Subgroups — #14662031

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622548	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622167	C₂	1	2	yes	maximal
3	C₂×#10622167	C₂	1	2	yes	maximal
4	C₂×#10622162	C₂	1	1	yes	maximal, characteristic
5	C₁₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₁	—	2	1	no	—
10	C₂²×C₄⋊Dic₁₁	—	2	1	no	—
11	C₂²×C₄⋊Dic₁₁	C₂²	1	2	yes	—
12	C₂³×C₁₁⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×#95	—	2	1	no	—
14	C₂×C₁₁×#95	—	2	1	no	—
15	#10622548	—	2	4	no	—
16	#10622167	—	2	4	no	—
17	#10622167	—	2	4	no	—
18	#10622162	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₁	—	2	1	no	—
20	C₂³×C₄×C₁₁	—	2	1	no	—
21	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₁	—	2	2	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
32	C₂×C₁₁×C₄⋊C₄	Q₈	1	2	yes	—
33	C₂×C₄²×C₁₁	—	2	2	no	—
34	C₂×C₄²×C₁₁	—	2	2	no	—
35	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
37	C₂×C₄⋊Dic₁₁	—	2	2	no	—
38	C₂×C₄⋊Dic₁₁	—	2	2	no	—
39	C₂×C₄⋊Dic₁₁	—	2	2	no	—
40	C₂×C₄⋊Dic₁₁	—	2	2	no	—
41	C₂×C₄⋊Dic₁₁	—	2	4	no	—
42	C₂×C₄⋊Dic₁₁	—	2	4	no	—
43	C₂×C₄⋊Dic₁₁	—	2	2	no	—
44	C₂×C₄⋊Dic₁₁	—	4	2	no	—
45	C₂×C₄⋊Dic₁₁	—	4	2	no	—
46	C₂×C₄⋊Dic₁₁	—	4	2	no	—
47	C₂×C₄⋊Dic₁₁	—	4	2	no	—
48	C₂×C₄⋊Dic₁₁	D₄	1	4	yes	—
49	C₂²×C₁₁⋊C₈	—	2	2	no	—
50	C₂²×C₁₁⋊C₈	—	2	2	no	—
51	C₂²×C₁₁⋊C₈	—	2	2	no	—
52	C₂²×C₁₁⋊C₈	—	2	2	no	—
53	C₂²×C₁₁⋊C₈	—	2	2	no	—
54	C₂²×C₁₁⋊C₈	—	2	2	no	—
55	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₁×#95	—	4	2	no	—
57	C₁₁×#95	—	4	2	no	—
58	#11267	—	11	1	no	maximal, Sylow
59	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	—	2	1	no	—
61	C₂²×C₄×C₁₁	—	2	1	no	—
62	C₂²×C₄×C₁₁	—	2	1	no	—
63	C₂²×C₄×C₁₁	—	2	1	no	—
64	C₂²×C₄×C₁₁	—	2	1	no	—
65	C₂²×C₄×C₁₁	—	2	1	no	—
66	C₂²×C₄×C₁₁	—	2	1	no	—
67	C₂²×C₄×C₁₁	—	2	1	no	—
68	C₂²×C₄×C₁₁	—	2	2	no	—
69	C₂²×C₄×C₁₁	—	2	2	no	—
70	C₂²×C₄×C₁₁	—	4	1	no	—
71	C₂²×C₄×C₁₁	—	4	1	no	—
72	C₂²×C₄×C₁₁	—	4	1	no	—
73	C₂²×C₄×C₁₁	—	4	1	no	—
74	C₂²×C₄×C₁₁	—	4	1	no	—
75	C₂²×C₄×C₁₁	—	4	1	no	—
76	C₂²×C₄×C₁₁	—	4	1	no	—
77	C₂²×C₄×C₁₁	—	4	1	no	—
78	C₂²×C₄×C₁₁	—	4	1	no	—
79	C₂²×C₄×C₁₁	—	4	1	no	—
80	C₂²×C₄×C₁₁	—	4	1	no	—
81	C₂²×C₄×C₁₁	—	4	1	no	—
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₁	D₈	1	2	yes	—
85	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	#41	1	2	yes	—
94	C₂²×C₄×C₁₁	#41	1	2	yes	—
95	C₂²×C₄×C₁₁	#41	1	2	yes	—
96	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
98	C₂²×Dic₁₁	—	2	4	no	—
99	C₂²×Dic₁₁	—	4	2	no	—
100	C₂²×Dic₁₁	—	4	2	no	—
101	C₂²×Dic₁₁	—	4	2	no	—
102	C₂²×Dic₁₁	—	4	2	no	—
103	C₂²×Dic₁₁	—	4	2	no	—
104	C₂²×Dic₁₁	—	4	2	no	—
105	C₁₁×C₄⋊C₄	—	2	4	no	—
106	C₁₁×C₄⋊C₄	—	2	4	no	—
107	C₁₁×C₄⋊C₄	—	4	2	no	—
108	C₁₁×C₄⋊C₄	—	4	2	no	—
109	C₄²×C₁₁	—	2	4	no	—
110	C₄²×C₁₁	—	2	4	no	—
111	C₄⋊Dic₁₁	—	2	4	no	—
112	C₄⋊Dic₁₁	—	2	4	no	—
