Group #13068360 — subgroups

Subgroups — #13068360

Order 1408.

296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₈×Dic₁₁	C₂	1	2	yes	maximal
2	C₄²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#336	C₂	1	1	yes	maximal, characteristic
4	#10622188	C₂	1	2	yes	maximal
5	#10622162	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₁	C₄	1	2	yes	—
9	C₂×C₄×Dic₁₁	C₄	1	2	yes	—
10	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁⋊C₈	C₂²	1	2	yes	—
13	C₈×Dic₁₁	C₄	1	8	yes	complemented
14	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₁	C₂×C₄	1	2	yes	—
17	C₂²×Dic₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	—	2	2	no	—
20	C₂×C₈×C₁₁	—	2	2	no	—
21	C₂×C₈×C₁₁	C₂×C₄	1	4	yes	—
22	C₄²×C₁₁	—	2	2	no	—
23	C₄×Dic₁₁	—	2	4	no	—
24	C₄×Dic₁₁	—	2	1	no	—
25	C₄×Dic₁₁	—	2	1	no	—
26	C₄×Dic₁₁	C₈	1	8	yes	complemented
27	C₄×Dic₁₁	C₂×C₄	1	4	yes	—
28	C₂×C₁₁⋊C₈	—	2	2	no	—
29	C₂×C₁₁⋊C₈	—	2	2	no	—
30	C₂×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
31	#1744	—	11	1	no	maximal, Sylow
32	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₁	—	2	2	no	—
34	C₂×C₄×C₁₁	—	2	2	no	—
35	C₂×C₄×C₁₁	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₁₁	#41	1	2	yes	—
38	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
39	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
40	C₂×Dic₁₁	—	2	2	no	—
41	C₂×Dic₁₁	—	2	2	no	—
42	C₂×Dic₁₁	C₄²	1	2	yes	—
43	C₂×Dic₁₁	C₄²	1	2	yes	—
44	C₂×Dic₁₁	C₂×C₈	1	4	yes	—
45	C₂×Dic₁₁	C₂×C₈	1	4	yes	—
46	C₂×Dic₁₁	M₁₆	1	4	yes	—
47	C₈×C₁₁	—	2	4	no	—
48	C₁₁⋊C₈	—	2	4	no	—
49	C₂×C₄×C₈	—	11	2	no	—
50	C₄³	—	11	1	no	—
51	#336	—	11	2	no	—
52	#336	—	11	1	no	—
53	#336	D₁₁	1	1	yes	characteristic
54	C₂²×C₁₁	C₂×C₄²	1	1	yes	characteristic
55	C₂²×C₁₁	#117	1	1	yes	characteristic
56	C₂²×C₁₁	#117	1	1	yes	characteristic
57	C₂²×C₁₁	C₂²×C₈	1	2	yes	—
58	C₂²×C₁₁	C₂×M₁₆	1	2	yes	—
59	C₄×C₁₁	—	2	4	no	—
60	C₄×C₁₁	#117	1	2	yes	—
61	C₄×C₁₁	#117	1	2	yes	—
62	Dic₁₁	—	2	4	no	—
63	Dic₁₁	C₄×C₈	1	4	yes	—
64	Dic₁₁	#97	1	4	yes	—
65	C₂²×C₈	—	11	2	no	—
66	C₂²×C₈	C₂×D₁₁	1	2	yes	—
67	C₂×C₄²	—	11	1	no	—
68	C₂×C₄²	—	11	2	no	—
69	C₂×C₄²	—	11	1	no	—
70	C₂×C₄²	—	11	2	no	—
71	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
72	C₄×C₈	—	11	8	no	—
73	C₂×C₁₁	#376	1	1	yes	characteristic
74	C₂×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
75	C₂×C₁₁	C₂×#97	1	1	yes	characteristic
76	C₂×C₁₁	#431	1	2	yes	—
77	C₂×C₁₁	#431	1	2	yes	—
78	C₂²×C₄	—	11	1	no	—
79	C₂²×C₄	—	11	1	no	—
80	C₂²×C₄	—	11	2	no	—
81	C₂²×C₄	C₄×D₁₁	1	2	yes	—
82	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	11	4	no	—
86	C₂×C₈	—	22	2	no	—
87	C₂×C₈	—	22	2	no	—
88	C₂×C₈	C₄×D₁₁	1	4	yes	—
89	C₄²	—	2	2	no	—
90	C₄²	—	11	8	no	—
91	C₄²	—	11	4	no	—
92	C₄²	—	22	4	no	—
93	C₄²	—	22	1	no	—
94	C₄²	—	22	1	no	—
95	C₁₁	#1744	1	1	yes	characteristic, complemented, Sylow
96	C₂³	C₂×C₄×D₁₁	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	11	2	no	—
100	C₂×C₄	—	11	2	no	—
101	C₂×C₄	—	11	4	no	—
102	C₂×C₄	—	11	4	no	—
103	C₂×C₄	—	11	4	no	—
104	C₂×C₄	—	22	2	no	—
105	C₂×C₄	—	22	2	no	—
106	C₂×C₄	C₈×D₁₁	1	4	yes	—
107	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
108	C₂×C₄	#4341	1	1	yes	characteristic
109	C₂×C₄	#4341	1	2	yes	—
110	C₂×C₄	#4343	1	1	yes	characteristic
111	C₈	—	2	4	no	—
112	C₈	—	22	4	no	—
113	C₂²	C₄²×D₁₁	1	1	yes	characteristic
114	C₂²	#66930	1	1	yes	characteristic
115	C₂²	#66945	1	1	yes	characteristic
116	C₂²	C₂×C₈×D₁₁	1	2	yes	—
117	C₂²	M₁₆×D₁₁	1	2	yes	—
118	C₄	—	2	4	no	—
119	C₄	—	11	4	no	—
120	C₄	—	11	4	no	—
121	C₄	—	22	4	no	—
122	C₄	#66930	1	2	yes	—
123	C₄	#66945	1	2	yes	—
124	C₂	#10622261	1	1	yes	characteristic
125	C₂	C₄×C₈×D₁₁	1	1	yes	characteristic
126	C₂	D₁₁×#97	1	1	yes	characteristic
127	C₂	#10622331	1	2	yes	—
128	C₂	#10622446	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₁₁

