Group #13077718 — subgroups

Subgroups — #13077718

Order 1408.

330 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 205 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×#533	C₂	1	1	yes	maximal, characteristic
2	#10622637	C₂	1	4	yes	maximal, complemented
3	Q₈×C₁₁⋊C₈	C₂	1	4	yes	maximal, complemented
4	#10622613	C₂	1	4	yes	maximal
5	#10622538	C₂	1	2	yes	maximal
6	C₁₁×C₄⋊Q₈	C₄	1	2	yes	—
7	C₁₁×#125	C₄	1	2	yes	—
8	C₁₁×C₂²⋊Q₈	C₄	1	4	yes	—
9	C₄×Q₈×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#117	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
13	C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
14	C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₄⋊(C₁₁⋊C₈)	C₂²	1	8	yes	—
16	#66867	C₂²	1	4	yes	—
17	C₄×C₁₁⋊C₈	C₂²	1	4	yes	—
18	C₄×C₁₁⋊C₈	C₂²	1	4	yes	—
19	C₂×Q₈×C₁₁	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
23	C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
24	C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
26	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₁	C₂³	1	2	yes	—
29	C₄²×C₁₁	C₂³	1	4	yes	—
30	C₂×C₁₁⋊C₈	C₂³	1	4	yes	—
31	C₂×C₁₁⋊C₈	C₂³	1	4	yes	—
32	#2986	—	11	1	no	maximal, Sylow
33	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	Q₈×C₁₁	—	2	8	no	—
35	C₂×C₄×C₁₁	—	2	4	no	—
36	C₂×C₄×C₁₁	—	2	2	no	—
37	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₁₁	C₂²×C₄	1	8	yes	—
40	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
41	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
42	C₁₁⋊C₈	—	2	4	no	—
43	C₁₁⋊C₈	—	2	4	no	—
44	#533	D₁₁	1	1	yes	characteristic
45	#446	—	11	4	no	—
46	C₈×Q₈	—	11	4	no	—
47	#433	—	11	4	no	—
48	#431	—	11	2	no	—
49	C₂²×C₁₁	—	2	1	no	—
50	C₂²×C₁₁	—	2	2	no	—
51	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
52	C₄×C₁₁	—	2	1	no	—
53	C₄×C₁₁	—	2	2	no	—
54	C₄×C₁₁	—	2	8	no	—
55	C₄×C₁₁	#131	1	4	yes	—
56	C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
57	C₄⋊Q₈	Dic₁₁	1	2	yes	—
58	#125	Dic₁₁	1	2	yes	—
59	C₂²⋊Q₈	Dic₁₁	1	4	yes	—
60	C₄×Q₈	C₂×D₁₁	1	4	yes	—
61	#117	C₂×D₁₁	1	2	yes	—
62	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
63	C₄⋊C₈	—	11	2	no	—
64	C₄⋊C₈	—	11	2	no	—
65	C₄⋊C₈	—	11	8	no	—
66	C₂²⋊C₈	—	11	4	no	—
67	#97	—	11	4	no	—
68	C₄×C₈	—	11	4	no	—
69	C₄×C₈	—	11	4	no	—
70	C₂×C₁₁	—	4	1	no	—
71	C₂×C₁₁	#519	1	1	yes	characteristic
72	C₂×C₁₁	C₂×#131	1	2	yes	—
73	C₂×Q₈	C₂×Dic₁₁	1	4	yes	—
74	C₂²×C₄	C₂×Dic₁₁	1	2	yes	—
75	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
76	C₂×C₈	—	11	4	no	—
77	C₂×C₈	—	11	4	no	—
78	C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
79	C₄⋊C₄	C₂×Dic₁₁	1	8	yes	—
80	C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
81	C₂²⋊C₄	C₂×Dic₁₁	1	4	yes	—
82	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
83	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
84	C₄²	C₂²×D₁₁	1	2	yes	—
85	C₄²	C₂²×D₁₁	1	4	yes	—
86	C₁₁	#2986	1	1	yes	characteristic, complemented, Sylow
87	C₂³	C₂²×Dic₁₁	1	1	yes	characteristic
88	Q₈	—	2	8	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₂²×Dic₁₁	1	2	yes	—
92	C₂×C₄	C₂²×Dic₁₁	1	8	yes	—
93	C₂×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₁₁	1	2	yes	—
95	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
96	C₈	—	22	4	no	—
97	C₈	—	22	4	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂³×Dic₁₁	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	2	2	no	—
103	C₄	—	2	8	no	—
104	C₄	#67001	1	4	yes	—
105	C₄	#67040	1	2	yes	—
106	C₂	—	4	1	no	—
107	C₂	#10623343	1	1	yes	characteristic
108	C₂	C₂×#67001	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#533

