Group #14587861 — subgroups

Subgroups — C₁₁×#10668 #14587861

Order 2816.

316 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 114 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×#1995	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1843	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1571	C₂	1	2	yes	maximal
4	C₁₁×#1481	C₂	1	2	yes	maximal
5	C₁₁×#1274	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#533	C₂²	1	1	yes	characteristic
7	C₁₁×#431	C₂²	1	2	yes	—
8	C₁₁×#423	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₁₁×#376	C₂²	1	1	yes	characteristic
12	C₁₁×#339	—	2	2	no	—
13	C₁₁×#335	—	2	4	no	—
14	C₁₁×Q₈⋊C₈	—	2	4	no	—
15	C₂×C₁₁×M₁₆	—	2	1	no	—
16	C₂²×C₈×C₁₁	—	2	2	no	—
17	C₁₁×C₄⋊Q₈	Q₈	1	2	yes	—
18	C₁₁×#125	—	2	1	no	—
19	C₁₁×C₂²⋊Q₈	—	2	2	no	—
20	C₄×Q₈×C₁₁	—	2	2	no	—
21	C₁₁×#117	—	2	1	no	—
22	C₂×C₄²×C₁₁	D₄	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₁₁×C₄⋊C₈	—	2	2	no	—
25	C₁₁×C₄⋊C₈	—	2	2	no	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₁₁×C₄⋊C₈	—	2	2	no	—
28	C₁₁×C₄⋊C₈	—	4	4	no	—
29	C₁₁×C₂²⋊C₈	—	2	2	no	—
30	C₄×C₈×C₁₁	D₄	1	4	yes	—
31	C₁₁×#95	—	2	2	no	—
32	#10668	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×Q₈×C₁₁	—	2	2	no	—
34	C₂²×C₄×C₁₁	—	2	2	no	—
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	#41	1	2	yes	—
37	C₁₁×M₁₆	—	4	2	no	—
38	C₂×C₈×C₁₁	—	2	4	no	—
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	—	4	1	no	—
41	C₂×C₈×C₁₁	—	4	4	no	—
42	C₁₁×C₄⋊C₄	—	2	2	no	—
43	C₁₁×C₄⋊C₄	—	2	2	no	—
44	C₁₁×C₄⋊C₄	—	4	2	no	—
45	C₁₁×C₂²⋊C₄	—	4	1	no	—
46	C₄²×C₁₁	—	2	2	no	—
47	C₄²×C₁₁	—	4	1	no	—
48	C₄²×C₁₁	Q₁₆	1	4	yes	—
49	C₄²×C₁₁	C₂×D₄	1	2	yes	—
50	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₁	#41	1	1	yes	characteristic
52	#1995	C₂×C₁₁	1	1	yes	characteristic
53	#1843	C₂×C₁₁	1	1	yes	characteristic
54	#1571	C₂×C₁₁	1	2	yes	—
55	#1481	C₂×C₁₁	1	2	yes	—
56	#1274	C₂×C₁₁	1	1	yes	characteristic
57	C₂³×C₁₁	#123	1	1	yes	characteristic
58	Q₈×C₁₁	—	4	4	no	—
59	C₂×C₄×C₁₁	—	2	4	no	—
60	C₂×C₄×C₁₁	—	4	2	no	—
61	C₂×C₄×C₁₁	—	4	4	no	—
62	C₂×C₄×C₁₁	—	4	2	no	—
63	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
64	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#123	1	2	yes	—
66	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
68	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
69	C₈×C₁₁	—	4	4	no	—
70	C₈×C₁₁	—	8	2	no	—
71	C₈×C₁₁	—	8	1	no	—
72	#533	C₂²×C₁₁	1	1	yes	characteristic
73	#431	C₂²×C₁₁	1	2	yes	—
