Subgroups — #37547520

Order 23168.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041989	C₂	1	1	yes	maximal, characteristic, complemented
2	#26041988	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041988	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041985	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041985	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041984	C₂	1	2	yes	maximal, complemented
7	#26041983	C₂	1	2	yes	maximal, complemented
8	#26041983	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₃₆₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041944	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041942	C₂	1	2	yes	maximal, complemented
12	#26041909	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041906	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041904	C₂	1	2	yes	maximal, complemented
15	#26041904	C₂	1	2	yes	maximal, complemented
16	#26041835	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041833	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#19153794	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₈₁	C₂	1	2	yes	maximal, complemented
20	#26041751	C₂	1	1	yes	maximal, characteristic
21	#26041751	C₂	1	1	yes	maximal, characteristic
22	C₄×D₄×D₁₈₁	C₂	1	1	yes	maximal, characteristic
23	#554×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₃₆₂	C₂²	1	2	yes	complemented
25	C₂×Q₈×D₁₈₁	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₈₁	C₂²	1	2	yes	—
28	#19153816	C₂²	1	1	yes	characteristic, complemented
29	#19153815	C₂²	1	1	yes	characteristic, complemented
30	#19153815	C₂²	1	2	yes	complemented
31	#19153815	C₂²	1	1	yes	characteristic, complemented
32	#19153815	C₂²	1	1	yes	characteristic, complemented
33	#19153815	C₂²	1	1	yes	characteristic, complemented
34	#19153815	C₂²	1	1	yes	characteristic, complemented
35	#19153814	C₂²	1	2	yes	complemented
36	#19153814	C₂²	1	1	yes	characteristic, complemented
37	#19153808	C₂²	1	1	yes	characteristic, complemented
38	#19153808	C₂²	1	1	yes	characteristic, complemented
39	#19153807	C₂²	1	1	yes	characteristic, complemented
40	#19153807	C₂²	1	1	yes	characteristic, complemented
41	#19153806	C₂²	1	2	yes	complemented
42	#19153806	C₂²	1	2	yes	complemented
43	#19153806	C₂²	1	1	yes	characteristic, complemented
44	#19153806	C₂²	1	1	yes	characteristic, complemented
45	#19153796	C₂²	1	1	yes	characteristic
46	#19153796	C₂²	1	2	yes	—
47	#19153796	C₂²	1	2	yes	complemented
48	#19153796	C₂²	1	2	yes	complemented
49	#19153795	C₂²	1	2	yes	complemented
50	#19153795	C₂²	1	2	yes	complemented
51	#19153795	C₂²	1	2	yes	complemented
52	#19153794	C₂²	1	2	yes	—
53	#19153794	C₂²	1	2	yes	—
54	#19153794	C₂²	1	2	yes	—
55	#19153794	C₂²	1	1	yes	characteristic
56	#19153794	C₂²	1	2	yes	—
57	#19153794	C₂²	1	1	yes	characteristic
