Subgroups — #14907364

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	#13070445	C₂	1	2	yes	maximal, complemented
3	#13070444	C₂	1	2	yes	maximal, complemented
4	#13070441	C₂	1	2	yes	maximal, complemented
5	C₁₆×C₂²⋊D₁₁	C₂	1	2	yes	maximal, complemented
6	#13070416	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070412	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070227	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070225	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	complemented
16	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₁₁)⋊C₈	C₄	1	1	yes	characteristic
26	C₂×Dic₁₁⋊C₈	C₄	1	1	yes	characteristic
27	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
28	C₂×#66876	C₂²	1	2	yes	complemented
29	C₂×#66862	C₂²	1	2	yes	complemented
30	C₂×C₁₆×D₁₁	C₂²	1	2	yes	complemented
31	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
34	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
35	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
36	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
37	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
38	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
39	#10622140	C₂²	1	2	yes	complemented
40	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
41	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
42	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
43	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
45	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	—	4	2	no	—
47	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₁	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₁₁)⋊C₄	C₈	1	1	yes	characteristic
63	C₂×Dic₁₁⋊C₄	C₈	1	1	yes	characteristic
64	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₁	—	4	2	no	—
68	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
72	C₂×C₁₁×C₁₆	—	4	2	no	—
73	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
74	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
75	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
78	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
81	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
83	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
84	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
85	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
86	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
90	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
91	#66876	—	4	2	no	—
92	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
93	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
94	#66862	—	4	2	no	—
95	C₁₆×D₁₁	—	4	2	no	—
96	#33488	—	11	1	no	maximal, Sylow
97	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
98	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	—	4	1	no	—
100	C₂²×C₄×C₁₁	—	4	1	no	—
101	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₁	—	2	4	no	—
108	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
113	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
114	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₁₁	—	4	1	no	—
116	C₂×C₄×D₁₁	—	4	1	no	—
117	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	4	1	no	—
125	C₂×C₈×C₁₁	—	4	1	no	—
126	C₂×C₈×C₁₁	—	4	1	no	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
132	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