74	#423	C₂²×C₁₁	1	1	yes	characteristic
75	C₂×C₄⋊C₈	—	2	2	no	—
76	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
77	#376	C₂²×C₁₁	1	1	yes	characteristic
78	#339	—	2	2	no	—
79	#335	—	2	4	no	—
80	Q₈⋊C₈	—	2	4	no	—
81	C₂²×C₁₁	—	2	2	no	—
82	C₂²×C₁₁	#399	1	1	yes	characteristic
83	C₂²×C₁₁	#484	1	2	yes	—
84	C₄×C₁₁	—	2	2	no	—
85	C₄×C₁₁	—	2	2	no	—
86	C₄×C₁₁	—	4	4	no	—
87	C₄×C₁₁	—	8	2	no	—
88	C₄×C₁₁	#477	1	2	yes	—
89	C₄×C₁₁	#494	1	1	yes	characteristic
90	C₄×C₁₁	#496	1	1	yes	characteristic
91	C₂×M₁₆	—	2	1	no	—
92	C₂²×C₈	—	2	2	no	—
93	C₄⋊Q₈	Q₈×C₁₁	1	2	yes	—
94	#125	—	2	1	no	—
95	C₂²⋊Q₈	—	2	2	no	—
96	C₄×Q₈	—	2	2	no	—
97	#117	—	2	1	no	—
98	C₂×C₄²	D₄×C₁₁	1	2	yes	—
99	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	2	2	no	—
102	C₄⋊C₈	—	2	2	no	—
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	4	4	no	—
105	C₂²⋊C₈	—	2	2	no	—
106	C₄×C₈	D₄×C₁₁	1	4	yes	—
107	#95	—	2	2	no	—
108	C₂×C₁₁	—	2	2	no	—
109	C₂×C₁₁	#2095	1	1	yes	characteristic
110	C₂×C₁₁	#2098	1	2	yes	—
111	C₂×Q₈	—	2	2	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
114	C₂²×C₄	C₁₁×#41	1	2	yes	—
115	M₁₆	—	4	2	no	—
116	C₂×C₈	—	2	4	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	4	1	no	—
119	C₂×C₈	—	4	4	no	—
120	C₄⋊C₄	—	2	2	no	—
121	C₄⋊C₄	—	2	2	no	—
122	C₄⋊C₄	—	4	2	no	—
123	C₂²⋊C₄	—	4	1	no	—
124	C₄²	—	2	2	no	—
125	C₄²	—	4	1	no	—
126	C₄²	C₁₁×Q₁₆	1	4	yes	—
127	C₄²	C₂×D₄×C₁₁	1	2	yes	—
128	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
129	C₄²	C₁₁×#41	1	1	yes	characteristic
130	C₁₁	#10668	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³	C₁₁×#123	1	1	yes	characteristic
132	Q₈	—	4	4	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	2	no	—
137	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
138	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄	C₁₁×#123	1	2	yes	—
140	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
141	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
142	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
143	C₈	—	4	4	no	—
144	C₈	—	8	2	no	—
145	C₈	—	8	1	no	—
146	C₂²	—	2	2	no	—
147	C₂²	C₁₁×#399	1	1	yes	characteristic
148	C₂²	C₁₁×#484	1	2	yes	—
149	C₄	—	2	2	no	—
150	C₄	—	2	2	no	—
151	C₄	—	4	4	no	—
152	C₄	—	8	2	no	—
153	C₄	C₁₁×#477	1	2	yes	—
154	C₄	C₁₁×#494	1	1	yes	characteristic
155	C₄	C₁₁×#496	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	C₁₁×#2095	1	1	yes	characteristic
158	C₂	C₁₁×#2098	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#1995

