Group #21462049 — subgroups

Subgroups — #21462049

Order 7808.

228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14519851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11758187	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11758187	C₂	1	4	yes	maximal, complemented
4	C₂×#14519784	C₂	1	1	yes	maximal, characteristic
5	#14519851	—	2	2	no	—
6	C₂×#11758187	—	2	2	no	—
7	C₂×#11758187	C₂²	1	2	yes	—
8	C₂×#11758187	C₂²	1	2	yes	—
9	#14519784	—	2	2	no	—
10	#14519784	—	2	2	no	—
11	C₂×#11758194	C₄	1	1	yes	characteristic
12	C₂×#11758194	C₄	1	2	yes	—
13	C₂²×#92418	C₂²	1	2	yes	—
14	C₂²×#92418	C₂²	1	1	yes	characteristic
15	C₂×#41×C₆₁	C₄	1	1	yes	characteristic
16	#41×C₆₁	—	2	2	no	—
17	#41×C₆₁	—	2	2	no	—
18	C₂×Q₈×C₆₁	C₈	1	1	yes	characteristic
19	C₂×D₄×C₆₁	C₈	1	2	yes	—
20	C₂×D₄×C₆₁	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
23	#11758194	—	2	2	no	—
24	#11758194	—	2	4	no	—
25	C₂×#92418	—	2	2	no	—
26	C₂×#92418	—	2	2	no	—
27	C₂×#92418	C₂×C₄	1	2	yes	—
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	D₄	1	2	yes	—
30	C₂×#92418	D₄	1	2	yes	—
31	C₂×#92418	C₂³	1	1	yes	characteristic
32	#11758187	—	2	2	no	—
33	#11758187	—	2	2	no	—
34	C₂³×C₆₁	C₂×C₈	1	2	yes	—
35	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
36	Q₈×C₆₁	—	2	2	no	—
37	D₄×C₆₁	—	2	4	no	—
38	D₄×C₆₁	—	2	2	no	—
39	C₂×C₄×C₆₁	—	2	2	no	—
40	C₂×C₄×C₆₁	—	2	2	no	—
41	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
43	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
45	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
46	#92418	—	2	2	no	—
47	#92418	C₂²⋊C₄	1	2	yes	—
48	#92418	C₂×D₄	1	1	yes	characteristic
49	#92418	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₆₁	—	2	2	no	—
51	C₂²×C₆₁	—	2	2	no	—
52	C₂²×C₆₁	—	2	4	no	—
53	C₂²×C₆₁	C₂²⋊C₈	1	2	yes	—
54	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
55	C₄×C₆₁	—	2	2	no	—
56	C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
57	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
59	#2113	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	—	2	2	no	—
61	C₂×C₆₁	—	4	2	no	—
62	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
63	C₂×C₆₁	#504	1	2	yes	—
64	C₂×#131	—	61	1	no	—
65	C₂×M₃₂	—	61	1	no	—
66	C₂²×C₁₆	—	61	1	no	—
67	C₂²⋊C₁₆	—	61	4	no	—
68	C₆₁	#2113	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	#6923	1	1	yes	characteristic
70	#131	—	122	2	no	—
71	#131	—	122	2	no	—
72	C₂×M₁₆	—	61	2	no	—
73	C₂×M₁₆	—	61	1	no	—
74	C₂²×C₈	—	61	1	no	—
75	C₂²×C₈	—	61	2	no	—
76	M₃₂	—	122	2	no	—
77	C₂×C₁₆	—	61	2	no	—
78	C₂×C₁₆	—	61	2	no	—
79	C₂×C₁₆	—	122	2	no	—
80	#41	—	2	2	no	—
81	#41	—	2	2	no	—
82	C₂×Q₈	#92420	1	1	yes	characteristic
83	C₂×D₄	#92420	1	2	yes	—
84	C₂×D₄	#92420	1	1	yes	characteristic
85	C₂²×C₄	C₂×#6923	1	2	yes	—
86	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
87	M₁₆	—	122	4	no	—
88	M₁₆	—	122	2	no	—
89	C₂×C₈	—	61	2	no	—
90	C₂×C₈	—	61	2	no	—
91	C₂×C₈	—	61	1	no	—
92	C₂×C₈	—	61	1	no	—
93	C₂×C₈	—	61	2	no	—
94	C₂×C₈	—	122	2	no	—
95	C₂×C₈	—	122	2	no	—
96	C₁₆	—	122	2	no	—
97	C₁₆	—	122	2	no	—
98	C₂³	C₂×#92420	1	2	yes	—
99	C₂³	C₂×#92420	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	D₄	—	2	4	no	—
102	D₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₂×#92420	1	2	yes	—
106	C₂×C₄	C₂×#92420	1	1	yes	characteristic
107	C₂×C₄	#11758217	1	2	yes	—
108	C₂×C₄	C₂²⋊#6923	1	2	yes	—
109	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
110	C₈	—	61	2	no	—
111	C₈	—	61	1	no	—
112	C₈	—	61	1	no	—
113	C₈	—	122	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	2	4	no	—
117	C₂²	C₂²⋊#92420	1	2	yes	—
118	C₂²	C₂²×#92420	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	C₂²⋊#92420	1	2	yes	—
121	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
122	C₄	C₂×#11758217	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	4	2	no	—
125	C₂	C₂×C₂²⋊#92420	1	1	yes	characteristic
126	C₂	#16840820	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519851

