Subgroups — #37547466

Order 23168.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041997	C₂	1	1	yes	maximal, characteristic, complemented
2	#26041990	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041987	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041970	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041970	C₂	1	2	yes	maximal, complemented
6	#26041969	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041968	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041965	C₂	1	2	yes	maximal, complemented
9	#26041963	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041959	C₂	1	2	yes	maximal, complemented
11	#26041954	C₂	1	2	yes	maximal, complemented
12	#26041906	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041893	C₂	1	2	yes	maximal, complemented
14	#26041886	C₂	1	2	yes	maximal, complemented
15	#26041852	C₂	1	1	yes	maximal, characteristic, complemented
16	#26041833	C₂	1	2	yes	maximal, complemented
17	#26041812	C₂	1	2	yes	maximal, complemented
18	#26041788	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#26041759	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041755	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668449	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₈₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₈₁	C₂²	1	1	yes	characteristic
27	#19153815	C₂²	1	2	yes	complemented
28	#19153815	C₂²	1	1	yes	characteristic, complemented
29	#19153814	C₂²	1	2	yes	complemented
30	#19153810	C₂²	1	2	yes	complemented
31	#19153810	C₂²	1	2	yes	complemented
32	#19153809	C₂²	1	2	yes	—
33	#19153809	C₂²	1	2	yes	—
34	#19153809	C₂²	1	2	yes	—
35	#19153809	C₂²	1	2	yes	complemented
36	#19153808	C₂²	1	2	yes	complemented
37	#19153808	C₂²	1	1	yes	characteristic, complemented
38	#19153807	C₂²	1	2	yes	complemented
39	#19153807	C₂²	1	1	yes	characteristic, complemented
40	#19153806	C₂²	1	2	yes	complemented
41	#19153806	C₂²	1	2	yes	complemented
42	#19153806	C₂²	1	2	yes	complemented
43	#19153806	C₂²	1	2	yes	complemented
44	#19153806	C₂²	1	2	yes	complemented
45	#19153802	C₂²	1	2	yes	—
46	#19153802	C₂²	1	2	yes	complemented
47	#19153801	C₂²	1	2	yes	—
48	#19153801	C₂²	1	2	yes	—
49	#19153801	C₂²	1	1	yes	characteristic
50	#19153798	C₂²	1	2	yes	—
51	#19153798	C₂²	1	2	yes	—
52	#19153798	C₂²	1	2	yes	—
53	#19153798	C₂²	1	1	yes	characteristic
54	#19153797	C₂²	1	2	yes	—
55	#19153796	C₂²	1	2	yes	—
56	#19153796	C₂²	1	1	yes	characteristic
57	#19153796	C₂²	1	1	yes	characteristic, complemented
58	#19153795	C₂²	1	1	yes	characteristic
59	#19153795	C₂²	1	1	yes	characteristic, complemented
60	#19153794	C₂²	1	2	yes	—
61	#19153794	C₂²	1	2	yes	—
62	#19153794	C₂²	1	1	yes	characteristic
63	#19153793	C₂²	1	1	yes	characteristic
64	#19153793	C₂²	1	2	yes	—
65	#19153793	C₂²	1	2	yes	complemented