113	C₄⋊Dic₁₁	—	4	8	no	—
114	C₄⋊Dic₁₁	—	4	8	no	—
115	C₄⋊Dic₁₁	—	4	2	no	—
116	C₄⋊Dic₁₁	—	4	2	no	—
117	C₂×C₁₁⋊C₈	—	2	4	no	—
118	C₂×C₁₁⋊C₈	—	2	4	no	—
119	C₂×C₁₁⋊C₈	—	2	4	no	—
120	C₂×C₁₁⋊C₈	—	4	2	no	—
121	C₂×C₁₁⋊C₈	—	4	2	no	—
122	C₂×C₁₁⋊C₈	—	4	2	no	—
123	C₂×C₁₁⋊C₈	—	4	2	no	—
124	C₂×#384	—	11	1	no	—
125	C₂×#340	—	11	2	no	—
126	C₂×#340	—	11	2	no	—
127	C₂×#336	—	11	1	no	—
128	C₄⋊#95	D₁₁	1	1	yes	characteristic
129	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₁	#120	1	1	yes	characteristic
131	C₂³×C₁₁	#121	1	1	yes	characteristic
132	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂³×C₁₁	#123	1	1	yes	characteristic
134	C₂³×C₁₁	#124	1	1	yes	characteristic
135	C₂³×C₁₁	#124	1	1	yes	characteristic
136	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
137	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
138	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
139	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
140	C₂³×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂³×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂³×C₁₁	#137	1	1	yes	characteristic
143	C₂³×C₁₁	#137	1	1	yes	characteristic
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	4	2	no	—
157	C₂×C₄×C₁₁	—	4	2	no	—
158	C₂×C₄×C₁₁	—	4	2	no	—
159	C₂×C₄×C₁₁	—	4	2	no	—
160	C₂×C₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	—	4	2	no	—
162	C₂×C₄×C₁₁	—	8	1	no	—
163	C₂×C₄×C₁₁	—	8	1	no	—
164	C₂×C₄×C₁₁	—	8	1	no	—
165	C₂×C₄×C₁₁	—	8	1	no	—
166	C₂×C₄×C₁₁	—	8	1	no	—
167	C₂×C₄×C₁₁	—	8	1	no	—
168	C₂×C₄×C₁₁	—	8	1	no	—
169	C₂×C₄×C₁₁	—	8	1	no	—
170	C₂×C₄×C₁₁	#106	1	4	yes	—
171	C₂×C₄×C₁₁	#107	1	4	yes	—
172	C₂×C₄×C₁₁	#117	1	2	yes	—
173	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₁	#121	1	2	yes	—
177	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₁	#123	1	2	yes	—
180	C₂×C₄×C₁₁	#123	1	2	yes	—
181	C₂×C₄×C₁₁	#124	1	2	yes	—
182	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
183	C₂×C₄×C₁₁	#125	1	2	yes	—
184	C₂×C₄×C₁₁	#125	1	2	yes	—
185	C₂×C₄×C₁₁	#126	1	2	yes	—
186	C₂×C₄×C₁₁	#126	1	2	yes	—
187	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
188	C₂×Dic₁₁	—	4	4	no	—
189	C₂×Dic₁₁	—	4	4	no	—
190	C₂×Dic₁₁	—	4	4	no	—
191	C₂×Dic₁₁	—	8	2	no	—
192	C₂×Dic₁₁	—	8	2	no	—
193	C₂×Dic₁₁	—	8	2	no	—
194	C₂×Dic₁₁	—	8	2	no	—
195	C₁₁⋊C₈	—	4	4	no	—
196	C₂³×C₈	—	11	2	no	—
197	C₂²×C₄⋊C₄	—	11	2	no	—
198	C₂²×C₄⋊C₄	—	22	1	no	—
199	C₂²×C₄⋊C₄	—	22	1	no	—
200	C₂²×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
202	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
203	#384	—	22	4	no	—
204	C₂×#95	—	2	1	no	—
205	C₂×#95	—	2	1	no	—
206	#340	—	22	4	no	—
207	#340	—	22	4	no	—
208	#336	—	11	4	no	—
209	C₂²×C₁₁	#382	1	1	yes	characteristic
210	C₂²×C₁₁	#385	1	1	yes	characteristic
211	C₂²×C₁₁	#389	1	1	yes	characteristic
