Group #13070063 — subgroups

Subgroups — #13070063

Order 1408.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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	#10622746	C₂	1	2	yes	maximal
2	#10622723	C₂	1	1	yes	maximal, characteristic
3	C₂×#66881	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622192	C₂	1	2	yes	maximal, complemented
6	C₂×#4339	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	C₂×#4318	C₂²	1	1	yes	characteristic
11	#66885	—	2	2	no	—
12	(C₂×D₁₁)⋊C₈	—	2	2	no	—
13	#66881	—	2	2	no	—
14	#66880	—	2	2	no	—
15	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₁	—	2	1	no	—
17	C₂²×Dic₁₁	—	2	2	no	—
18	#4339	—	2	2	no	—
19	#4339	—	2	2	no	—
20	C₂×D₄₄	D₄	1	1	yes	characteristic
21	C₂×C₄×D₁₁	—	2	1	no	—
22	C₂×Dic₂₂	D₄	1	1	yes	characteristic
23	C₁₁×M₁₆	—	2	2	no	—
24	C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₈×C₁₁	—	2	2	no	—
26	C₂×C₈×C₁₁	—	2	2	no	—
27	C₂×C₈×C₁₁	D₄	1	2	yes	—
28	C₄⋊Dic₁₁	—	2	2	no	—
29	C₄⋊Dic₁₁	—	2	2	no	—
30	#4318	—	2	2	no	—
31	C₂×C₁₁⋊C₈	—	2	1	no	—
32	#2079	—	11	1	no	maximal, Sylow
33	C₂³×C₁₁	#41	1	1	yes	characteristic
34	C₂²×D₁₁	—	2	1	no	—
35	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₁	#41	1	2	yes	—
38	C₂×C₄×C₁₁	#41	1	2	yes	—
39	C₂²⋊D₁₁	—	4	2	no	—
40	C₂×Dic₁₁	—	2	1	no	—
41	C₂×Dic₁₁	—	4	2	no	—
42	C₂×Dic₁₁	—	8	2	no	—
43	D₄₄	—	2	2	no	—
44	C₄×D₁₁	—	4	1	no	—
45	C₄×D₁₁	—	4	1	no	—
46	Dic₂₂	—	2	2	no	—
47	C₈×C₁₁	—	2	2	no	—
48	C₈×C₁₁	—	4	2	no	—
49	C₁₁⋊C₈	—	4	1	no	—
50	C₂×#106	—	11	1	no	—
51	#417	—	11	2	no	—
52	#408	—	11	1	no	—
53	#343	—	11	2	no	—
54	#341	D₁₁	1	1	yes	characteristic, complemented
55	C₂²×C₁₁	—	2	2	no	—
56	C₂²×C₁₁	#121	1	1	yes	characteristic
57	C₂²×C₁₁	#126	1	2	yes	—
58	C₂×D₁₁	—	4	1	no	—
59	C₂×D₁₁	—	4	2	no	—
60	C₄×C₁₁	#123	1	2	yes	—
61	C₄×C₁₁	#123	1	1	yes	characteristic
62	C₄×C₁₁	#124	1	1	yes	characteristic
63	Dic₁₁	—	4	1	no	—
64	Dic₁₁	—	8	2	no	—
65	C₂×#41	—	11	1	no	—
66	C₂×M₁₆	—	11	1	no	—
67	C₂×M₁₆	C₂×D₁₁	1	2	yes	—
68	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	11	2	no	—
70	#106	—	22	2	no	—
71	#103	—	22	2	no	—
72	#102	—	22	2	no	—
73	C₂²⋊C₈	—	22	2	no	—
74	C₂×C₁₁	—	2	2	no	—
75	C₂×C₁₁	#397	1	1	yes	characteristic
76	C₂×C₁₁	#471	1	2	yes	—
77	D₁₁	—	8	1	no	—
78	#41	—	22	2	no	—
79	#41	—	22	2	no	—
80	C₂×Q₈	—	11	1	no	—
81	C₂×D₄	—	11	1	no	—
82	C₂×D₄	—	22	1	no	—
83	C₂²×C₄	—	22	1	no	—
84	C₂²×C₄	—	22	2	no	—
85	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	22	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	22	1	no	—
92	C₂×C₈	D₄₄	1	2	yes	—
93	C₄⋊C₄	—	22	2	no	—
94	C₄⋊C₄	—	22	2	no	—
95	C₁₁	#2079	1	1	yes	characteristic, complemented, Sylow
96	C₂³	—	22	1	no	—
97	C₂³	#4343	1	1	yes	characteristic
98	Q₈	—	22	2	no	—
99	D₄	—	22	2	no	—
100	D₄	—	44	2	no	—
101	C₂×C₄	—	22	1	no	—
102	C₂×C₄	—	44	1	no	—
103	C₂×C₄	—	44	1	no	—
104	C₂×C₄	—	44	2	no	—
105	C₂×C₄	—	88	2	no	—
106	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
107	C₂×C₄	#4339	1	2	yes	—
108	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
109	C₂×C₄	#4341	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	4	2	no	—
112	C₈	—	44	1	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	44	2	no	—
115	C₂²	—	44	1	no	—
116	C₂²	#66948	1	1	yes	characteristic
117	C₂²	#66951	1	2	yes	—
118	C₄	—	44	1	no	—
119	C₄	—	88	2	no	—
120	C₄	#66928	1	1	yes	characteristic
121	C₄	#66936	1	2	yes	—
122	C₄	#66939	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	88	1	no	—
125	C₂	#10622287	1	1	yes	characteristic
126	C₂	#10622511	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10622746

