Subgroups — #14907293

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#4341	C₂	1	1	yes	maximal, characteristic
2	#13070523	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070522	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070446	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070445	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070442	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070441	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070438	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070414	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070412	C₂	1	1	yes	maximal, characteristic, complemented
11	#13070412	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070209	C₂	1	1	yes	maximal, characteristic, complemented
13	M₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#4341	C₄	1	1	yes	characteristic
17	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
26	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
27	C₂×#66862	C₂²	1	1	yes	characteristic
28	C₂×#66862	C₂²	1	1	yes	characteristic
29	#10622446	C₄	1	1	yes	characteristic
30	#10622443	C₄	1	1	yes	characteristic
31	(C₂²⋊D₁₁)⋊C₈	C₄	1	1	yes	characteristic
32	(C₂²⋊D₁₁)⋊C₈	C₄	1	1	yes	characteristic
33	#10622331	C₄	1	1	yes	characteristic
34	#10622331	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
37	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₁₁×#346	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
43	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
44	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
45	#10622140	C₂²	1	1	yes	characteristic
46	#10622140	C₂²	1	1	yes	characteristic
47	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
48	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
49	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
50	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
55	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
56	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
57	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
58	#10622099	C₂²	1	1	yes	characteristic
59	C₂×#4341	C₈	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
63	D₄×Dic₁₁	C₈	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
72	#66945	C₈	1	1	yes	characteristic
73	#66940	C₈	1	1	yes	characteristic
74	(C₂²⋊D₁₁)⋊C₄	C₈	1	1	yes	characteristic
75	(C₂²⋊D₁₁)⋊C₄	C₈	1	1	yes	characteristic
76	#66930	C₈	1	1	yes	characteristic
77	#66930	C₈	1	1	yes	characteristic
78	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
80	C₁₁×M₃₂	—	2	2	no	—
81	C₂×C₁₁×C₁₆	—	2	2	no	—
82	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
90	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
95	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
96	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
97	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
104	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
105	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
106	#66876	—	2	2	no	—
107	C₂×C₁₁⋊C₁₆	—	2	2	no	—
108	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
112	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
113	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
114	#66862	—	2	2	no	—
115	#66862	—	2	2	no	—
116	#33479	—	11	1	no	maximal, Sylow
117	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
124	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
125	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