66	#19153792	C₂²	1	2	yes	—
67	#19153792	C₂²	1	2	yes	—
68	#19153792	C₂²	1	1	yes	characteristic
69	#19153792	C₂²	1	2	yes	complemented
70	#19153792	C₂²	1	1	yes	characteristic, complemented
71	#19153789	C₂²	1	1	yes	characteristic
72	#19153788	C₂²	1	1	yes	characteristic
73	#19153786	C₂²	1	1	yes	characteristic
74	#19153784	C₂²	1	1	yes	characteristic
75	Q₈×Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
77	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
78	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
79	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
80	#19153781	C₂²	1	2	yes	complemented
81	#19153781	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₇₂₄	C₂²	1	2	yes	—
83	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
84	#19153778	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
87	#19153776	C₂²	1	2	yes	—
88	#19153776	C₂²	1	2	yes	—
89	#19153776	C₂²	1	2	yes	complemented
90	#19153775	C₂²	1	1	yes	characteristic
91	#19153774	C₂²	1	1	yes	characteristic
92	#19153774	C₂²	1	2	yes	—
93	#19153774	C₂²	1	1	yes	characteristic
94	#19153774	C₂²	1	2	yes	complemented
95	#19153774	C₂²	1	1	yes	characteristic, complemented
96	#19153773	C₂²	1	1	yes	characteristic
97	#19153773	C₂²	1	2	yes	—
98	#19153773	C₂²	1	2	yes	—
99	#19153773	C₂²	1	2	yes	—
100	#19153773	C₂²	1	2	yes	—
101	#19153772	C₂²	1	2	yes	—
102	#19153772	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
111	C₄²×D₁₈₁	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₈₁	C₂²	1	2	yes	—
114	#126×C₁₈₁	C₂²	1	2	yes	complemented
115	#124×C₁₈₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₁₈₁	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
121	#117×C₁₈₁	C₂²	1	1	yes	characteristic
122	#117×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	1	yes	characteristic
124	#15668449	—	2	4	no	—
125	C₂×Dic₃₆₂	C₂³	1	2	yes	—
126	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₃₆₂	C₂³	1	2	yes	—
129	Q₈×D₁₈₁	—	2	4	no	—
130	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
131	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
138	C₂×C₄×D₁₈₁	—	2	4	no	—
139	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
141	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
142	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
146	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
148	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
153	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
154	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
155	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
156	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
158	#15668428	C₂³	1	2	yes	—
159	#15668428	C₂³	1	2	yes	—
160	#15668428	C₂³	1	2	yes	—
161	#15668428	C₂³	1	2	yes	—
162	#15668428	C₂³	1	2	yes	—
