented
45	#19153806	C₂²	1	1	yes	characteristic, complemented
46	#19153805	C₂²	1	1	yes	characteristic, complemented
47	#19153803	C₂²	1	1	yes	characteristic
48	#19153803	C₂²	1	1	yes	characteristic, complemented
49	#19153802	C₂²	1	1	yes	characteristic
50	#19153802	C₂²	1	2	yes	complemented
51	#19153802	C₂²	1	2	yes	complemented
52	#19153802	C₂²	1	2	yes	complemented
53	#19153801	C₂²	1	2	yes	complemented
54	#19153800	C₂²	1	1	yes	characteristic, complemented
55	#19153799	C₂²	1	2	yes	complemented
56	#19153798	C₂²	1	2	yes	complemented
57	#19153798	C₂²	1	2	yes	complemented
58	#19153798	C₂²	1	2	yes	complemented
59	#19153797	C₂²	1	1	yes	characteristic, complemented
60	#19153796	C₂²	1	2	yes	complemented
61	#19153796	C₂²	1	1	yes	characteristic, complemented
62	#19153795	C₂²	1	2	yes	complemented
63	#19153793	C₂²	1	1	yes	characteristic, complemented
64	#19153793	C₂²	1	2	yes	complemented
65	#19153790	C₂²	1	1	yes	characteristic
66	#19153790	C₂²	1	2	yes	complemented
67	#19153790	C₂²	1	2	yes	complemented
68	#19153790	C₂²	1	1	yes	characteristic, complemented
69	#19153789	C₂²	1	2	yes	—
70	#19153789	C₂²	1	2	yes	complemented
71	#19153789	C₂²	1	2	yes	complemented
72	#19153789	C₂²	1	2	yes	complemented
73	#19153789	C₂²	1	2	yes	complemented
74	#19153789	C₂²	1	2	yes	complemented
75	#19153789	C₂²	1	2	yes	complemented
76	#19153788	C₂²	1	2	yes	—
77	#19153788	C₂²	1	1	yes	characteristic
78	#19153788	C₂²	1	2	yes	complemented
79	#19153788	C₂²	1	2	yes	complemented
80	#19153788	C₂²	1	2	yes	complemented
81	#19153787	C₂²	1	1	yes	characteristic
82	#19153787	C₂²	1	2	yes	complemented
83	#19153787	C₂²	1	2	yes	complemented
84	#19153787	C₂²	1	2	yes	complemented
85	#19153787	C₂²	1	2	yes	complemented
86	#19153786	C₂²	1	2	yes	complemented
87	#19153786	C₂²	1	2	yes	complemented
88	#19153785	C₂²	1	2	yes	—
89	#19153785	C₂²	1	2	yes	complemented
90	#19153785	C₂²	1	2	yes	complemented
91	#19153784	C₂²	1	2	yes	—
92	#19153784	C₂²	1	2	yes	complemented
93	Q₈×Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
94	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
95	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
97	#19153778	C₂²	1	2	yes	complemented
98	#19153778	C₂²	1	1	yes	characteristic, complemented
99	#19153778	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
105	#19153776	C₂²	1	2	yes	complemented
106	#19153775	C₂²	1	1	yes	characteristic, complemented
107	#19153773	C₂²	1	1	yes	characteristic, complemented
108	#19153772	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
114	#124×C₁₈₁	C₂²	1	1	yes	characteristic
115	#123×C₁₈₁	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₈₁	C₂²	1	1	yes	characteristic
118	#121×C₁₈₁	C₂²	1	2	yes	complemented
119	#120×C₁₈₁	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₈₁	C₂²	1	2	yes	complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	#15668450	—	4	2	no	—
125	#15668449	—	4	2	no	—