212	C₂²×C₁₁	#393	1	1	yes	characteristic
213	C₂²×C₁₁	#394	1	1	yes	characteristic
214	C₂²×C₁₁	#397	1	1	yes	characteristic
215	C₂²×C₁₁	#400	1	1	yes	characteristic
216	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
217	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
218	C₂²×C₁₁	#428	1	1	yes	characteristic
219	C₂²×C₁₁	#428	1	1	yes	characteristic
220	C₂²×C₁₁	#447	1	1	yes	characteristic
221	C₂²×C₁₁	#448	1	1	yes	characteristic
222	C₂²×C₁₁	#450	1	1	yes	characteristic
223	C₂²×C₁₁	#451	1	1	yes	characteristic
224	C₂²×C₁₁	#459	1	1	yes	characteristic
225	C₂²×C₁₁	#460	1	1	yes	characteristic
226	C₂²×C₁₁	#461	1	1	yes	characteristic
227	C₂²×C₁₁	#462	1	1	yes	characteristic
228	C₂²×C₁₁	#474	1	1	yes	characteristic
229	C₂²×C₁₁	#475	1	1	yes	characteristic
230	C₂²×C₁₁	#476	1	1	yes	characteristic
231	C₂²×C₁₁	#477	1	1	yes	characteristic
232	C₂²×C₁₁	#480	1	1	yes	characteristic
233	C₂²×C₁₁	#481	1	1	yes	characteristic
234	C₂²×C₁₁	#483	1	1	yes	characteristic
235	C₂²×C₁₁	#484	1	1	yes	characteristic
236	C₂²×C₁₁	#486	1	1	yes	characteristic
237	C₂²×C₁₁	#486	1	1	yes	characteristic
238	C₂²×C₁₁	#487	1	1	yes	characteristic
239	C₂²×C₁₁	#487	1	1	yes	characteristic
240	C₂²×C₁₁	#489	1	1	yes	characteristic
241	C₂²×C₁₁	#489	1	1	yes	characteristic
242	C₂²×C₁₁	#490	1	1	yes	characteristic
243	C₂²×C₁₁	#491	1	1	yes	characteristic
244	C₄×C₁₁	—	2	4	no	—
245	C₄×C₁₁	—	2	4	no	—
246	C₄×C₁₁	—	8	2	no	—
247	C₄×C₁₁	—	8	2	no	—
248	C₄×C₁₁	#387	1	2	yes	—
249	C₄×C₁₁	#388	1	2	yes	—
250	C₄×C₁₁	#398	1	2	yes	—
251	C₄×C₁₁	#400	1	2	yes	—
252	Dic₁₁	—	8	4	no	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	22	2	no	—
256	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
257	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
259	C₂²×C₈	—	11	4	no	—
260	C₂²×C₈	—	22	2	no	—
261	C₂²×C₈	—	22	2	no	—
262	C₂²×C₈	—	22	2	no	—
263	C₂²×C₈	—	22	2	no	—
264	C₂²×C₈	—	22	2	no	—
265	C₂²×C₈	—	22	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	11	4	no	—
273	C₂×C₄⋊C₄	—	22	2	no	—
274	C₂×C₄⋊C₄	—	22	2	no	—
275	C₂×C₄⋊C₄	—	22	2	no	—
276	C₂×C₄⋊C₄	—	22	2	no	—
277	C₂×C₄⋊C₄	—	22	4	no	—
278	C₂×C₄⋊C₄	—	22	4	no	—
279	C₂×C₄⋊C₄	—	22	2	no	—
280	C₂×C₄⋊C₄	—	44	2	no	—
281	C₂×C₄⋊C₄	—	44	2	no	—
282	C₂×C₄⋊C₄	—	44	2	no	—
283	C₂×C₄⋊C₄	—	44	2	no	—
284	C₂×C₄⋊C₄	Dic₂₂	1	2	yes	—
285	C₂×C₄⋊C₄	D₄₄	1	2	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	Dic₂₂	1	2	yes	—
289	C₂×C₄²	C₄×D₁₁	1	2	yes	—
290	#95	—	4	2	no	—
291	#95	—	4	2	no	—
292	C₂×C₁₁	#1442	1	1	yes	characteristic
293	C₂×C₁₁	#1834	1	1	yes	characteristic
294	C₂×C₁₁	#1836	1	1	yes	characteristic
295	C₂×C₁₁	#1852	1	1	yes	characteristic
296	C₂×C₁₁	#1853	1	1	yes	characteristic
297	C₂×C₁₁	#1947	1	1	yes	characteristic
298	C₂×C₁₁	#1948	1	1	yes	characteristic
299	C₂×C₁₁	#2023	1	1	yes	characteristic
300	C₂×C₁₁	#2024	1	1	yes	characteristic
