Subgroups — C₁₁×#7918 #14585111

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#431	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1281	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#431	—	2	2	no	—
7	C₁₁×#431	—	2	2	no	—
8	C₁₁×#431	C₄	1	4	yes	—
9	C₁₁×#431	C₂²	1	4	yes	—
10	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
11	C₂×C₁₁×C₂²⋊C₈	C₄	1	4	yes	—
12	C₄×C₁₁×M₁₆	—	2	2	no	—
13	C₄×C₁₁×M₁₆	—	2	2	no	—
14	C₂×C₁₁×#97	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	—	2	2	no	—
16	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₁₆	—	2	4	no	—
20	C₂×C₁₁×M₁₆	—	2	4	no	—
21	C₂×C₁₁×M₁₆	C₈	1	8	yes	complemented
22	C₂²×C₈×C₁₁	—	2	4	no	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	2	yes	—
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
31	C₁₁×C₄⋊C₈	—	2	4	no	—
32	C₁₁×C₄⋊C₈	—	2	4	no	—
33	C₁₁×C₂²⋊C₈	—	2	4	no	—
34	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
35	C₁₁×#97	—	2	4	no	—
36	C₄×C₈×C₁₁	—	2	4	no	—
37	C₄×C₈×C₁₁	—	2	2	no	—
38	C₄×C₈×C₁₁	—	2	2	no	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	#7918	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	—	4	4	no	—
43	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
44	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
52	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
53	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₁₁×M₁₆	—	2	16	no	—
56	C₂×C₈×C₁₁	—	2	4	no	—
57	C₂×C₈×C₁₁	—	2	8	no	—
58	C₂×C₈×C₁₁	—	2	4	no	—
59	C₂×C₈×C₁₁	—	4	8	no	—
60	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
61	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₂×D₄	1	2	yes	—
69	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
71	C₂×#431	C₂×C₁₁	1	2	yes	—
72	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic
73	#1281	C₂×C₁₁	1	4	yes	complemented
74	C₂³×C₁₁	—	4	2	no	—
75	C₂³×C₁₁	#95	1	2	yes	—
76	C₂³×C₁₁	C₄×C₈	1	2	yes	—
77	C₂³×C₁₁	#97	1	2	yes	—
78	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₁	—	2	4	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	4	no	—
82	C₂×C₄×C₁₁	—	4	2	no	—
83	C₂×C₄×C₁₁	—	4	2	no	—
84	C₂×C₄×C₁₁	—	4	2	no	—
85	C₂×C₄×C₁₁	#95	1	2	yes	—
86	C₂×C₄×C₁₁	#95	1	2	yes	—
87	C₂×C₄×C₁₁	#95	1	2	yes	—
88	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
89	C₂×C₄×C₁₁	#97	1	2	yes	—
90	C₂×C₄×C₁₁	C₂²⋊C₈	1	8	yes	—
91	C₂×C₄×C₁₁	C₄⋊C₈	1	8	yes	—
92	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
93	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
95	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
98	C₈×C₁₁	—	2	8	no	—
99	C₈×C₁₁	—	4	8	no	—
100	C₂²×M₁₆	C₄×C₁₁	1	2	yes	—
101	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
102	#431	—	2	2	no	—
103	#431	—	2	2	no	—
104	#431	C₄×C₁₁	1	4	yes	—
105	#431	C₂²×C₁₁	1	4	yes	—
106	C₂×C₄⋊C₈	—	2	2	no	—
107	C₂×C₂²⋊C₈	C₄×C₁₁	1	4	yes	—
108	C₄×M₁₆	—	2	2	no	—
109	C₄×M₁₆	—	2	2	no	—
110	C₂×#97	C₂²×C₁₁	1	2	yes	—
111	C₂×C₄×C₈	—	2	2	no	—
112	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
113	C₂²×C₁₁	—	2	2	no	—
114	C₂²×C₁₁	—	2	2	no	—
115	C₂²×C₁₁	—	2	2	no	—
116	C₂²×C₁₁	—	4	2	no	—
117	C₂²×C₁₁	—	4	2	no	—
118	C₂²×C₁₁	#336	1	4	yes	—
119	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
120	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
121	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
122	C₄×C₁₁	—	2	2	no	—
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	—	2	2	no	—
125	C₄×C₁₁	#336	1	4	yes	—
126	C₄×C₁₁	#344	1	4	yes	—
127	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
128	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
129	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
130	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
131	C₂×M₁₆	—	2	4	no	—
132	C₂×M₁₆	—	2	4	no	—
133	C₂×M₁₆	C₈×C₁₁	1	8	yes	complemented
134	C₂²×C₈	—	2	4	no	—
135	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
