Group #13069737 — subgroups

Subgroups — #13069737

Order 1408.

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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×#67004	C₂	1	2	yes	maximal
2	C₂²×Dic₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#408	C₂	1	1	yes	maximal, characteristic
4	C₂×#66888	C₂	1	2	yes	maximal, complemented
5	#10622190	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₂	C₂²	1	2	yes	—
8	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#67004	—	2	4	no	—
11	#67004	—	2	4	no	—
12	C₂×#4326	—	2	2	no	—
13	C₂×#4324	—	2	2	no	—
14	C₂×#4318	C₂²	1	2	yes	—
15	C₂×Dic₄₄	—	2	4	no	—
16	C₂×Dic₄₄	—	2	2	no	—
17	C₁₁×C₂²⋊C₈	—	2	2	no	—
18	#66888	—	2	4	no	—
19	C₁₁×#41	—	2	2	no	—
20	C₁₁×#41	—	2	2	no	—
21	C₂×Q₈×C₁₁	D₄	1	1	yes	characteristic
22	C₂×D₄×C₁₁	—	2	1	no	—
23	C₂×D₄×C₁₁	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₁	—	2	1	no	—
25	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₁	—	2	2	no	—
27	C₂×Dic₂₂	—	2	2	no	—
28	C₂×Dic₂₂	—	2	2	no	—
29	C₂×Dic₂₂	—	2	2	no	—
30	C₂×Dic₂₂	—	2	2	no	—
31	C₂×Dic₂₂	—	2	2	no	—
32	C₂×Dic₂₂	D₄	1	4	yes	—
33	C₁₁×M₁₆	—	2	2	no	—
34	C₂×C₈×C₁₁	—	2	2	no	—
35	C₂×C₈×C₁₁	—	2	1	no	—
36	C₂×C₈×C₁₁	D₄	1	2	yes	—
37	#4326	—	2	8	no	—
38	#4324	—	2	8	no	—
39	#4318	—	2	2	no	—
40	#4318	D₄	1	4	yes	—
41	C₂×C₁₁⋊C₈	—	2	2	no	—
42	Dic₄₄	—	2	8	no	—
43	#2020	—	11	1	no	maximal, Sylow
44	C₂³×C₁₁	—	2	1	no	—
45	C₂³×C₁₁	#41	1	1	yes	characteristic
46	Q₈×C₁₁	—	2	2	no	—
47	D₄×C₁₁	—	2	2	no	—
48	D₄×C₁₁	—	4	2	no	—
49	C₂×C₄×C₁₁	—	2	1	no	—
50	C₂×C₄×C₁₁	—	4	1	no	—
51	C₂×C₄×C₁₁	—	4	1	no	—
52	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×Dic₁₁	—	2	4	no	—
57	C₂×Dic₁₁	—	4	2	no	—
58	C₂×Dic₁₁	—	4	2	no	—
59	Dic₂₂	—	2	4	no	—
60	Dic₂₂	—	2	4	no	—
61	Dic₂₂	—	4	2	no	—
62	Dic₂₂	—	4	2	no	—
63	C₈×C₁₁	—	2	2	no	—
64	C₈×C₁₁	—	4	1	no	—
65	C₁₁⋊C₈	—	2	4	no	—
66	C₂×#137	—	11	2	no	—
67	C₂²×Q₁₆	—	11	1	no	—
68	C₂×#101	—	11	2	no	—
69	#408	D₁₁	1	1	yes	characteristic
70	#341	—	11	1	no	—
71	C₂²×C₁₁	—	2	2	no	—
72	C₂²×C₁₁	—	4	1	no	—
73	C₂²×C₁₁	—	4	2	no	—
74	C₂²×C₁₁	#121	1	2	yes	—
75	C₂²×C₁₁	#121	1	1	yes	characteristic
76	C₄×C₁₁	—	4	1	no	—
77	C₄×C₁₁	#120	1	2	yes	—
78	C₄×C₁₁	#120	1	1	yes	characteristic
79	C₄×C₁₁	#127	1	1	yes	characteristic
80	Dic₁₁	—	4	4	no	—
81	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
82	C₂²×Q₈	—	11	2	no	—
83	#137	—	22	4	no	—
84	#137	—	22	4	no	—
85	C₂×Q₁₆	—	22	4	no	—
86	C₂×Q₁₆	—	22	2	no	—
87	C₂×Q₁₆	—	22	2	no	—
88	C₂×SD₁₆	—	22	2	no	—
89	C₂×M₁₆	—	11	2	no	—
90	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
91	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
92	#101	—	22	4	no	—
93	C₂²⋊C₈	—	2	2	no	—
94	C₂×C₁₁	—	2	2	no	—
95	C₂×C₁₁	—	8	1	no	—
96	C₂×C₁₁	#392	1	1	yes	characteristic
97	C₂×C₁₁	#473	1	2	yes	—
98	#41	—	2	2	no	—
99	#41	—	2	2	no	—
100	C₂×Q₈	—	11	4	no	—
101	C₂×Q₈	—	22	2	no	—
102	C₂×Q₈	—	22	2	no	—
103	C₂×Q₈	—	22	2	no	—
104	C₂×Q₈	—	22	2	no	—
105	C₂×Q₈	—	22	2	no	—
106	C₂×Q₈	D₄₄	1	1	yes	characteristic
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	D₄₄	1	1	yes	characteristic
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	—	22	2	no	—
111	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
112	Q₁₆	—	22	8	no	—
113	Q₁₆	—	22	8	no	—
114	SD₁₆	—	22	8	no	—
115	M₁₆	—	2	2	no	—
116	M₁₆	—	11	4	no	—
117	M₁₆	—	22	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	1	no	—
120	C₂×C₈	—	22	2	no	—
121	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
122	C₁₁	#2020	1	1	yes	characteristic, complemented, Sylow
123	C₂³	—	2	1	no	—
124	C₂³	#4339	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	Q₈	—	22	4	no	—
127	Q₈	—	22	4	no	—
128	Q₈	—	44	2	no	—
129	Q₈	—	44	2	no	—
130	D₄	—	2	2	no	—
131	D₄	—	4	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	22	4	no	—
136	C₂×C₄	—	44	2	no	—
137	C₂×C₄	—	44	2	no	—
138	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
139	C₂×C₄	D₄×D₁₁	1	2	yes	—
140	C₂×C₄	D₄×D₁₁	1	2	yes	—
141	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	4	1	no	—
144	C₈	—	22	4	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	4	2	no	—
147	C₂²	—	4	1	no	—
148	C₂²	#66937	1	2	yes	—
149	C₂²	#66983	1	1	yes	characteristic
150	C₄	—	4	1	no	—
151	C₄	—	44	4	no	—
152	C₄	#66935	1	2	yes	—
153	C₄	#66990	1	1	yes	characteristic
154	C₄	#66993	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	8	1	no	—
157	C₂	#10622573	1	1	yes	characteristic
158	C₂	#10622756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#67004

