Group #13073645 — subgroups

Subgroups — #13073645

Order 1408.

556 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 197 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×#66941	C₂	1	4	yes	maximal
2	C₁₁×#384	C₂	1	1	yes	maximal, characteristic
3	#10622592	C₂	1	4	yes	maximal
4	#10622586	C₂	1	4	yes	maximal
5	C₄×C₄⋊Dic₁₁	C₂	1	2	yes	maximal
6	C₂²×Dic₂₂	C₂²	1	4	yes	—
7	C₂×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
12	C₂×Dic₁₁⋊C₄	C₂²	1	8	yes	—
13	C₂×C₄×Dic₁₁	C₂²	1	4	yes	—
14	#66941	—	2	16	no	—
15	C₁₁⋊#95	C₂²	1	4	yes	—
16	C₁₁⋊#95	C₂²	1	4	yes	—
17	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
20	C₂²×Dic₁₁	C₂³	1	4	yes	—
21	C₂²×Dic₁₁	C₂³	1	4	yes	—
22	C₂×Dic₂₂	—	2	16	no	—
23	C₂×Dic₂₂	—	4	4	no	—
24	C₁₁×C₄⋊C₄	—	2	8	no	—
25	C₁₁×C₄⋊C₄	—	4	2	no	—
26	C₄²×C₁₁	Q₈	1	4	yes	complemented
27	C₄⋊Dic₁₁	D₄	1	8	yes	—
28	C₄⋊Dic₁₁	Q₈	1	8	yes	complemented
29	Dic₁₁⋊C₄	—	2	16	no	—
30	C₄×Dic₁₁	—	2	8	no	—
31	#2551	—	11	1	no	maximal, Sylow
32	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
33	C₂×C₄×C₁₁	—	2	1	no	—
34	C₂×C₄×C₁₁	—	2	1	no	—
35	C₂×C₄×C₁₁	—	2	8	no	—
36	C₂×C₄×C₁₁	—	2	4	no	—
37	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
38	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
39	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
40	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
41	C₂×Dic₁₁	—	2	4	no	—
42	C₂×Dic₁₁	—	2	4	no	—
43	C₂×Dic₁₁	—	2	4	no	—
44	C₂×Dic₁₁	—	2	4	no	—
45	C₂×Dic₁₁	C₂×D₄	1	8	yes	—
46	C₂×Dic₁₁	C₂×Q₈	1	8	yes	—
47	Dic₂₂	—	4	16	no	—
48	C₂×C₄⋊Q₈	—	11	4	no	—
49	#395	—	11	4	no	—
50	#389	—	11	4	no	—
51	#384	D₁₁	1	1	yes	characteristic
52	C₄×C₄⋊C₄	—	11	2	no	—
53	C₂²×C₁₁	C₂²×D₄	1	2	yes	—
54	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
55	C₂²×C₁₁	C₂²×Q₈	1	2	yes	—
56	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
57	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
58	C₄×C₁₁	—	2	2	no	—
59	C₄×C₁₁	—	4	4	no	—
60	C₄×C₁₁	C₄⋊Q₈	1	8	yes	complemented
61	Dic₁₁	—	2	8	no	—
62	Dic₁₁	—	2	8	no	—
63	C₂²×Q₈	—	11	4	no	—
64	C₄⋊Q₈	—	22	16	no	—
65	C₂×C₄⋊C₄	—	11	2	no	—
66	C₂×C₄⋊C₄	—	11	2	no	—
67	C₂×C₄⋊C₄	—	11	8	no	—
68	C₂×C₄⋊C₄	C₂×D₁₁	1	4	yes	—
69	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
70	C₂×C₄²	—	11	4	no	—
71	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
72	#95	—	11	4	no	—
73	#95	—	11	4	no	—
74	C₂×C₁₁	C₂×C₄⋊Q₈	1	2	yes	—
75	C₂×C₁₁	#544	1	1	yes	characteristic
76	C₂×C₁₁	D₄²	1	1	yes	characteristic
77	C₂×C₁₁	D₄×Q₈	1	2	yes	—
78	C₂×C₁₁	Q₈²	1	1	yes	characteristic
79	C₂×Q₈	—	22	16	no	—
80	C₂×Q₈	—	44	4	no	—
81	C₂²×C₄	—	11	4	no	—
82	C₂²×C₄	—	11	4	no	—
83	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
84	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
85	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
86	C₄⋊C₄	—	2	8	no	—
87	C₄⋊C₄	—	4	2	no	—
88	C₄⋊C₄	—	11	8	no	—
89	C₄⋊C₄	—	11	8	no	—
90	C₄⋊C₄	—	22	16	no	—
91	C₄²	—	22	8	no	—
92	C₄²	Dic₂₂	1	4	yes	complemented
93	C₁₁	#2551	1	1	yes	characteristic, complemented, Sylow
94	C₂³	C₂³×D₁₁	1	1	yes	characteristic
95	Q₈	—	44	16	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	2	8	no	—
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	11	8	no	—
101	C₂×C₄	—	11	8	no	—
102	C₂×C₄	—	22	4	no	—
103	C₂×C₄	—	22	4	no	—
104	C₂×C₄	—	22	4	no	—
105	C₂×C₄	—	22	4	no	—
106	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
107	C₂×C₄	C₂×Dic₂₂	1	4	yes	—
108	C₂×C₄	D₄×D₁₁	1	4	yes	—
109	C₂×C₄	Q₈×D₁₁	1	4	yes	—
110	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
111	C₂²	C₂×D₄×D₁₁	1	2	yes	—
112	C₂²	#67037	1	1	yes	characteristic
113	C₂²	C₂×Q₈×D₁₁	1	2	yes	—
114	C₂²	#67040	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	4	4	no	—
117	C₄	—	22	8	no	—
118	C₄	—	22	8	no	—
119	C₄	#66941	1	8	yes	complemented
120	C₂	C₂×#66941	1	2	yes	—
121	C₂	#10623031	1	1	yes	characteristic
122	C₂	#10623248	1	1	yes	characteristic
123	C₂	#10623253	1	1	yes	characteristic
124	C₂	#10623258	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#66941

