Group #13077557 — subgroups

Subgroups — #13077557

Order 1408.

348 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#533	C₂	1	1	yes	maximal, characteristic
2	#10622637	C₂	1	8	yes	maximal, complemented
3	#10622612	C₂	1	2	yes	maximal
4	#10622610	C₂	1	2	yes	maximal
5	#10622537	C₂	1	1	yes	maximal, characteristic
6	C₂×#66867	C₂	1	1	yes	maximal, characteristic
7	C₁₁×C₄⋊Q₈	C₄	1	2	yes	—
8	C₁₁×#125	C₄	1	2	yes	—
9	C₁₁×C₂²⋊Q₈	C₄	1	4	yes	—
10	C₄×Q₈×C₁₁	C₂²	1	4	yes	—
11	C₁₁×#117	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×#4318	C₂²	1	2	yes	—
14	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
17	C₄⋊(C₁₁⋊C₈)	C₂²	1	8	yes	—
18	#66867	C₂²	1	4	yes	—
19	#66867	C₂²	1	4	yes	—
20	C₄×C₁₁⋊C₈	C₂²	1	4	yes	—
21	C₂×Q₈×C₁₁	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
26	C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
27	C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
28	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₁₁	C₂³	1	4	yes	—
31	C₄²×C₁₁	C₂³	1	2	yes	—
32	#4318	—	2	4	no	—
33	C₂×C₁₁⋊C₈	—	2	2	no	—
34	C₂×C₁₁⋊C₈	Q₈	1	4	yes	complemented
35	C₂×C₁₁⋊C₈	C₂³	1	4	yes	—
36	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
37	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
38	#2961	—	11	1	no	maximal, Sylow
39	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	Q₈×C₁₁	—	4	4	no	—
41	C₂×C₄×C₁₁	—	4	2	no	—
42	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₁₁	C₂²×C₄	1	8	yes	—
45	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₁	#41	1	2	yes	—
48	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
49	C₁₁⋊C₈	—	2	2	no	—
50	C₁₁⋊C₈	—	2	4	no	—
51	C₁₁⋊C₈	C₂×Q₈	1	4	yes	—
52	#533	D₁₁	1	1	yes	characteristic
53	#446	—	11	8	no	—
54	#424	—	11	2	no	—
55	#423	—	11	1	no	—
56	#405	—	11	2	no	—
57	C₂×#97	—	11	1	no	—
58	C₂²×C₁₁	—	2	2	no	—
59	C₂²×C₁₁	C₄×Q₈	1	2	yes	—
60	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
61	C₄×C₁₁	—	2	2	no	—
62	C₄×C₁₁	—	2	2	no	—
63	C₄×C₁₁	—	2	8	no	—
64	C₄×C₁₁	C₄×Q₈	1	2	yes	—
65	C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
66	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
67	C₂×M₁₆	—	11	2	no	—
68	C₂²×C₈	—	11	1	no	—
69	C₂²×C₈	—	11	1	no	—
70	C₄⋊Q₈	Dic₁₁	1	2	yes	—
71	#125	Dic₁₁	1	2	yes	—
72	C₂²⋊Q₈	Dic₁₁	1	4	yes	—
73	C₄×Q₈	C₂×D₁₁	1	4	yes	—
74	#117	C₂×D₁₁	1	2	yes	—
75	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
76	C₄⋊C₈	—	11	4	no	—
77	C₄⋊C₈	—	11	8	no	—
78	#97	—	11	4	no	—
79	#97	—	11	4	no	—
80	C₄×C₈	—	11	4	no	—
81	C₂×C₁₁	—	2	2	no	—
82	C₂×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
83	C₂×C₁₁	#568	1	2	yes	—
84	C₂×Q₈	C₂×Dic₁₁	1	4	yes	—
85	C₂²×C₄	C₂×Dic₁₁	1	2	yes	—
86	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
87	M₁₆	—	22	4	no	—
88	C₂×C₈	—	11	4	no	—
89	C₂×C₈	—	11	2	no	—
90	C₂×C₈	—	11	4	no	—
91	C₂×C₈	—	11	2	no	—
92	C₂×C₈	—	22	2	no	—
93	C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
94	C₄⋊C₄	C₂×Dic₁₁	1	8	yes	—
95	C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
96	C₂²⋊C₄	C₂×Dic₁₁	1	4	yes	—
97	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
98	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
99	C₄²	C₂²×D₁₁	1	4	yes	—
100	C₄²	C₂²×D₁₁	1	2	yes	—
101	C₁₁	#2961	1	1	yes	characteristic, complemented, Sylow
102	C₂³	C₂²×Dic₁₁	1	1	yes	characteristic
103	Q₈	—	4	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	Q₈×D₁₁	1	2	yes	—
106	C₂×C₄	#4343	1	2	yes	—
107	C₂×C₄	C₂²×Dic₁₁	1	2	yes	—
108	C₂×C₄	C₂²×Dic₁₁	1	2	yes	—
109	C₂×C₄	C₂²×Dic₁₁	1	8	yes	—
110	C₂×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
111	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
112	C₈	—	11	4	no	—
113	C₈	—	22	2	no	—
114	C₈	—	22	4	no	—
115	C₂²	—	2	2	no	—
116	C₂²	Q₈×Dic₁₁	1	2	yes	—
117	C₂²	C₂³×Dic₁₁	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	2	8	no	—
121	C₄	Q₈×Dic₁₁	1	2	yes	—
122	C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
123	C₄	C₂×#4343	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	C₂×Q₈×Dic₁₁	1	1	yes	characteristic
126	C₂	#10623350	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#533

