Group #13076684 — subgroups

Subgroups — #13076684

Order 1408.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66923	C₂	1	2	yes	maximal
2	C₁₁×#382	C₂	1	1	yes	maximal, characteristic
3	#10622596	C₂	1	4	yes	maximal
4	#10622274	C₂	1	4	yes	maximal
5	#10622272	C₂	1	4	yes	maximal
6	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
11	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
13	#66923	—	2	8	no	—
14	C₁₁×#95	C₂²	1	4	yes	—
15	C₁₁⋊#95	C₂²	1	4	yes	—
16	C₁₁⋊#95	C₂²	1	8	yes	—
17	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
19	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₁	C₂³	1	4	yes	—
21	C₂²×Dic₁₁	C₂³	1	4	yes	—
22	C₁₁×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₁₁	D₄	1	4	yes	—
24	C₄⋊Dic₁₁	—	2	4	no	—
25	C₄⋊Dic₁₁	—	2	4	no	—
26	C₄⋊Dic₁₁	—	4	4	no	—
27	Dic₁₁⋊C₄	—	2	8	no	—
28	Dic₁₁⋊C₄	—	2	8	no	—
29	#2822	—	11	1	no	maximal, Sylow
30	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₁₁	—	2	1	no	—
32	C₂×C₄×C₁₁	—	2	1	no	—
33	C₂×C₄×C₁₁	—	2	4	no	—
34	C₂×C₄×C₁₁	—	2	4	no	—
35	C₂×C₄×C₁₁	—	2	8	no	—
36	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
38	C₂×Dic₁₁	—	2	4	no	—
39	C₂×Dic₁₁	—	2	4	no	—
40	C₂×Dic₁₁	—	2	4	no	—
41	C₂×Dic₁₁	—	2	4	no	—
42	C₂×Dic₁₁	—	2	8	no	—
43	C₂×#125	—	11	2	no	—
44	#400	—	11	4	no	—
45	#398	—	11	4	no	—
46	#398	—	11	4	no	—
47	#382	D₁₁	1	1	yes	characteristic
48	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
49	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
50	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
51	C₂²×C₁₁	2₋¹⁺⁴	1	4	yes	—
52	C₄×C₁₁	—	2	4	no	—
53	C₄×C₁₁	—	2	2	no	—
54	C₄×C₁₁	—	4	4	no	—
55	Dic₁₁	—	4	4	no	—
56	Dic₁₁	—	4	4	no	—
57	#125	—	22	8	no	—
58	C₂×C₄⋊C₄	—	11	4	no	—
59	C₂×C₄⋊C₄	—	11	2	no	—
60	C₂×C₄⋊C₄	—	11	4	no	—
61	C₂×C₄⋊C₄	—	11	2	no	—
62	C₂×C₄⋊C₄	—	11	4	no	—
63	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
64	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
65	#95	—	11	8	no	—
66	#95	—	11	4	no	—
67	#95	C₂×D₁₁	1	4	yes	—
68	C₂×C₁₁	#536	1	2	yes	—
69	C₂×C₁₁	#537	1	1	yes	characteristic
70	C₂×C₁₁	#563	1	2	yes	—
71	C₂×C₁₁	#564	1	2	yes	—
72	C₂²×C₄	—	11	4	no	—
73	C₂²×C₄	—	11	4	no	—
74	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
75	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
76	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
77	C₄⋊C₄	—	4	2	no	—
78	C₄⋊C₄	—	22	8	no	—
79	C₄⋊C₄	—	22	8	no	—
80	C₄⋊C₄	—	22	4	no	—
81	C₄⋊C₄	—	22	4	no	—
82	C₄⋊C₄	—	44	4	no	—
83	C₄²	D₄₄	1	4	yes	—
84	C₁₁	#2822	1	1	yes	characteristic, complemented, Sylow
85	C₂³	C₂³×D₁₁	1	1	yes	characteristic
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	22	4	no	—
92	C₂×C₄	—	22	4	no	—
93	C₂×C₄	—	22	4	no	—
94	C₂×C₄	—	22	4	no	—
95	C₂×C₄	—	22	8	no	—
96	C₂×C₄	C₂×D₄₄	1	2	yes	—
97	C₂×C₄	C₂×D₄₄	1	4	yes	—
98	C₂²	C₂²×D₄₄	1	1	yes	characteristic
99	C₂²	#67037	1	1	yes	characteristic
100	C₂²	#67040	1	1	yes	characteristic
101	C₂²	#67043	1	4	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	4	no	—
104	C₄	—	4	4	no	—
105	C₄	—	44	4	no	—
106	C₄	—	44	4	no	—
107	C₂	#10623041	1	1	yes	characteristic
108	C₂	#10623057	1	2	yes	—
109	C₂	#10623203	1	2	yes	—
110	C₂	C₁₁⋊#564	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#66923

C₂

yes

maximal

C₁₁×#382

C₂

yes

maximal, characteristic

#10622596

C₂

yes

maximal

#10622274

C₂

yes

maximal

#10622272

C₂

yes

maximal

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

#66923

—

C₁₁×#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

Dic₁₁⋊C₄

—

#2822

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

—

—

—

—

D₁₁

yes

characteristic

C₂²×C₁₁

C₂²×D₄

yes

characteristic

C₂²×C₁₁

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₁

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₁

2₋¹⁺⁴

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

Dic₁₁

—

Dic₁₁

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄²

C₂×D₁₁

yes

—

—

C₂×D₁₁

yes

—

C₂×C₁₁

#536

yes

—

C₂×C₁₁

#537

yes

characteristic

C₂×C₁₁

#563

yes

—

C₂×C₁₁

#564

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄₄

yes

—

C₁₁

#2822

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄₄

yes

—

C₂×C₄

C₂×D₄₄

yes

—

C₂²

C₂²×D₄₄

yes

characteristic

C₂²

#67037

yes

characteristic

100

C₂²

#67040

yes

characteristic

101

C₂²

#67043

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₂

#10623041

yes

characteristic

108

C₂

#10623057

yes

—

109

C₂

#10623203

yes

—

110

C₂

C₁₁⋊#564

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#382	C₂
hypercenter	#382	D₁₁
hypocenter	C₁₁	#2822
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#382

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
84. C₁₁	#2822	semidirect

H ≅ G/N

type

84. C₁₁

#2822

semidirect

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

subgroup	index
C₂×#66923	2
C₁₁×#382	2
#10622596	2
#10622274	2
#10622272	2
#2822	11

subgroup

index

C₁₁×#382

Subgroups — #13076684

Conjugacy classes of subgroups

Complements

Maximal subgroups