126	#4341	—	2	4	no	—
127	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
139	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
140	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
141	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
145	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
146	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
148	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
149	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
150	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
151	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₁₁⋊C₈	—	2	2	no	—
162	C₂×C₁₁⋊C₈	—	2	2	no	—
163	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
167	C₈×D₁₁	—	2	1	no	—
168	C₈×D₁₁	—	2	1	no	—
169	C₈×D₁₁	—	2	2	no	—
170	C₁₁×C₁₆	—	2	1	no	—
171	C₁₁×C₁₆	—	2	1	no	—
172	C₁₁×C₁₆	—	2	1	no	—
173	C₁₁×C₁₆	#41	1	2	yes	complemented
174	C₁₁⋊C₁₆	—	2	1	no	—
175	C₁₁⋊C₁₆	—	2	1	no	—
176	C₁₁⋊C₁₆	—	2	1	no	—
177	C₁₁⋊C₁₆	#41	1	2	yes	complemented
178	C₈×#41	—	11	1	no	—
179	#2183	—	11	1	no	—
180	#2183	—	11	1	no	—
181	#2169	—	11	1	no	—
182	#2169	—	11	1	no	—
183	#2168	—	11	1	no	—
184	#2168	—	11	1	no	—
185	#2168	—	11	1	no	—
186	#2168	D₁₁	1	1	yes	characteristic, complemented
187	#2162	—	11	1	no	—
188	#2162	—	11	1	no	—
189	#2162	—	11	1	no	—
190	C₄×M₃₂	—	11	1	no	—
191	C₄×M₃₂	—	11	1	no	—
192	C₂×C₄×C₁₆	—	11	1	no	—
193	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
194	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
195	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
196	D₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
206	C₂²⋊D₁₁	—	2	2	no	—
207	C₂²⋊D₁₁	—	2	2	no	—
208	C₂×Dic₁₁	—	2	2	no	—
209	C₂×Dic₁₁	—	2	2	no	—
210	C₂×Dic₁₁	—	2	2	no	—
211	C₂×Dic₁₁	M₃₂	1	4	yes	complemented
212	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
213	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
214	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
215	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
216	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
217	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
219	C₄×D₁₁	—	2	1	no	—
220	C₄×D₁₁	—	2	1	no	—
221	C₄×D₁₁	—	2	2	no	—
222	C₄×D₁₁	—	2	2	no	—
223	Dic₂₂	—	2	2	no	—
224	C₈×C₁₁	—	2	1	no	—
225	C₈×C₁₁	—	2	1	no	—
226	C₈×C₁₁	—	2	1	no	—
227	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
228	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
229	C₁₁⋊C₈	—	2	1	no	—
230	C₁₁⋊C₈	—	2	1	no	—
231	C₁₁⋊C₈	—	2	1	no	—
232	C₁₁⋊C₈	#131	1	2	yes	—
233	C₄×#41	—	11	1	no	—
234	C₂×M₃₂	—	11	1	no	—
235	C₂×M₃₂	—	11	1	no	—
236	C₂×M₃₂	—	11	1	no	—
237	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
238	C₂²×C₁₆	—	11	1	no	—
239	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
240	C₈×Q₈	—	11	1	no	—
241	C₈×Q₈	—	11	1	no	—
242	C₈×D₄	—	11	1	no	—
243	C₈×D₄	—	11	1	no	—
244	C₈×D₄	—	11	1	no	—
245	C₈×D₄	—	11	1	no	—
246	C₈×D₄	—	11	1	no	—
247	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
248	#431	—	11	1	no	—
249	#431	—	11	1	no	—
250	#431	—	11	1	no	—
251	C₂×C₄×C₈	—	11	1	no	—
252	C₂×C₄×C₈	—	11	1	no	—
253	C₂×C₄×C₈	—	11	1	no	—
254	C₄⋊C₁₆	—	11	1	no	—
255	C₄⋊C₁₆	—	11	1	no	—
256	C₄⋊C₁₆	—	11	1	no	—
257	C₄⋊C₁₆	—	11	1	no	—
258	C₄⋊C₁₆	—	11	1	no	—
259	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
260	C₂²⋊C₁₆	—	11	1	no	—
261	C₂²⋊C₁₆	—	11	1	no	—
262	C₂²⋊C₁₆	—	11	1	no	—
263	C₂²⋊C₁₆	—	11	1	no	—
264	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
