Group #13074591 — subgroups

Subgroups — #13074591

Order 1408.

360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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×#376	C₂	1	1	yes	maximal, characteristic
2	#10622549	C₂	1	1	yes	maximal, characteristic
3	#10622548	C₂	1	1	yes	maximal, characteristic
4	#10622541	C₂	1	2	yes	maximal
5	#10622541	C₂	1	2	yes	maximal
6	#10622273	C₂	1	4	yes	maximal
7	#10622270	C₂	1	4	yes	maximal
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	2	yes	—
13	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
14	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
15	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
16	C₁₁×#95	C₂²	1	2	yes	—
17	C₁₁×#95	C₂²	1	2	yes	—
18	C₁₁⋊#95	C₂²	1	4	yes	—
19	C₁₁⋊#95	C₂²	1	4	yes	—
20	C₁₁⋊#95	C₂²	1	4	yes	—
21	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
25	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₁	C₂³	1	4	yes	—
27	C₂²×Dic₁₁	C₂³	1	4	yes	—
28	C₄²×C₁₁	—	2	2	no	—
29	C₄²×C₁₁	—	2	2	no	—
30	C₄²×C₁₁	Q₈	1	4	yes	—
31	C₄⋊Dic₁₁	—	2	4	no	—
32	C₄⋊Dic₁₁	—	2	4	no	—
33	C₄⋊Dic₁₁	—	4	4	no	—
34	Dic₁₁⋊C₄	—	4	4	no	—
35	Dic₁₁⋊C₄	—	4	4	no	—
36	#2647	—	11	1	no	maximal, Sylow
37	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
38	C₂×C₄×C₁₁	—	2	2	no	—
39	C₂×C₄×C₁₁	—	2	2	no	—
40	C₂×C₄×C₁₁	—	2	1	no	—
41	C₂×C₄×C₁₁	—	2	1	no	—
42	C₂×C₄×C₁₁	—	2	2	no	—
43	C₂×C₄×C₁₁	—	2	2	no	—
44	C₂×C₄×C₁₁	—	2	2	no	—
45	C₂×C₄×C₁₁	—	2	2	no	—
46	C₂×C₄×C₁₁	—	2	2	no	—
47	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
48	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₁₁	#41	1	2	yes	—
50	C₂×C₄×C₁₁	#41	1	2	yes	—
51	C₂×Dic₁₁	—	2	4	no	—
52	C₂×Dic₁₁	—	2	4	no	—
53	C₂×Dic₁₁	—	2	4	no	—
54	C₂×Dic₁₁	—	2	4	no	—
55	C₂×Dic₁₁	—	2	4	no	—
56	C₂×Dic₁₁	—	2	4	no	—
57	#400	—	11	4	no	—
58	#398	—	11	4	no	—
59	#389	—	11	2	no	—
60	#389	—	11	2	no	—
61	#384	—	11	1	no	—
62	#382	—	11	1	no	—
63	#376	D₁₁	1	1	yes	characteristic
64	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
65	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
66	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
67	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
68	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
69	C₄×C₁₁	—	2	4	no	—
70	C₄×C₁₁	—	4	1	no	—
71	C₄×C₁₁	—	4	1	no	—
72	C₄×C₁₁	—	4	2	no	—
73	C₄×C₁₁	#125	1	4	yes	—
74	Dic₁₁	—	4	4	no	—
75	Dic₁₁	—	4	4	no	—
76	C₂×C₄⋊C₄	—	11	2	no	—
77	C₂×C₄⋊C₄	—	11	2	no	—
78	C₂×C₄⋊C₄	—	11	4	no	—
79	C₂×C₄⋊C₄	—	11	4	no	—
80	C₂×C₄⋊C₄	—	11	4	no	—
81	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
82	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
83	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
84	#95	—	11	4	no	—
85	#95	—	11	4	no	—
86	#95	—	11	4	no	—
87	#95	C₂×D₁₁	1	2	yes	—
88	#95	C₂×D₁₁	1	2	yes	—
89	C₂×C₁₁	C₂×#125	1	1	yes	characteristic
90	C₂×C₁₁	#540	1	1	yes	characteristic
91	C₂×C₁₁	#541	1	1	yes	characteristic
92	C₂×C₁₁	#542	1	2	yes	—
93	C₂×C₁₁	#544	1	2	yes	—
94	C₂²×C₄	—	11	4	no	—
95	C₂²×C₄	—	11	4	no	—
96	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
97	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
98	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
99	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
100	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
101	C₄⋊C₄	—	22	4	no	—
102	C₄⋊C₄	—	22	4	no	—
103	C₄⋊C₄	—	44	4	no	—
104	C₄⋊C₄	—	44	4	no	—
105	C₄⋊C₄	—	44	4	no	—
106	C₄²	—	2	2	no	—
107	C₄²	—	2	2	no	—
108	C₄²	Dic₂₂	1	4	yes	—
109	C₁₁	#2647	1	1	yes	characteristic, complemented, Sylow
110	C₂³	C₂³×D₁₁	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	22	4	no	—
121	C₂×C₄	—	22	4	no	—
122	C₂×C₄	—	22	4	no	—
123	C₂×C₄	—	22	4	no	—
124	C₂×C₄	—	22	4	no	—
125	C₂×C₄	—	22	4	no	—
126	C₂×C₄	C₂×Dic₂₂	1	4	yes	—
127	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
128	C₂×C₄	#4339	1	2	yes	—
129	C₂×C₄	#4339	1	2	yes	—
130	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
131	C₂²	C₂×#4339	1	1	yes	characteristic
132	C₂²	C₂×#4339	1	1	yes	characteristic
133	C₂²	#67042	1	2	yes	—
134	C₂²	#67043	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	2	no	—
138	C₄	—	4	1	no	—
139	C₄	—	44	4	no	—
140	C₄	—	44	4	no	—
141	C₄	#66923	1	4	yes	—
142	C₂	C₂×#66923	1	1	yes	characteristic
143	C₂	#10623049	1	1	yes	characteristic
144	C₂	#10623050	1	2	yes	—
145	C₂	#10623065	1	2	yes	—
146	C₂	#10623066	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#376