58	#19153794	C₂²	1	2	yes	complemented
59	#19153794	C₂²	1	2	yes	complemented
60	#19153794	C₂²	1	2	yes	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	#19153794	C₂²	1	2	yes	complemented
66	#19153793	C₂²	1	2	yes	complemented
67	#19153793	C₂²	1	2	yes	complemented
68	#19153793	C₂²	1	2	yes	complemented
69	#19153793	C₂²	1	2	yes	complemented
70	#19153793	C₂²	1	2	yes	complemented
71	#19153793	C₂²	1	2	yes	complemented
72	#19153792	C₂²	1	1	yes	characteristic
73	#19153792	C₂²	1	2	yes	—
74	#19153792	C₂²	1	2	yes	complemented
75	#19153792	C₂²	1	2	yes	complemented
76	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, 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	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
85	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
87	#19153778	C₂²	1	1	yes	characteristic
88	#19153778	C₂²	1	1	yes	characteristic
89	#19153778	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
93	#19153776	C₂²	1	2	yes	—
94	#19153776	C₂²	1	2	yes	—
95	#19153776	C₂²	1	2	yes	—
96	#19153774	C₂²	1	1	yes	characteristic
97	#19153774	C₂²	1	1	yes	characteristic
98	#19153773	C₂²	1	1	yes	characteristic
99	#19153773	C₂²	1	1	yes	characteristic
100	C₂×#15668428	C₂²	1	2	yes	complemented
101	C₂×#15668428	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
106	C₂×#15668426	C₂²	1	2	yes	—
107	C₂×#15668426	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
111	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
114	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	2	yes	complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	C₂×Dic₃₆₂	—	4	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	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₆₂	C₂³	1	2	yes	—
131	C₂×Dic₃₆₂	C₂³	1	2	yes	—
132	C₂×Dic₃₆₂	C₂³	1	2	yes	—
133	Q₈×D₁₈₁	—	4	4	no	—
134	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
136	D₄×D₁₈₁	Q₈	1	8	yes	complemented
137	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
138	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
139	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₈₁	—	4	4	no	—
141	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
150	C₂×C₄×D₁₈₁	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	1	yes	characteristic
156	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
160	#15668428	C₂³	1	2	yes	—
161	#15668428	C₂³	1	1	yes	characteristic
162	#15668428	C₂³	1	1	yes	characteristic
163	#15668428	C₂³	1	2	yes	—
164	#15668428	C₂³	1	2	yes	—
165	#15668428	C₂³	1	2	yes	—
166	#15668428	C₂³	1	2	yes	—
167	#15668428	C₂³	1	1	yes	characteristic
168	#15668428	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	1	yes	characteristic
176	#15668428	C₂³	1	1	yes	characteristic
177	#15668428	C₂³	1	2	yes	—
178	#15668428	C₂³	1	2	yes	—