C₂

yes

maximal

#10622723

C₂

yes

maximal, characteristic

C₂×#66881

C₂

yes

maximal, characteristic, complemented

C₁₁×#341

C₂

yes

maximal, characteristic, complemented

#10622192

C₂

yes

maximal, complemented

C₂×#4339

C₂²

yes

characteristic

C₂×C₁₁×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×#4318

C₂²

yes

characteristic

#66885

—

(C₂×D₁₁)⋊C₈

—

#66881

—

#66880

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂×C₂²⋊D₁₁

—

C₂²×Dic₁₁

—

#4339

—

#4339

—

C₂×D₄₄

D₄

yes

characteristic

C₂×C₄×D₁₁

—

C₂×Dic₂₂

D₄

yes

characteristic

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₄

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

—

C₂³×C₁₁

yes

C₂²×D₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂²⋊D₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

D₄₄

—

C₄×D₁₁

—

C₄×D₁₁

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic, complemented

C₂²×C₁₁

—

C₂²×C₁₁

#121

yes

characteristic

C₂²×C₁₁

#126

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

#123

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

Dic₁₁

—

Dic₁₁

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₁

yes

—

C₂²×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄⋊C₄

—

#106

—

#103

—

#102

—

C₂²⋊C₈

—

C₂×C₁₁

—

C₂×C₁₁

#397

yes

characteristic

C₂×C₁₁

#471

yes

—

D₁₁

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₁₁

#2079

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

#4343

yes

characteristic

Q₈

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₂×D₄₄

yes

characteristic

107

C₂×C₄

#4339

yes

—

108

C₂×C₄

D₄×D₁₁

yes

characteristic

109

C₂×C₄

#4341

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

#66948

yes

characteristic

117

C₂²

#66951

yes

—

118

C₄

—

119

C₄

—

120

C₄

#66928

yes

characteristic

121

C₄

#66936

yes

—

122

C₄

#66939

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#10622287

yes

characteristic

126

C₂

#10622511

yes

—

	subgroup	G/H
center	C₂²	#66948
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#341	C₂
socle	C₂²×C₁₁	#121
prime radical	C₂×#4339	C₂²
hypercenter	#341	D₁₁
hypocenter	C₁₁	#2079
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#66948

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₁₁×#341

C₂

C₂²×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
3. C₂×#66881	C₂	semidirect
4. C₁₁×#341	C₂	semidirect
5. #10622192	C₂	semidirect
54. #341	D₁₁	semidirect
95. C₁₁	#2079	semidirect

H ≅ G/N

type

3. C₂×#66881

C₂

semidirect

4. C₁₁×#341

C₂

semidirect

5. #10622192

C₂

semidirect

54. #341

D₁₁

semidirect

95. C₁₁

#2079

semidirect

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

subgroup	index
#10622746	2
#10622723	2
C₂×#66881	2
C₁₁×#341	2
#10622192	2
#2079	11

subgroup

index

C₁₁×#341

Subgroups — #13070063

Conjugacy classes of subgroups

Complements

Maximal subgroups