133	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
134	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
135	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
136	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
137	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
138	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
142	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₁₁⋊C₈	—	4	1	no	—
148	C₂×C₁₁⋊C₈	—	4	1	no	—
149	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	C₈×D₁₁	—	2	2	no	—
154	C₈×D₁₁	—	2	2	no	—
155	C₈×D₁₁	—	4	1	no	—
156	C₈×D₁₁	—	4	1	no	—
157	C₁₁×C₁₆	—	2	2	no	—
158	C₁₁×C₁₆	—	2	2	no	—
159	C₁₁⋊C₁₆	—	2	2	no	—
160	C₁₁⋊C₁₆	—	2	2	no	—
161	C₂×C₈×D₄	—	11	1	no	—
162	#2169	—	11	2	no	—
163	#2168	—	11	2	no	—
164	#2168	—	11	2	no	—
165	D₄×C₁₆	—	11	2	no	—
166	#2163	—	11	1	no	—
167	#2162	—	11	1	no	—
168	#2112	—	11	1	no	—
169	#2112	—	11	1	no	—
170	C₂×C₂²⋊C₁₆	—	11	1	no	—
171	C₂×C₂²⋊C₁₆	D₁₁	1	1	yes	characteristic, complemented
172	C₂³×C₁₁	—	2	2	no	—
173	C₂³×C₁₁	—	2	2	no	—
174	C₂³×C₁₁	—	4	1	no	—
175	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
176	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₁₁	—	2	2	no	—
179	C₂²×D₁₁	—	2	2	no	—
180	C₂²×D₁₁	—	4	1	no	—
181	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
182	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	4	1	no	—
190	C₂×C₄×C₁₁	—	4	1	no	—
191	C₂×C₄×C₁₁	—	4	1	no	—
192	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
196	C₂²⋊D₁₁	—	2	2	no	—
197	C₂²⋊D₁₁	—	2	2	no	—
198	C₂²⋊D₁₁	—	2	2	no	—
199	C₂²⋊D₁₁	M₃₂	1	4	yes	complemented
200	C₂×Dic₁₁	—	2	2	no	—
201	C₂×Dic₁₁	—	2	2	no	—
202	C₂×Dic₁₁	—	4	1	no	—
203	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
204	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
209	C₄×D₁₁	—	2	1	no	—
210	C₄×D₁₁	—	2	1	no	—
211	C₄×D₁₁	—	2	1	no	—
212	C₄×D₁₁	—	2	1	no	—
213	C₄×D₁₁	—	4	1	no	—
214	C₄×D₁₁	—	4	1	no	—
215	C₈×C₁₁	—	2	1	no	—
216	C₈×C₁₁	—	2	1	no	—
217	C₈×C₁₁	—	2	1	no	—
218	C₈×C₁₁	H(5,𝔽₂)	1	2	yes	—
219	C₁₁⋊C₈	—	2	1	no	—
220	C₁₁⋊C₈	—	2	1	no	—
221	C₁₁⋊C₈	—	2	1	no	—
222	C₁₁⋊C₈	—	2	1	no	—
223	C₂³×C₈	—	11	1	no	—
224	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
225	C₂×C₄×D₄	—	11	1	no	—
226	C₂×M₃₂	—	11	2	no	—
227	C₂×M₃₂	—	11	2	no	—
228	C₂²×C₁₆	—	11	2	no	—
229	C₂²×C₁₆	C₂×D₁₁	1	2	yes	complemented
230	C₈×D₄	—	11	1	no	—
231	C₈×D₄	—	11	1	no	—
232	C₈×D₄	—	11	1	no	—
233	C₈×D₄	—	11	1	no	—
234	C₈×D₄	—	11	1	no	—
235	C₈×D₄	—	11	1	no	—
236	C₈×D₄	—	11	1	no	—
237	C₈×D₄	—	11	1	no	—
238	C₂×C₄⋊C₈	—	11	1	no	—
239	C₂×C₂²⋊C₈	—	11	1	no	—
240	C₂×C₂²⋊C₈	—	11	1	no	—
241	C₂×C₄×C₈	—	11	1	no	—
242	C₄⋊C₁₆	—	11	2	no	—
243	C₄⋊C₁₆	—	11	2	no	—
244	C₂²⋊C₁₆	—	11	1	no	—
245	C₂²⋊C₁₆	—	11	1	no	—
246	C₂²⋊C₁₆	—	11	2	no	—
247	C₂²⋊C₁₆	—	11	2	no	—
248	C₂²⋊C₁₆	—	11	2	no	—
249	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
250	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
251	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	complemented
252	#346	—	11	2	no	—
253	C₄×C₁₆	—	11	2	no	—
254	C₂²×C₁₁	—	2	1	no	—
255	C₂²×C₁₁	—	2	1	no	—
256	C₂²×C₁₁	—	2	1	no	—
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	1	no	—
260	C₂²×C₁₁	—	2	1	no	—
261	C₂²×C₁₁	—	4	4	no	—
262	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
263	C₂²×C₁₁	#504	1	2	yes	—
264	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
265	C₂×D₁₁	—	2	1	no	—