C₂

yes

maximal, characteristic

#10622637

C₂

yes

maximal, complemented

Q₈×C₁₁⋊C₈

C₂

yes

maximal, complemented

#10622613

C₂

yes

maximal

#10622538

C₂

yes

maximal

C₁₁×C₄⋊Q₈

C₄

yes

—

C₁₁×#125

C₄

yes

—

C₁₁×C₂²⋊Q₈

C₄

yes

—

C₄×Q₈×C₁₁

C₂²

yes

—

C₁₁×#117

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂²⋊(C₁₁⋊C₈)

C₂²

yes

—

C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

#66867

C₂²

yes

—

C₄×C₁₁⋊C₈

C₂²

yes

—

C₄×C₁₁⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₁

C₂×C₄

yes

—

C₂²×C₄×C₁₁

C₂×C₄

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₄⋊C₄

C₂×C₄

yes

—

C₁₁×C₂²⋊C₄

C₂×C₄

yes

—

C₄²×C₁₁

C₂×C₄

yes

characteristic

C₄²×C₁₁

C₂×C₄

yes

characteristic

C₄²×C₁₁

C₂³

yes

—

C₄²×C₁₁

C₂³

yes

—

C₂×C₁₁⋊C₈

C₂³

yes

—

C₂×C₁₁⋊C₈

C₂³

yes

—

#2986

—

maximal, Sylow

C₂³×C₁₁

C₂²×C₄

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂²×C₄

yes

—

C₂×C₄×C₁₁

C₂⁴

yes

characteristic

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#533

D₁₁

yes

characteristic

#446

—

C₈×Q₈

—

#433

—

#431

—

C₂²×C₁₁

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂³×C₄

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#131

yes

—

C₄×C₁₁

2₋¹⁺⁴

yes

—

C₄⋊Q₈

Dic₁₁

yes

—

#125

Dic₁₁

yes

—

C₂²⋊Q₈

Dic₁₁

yes

—

C₄×Q₈

C₂×D₁₁

yes

—

#117

C₂×D₁₁

yes

—

C₂×C₄²

C₂×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₁

—

C₂×C₁₁

#519

yes

characteristic

C₂×C₁₁

C₂×#131

yes

—

C₂×Q₈

C₂×Dic₁₁

yes

—

C₂²×C₄

C₂×Dic₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₄⋊C₄

C₂×Dic₁₁

yes

—

C₂²⋊C₄

C₂×Dic₁₁

yes

—

C₄²

C₂×Dic₁₁

yes

characteristic

C₄²

C₂×Dic₁₁

yes

characteristic

C₄²

C₂²×D₁₁

yes

—

C₄²

C₂²×D₁₁

yes

—

C₁₁

#2986

yes

characteristic, complemented, Sylow

C₂³

C₂²×Dic₁₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₁₁

yes

—

C₂×C₄

C₂²×Dic₁₁

yes

—

C₂×C₄

C₂²×Dic₁₁

yes

characteristic

C₂×C₄

C₂²×Dic₁₁

yes

—

C₂×C₄

C₂³×D₁₁

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

C₂³×Dic₁₁

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

#67001

yes

—

105

C₄

#67040

yes

—

106

C₂

—

107

C₂

#10623343

yes

characteristic

108

C₂

C₂×#67001

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#533	C₂
prime radical	C₂³×C₁₁	C₂²×C₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#533	D₁₁
hypocenter	C₁₁	#2986
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #533

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₁

commutator, socle

C₂²×C₁₁

C₂³×C₄

Fitting

C₁₁×#533

C₂

prime radical

C₂³×C₁₁

C₂²×C₄

cosocle

C₂×C₄×C₁₁

C₂⁴

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₁₁

C₁ ◁ C₂×C₄ ◁ #533

N	H ≅ G/N	type
2. #10622637	C₂	semidirect
3. Q₈×C₁₁⋊C₈	C₂	semidirect
86. C₁₁	#2986	semidirect

H ≅ G/N

type

2. #10622637

C₂

semidirect

3. Q₈×C₁₁⋊C₈

C₂

semidirect

86. C₁₁

#2986

semidirect

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

subgroup	index
C₁₁×#533	2
#10622637	2
Q₈×C₁₁⋊C₈	2
#10622613	2
#10622538	2
#2986	11

subgroup

index

C₁₁×#533

Q₈×C₁₁⋊C₈

Subgroups — #13077718

Conjugacy classes of subgroups

Complements

Maximal subgroups