265	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
266	#346	—	11	1	no	—
267	#346	—	11	1	no	—
268	#346	—	11	1	no	—
269	#346	C₂×D₁₁	1	1	yes	characteristic
270	C₄×C₁₆	—	11	1	no	—
271	C₄×C₁₆	—	11	1	no	—
272	C₄×C₁₆	—	11	1	no	—
273	C₄×C₁₆	—	11	1	no	—
274	C₄×C₁₆	—	11	1	no	—
275	C₄×C₁₆	—	11	1	no	—
276	C₂²×C₁₁	—	2	1	no	—
277	C₂²×C₁₁	—	2	1	no	—
278	C₂²×C₁₁	—	2	1	no	—
279	C₂²×C₁₁	—	2	1	no	—
280	C₂²×C₁₁	—	2	1	no	—
281	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
282	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
283	C₂×D₁₁	—	2	1	no	—
284	C₂×D₁₁	—	2	1	no	—
285	C₂×D₁₁	—	2	1	no	—
286	C₄×C₁₁	—	2	1	no	—
287	C₄×C₁₁	—	2	1	no	—
288	C₄×C₁₁	—	2	1	no	—
289	C₄×C₁₁	—	2	1	no	—
290	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
291	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
292	Dic₁₁	—	2	1	no	—
293	Dic₁₁	—	2	1	no	—
294	Dic₁₁	—	2	1	no	—
295	Dic₁₁	—	2	1	no	—
296	Dic₁₁	C₂×M₃₂	1	2	yes	—
297	Dic₁₁	C₂×M₃₂	1	2	yes	—
298	Dic₁₁	#504	1	2	yes	—
299	C₂×#41	—	11	1	no	—
300	C₂²×C₈	—	11	1	no	—
301	C₂²×C₈	—	11	1	no	—
302	C₂²×C₈	—	11	1	no	—
303	C₂²×C₈	—	11	1	no	—
304	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
306	C₄×Q₈	—	11	1	no	—
307	C₄×Q₈	—	11	1	no	—
308	C₄×D₄	—	11	1	no	—
309	C₄×D₄	—	11	1	no	—
310	C₄×D₄	—	11	1	no	—
311	C₄×D₄	—	11	1	no	—
312	C₄×D₄	—	11	1	no	—
313	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
314	#117	—	11	1	no	—
315	#117	—	11	1	no	—
316	#117	—	11	1	no	—
317	C₂×C₄²	—	11	1	no	—
318	C₂×C₄²	—	11	1	no	—
319	C₂×C₄²	—	11	1	no	—
320	M₃₂	—	2	2	no	—
321	M₃₂	—	22	2	no	—
322	M₃₂	—	22	2	no	—
323	M₃₂	—	22	2	no	—
324	C₂×C₁₆	—	2	2	no	—
325	C₂×C₁₆	—	11	1	no	—
326	C₂×C₁₆	—	11	1	no	—
327	C₂×C₁₆	—	11	1	no	—
328	C₂×C₁₆	—	11	1	no	—
329	C₂×C₁₆	—	22	2	no	—
330	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
331	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
332	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
333	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
334	C₄⋊C₈	—	11	1	no	—
335	C₄⋊C₈	—	11	1	no	—
336	C₄⋊C₈	—	11	1	no	—
337	C₄⋊C₈	—	11	1	no	—
338	C₄⋊C₈	—	11	1	no	—
339	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
340	C₂²⋊C₈	—	11	1	no	—
341	C₂²⋊C₈	—	11	1	no	—
342	C₂²⋊C₈	—	11	1	no	—
343	C₂²⋊C₈	—	11	1	no	—
344	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
345	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
346	C₄×C₈	—	11	1	no	—
347	C₄×C₈	—	11	1	no	—
348	C₄×C₈	—	11	1	no	—
349	C₄×C₈	—	11	1	no	—
350	C₄×C₈	—	11	1	no	—
351	C₄×C₈	—	11	1	no	—
352	C₄×C₈	—	11	1	no	—
353	C₄×C₈	—	11	1	no	—
354	C₄×C₈	—	11	1	no	—
355	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
356	C₂×C₁₁	—	2	2	no	—
357	C₂×C₁₁	—	4	1	no	—
358	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
359	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
360	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
361	D₁₁	—	4	1	no	—
362	#41	—	22	4	no	—
363	C₂×Q₈	—	11	1	no	—
364	C₂×D₄	—	11	1	no	—
365	C₂×D₄	—	11	1	no	—
366	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
367	C₂²×C₄	—	11	1	no	—
368	C₂²×C₄	—	11	1	no	—
369	C₂²×C₄	—	11	1	no	—
370	C₂²×C₄	—	11	1	no	—
371	C₂²×C₄	—	11	1	no	—
372	C₂²×C₄	—	11	1	no	—
373	C₂²×C₄	—	11	1	no	—
374	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	11	1	no	—
381	C₂×C₈	—	11	1	no	—
382	C₂×C₈	—	11	1	no	—
383	C₂×C₈	—	11	1	no	—
384	C₂×C₈	—	22	2	no	—
385	C₂×C₈	—	22	2	no	—
386	C₂×C₈	—	22	2	no	—
387	C₂×C₈	—	22	1	no	—
388	C₂×C₈	—	22	1	no	—
389	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
390	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