C₂

yes

maximal, characteristic

C₁₁×#1843

C₂

yes

maximal, characteristic

C₁₁×#1571

C₂

yes

maximal

C₁₁×#1481

C₂

yes

maximal

C₁₁×#1274

C₂

yes

maximal, characteristic

C₁₁×#533

C₂²

yes

characteristic

C₁₁×#431

C₂²

yes

—

C₁₁×#423

C₂²

yes

characteristic

C₂×C₁₁×C₄⋊C₈

—

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₁₁×#376

C₂²

yes

characteristic

C₁₁×#339

—

C₁₁×#335

—

C₁₁×Q₈⋊C₈

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

—

C₁₁×C₄⋊Q₈

Q₈

yes

—

C₁₁×#125

—

C₁₁×C₂²⋊Q₈

—

C₄×Q₈×C₁₁

—

C₁₁×#117

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

D₄

yes

—

C₁₁×#95

—

#10668

C₁₁

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

C₄²×C₁₁

yes

C₂×C₁₁

yes

characteristic

#1843

C₂×C₁₁

yes

characteristic

#1571

C₂×C₁₁

yes

—

#1481

C₂×C₁₁

yes

—

#1274

C₂×C₁₁

yes

characteristic

C₂³×C₁₁

#123

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

#533

C₂²×C₁₁

yes

characteristic

#431

C₂²×C₁₁

yes

—

#423

C₂²×C₁₁

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂²×C₁₁

yes

—

#376

C₂²×C₁₁

yes

characteristic

#339

—

#335

—

Q₈⋊C₈

—

C₂²×C₁₁

—

C₂²×C₁₁

#399

yes

characteristic

C₂²×C₁₁

#484

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#477

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

Q₈×C₁₁

yes

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

D₄×C₁₁

yes

—

C₂×C₄²

C₂³×C₁₁

yes

characteristic

100

C₄⋊C₈

—

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₂²⋊C₈

—

106

C₄×C₈

D₄×C₁₁

yes

—

107

#95

—

108

C₂×C₁₁

—

109

C₂×C₁₁

#2095

yes

characteristic

110

C₂×C₁₁

#2098

yes

—

111

C₂×Q₈

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×D₄×C₁₁

yes

characteristic

114

C₂²×C₄

C₁₁×#41

yes

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₄²

C₁₁×Q₁₆

yes

—

127

C₄²

C₂×D₄×C₁₁

yes

—

128

C₄²

C₂×Q₈×C₁₁

yes

characteristic

129

C₄²

C₁₁×#41

yes

characteristic

130

C₁₁

#10668

yes

characteristic, direct product factor, Sylow

131

C₂³

C₁₁×#123

yes

characteristic

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₁₁×C₂²⋊Q₈

yes

—

138

C₂×C₄

C₁₁×C₂²⋊Q₈

yes

characteristic

139

C₂×C₄

C₁₁×#123

yes

—

140

C₂×C₄

C₁₁×#127

yes

characteristic

141

C₂×C₄

C₂×C₁₁×Q₁₆

yes

—

142

C₂×C₄

C₁₁×AGL(1,ℤ/8)

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₂²

—

147

C₂²

C₁₁×#399

yes

characteristic

148

C₂²

C₁₁×#484

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

C₁₁×#477

yes

—

154

C₄

C₁₁×#494

yes

characteristic

155

C₄

C₁₁×#496

yes

characteristic

156

C₂

—

157

C₂

C₁₁×#2095

yes

characteristic

158

C₂

C₁₁×#2098

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#399
prime radical	C₂³×C₁₁	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₁

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₁

C₂²×C₁₁

C₂³×C₁₁

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

N	H ≅ G/N	type
32. #10668	C₁₁	direct (N × H)
130. C₁₁	#10668	direct (N × H)

H ≅ G/N

type

32. #10668

C₁₁

direct (N × H)

130. C₁₁

#10668

direct (N × H)

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

subgroup	index
C₁₁×#1995	2
C₁₁×#1843	2
C₁₁×#1571	2
C₁₁×#1481	2
C₁₁×#1274	2
#10668	11

subgroup

index

C₁₁×#1995

C₁₁×#1843

C₁₁×#1571

C₁₁×#1481

C₁₁×#1274

#10668

Subgroups — C₁₁×#10668 #14587861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#10668 #14587861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#10668 #14587861