Subgroups — C₂×C₁₁×#2117 #14610532

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2117	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₁×#350	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₁×#41	C₄	1	1	yes	characteristic
7	C₂×C₁₁×#131	—	2	1	no	—
8	C₂×C₁₁×#131	—	2	2	no	—
9	C₂×C₁₁×#131	—	2	2	no	—
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₂×C₁₁×#131	C₄	1	2	yes	—
12	C₂×C₁₁×#131	C₄	1	4	yes	—
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₂×C₁₁×#131	C₂²	1	4	yes	—
15	C₂²×C₁₁×M₁₆	—	2	1	no	—
16	C₂²×C₁₁×M₁₆	C₄	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	—	2	1	no	—
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×M₃₂	—	2	2	no	—
20	C₂×C₁₁×M₃₂	—	2	1	no	—
21	C₂×C₁₁×M₃₂	—	2	1	no	—
22	C₂×C₁₁×M₃₂	—	2	2	no	—
23	C₂×C₁₁×M₃₂	—	2	1	no	—
24	C₂×C₁₁×M₃₂	C₂²	1	2	yes	complemented
25	C₂×C₁₁×M₃₂	C₂²	1	4	yes	complemented
26	C₂×C₁₁×M₃₂	C₂²	1	4	yes	complemented
27	C₂²×C₁₁×C₁₆	—	2	1	no	—
28	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	complemented
29	C₁₁×#350	C₂²	1	16	yes	complemented
30	C₂×C₁₁×#41	—	2	2	no	—
31	C₂×C₁₁×#41	—	2	1	no	—
32	C₂×C₁₁×#41	—	2	1	no	—
33	C₂×C₁₁×#41	—	2	2	no	—
34	C₂×C₁₁×#41	C₈	1	2	yes	—
35	C₂×C₁₁×#41	C₈	1	4	yes	—
36	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
37	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
38	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
39	C₂²×D₄×C₁₁	—	2	1	no	—
40	C₂²×D₄×C₁₁	C₈	1	1	yes	characteristic
41	C₂³×C₄×C₁₁	—	2	1	no	—
42	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₁₁×#131	—	2	4	no	—
44	C₁₁×#131	—	2	4	no	—
45	C₁₁×#131	—	2	4	no	—
46	C₁₁×#131	—	2	2	no	—
47	C₁₁×#131	—	2	4	no	—
48	C₁₁×#131	—	2	4	no	—
49	C₁₁×#131	—	2	2	no	—
50	C₁₁×#131	C₂×C₄	1	4	yes	—
51	C₁₁×#131	C₂×C₄	1	8	yes	—
52	C₁₁×#131	C₂³	1	4	yes	—
53	C₂×C₁₁×M₁₆	—	2	2	no	—
54	C₂×C₁₁×M₁₆	—	2	1	no	—
55	C₂×C₁₁×M₁₆	—	2	4	no	—
56	C₂×C₁₁×M₁₆	—	2	2	no	—
57	C₂×C₁₁×M₁₆	—	2	2	no	—
58	C₂×C₁₁×M₁₆	—	2	4	no	—
59	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₁₁	—	2	1	no	—
62	C₂²×C₈×C₁₁	—	2	2	no	—
63	C₂²×C₈×C₁₁	—	2	4	no	—
64	C₂²×C₈×C₁₁	—	2	4	no	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	D₄	1	2	yes	—
71	C₂²×C₈×C₁₁	D₄	1	2	yes	—
72	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×M₃₂	—	2	4	no	—
77	C₁₁×M₃₂	—	2	2	no	—
78	C₁₁×M₃₂	—	2	4	no	—
79	C₁₁×M₃₂	—	2	4	no	—
80	C₁₁×M₃₂	C₂³	1	4	yes	complemented
81	C₂×C₁₁×C₁₆	—	2	4	no	—
82	C₂×C₁₁×C₁₆	—	2	2	no	—
83	C₂×C₁₁×C₁₆	—	2	2	no	—
84	C₂×C₁₁×C₁₆	—	2	2	no	—
85	C₂×C₁₁×C₁₆	C₂³	1	4	yes	complemented
86	C₂×#2117	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₁	—	2	1	no	—
88	C₂⁴×C₁₁	M₁₆	1	1	yes	characteristic
89	C₁₁×#41	—	2	4	no	—
90	C₁₁×#41	—	2	4	no	—
91	C₁₁×#41	—	2	4	no	—
92	C₁₁×#41	—	2	2	no	—
93	C₁₁×#41	—	2	4	no	—
94	C₁₁×#41	—	2	2	no	—
95	C₁₁×#41	—	2	4	no	—
96	C₁₁×#41	C₂×C₈	1	4	yes	—
97	C₁₁×#41	C₂×C₈	1	8	yes	—
98	C₁₁×#41	C₂²×C₄	1	4	yes	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	2	1	no	—
101	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	—
102	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	4	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	1	no	—
109	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	—
110	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
111	C₂²×C₄×C₁₁	—	2	1	no	—
112	C₂²×C₄×C₁₁	—	2	4	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	4	no	—
115	C₂²×C₄×C₁₁	—	2	2	no	—
116	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
