Group #13071335 — subgroups

Subgroups — #13071335

Order 1408.

516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂×#66922	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₂	C₂	1	2	yes	maximal
3	C₁₁×#376	C₂	1	1	yes	maximal, characteristic
4	#10622549	C₂	1	1	yes	maximal, characteristic
5	#10622542	C₂	1	2	yes	maximal
6	#10622266	C₂	1	8	yes	maximal
7	C₂²×Dic₂₂	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
13	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄×Dic₁₁	C₂²	1	4	yes	—
15	#66922	C₄	1	8	yes	complemented
16	C₄×Dic₂₂	—	2	8	no	—
17	C₁₁×#95	C₂²	1	4	yes	—
18	C₁₁⋊#95	C₂²	1	8	yes	—
19	C₁₁⋊#95	C₂²	1	4	yes	—
20	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
21	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₁	C₂³	1	4	yes	—
25	C₂²×Dic₁₁	C₂³	1	4	yes	—
26	C₂×Dic₂₂	—	2	4	no	—
27	C₂×Dic₂₂	—	2	4	no	—
28	C₂×Dic₂₂	C₂×C₄	1	8	yes	—
29	C₄²×C₁₁	—	2	2	no	—
30	C₄²×C₁₁	C₂×C₄	1	4	yes	—
31	C₄²×C₁₁	D₄	1	4	yes	—
32	C₄⋊Dic₁₁	—	2	4	no	—
33	C₄⋊Dic₁₁	C₂×C₄	1	16	yes	—
34	Dic₁₁⋊C₄	—	2	8	no	—
35	C₄×Dic₁₁	—	2	8	no	—
36	#2327	—	11	1	no	maximal, Sylow
37	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
38	C₂×C₄×C₁₁	—	2	4	no	—
39	C₂×C₄×C₁₁	—	2	4	no	—
40	C₂×C₄×C₁₁	—	2	2	no	—
41	C₂×C₄×C₁₁	—	2	4	no	—
42	C₂×C₄×C₁₁	C₂²×C₄	1	4	yes	—
43	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
45	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₁	#41	1	2	yes	—
47	C₂×Dic₁₁	—	2	4	no	—
48	C₂×Dic₁₁	—	2	4	no	—
49	C₂×Dic₁₁	—	2	4	no	—
50	C₂×Dic₁₁	—	2	8	no	—
51	C₂×Dic₁₁	C₂²×C₄	1	8	yes	—
52	Dic₂₂	—	2	16	no	—
53	C₂×C₄⋊Q₈	—	11	1	no	—
54	C₂×C₄×Q₈	—	11	2	no	—
55	#391	—	11	2	no	—
56	#387	—	11	8	no	—
57	#382	—	11	1	no	—
58	#376	D₁₁	1	1	yes	characteristic
59	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
61	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
62	C₂²×C₁₁	2₋¹⁺⁴	1	4	yes	—
63	C₄×C₁₁	—	2	4	no	—
64	C₄×C₁₁	—	2	4	no	—
65	C₄×C₁₁	—	4	2	no	—
66	C₄×C₁₁	C₄×D₄	1	4	yes	—
67	Dic₁₁	—	2	8	no	—
68	Dic₁₁	—	4	4	no	—
69	C₂²×Q₈	—	11	2	no	—
70	C₄⋊Q₈	—	11	8	no	—
71	C₄×Q₈	—	22	8	no	—
72	C₂×C₄⋊C₄	—	11	4	no	—
73	C₂×C₄⋊C₄	—	11	2	no	—
74	C₂×C₄⋊C₄	—	11	4	no	—
75	C₂×C₄²	—	11	4	no	—
76	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
77	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
79	#95	—	11	4	no	—
80	#95	—	11	8	no	—
81	#95	C₂×D₁₁	1	4	yes	—
82	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
83	C₂×C₁₁	#519	1	2	yes	—
84	C₂×C₁₁	#536	1	2	yes	—
85	C₂×C₁₁	#541	1	2	yes	—
86	C₂×Q₈	—	11	8	no	—
87	C₂×Q₈	—	22	4	no	—
88	C₂×Q₈	—	22	4	no	—
89	C₂²×C₄	—	11	4	no	—
90	C₂²×C₄	—	11	4	no	—
91	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
92	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
93	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
94	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
95	C₄⋊C₄	—	11	16	no	—
96	C₄⋊C₄	—	22	8	no	—
97	C₄⋊C₄	—	22	4	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	22	8	no	—
100	C₄²	C₄×D₁₁	1	4	yes	—
101	C₄²	D₄₄	1	4	yes	—
102	C₁₁	#2327	1	1	yes	characteristic, complemented, Sylow
103	C₂³	C₂³×D₁₁	1	1	yes	characteristic
104	Q₈	—	22	16	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	11	8	no	—
110	C₂×C₄	—	22	4	no	—
111	C₂×C₄	—	22	4	no	—
112	C₂×C₄	—	22	4	no	—
113	C₂×C₄	—	22	8	no	—
114	C₂×C₄	C₂×C₄×D₁₁	1	4	yes	—
115	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
116	C₂×C₄	C₂×D₄₄	1	4	yes	—
117	C₂×C₄	C₂×D₄₄	1	2	yes	—
118	C₂×C₄	#4339	1	2	yes	—
119	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
120	C₂²	C₂²×D₄₄	1	1	yes	characteristic
121	C₂²	C₂×#4339	1	1	yes	characteristic
122	C₂²	#67043	1	4	yes	—
123	C₄	—	2	4	no	—
124	C₄	—	2	4	no	—
125	C₄	—	4	2	no	—
126	C₄	—	22	8	no	—
127	C₄	—	44	4	no	—
128	C₄	C₄×D₄₄	1	4	yes	—
129	C₂	C₂×C₄×D₄₄	1	1	yes	characteristic
130	C₂	#10623047	1	2	yes	—
131	C₂	#10623049	1	2	yes	—
132	C₂	#10623057	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#66922

