Group #14670192 — subgroups

Subgroups — #14670192

Order 2816.

342 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 159 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×#10622149	C₂	1	4	yes	maximal
2	#13070372	C₂	1	1	yes	maximal, characteristic
3	#13068302	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66879	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
9	C₂×#66876	C₂²	1	2	yes	—
10	#10622545	C₄	1	1	yes	characteristic
11	C₂×#66867	C₄	1	1	yes	characteristic
12	C₁₁×C₄⋊C₁₆	—	2	2	no	—
13	#10622149	—	2	8	no	—
14	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
19	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
20	C₁₁×M₃₂	—	2	4	no	—
21	C₂×C₁₁×C₁₆	—	2	2	no	—
22	C₄×C₈×C₁₁	D₄	1	2	yes	—
23	C₄×C₈×C₁₁	Q₈	1	2	yes	—
24	C₁₁⋊#95	—	2	2	no	—
25	#66879	—	2	4	no	—
26	C₈×Dic₁₁	D₄	1	4	yes	—
27	C₈×Dic₁₁	Q₈	1	4	yes	—
28	#66876	—	2	4	no	—
29	C₂×C₁₁⋊C₁₆	—	2	2	no	—
30	#66867	C₈	1	4	yes	—
31	#12901	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
33	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₁	—	2	2	no	—
35	C₂×C₈×C₁₁	—	2	2	no	—
36	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
37	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
38	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
41	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₁	C₂×C₈	1	2	yes	—
43	C₄×Dic₁₁	—	2	2	no	—
44	C₄×Dic₁₁	C₄⋊C₄	1	4	yes	—
45	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
46	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
47	C₂×C₁₁⋊C₈	M₁₆	1	4	yes	—
48	C₁₁×C₁₆	—	4	2	no	—
49	C₁₁⋊C₁₆	—	4	2	no	—
50	C₂×#364	—	11	4	no	—
51	#2150	—	11	1	no	—
52	#2150	D₁₁	1	1	yes	characteristic
53	#1726	—	11	1	no	—
54	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₄×C₁₁	—	4	2	no	—
56	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
61	C₂×Dic₁₁	—	2	4	no	—
62	C₂×Dic₁₁	—	4	4	no	—
63	C₈×C₁₁	—	2	2	no	—
64	C₈×C₁₁	#127	1	1	yes	characteristic
65	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
66	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
67	C₁₁⋊C₈	C₄⋊C₈	1	8	yes	—
68	C₂×M₃₂	—	11	2	no	—
69	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
70	C₂×#97	—	11	1	no	—
71	C₂×#97	—	11	2	no	—
72	C₂×C₄×C₈	—	11	2	no	—
73	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
74	#376	—	11	1	no	—
75	#364	—	22	8	no	—
76	C₄⋊C₁₆	—	2	2	no	—
77	C₄⋊C₁₆	—	22	2	no	—
78	C₂²×C₁₁	—	2	2	no	—
79	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
80	C₂²×C₁₁	#423	1	2	yes	—
81	C₄×C₁₁	—	2	4	no	—
82	C₄×C₁₁	#384	1	1	yes	characteristic
83	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
84	C₄×C₁₁	#423	1	1	yes	characteristic
85	Dic₁₁	—	4	4	no	—
86	C₂²×C₈	—	11	2	no	—
87	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
88	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
89	C₂×C₄²	—	11	2	no	—
90	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
91	M₃₂	—	2	4	no	—
92	M₃₂	—	22	4	no	—
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	—	22	2	no	—
95	#97	—	11	4	no	—
96	#97	—	22	4	no	—
97	C₄×C₈	—	11	4	no	—
98	C₄×C₈	—	11	4	no	—
99	C₄×C₈	Dic₂₂	1	2	yes	—
100	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
101	#95	—	22	2	no	—
102	C₂×C₁₁	—	2	2	no	—
103	C₂×C₁₁	#1842	1	1	yes	characteristic
104	C₂×C₁₁	#2153	1	2	yes	—
105	C₂²×C₄	—	22	2	no	—
106	C₂²×C₄	#4313	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	11	4	no	—
110	C₂×C₈	—	11	4	no	—
111	C₂×C₈	—	11	4	no	—
112	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
113	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
114	C₂×C₈	D₄×D₁₁	1	2	yes	—
115	C₂×C₈	Q₈×D₁₁	1	2	yes	—
116	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
117	C₄²	—	11	4	no	—
118	C₄²	—	22	2	no	—
119	C₄²	C₈×D₁₁	1	2	yes	—
120	C₄²	Dic₁₁⋊C₄	1	2	yes	—
121	C₁₆	—	4	2	no	—
122	C₁₆	—	44	2	no	—
123	C₁₁	#12901	1	1	yes	characteristic, complemented, Sylow
124	C₂³	C₂×#4313	1	1	yes	characteristic
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	22	4	no	—
127	C₂×C₄	—	44	4	no	—
128	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
129	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
130	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
131	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
132	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	11	8	no	—
135	C₈	#66941	1	2	yes	—
136	C₈	#66993	1	1	yes	characteristic
137	C₈	#66997	1	1	yes	characteristic
138	C₂²	—	2	2	no	—
139	C₂²	#10622450	1	2	yes	—
140	C₂²	C₂×Dic₁₁⋊C₈	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	44	4	no	—
143	C₄	D₁₁×C₄⋊C₈	1	2	yes	—
144	C₄	#10622589	1	1	yes	characteristic
145	C₄	#10622731	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	#13068767	1	1	yes	characteristic
148	C₂	#13070381	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622149

