Subgroups — C₁₁⋊#7050 #14640385

Order 2816.

332 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068768	C₂	1	2	yes	maximal
2	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
4	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
5	C₄³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
7	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
8	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	4	yes	—
9	C₂²×C₈×C₁₁	—	2	2	no	—
10	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	D₄	1	2	yes	—
14	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₈	—	2	4	no	—
16	C₁₁×C₄⋊C₈	—	4	2	no	—
17	C₁₁×C₄⋊C₈	—	4	2	no	—
18	C₁₁×C₄⋊C₈	—	4	2	no	—
19	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
20	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
21	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
22	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
23	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
24	#7050	—	11	1	no	maximal, Sylow
25	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
27	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	—	4	2	no	—
31	C₂×C₈×C₁₁	—	4	4	no	—
32	C₄²×C₁₁	—	2	2	no	—
33	C₄²×C₁₁	—	2	1	no	—
34	C₄²×C₁₁	—	2	2	no	—
35	C₄²×C₁₁	—	2	1	no	—
36	C₄²×C₁₁	—	4	1	no	—
37	C₄²×C₁₁	D₈	1	1	yes	characteristic
38	C₄²×C₁₁	D₈	1	2	yes	—
39	C₄²×C₁₁	SD₁₆	1	2	yes	—
40	C₄²×C₁₁	SD₁₆	1	2	yes	—
41	C₄²×C₁₁	SD₁₆	1	2	yes	—
42	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
43	C₄²×C₁₁	Q₁₆	1	2	yes	—
44	C₂×C₁₁⋊C₈	—	4	4	no	—
45	C₂×C₁₁⋊C₈	—	4	4	no	—
46	C₂×C₁₁⋊C₈	—	4	4	no	—
47	#1842	—	11	2	no	—
48	#1842	D₁₁	1	1	yes	characteristic
49	C₂³×C₁₁	#95	1	1	yes	characteristic
50	C₂×C₄×C₁₁	—	2	2	no	—
51	C₂×C₄×C₁₁	—	2	1	no	—
52	C₂×C₄×C₁₁	—	2	1	no	—
53	C₂×C₄×C₁₁	—	2	2	no	—
54	C₂×C₄×C₁₁	—	2	1	no	—
55	C₂×C₄×C₁₁	—	2	2	no	—
56	C₂×C₄×C₁₁	#100	1	2	yes	—
57	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#101	1	2	yes	—
59	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
60	C₂×C₄×C₁₁	#102	1	2	yes	—
61	C₂×C₄×C₁₁	#102	1	2	yes	—
62	C₂×C₄×C₁₁	#102	1	2	yes	—
63	C₂×C₄×C₁₁	#103	1	2	yes	—
64	C₂×C₄×C₁₁	#103	1	2	yes	—
65	C₂×C₄×C₁₁	#103	1	2	yes	—
66	C₂×C₄×C₁₁	#106	1	2	yes	—
67	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#107	1	2	yes	—
69	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
70	C₈×C₁₁	—	8	2	no	—
71	C₁₁⋊C₈	—	8	4	no	—
72	C₂×C₄⋊C₈	—	2	2	no	—
73	C₂×C₄⋊C₈	—	11	4	no	—
74	C₂×C₄⋊C₈	—	22	2	no	—
75	C₂×C₄⋊C₈	—	22	2	no	—
76	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
77	C₄³	C₂×D₁₁	1	1	yes	characteristic
78	C₂²×C₁₁	#338	1	1	yes	characteristic
79	C₂²×C₁₁	#340	1	2	yes	—
80	C₂²×C₁₁	#340	1	1	yes	characteristic
81	C₂²×C₁₁	#343	1	1	yes	characteristic
82	C₂²×C₁₁	#343	1	2	yes	—
83	C₄×C₁₁	—	2	2	no	—
84	C₄×C₁₁	—	2	1	no	—
85	C₄×C₁₁	—	2	2	no	—
86	C₄×C₁₁	—	2	1	no	—
87	C₄×C₁₁	—	4	1	no	—
88	C₄×C₁₁	#331	1	2	yes	—
89	C₄×C₁₁	#331	1	1	yes	characteristic
90	C₄×C₁₁	#332	1	2	yes	—
91	C₄×C₁₁	#332	1	2	yes	—
92	C₄×C₁₁	#332	1	2	yes	—
93	C₄×C₁₁	#333	1	2	yes	—
94	C₄×C₁₁	#333	1	1	yes	characteristic
95	C₂²×C₈	—	2	2	no	—
96	C₂²×C₈	—	22	4	no	—
97	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