126	#15668449	—	4	2	no	—
127	#15668449	—	4	4	no	—
128	#15668448	—	4	4	no	—
129	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₆₂	C₂³	1	2	yes	—
132	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
133	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
134	C₂×D₇₂₄	C₂³	1	2	yes	—
135	C₂×D₇₂₄	C₂³	1	2	yes	—
136	C₂×D₇₂₄	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₈₁	—	4	4	no	—
138	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
152	D₄×D₁₈₁	—	4	2	no	—
153	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
155	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
159	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
160	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
161	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
162	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
163	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
168	#15668428	C₂³	1	1	yes	characteristic
169	#15668428	C₂³	1	2	yes	—
170	#15668428	C₂³	1	1	yes	characteristic
171	#15668428	C₂³	1	1	yes	characteristic
172	#15668428	C₂³	1	1	yes	characteristic
173	#15668428	C₂³	1	2	yes	—
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	2	yes	—
176	#15668428	C₂³	1	2	yes	—
177	#15668428	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
188	#15668426	C₂³	1	1	yes	characteristic
189	#15668426	C₂³	1	2	yes	—
190	#15668426	C₂³	1	1	yes	characteristic
191	#15668426	C₂³	1	1	yes	characteristic
192	#15668426	C₂³	1	2	yes	—
193	#15668426	C₂³	1	1	yes	characteristic
194	#15668426	C₂³	1	2	yes	—
195	#15668426	C₂³	1	2	yes	—
196	#15668426	C₂³	1	2	yes	—
197	#15668426	C₂³	1	2	yes	—
198	#15668426	C₂³	1	2	yes	—
199	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₈₁	C₂³	1	2	yes	—
204	C₄×Dic₁₈₁	C₂³	1	2	yes	—
205	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
206	C₂⁴×C₁₈₁	C₂³	1	2	yes	—
207	#41×C₁₈₁	—	4	2	no	—
208	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₈₁	—	4	2	no	—
210	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
214	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
215	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
216	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
229	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
230	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
231	C₂²×D₁₈₁	—	4	2	no	—
232	C₂²×D₁₈₁	—	4	2	no	—
233	C₂²×D₁₈₁	—	4	2	no	—
234	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
236	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
237	Dic₃₆₂	—	2	2	no	—
238	Dic₃₆₂	—	2	2	no	—
239	Dic₃₆₂	—	4	2	no	—
240	D₇₂₄	—	2	2	no	—
241	D₇₂₄	—	2	2	no	—
242	D₇₂₄	—	4	2	no	—
243	D₇₂₄	—	4	2	no	—
244	D₇₂₄	—	4	2	no	—
245	C₂²⋊D₁₈₁	—	2	2	no	—
246	C₂²⋊D₁₈₁	—	2	4	no	—
247	C₂²⋊D₁₈₁	—	4	2	no	—
248	C₂²⋊D₁₈₁	—	4	2	no	—
249	C₂²⋊D₁₈₁	—	4	2	no	—
250	C₂²⋊D₁₈₁	—	4	2	no	—
251	C₂²⋊D₁₈₁	—	4	2	no	—
252	C₂²⋊D₁₈₁	—	4	2	no	—
253	C₂²⋊D₁₈₁	—	4	1	no	—