C₂

yes

maximal

#13070372

C₂

yes

maximal, characteristic

#13068302

C₂

yes

maximal, characteristic

C₁₁×#2150

C₂

yes

maximal, characteristic

C₂×C₁₁×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66879

C₄

yes

—

C₂×C₈×Dic₁₁

C₂²

yes

—

C₂×#66876

C₂²

yes

—

#10622545

C₄

yes

characteristic

C₂×#66867

C₄

yes

characteristic

C₁₁×C₄⋊C₁₆

—

#10622149

—

C₄⋊(C₁₁⋊C₁₆)

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₁

C₂×C₄

yes

—

C₂²×C₁₁⋊C₈

C₂×C₄

yes

—

C₁₁×M₃₂

—

C₂×C₁₁×C₁₆

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

C₁₁⋊#95

—

#66879

—

C₈×Dic₁₁

D₄

yes

—

C₈×Dic₁₁

Q₈

yes

—

#66876

—

C₂×C₁₁⋊C₁₆

—

#66867

C₈

yes

—

#12901

—

maximal, Sylow

C₂²×C₄×C₁₁

M₁₆

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂×C₈

yes

—

C₄×Dic₁₁

—

C₄×Dic₁₁

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₂×C₈

yes

—

C₂×C₁₁⋊C₈

M₁₆

yes

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

C₂×#364

—

#2150

—

#2150

D₁₁

yes

characteristic

#1726

—

C₂³×C₁₁

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₁

C₂×M₁₆

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

#127

yes

characteristic

C₈×C₁₁

C₄⋊Q₈

yes

—

C₈×C₁₁

C₄⋊Q₈

yes

characteristic

C₁₁⋊C₈

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₁

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#376

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₁

#423

yes

—

C₄×C₁₁

—

C₄×C₁₁

#384

yes

characteristic

C₄×C₁₁

C₂×C₄⋊C₈

yes

—

C₄×C₁₁

#423

yes

characteristic

Dic₁₁

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₁

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₂₂

yes

—

100

C₄×C₈

C₂²⋊D₁₁

yes

—

101

#95

—

102

C₂×C₁₁

—

103

C₂×C₁₁

#1842

yes

characteristic

104

C₂×C₁₁

#2153

yes

—

105

C₂²×C₄

—

106

C₂²×C₄

#4313

yes

—

107

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

Dic₁₁⋊C₄

yes

—

113

C₂×C₈

C₂×Dic₂₂

yes

characteristic

114

C₂×C₈

D₄×D₁₁

yes

—

115

C₂×C₈

Q₈×D₁₁

yes

—

116

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

117

C₄²

—

118

C₄²

—

119

C₄²

C₈×D₁₁

yes

—

120

C₄²

Dic₁₁⋊C₄

yes

—

121

C₁₆

—

122

C₁₆

—

123

C₁₁

#12901

yes

characteristic, complemented, Sylow

124

C₂³

C₂×#4313

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

Dic₁₁⋊C₈

yes

—

129

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

130

C₂×C₄

C₂×C₈×D₁₁

yes

characteristic

131

C₂×C₄

M₁₆×D₁₁

yes

—

132

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

#66941

yes

—

136

C₈

#66993

yes

characteristic

137

C₈

#66997

yes

characteristic

138

C₂²

—

139

C₂²

#10622450

yes

—

140

C₂²

C₂×Dic₁₁⋊C₈

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

D₁₁×C₄⋊C₈

yes

—

144

C₄

#10622589

yes

characteristic

145

C₄

#10622731

yes

characteristic

146

C₂

—

147

C₂

#13068767

yes

characteristic

148

C₂

#13070381

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2150	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#2150	D₁₁
hypocenter	C₁₁	#12901
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₁₁

commutator

C₂×C₄×C₁₁

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#2150

C₂

socle

C₂²×C₁₁

C₂×C₄⋊C₈

prime radical

C₂³×C₁₁

C₂×M₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
123. C₁₁	#12901	semidirect

H ≅ G/N

type

123. C₁₁

#12901

semidirect

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

subgroup	index
C₂×#10622149	2
#13070372	2
#13068302	2
C₁₁×#2150	2
#12901	11

subgroup

index

C₁₁×#2150

Subgroups — #14670192

Conjugacy classes of subgroups

Complements

Maximal subgroups