266	C₂×D₁₁	—	2	1	no	—
267	C₂×D₁₁	—	2	1	no	—
268	C₂×D₁₁	—	2	1	no	—
269	C₂×D₁₁	—	2	1	no	—
270	C₂×D₁₁	—	4	4	no	—
271	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
272	C₄×C₁₁	—	2	1	no	—
273	C₄×C₁₁	—	2	1	no	—
274	C₄×C₁₁	—	2	1	no	—
275	C₄×C₁₁	#518	1	1	yes	characteristic
276	C₄×C₁₁	#568	1	1	yes	characteristic
277	Dic₁₁	—	2	1	no	—
278	Dic₁₁	—	2	1	no	—
279	Dic₁₁	—	2	1	no	—
280	Dic₁₁	—	2	1	no	—
281	Dic₁₁	—	2	1	no	—
282	Dic₁₁	C₂×M₃₂	1	2	yes	—
283	C₂²×D₄	—	11	1	no	—
284	C₂³×C₄	—	11	1	no	—
285	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
286	C₂²×C₈	—	4	2	no	—
287	C₂²×C₈	—	11	1	no	—
288	C₂²×C₈	—	11	1	no	—
289	C₂²×C₈	—	11	1	no	—
290	C₂²×C₈	—	11	1	no	—
291	C₂²×C₈	—	11	1	no	—
292	C₂²×C₈	—	11	1	no	—
293	C₂²×C₈	—	44	2	no	—
294	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
295	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
296	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
298	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
300	C₄×D₄	—	11	1	no	—
301	C₄×D₄	—	11	1	no	—
302	C₄×D₄	—	11	1	no	—
303	C₄×D₄	—	11	1	no	—
304	C₄×D₄	—	11	1	no	—
305	C₄×D₄	—	11	1	no	—
306	C₄×D₄	—	11	1	no	—
307	C₄×D₄	—	11	1	no	—
308	C₂×C₄⋊C₄	—	11	1	no	—
309	C₂×C₂²⋊C₄	—	11	1	no	—
310	C₂×C₂²⋊C₄	—	11	1	no	—
311	C₂×C₄²	—	11	1	no	—
312	M₃₂	—	44	2	no	—
313	M₃₂	—	44	2	no	—
314	C₂×C₁₆	—	4	2	no	—
315	C₂×C₁₆	—	11	2	no	—
316	C₂×C₁₆	—	11	2	no	—
317	C₂×C₁₆	—	44	2	no	—
318	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
319	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
320	C₄⋊C₈	—	11	1	no	—
321	C₄⋊C₈	—	11	1	no	—
322	C₄⋊C₈	—	11	1	no	—
323	C₄⋊C₈	—	11	1	no	—
324	C₂²⋊C₈	—	11	1	no	—
325	C₂²⋊C₈	—	11	1	no	—
326	C₂²⋊C₈	—	11	1	no	—
327	C₂²⋊C₈	—	11	1	no	—
328	C₂²⋊C₈	—	11	1	no	—
329	C₂²⋊C₈	—	11	1	no	—
330	C₂²⋊C₈	—	11	1	no	—
331	C₂²⋊C₈	—	11	1	no	—
332	C₄×C₈	—	11	1	no	—
333	C₄×C₈	—	11	1	no	—
334	C₄×C₈	—	11	1	no	—
335	C₄×C₈	—	11	1	no	—
336	C₂×C₁₁	—	2	2	no	—
337	C₂×C₁₁	—	2	2	no	—
338	C₂×C₁₁	—	4	1	no	—
339	C₂×C₁₁	#2972	1	1	yes	characteristic
340	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
341	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
342	D₁₁	—	2	2	no	—
343	D₁₁	—	4	1	no	—
344	C₂⁴	—	11	1	no	—
345	C₂⁴	C₈×D₁₁	1	1	yes	characteristic
346	C₂×D₄	—	11	1	no	—
347	C₂×D₄	—	11	1	no	—
348	C₂×D₄	—	11	1	no	—
349	C₂×D₄	—	11	1	no	—
350	C₂×D₄	—	22	4	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	11	1	no	—
354	C₂²×C₄	—	11	1	no	—
355	C₂²×C₄	—	11	1	no	—
356	C₂²×C₄	—	11	1	no	—
357	C₂²×C₄	—	11	1	no	—
358	C₂²×C₄	—	11	1	no	—
359	C₂²×C₄	—	11	1	no	—
360	C₂²×C₄	—	44	1	no	—
361	C₂²×C₄	—	44	1	no	—
362	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
363	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
364	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	11	1	no	—
375	C₂×C₈	—	11	1	no	—
376	C₂×C₈	—	11	1	no	—
377	C₂×C₈	—	11	1	no	—
378	C₂×C₈	—	22	2	no	—
379	C₂×C₈	—	22	2	no	—
380	C₂×C₈	—	44	1	no	—
381	C₂×C₈	—	44	1	no	—
382	C₂×C₈	—	44	1	no	—
383	C₂×C₈	—	44	1	no	—
384	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
385	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
386	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
387	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
388	C₄⋊C₄	—	11	1	no	—
389	C₄⋊C₄	—	11	1	no	—
390	C₄⋊C₄	—	11	1	no	—
391	C₄⋊C₄	—	11	1	no	—
392	C₂²⋊C₄	—	11	1	no	—
393	C₂²⋊C₄	—	11	1	no	—
394	C₂²⋊C₄	—	11	1	no	—