179	#15668428	C₂³	1	1	yes	characteristic
180	#15668428	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
184	#15668426	C₂³	1	1	yes	characteristic
185	#15668426	C₂³	1	1	yes	characteristic
186	#15668426	C₂³	1	2	yes	—
187	#15668426	C₂³	1	2	yes	—
188	#15668426	C₂³	1	2	yes	—
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	2	yes	—
194	#15668426	C₂³	1	2	yes	—
195	#15668426	C₂³	1	2	yes	—
196	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₈₁	C₂³	1	2	yes	—
202	C₄×Dic₁₈₁	C₂³	1	2	yes	—
203	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₁₈₁	C₂³	1	2	yes	—
205	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
223	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
224	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
225	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
226	C₂²×D₁₈₁	—	4	2	no	—
227	C₂²×D₁₈₁	—	4	2	no	—
228	C₂²×D₁₈₁	C₂×Q₈	1	8	yes	complemented
229	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
231	Dic₃₆₂	—	2	2	no	—
232	Dic₃₆₂	—	2	4	no	—
233	Dic₃₆₂	—	2	2	no	—
234	Dic₃₆₂	—	4	2	no	—
235	Dic₃₆₂	—	4	2	no	—
236	Dic₃₆₂	—	4	2	no	—
237	Dic₃₆₂	—	4	1	no	—
238	Dic₃₆₂	—	4	2	no	—
239	D₇₂₄	C₂×Q₈	1	4	yes	complemented
240	C₂²⋊D₁₈₁	C₂×Q₈	1	8	yes	complemented
241	C₂×Dic₁₈₁	—	2	4	no	—
242	C₂×Dic₁₈₁	—	4	2	no	—
243	C₂×Dic₁₈₁	—	4	2	no	—
244	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
248	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
249	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
252	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₈₁	—	2	2	no	—
255	C₄×D₁₈₁	—	2	4	no	—
256	C₄×D₁₈₁	—	4	2	no	—
257	C₄×D₁₈₁	—	4	2	no	—
258	C₄×D₁₈₁	—	4	2	no	—
259	C₄×D₁₈₁	—	4	2	no	—
260	C₄×D₁₈₁	—	4	1	no	—
261	C₄×D₁₈₁	—	4	2	no	—
262	C₄×D₁₈₁	—	4	2	no	—
263	C₄×D₁₈₁	C₂×Q₈	1	4	yes	complemented
264	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
265	Q₈×C₁₈₁	—	4	1	no	—
266	Q₈×C₁₈₁	—	4	2	no	—
267	D₄×C₁₈₁	C₂×Q₈	1	4	yes	complemented
268	C₂×C₄×C₁₈₁	—	4	2	no	—
269	C₂×C₄×C₁₈₁	—	4	2	no	—
270	C₂×C₄×C₁₈₁	—	4	2	no	—
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	1	yes	characteristic
275	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₁₈₁	—	2	2	no	—
282	C₂²×C₁₈₁	—	2	2	no	—
283	C₂²×C₁₈₁	C₂²×Q₈	1	4	yes	—
284	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
285	C₂×D₁₈₁	—	2	2	no	—
286	C₂×D₁₈₁	—	2	1	no	—
287	C₂×D₁₈₁	—	2	2	no	—
288	C₂×D₁₈₁	—	2	1	no	—
289	C₂×D₁₈₁	—	4	8	no	—
290	C₂×D₁₈₁	C₂²×Q₈	1	2	yes	—
291	C₂×D₁₈₁	C₂²×Q₈	1	4	yes	—
292	C₄×C₁₈₁	—	2	1	no	—
293	C₄×C₁₈₁	—	2	1	no	—
294	C₄×C₁₈₁	—	2	2	no	—
295	C₄×C₁₈₁	—	2	2	no	—
296	C₄×C₁₈₁	—	2	1	no	—
297	C₄×C₁₈₁	—	2	1	no	—
298	C₄×C₁₈₁	—	2	2	no	—
299	C₄×C₁₈₁	—	2	1	no	—
300	C₄×C₁₈₁	—	2	1	no	—
301	C₄×C₁₈₁	C₂²×Q₈	1	2	yes	—
302	Dic₁₈₁	—	2	2	no	—
303	Dic₁₈₁	—	2	1	no	—
304	Dic₁₈₁	—	2	2	no	—
305	Dic₁₈₁	—	2	1	no	—
306	Dic₁₈₁	—	2	1	no	—
307	Dic₁₈₁	—	2	2	no	—
