Group #21461024 — subgroups

Subgroups — #21461024

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	#16840779	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#92420	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	#16839812	C₂	1	1	yes	maximal, characteristic
6	C₂²×#92420	C₄	1	2	yes	—
7	#14519844	C₄	1	2	yes	—
8	C₂²⋊#92420	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	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
14	#14519706	C₄	1	2	yes	—
15	C₂²⋊#92418	C₄	1	1	yes	characteristic
16	C₈×Dic₆₁	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₆₁	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×#92420	C₈	1	8	yes	complemented
22	C₂×#92420	C₂×C₄	1	4	yes	—
23	C₂×#92420	C₂×C₄	1	2	yes	—
24	C₂×#92420	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₄×Dic₆₁	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	C₂³×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	2	no	—
33	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
39	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
41	#92420	—	2	4	no	—
42	#92420	C₂×C₈	1	4	yes	—
43	#92420	C₂×C₈	1	4	yes	—
44	C₈×C₆₁	—	2	2	no	—
45	#92418	—	2	2	no	—
46	C₂²×C₆₁	—	2	1	no	—
47	C₂²×C₆₁	—	2	1	no	—
48	C₂²×C₆₁	C₄×C₈	1	2	yes	—
49	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₆₁	—	2	1	no	—
51	C₄×C₆₁	#131	1	2	yes	—
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	C₄×C₈	1	2	yes	—
54	Dic₆₁	C₂²×C₈	1	2	yes	—
55	Dic₆₁	#131	1	2	yes	—
56	#1450	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	2	2	no	—
58	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×C₆₁	#405	1	1	yes	characteristic
60	C₂×C₆₁	#405	1	1	yes	characteristic
61	#431	—	61	1	no	—
62	#431	—	61	1	no	—
63	C₂×C₄×C₈	—	61	1	no	—
64	#322	—	61	2	no	—
65	C₈²	—	61	2	no	—
66	C₆₁	#1450	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	2	no	—
68	C₂×C₄²	—	61	1	no	—
69	C₄⋊C₈	—	61	2	no	—
70	C₄⋊C₈	—	61	2	no	—
71	C₂²⋊C₈	—	61	2	no	—
72	C₂²⋊C₈	—	61	1	no	—
73	C₂²⋊C₈	#6923	1	1	yes	characteristic
74	C₄×C₈	—	61	2	no	—
75	C₄×C₈	—	61	1	no	—
76	C₄×C₈	—	61	2	no	—
77	C₄×C₈	—	61	1	no	—
78	C₄×C₈	—	61	2	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	1	no	—
81	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	61	2	no	—
84	C₂×C₈	—	61	8	no	—
85	C₂×C₈	—	61	4	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	C₂×#6923	1	2	yes	—
88	C₄²	—	61	1	no	—
89	C₄²	—	61	1	no	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₂³	C₄×#6923	1	1	yes	characteristic
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	61	4	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	122	2	no	—
100	C₂×C₄	C₄×#6923	1	1	yes	characteristic
101	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
102	C₈	—	2	2	no	—
103	C₈	—	61	4	no	—
104	C₈	—	61	4	no	—
105	C₈	—	122	4	no	—
106	C₈	—	122	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	C₈×#6923	1	2	yes	—
110	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	61	2	no	—
113	C₄	—	61	2	no	—
114	C₄	—	61	2	no	—
115	C₄	—	122	1	no	—
116	C₄	#14519864	1	2	yes	—
117	C₂	—	2	2	no	—
118	C₂	C₂×C₈×#6923	1	1	yes	characteristic
119	C₂	#16840726	1	1	yes	characteristic
120	C₂	#16840728	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840779

C₂

yes

maximal, characteristic

C₂×C₄×#92420

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, complemented

C₈×#92420

C₂

yes

maximal, complemented

#16839812

C₂

yes

maximal, characteristic

C₂²×#92420

C₄

yes

—

#14519844

C₄

yes

—

C₂²⋊#92420

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

C₄

yes

—

C₂²⋊#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

—

C₂²⋊C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92420

C₈

yes

complemented

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

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

—

C₂³×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

#92420

—

#92420

C₂×C₈

yes

—

#92420

C₂×C₈

yes

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×C₈

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#131

yes

—

Dic₆₁

—

Dic₆₁

C₄×C₈

yes

—

Dic₆₁

C₂²×C₈

yes

—

Dic₆₁

#131

yes

—

#1450

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄×C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₆₁

#1450

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

#6923

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

100

C₂×C₄

C₄×#6923

yes

characteristic

101

C₂×C₄

C₂²×#6923

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

122

—

106

C₈

—

122

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₈×#6923

yes

—

110

C₂²

C₂×C₄×#6923

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

122

—

116

C₄

#14519864

yes

—

117

C₂

—

118

C₂

C₂×C₈×#6923

yes

characteristic

119

C₂

#16840726

yes

characteristic

120

C₂

#16840728

yes

characteristic

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

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Fitting

C₂²⋊C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₂²⋊C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
3. #92420⋊C₈	C₂	semidirect
4. C₈×#92420	C₂	semidirect
21. C₂×#92420	C₈	semidirect
66. C₆₁	#1450	semidirect

H ≅ G/N

type

3. #92420⋊C₈

C₂

semidirect

4. C₈×#92420

C₂

semidirect

21. C₂×#92420

C₈

semidirect

66. C₆₁

#1450

semidirect

Subgroups — #21461024

Conjugacy classes of subgroups

Complements