C₂

yes

maximal

C₂²×Dic₄₄

C₂

yes

maximal, characteristic, complemented

C₁₁×#408

C₂

yes

maximal, characteristic

C₂×#66888

C₂

yes

maximal, complemented

#10622190

C₂

yes

maximal, characteristic, complemented

C₂×C₁₁×#41

C₂²

yes

characteristic

C₂²×Dic₂₂

C₂²

yes

—

C₂×C₁₁×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₁₁

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₁₁×C₂²⋊C₈

—

#66888

—

C₁₁×#41

—

C₁₁×#41

—

C₂×Q₈×C₁₁

D₄

yes

characteristic

C₂×D₄×C₁₁

—

C₂×D₄×C₁₁

D₄

yes

characteristic

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

D₄

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₄

yes

—

—

—

—

D₄

yes

—

C₂×C₁₁⋊C₈

—

Dic₄₄

—

#2020

—

maximal, Sylow

C₂³×C₁₁

—

C₂³×C₁₁

#41

yes

characteristic

Q₈×C₁₁

—

D₄×C₁₁

—

D₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×#137

—

C₂²×Q₁₆

—

C₂×#101

—

#408

D₁₁

yes

characteristic

#341

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

#121

yes

—

C₂²×C₁₁

#121

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

#120

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

Dic₁₁

—

C₂×#41

C₂×D₁₁

yes

characteristic

C₂²×Q₈

—

#137

—

#137

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₈

C₂×D₁₁

yes

characteristic

#101

—

C₂²⋊C₈

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#392

yes

characteristic

C₂×C₁₁

#473

yes

—

#41

—

#41

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

D₄₄

yes

characteristic

107

C₂×D₄

—

108

C₂×D₄

D₄₄

yes

characteristic

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²×D₁₁

yes

characteristic

112

Q₁₆

—

113

Q₁₆

—

114

SD₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

C₂²⋊D₁₁

yes

—

122

C₁₁

#2020

yes

characteristic, complemented, Sylow

123

C₂³

—

124

C₂³

#4339

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₂×D₄₄

yes

characteristic

139

C₂×C₄

D₄×D₁₁

yes

—

140

C₂×C₄

D₄×D₁₁

yes

—

141

C₂×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#66937

yes

—

149

C₂²

#66983

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

#66935

yes

—

153

C₄

#66990

yes

characteristic

154

C₄

#66993

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

#10622573

yes

characteristic

158

C₂

#10622756

yes

—

	subgroup	G/H
center	C₂²	#66983
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#408	C₂
socle	C₂²×C₁₁	#121
prime radical	C₂×C₁₁×#41	C₂²
hypercenter	#408	D₁₁
hypocenter	C₁₁	#2020
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₂²

#66983

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₁₁×#408

C₂

socle

C₂²×C₁₁

#121

prime radical

C₂×C₁₁×#41

C₂²

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
2. C₂²×Dic₄₄	C₂	semidirect
4. C₂×#66888	C₂	semidirect
5. #10622190	C₂	semidirect
122. C₁₁	#2020	semidirect

H ≅ G/N

type

2. C₂²×Dic₄₄

C₂

semidirect

4. C₂×#66888

C₂

semidirect

5. #10622190

C₂

semidirect

122. C₁₁

#2020

semidirect

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

subgroup	index
C₂×#67004	2
C₂²×Dic₄₄	2
C₁₁×#408	2
C₂×#66888	2
#10622190	2
#2020	11

subgroup

index

C₂×#67004

C₂²×Dic₄₄

C₁₁×#408

C₂×#66888

#10622190

#2020

Subgroups — #13069737

Conjugacy classes of subgroups

Complements

Maximal subgroups