Group #14670189 — subgroups

Subgroups — #14670189

Order 2816.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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	C₄×C₈×Dic₁₁	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×C₈×Dic₁₁	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
9	C₂×#66876	C₂²	1	2	yes	—
10	C₄²×Dic₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	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	—	2	2	no	—
19	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
20	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
21	C₁₁×M₃₂	—	2	4	no	—
22	C₂×C₁₁×C₁₆	—	2	2	no	—
23	C₄×C₈×C₁₁	D₄	1	2	yes	—
24	C₄×C₈×C₁₁	Q₈	1	2	yes	—
25	C₈×Dic₁₁	—	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	C₄×C₁₁⋊C₈	C₈	1	2	yes	—
31	C₄×C₁₁⋊C₈	C₈	1	2	yes	—
32	#12900	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
34	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂²×Dic₁₁	—	2	2	no	—
36	C₂×C₈×C₁₁	—	2	2	no	—
37	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
38	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
39	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
42	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
43	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
44	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
45	C₄×Dic₁₁	—	2	8	no	—
46	C₄×Dic₁₁	—	2	2	no	—
47	C₄×Dic₁₁	C₄⋊C₄	1	4	yes	—
48	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
49	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
50	C₂×C₁₁⋊C₈	M₁₆	1	4	yes	—
51	C₁₁×C₁₆	—	4	2	no	—
52	C₁₁⋊C₁₆	—	4	2	no	—
53	C₂×#364	—	11	4	no	—
54	#2150	—	11	1	no	—
55	#2150	D₁₁	1	1	yes	characteristic
56	C₄²×C₈	—	11	1	no	—
57	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
58	C₂×C₄×C₁₁	—	2	4	no	—
59	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
60	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
61	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
65	C₂×Dic₁₁	—	2	8	no	—
66	C₂×Dic₁₁	—	2	4	no	—
67	C₈×C₁₁	—	2	2	no	—
68	C₈×C₁₁	#127	1	1	yes	characteristic
69	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
70	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
71	C₁₁⋊C₈	C₄⋊C₈	1	8	yes	—
72	C₂×M₃₂	—	11	2	no	—
73	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
74	C₂×C₄×C₈	—	11	2	no	—
75	C₂×C₄×C₈	—	11	1	no	—
76	C₂×C₄×C₈	—	11	2	no	—
77	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
78	C₄³	—	11	1	no	—
79	#364	—	22	8	no	—
80	C₄⋊C₁₆	—	2	2	no	—
81	C₄⋊C₁₆	—	22	2	no	—
82	C₂²×C₁₁	—	2	2	no	—
83	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
84	C₂²×C₁₁	#423	1	2	yes	—
85	C₄×C₁₁	—	2	2	no	—
86	C₄×C₁₁	#364	1	4	yes	complemented
87	C₄×C₁₁	#384	1	1	yes	characteristic
88	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
89	C₄×C₁₁	#423	1	1	yes	characteristic
90	Dic₁₁	—	2	8	no	—
91	C₂²×C₈	—	11	2	no	—
92	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
93	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
94	C₂×C₄²	—	11	2	no	—
95	C₂×C₄²	—	22	2	no	—
96	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
97	M₃₂	—	2	4	no	—
98	M₃₂	—	22	4	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	22	2	no	—
101	C₄×C₈	—	11	4	no	—
102	C₄×C₈	—	11	4	no	—
103	C₄×C₈	—	11	2	no	—
104	C₄×C₈	—	11	2	no	—
105	C₄×C₈	—	22	4	no	—
106	C₄×C₈	Dic₂₂	1	2	yes	—
107	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
108	C₂×C₁₁	—	2	2	no	—
109	C₂×C₁₁	#1842	1	1	yes	characteristic
110	C₂×C₁₁	C₂×#364	1	2	yes	—
111	C₂²×C₄	—	22	2	no	—
112	C₂²×C₄	#4313	1	2	yes	—
113	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	11	4	no	—
116	C₂×C₈	—	11	4	no	—
117	C₂×C₈	—	11	4	no	—
118	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
119	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
120	C₂×C₈	D₄×D₁₁	1	2	yes	—
121	C₂×C₈	Q₈×D₁₁	1	2	yes	—
122	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
123	C₄²	—	11	4	no	—
124	C₄²	—	22	8	no	—
125	C₄²	—	22	2	no	—
126	C₄²	C₈×D₁₁	1	1	yes	characteristic
127	C₄²	C₈×D₁₁	1	1	yes	characteristic
128	C₄²	Dic₁₁⋊C₄	1	2	yes	—
129	C₁₆	—	4	2	no	—
130	C₁₆	—	44	2	no	—
131	C₁₁	#12900	1	1	yes	characteristic, complemented, Sylow
132	C₂³	C₂×#4313	1	1	yes	characteristic
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	22	8	no	—
135	C₂×C₄	—	22	4	no	—
136	C₂×C₄	Dic₁₁⋊C₈	1	2	yes	—
137	C₂×C₄	Dic₁₁⋊C₈	1	2	yes	—
138	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
139	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
140	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
141	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	11	8	no	—
144	C₈	#66941	1	2	yes	—
145	C₈	#66993	1	1	yes	characteristic
146	C₈	#66997	1	1	yes	characteristic
147	C₂²	—	2	2	no	—
148	C₂²	#10622450	1	2	yes	—
149	C₂²	C₂×Dic₁₁⋊C₈	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	22	8	no	—
152	C₄	#10622149	1	4	yes	complemented
153	C₄	D₁₁×C₄⋊C₈	1	2	yes	—
154	C₄	#10622589	1	1	yes	characteristic
155	C₄	#10622731	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	#13068767	1	1	yes	characteristic
158	C₂	C₂×#10622149	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622149