254	C₂²⋊D₁₈₁	—	4	2	no	—
255	C₂²⋊D₁₈₁	—	4	2	no	—
256	C₂²⋊D₁₈₁	—	4	2	no	—
257	C₂²⋊D₁₈₁	—	4	2	no	—
258	C₂²⋊D₁₈₁	—	4	2	no	—
259	C₂×Dic₁₈₁	—	2	4	no	—
260	C₂×Dic₁₈₁	—	2	2	no	—
261	C₂×Dic₁₈₁	—	4	1	no	—
262	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
271	C₄×D₁₈₁	—	2	2	no	—
272	C₄×D₁₈₁	—	2	4	no	—
273	C₄×D₁₈₁	—	4	2	no	—
274	C₄×D₁₈₁	—	4	2	no	—
275	C₄×D₁₈₁	—	4	2	no	—
276	C₄×D₁₈₁	—	4	2	no	—
277	C₂³×C₁₈₁	—	4	2	no	—
278	C₂³×C₁₈₁	—	4	2	no	—
279	C₂³×C₁₈₁	—	4	2	no	—
280	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
281	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
282	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
283	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
284	Q₈×C₁₈₁	—	2	2	no	—
285	D₄×C₁₈₁	—	2	2	no	—
286	D₄×C₁₈₁	—	2	2	no	—
287	D₄×C₁₈₁	—	4	2	no	—
288	D₄×C₁₈₁	—	4	1	no	—
289	D₄×C₁₈₁	—	4	2	no	—
290	D₄×C₁₈₁	—	4	2	no	—
291	C₂×C₄×C₁₈₁	—	2	2	no	—
292	C₂×C₄×C₁₈₁	—	2	2	no	—
293	C₂×C₄×C₁₈₁	—	4	2	no	—
294	C₂×C₄×C₁₈₁	—	4	2	no	—
295	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
298	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₁₈₁	—	2	1	no	—
303	C₂²×C₁₈₁	—	2	1	no	—
304	C₂²×C₁₈₁	—	2	2	no	—
305	C₂²×C₁₈₁	—	2	2	no	—
306	C₂²×C₁₈₁	—	2	2	no	—
307	C₂²×C₁₈₁	—	2	1	no	—
308	C₂²×C₁₈₁	—	2	2	no	—
309	C₂²×C₁₈₁	—	2	1	no	—
310	C₂²×C₁₈₁	—	2	1	no	—
311	C₂²×C₁₈₁	—	2	1	no	—
312	C₂²×C₁₈₁	—	2	2	no	—
313	C₂²×C₁₈₁	—	2	2	no	—
314	C₂²×C₁₈₁	—	8	4	no	—
315	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
316	C₂×D₁₈₁	—	2	2	no	—
317	C₂×D₁₈₁	—	2	1	no	—
318	C₂×D₁₈₁	—	2	2	no	—
319	C₂×D₁₈₁	—	2	2	no	—
320	C₂×D₁₈₁	—	2	2	no	—
321	C₂×D₁₈₁	—	2	1	no	—
322	C₂×D₁₈₁	—	2	2	no	—
323	C₂×D₁₈₁	—	2	2	no	—
324	C₂×D₁₈₁	—	2	1	no	—
325	C₂×D₁₈₁	—	8	4	no	—
326	C₄×C₁₈₁	—	2	1	no	—
327	C₄×C₁₈₁	—	2	1	no	—
328	C₄×C₁₈₁	—	2	1	no	—
329	C₄×C₁₈₁	—	2	2	no	—
330	C₄×C₁₈₁	—	2	2	no	—
331	C₄×C₁₈₁	—	2	1	no	—
332	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
333	Dic₁₈₁	—	2	1	no	—
334	Dic₁₈₁	—	2	1	no	—
335	Dic₁₈₁	—	2	2	no	—
336	Dic₁₈₁	—	2	2	no	—
337	Dic₁₈₁	—	2	1	no	—
338	Dic₁₈₁	—	2	1	no	—
339	Dic₁₈₁	—	2	1	no	—
340	Dic₁₈₁	—	2	1	no	—
341	Dic₁₈₁	H(5,𝔽₂)	1	2	yes	—
342	C₂×C₁₈₁	—	4	2	no	—
343	C₂×C₁₈₁	—	4	1	no	—
344	C₂×C₁₈₁	—	4	2	no	—
345	C₂×C₁₈₁	—	4	1	no	—
346	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₁₈₁	#585	1	1	yes	characteristic
349	D₁₈₁	—	4	2	no	—
350	D₁₈₁	—	4	2	no	—
351	D₁₈₁	—	4	1	no	—
352	C₁₈₁	#3546	1	1	yes	characteristic, complemented, Sylow
353	#3546	—	181	1	no	maximal, Sylow
354	#560	—	181	2	no	—
355	#560	—	181	2	no	—
356	#556	—	181	1	no	—
357	#553	—	181	2	no	—
358	#550	—	181	1	no	—
359	#550	—	181	1	no	—
360	#550	—	181	1	no	—
361	#547	—	181	1	no	—
362	#546	—	181	1	no	—
363	#546	—	181	2	no	—
364	#546	D₁₈₁	1	1	yes	characteristic, complemented
365	D₄²	—	181	1	no	—
366	#542	—	181	1	no	—
367	#542	—	181	1	no	—
368	#538	—	181	2	no	—
369	#538	—	181	2	no	—
370	#537	—	181	2	no	—
371	#535	—	181	1	no	—
