Group #13064933 — subgroups

Subgroups — C₁₁×#2095 #13064933

Order 1408.

254 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 108 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×C₁₁×#107	C₂	1	2	yes	maximal
2	C₂×C₁₁×#103	C₂	1	2	yes	maximal
3	C₁₁×#391	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#384	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
9	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#107	—	2	4	no	—
13	C₁₁×#103	—	2	4	no	—
14	C₁₁×#95	—	2	2	no	—
15	C₂×Q₈×C₁₁	—	2	1	no	—
16	C₂×Q₈×C₁₁	—	2	2	no	—
17	C₂×Q₈×C₁₁	—	2	2	no	—
18	C₂×Q₈×C₁₁	Q₈	1	2	yes	—
19	C₂²×C₄×C₁₁	—	2	1	no	—
20	C₂²×C₄×C₁₁	—	2	1	no	—
21	C₂²×C₄×C₁₁	—	2	2	no	—
22	C₂²×C₄×C₁₁	D₄	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₁	—	2	2	no	—
25	C₂×C₈×C₁₁	—	2	2	no	—
26	C₂×C₈×C₁₁	D₄	1	4	yes	—
27	C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₁₁×C₄⋊C₄	—	2	2	no	—
30	C₁₁×C₄⋊C₄	—	4	4	no	—
31	C₄²×C₁₁	—	2	2	no	—
32	#2095	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
34	Q₈×C₁₁	—	2	4	no	—
35	Q₈×C₁₁	—	4	2	no	—
36	C₂×C₄×C₁₁	—	2	2	no	—
37	C₂×C₄×C₁₁	—	2	2	no	—
38	C₂×C₄×C₁₁	—	2	2	no	—
39	C₂×C₄×C₁₁	—	4	1	no	—
40	C₂×C₄×C₁₁	—	4	1	no	—
41	C₂×C₄×C₁₁	—	4	2	no	—
42	C₂×C₄×C₁₁	—	4	1	no	—
43	C₂×C₄×C₁₁	—	4	4	no	—
44	C₂×C₄×C₁₁	—	4	2	no	—
45	C₂×C₄×C₁₁	Q₁₆	1	4	yes	—
46	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₁	#41	1	2	yes	—
49	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
50	C₈×C₁₁	—	2	4	no	—
51	C₂×#107	C₂×C₁₁	1	2	yes	—
52	C₂×#103	C₂×C₁₁	1	2	yes	—
53	#391	C₂×C₁₁	1	1	yes	characteristic
54	#384	C₂×C₁₁	1	1	yes	characteristic
55	#336	C₂×C₁₁	1	1	yes	characteristic
56	C₂²×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₁	#123	1	1	yes	characteristic
58	C₂²×C₁₁	#127	1	1	yes	characteristic
59	C₂²×C₁₁	C₂×Q₁₆	1	2	yes	—
60	C₂²×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
61	C₄×C₁₁	—	2	4	no	—
62	C₄×C₁₁	—	4	2	no	—
63	C₄×C₁₁	—	8	2	no	—
64	C₄×C₁₁	—	8	1	no	—
65	C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
66	C₄×C₁₁	#123	1	2	yes	—
67	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
68	C₂²×C₈	C₂²×C₁₁	1	2	yes	—
69	C₂×C₄⋊C₄	—	2	2	no	—
70	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
71	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
72	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
73	#107	—	2	4	no	—
74	#103	—	2	4	no	—
75	#95	—	2	2	no	—
76	C₂×C₁₁	#399	1	1	yes	characteristic
77	C₂×C₁₁	#477	1	2	yes	—
78	C₂×C₁₁	#484	1	2	yes	—
79	C₂×C₁₁	#494	1	1	yes	characteristic
80	C₂×C₁₁	#496	1	1	yes	characteristic
81	C₂×Q₈	—	2	1	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	Q₈×C₁₁	1	2	yes	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	D₄×C₁₁	1	2	yes	—
89	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	D₄×C₁₁	1	4	yes	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	4	4	no	—
97	C₄²	—	2	2	no	—
98	C₁₁	#2095	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	—	4	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	C₁₁×Q₁₆	1	4	yes	—
112	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
113	C₂×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
114	C₂×C₄	C₁₁×#41	1	2	yes	—
115	C₂×C₄	C₁₁×#41	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₂²	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
118	C₂²	C₁₁×#123	1	1	yes	characteristic
119	C₂²	C₁₁×#127	1	1	yes	characteristic
120	C₂²	C₂×C₁₁×Q₁₆	1	2	yes	—
121	C₂²	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	2	no	—
125	C₄	—	8	1	no	—
126	C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
127	C₄	C₁₁×#123	1	2	yes	—
128	C₂	C₁₁×#399	1	1	yes	characteristic
129	C₂	C₁₁×#477	1	2	yes	—
130	C₂	C₁₁×#484	1	2	yes	—
131	C₂	C₁₁×#494	1	1	yes	characteristic
132	C₂	C₁₁×#496	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₁×#107