163	#15668428	C₂³	1	2	yes	—
164	#15668428	C₂³	1	2	yes	—
165	#15668428	C₂³	1	1	yes	characteristic
166	#15668428	C₂³	1	2	yes	—
167	#15668428	C₂³	1	1	yes	characteristic
168	#15668428	C₂³	1	2	yes	—
169	#15668428	C₂³	1	2	yes	—
170	#15668428	C₂³	1	2	yes	—
171	#15668428	C₂³	1	2	yes	—
172	#15668428	C₂³	1	2	yes	—
173	#15668428	C₂³	1	2	yes	—
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
181	#15668426	C₂³	1	2	yes	—
182	#15668426	C₂³	1	2	yes	—
183	#15668426	C₂³	1	2	yes	—
184	#15668426	C₂³	1	2	yes	—
185	#15668426	C₂³	1	1	yes	characteristic
186	#15668426	C₂³	1	1	yes	characteristic
187	#15668426	C₂³	1	1	yes	characteristic
188	#15668426	C₂³	1	1	yes	characteristic
189	#15668426	C₂³	1	1	yes	characteristic
190	#15668426	C₂³	1	2	yes	—
191	#15668426	C₂³	1	2	yes	—
192	#15668426	C₂³	1	2	yes	—
193	#15668426	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₈₁	C₂³	1	2	yes	—
195	C₄×Dic₁₈₁	C₂³	1	2	yes	—
196	C₄×Dic₁₈₁	C₂³	1	2	yes	—
197	C₄×Dic₁₈₁	C₂³	1	2	yes	—
198	C₄×Dic₁₈₁	C₂³	1	2	yes	—
199	C₄×Dic₁₈₁	C₂³	1	2	yes	—
200	C₄×Dic₁₈₁	C₂³	1	2	yes	—
201	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₈₁	C₂³	1	2	yes	—
204	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₄²×C₁₈₁	C₂³	1	2	yes	—
222	C₄²×C₁₈₁	C₂³	1	2	yes	—
223	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
224	C₄²×C₁₈₁	C₂³	1	2	yes	—
225	C₂²×D₁₈₁	—	2	2	no	—
226	C₂²×D₁₈₁	—	2	2	no	—
227	C₂²×D₁₈₁	—	4	1	no	—
228	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
231	Dic₃₆₂	—	2	2	no	—
232	Dic₃₆₂	—	2	4	no	—
233	Dic₃₆₂	—	2	2	no	—
234	Dic₃₆₂	—	4	2	no	—
235	D₇₂₄	—	2	2	no	—
236	D₇₂₄	—	2	2	no	—
237	C₂²⋊D₁₈₁	—	2	2	no	—
238	C₂²⋊D₁₈₁	—	2	2	no	—
239	C₂²⋊D₁₈₁	—	2	2	no	—
240	C₂²⋊D₁₈₁	—	4	1	no	—
241	C₂×Dic₁₈₁	—	2	2	no	—
242	C₂×Dic₁₈₁	—	4	2	no	—
243	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
244	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
247	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
248	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
250	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
252	C₄×D₁₈₁	—	2	2	no	—
253	C₄×D₁₈₁	—	2	4	no	—
254	C₄×D₁₈₁	—	2	4	no	—
255	C₄×D₁₈₁	—	2	2	no	—
256	C₄×D₁₈₁	—	2	2	no	—
257	C₄×D₁₈₁	—	2	2	no	—
258	C₄×D₁₈₁	—	4	2	no	—
259	C₄×D₁₈₁	—	4	2	no	—
260	C₄×D₁₈₁	—	4	2	no	—
261	C₄×D₁₈₁	#41	1	4	yes	—
262	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
263	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
264	Q₈×C₁₈₁	—	2	2	no	—
265	Q₈×C₁₈₁	—	4	2	no	—
266	D₄×C₁₈₁	—	4	1	no	—
267	C₂×C₄×C₁₈₁	—	2	2	no	—
268	C₂×C₄×C₁₈₁	—	2	2	no	—
269	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
276	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₁₈₁	—	2	1	no	—
279	C₂²×C₁₈₁	—	2	1	no	—
280	C₂²×C₁₈₁	—	2	1	no	—
281	C₂²×C₁₈₁	—	2	1	no	—
282	C₂²×C₁₈₁	—	2	1	no	—
283	C₂²×C₁₈₁	—	2	1	no	—