301	C₂×C₁₁	#2041	1	1	yes	characteristic
302	C₂×C₁₁	#2043	1	1	yes	characteristic
303	C₂×C₁₁	#2071	1	1	yes	characteristic
304	C₂×C₁₁	#2072	1	1	yes	characteristic
305	C₂×C₁₁	#2099	1	1	yes	characteristic
306	C₂×C₁₁	#2100	1	1	yes	characteristic
307	C₂⁴	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	22	4	no	—
331	C₂²×C₄	—	44	2	no	—
332	C₂²×C₄	—	44	2	no	—
333	C₂²×C₄	—	44	2	no	—
334	C₂²×C₄	—	44	2	no	—
335	C₂²×C₄	—	44	2	no	—
336	C₂²×C₄	—	44	2	no	—
337	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
338	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
339	C₂²×C₄	#4323	1	2	yes	—
340	C₂²×C₄	#4324	1	2	yes	—
341	C₂²×C₄	#4325	1	2	yes	—
342	C₂²×C₄	#4326	1	2	yes	—
343	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
344	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
347	C₂²×C₄	#4339	1	1	yes	characteristic
348	C₂²×C₄	#4339	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₁	1	2	yes	—
350	C₂²×C₄	#4341	1	2	yes	—
351	C₂²×C₄	#4341	1	2	yes	—
352	C₂²×C₄	#4343	1	2	yes	—
353	C₂×C₈	—	22	4	no	—
354	C₂×C₈	—	22	4	no	—
355	C₂×C₈	—	22	4	no	—
356	C₂×C₈	—	44	2	no	—
357	C₂×C₈	—	44	2	no	—
358	C₂×C₈	—	44	2	no	—
359	C₂×C₈	—	44	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	22	4	no	—
365	C₄⋊C₄	—	22	4	no	—
366	C₄⋊C₄	—	44	8	no	—
367	C₄⋊C₄	—	44	8	no	—
368	C₄⋊C₄	—	44	2	no	—
369	C₄⋊C₄	—	44	2	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	4	no	—
372	C₁₁	#11267	1	1	yes	characteristic, complemented, Sylow
373	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
374	C₂³	#66977	1	1	yes	characteristic
375	C₂³	#66983	1	1	yes	characteristic
376	C₂³	C₂×#4323	1	1	yes	characteristic
377	C₂³	C₂×#4324	1	1	yes	characteristic
378	C₂³	#66988	1	1	yes	characteristic
379	C₂³	#66989	1	1	yes	characteristic
380	C₂³	#66990	1	1	yes	characteristic
381	C₂³	C₂×#4325	1	1	yes	characteristic
382	C₂³	C₂×#4326	1	1	yes	characteristic
383	C₂³	#67000	1	1	yes	characteristic
384	C₂³	#67002	1	1	yes	characteristic
385	C₂³	#67002	1	1	yes	characteristic
386	C₂³	#67004	1	1	yes	characteristic
387	C₂³	#67004	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	—	8	1	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	44	4	no	—
415	C₂×C₄	—	44	4	no	—
416	C₂×C₄	—	44	4	no	—
417	C₂×C₄	—	88	2	no	—
418	C₂×C₄	—	88	2	no	—
419	C₂×C₄	—	88	2	no	—
420	C₂×C₄	—	88	2	no	—
421	C₂×C₄	#66871	1	4	yes	—
422	C₂×C₄	#66872	1	4	yes	—
423	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
424	C₂×C₄	#66922	1	1	yes	characteristic
425	C₂×C₄	#66923	1	1	yes	characteristic
426	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
427	C₂×C₄	#66931	1	2	yes	—
428	C₂×C₄	#66931	1	2	yes	—
429	C₂×C₄	#66932	1	2	yes	—
430	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
431	C₂×C₄	#66938	1	2	yes	—
432	C₂×C₄	#66939	1	2	yes	—
433	C₂×C₄	#66943	1	2	yes	—