372	#535	—	181	1	no	—
373	#535	—	181	2	no	—
374	#532	—	181	1	no	—
375	#532	—	181	1	no	—
376	#529	—	181	1	no	—
377	C₂×#41	—	181	1	no	—
378	C₂×#41	—	181	2	no	—
379	C₂×#41	—	181	1	no	—
380	C₂×#41	—	181	1	no	—
381	C₂×#41	—	181	2	no	—
382	C₂×#41	C₂×D₁₈₁	1	1	yes	characteristic, complemented
383	C₂²×D₄	—	181	2	no	—
384	C₂²×D₄	—	181	1	no	—
385	C₂²×D₄	C₂×D₁₈₁	1	1	yes	characteristic
386	C₄⋊Q₈	—	181	1	no	—
387	C₄⋊Q₈	—	181	1	no	—
388	#127	—	181	1	no	—
389	#127	—	181	1	no	—
390	#127	—	181	1	no	—
391	#127	—	181	2	no	—
392	#127	—	181	2	no	—
393	#127	—	181	1	no	—
394	#126	—	181	1	no	—
395	#126	—	181	2	no	—
396	#126	—	181	1	no	—
397	#126	—	181	2	no	—
398	#126	—	181	2	no	—
399	#126	—	181	2	no	—
400	#125	—	181	1	no	—
401	#124	—	181	1	no	—
402	#124	—	181	1	no	—
403	#124	—	181	1	no	—
404	#124	—	181	1	no	—
405	#124	—	181	2	no	—
406	#124	—	181	2	no	—
407	#124	—	181	2	no	—
408	#124	C₂×D₁₈₁	1	1	yes	characteristic
409	#123	—	181	1	no	—
410	#123	—	181	2	no	—
411	#123	—	181	2	no	—
412	#123	—	181	1	no	—
413	#123	—	181	2	no	—
414	#123	—	181	2	no	—
415	#123	—	181	2	no	—
416	#123	C₂×D₁₈₁	1	2	yes	complemented
417	C₂²⋊Q₈	—	181	2	no	—
418	C₂²⋊Q₈	—	181	2	no	—
419	C₂²⋊Q₈	—	181	1	no	—
420	C₂²⋊Q₈	—	181	1	no	—
421	C₂²⋊Q₈	—	181	2	no	—
422	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
423	#121	—	181	1	no	—
424	#121	—	181	2	no	—
425	#121	—	181	2	no	—
426	#121	—	181	2	no	—
427	#121	—	181	2	no	—
428	#121	—	181	2	no	—
429	#121	—	181	2	no	—
430	#121	—	181	2	no	—
431	#121	—	181	2	no	—
432	#121	—	181	1	no	—
433	#121	—	181	1	no	—
434	#121	—	181	2	no	—
435	#121	—	181	2	no	—
436	#121	—	181	1	no	—
437	#121	—	181	2	no	—
438	#121	—	181	2	no	—
439	#121	—	181	2	no	—
440	#121	—	181	2	no	—
441	#121	—	181	2	no	—
442	#121	—	181	2	no	—
443	#121	—	181	2	no	—
444	#121	C₂×D₁₈₁	1	1	yes	characteristic
445	#121	C₂×D₁₈₁	1	2	yes	complemented
446	#120	—	181	2	no	—
447	#120	—	181	2	no	—
448	#120	—	181	2	no	—
449	#120	—	181	2	no	—
450	#120	—	181	2	no	—
451	#120	—	181	2	no	—
452	#120	—	181	2	no	—
453	#120	C₂×D₁₈₁	1	2	yes	complemented
454	C₄×Q₈	—	181	1	no	—
455	C₄×Q₈	—	181	1	no	—
456	C₄×Q₈	—	181	1	no	—
457	C₄×D₄	—	181	1	no	—
458	C₄×D₄	—	181	1	no	—
459	C₄×D₄	—	181	1	no	—
460	C₄×D₄	—	181	2	no	—
461	C₄×D₄	—	181	2	no	—
462	C₄×D₄	—	181	2	no	—
463	C₄×D₄	—	181	1	no	—
464	C₄×D₄	—	181	2	no	—
465	C₄×D₄	—	181	1	no	—
466	C₄×D₄	—	181	2	no	—
467	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
469	#117	—	181	1	no	—
470	#117	—	181	2	no	—
471	#117	—	181	1	no	—
472	C₂×C₄⋊C₄	—	181	2	no	—
473	C₂×C₂²⋊C₄	—	181	2	no	—
474	C₂×C₂²⋊C₄	C₂×D₁₈₁	1	2	yes	complemented
475	C₂×C₄²	—	181	1	no	—
476	C₂⁴	—	181	2	no	—
477	C₂⁴	C₂²×D₁₈₁	1	2	yes	—
478	#41	—	4	2	no	—
479	#41	—	724	2	no	—
480	#41	—	724	2	no	—
481	#41	—	724	4	no	—
482	#41	—	724	4	no	—
483	#41	—	724	2	no	—
484	C₂×Q₈	—	181	1	no	—
485	C₂×Q₈	—	181	1	no	—
486	C₂×Q₈	—	181	2	no	—
487	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	181	1	no	—