308	Dic₁₈₁	—	2	1	no	—
309	Dic₁₈₁	—	2	1	no	—
310	Dic₁₈₁	C₂²×Q₈	1	2	yes	—
311	Dic₁₈₁	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₁₈₁	—	2	4	no	—
313	C₂×C₁₈₁	C₂³×Q₈	1	1	yes	characteristic
314	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₁₈₁	#585	1	1	yes	characteristic
316	D₁₈₁	—	2	2	no	—
317	D₁₈₁	—	2	4	no	—
318	C₁₈₁	#3501	1	1	yes	characteristic, complemented, Sylow
319	#3501	—	181	1	no	maximal, Sylow
320	#554	—	181	1	no	—
321	#554	—	181	1	no	—
322	#554	—	181	2	no	—
323	#554	—	181	2	no	—
324	#554	—	181	1	no	—
325	#554	—	181	1	no	—
326	#554	—	181	1	no	—
327	#554	—	181	2	no	—
328	#554	D₁₈₁	1	1	yes	characteristic, complemented
329	D₄×Q₈	—	181	1	no	—
330	D₄×Q₈	—	181	2	no	—
331	D₄×Q₈	—	181	1	no	—
332	#544	—	181	1	no	—
333	#544	—	181	1	no	—
334	#543	—	181	2	no	—
335	#543	—	181	2	no	—
336	#533	—	181	1	no	—
337	#533	—	181	1	no	—
338	C₂×C₂²⋊Q₈	—	181	2	no	—
339	C₂×C₂²⋊Q₈	—	181	2	no	—
340	#518	—	181	1	no	—
341	#518	—	181	1	no	—
342	C₂×C₄×D₄	—	181	1	no	—
343	C₂²×Q₈	—	181	2	no	—
344	C₂²×Q₈	—	181	2	no	—
345	C₂²×D₄	—	181	1	no	—
346	C₂³×C₄	—	181	2	no	—
347	C₄⋊Q₈	—	181	1	no	—
348	C₄⋊Q₈	—	181	2	no	—
349	C₄⋊Q₈	—	181	1	no	—
350	C₄⋊Q₈	—	181	1	no	—
351	C₄⋊Q₈	—	181	1	no	—
352	C₄⋊Q₈	—	181	2	no	—
353	C₄⋊Q₈	—	181	1	no	—
354	C₄⋊Q₈	—	181	1	no	—
355	C₄⋊Q₈	—	181	1	no	—
356	C₄⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
357	#125	—	181	1	no	—
358	#125	—	181	1	no	—
359	#125	—	181	2	no	—
360	#125	—	181	2	no	—
361	#125	—	181	1	no	—
362	#125	—	181	1	no	—
363	#125	—	181	1	no	—
364	#125	—	181	1	no	—
365	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
366	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
367	C₂²⋊Q₈	—	181	2	no	—
368	C₂²⋊Q₈	—	181	1	no	—
369	C₂²⋊Q₈	—	181	2	no	—
370	C₂²⋊Q₈	—	181	2	no	—
371	C₂²⋊Q₈	—	181	2	no	—
372	C₂²⋊Q₈	—	181	2	no	—
373	C₂²⋊Q₈	—	181	2	no	—
374	C₂²⋊Q₈	—	181	1	no	—
375	C₂²⋊Q₈	—	181	2	no	—
376	C₂²⋊Q₈	—	181	1	no	—
377	C₂²⋊Q₈	—	181	2	no	—
378	C₂²⋊Q₈	—	181	2	no	—
379	C₂²⋊Q₈	—	181	2	no	—
380	C₂²⋊Q₈	—	181	2	no	—
381	C₂²⋊Q₈	—	181	2	no	—
382	C₂²⋊Q₈	—	181	2	no	—
383	C₂²⋊Q₈	—	181	2	no	—
384	C₂²⋊Q₈	—	181	2	no	—
385	C₂²⋊Q₈	—	181	1	no	—
386	C₂²⋊Q₈	—	181	2	no	—
387	C₂²⋊Q₈	—	181	2	no	—
388	C₂²⋊Q₈	—	181	2	no	—
389	C₂²⋊Q₈	—	181	2	no	—
390	C₂²⋊Q₈	—	181	2	no	—
391	C₂²⋊Q₈	—	181	2	no	—
392	C₂²⋊Q₈	—	181	2	no	—
393	C₂²⋊Q₈	—	181	2	no	—
394	C₂²⋊Q₈	—	181	2	no	—
395	C₂²⋊Q₈	—	181	2	no	—
396	C₂²⋊Q₈	—	181	2	no	—
397	C₂²⋊Q₈	—	181	2	no	—
398	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	complemented
399	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	complemented
400	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	complemented
401	C₄×Q₈	—	181	2	no	—
402	C₄×Q₈	—	181	2	no	—
403	C₄×Q₈	—	181	1	no	—
404	C₄×Q₈	—	181	1	no	—
405	C₄×Q₈	—	181	1	no	—
406	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