122	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₁₁×M₁₆	—	2	4	no	—
127	C₁₁×M₁₆	—	2	8	no	—
128	C₁₁×M₁₆	—	2	4	no	—
129	C₁₁×M₁₆	—	2	2	no	—
130	C₁₁×M₁₆	—	2	4	no	—
131	C₁₁×M₁₆	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₁₁	—	2	8	no	—
133	C₂×C₈×C₁₁	—	2	4	no	—
134	C₂×C₈×C₁₁	—	2	4	no	—
135	C₂×C₈×C₁₁	—	2	4	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
140	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
155	C₁₁×C₁₆	—	2	4	no	—
156	C₁₁×C₁₆	—	2	4	no	—
157	C₂²×#131	C₂×C₁₁	1	1	yes	characteristic
158	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
159	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
160	#2117	C₂×C₁₁	1	8	yes	direct product factor
161	C₂×#350	C₂×C₁₁	1	4	yes	complemented
162	C₂³×C₁₁	—	2	4	no	—
163	C₂³×C₁₁	—	2	2	no	—
164	C₂³×C₁₁	—	4	2	no	—
165	C₂³×C₁₁	—	4	4	no	—
166	C₂³×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
167	C₂³×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
168	C₂³×C₁₁	C₂²⋊C₈	1	2	yes	—
169	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
170	C₂³×C₁₁	C₂×M₁₆	1	2	yes	—
171	Q₈×C₁₁	—	2	2	no	—
172	Q₈×C₁₁	—	2	4	no	—
173	Q₈×C₁₁	C₂²×C₈	1	4	yes	—
174	D₄×C₁₁	—	2	4	no	—
175	D₄×C₁₁	—	2	8	no	—
176	D₄×C₁₁	—	2	4	no	—
177	D₄×C₁₁	—	2	2	no	—
178	D₄×C₁₁	—	2	4	no	—
179	D₄×C₁₁	C₂²×C₈	1	4	yes	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	4	no	—
183	C₂×C₄×C₁₁	—	2	8	no	—
184	C₂×C₄×C₁₁	—	2	4	no	—
185	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
186	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
188	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
190	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
191	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
192	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
197	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
199	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
203	C₈×C₁₁	—	2	4	no	—
204	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
205	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
208	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
209	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
210	C₂²×#41	C₄×C₁₁	1	1	yes	characteristic
211	C₂×#131	—	2	1	no	—
212	C₂×#131	—	2	2	no	—
213	C₂×#131	—	2	1	no	—
214	C₂×#131	—	2	2	no	—
215	C₂×#131	C₄×C₁₁	1	2	yes	—
216	C₂×#131	C₄×C₁₁	1	4	yes	—
217	C₂×#131	C₂²×C₁₁	1	2	yes	—
218	C₂×#131	C₂²×C₁₁	1	4	yes	—
219	C₂²×M₁₆	—	2	1	no	—
220	C₂²×M₁₆	C₄×C₁₁	1	1	yes	characteristic
221	C₂³×C₈	—	2	1	no	—
222	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×M₃₂	—	2	1	no	—
224	C₂×M₃₂	—	2	2	no	—
225	C₂×M₃₂	—	2	1	no	—
226	C₂×M₃₂	—	2	1	no	—
227	C₂×M₃₂	—	2	2	no	—
228	C₂×M₃₂	C₂²×C₁₁	1	2	yes	complemented
229	C₂×M₃₂	C₂²×C₁₁	1	4	yes	complemented
230	C₂×M₃₂	C₂²×C₁₁	1	4	yes	complemented
231	C₂²×C₁₆	—	2	1	no	—
232	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	complemented
233	#350	C₂²×C₁₁	1	16	yes	complemented
234	C₂²×C₁₁	—	2	2	no	—
235	C₂²×C₁₁	—	2	2	no	—
236	C₂²×C₁₁	—	2	2	no	—
237	C₂²×C₁₁	—	2	4	no	—
238	C₂²×C₁₁	—	4	2	no	—
239	C₂²×C₁₁	—	4	2	no	—
240	C₂²×C₁₁	—	4	8	no	—
241	C₂²×C₁₁	—	4	4	no	—
242	C₂²×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
243	C₂²×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
244	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
245	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
246	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
247	C₄×C₁₁	—	2	4	no	—