490	C₂×D₄	—	181	2	no	—
491	C₂×D₄	—	181	2	no	—
492	C₂×D₄	—	181	2	no	—
493	C₂×D₄	—	181	1	no	—
494	C₂×D₄	—	181	2	no	—
495	C₂×D₄	—	181	2	no	—
496	C₂×D₄	—	181	2	no	—
497	C₂×D₄	—	181	2	no	—
498	C₂×D₄	—	181	2	no	—
499	C₂×D₄	—	181	2	no	—
500	C₂×D₄	—	181	2	no	—
501	C₂×D₄	—	181	2	no	—
502	C₂×D₄	—	181	2	no	—
503	C₂×D₄	—	181	1	no	—
504	C₂×D₄	—	181	1	no	—
505	C₂×D₄	—	181	2	no	—
506	C₂×D₄	—	181	2	no	—
507	C₂×D₄	—	181	2	no	—
508	C₂×D₄	—	724	2	no	—
509	C₂×D₄	—	724	4	no	—
510	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
511	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
512	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
513	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
514	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
515	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
516	C₂²×C₄	—	181	1	no	—
517	C₂²×C₄	—	181	2	no	—
518	C₂²×C₄	—	181	2	no	—
519	C₂²×C₄	—	181	1	no	—
520	C₂²×C₄	—	181	1	no	—
521	C₂²×C₄	—	181	2	no	—
522	C₂²×C₄	—	181	2	no	—
523	C₂²×C₄	—	181	2	no	—
524	C₂²×C₄	—	181	2	no	—
525	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
528	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
529	C₄⋊C₄	—	181	1	no	—
530	C₄⋊C₄	—	181	2	no	—
531	C₄⋊C₄	—	181	2	no	—
532	C₄⋊C₄	—	181	1	no	—
533	C₄⋊C₄	—	181	1	no	—
534	C₄⋊C₄	—	181	1	no	—
535	C₄⋊C₄	—	181	1	no	—
536	C₄⋊C₄	—	181	1	no	—
537	C₄⋊C₄	—	181	1	no	—
538	C₄⋊C₄	—	181	1	no	—
539	C₄⋊C₄	—	181	2	no	—
540	C₄⋊C₄	—	181	2	no	—
541	C₄⋊C₄	—	181	2	no	—
542	C₄⋊C₄	—	181	2	no	—
543	C₄⋊C₄	—	181	1	no	—
544	C₄⋊C₄	—	181	1	no	—
545	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
546	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
548	C₂²⋊C₄	—	181	2	no	—
549	C₂²⋊C₄	—	181	2	no	—
550	C₂²⋊C₄	—	181	1	no	—
551	C₂²⋊C₄	—	181	1	no	—
552	C₂²⋊C₄	—	181	2	no	—
553	C₂²⋊C₄	—	181	1	no	—
554	C₂²⋊C₄	—	181	2	no	—
555	C₂²⋊C₄	—	181	2	no	—
556	C₂²⋊C₄	—	181	2	no	—
557	C₂²⋊C₄	—	181	1	no	—
558	C₂²⋊C₄	—	181	1	no	—
559	C₂²⋊C₄	—	181	2	no	—
560	C₂²⋊C₄	—	181	1	no	—
561	C₂²⋊C₄	—	181	1	no	—
562	C₂²⋊C₄	—	181	2	no	—
563	C₂²⋊C₄	—	181	1	no	—
564	C₂²⋊C₄	—	181	2	no	—
565	C₂²⋊C₄	—	181	2	no	—
566	C₂²⋊C₄	—	181	2	no	—
567	C₂²⋊C₄	—	181	2	no	—
568	C₂²⋊C₄	—	181	2	no	—
569	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
576	C₄²	—	181	1	no	—
577	C₄²	—	181	1	no	—
578	C₄²	—	181	1	no	—
579	C₄²	—	181	1	no	—
580	C₄²	—	181	1	no	—
581	C₄²	—	181	2	no	—
582	C₄²	—	181	2	no	—
583	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	181	1	no	—
588	C₂³	—	181	2	no	—
589	C₂³	—	181	2	no	—
590	C₂³	—	724	2	no	—
591	C₂³	—	724	2	no	—
592	C₂³	—	724	2	no	—
593	C₂³	C₂³×D₁₈₁	1	2	yes	—
594	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
595	C₂³	C₂³×D₁₈₁	1	2	yes	—
596	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	362	2	no	—
599	Q₈	—	362	2	no	—
600	Q₈	—	724	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	1	no	—
607	D₄	—	362	2	no	—
