Subgroups — C₁₁×#13193 #14590386

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#350	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#131	C₂²	1	2	yes	—
6	C₁₁×#532	C₄	1	1	yes	characteristic
7	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
8	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₁₁×#436	—	2	1	no	—
10	C₁₁×#436	—	2	1	no	—
11	C₈×D₄×C₁₁	—	2	1	no	—
12	C₈×D₄×C₁₁	—	2	1	no	—
13	C₁₁×#423	C₄	1	1	yes	characteristic
14	C₁₁×#408	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×C₄⋊C₁₆	—	2	1	no	—
17	C₁₁×C₄⋊C₁₆	—	2	1	no	—
18	C₁₁×#350	—	2	8	no	—
19	C₁₁×#346	—	2	1	no	—
20	C₄×C₁₁×C₁₆	—	2	1	no	—
21	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
22	C₁₁×#131	—	2	4	no	—
23	C₁₁×#131	—	2	4	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₁	—	2	2	no	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×C₄⋊Q₈	C₈	1	1	yes	characteristic
30	C₁₁×#127	C₈	1	1	yes	characteristic
31	C₁₁×#124	C₈	1	2	yes	—
32	C₁₁×#121	—	2	1	no	—
33	C₁₁×#121	—	2	1	no	—
34	C₄×D₄×C₁₁	—	2	1	no	—
35	C₄×D₄×C₁₁	—	2	1	no	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₁₁×M₃₂	—	2	2	no	—
38	C₁₁×M₃₂	D₄	1	4	yes	complemented
39	C₂×C₁₁×C₁₆	—	2	2	no	—
40	C₂×C₁₁×C₁₆	—	2	4	no	—
41	C₂×C₁₁×C₁₆	—	2	2	no	—
42	C₁₁×C₄⋊C₈	—	2	1	no	—
43	C₁₁×C₄⋊C₈	—	2	1	no	—
44	C₁₁×C₂²⋊C₈	—	2	2	no	—
45	C₁₁×C₂²⋊C₈	—	2	2	no	—
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
50	#13193	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₁₁×#41	—	2	4	no	—
52	C₁₁×#41	—	2	4	no	—
53	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
54	C₂×D₄×C₁₁	—	2	2	no	—
55	C₂×D₄×C₁₁	—	2	1	no	—
56	C₂×D₄×C₁₁	—	2	1	no	—
57	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
58	C₂²×C₄×C₁₁	—	2	2	no	—
59	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₁₁×M₁₆	—	2	4	no	—
63	C₁₁×M₁₆	—	4	2	no	—
64	C₁₁×M₁₆	—	4	2	no	—
65	C₂×C₈×C₁₁	—	2	2	no	—
66	C₂×C₈×C₁₁	—	2	2	no	—
67	C₂×C₈×C₁₁	—	4	4	no	—
68	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	#41	1	2	yes	—
74	C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₁₁×C₄⋊C₄	—	2	1	no	—
76	C₁₁×C₂²⋊C₄	—	2	2	no	—
77	C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
81	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
82	C₁₁×C₁₆	—	2	4	no	—
83	C₁₁×C₁₆	—	4	2	no	—
84	#2931	C₂×C₁₁	1	1	yes	characteristic
85	C₂×C₄⋊C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
86	C₂×#350	C₂×C₁₁	1	4	yes	complemented
87	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
88	C₂³×C₁₁	—	2	2	no	—
89	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
90	Q₈×C₁₁	—	2	4	no	—
91	D₄×C₁₁	—	2	4	no	—
92	D₄×C₁₁	—	4	2	no	—
93	D₄×C₁₁	—	4	4	no	—
94	D₄×C₁₁	—	4	2	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	4	1	no	—
98	C₂×C₄×C₁₁	—	4	2	no	—
99	C₂×C₄×C₁₁	—	4	2	no	—
100	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#131	1	2	yes	—
108	C₈×C₁₁	—	2	1	no	—
109	C₈×C₁₁	—	2	1	no	—
110	C₈×C₁₁	—	4	2	no	—
111	C₈×C₁₁	#121	1	2	yes	—
112	C₈×C₁₁	#124	1	1	yes	characteristic
113	C₈×C₁₁	#127	1	1	yes	characteristic
114	C₂×#131	C₂²×C₁₁	1	2	yes	—
115	#532	C₄×C₁₁	1	1	yes	characteristic
116	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
117	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
118	#436	—	2	1	no	—
119	#436	—	2	1	no	—
120	C₈×D₄	—	2	1	no	—
121	C₈×D₄	—	2	1	no	—
122	#423	C₄×C₁₁	1	1	yes	characteristic
123	#408	C₄×C₁₁	1	2	yes	—
124	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
125	C₄⋊C₁₆	—	2	1	no	—
126	C₄⋊C₁₆	—	2	1	no	—
127	#350	—	2	8	no	—
128	#346	—	2	1	no	—
129	C₄×C₁₆	—	2	1	no	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	2	1	no	—
132	C₂²×C₁₁	—	4	2	no	—
133	C₂²×C₁₁	—	4	2	no	—
134	C₂²×C₁₁	—	4	2	no	—
135	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
136	C₂²×C₁₁	#436	1	2	yes	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	4	2	no	—
141	C₄×C₁₁	#350	1	2	yes	complemented
142	C₄×C₁₁	#390	1	1	yes	characteristic
143	C₄×C₁₁	#408	1	1	yes	characteristic
144	C₄×C₁₁	C₈×D₄	1	2	yes	—
145	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
146	#131	—	2	4	no	—