136	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
137	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
138	C₂×C₄²	D₄×C₁₁	1	2	yes	—
139	C₂×C₄²	D₄×C₁₁	1	2	yes	—
140	C₂×C₄²	D₄×C₁₁	1	2	yes	—
141	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
142	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
143	C₄⋊C₈	—	2	4	no	—
144	C₄⋊C₈	—	2	4	no	—
145	C₂²⋊C₈	—	2	4	no	—
146	C₂²⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
147	#97	—	2	4	no	—
148	C₄×C₈	—	2	4	no	—
149	C₄×C₈	—	2	2	no	—
150	C₄×C₈	—	2	2	no	—
151	C₄×C₈	—	2	4	no	—
152	C₂×C₁₁	—	2	4	no	—
153	C₂×C₁₁	—	2	1	no	—
154	C₂×C₁₁	—	2	1	no	—
155	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
156	C₂×C₁₁	C₂×#344	1	2	yes	—
157	C₂⁴	C₄²×C₁₁	1	1	yes	characteristic
158	C₂²×C₄	—	4	4	no	—
159	C₂²×C₄	C₄²×C₁₁	1	2	yes	—
160	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
161	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
162	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
163	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
164	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
165	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
166	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
167	C₂²×C₄	C₂×C₈×C₁₁	1	4	yes	—
168	C₂²×C₄	C₁₁×M₁₆	1	4	yes	—
169	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
170	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
171	M₁₆	—	2	16	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	8	no	—
175	C₂×C₈	—	4	8	no	—
176	C₂×C₈	C₂×C₈×C₁₁	1	8	yes	complemented
177	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
178	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
179	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
180	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
181	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
182	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
183	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
184	C₄²	C₂×D₄×C₁₁	1	2	yes	—
185	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
186	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
187	C₁₁	#7918	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³	—	4	2	no	—
189	C₂³	C₁₁×#95	1	2	yes	—
190	C₂³	C₄×C₈×C₁₁	1	2	yes	—
191	C₂³	C₁₁×#97	1	2	yes	—
192	C₂³	C₂×C₄²×C₁₁	1	1	yes	characteristic
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	C₁₁×#95	1	2	yes	—
200	C₂×C₄	C₁₁×#95	1	2	yes	—
201	C₂×C₄	C₁₁×#95	1	2	yes	—
202	C₂×C₄	C₄×C₈×C₁₁	1	2	yes	—
203	C₂×C₄	C₁₁×#97	1	2	yes	—
204	C₂×C₄	C₁₁×C₂²⋊C₈	1	8	yes	—
205	C₂×C₄	C₁₁×C₄⋊C₈	1	8	yes	—
206	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
209	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
211	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
212	C₈	—	2	8	no	—
213	C₈	—	4	8	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	2	2	no	—
217	C₂²	—	4	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	C₁₁×#336	1	4	yes	—
220	C₂²	C₂×C₁₁×#95	1	1	yes	characteristic
221	C₂²	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
222	C₂²	C₂×C₁₁×#97	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	2	2	no	—
226	C₄	C₁₁×#336	1	4	yes	—
227	C₄	C₁₁×#344	1	4	yes	—
228	C₄	C₂×C₁₁×C₂²⋊C₈	1	2	yes	—
229	C₄	C₂×C₁₁×C₄⋊C₈	1	2	yes	—
230	C₂	—	2	4	no	—
231	C₂	—	2	1	no	—
232	C₂	—	2	1	no	—
233	C₂	C₂×C₁₁×#336	1	1	yes	characteristic
234	C₂	C₂×C₁₁×#344	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₁	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1281	C₂	semidirect
21. C₂×C₁₁×M₁₆	C₈	semidirect
40. #7918	C₁₁	direct (N × H)
60. C₂×C₈×C₁₁	C₂×C₈	semidirect
73. #1281	C₂×C₁₁	semidirect
133. C₂×M₁₆	C₈×C₁₁	semidirect
176. C₂×C₈	C₂×C₈×C₁₁	semidirect
187. C₁₁	#7918	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#431	2
C₂×C₄×C₁₁×M₁₆	2
C₁₁×#1281	2
#7918	11

Subgroups — C11×#7918 #14585111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7918 #14585111