608	D₄	—	362	4	no	—
609	D₄	—	362	2	no	—
610	D₄	—	362	2	no	—
611	D₄	—	724	2	no	—
612	D₄	—	724	2	no	—
613	D₄	—	724	2	no	—
614	D₄	—	724	2	no	—
615	D₄	—	724	2	no	—
616	D₄	—	724	2	no	—
617	D₄	—	724	2	no	—
618	D₄	—	724	2	no	—
619	D₄	—	724	2	no	—
620	D₄	—	724	2	no	—
621	D₄	—	724	2	no	—
622	D₄	—	724	2	no	—
623	D₄	—	724	2	no	—
624	D₄	—	724	1	no	—
625	D₄	—	724	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	362	4	no	—
631	C₂×C₄	—	362	4	no	—
632	C₂×C₄	—	362	2	no	—
633	C₂×C₄	—	362	2	no	—
634	C₂×C₄	—	181	1	no	—
635	C₂×C₄	—	181	1	no	—
636	C₂×C₄	—	181	1	no	—
637	C₂×C₄	—	181	1	no	—
638	C₂×C₄	—	181	2	no	—
639	C₂×C₄	—	181	1	no	—
640	C₂×C₄	—	181	2	no	—
641	C₂×C₄	—	181	1	no	—
642	C₂×C₄	—	181	1	no	—
643	C₂×C₄	—	724	2	no	—
644	C₂×C₄	—	724	2	no	—
645	C₂×C₄	—	724	2	no	—
646	C₂×C₄	—	724	2	no	—
647	C₂×C₄	—	724	1	no	—
648	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
651	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
653	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	8	4	no	—
668	C₂²	—	362	2	no	—
669	C₂²	—	362	2	no	—
670	C₂²	—	362	1	no	—
671	C₂²	—	362	2	no	—
672	C₂²	—	362	2	no	—
673	C₂²	—	362	1	no	—
674	C₂²	—	362	1	no	—
675	C₂²	—	362	2	no	—
676	C₂²	—	362	2	no	—
677	C₂²	—	1448	4	no	—
678	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	362	1	no	—
686	C₄	—	362	1	no	—
687	C₄	—	362	1	no	—
688	C₄	—	362	2	no	—
689	C₄	—	362	1	no	—
690	C₄	—	362	1	no	—
691	C₄	—	362	1	no	—
692	C₄	—	362	2	no	—
693	C₄	—	181	2	no	—
694	C₄	#19153861	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	724	1	no	—
700	C₂	—	724	2	no	—
701	C₂	—	724	2	no	—
702	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
703	C₂	C₂×#19153861	1	1	yes	characteristic
704	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#546×C₁₈₁	C₂
hypercenter	#546	D₁₈₁
hypocenter	C₁₈₁	#3546
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #26042018	C₂	semidirect
2. #26042017	C₂	semidirect
3. #26041998	C₂	semidirect
4. #26041974	C₂	semidirect
5. #26041950	C₂	semidirect
6. #26041950	C₂	semidirect
7. #26041948	C₂	semidirect
8. #26041931	C₂	semidirect
9. #26041926	C₂	semidirect
10. #26041919	C₂	semidirect
11. D₄×C₂²⋊D₁₈₁	C₂	semidirect
12. #26041902	C₂	semidirect
13. #26041894	C₂	semidirect
14. #26041867	C₂	semidirect
15. #26041865	C₂	semidirect
16. #26041858	C₂	semidirect
17. #26041847	C₂	semidirect
18. #26041846	C₂	semidirect
19. #26041844	C₂	semidirect
20. #26041825	C₂	semidirect
21. #26041824	C₂	semidirect
22. #26041809	C₂	semidirect
23. #546×C₁₈₁	C₂	semidirect
24. C₂×#15668450	C₂²	semidirect
25. C₂×#15668449	C₂²	semidirect
26. C₂×#15668449	C₂²	semidirect
27. C₂×#15668449	C₂²	semidirect
28. C₂×#15668448	C₂²	semidirect
31. #19153815	C₂²	semidirect
32. #19153814	C₂²	semidirect
33. #19153813	C₂²	semidirect
36. #19153812	C₂²	semidirect
37. #19153812	C₂²	semidirect
38. #19153812	C₂²	semidirect
39. #19153811	C₂²	semidirect