284	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
285	C₂×D₁₈₁	—	2	1	no	—
286	C₂×D₁₈₁	—	2	1	no	—
287	C₂×D₁₈₁	—	2	1	no	—
288	C₂×D₁₈₁	—	2	1	no	—
289	C₂×D₁₈₁	—	2	1	no	—
290	C₂×D₁₈₁	—	2	1	no	—
291	C₂×D₁₈₁	—	2	1	no	—
292	C₂×D₁₈₁	—	4	4	no	—
293	C₂×D₁₈₁	C₂×#41	1	2	yes	—
294	C₂×D₁₈₁	2₋¹⁺⁴	1	2	yes	—
295	C₄×C₁₈₁	—	2	1	no	—
296	C₄×C₁₈₁	—	2	1	no	—
297	C₄×C₁₈₁	—	2	2	no	—
298	C₄×C₁₈₁	—	2	2	no	—
299	C₄×C₁₈₁	—	2	1	no	—
300	C₄×C₁₈₁	—	2	1	no	—
301	C₄×C₁₈₁	—	2	2	no	—
302	C₄×C₁₈₁	—	2	2	no	—
303	C₄×C₁₈₁	C₂×#41	1	2	yes	—
304	Dic₁₈₁	—	2	1	no	—
305	Dic₁₈₁	—	2	1	no	—
306	Dic₁₈₁	—	2	2	no	—
307	Dic₁₈₁	—	2	2	no	—
308	Dic₁₈₁	—	2	1	no	—
309	Dic₁₈₁	—	2	2	no	—
310	Dic₁₈₁	—	2	2	no	—
311	Dic₁₈₁	—	2	1	no	—
312	Dic₁₈₁	C₂×#41	1	2	yes	—
313	C₂×C₁₈₁	—	4	1	no	—
314	C₂×C₁₈₁	—	4	1	no	—
315	C₂×C₁₈₁	C₂²×#41	1	1	yes	characteristic
316	C₂×C₁₈₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂×C₁₈₁	#585	1	1	yes	characteristic
318	D₁₈₁	—	2	2	no	—
319	D₁₈₁	—	2	2	no	—
320	D₁₈₁	—	4	1	no	—
321	C₁₈₁	#3495	1	1	yes	characteristic, complemented, Sylow
322	#3495	—	181	1	no	maximal, Sylow
323	#556	—	181	1	no	—
324	#556	D₁₈₁	1	1	yes	characteristic, complemented
325	#554	—	181	1	no	—
326	#554	—	181	1	no	—
327	#552	—	181	2	no	—
328	#552	—	181	1	no	—
329	#552	—	181	1	no	—
330	#552	—	181	2	no	—
331	#552	—	181	1	no	—
332	#552	—	181	1	no	—
333	#551	—	181	2	no	—
334	#551	—	181	2	no	—
335	#544	—	181	1	no	—
336	#542	—	181	2	no	—
337	#541	—	181	2	no	—
338	#536	—	181	1	no	—
339	#533	—	181	2	no	—
340	#529	—	181	2	no	—
341	#525	—	181	1	no	—
342	C₂×C₂²⋊Q₈	—	181	1	no	—
343	#520	—	181	1	no	—
344	#519	—	181	1	no	—
345	C₂×#117	—	181	1	no	—
346	C₂×#41	—	181	1	no	—
347	C₂²×Q₈	—	181	1	no	—
348	C₂³×C₄	—	181	1	no	—
349	C₄⋊Q₈	—	181	2	no	—
350	C₄⋊Q₈	—	181	2	no	—
351	C₄⋊Q₈	—	181	1	no	—
352	C₄⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
353	#126	—	181	2	no	—
354	#126	—	181	2	no	—
355	#126	—	181	2	no	—
356	#126	—	181	2	no	—
357	#126	—	181	2	no	—
358	#126	—	181	2	no	—
359	#126	C₂×D₁₈₁	1	2	yes	—
360	#126	C₂×D₁₈₁	1	2	yes	complemented
361	#125	—	181	2	no	—
362	#125	—	181	2	no	—
363	#125	—	181	2	no	—
364	#125	—	181	2	no	—
365	#125	—	181	2	no	—
366	#125	—	181	2	no	—
367	#125	—	181	1	no	—
368	#125	—	181	2	no	—
369	#125	—	181	1	no	—
370	#124	—	181	2	no	—
371	#124	—	181	2	no	—
372	#124	C₂×D₁₈₁	1	2	yes	—
373	#123	—	181	2	no	—
374	#123	—	181	1	no	—
375	#123	—	181	2	no	—
376	#123	—	181	2	no	—
377	#123	—	181	1	no	—
378	#123	—	181	2	no	—
379	#123	—	181	2	no	—
380	#123	—	181	2	no	—
381	C₂²⋊Q₈	—	181	1	no	—
382	C₂²⋊Q₈	—	181	2	no	—
383	C₂²⋊Q₈	—	181	1	no	—
384	C₂²⋊Q₈	—	181	2	no	—
385	C₂²⋊Q₈	—	181	2	no	—
386	C₂²⋊Q₈	—	181	1	no	—
387	C₂²⋊Q₈	—	181	1	no	—
388	C₂²⋊Q₈	—	181	2	no	—
389	C₂²⋊Q₈	—	181	1	no	—
390	C₂²⋊Q₈	—	181	1	no	—
391	C₂²⋊Q₈	—	181	2	no	—
392	C₂²⋊Q₈	—	181	1	no	—