C₂

yes

maximal, characteristic

#10622637

C₂

yes

maximal, complemented

#10622612

C₂

yes

maximal

#10622610

C₂

yes

maximal

#10622537

C₂

yes

maximal, characteristic

C₂×#66867

C₂

yes

maximal, characteristic

C₁₁×C₄⋊Q₈

C₄

yes

—

C₁₁×#125

C₄

yes

—

C₁₁×C₂²⋊Q₈

C₄

yes

—

C₄×Q₈×C₁₁

C₂²

yes

—

C₁₁×#117

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×#4318

C₂²

yes

—

C₂²×C₁₁⋊C₈

C₂²

yes

characteristic

C₂²×C₁₁⋊C₈

C₂²

yes

characteristic

C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

#66867

C₂²

yes

—

#66867

C₂²

yes

—

C₄×C₁₁⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₁

C₂×C₄

yes

—

C₂²×C₄×C₁₁

C₂×C₄

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₂²⋊C₄

C₂×C₄

yes

—

C₄²×C₁₁

C₂×C₄

yes

characteristic

C₄²×C₁₁

C₂×C₄

yes

characteristic

C₄²×C₁₁

C₂³

yes

—

C₄²×C₁₁

C₂³

yes

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

Q₈

yes

complemented

C₂×C₁₁⋊C₈

C₂³

yes

—

C₂×C₁₁⋊C₈

C₂³

yes

—

C₂×C₁₁⋊C₈

C₂³

yes

—

#2961

—

maximal, Sylow

C₂³×C₁₁

C₂²×C₄

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

C₂⁴

yes

characteristic

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

C₂×Q₈

yes

—

#533

D₁₁

yes

—

—

—

—

C₂×#97

—

C₂²×C₁₁

—

C₂²×C₁₁

C₄×Q₈

yes

—

C₂²×C₁₁

C₂³×C₄

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₄×Q₈

yes

—

C₄×C₁₁

C₂²×Q₈

yes

characteristic

C₄×C₁₁

C₂×#41

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

Dic₁₁

yes

—

#125

Dic₁₁

yes

—

C₂²⋊Q₈

Dic₁₁

yes

—

C₄×Q₈

C₂×D₁₁

yes

—

#117

C₂×D₁₁

yes

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂×C₁₁

—

C₂×C₁₁

C₂×C₄×Q₈

yes

characteristic

C₂×C₁₁

#568

yes

—

C₂×Q₈

C₂×Dic₁₁

yes

—

C₂²×C₄

C₂×Dic₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₂²⋊C₄

C₂×Dic₁₁

yes

—

C₄²

C₂×Dic₁₁

yes

characteristic

C₄²

C₂×Dic₁₁

yes

characteristic

C₄²

C₂²×D₁₁

yes

—

100

C₄²

C₂²×D₁₁

yes

—

101

C₁₁

#2961

yes

characteristic, complemented, Sylow

102

C₂³

C₂²×Dic₁₁

yes

characteristic

103

Q₈

—

104

C₂×C₄

—

105

C₂×C₄

Q₈×D₁₁

yes

—

106

C₂×C₄

#4343

yes

—

107

C₂×C₄

C₂²×Dic₁₁

yes

—

108

C₂×C₄

C₂²×Dic₁₁

yes

—

109

C₂×C₄

C₂²×Dic₁₁

yes

—

110

C₂×C₄

C₂²×Dic₁₁

yes

characteristic

111

C₂×C₄

C₂³×D₁₁

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

Q₈×Dic₁₁

yes

—

117

C₂²

C₂³×Dic₁₁

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

Q₈×Dic₁₁

yes

—

122

C₄

C₂×Q₈×D₁₁

yes

characteristic

123

C₄

C₂×#4343

yes

characteristic

124

C₂

—

125

C₂

C₂×Q₈×Dic₁₁

yes

characteristic

126

C₂

#10623350

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#533	C₂
prime radical	C₂³×C₁₁	C₂²×C₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#533	D₁₁
hypocenter	C₁₁	#2961
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #533

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₁

commutator, socle

C₂²×C₁₁

C₂³×C₄

Fitting

C₁₁×#533

C₂

prime radical

C₂³×C₁₁

C₂²×C₄

cosocle

C₂×C₄×C₁₁

C₂⁴

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₁₁

C₁ ◁ C₂×C₄ ◁ #533

N	H ≅ G/N	type
2. #10622637	C₂	semidirect
34. C₂×C₁₁⋊C₈	Q₈	semidirect
101. C₁₁	#2961	semidirect

H ≅ G/N

type

2. #10622637

C₂

semidirect

34. C₂×C₁₁⋊C₈

Q₈

semidirect

101. C₁₁

#2961

semidirect

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

subgroup	index
C₁₁×#533	2
#10622637	2
#10622612	2
#10622610	2
#10622537	2
C₂×#66867	2
#2961	11

subgroup

index

C₁₁×#533

Subgroups — #13077557

Conjugacy classes of subgroups

Complements

Maximal subgroups