407	C₄×D₄	—	181	1	no	—
408	C₄×D₄	—	181	1	no	—
409	C₄×D₄	—	181	1	no	—
410	C₄×D₄	—	181	2	no	—
411	C₄×D₄	—	181	2	no	—
412	C₄×D₄	—	181	2	no	—
413	C₄×D₄	—	181	1	no	—
414	C₄×D₄	—	181	1	no	—
415	C₄×D₄	—	181	1	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	—	181	1	no	—
421	C₄×D₄	—	181	1	no	—
422	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
423	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
425	#117	—	181	1	no	—
426	#117	—	181	1	no	—
427	#117	—	181	1	no	—
428	#117	—	181	1	no	—
429	C₂×C₄⋊C₄	—	181	2	no	—
430	C₂×C₄⋊C₄	—	181	2	no	—
431	C₂×C₄⋊C₄	—	181	1	no	—
432	C₂×C₄⋊C₄	—	181	2	no	—
433	C₂×C₄⋊C₄	—	181	2	no	—
434	C₂×C₄⋊C₄	—	181	2	no	—
435	C₂×C₄⋊C₄	C₂×D₁₈₁	1	2	yes	complemented
436	C₂×C₂²⋊C₄	—	181	2	no	—
437	C₂×C₂²⋊C₄	—	181	2	no	—
438	C₂×C₂²⋊C₄	—	181	2	no	—
439	C₂×C₂²⋊C₄	—	181	2	no	—
440	C₂×C₂²⋊C₄	—	181	2	no	—
441	C₂×C₄²	—	181	1	no	—
442	C₂⁴	—	181	2	no	—
443	C₂×Q₈	—	181	2	no	—
444	C₂×Q₈	—	181	1	no	—
445	C₂×Q₈	—	181	1	no	—
446	C₂×Q₈	—	181	2	no	—
447	C₂×Q₈	—	181	1	no	—
448	C₂×Q₈	—	181	2	no	—
449	C₂×Q₈	—	181	2	no	—
450	C₂×Q₈	—	181	2	no	—
451	C₂×Q₈	—	724	4	no	—
452	C₂×Q₈	—	724	4	no	—
453	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₁₈₁	1	2	yes	—
455	C₂×D₄	—	181	2	no	—
456	C₂×D₄	—	181	8	no	—
457	C₂×D₄	—	181	1	no	—
458	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
459	C₂²×C₄	—	181	2	no	—
460	C₂²×C₄	—	181	1	no	—
461	C₂²×C₄	—	181	2	no	—
462	C₂²×C₄	—	181	1	no	—
463	C₂²×C₄	—	181	2	no	—
464	C₂²×C₄	—	181	2	no	—
465	C₂²×C₄	—	181	1	no	—
466	C₂²×C₄	—	181	2	no	—
467	C₂²×C₄	—	181	2	no	—
468	C₂²×C₄	—	181	2	no	—
469	C₂²×C₄	—	181	2	no	—
470	C₂²×C₄	—	181	2	no	—
471	C₂²×C₄	—	181	2	no	—
472	C₂²×C₄	—	724	4	no	—
473	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
476	C₄⋊C₄	—	181	1	no	—
477	C₄⋊C₄	—	181	2	no	—
478	C₄⋊C₄	—	181	1	no	—
479	C₄⋊C₄	—	181	2	no	—
480	C₄⋊C₄	—	181	1	no	—
481	C₄⋊C₄	—	181	1	no	—
482	C₄⋊C₄	—	181	2	no	—
483	C₄⋊C₄	—	181	1	no	—
484	C₄⋊C₄	—	181	2	no	—
485	C₄⋊C₄	—	181	2	no	—
486	C₄⋊C₄	—	181	2	no	—
487	C₄⋊C₄	—	181	2	no	—
488	C₄⋊C₄	—	181	2	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	1	no	—
494	C₄⋊C₄	—	181	1	no	—
495	C₄⋊C₄	—	181	1	no	—
496	C₄⋊C₄	—	181	1	no	—
497	C₄⋊C₄	—	181	1	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	1	no	—
503	C₄⋊C₄	—	181	1	no	—
504	C₄⋊C₄	—	181	2	no	—
505	C₄⋊C₄	—	181	1	no	—
506	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
510	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
517	C₂²⋊C₄	—	181	2	no	—
518	C₂²⋊C₄	—	181	2	no	—
519	C₂²⋊C₄	—	181	2	no	—
520	C₂²⋊C₄	—	181	2	no	—
521	C₂²⋊C₄	—	181	1	no	—
522	C₂²⋊C₄	—	181	1	no	—
523	C₂²⋊C₄	—	181	2	no	—
524	C₂²⋊C₄	—	181	1	no	—
525	C₂²⋊C₄	—	181	1	no	—
526	C₂²⋊C₄	—	181	2	no	—
527	C₂²⋊C₄	—	181	2	no	—
528	C₂²⋊C₄	—	181	2	no	—
529	C₂²⋊C₄	—	181	2	no	—
530	C₂²⋊C₄	—	181	2	no	—