393	C₂²⋊Q₈	—	181	2	no	—
394	C₂²⋊Q₈	—	181	2	no	—
395	C₂²⋊Q₈	—	181	1	no	—
396	C₂²⋊Q₈	—	181	2	no	—
397	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic
398	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
399	#121	—	181	1	no	—
400	#121	—	181	1	no	—
401	#120	—	181	1	no	—
402	#120	—	181	1	no	—
403	C₄×Q₈	—	181	1	no	—
404	C₄×Q₈	—	181	2	no	—
405	C₄×Q₈	—	181	1	no	—
406	C₄×Q₈	—	181	2	no	—
407	C₄×Q₈	—	181	1	no	—
408	C₄×Q₈	—	181	2	no	—
409	C₄×Q₈	—	181	2	no	—
410	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
411	C₄×Q₈	C₂×D₁₈₁	1	2	yes	complemented
412	C₄×D₄	—	181	1	no	—
413	C₄×D₄	—	181	1	no	—
414	C₄×D₄	—	181	2	no	—
415	C₄×D₄	—	181	2	no	—
416	C₄×D₄	—	181	2	no	—
417	C₄×D₄	—	181	2	no	—
418	C₄×D₄	—	181	2	no	—
419	C₄×D₄	—	181	1	no	—
420	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
421	#117	—	181	1	no	—
422	#117	—	181	1	no	—
423	#117	—	181	1	no	—
424	#117	—	181	2	no	—
425	#117	—	181	1	no	—
426	#117	—	181	2	no	—
427	#117	—	181	2	no	—
428	#117	—	181	2	no	—
429	#117	—	181	2	no	—
430	#117	—	181	1	no	—
431	#117	—	181	2	no	—
432	#117	—	181	2	no	—
433	#117	—	181	2	no	—
434	#117	C₂×D₁₈₁	1	1	yes	characteristic
435	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	181	1	no	—
437	C₂×C₄⋊C₄	—	181	1	no	—
438	C₂×C₄⋊C₄	—	181	1	no	—
439	C₂×C₄⋊C₄	—	181	1	no	—
440	C₂×C₄⋊C₄	—	181	1	no	—
441	C₂×C₄⋊C₄	—	181	2	no	—
442	C₂×C₂²⋊C₄	—	181	2	no	—
443	C₂×C₂²⋊C₄	—	181	2	no	—
444	C₂×C₄²	—	181	2	no	—
445	C₂⁴	—	181	1	no	—
446	#41	—	362	4	no	—
447	C₂×Q₈	—	362	4	no	—
448	C₂×Q₈	—	181	1	no	—
449	C₂×Q₈	—	181	2	no	—
450	C₂×Q₈	—	181	1	no	—
451	C₂×Q₈	—	181	2	no	—
452	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₈₁	1	2	yes	—
454	C₂×D₄	—	181	1	no	—
455	C₂×D₄	—	181	1	no	—
456	C₂×D₄	—	181	1	no	—
457	C₂×D₄	—	181	1	no	—
458	C₂×D₄	—	181	1	no	—
459	C₂×D₄	—	181	1	no	—
460	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
461	C₂²×C₄	—	362	4	no	—
462	C₂²×C₄	—	181	1	no	—
463	C₂²×C₄	—	181	1	no	—
464	C₂²×C₄	—	181	2	no	—
465	C₂²×C₄	—	181	2	no	—
466	C₂²×C₄	—	181	1	no	—
467	C₂²×C₄	—	181	1	no	—
468	C₂²×C₄	—	181	1	no	—
469	C₂²×C₄	—	181	1	no	—
470	C₂²×C₄	—	181	2	no	—
471	C₂²×C₄	—	181	2	no	—
472	C₂²×C₄	—	181	2	no	—
473	C₂²×C₄	—	181	2	no	—
474	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
476	C₄⋊C₄	—	181	1	no	—
477	C₄⋊C₄	—	181	1	no	—
478	C₄⋊C₄	—	181	2	no	—
479	C₄⋊C₄	—	181	1	no	—
480	C₄⋊C₄	—	181	2	no	—
481	C₄⋊C₄	—	181	2	no	—
482	C₄⋊C₄	—	181	2	no	—
483	C₄⋊C₄	—	181	2	no	—
484	C₄⋊C₄	—	181	2	no	—
485	C₄⋊C₄	—	181	2	no	—
486	C₄⋊C₄	—	181	2	no	—
487	C₄⋊C₄	—	181	1	no	—
488	C₄⋊C₄	—	181	1	no	—
489	C₄⋊C₄	—	181	2	no	—
490	C₄⋊C₄	—	181	2	no	—
491	C₄⋊C₄	—	181	2	no	—
492	C₄⋊C₄	—	181	2	no	—
493	C₄⋊C₄	—	181	2	no	—
494	C₄⋊C₄	—	181	2	no	—
495	C₄⋊C₄	—	181	2	no	—
496	C₄⋊C₄	—	181	2	no	—
497	C₄⋊C₄	—	181	2	no	—
498	C₄⋊C₄	—	181	1	no	—
499	C₄⋊C₄	—	181	1	no	—