C₂

yes

maximal, characteristic

#10622549

C₂

yes

maximal, characteristic

#10622548

C₂

yes

maximal, characteristic

#10622541

C₂

yes

maximal

#10622541

C₂

yes

maximal

#10622273

C₂

yes

maximal

#10622270

C₂

yes

maximal

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×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₁₁×#95

C₂²

yes

—

C₁₁×#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

Q₈

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

Dic₁₁⋊C₄

—

#2647

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

—

—

—

—

—

—

D₁₁

yes

characteristic

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

characteristic

C₂²×C₁₁

H(5,𝔽₂)

yes

—

C₂²×C₁₁

2₋¹⁺⁴

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#125

yes

—

Dic₁₁

—

Dic₁₁

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₂×C₄²

C₂×D₁₁

yes

—

—

—

C₂×D₁₁

yes

—

#95

C₂×D₁₁

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂×C₁₁

#544

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂²×C₄

C₂²×D₁₁

yes

—

100

C₂²×C₄

C₂²×D₁₁

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

Dic₂₂

yes

—

109

C₁₁

#2647

yes

characteristic, complemented, Sylow

110

C₂³

C₂³×D₁₁

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₂₂

yes

—

127

C₂×C₄

C₂×Dic₂₂

yes

—

128

C₂×C₄

#4339

yes

—

129

C₂×C₄

#4339

yes

—

130

C₂²

C₂²×Dic₂₂

yes

characteristic

131

C₂²

C₂×#4339

yes

characteristic

132

C₂²

C₂×#4339

yes

characteristic

133

C₂²

#67042

yes

—

134

C₂²

#67043

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

#66923

yes

—

142

C₂

C₂×#66923

yes

characteristic

143

C₂

#10623049

yes

characteristic

144

C₂

#10623050

yes

—

145

C₂

#10623065

yes

—

146

C₂

#10623066

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#376	C₂
hypercenter	#376	D₁₁
hypocenter	C₁₁	#2647
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#376

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
109. C₁₁	#2647	semidirect

H ≅ G/N

type

109. C₁₁

#2647

semidirect

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

subgroup	index
C₁₁×#376	2
#10622549	2
#10622548	2
#10622541	2
#10622273	2
#10622270	2
#2647	11

subgroup

index

C₁₁×#376

Subgroups — #13074591

Conjugacy classes of subgroups

Complements

Maximal subgroups