C₂

yes

maximal

C₁₁×#384

C₂

yes

maximal, characteristic

#10622592

C₂

yes

maximal

#10622586

C₂

yes

maximal

C₄×C₄⋊Dic₁₁

C₂

yes

maximal

C₂²×Dic₂₂

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

#66941

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

Q₈

yes

complemented

C₄⋊Dic₁₁

D₄

yes

—

C₄⋊Dic₁₁

Q₈

yes

complemented

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

#2551

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

C₂×D₄

yes

—

C₂×Dic₁₁

C₂×Q₈

yes

—

Dic₂₂

—

C₂×C₄⋊Q₈

—

#395

—

#389

—

#384

D₁₁

yes

characteristic

C₄×C₄⋊C₄

—

C₂²×C₁₁

C₂²×D₄

yes

—

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

C₂²×Q₈

yes

—

C₂²×C₁₁

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₁

2₋¹⁺⁴

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

C₄⋊Q₈

yes

complemented

Dic₁₁

—

Dic₁₁

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

#95

—

#95

—

C₂×C₁₁

C₂×C₄⋊Q₈

yes

—

C₂×C₁₁

#544

yes

characteristic

C₂×C₁₁

D₄²

yes

characteristic

C₂×C₁₁

D₄×Q₈

yes

—

C₂×C₁₁

Q₈²

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂²×C₄

C₂²×D₁₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₂₂

yes

complemented

C₁₁

#2551

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₁

yes

characteristic

Q₈

—

C₂×C₄

—

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

C₂×Dic₂₂

yes

—

107

C₂×C₄

C₂×Dic₂₂

yes

—

108

C₂×C₄

D₄×D₁₁

yes

—

109

C₂×C₄

Q₈×D₁₁

yes

—

110

C₂²

C₂²×Dic₂₂

yes

characteristic

111

C₂²

C₂×D₄×D₁₁

yes

—

112

C₂²

#67037

yes

characteristic

113

C₂²

C₂×Q₈×D₁₁

yes

—

114

C₂²

#67040

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

#66941

yes

complemented

120

C₂

C₂×#66941

yes

—

121

C₂

#10623031

yes

characteristic

122

C₂

#10623248

yes

characteristic

123

C₂

#10623253

yes

characteristic

124

C₂

#10623258

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#384	C₂
hypercenter	#384	D₁₁
hypocenter	C₁₁	#2551
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#384

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
26. C₄²×C₁₁	Q₈	semidirect
28. C₄⋊Dic₁₁	Q₈	semidirect
60. C₄×C₁₁	C₄⋊Q₈	semidirect
92. C₄²	Dic₂₂	semidirect
93. C₁₁	#2551	semidirect
119. C₄	#66941	semidirect

H ≅ G/N

type

26. C₄²×C₁₁

Q₈

semidirect

28. C₄⋊Dic₁₁

Q₈

semidirect

60. C₄×C₁₁

C₄⋊Q₈

semidirect

92. C₄²

Dic₂₂

semidirect

93. C₁₁

#2551

semidirect

119. C₄

#66941

semidirect

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

subgroup	index
C₂×#66941	2
C₁₁×#384	2
#10622592	2
#10622586	2
C₄×C₄⋊Dic₁₁	2
#2551	11

subgroup

index

C₁₁×#384

C₄×C₄⋊Dic₁₁

Subgroups — #13073645

Conjugacy classes of subgroups

Complements

Maximal subgroups