Group #13068789 — subgroups

Subgroups — #13068789

Order 1408.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#66886	C₂	1	2	yes	maximal
3	#10622731	C₂	1	2	yes	maximal
4	C₂×#66883	C₂	1	1	yes	maximal, characteristic
5	C₂×#66879	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
9	C₂×#4318	C₂²	1	2	yes	—
10	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₁×#108	—	2	2	no	—
12	#66886	—	2	4	no	—
13	#66883	—	2	2	no	—
14	#66879	C₄	1	4	yes	—
15	Dic₁₁⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₁	Q₈	1	2	yes	—
18	C₁₁×M₁₆	—	2	2	no	—
19	C₁₁×M₁₆	—	2	2	no	—
20	C₂×C₈×C₁₁	—	2	2	no	—
21	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₁	D₄	1	2	yes	—
23	C₂×C₈×C₁₁	Q₈	1	2	yes	—
24	C₄×Dic₁₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₁₁	D₄	1	2	yes	—
26	#4318	—	2	2	no	—
27	#4318	—	2	2	no	—
28	C₂×C₁₁⋊C₈	—	2	2	no	—
29	C₂×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₁₁⋊C₈	D₄	1	2	yes	—
31	C₂×C₁₁⋊C₈	Q₈	1	2	yes	—
32	#1849	—	11	1	no	maximal, Sylow
33	C₂³×C₁₁	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×Dic₁₁	—	4	2	no	—
41	C₂×Dic₁₁	C₄⋊C₄	1	4	yes	—
42	C₈×C₁₁	—	4	2	no	—
43	C₈×C₁₁	C₄⋊C₄	1	4	yes	—
44	C₁₁⋊C₈	—	4	2	no	—
45	C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
46	C₂×#108	—	11	2	no	—
47	C₂×#108	—	11	1	no	—
48	C₂×#108	D₁₁	1	1	yes	characteristic
49	#423	—	11	2	no	—
50	C₂×#97	—	11	1	no	—
51	C₂²×C₁₁	—	2	2	no	—
52	C₂²×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
54	C₂²×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
55	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₁₁	#127	1	1	yes	characteristic
58	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₁₁	—	2	4	no	—
60	C₂×M₁₆	—	11	2	no	—
61	C₂×M₁₆	C₂×D₁₁	1	2	yes	—
62	C₂²×C₈	—	11	1	no	—
63	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
64	C₂×C₄²	—	11	1	no	—
65	#108	—	2	2	no	—
66	#108	—	22	4	no	—
67	#108	—	22	2	no	—
68	C₄⋊C₈	—	22	4	no	—
69	#97	—	11	4	no	—
70	C₂×C₁₁	—	2	1	no	—
71	C₂×C₁₁	—	2	1	no	—
72	C₂×C₁₁	#384	1	1	yes	characteristic
73	C₂×C₁₁	#430	1	2	yes	—
74	C₂²×C₄	—	11	2	no	—
75	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
76	M₁₆	—	2	2	no	—
77	M₁₆	—	2	2	no	—
78	M₁₆	—	22	2	no	—
79	M₁₆	—	22	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	11	2	no	—
82	C₂×C₈	—	11	2	no	—
83	C₂×C₈	—	11	2	no	—
84	C₂×C₈	—	22	2	no	—
85	C₂×C₈	Dic₂₂	1	2	yes	—
86	C₂×C₈	C₄×D₁₁	1	2	yes	—
87	C₂×C₈	C₂²⋊D₁₁	1	2	yes	—
88	C₄²	—	11	2	no	—
89	C₄²	—	11	2	no	—
90	C₁₁	#1849	1	1	yes	characteristic, complemented, Sylow
91	C₂³	Q₈×D₁₁	1	1	yes	characteristic
92	C₂×C₄	—	11	4	no	—
93	C₂×C₄	—	44	2	no	—
94	C₂×C₄	C₂×Dic₂₂	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
97	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₁₁	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	11	4	no	—
102	C₈	—	44	2	no	—
103	C₈	Dic₁₁⋊C₄	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#66941	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₁₁	1	1	yes	characteristic
107	C₂²	#66997	1	1	yes	characteristic
108	C₄	—	22	4	no	—
109	C₄	#66941	1	1	yes	characteristic
110	C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
111	C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
112	C₄	#66993	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#10622506	1	2	yes	—
116	C₂	#10622589	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₁×#108