C₂

yes

maximal, characteristic, complemented

C₂²×#11758187

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11758187

C₂

yes

maximal, complemented

C₂×#14519784

C₂

yes

maximal, characteristic

#14519851

—

C₂×#11758187

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

—

#14519784

—

#14519784

—

C₂×#11758194

C₄

yes

characteristic

C₂×#11758194

C₄

yes

—

C₂²×#92418

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×#41×C₆₁

C₄

yes

characteristic

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

C₈

yes

characteristic

C₂×D₄×C₆₁

C₈

yes

—

C₂×D₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

—

C₂×#92418

D₄

yes

—

C₂×#92418

C₂³

yes

characteristic

#11758187

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

#92418

—

#92418

C₂²⋊C₄

yes

—

#92418

C₂×D₄

yes

characteristic

#92418

C₂×D₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊C₈

yes

—

C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

#2113

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₆₁

#2113

yes

characteristic, complemented, Sylow

C₂×#41

#6923

yes

characteristic

#131

—

122

—

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#41

—

#41

—

C₂×Q₈

#92420

yes

characteristic

C₂×D₄

#92420

yes

—

C₂×D₄

#92420

yes

characteristic

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

C₂×#92420

yes

—

C₂³

C₂×#92420

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×#92420

yes

—

106

C₂×C₄

C₂×#92420

yes

characteristic

107

C₂×C₄

#11758217

yes

—

108

C₂×C₄

C₂²⋊#6923

yes

—

109

C₂×C₄

C₂²×#6923

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

122

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂²⋊#92420

yes

—

118

C₂²

C₂²×#92420

yes

characteristic

119

C₄

—

120

C₄

C₂²⋊#92420

yes

—

121

C₄

C₂×C₂²⋊#6923

yes

characteristic

122

C₄

C₂×#11758217

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂×C₂²⋊#92420

yes

characteristic

126

C₂

#16840820

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×#41×C₆₁	C₄
hypercenter	C₂×#41	#6923
hypocenter	C₆₁	#2113
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×#41×C₆₁

C₄

C₂×#41

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#14519851	C₂	semidirect
2. C₂²×#11758187	C₂	semidirect
3. C₂²⋊#11758187	C₂	semidirect
68. C₆₁	#2113	semidirect

H ≅ G/N

type

1. C₂×#14519851

C₂

semidirect

2. C₂²×#11758187

C₂

semidirect

3. C₂²⋊#11758187

C₂

semidirect

68. C₆₁

#2113

semidirect

Subgroups — #21462049

Conjugacy classes of subgroups

Complements