Group #21460663 — subgroups

Subgroups — #21460663

Order 7808.

160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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×#14519844	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758217	C₂	1	1	yes	maximal, characteristic
3	#16839812	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758217	C₄	1	2	yes	—
5	C₂²×#92420	C₄	1	2	yes	—
6	#14519844	—	2	1	no	—
7	#14519844	—	2	1	no	—
8	#14519832	—	2	1	no	—
9	C₄×#92420	—	2	1	no	—
10	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
11	#14519706	—	2	1	no	—
12	C₂²⋊#92418	C₄	1	1	yes	characteristic
13	C₈×Dic₆₁	—	2	1	no	—
14	C₂²⋊C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758217	—	2	2	no	—
19	#11758217	C₈	1	4	yes	complemented
20	C₂×#92420	—	2	2	no	—
21	C₂×#92420	—	2	2	no	—
22	C₂×#92420	—	4	2	no	—
23	C₂×C₈×C₆₁	—	2	1	no	—
24	C₄×Dic₆₁	D₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₄×Dic₆₁	D₄	1	1	yes	characteristic
27	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
28	C₂×#92418	—	2	1	no	—
29	C₂³×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	4	1	no	—
31	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	—	2	1	no	—
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
40	C₂×Dic₆₁	M₁₆	1	2	yes	—
41	#92420	—	2	4	no	—
42	#92420	—	4	2	no	—
43	C₈×C₆₁	—	4	1	no	—
44	#92418	—	4	1	no	—
45	C₂²×C₆₁	—	2	1	no	—
46	C₂²×C₆₁	—	2	1	no	—
47	C₂²×C₆₁	#95	1	1	yes	characteristic
48	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
49	C₂²×C₆₁	#97	1	1	yes	characteristic
50	C₄×C₆₁	—	2	1	no	—
51	C₄×C₆₁	—	2	1	no	—
52	Dic₆₁	—	2	1	no	—
53	Dic₆₁	C₂²⋊C₈	1	2	yes	—
54	Dic₆₁	#100	1	1	yes	characteristic
55	Dic₆₁	#101	1	1	yes	characteristic
56	Dic₆₁	C₄⋊C₈	1	2	yes	—
57	#1283	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	—	2	1	no	—
59	C₂×C₆₁	—	2	1	no	—
60	C₂×C₆₁	#336	1	1	yes	characteristic
61	C₂×C₆₁	#343	1	1	yes	characteristic
62	C₂×C₆₁	#344	1	1	yes	characteristic
63	#431	—	61	1	no	—
64	C₂×C₄⋊C₈	—	61	1	no	—
65	C₄×M₁₆	—	61	1	no	—
66	C₆₁	#1283	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	61	2	no	—
68	C₂²×C₈	—	61	2	no	—
69	C₂×C₄²	—	61	1	no	—
70	C₄⋊C₈	—	122	1	no	—
71	C₄⋊C₈	—	122	1	no	—
72	C₄⋊C₈	—	122	1	no	—
73	C₂²⋊C₈	—	61	1	no	—
74	C₂²⋊C₈	#6923	1	1	yes	characteristic
75	#97	—	122	1	no	—
76	C₄×C₈	—	122	1	no	—
77	C₄×C₈	—	122	1	no	—
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
81	M₁₆	—	61	4	no	—
82	M₁₆	—	122	2	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	122	2	no	—
85	C₂×C₈	—	122	2	no	—
86	C₂×C₈	—	122	1	no	—
87	C₂×C₈	—	244	2	no	—
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	—	4	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	2	no	—
98	C₂×C₄	—	61	2	no	—
99	C₂×C₄	—	61	1	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	C₂²⋊#6923	1	1	yes	characteristic
104	C₈	—	4	1	no	—
105	C₈	—	122	4	no	—
106	C₈	—	244	1	no	—
107	C₈	—	244	2	no	—
108	C₂²	—	2	1	no	—
109	C₂²	—	2	1	no	—
110	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
111	C₂²	C₈×#6923	1	1	yes	characteristic
112	C₂²	#14519831	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	61	2	no	—
116	C₄	—	61	2	no	—
117	C₄	—	61	1	no	—
118	C₄	—	61	1	no	—
119	C₄	—	122	1	no	—
120	C₂	—	2	1	no	—
121	C₂	—	2	1	no	—
122	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic
123	C₂	#16840641	1	1	yes	characteristic
124	C₂	#16840643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519844

C₂

yes

maximal, characteristic

C₄×#11758217

C₂

yes

maximal, characteristic

#16839812

C₂

yes

maximal, characteristic

C₂×#11758217

C₄

yes

—

C₂²×#92420

C₄

yes

—

—

—

—

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

—

C₂²⋊#92418

C₄

yes

characteristic

C₈×Dic₆₁

—

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

#11758217

—

#11758217

C₈

yes

—

—

—

C₂×C₈×C₆₁

—

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

C₂³×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

M₁₆

yes

—

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

#97

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

C₂²⋊C₈

yes

—

Dic₆₁

yes

Dic₆₁

yes

Dic₆₁

C₄⋊C₈

yes

—

#1283

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₄⋊C₈

—

C₄×M₁₆

—

C₆₁

#1283

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

C₂²⋊C₈

#6923

yes

characteristic

#97

—

122

—

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

C₄⋊#6923

yes

characteristic

103

C₂×C₄

C₂²⋊#6923

yes

characteristic

104

C₈

—

105

C₈

—

122

—

106

C₈

—

244

—

107

C₈

—

244

—

108

C₂²

—

109

C₂²

—

110

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

111

C₂²

C₈×#6923

yes

characteristic

112

C₂²

#14519831

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

122

—

120

C₂

—

121

C₂

—

122

C₂

(C₂×#6923)⋊C₈

yes

characteristic

123

C₂

#16840641

yes

characteristic

124

C₂

#16840643

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂²×C₆₁	C₄×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂²⋊C₈	#6923
hypocenter	C₆₁	#1283
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂²×C₆₁

C₄×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂²⋊C₈×C₆₁

C₄

C₂²×C₆₁

C₂²⋊C₈

C₆₁

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
19. #11758217	C₈	semidirect
66. C₆₁	#1283	semidirect

H ≅ G/N

type

19. #11758217

C₈

semidirect

66. C₆₁

#1283

semidirect

Subgroups — #21460663

Conjugacy classes of subgroups

Complements