C₂

yes

maximal, characteristic

C₂×#66886

C₂

yes

maximal

#10622731

C₂

yes

maximal

C₂×#66883

C₂

yes

maximal, characteristic

C₂×#66879

C₂

yes

maximal, characteristic

C₂×C₁₁×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂×#4318

C₂²

yes

—

C₂²×C₁₁⋊C₈

C₂²

yes

characteristic

C₁₁×#108

—

#66886

—

#66883

—

#66879

C₄

yes

—

Dic₁₁⋊C₈

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

Q₈

yes

—

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×C₄

yes

—

C₂×C₈×C₁₁

D₄

yes

—

C₂×C₈×C₁₁

Q₈

yes

—

C₄×Dic₁₁

C₂×C₄

yes

—

C₄×Dic₁₁

D₄

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₂×C₄

yes

—

C₂×C₁₁⋊C₈

D₄

yes

—

C₂×C₁₁⋊C₈

Q₈

yes

—

#1849

—

maximal, Sylow

C₂³×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

C₄⋊C₄

yes

—

C₈×C₁₁

—

C₈×C₁₁

C₄⋊C₄

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×#108

—

C₂×#108

—

C₂×#108

D₁₁

yes

characteristic

#423

—

C₂×#97

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₁

C₄⋊Q₈

yes

characteristic

C₂²×C₁₁

C₄⋊Q₈

yes

characteristic

C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₁

#127

yes

characteristic

C₄×C₁₁

C₄⋊Q₈

yes

characteristic

Dic₁₁

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₁

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

#108

—

C₄⋊C₈

—

#97

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#384

yes

characteristic

C₂×C₁₁

#430

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₂₂

yes

—

C₂×C₈

C₄×D₁₁

yes

—

C₂×C₈

C₂²⋊D₁₁

yes

—

C₄²

—

C₄²

—

C₁₁

#1849

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₂₂

yes

characteristic

C₂×C₄

C₂×C₄×D₁₁

yes

characteristic

C₂×C₄

D₄×D₁₁

yes

characteristic

C₂×C₄

D₄×D₁₁

yes

characteristic

C₂×C₄

Q₈×D₁₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

Dic₁₁⋊C₄

yes

—

104

C₂²

—

105

C₂²

#66941

yes

characteristic

106

C₂²

C₄⋊C₄×D₁₁

yes

characteristic

107

C₂²

#66997

yes

characteristic

108

C₄

—

109

C₄

#66941

yes

characteristic

110

C₄

C₄⋊C₄×D₁₁

yes

characteristic

111

C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

112

C₄

#66993

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#10622506

yes

—

116

C₂

#10622589

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₂×C₁₁×#108	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₄
prime radical	C₂³×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	C₂×#108	D₁₁
hypocenter	C₁₁	#1849
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₁

commutator

C₂×C₄×C₁₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₂×C₁₁×#108

C₂

socle

C₂²×C₁₁

C₂×C₄⋊C₄

prime radical

C₂³×C₁₁

C₂×Q₈

cosocle

C₂²×C₄×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
90. C₁₁	#1849	semidirect

H ≅ G/N

type

90. C₁₁

#1849

semidirect

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

subgroup	index
C₂×C₁₁×#108	2
C₂×#66886	2
#10622731	2
C₂×#66883	2
C₂×#66879	2
#1849	11

subgroup

index

C₂×C₁₁×#108

Subgroups — #13068789

Conjugacy classes of subgroups

Complements

Maximal subgroups