531	C₂²⋊C₄	—	181	2	no	—
532	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
535	C₄²	—	181	1	no	—
536	C₄²	—	181	1	no	—
537	C₄²	—	181	1	no	—
538	C₄²	—	181	1	no	—
539	C₄²	—	181	1	no	—
540	C₄²	—	181	2	no	—
541	C₄²	—	181	2	no	—
542	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
543	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
544	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
545	C₂³	—	181	1	no	—
546	C₂³	—	181	2	no	—
547	C₂³	—	181	8	no	—
548	C₂³	—	724	2	no	—
549	C₂³	—	724	2	no	—
550	C₂³	C₂³×D₁₈₁	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	362	2	no	—
554	Q₈	—	362	4	no	—
555	Q₈	—	362	2	no	—
556	Q₈	—	724	2	no	—
557	Q₈	—	724	2	no	—
558	Q₈	—	724	2	no	—
559	Q₈	—	724	2	no	—
560	Q₈	—	724	1	no	—
561	D₄	—	181	8	no	—
562	D₄	—	181	4	no	—
563	D₄	Q₈×D₁₈₁	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	362	2	no	—
568	C₂×C₄	—	362	4	no	—
569	C₂×C₄	—	362	4	no	—
570	C₂×C₄	—	181	1	no	—
571	C₂×C₄	—	181	1	no	—
572	C₂×C₄	—	181	2	no	—
573	C₂×C₄	—	181	1	no	—
574	C₂×C₄	—	181	1	no	—
575	C₂×C₄	—	181	2	no	—
576	C₂×C₄	—	181	1	no	—
577	C₂×C₄	—	181	2	no	—
578	C₂×C₄	—	181	1	no	—
579	C₂×C₄	—	181	1	no	—
580	C₂×C₄	—	181	4	no	—
581	C₂×C₄	—	724	2	no	—
582	C₂×C₄	—	724	2	no	—
583	C₂×C₄	—	724	2	no	—
584	C₂×C₄	—	724	2	no	—
585	C₂×C₄	—	724	2	no	—
586	C₂×C₄	—	724	2	no	—
587	C₂×C₄	—	724	1	no	—
588	C₂×C₄	—	724	2	no	—
589	C₂×C₄	—	724	2	no	—
590	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
593	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
594	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
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	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	362	2	no	—
603	C₂²	—	362	1	no	—
604	C₂²	—	362	2	no	—
605	C₂²	—	362	1	no	—
606	C₂²	—	181	2	no	—
607	C₂²	—	181	4	no	—
608	C₂²	—	724	8	no	—
609	C₂²	C₂×Q₈×D₁₈₁	1	4	yes	—
610	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	362	1	no	—
621	C₄	—	362	2	no	—
622	C₄	—	362	1	no	—
623	C₄	—	362	1	no	—
624	C₄	—	362	2	no	—
625	C₄	—	362	1	no	—
626	C₄	—	362	2	no	—
627	C₄	—	362	1	no	—
628	C₄	—	181	2	no	—
629	C₄	—	181	2	no	—
630	C₄	C₂×Q₈×D₁₈₁	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	362	2	no	—
633	C₂	—	362	4	no	—
634	C₂	C₂²×Q₈×D₁₈₁	1	1	yes	characteristic
635	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
636	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#554×C₁₈₁	C₂
prime radical	C₂×D₄×D₁₈₁	C₂²
hypercenter	#554	D₁₈₁
hypocenter	C₁₈₁	#3501
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #26041989	C₂	semidirect
2. #26041988	C₂	semidirect
3. #26041988	C₂	semidirect
4. #26041985	C₂	semidirect
5. #26041985	C₂	semidirect
6. #26041984	C₂	semidirect
7. #26041983	C₂	semidirect
8. #26041983	C₂	semidirect
9. D₄×Dic₃₆₂	C₂	semidirect
10. #26041944	C₂	semidirect
11. #26041942	C₂	semidirect