C₂

yes

maximal

C₄²×Dic₁₁

C₂

yes

maximal, characteristic

C₁₁×#336

C₂

yes

maximal, characteristic

#10622188

C₂

yes

maximal

#10622162

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₁

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₁

C₄

yes

—

C₂×C₄×Dic₁₁

C₄

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂²×C₁₁⋊C₈

C₂²

yes

—

C₈×Dic₁₁

C₄

yes

complemented

C₂²×C₄×C₁₁

C₂×C₄

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂×C₄

yes

—

C₂²×Dic₁₁

C₂×C₄

yes

characteristic

C₂²×Dic₁₁

C₂×C₄

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×C₄

yes

—

C₄²×C₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

C₈

yes

complemented

C₄×Dic₁₁

C₂×C₄

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₂×C₄

yes

—

#1744

—

maximal, Sylow

C₂³×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₈

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

C₄²

yes

—

C₂×Dic₁₁

C₄²

yes

—

C₂×Dic₁₁

C₂×C₈

yes

—

C₂×Dic₁₁

C₂×C₈

yes

—

C₂×Dic₁₁

M₁₆

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

—

#336

D₁₁

yes

characteristic

C₂²×C₁₁

C₂×C₄²

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

C₂²×C₈

yes

—

C₂²×C₁₁

C₂×M₁₆

yes

—

C₄×C₁₁

—

C₄×C₁₁

#117

yes

—

C₄×C₁₁

#117

yes

—

Dic₁₁

—

Dic₁₁

C₄×C₈

yes

—

Dic₁₁

#97

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₄×C₈

—

C₂×C₁₁

#376

yes

characteristic

C₂×C₁₁

C₂×C₄×C₈

yes

characteristic

C₂×C₁₁

C₂×#97

yes

characteristic

C₂×C₁₁

#431

yes

—

C₂×C₁₁

#431

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₁

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₁

#1744

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₁₁

yes

—

107

C₂×C₄

C₂×C₄×D₁₁

yes

—

108

C₂×C₄

#4341

yes

characteristic

109

C₂×C₄

#4341

yes

—

110

C₂×C₄

#4343

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

C₄²×D₁₁

yes

characteristic

114

C₂²

#66930

yes

characteristic

115

C₂²

#66945

yes

characteristic

116

C₂²

C₂×C₈×D₁₁

yes

—

117

C₂²

M₁₆×D₁₁

yes

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#66930

yes

—

123

C₄

#66945

yes

—

124

C₂

#10622261

yes

characteristic

125

C₂

C₄×C₈×D₁₁

yes

characteristic

126

C₂

D₁₁×#97

yes

characteristic

127

C₂

#10622331

yes

—

128

C₂

#10622446

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₁
commutator	C₂×C₁₁	C₂×C₄×C₈
Fitting	C₁₁×#336	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	#336	D₁₁
hypocenter	C₁₁	#1744
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₁

commutator

C₂×C₁₁

C₂×C₄×C₈

Fitting

C₁₁×#336

C₂

socle, prime radical

C₂³×C₁₁

C₂²×C₄

cosocle

C₂²×C₄×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₁₁ ▷ C₁₁

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
13. C₈×Dic₁₁	C₄	semidirect
26. C₄×Dic₁₁	C₈	semidirect
95. C₁₁	#1744	semidirect

H ≅ G/N

type

13. C₈×Dic₁₁

C₄

semidirect

26. C₄×Dic₁₁

C₈

semidirect

95. C₁₁

#1744

semidirect

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

subgroup	index
C₂×C₈×Dic₁₁	2
C₄²×Dic₁₁	2
C₁₁×#336	2
#10622188	2
#10622162	2
#1744	11

subgroup

index

C₂×C₈×Dic₁₁

C₄²×Dic₁₁

C₁₁×#336

#10622188

#10622162

#1744

Subgroups — #13068360

Conjugacy classes of subgroups

Complements

Maximal subgroups