C₂

yes

maximal

#13070372

C₂

yes

maximal, characteristic

C₄×C₈×Dic₁₁

C₂

yes

maximal, characteristic

C₁₁×#2150

C₂

yes

maximal, characteristic

C₂×C₁₁×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₈×Dic₁₁

C₄

yes

—

C₂×C₈×Dic₁₁

C₂²

yes

—

C₂×#66876

C₂²

yes

—

C₄²×Dic₁₁

C₄

yes

characteristic

C₂×C₄×C₁₁⋊C₈

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×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

—

C₈×Dic₁₁

—

C₈×Dic₁₁

D₄

yes

—

C₈×Dic₁₁

Q₈

yes

—

#66876

—

C₂×C₁₁⋊C₁₆

—

C₄×C₁₁⋊C₈

C₈

yes

—

C₄×C₁₁⋊C₈

C₈

yes

—

#12900

—

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

characteristic

C₄²×C₁₁

C₂×C₈

yes

characteristic

C₄×Dic₁₁

—

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

C₄²×C₈

—

C₂³×C₁₁

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

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×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄³

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₁

#423

yes

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

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

—

C₂×C₄²

C₄×D₁₁

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

Dic₂₂

yes

—

107

C₄×C₈

C₂²⋊D₁₁

yes

—

108

C₂×C₁₁

—

109

C₂×C₁₁

#1842

yes

characteristic

110

C₂×C₁₁

C₂×#364

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

#4313

yes

—

113

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

Dic₁₁⋊C₄

yes

—

119

C₂×C₈

C₂×Dic₂₂

yes

characteristic

120

C₂×C₈

D₄×D₁₁

yes

—

121

C₂×C₈

Q₈×D₁₁

yes

—

122

C₂×C₈

C₂×C₂²⋊D₁₁

yes

characteristic

123

C₄²

—

124

C₄²

—

125

C₄²

—

126

C₄²

C₈×D₁₁

yes

characteristic

127

C₄²

C₈×D₁₁

yes

characteristic

128

C₄²

Dic₁₁⋊C₄

yes

—

129

C₁₆

—

130

C₁₆

—

131

C₁₁

#12900

yes

characteristic, complemented, Sylow

132

C₂³

C₂×#4313

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

Dic₁₁⋊C₈

yes

—

137

C₂×C₄

Dic₁₁⋊C₈

yes

—

138

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

139

C₂×C₄

C₂×C₈×D₁₁

yes

characteristic

140

C₂×C₄

M₁₆×D₁₁

yes

—

141

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

#66941

yes

—

145

C₈

#66993

yes

characteristic

146

C₈

#66997

yes

characteristic

147

C₂²

—

148

C₂²

#10622450

yes

—

149

C₂²

C₂×Dic₁₁⋊C₈

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

#10622149

yes

complemented

153

C₄

D₁₁×C₄⋊C₈

yes

—

154

C₄

#10622589

yes

characteristic

155

C₄

#10622731

yes

characteristic

156

C₂

—

157

C₂

#13068767

yes

characteristic

158

C₂

C₂×#10622149

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	#12900
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
86. C₄×C₁₁	#364	semidirect
131. C₁₁	#12900	semidirect
152. C₄	#10622149	semidirect

H ≅ G/N

type

86. C₄×C₁₁

#364

semidirect

131. C₁₁

#12900

semidirect

152. C₄

#10622149

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
C₄×C₈×Dic₁₁	2
C₁₁×#2150	2
#12900	11

subgroup

index

C₂×#10622149

#13070372

C₄×C₈×Dic₁₁

C₁₁×#2150

#12900

Subgroups — #14670189

Conjugacy classes of subgroups

Complements

Maximal subgroups