C₂

yes

maximal, characteristic

C₂×C₄×Dic₂₂

C₂

yes

maximal

C₁₁×#376

C₂

yes

maximal, characteristic

#10622549

C₂

yes

maximal, characteristic

#10622542

C₂

yes

maximal

#10622266

C₂

yes

maximal

C₂²×Dic₂₂

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

#66922

C₄

yes

complemented

C₄×Dic₂₂

—

C₁₁×#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

C₂×C₄

yes

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂×C₄

yes

—

C₄²×C₁₁

D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

C₂×C₄

yes

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

#2327

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

C₂²×C₄

yes

—

Dic₂₂

—

C₂×C₄⋊Q₈

—

C₂×C₄×Q₈

—

—

—

—

D₁₁

yes

characteristic

C₂²×C₁₁

C₂³×C₄

yes

characteristic

C₂²×C₁₁

C₂²×D₄

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

characteristic

C₂²×C₁₁

2₋¹⁺⁴

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₄×D₄

yes

—

Dic₁₁

—

Dic₁₁

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₂×C₄²

C₂×D₁₁

yes

—

—

C₂×D₁₁

yes

—

C₂×C₁₁

C₂×C₄×D₄

yes

characteristic

C₂×C₁₁

#519

yes

—

C₂×C₁₁

#536

yes

—

C₂×C₁₁

#541

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

100

C₄²

C₄×D₁₁

yes

—

101

C₄²

D₄₄

yes

—

102

C₁₁

#2327

yes

characteristic, complemented, Sylow

103

C₂³

C₂³×D₁₁

yes

characteristic

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×C₄×D₁₁

yes

—

115

C₂×C₄

C₂×C₄×D₁₁

yes

—

116

C₂×C₄

C₂×D₄₄

yes

—

117

C₂×C₄

C₂×D₄₄

yes

—

118

C₂×C₄

#4339

yes

—

119

C₂²

C₂²×C₄×D₁₁

yes

characteristic

120

C₂²

C₂²×D₄₄

yes

characteristic

121

C₂²

C₂×#4339

yes

characteristic

122

C₂²

#67043

yes

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

C₄×D₄₄

yes

—

129

C₂

C₂×C₄×D₄₄

yes

characteristic

130

C₂

#10623047

yes

—

131

C₂

#10623049

yes

—

132

C₂

#10623057

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#376	C₂
socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
hypercenter	#376	D₁₁
hypocenter	C₁₁	#2327
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator

C₂²×C₁₁

C₂³×C₄

Fitting

C₁₁×#376

C₂

socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
15. #66922	C₄	semidirect
102. C₁₁	#2327	semidirect

H ≅ G/N

type

15. #66922

C₄

semidirect

102. C₁₁

#2327

semidirect

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

subgroup	index
C₂×#66922	2
C₂×C₄×Dic₂₂	2
C₁₁×#376	2
#10622549	2
#10622542	2
#10622266	2
#2327	11

subgroup

index

C₂×#66922

C₂×C₄×Dic₂₂

C₁₁×#376

Subgroups — #13071335

Conjugacy classes of subgroups

Complements

Maximal subgroups