Group #21461025 — subgroups

Subgroups — #21461025

Order 7808.

212 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 104 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	#16840781	C₂	1	1	yes	maximal, characteristic
2	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#92420⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₈×#92420	C₂	1	2	yes	maximal, complemented
5	#16839814	C₂	1	1	yes	maximal, characteristic
6	C₂×D₆₁⋊C₈	C₄	1	2	yes	—
7	C₄⋊#92420	C₄	1	2	yes	—
8	#14519834	C₄	1	2	yes	—
9	C₄×#92420	C₄	1	2	yes	—
10	C₄×#92420	C₂²	1	1	yes	characteristic
11	C₄×#92420	C₂²	1	1	yes	characteristic
12	C₄×#92420	C₂²	1	2	yes	—
13	C₄²×D₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊#92418	C₄	1	1	yes	characteristic
15	#14519689	C₄	1	2	yes	—
16	C₈×Dic₆₁	C₂²	1	2	yes	—
17	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×#92420	C₂×C₄	1	4	yes	—
22	C₂×#92420	C₂×C₄	1	2	yes	—
23	C₂×#92420	C₂×C₄	1	2	yes	—
24	D₆₁⋊C₈	C₈	1	8	yes	complemented
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
30	C₂×#92418	C₂×C₄	1	2	yes	—
31	C₂²×D₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₄×D₆₁	—	2	1	no	—
39	C₄×D₆₁	—	2	1	no	—
40	C₄×D₆₁	—	2	2	no	—
41	C₄×D₆₁	C₂×C₈	1	4	yes	—
42	#92420	—	2	4	no	—
43	#92420	C₂×C₈	1	4	yes	—
44	#92420	C₂×C₈	1	4	yes	—
45	C₈×C₆₁	—	2	2	no	—
46	#92418	—	2	2	no	—
47	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
48	C₂×D₆₁	—	2	1	no	—
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	C₄×C₈	1	2	yes	—
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	C₄×C₈	1	2	yes	—
53	C₄×C₆₁	#131	1	1	yes	characteristic
54	C₄×C₆₁	#131	1	1	yes	characteristic
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	C₂²×C₈	1	2	yes	—
57	Dic₆₁	#131	1	2	yes	—
58	#1450	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
60	C₂×C₆₁	#405	1	1	yes	characteristic
61	C₂×C₆₁	#405	1	1	yes	characteristic
62	D₆₁	—	2	2	no	—
63	#431	—	61	1	no	—
64	#431	—	61	1	no	—
65	C₂×C₄×C₈	—	61	1	no	—
66	#322	—	61	2	no	—
67	C₈²	—	61	2	no	—
68	C₆₁	#1450	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	61	2	no	—
70	C₂×C₄²	—	61	1	no	—
71	C₄⋊C₈	—	61	2	no	—
72	C₄⋊C₈	—	61	1	no	—
73	C₄⋊C₈	#6923	1	1	yes	characteristic
74	C₂²⋊C₈	—	61	2	no	—
75	C₂²⋊C₈	—	61	2	no	—
76	C₄×C₈	—	61	2	no	—
77	C₄×C₈	—	61	1	no	—
78	C₄×C₈	—	61	2	no	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	2	no	—
81	C₂²×C₄	—	61	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	61	2	no	—
86	C₂×C₈	—	61	8	no	—
87	C₂×C₈	—	61	4	no	—
88	C₂×C₈	—	61	2	no	—
89	C₂×C₈	C₂×#6923	1	2	yes	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	1	no	—
93	C₄²	C₂×#6923	1	1	yes	characteristic
94	C₂³	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	4	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	122	2	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	C₄×#6923	1	1	yes	characteristic
103	C₂×C₄	C₄×#6923	1	1	yes	characteristic
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	61	4	no	—
107	C₈	—	61	4	no	—
108	C₈	—	122	4	no	—
109	C₈	—	122	2	no	—
110	C₂²	—	61	2	no	—
111	C₂²	—	122	1	no	—
112	C₂²	—	122	1	no	—
113	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	61	2	no	—
116	C₄	—	61	2	no	—
117	C₄	—	122	1	no	—
118	C₄	C₈×#6923	1	2	yes	—
119	C₄	#14519864	1	1	yes	characteristic
120	C₄	#14519865	1	1	yes	characteristic
121	C₂	—	122	2	no	—
122	C₂	C₂×C₈×#6923	1	1	yes	characteristic
123	C₂	#16840727	1	1	yes	characteristic
124	C₂	#16840728	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840781

C₂

yes

maximal, characteristic

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, complemented

C₈×#92420

C₂

yes

maximal, complemented

#16839814

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₄

yes

—

C₄⋊#92420

C₄

yes

—

#14519834

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic

#14519689

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₄⋊C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

D₆₁⋊C₈

C₈

yes

complemented

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₂²×D₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂×C₈

yes

—

#92420

—

#92420

C₂×C₈

yes

—

#92420

C₂×C₈

yes

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₄×C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

C₂²×C₈

yes

—

Dic₆₁

#131

yes

—

#1450

—

maximal, Sylow

C₂×C₆₁

C₂×C₄×C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#431

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₆₁

#1450

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#6923

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

C₄×#6923

yes

characteristic

103

C₂×C₄

C₄×#6923

yes

characteristic

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

122

—

109

C₈

—

122

—

110

C₂²

—

111

C₂²

—

122

—

112

C₂²

—

122

—

113

C₂²

C₂×C₄×#6923

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₄

C₈×#6923

yes

—

119

C₄

#14519864

yes

characteristic

120

C₄

#14519865

yes

characteristic

121

C₂

—

122

—

122

C₂

C₂×C₈×#6923

yes

characteristic

123

C₂

#16840727

yes

characteristic

124

C₂

#16840728

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1450
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Fitting

C₄⋊C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₄⋊C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #92420⋊C₈	C₂	semidirect
4. C₈×#92420	C₂	semidirect
24. D₆₁⋊C₈	C₈	semidirect
68. C₆₁	#1450	semidirect

H ≅ G/N

type

3. #92420⋊C₈

C₂

semidirect

4. C₈×#92420

C₂

semidirect

24. D₆₁⋊C₈

C₈

semidirect

68. C₆₁

#1450

semidirect

Subgroups — #21461025

Conjugacy classes of subgroups

Complements