Group #21462729 — subgroups

Subgroups — #21462729

Order 7808.

330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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	#16840814	C₂	1	4	yes	maximal, complemented
2	#16840811	C₂	1	4	yes	maximal, complemented
3	#16840787	C₂	1	4	yes	maximal
4	#16840780	C₂	1	2	yes	maximal
5	#16840318	C₂	1	1	yes	maximal, characteristic
6	#14519844	C₂²	1	2	yes	—
7	#14519844	C₂²	1	2	yes	—
8	#14519844	C₂²	1	4	yes	—
9	C₄⋊#92420	C₂²	1	4	yes	—
10	#14519834	C₂²	1	4	yes	—
11	#14519832	C₂²	1	4	yes	—
12	C₄×#92420	C₂²	1	4	yes	—
13	C₄×#92420	C₂²	1	4	yes	—
14	#14519776	C₄	1	2	yes	—
15	#14519769	C₄	1	1	yes	characteristic
16	#14519755	C₄	1	4	yes	—
17	#14519742	C₂²	1	4	yes	—
18	#14519735	C₂²	1	2	yes	—
19	C₄²×D₆₁	C₂²	1	1	yes	characteristic
20	#125×C₆₁	C₄	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
22	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₂₂	C₂×C₄	1	4	yes	—
24	C₂×#92420	C₂³	1	4	yes	—
25	C₂×#92420	C₂³	1	4	yes	—
26	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
27	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
28	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
29	#11758198	C₂×C₄	1	4	yes	—
30	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
31	#11758196	C₂×C₄	1	4	yes	—
32	#11758196	C₂×C₄	1	4	yes	—
33	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₆₁	C₂³	1	2	yes	—
35	C₄×Dic₆₁	C₂³	1	4	yes	—
36	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₆₁	C₂²×C₄	1	4	yes	—
40	C₂×Dic₆₁	C₂²×C₄	1	4	yes	—
41	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
42	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
43	C₄×D₆₁	—	2	4	no	—
44	C₄×D₆₁	—	2	2	no	—
45	Dic₁₂₂	—	2	8	no	—
46	#92420	—	2	4	no	—
47	#92420	—	2	4	no	—
48	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	—	2	2	no	—
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	—	2	4	no	—
53	C₄×C₆₁	—	2	2	no	—
54	Dic₆₁	—	2	4	no	—
55	Dic₆₁	#131	1	4	yes	—
56	Dic₆₁	2₋¹⁺⁴	1	2	yes	—
57	#2986	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#519	1	1	yes	characteristic
59	C₂×C₆₁	C₂×#131	1	2	yes	—
60	D₆₁	—	4	1	no	—
61	#533	—	61	1	no	—
62	#446	—	61	4	no	—
63	C₈×Q₈	—	61	4	no	—
64	#433	—	61	4	no	—
65	#431	—	61	2	no	—
66	C₆₁	#2986	1	1	yes	characteristic, complemented, Sylow
67	C₄⋊Q₈	—	61	2	no	—
68	#125	—	61	1	no	—
69	#125	#6923	1	1	yes	characteristic
70	C₂²⋊Q₈	—	61	4	no	—
71	C₄×Q₈	—	61	4	no	—
72	#117	—	61	2	no	—
73	C₂×C₄²	—	61	1	no	—
74	C₄⋊C₈	—	61	4	no	—
75	C₄⋊C₈	—	61	2	no	—
76	C₄⋊C₈	—	61	2	no	—
77	C₄⋊C₈	—	61	4	no	—
78	C₂²⋊C₈	—	61	4	no	—
79	#97	—	61	4	no	—
80	C₄×C₈	—	61	4	no	—
81	C₄×C₈	—	61	4	no	—
82	C₂×Q₈	—	61	4	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	2	no	—
85	C₂×C₈	—	61	4	no	—
86	C₂×C₈	—	61	4	no	—
87	C₄⋊C₄	—	61	4	no	—
88	C₄⋊C₄	—	61	4	no	—
89	C₄⋊C₄	—	61	2	no	—
90	C₄⋊C₄	C₂×#6923	1	2	yes	—
91	C₄⋊C₄	C₂×#6923	1	4	yes	—
92	C₂²⋊C₄	—	61	4	no	—
93	C₄²	—	61	2	no	—
94	C₄²	—	61	4	no	—
95	C₄²	—	61	1	no	—
96	C₄²	C₂×#6923	1	1	yes	characteristic
97	C₂³	—	61	1	no	—
98	Q₈	—	122	8	no	—
99	C₂×C₄	—	61	2	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	4	no	—
102	C₂×C₄	—	122	2	no	—
103	C₂×C₄	—	122	4	no	—
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₂×C₄	C₂²×#6923	1	2	yes	—
106	C₂×C₄	C₂²×#6923	1	4	yes	—
107	C₈	—	122	4	no	—
108	C₈	—	122	4	no	—
109	C₂²	—	122	1	no	—
110	C₂²	—	122	2	no	—
111	C₂²	C₂³×#6923	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	2	no	—
114	C₄	—	2	4	no	—
115	C₄	—	61	2	no	—
116	C₄	—	61	4	no	—
117	C₄	—	122	4	no	—
118	C₂	—	244	1	no	—
119	C₂	#16840830	1	1	yes	characteristic
120	C₂	D₆₁⋊#131	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840814

C₂

yes

maximal, complemented

#16840811

C₂

yes

maximal, complemented

#16840787

C₂

yes

maximal

#16840780

C₂

yes

maximal

#16840318

C₂

yes

maximal, characteristic

#14519844

C₂²

yes

—

#14519844

C₂²

yes

—

#14519844

C₂²

yes

—

C₄⋊#92420

C₂²

yes

—

#14519834

C₂²

yes

—

#14519832

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₄×#92420

C₂²

yes

—

#14519776

C₄

yes

—

#14519769

C₄

yes

characteristic

#14519755

C₄

yes

—

#14519742

C₂²

yes

—

#14519735

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#125×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×Dic₁₂₂

C₂×C₄

yes

—

C₂×#92420

C₂³

yes

—

C₂×#92420

C₂³

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

C₂×C₄

yes

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

C₂×C₄

yes

—

#11758196

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂³

yes

—

C₄×Dic₆₁

C₂³

yes

—

C₂²×D₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

—

C₂×Dic₆₁

C₂⁴

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

#92420

—

#92420

—

C₂²×C₆₁

C₂³×C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

#131

yes

—

Dic₆₁

2₋¹⁺⁴

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

#533

—

#446

—

C₈×Q₈

—

#433

—

#431

—

C₆₁

#2986

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#6923

yes

—

C₄⋊C₄

C₂×#6923

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

Q₈

—

122

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₂×C₄

C₂²×#6923

yes

—

106

C₂×C₄

C₂²×#6923

yes

—

107

C₈

—

122

—

108

C₈

—

122

—

109

C₂²

—

122

—

110

C₂²

—

122

—

111

C₂²

C₂³×#6923

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₂

—

244

—

119

C₂

#16840830

yes

characteristic

120

C₂

D₆₁⋊#131

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	#125×C₆₁	C₄
hypercenter	#125	#6923
hypocenter	C₆₁	#2986
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#6923

commutator, socle

C₂²×C₆₁

C₂³×C₄

Fitting

#125×C₆₁

C₄

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #16840814	C₂	semidirect
2. #16840811	C₂	semidirect
66. C₆₁	#2986	semidirect

H ≅ G/N

type

1. #16840814

C₂

semidirect

2. #16840811

C₂

semidirect

66. C₆₁

#2986

semidirect

Subgroups — #21462729

Conjugacy classes of subgroups

Complements