500	C₄⋊C₄	—	181	1	no	—
501	C₄⋊C₄	—	181	2	no	—
502	C₄⋊C₄	—	181	2	no	—
503	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
509	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
511	C₂²⋊C₄	—	181	2	no	—
512	C₂²⋊C₄	—	181	2	no	—
513	C₂²⋊C₄	—	181	2	no	—
514	C₂²⋊C₄	—	181	1	no	—
515	C₂²⋊C₄	—	181	1	no	—
516	C₂²⋊C₄	—	181	2	no	—
517	C₂²⋊C₄	—	181	2	no	—
518	C₂²⋊C₄	—	181	2	no	—
519	C₂²⋊C₄	—	181	2	no	—
520	C₂²⋊C₄	—	181	1	no	—
521	C₂²⋊C₄	—	181	1	no	—
522	C₂²⋊C₄	—	181	1	no	—
523	C₂²⋊C₄	—	181	1	no	—
524	C₂²⋊C₄	—	181	1	no	—
525	C₂²⋊C₄	—	181	2	no	—
526	C₂²⋊C₄	—	181	2	no	—
527	C₂²⋊C₄	—	181	1	no	—
528	C₂²⋊C₄	—	181	2	no	—
529	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
535	C₄²	—	181	2	no	—
536	C₄²	—	181	2	no	—
537	C₄²	—	181	2	no	—
538	C₄²	—	181	2	no	—
539	C₄²	—	181	2	no	—
540	C₄²	—	181	2	no	—
541	C₄²	—	181	2	no	—
542	C₄²	—	181	1	no	—
543	C₄²	C₂²×D₁₈₁	1	2	yes	—
544	C₄²	C₂²×D₁₈₁	1	2	yes	—
545	C₄²	C₂²×D₁₈₁	1	2	yes	—
546	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
547	C₂³	—	362	2	no	—
548	C₂³	—	362	2	no	—
549	C₂³	—	181	1	no	—
550	C₂³	—	181	1	no	—
551	C₂³	—	181	1	no	—
552	C₂³	—	724	1	no	—
553	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
554	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	362	4	no	—
558	Q₈	—	362	2	no	—
559	Q₈	—	362	2	no	—
560	Q₈	—	724	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	362	2	no	—
563	D₄	—	362	2	no	—
564	D₄	—	362	2	no	—
565	D₄	—	362	2	no	—
566	D₄	—	362	2	no	—
567	D₄	—	724	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	362	2	no	—
571	C₂×C₄	—	362	4	no	—
572	C₂×C₄	—	362	4	no	—
573	C₂×C₄	—	362	2	no	—
574	C₂×C₄	—	362	2	no	—
575	C₂×C₄	—	362	2	no	—
576	C₂×C₄	—	362	2	no	—
577	C₂×C₄	—	181	2	no	—
578	C₂×C₄	—	181	1	no	—
579	C₂×C₄	—	181	1	no	—
580	C₂×C₄	—	181	2	no	—
581	C₂×C₄	—	181	2	no	—
582	C₂×C₄	—	181	1	no	—
583	C₂×C₄	—	181	2	no	—
584	C₂×C₄	—	181	1	no	—
585	C₂×C₄	—	181	1	no	—
586	C₂×C₄	—	181	4	no	—
587	C₂×C₄	—	724	2	no	—
588	C₂×C₄	—	724	2	no	—
589	C₂×C₄	—	724	2	no	—
590	C₂×C₄	—	724	2	no	—
591	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
592	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
595	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
596	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
599	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	362	1	no	—
607	C₂²	—	362	1	no	—
608	C₂²	—	362	1	no	—
609	C₂²	—	362	1	no	—
610	C₂²	—	362	1	no	—
611	C₂²	—	362	1	no	—
612	C₂²	—	362	1	no	—
613	C₂²	—	181	2	no	—
614	C₂²	—	181	2	no	—
615	C₂²	—	724	4	no	—
616	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	362	2	no	—
626	C₄	—	362	2	no	—
627	C₄	—	362	1	no	—
628	C₄	—	362	1	no	—
629	C₄	—	362	1	no	—
630	C₄	—	362	2	no	—
631	C₄	—	362	2	no	—
632	C₄	—	362	1	no	—
633	C₄	—	181	2	no	—