248	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
249	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
250	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
251	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
252	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
254	C₂×#41	—	2	1	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	1	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	C₈×C₁₁	1	2	yes	—
259	C₂×#41	C₈×C₁₁	1	4	yes	—
260	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
262	C₂²×Q₈	C₈×C₁₁	1	1	yes	characteristic
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₈×C₁₁	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
267	#131	—	2	4	no	—
268	#131	—	2	4	no	—
269	#131	—	2	4	no	—
270	#131	—	2	2	no	—
271	#131	—	2	4	no	—
272	#131	—	2	4	no	—
273	#131	—	2	2	no	—
274	#131	C₂×C₄×C₁₁	1	4	yes	—
275	#131	C₂×C₄×C₁₁	1	8	yes	—
276	#131	C₂³×C₁₁	1	4	yes	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
284	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	4	no	—
290	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
291	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
292	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
293	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
294	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
295	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
296	C₂²×C₈	D₄×C₁₁	1	2	yes	—
297	C₂²×C₈	D₄×C₁₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
300	M₃₂	—	2	4	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	—	2	4	no	—
303	M₃₂	—	2	4	no	—
304	M₃₂	C₂³×C₁₁	1	4	yes	complemented
305	C₂×C₁₆	—	2	2	no	—
306	C₂×C₁₆	—	2	4	no	—
307	C₂×C₁₆	—	2	2	no	—
308	C₂×C₁₆	—	2	2	no	—
309	C₂×C₁₆	C₂³×C₁₁	1	4	yes	complemented
310	C₂×C₁₁	—	2	2	no	—
311	C₂×C₁₁	—	2	1	no	—
312	C₂×C₁₁	—	2	2	no	—
313	C₂×C₁₁	—	2	1	no	—
314	C₂×C₁₁	—	4	4	no	—
315	C₂×C₁₁	#2117	1	2	yes	direct product factor
316	C₂×C₁₁	C₂²×C₂²⋊C₈	1	1	yes	characteristic
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₁₁×M₁₆	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	2	no	—
323	#41	—	2	4	no	—
324	#41	—	2	2	no	—
325	#41	—	2	4	no	—
326	#41	C₂×C₈×C₁₁	1	4	yes	—
327	#41	C₂×C₈×C₁₁	1	8	yes	—
328	#41	C₂²×C₄×C₁₁	1	4	yes	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	C₂×C₈×C₁₁	1	4	yes	—
332	C₂×Q₈	C₂×C₈×C₁₁	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	C₂×C₈×C₁₁	1	4	yes	—
340	C₂×D₄	C₂×C₈×C₁₁	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
349	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
352	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
353	C₂²×C₄	C₁₁×M₁₆	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	8	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	C₂²×C₄×C₁₁	1	4	yes	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
368	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
371	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
372	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
373	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
374	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
375	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
380	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
384	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
385	C₁₆	—	2	4	no	—
386	C₁₆	—	2	4	no	—
387	C₁₁	C₂×#2117	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	4	no	—
