Group #13069884 — subgroups

Subgroups — #13069884

Order 1408.

256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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	C₂²×Dic₄₄	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×#66888	C₂	1	2	yes	maximal
4	#10622617	C₂	1	2	yes	maximal
5	#10622190	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₂	C₂²	1	2	yes	—
7	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#117	C₂²	1	1	yes	characteristic
10	C₂×#4318	C₂²	1	2	yes	—
11	C₂×Dic₄₄	—	2	4	no	—
12	C₂×Dic₄₄	—	2	2	no	—
13	C₁₁×C₄⋊C₈	—	2	2	no	—
14	#66888	—	2	4	no	—
15	#66874	—	2	4	no	—
16	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₁	—	2	2	no	—
18	C₂×Dic₂₂	—	2	2	no	—
19	C₂×Dic₂₂	—	2	2	no	—
20	C₂×Dic₂₂	—	2	2	no	—
21	C₂×Dic₂₂	—	2	2	no	—
22	C₂×Dic₂₂	—	2	2	no	—
23	C₂×Dic₂₂	D₄	1	4	yes	—
24	C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₈×C₁₁	—	2	2	no	—
26	C₂×C₈×C₁₁	—	2	1	no	—
27	C₂×C₈×C₁₁	D₄	1	2	yes	—
28	C₁₁×C₄⋊C₄	D₄	1	2	yes	—
29	C₁₁×C₂²⋊C₄	—	2	1	no	—
30	C₄²×C₁₁	—	2	1	no	—
31	#4318	—	2	2	no	—
32	#4318	—	2	2	no	—
33	C₂×C₁₁⋊C₈	—	2	2	no	—
34	Dic₄₄	—	2	8	no	—
35	#2047	—	11	1	no	maximal, Sylow
36	C₂³×C₁₁	#41	1	1	yes	characteristic
37	C₂×C₄×C₁₁	—	2	2	no	—
38	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₁	#41	1	2	yes	—
42	C₂×Dic₁₁	—	2	4	no	—
43	C₂×Dic₁₁	—	4	2	no	—
44	C₂×Dic₁₁	—	4	2	no	—
45	Dic₂₂	—	2	4	no	—
46	Dic₂₂	—	2	4	no	—
47	Dic₂₂	—	4	2	no	—
48	Dic₂₂	—	4	2	no	—
49	C₈×C₁₁	—	2	2	no	—
50	C₈×C₁₁	—	4	1	no	—
51	C₁₁⋊C₈	—	4	2	no	—
52	C₂²×Q₁₆	—	11	1	no	—
53	#424	D₁₁	1	1	yes	characteristic
54	#419	—	11	2	no	—
55	C₂×#101	—	11	2	no	—
56	#341	—	11	1	no	—
57	C₂²×C₁₁	—	2	2	no	—
58	C₂²×C₁₁	#121	1	1	yes	characteristic
59	C₂²×C₁₁	#123	1	2	yes	—
60	C₄×C₁₁	—	4	2	no	—
61	C₄×C₁₁	#120	1	1	yes	characteristic
62	C₄×C₁₁	#121	1	2	yes	—
63	C₄×C₁₁	#124	1	1	yes	characteristic
64	Dic₁₁	—	4	4	no	—
65	C₂²×Q₈	—	11	2	no	—
66	C₂×Q₁₆	—	22	4	no	—
67	C₂×Q₁₆	—	22	2	no	—
68	C₂×M₁₆	—	11	2	no	—
69	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
71	#117	C₂×D₁₁	1	1	yes	characteristic
72	C₄⋊C₈	—	2	2	no	—
73	#103	—	22	4	no	—
74	#101	—	22	4	no	—
75	C₂×C₁₁	—	2	2	no	—
76	C₂×C₁₁	#394	1	1	yes	characteristic
77	C₂×C₁₁	#473	1	2	yes	—
78	C₂×Q₈	—	11	4	no	—
79	C₂×Q₈	—	22	2	no	—
80	C₂×Q₈	—	22	2	no	—
81	C₂×Q₈	—	22	2	no	—
82	C₂×Q₈	—	22	2	no	—
83	C₂×Q₈	—	22	2	no	—
84	C₂²×C₄	—	22	2	no	—
85	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
86	Q₁₆	—	22	8	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	22	2	no	—
89	M₁₆	—	22	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	22	2	no	—
93	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
94	C₄⋊C₄	D₄₄	1	2	yes	—
95	C₂²⋊C₄	—	2	1	no	—
96	C₄²	—	2	1	no	—
97	C₁₁	#2047	1	1	yes	characteristic, complemented, Sylow
98	C₂³	#4339	1	1	yes	characteristic
99	Q₈	—	22	4	no	—
100	Q₈	—	22	4	no	—
101	Q₈	—	44	2	no	—
102	Q₈	—	44	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	22	4	no	—
105	C₂×C₄	—	44	2	no	—
106	C₂×C₄	—	44	2	no	—
107	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
108	C₂×C₄	D₄×D₁₁	1	2	yes	—
109	C₂×C₄	#4343	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	1	no	—
113	C₈	—	44	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#66947	1	2	yes	—
116	C₂²	#66983	1	1	yes	characteristic
117	C₄	—	4	2	no	—
118	C₄	—	44	4	no	—
119	C₄	#66948	1	2	yes	—
120	C₄	#66990	1	1	yes	characteristic
121	C₄	#67000	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#10622604	1	1	yes	characteristic
124	C₂	#10622756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₄₄