434	C₂×C₄	#66943	1	2	yes	—
435	C₂×C₄	#66945	1	2	yes	—
436	C₂×C₄	#66947	1	2	yes	—
437	C₂×C₄	#66948	1	2	yes	—
438	C₂×C₄	#66951	1	2	yes	—
439	C₈	—	44	4	no	—
440	C₂²	#10622541	1	1	yes	characteristic
441	C₂²	#10622559	1	1	yes	characteristic
442	C₂²	#10622560	1	1	yes	characteristic
443	C₂²	#10622566	1	1	yes	characteristic
444	C₂²	C₂×#66871	1	1	yes	characteristic
445	C₂²	C₂×#66872	1	1	yes	characteristic
446	C₂²	#10622590	1	1	yes	characteristic
447	C₂²	#10622599	1	1	yes	characteristic
448	C₂²	#10622604	1	1	yes	characteristic
449	C₂²	#10622608	1	1	yes	characteristic
450	C₂²	#10622608	1	1	yes	characteristic
451	C₂²	#10622620	1	1	yes	characteristic
452	C₂²	#10622621	1	1	yes	characteristic
453	C₂²	#10622628	1	1	yes	characteristic
454	C₂²	#10622632	1	1	yes	characteristic
455	C₂²	#10622633	1	1	yes	characteristic
456	C₂²	#10622634	1	1	yes	characteristic
457	C₂²	#10622640	1	1	yes	characteristic
458	C₂²	#10622644	1	1	yes	characteristic
459	C₂²	#10622646	1	1	yes	characteristic
460	C₂²	#10622647	1	1	yes	characteristic
461	C₂²	#10622649	1	1	yes	characteristic
462	C₂²	#10622653	1	1	yes	characteristic
463	C₂²	#10622656	1	1	yes	characteristic
464	C₂²	#10622657	1	1	yes	characteristic
465	C₂²	#10622659	1	1	yes	characteristic
466	C₂²	#10622663	1	1	yes	characteristic
467	C₂²	#10622668	1	1	yes	characteristic
468	C₂²	#10622668	1	1	yes	characteristic
469	C₂²	#10622680	1	1	yes	characteristic
470	C₂²	#10622682	1	1	yes	characteristic
471	C₂²	#10622683	1	1	yes	characteristic
472	C₂²	#10622694	1	1	yes	characteristic
473	C₂²	#10622701	1	1	yes	characteristic
474	C₂²	#10622706	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	—	88	4	no	—
480	C₄	#10622268	1	2	yes	—
481	C₄	#10622273	1	2	yes	—
482	C₄	#10622274	1	2	yes	—
483	C₄	#10622283	1	2	yes	—
484	C₂	#13066872	1	1	yes	characteristic
485	C₂	#13068743	1	1	yes	characteristic
486	C₂	#13068749	1	1	yes	characteristic
487	C₂	#13068803	1	1	yes	characteristic
488	C₂	#13068808	1	1	yes	characteristic
489	C₂	#13069374	1	1	yes	characteristic
490	C₂	#13069379	1	1	yes	characteristic
491	C₂	#13069752	1	1	yes	characteristic
492	C₂	#13069757	1	1	yes	characteristic
493	C₂	#13069850	1	1	yes	characteristic
494	C₂	#13069862	1	1	yes	characteristic
495	C₂	#13070019	1	1	yes	characteristic
496	C₂	#13070024	1	1	yes	characteristic
497	C₂	#13070174	1	1	yes	characteristic
498	C₂	#13070179	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₁
Fitting	C₁₁×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₁	C₂×D₄
cosocle	C₂³×C₄×C₁₁	C₂³
hypercenter	C₄⋊#95	D₁₁
hypocenter	C₁₁	#11267
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
18. #10622162	C₄	semidirect
372. C₁₁	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622548	2
C₂×#10622167	2
C₂×#10622162	2
C₁₁×C₄⋊#95	2
#11267	11