395	C₂²⋊C₄	—	11	1	no	—
396	C₂²⋊C₄	—	11	1	no	—
397	C₂²⋊C₄	—	11	1	no	—
398	C₂²⋊C₄	—	11	1	no	—
399	C₂²⋊C₄	—	11	1	no	—
400	C₄²	—	11	1	no	—
401	C₄²	—	11	1	no	—
402	C₄²	—	11	1	no	—
403	C₄²	—	11	1	no	—
404	C₁₆	—	2	2	no	—
405	C₁₆	—	2	2	no	—
406	C₁₆	—	22	2	no	—
407	C₁₆	—	22	2	no	—
408	C₁₁	#33488	1	1	yes	characteristic, complemented, Sylow
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	11	1	no	—
413	C₂³	—	11	1	no	—
414	C₂³	—	22	2	no	—
415	C₂³	—	22	2	no	—
416	C₂³	—	44	1	no	—
417	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
418	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
419	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
420	D₄	—	11	4	no	—
421	D₄	—	22	2	no	—
422	D₄	—	22	2	no	—
423	D₄	—	22	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	11	1	no	—
434	C₂×C₄	—	11	1	no	—
435	C₂×C₄	—	11	1	no	—
436	C₂×C₄	—	11	1	no	—
437	C₂×C₄	—	11	1	no	—
438	C₂×C₄	—	11	1	no	—
439	C₂×C₄	—	22	2	no	—
440	C₂×C₄	—	22	2	no	—
441	C₂×C₄	—	22	1	no	—
442	C₂×C₄	—	22	1	no	—
443	C₂×C₄	—	22	1	no	—
444	C₂×C₄	—	22	1	no	—
445	C₂×C₄	—	44	1	no	—
446	C₂×C₄	—	44	1	no	—
447	C₂×C₄	—	44	1	no	—
448	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
450	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	22	1	no	—
456	C₈	—	22	1	no	—
457	C₈	—	22	1	no	—
458	C₈	—	22	1	no	—
459	C₈	#67037	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	11	2	no	—
469	C₂²	—	22	1	no	—
470	C₂²	—	22	1	no	—
471	C₂²	—	22	1	no	—
472	C₂²	—	22	1	no	—
473	C₂²	—	22	1	no	—
474	C₂²	—	44	4	no	—
475	C₂²	#10622514	1	2	yes	—
476	C₂²	D₁₁×M₃₂	1	2	yes	—
477	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	11	2	no	—
482	C₄	—	22	1	no	—
483	C₄	—	22	1	no	—
484	C₄	—	22	1	no	—
485	C₄	—	22	1	no	—
486	C₄	—	22	1	no	—
487	C₄	#10623017	1	1	yes	characteristic
488	C₄	#10623276	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	4	1	no	—
492	C₂	—	22	2	no	—
493	C₂	—	44	1	no	—
494	C₂	#13077638	1	1	yes	characteristic
495	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
496	C₂	C₂×#10622514	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₂×C₁₁×C₂²⋊C₁₆	C₂
prime radical	C₂²×C₂²⋊D₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₁₁
hypocenter	C₁₁	#33488
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #13070445	C₂	semidirect
3. #13070444	C₂	semidirect
4. #13070441	C₂	semidirect
5. C₁₆×C₂²⋊D₁₁	C₂	semidirect
6. #13070416	C₂	semidirect
7. #13070412	C₂	semidirect
8. #13070227	C₂	semidirect
9. #13070225	C₂	semidirect
10. D₁₁×C₂²⋊C₁₆	C₂	semidirect
11. C₂×C₁₁×C₂²⋊C₁₆	C₂	semidirect
15. C₂²×C₁₁×C₁₆	C₂²	semidirect
28. C₂×#66876	C₂²	semidirect
29. C₂×#66862	C₂²	semidirect
30. C₂×C₁₆×D₁₁	C₂²	semidirect
33. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
36. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
37. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
38. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
39. #10622140	C₂²	semidirect
40. Dic₁₁⋊C₁₆	C₂²	semidirect
41. Dic₁₁⋊C₁₆	C₂²	semidirect
42. C₁₆×Dic₁₁	C₂²	semidirect
171. C₂×C₂²⋊C₁₆	D₁₁	semidirect
199. C₂²⋊D₁₁	M₃₂	semidirect
229. C₂²×C₁₆	C₂×D₁₁	semidirect
251. C₂²⋊C₁₆	C₂×D₁₁	semidirect
408. C₁₁	#33488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂²⋊D₁₁	2
#13070445	2
#13070444	2
#13070441	2
C₁₆×C₂²⋊D₁₁	2
#13070416	2
#13070412	2
#13070227	2
#13070225	2
D₁₁×C₂²⋊C₁₆	2
C₂×C₁₁×C₂²⋊C₁₆	2
#33488	11