C₂

yes

maximal, characteristic

C₁₁×#424

C₂

yes

maximal, characteristic

C₂×#66888

C₂

yes

maximal

#10622617

C₂

yes

maximal

#10622190

C₂

yes

maximal, characteristic

C₂²×Dic₂₂

C₂²

yes

—

C₂×C₁₁×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₁₁

C₂²

yes

characteristic

C₁₁×#117

C₂²

yes

characteristic

C₂×#4318

C₂²

yes

—

C₂×Dic₄₄

—

C₂×Dic₄₄

—

C₁₁×C₄⋊C₈

—

#66888

—

#66874

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

—

C₂×Dic₂₂

D₄

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊C₄

D₄

yes

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

Dic₄₄

—

—

C₂³×C₁₁

yes

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂²×Q₁₆

—

#424

D₁₁

yes

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#121

yes

characteristic

C₂²×C₁₁

#123

yes

—

C₄×C₁₁

—

C₄×C₁₁

#120

yes

characteristic

C₄×C₁₁

#121

yes

—

C₄×C₁₁

#124

yes

characteristic

Dic₁₁

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₈

C₂×D₁₁

yes

characteristic

#117

C₂×D₁₁

yes

characteristic

C₄⋊C₈

—

#103

—

#101

—

C₂×C₁₁

—

C₂×C₁₁

#394

yes

characteristic

C₂×C₁₁

#473

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₁

yes

—

C₄⋊C₄

D₄₄

yes

—

C₂²⋊C₄

—

C₄²

—

C₁₁

#2047

yes

characteristic, complemented, Sylow

C₂³

#4339

yes

characteristic

Q₈

—

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂×D₄₄

yes

characteristic

108

C₂×C₄

D₄×D₁₁

yes

—

109

C₂×C₄

#4343

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

#66947

yes

—

116

C₂²

#66983

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

#66948

yes

—

120

C₄

#66990

yes

characteristic

121

C₄

#67000

yes

characteristic

122

C₂

—

123

C₂

#10622604

yes

characteristic

124

C₂

#10622756

yes

—

	subgroup	G/H
center	C₂²	#66983
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#424	C₂
socle	C₂²×C₁₁	#121
prime radical	C₂³×C₁₁	#41
hypercenter	#424	D₁₁
hypocenter	C₁₁	#2047
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#66983

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₁₁×#424

C₂

C₂²×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
97. C₁₁	#2047	semidirect

H ≅ G/N

type

97. C₁₁

#2047

semidirect

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

subgroup	index
C₂²×Dic₄₄	2
C₁₁×#424	2
C₂×#66888	2
#10622617	2
#10622190	2
#2047	11

subgroup

index

C₂²×Dic₄₄

C₁₁×#424

Subgroups — #13069884

Conjugacy classes of subgroups

Complements

Maximal subgroups