392	C₂³	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
393	C₂³	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
394	C₂³	C₁₁×C₂²⋊C₈	1	2	yes	—
395	C₂³	C₂×C₁₁×M₁₆	1	1	yes	characteristic
396	C₂³	C₂×C₁₁×M₁₆	1	2	yes	—
397	Q₈	—	2	2	no	—
398	Q₈	—	2	4	no	—
399	Q₈	C₂²×C₈×C₁₁	1	4	yes	—
400	D₄	—	2	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	4	no	—
405	D₄	C₂²×C₈×C₁₁	1	4	yes	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
412	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
413	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
414	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
415	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
416	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
417	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
418	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
419	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
421	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
423	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
425	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
427	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
428	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
431	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
432	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
433	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
434	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
435	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	4	no	—
444	C₂²	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
445	C₂²	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
446	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
447	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
448	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
451	C₄	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
452	C₄	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
453	C₄	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
454	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
455	C₄	C₂³×C₈×C₁₁	1	1	yes	characteristic
456	C₂	—	2	2	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	C₁₁×#2117	1	2	yes	direct product factor
462	C₂	C₂²×C₁₁×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₄	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂²×C₁₁×#41	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×M₃₂	C₂	semidirect
3. C₂²×C₁₁×M₃₂	C₂	semidirect
4. C₁₁×#2117	C₂	direct (N × H)
5. C₂×C₁₁×#350	C₂	semidirect
24. C₂×C₁₁×M₃₂	C₂²	semidirect
25. C₂×C₁₁×M₃₂	C₂²	semidirect
26. C₂×C₁₁×M₃₂	C₂²	semidirect
28. C₂²×C₁₁×C₁₆	C₂²	semidirect
29. C₁₁×#350	C₂²	semidirect
80. C₁₁×M₃₂	C₂³	semidirect
85. C₂×C₁₁×C₁₆	C₂³	semidirect
86. C₂×#2117	C₁₁	direct (N × H)
158. C₂²×M₃₂	C₂×C₁₁	semidirect
159. C₂²×M₃₂	C₂×C₁₁	semidirect
160. #2117	C₂×C₁₁	direct (N × H)
161. C₂×#350	C₂×C₁₁	semidirect
228. C₂×M₃₂	C₂²×C₁₁	semidirect
229. C₂×M₃₂	C₂²×C₁₁	semidirect
230. C₂×M₃₂	C₂²×C₁₁	semidirect
232. C₂²×C₁₆	C₂²×C₁₁	semidirect
233. #350	C₂²×C₁₁	semidirect
304. M₃₂	C₂³×C₁₁	semidirect
309. C₂×C₁₆	C₂³×C₁₁	semidirect
315. C₂×C₁₁	#2117	direct (N × H)
387. C₁₁	C₂×#2117	direct (N × H)
461. C₂	C₁₁×#2117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#131	2
C₂²×C₁₁×M₃₂	2
C₁₁×#2117	2
C₂×C₁₁×#350	2
C₂×#2117	11

Subgroups — C2×C11×#2117 #14610532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2117 #14610532