147	#131	—	2	4	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
152	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
153	C₄⋊Q₈	C₈×C₁₁	1	1	yes	characteristic
154	#127	C₈×C₁₁	1	1	yes	characteristic
155	#124	C₈×C₁₁	1	2	yes	—
156	#121	—	2	1	no	—
157	#121	—	2	1	no	—
158	C₄×D₄	—	2	1	no	—
159	C₄×D₄	—	2	1	no	—
160	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
161	M₃₂	—	2	2	no	—
162	M₃₂	D₄×C₁₁	1	4	yes	complemented
163	C₂×C₁₆	—	2	2	no	—
164	C₂×C₁₆	—	2	4	no	—
165	C₂×C₁₆	—	2	2	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	2	1	no	—
168	C₂²⋊C₈	—	2	2	no	—
169	C₂²⋊C₈	—	2	2	no	—
170	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
171	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
172	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
173	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
174	C₂×C₁₁	—	2	2	no	—
175	C₂×C₁₁	—	8	2	no	—
176	C₂×C₁₁	#1954	1	1	yes	characteristic
177	C₂×C₁₁	C₂×#350	1	1	yes	characteristic
178	C₂×C₁₁	#2117	1	1	yes	characteristic
179	#41	—	2	4	no	—
180	#41	—	2	4	no	—
181	C₂×Q₈	C₂×C₈×C₁₁	1	2	yes	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	2	1	no	—
185	C₂×D₄	C₂×C₈×C₁₁	1	2	yes	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
188	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
189	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
190	M₁₆	—	2	4	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	4	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	4	4	no	—
196	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
199	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
200	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
201	C₂×C₈	C₁₁×#41	1	2	yes	—
202	C₄⋊C₄	—	2	1	no	—
203	C₄⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	2	2	no	—
205	C₂²⋊C₄	—	2	2	no	—
206	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
207	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
208	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
209	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
210	C₁₆	—	2	4	no	—
211	C₁₆	—	4	2	no	—
212	C₁₁	#13193	1	1	yes	characteristic, direct product factor, Sylow
213	C₂³	—	2	2	no	—
214	C₂³	C₂×C₁₁×M₁₆	1	1	yes	characteristic
215	Q₈	—	2	4	no	—
216	D₄	—	2	4	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	4	no	—
219	D₄	—	4	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
226	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
227	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
228	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
229	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
231	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
232	C₂×C₄	C₁₁×#131	1	2	yes	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	4	2	no	—
236	C₈	C₁₁×#121	1	2	yes	—
237	C₈	C₁₁×#124	1	1	yes	characteristic
238	C₈	C₁₁×#127	1	1	yes	characteristic
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	2	no	—
244	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
245	C₂²	C₁₁×#436	1	2	yes	—
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	4	2	no	—
250	C₄	C₁₁×#350	1	2	yes	complemented
251	C₄	C₁₁×#390	1	1	yes	characteristic
252	C₄	C₁₁×#408	1	1	yes	characteristic
253	C₄	C₈×D₄×C₁₁	1	2	yes	—
254	C₂	—	2	2	no	—
255	C₂	—	8	2	no	—
256	C₂	C₁₁×#1954	1	1	yes	characteristic
257	C₂	C₂×C₁₁×#350	1	1	yes	characteristic
258	C₂	C₁₁×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₁₁×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₄⋊C₁₆	C₂	semidirect
3. C₂×C₁₁×#350	C₂	semidirect
4. C₄×C₁₁×M₃₂	C₂	semidirect
38. C₁₁×M₃₂	D₄	semidirect
50. #13193	C₁₁	direct (N × H)
85. C₂×C₄⋊C₁₆	C₂×C₁₁	semidirect
86. C₂×#350	C₂×C₁₁	semidirect
87. C₄×M₃₂	C₂×C₁₁	semidirect
141. C₄×C₁₁	#350	semidirect
162. M₃₂	D₄×C₁₁	semidirect
212. C₁₁	#13193	direct (N × H)
250. C₄	C₁₁×#350	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2931	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂×C₁₁×#350	2
C₄×C₁₁×M₃₂	2
#13193	11

Subgroups — C11×#13193 #14590386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13193 #14590386