98	C₂×C₄²	C₄×D₁₁	1	2	yes	—
99	C₂×C₄²	D₄₄	1	1	yes	characteristic
100	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
101	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
102	C₄⋊C₈	—	4	2	no	—
103	C₄⋊C₈	—	4	2	no	—
104	C₄⋊C₈	—	4	2	no	—
105	C₄⋊C₈	—	44	4	no	—
106	C₄⋊C₈	—	44	2	no	—
107	C₄⋊C₈	—	44	2	no	—
108	C₄⋊C₈	—	44	2	no	—
109	C₄⋊C₈	—	44	2	no	—
110	C₂×C₁₁	#1292	1	2	yes	—
111	C₂×C₁₁	#1292	1	1	yes	characteristic
112	C₂×C₁₁	#1296	1	1	yes	characteristic
113	C₂×C₁₁	#1296	1	2	yes	—
114	C₂×C₁₁	#1309	1	1	yes	characteristic
115	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
116	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
117	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
118	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
119	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
120	C₂×C₈	—	4	4	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	44	4	no	—
123	C₂×C₈	—	44	4	no	—
124	C₂×C₈	—	44	4	no	—
125	C₄²	—	2	2	no	—
126	C₄²	—	2	2	no	—
127	C₄²	—	2	1	no	—
128	C₄²	—	2	1	no	—
129	C₄²	—	4	1	no	—
130	C₄²	#4314	1	2	yes	—
131	C₄²	D₈₈	1	1	yes	characteristic
132	C₄²	Dic₄₄	1	1	yes	characteristic
133	C₄²	#4323	1	2	yes	—
134	C₄²	#4324	1	2	yes	—
135	C₄²	#4325	1	2	yes	—
136	C₄²	#4326	1	2	yes	—
137	C₁₁	#7050	1	1	yes	characteristic, complemented, Sylow
138	C₂³	C₁₁⋊#95	1	1	yes	characteristic
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	#66871	1	2	yes	—
146	C₂×C₄	#66872	1	2	yes	—
147	C₂×C₄	#66873	1	2	yes	—
148	C₂×C₄	#66874	1	2	yes	—
149	C₂×C₄	#66880	1	2	yes	—
150	C₂×C₄	#66881	1	1	yes	characteristic
151	C₂×C₄	#66882	1	1	yes	characteristic
152	C₂×C₄	#66885	1	2	yes	—
153	C₂×C₄	#66887	1	2	yes	—
154	C₂×C₄	#66888	1	2	yes	—
155	C₂×C₄	#66896	1	2	yes	—
156	C₂×C₄	#66897	1	1	yes	characteristic
157	C₂×C₄	#66899	1	2	yes	—
158	C₂×C₄	#66900	1	1	yes	characteristic
159	C₈	—	8	2	no	—
160	C₈	—	88	4	no	—
161	C₂²	#10622167	1	2	yes	—
162	C₂²	#10622168	1	1	yes	characteristic
163	C₂²	#10622189	1	1	yes	characteristic
164	C₂²	#10622192	1	2	yes	—
165	C₂²	C₁₁⋊#338	1	1	yes	characteristic
166	C₄	—	2	2	no	—
167	C₄	—	2	2	no	—
168	C₄	—	2	1	no	—
169	C₄	—	2	1	no	—
170	C₄	—	4	1	no	—
171	C₄	#10622119	1	2	yes	—
172	C₄	#10622120	1	2	yes	—
173	C₄	#10622123	1	2	yes	—
174	C₄	#10622124	1	2	yes	—
175	C₄	#10622182	1	1	yes	characteristic
176	C₄	#10622184	1	1	yes	characteristic
177	C₄	#10622185	1	2	yes	—
178	C₂	#13066490	1	2	yes	—
179	C₂	#13066491	1	1	yes	characteristic
180	C₂	#13066499	1	1	yes	characteristic
181	C₂	#13066500	1	2	yes	—
182	C₂	C₁₁⋊#1309	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₁⋊#95
commutator	C₂²×C₄×C₁₁	C₄²
Frattini	C₄³	C₂×D₁₁
Fitting	C₁₁×#1842	C₂
socle, prime radical	C₂³×C₁₁	#95
cosocle	C₄³×C₁₁	C₂²
hypercenter	#1842	D₁₁
hypocenter	C₁₁	#7050
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
137. C₁₁	#7050	semidirect

Maximal subgroups

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

subgroup	index
#13068768	2
C₁₁×#1842	2
#7050	11

Subgroups — C11⋊#7050 #14640385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊#7050 #14640385