634	C₄	#41×D₁₈₁	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	362	2	no	—
638	C₂	—	362	2	no	—
639	C₂	—	724	1	no	—
640	C₂	C₂×#41×D₁₈₁	1	1	yes	characteristic
641	C₂	2₋¹⁺⁴×D₁₈₁	1	1	yes	characteristic
642	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#556×C₁₈₁	C₂
prime radical	#26041788	C₂
hypercenter	#556	D₁₈₁
hypocenter	C₁₈₁	#3495
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #26041997	C₂	semidirect
2. #26041990	C₂	semidirect
3. #26041987	C₂	semidirect
4. #26041970	C₂	semidirect
5. #26041970	C₂	semidirect
6. #26041969	C₂	semidirect
7. #26041968	C₂	semidirect
8. #26041965	C₂	semidirect
9. #26041963	C₂	semidirect
10. #26041959	C₂	semidirect
11. #26041954	C₂	semidirect
12. #26041906	C₂	semidirect
13. #26041893	C₂	semidirect
14. #26041886	C₂	semidirect
15. #26041852	C₂	semidirect
16. #26041833	C₂	semidirect
17. #26041812	C₂	semidirect
19. C₂²⋊Q₈×D₁₈₁	C₂	semidirect
20. #26041759	C₂	semidirect
21. #26041755	C₂	semidirect
22. #117×D₁₈₁	C₂	semidirect
23. #556×C₁₈₁	C₂	semidirect
27. #19153815	C₂²	semidirect
28. #19153815	C₂²	semidirect
29. #19153814	C₂²	semidirect
30. #19153810	C₂²	semidirect
31. #19153810	C₂²	semidirect
35. #19153809	C₂²	semidirect
36. #19153808	C₂²	semidirect
37. #19153808	C₂²	semidirect
38. #19153807	C₂²	semidirect
39. #19153807	C₂²	semidirect
40. #19153806	C₂²	semidirect
41. #19153806	C₂²	semidirect
42. #19153806	C₂²	semidirect
43. #19153806	C₂²	semidirect
44. #19153806	C₂²	semidirect
46. #19153802	C₂²	semidirect
57. #19153796	C₂²	semidirect
59. #19153795	C₂²	semidirect
65. #19153793	C₂²	semidirect
69. #19153792	C₂²	semidirect
70. #19153792	C₂²	semidirect
75. Q₈×Dic₁₈₁	C₂²	semidirect
76. C₄×Dic₃₆₂	C₂²	semidirect
77. C₄×Dic₃₆₂	C₂²	semidirect
78. C₄×Dic₃₆₂	C₂²	semidirect
79. C₄×Dic₃₆₂	C₂²	semidirect
80. #19153781	C₂²	semidirect
81. #19153781	C₂²	semidirect
89. #19153776	C₂²	semidirect
94. #19153774	C₂²	semidirect
95. #19153774	C₂²	semidirect
102. #19153772	C₂²	semidirect
103. C₂×C₄⋊Dic₁₈₁	C₂²	semidirect
108. C₄⋊C₄×D₁₈₁	C₂²	semidirect
112. C₄⋊Q₈×C₁₈₁	C₂²	semidirect
114. #126×C₁₈₁	C₂²	semidirect
117. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. C₄×Q₈×C₁₈₁	C₂²	semidirect
119. C₄×Q₈×C₁₈₁	C₂²	semidirect
122. #117×C₁₈₁	C₂²	semidirect
321. C₁₈₁	#3495	semidirect
324. #556	D₁₈₁	semidirect
352. C₄⋊Q₈	C₂×D₁₈₁	semidirect
360. #126	C₂×D₁₈₁	semidirect
398. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
410. C₄×Q₈	C₂×D₁₈₁	semidirect
411. C₄×Q₈	C₂×D₁₈₁	semidirect
435. #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
#26041997	2
#26041990	2
#26041987	2
#26041970	2
#26041969	2
#26041968	2
#26041965	2
#26041963	2
#26041959	2
#26041954	2
#26041906	2
#26041893	2
#26041886	2
#26041852	2
#26041833	2
#26041812	2
#26041788	2
C₂²⋊Q₈×D₁₈₁	2
#26041759	2
#26041755	2
#117×D₁₈₁	2
#556×C₁₈₁	2
#3495	181