12. #26041909	C₂	semidirect
13. #26041906	C₂	semidirect
14. #26041904	C₂	semidirect
15. #26041904	C₂	semidirect
16. #26041835	C₂	semidirect
17. #26041833	C₂	semidirect
18. C₂×#19153794	C₂	semidirect
19. C₂²⋊Q₈×D₁₈₁	C₂	semidirect
23. #554×C₁₈₁	C₂	semidirect
24. C₂²×Dic₃₆₂	C₂²	semidirect
25. C₂×Q₈×D₁₈₁	C₂²	semidirect
28. #19153816	C₂²	semidirect
29. #19153815	C₂²	semidirect
30. #19153815	C₂²	semidirect
31. #19153815	C₂²	semidirect
32. #19153815	C₂²	semidirect
33. #19153815	C₂²	semidirect
34. #19153815	C₂²	semidirect
35. #19153814	C₂²	semidirect
36. #19153814	C₂²	semidirect
37. #19153808	C₂²	semidirect
38. #19153808	C₂²	semidirect
39. #19153807	C₂²	semidirect
40. #19153807	C₂²	semidirect
41. #19153806	C₂²	semidirect
42. #19153806	C₂²	semidirect
43. #19153806	C₂²	semidirect
44. #19153806	C₂²	semidirect
47. #19153796	C₂²	semidirect
48. #19153796	C₂²	semidirect
49. #19153795	C₂²	semidirect
50. #19153795	C₂²	semidirect
51. #19153795	C₂²	semidirect
58. #19153794	C₂²	semidirect
59. #19153794	C₂²	semidirect
60. #19153794	C₂²	semidirect
61. #19153794	C₂²	semidirect
62. #19153794	C₂²	semidirect
63. #19153794	C₂²	semidirect
64. #19153794	C₂²	semidirect
65. #19153794	C₂²	semidirect
66. #19153793	C₂²	semidirect
67. #19153793	C₂²	semidirect
68. #19153793	C₂²	semidirect
69. #19153793	C₂²	semidirect
70. #19153793	C₂²	semidirect
71. #19153793	C₂²	semidirect
74. #19153792	C₂²	semidirect
75. #19153792	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
100. C₂×#15668428	C₂²	semidirect
101. C₂×#15668428	C₂²	semidirect
103. C₄⋊C₄×D₁₈₁	C₂²	semidirect
104. C₄⋊C₄×D₁₈₁	C₂²	semidirect
105. C₄⋊C₄×D₁₈₁	C₂²	semidirect
112. C₄⋊Q₈×C₁₈₁	C₂²	semidirect
113. #125×C₁₈₁	C₂²	semidirect
114. #125×C₁₈₁	C₂²	semidirect
115. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
117. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. C₄×Q₈×C₁₈₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
136. D₄×D₁₈₁	Q₈	semidirect
228. C₂²×D₁₈₁	C₂×Q₈	semidirect
239. D₇₂₄	C₂×Q₈	semidirect
240. C₂²⋊D₁₈₁	C₂×Q₈	semidirect
263. C₄×D₁₈₁	C₂×Q₈	semidirect
267. D₄×C₁₈₁	C₂×Q₈	semidirect
318. C₁₈₁	#3501	semidirect
328. #554	D₁₈₁	semidirect
356. C₄⋊Q₈	C₂×D₁₈₁	semidirect
365. #125	C₂×D₁₈₁	semidirect
366. #125	C₂×D₁₈₁	semidirect
398. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
399. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
400. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
406. C₄×Q₈	C₂×D₁₈₁	semidirect
435. C₂×C₄⋊C₄	C₂×D₁₈₁	semidirect
563. D₄	Q₈×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26041989	2
#26041988	2
#26041985	2
#26041984	2
#26041983	2
D₄×Dic₃₆₂	2
#26041944	2
#26041942	2
#26041909	2
#26041906	2
#26041904	2
#26041835	2
#26041833	2
C₂×#19153794	2
C₂²⋊Q₈×D₁₈₁	2
#26041751	2
C₄×D₄×D₁₈₁	2
#554×C₁₈₁	2
#3501	181