40. #19153811	C₂²	semidirect
41. #19153809	C₂²	semidirect
42. #19153809	C₂²	semidirect
43. #19153809	C₂²	semidirect
44. #19153809	C₂²	semidirect
45. #19153806	C₂²	semidirect
46. #19153805	C₂²	semidirect
48. #19153803	C₂²	semidirect
50. #19153802	C₂²	semidirect
51. #19153802	C₂²	semidirect
52. #19153802	C₂²	semidirect
53. #19153801	C₂²	semidirect
54. #19153800	C₂²	semidirect
55. #19153799	C₂²	semidirect
56. #19153798	C₂²	semidirect
57. #19153798	C₂²	semidirect
58. #19153798	C₂²	semidirect
59. #19153797	C₂²	semidirect
60. #19153796	C₂²	semidirect
61. #19153796	C₂²	semidirect
62. #19153795	C₂²	semidirect
63. #19153793	C₂²	semidirect
64. #19153793	C₂²	semidirect
66. #19153790	C₂²	semidirect
67. #19153790	C₂²	semidirect
68. #19153790	C₂²	semidirect
70. #19153789	C₂²	semidirect
71. #19153789	C₂²	semidirect
72. #19153789	C₂²	semidirect
73. #19153789	C₂²	semidirect
74. #19153789	C₂²	semidirect
75. #19153789	C₂²	semidirect
78. #19153788	C₂²	semidirect
79. #19153788	C₂²	semidirect
80. #19153788	C₂²	semidirect
82. #19153787	C₂²	semidirect
83. #19153787	C₂²	semidirect
84. #19153787	C₂²	semidirect
85. #19153787	C₂²	semidirect
86. #19153786	C₂²	semidirect
87. #19153786	C₂²	semidirect
89. #19153785	C₂²	semidirect
90. #19153785	C₂²	semidirect
92. #19153784	C₂²	semidirect
93. Q₈×Dic₁₈₁	C₂²	semidirect
94. C₄×Dic₃₆₂	C₂²	semidirect
95. C₄×Dic₃₆₂	C₂²	semidirect
97. #19153778	C₂²	semidirect
98. #19153778	C₂²	semidirect
99. #19153778	C₂²	semidirect
101. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
102. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
103. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
104. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
105. #19153776	C₂²	semidirect
106. #19153775	C₂²	semidirect
107. #19153773	C₂²	semidirect
108. #19153772	C₂²	semidirect
109. C₄⋊C₄×D₁₈₁	C₂²	semidirect
110. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
111. C₂×C₄×Dic₁₈₁	C₂²	semidirect
112. C₂×#41×C₁₈₁	C₂²	semidirect
115. #123×C₁₈₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. #121×C₁₈₁	C₂²	semidirect
119. #120×C₁₈₁	C₂²	semidirect
120. C₄×D₄×C₁₈₁	C₂²	semidirect
121. C₄×D₄×C₁₈₁	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₈₁	C₂²	semidirect
352. C₁₈₁	#3546	semidirect
364. #546	D₁₈₁	semidirect
382. C₂×#41	C₂×D₁₈₁	semidirect
416. #123	C₂×D₁₈₁	semidirect
422. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
445. #121	C₂×D₁₈₁	semidirect
453. #120	C₂×D₁₈₁	semidirect
467. C₄×D₄	C₂×D₁₈₁	semidirect
468. C₄×D₄	C₂×D₁₈₁	semidirect
474. C₂×C₂²⋊C₄	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042018	2
#26042017	2
#26041998	2
#26041974	2
#26041950	2
#26041948	2
#26041931	2
#26041926	2
#26041919	2
D₄×C₂²⋊D₁₈₁	2
#26041902	2
#26041894	2
#26041867	2
#26041865	2
#26041858	2
#26041847	2
#26041846	2
#26041844	2
#26041825	2
#26041824	2
#26041809	2
#546×C₁₈₁	2
#3546	181