392	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
393	C₄⋊C₄	—	11	1	no	—
394	C₄⋊C₄	—	11	1	no	—
395	C₄⋊C₄	—	11	1	no	—
396	C₄⋊C₄	—	11	1	no	—
397	C₄⋊C₄	—	11	1	no	—
398	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
399	C₂²⋊C₄	—	11	1	no	—
400	C₂²⋊C₄	—	11	1	no	—
401	C₂²⋊C₄	—	11	1	no	—
402	C₂²⋊C₄	—	11	1	no	—
403	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
404	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
405	C₄²	—	11	1	no	—
406	C₄²	—	11	1	no	—
407	C₄²	—	11	1	no	—
408	C₄²	—	11	1	no	—
409	C₄²	—	11	1	no	—
410	C₄²	—	11	1	no	—
411	C₄²	—	11	1	no	—
412	C₄²	—	11	1	no	—
413	C₄²	—	11	1	no	—
414	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
415	C₁₆	—	2	1	no	—
416	C₁₆	—	2	1	no	—
417	C₁₆	—	2	1	no	—
418	C₁₆	—	11	2	no	—
419	C₁₆	—	22	1	no	—
420	C₁₆	—	22	1	no	—
421	C₁₆	—	22	1	no	—
422	C₁₆	#4341	1	2	yes	complemented
423	C₁₁	#33479	1	1	yes	characteristic, complemented, Sylow
424	C₂³	—	11	1	no	—
425	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
426	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
427	Q₈	—	22	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	22	2	no	—
430	D₄	—	22	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	11	1	no	—
436	C₂×C₄	—	11	1	no	—
437	C₂×C₄	—	11	1	no	—
438	C₂×C₄	—	11	4	no	—
439	C₂×C₄	—	11	1	no	—
440	C₂×C₄	—	11	1	no	—
441	C₂×C₄	—	11	1	no	—
442	C₂×C₄	—	11	1	no	—
443	C₂×C₄	—	22	2	no	—
444	C₂×C₄	—	22	2	no	—
445	C₂×C₄	—	22	2	no	—
446	C₂×C₄	—	22	2	no	—
447	C₂×C₄	—	22	2	no	—
448	C₂×C₄	—	22	1	no	—
449	C₂×C₄	—	22	1	no	—
450	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
451	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
453	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	11	2	no	—
459	C₈	—	22	1	no	—
460	C₈	—	22	1	no	—
461	C₈	—	22	1	no	—
462	C₈	C₂×#4341	1	1	yes	characteristic
463	C₈	#41×D₁₁	1	1	yes	characteristic
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	22	1	no	—
470	C₂²	—	22	1	no	—
471	C₂²	—	22	1	no	—
472	C₂²	D₁₁×M₃₂	1	2	yes	—
473	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	11	2	no	—
479	C₄	—	11	2	no	—
480	C₄	—	11	2	no	—
481	C₄	—	22	1	no	—
482	C₄	—	22	1	no	—
483	C₄	—	22	1	no	—
484	C₄	—	22	1	no	—
485	C₄	C₄×#4341	1	1	yes	characteristic
486	C₄	D₁₁×#131	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	44	1	no	—
490	C₂	C₈×#4341	1	1	yes	characteristic
491	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
492	C₂	D₁₁×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2168	C₂
prime radical	C₂×#4341	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2168	D₁₁
hypocenter	C₁₁	#33479
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #13070523	C₂	semidirect
3. #13070522	C₂	semidirect
4. #13070446	C₂	semidirect
5. #13070445	C₂	semidirect
6. #13070442	C₂	semidirect
7. #13070441	C₂	semidirect
8. #13070438	C₂	semidirect
9. #13070414	C₂	semidirect
10. #13070412	C₂	semidirect
11. #13070412	C₂	semidirect
12. #13070209	C₂	semidirect
13. M₃₂×Dic₁₁	C₂	semidirect
14. C₂×C₁₆×Dic₁₁	C₂	semidirect
15. C₁₁×#2168	C₂	semidirect
173. C₁₁×C₁₆	#41	semidirect
177. C₁₁⋊C₁₆	#41	semidirect
186. #2168	D₁₁	semidirect
211. C₂×Dic₁₁	M₃₂	semidirect
422. C₁₆	#4341	semidirect
423. C₁₁	#33479	semidirect

Maximal subgroups

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

subgroup	index
C₈×#4341	2
#13070523	2
#13070522	2
#13070446	2
#13070445	2
#13070442	2
#13070441	2
#13070438	2
#13070414	2
#13070412	2
#13070209	2
M₃₂×Dic₁₁	2
C₂×C₁₆×Dic₁₁	2
C₁₁×#2168	2
#33479	11