C₂

yes

maximal

C₂×C₁₁×#103

C₂

yes

maximal

C₁₁×#391

C₂

yes

maximal, characteristic

C₁₁×#384

C₂

yes

maximal, characteristic

C₁₁×#336

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₁

C₂²

yes

characteristic

C₂²×C₈×C₁₁

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₁₁×#107

—

C₁₁×#103

—

C₁₁×#95

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

Q₈

yes

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

D₄

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

—

#2095

C₁₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₁

C₂×D₄

yes

characteristic

Q₈×C₁₁

—

Q₈×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×C₄×C₁₁

Q₁₆

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

characteristic

C₈×C₁₁

—

C₂×#107

C₂×C₁₁

yes

—

C₂×#103

C₂×C₁₁

yes

—

#391

C₂×C₁₁

yes

characteristic

#384

C₂×C₁₁

yes

characteristic

#336

C₂×C₁₁

yes

characteristic

C₂²×C₁₁

C₂²⋊Q₈

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

C₂×Q₁₆

yes

—

C₂²×C₁₁

AGL(1,ℤ/8)

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₂²⋊Q₈

yes

—

C₄×C₁₁

#123

yes

—

C₂²×Q₈

C₂²×C₁₁

yes

characteristic

C₂²×C₈

C₂²×C₁₁

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²×C₁₁

yes

—

C₂×C₄⋊C₄

C₂²×C₁₁

yes

characteristic

C₂×C₄²

C₂²×C₁₁

yes

—

—

—

C₂×C₁₁

#399

yes

characteristic

C₂×C₁₁

#477

yes

—

C₂×C₁₁

#484

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Q₈×C₁₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₁₁

yes

—

C₂²×C₄

C₂³×C₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₁

#2095

yes

characteristic, direct product factor, Sylow

C₂³

C₂×D₄×C₁₁

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₁₁×Q₁₆

yes

—

112

C₂×C₄

C₂×D₄×C₁₁

yes

—

113

C₂×C₄

C₂×Q₈×C₁₁

yes

characteristic

114

C₂×C₄

C₁₁×#41

yes

—

115

C₂×C₄

C₁₁×#41

yes

characteristic

116

C₈

—

117

C₂²

C₁₁×C₂²⋊Q₈

yes

characteristic

118

C₂²

C₁₁×#123

yes

characteristic

119

C₂²

C₁₁×#127

yes

characteristic

120

C₂²

C₂×C₁₁×Q₁₆

yes

—

121

C₂²

C₁₁×AGL(1,ℤ/8)

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

C₁₁×C₂²⋊Q₈

yes

—

127

C₄

C₁₁×#123

yes

—

128

C₂

C₁₁×#399

yes

characteristic

129

C₂

C₁₁×#477

yes

—

130

C₂

C₁₁×#484

yes

—

131

C₂

C₁₁×#494

yes

characteristic

132

C₂

C₁₁×#496

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₁

C₂×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₁

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

N	H ≅ G/N	type
32. #2095	C₁₁	direct (N × H)
98. C₁₁	#2095	direct (N × H)

H ≅ G/N

type

32. #2095

C₁₁

direct (N × H)

98. C₁₁

#2095

direct (N × H)

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

subgroup	index
C₂×C₁₁×#107	2
C₂×C₁₁×#103	2
C₁₁×#391	2
C₁₁×#384	2
C₁₁×#336	2
#2095	11

subgroup

index

C₂×C₁₁×#107

C₂×C₁₁×#103

C₁₁×#391

C₁₁×#384

C₁₁×#336

#2095

Subgroups — C₁₁×#2095 #13064933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C11×#2095 #13064933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2095 #13064933