Group #21462043 — subgroups

Subgroups — C₂×C₂²⋊#11758187 #21462043

Order 7808.

272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 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	C₂²×#11758187	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11758187	C₂	1	4	yes	maximal, direct product factor
3	C₂³×#92418	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	4	no	—
5	C₂×#11758187	C₂²	1	4	yes	complemented
6	C₂²×#92418	—	2	4	no	—
7	C₂²×#92418	C₄	1	1	yes	characteristic
8	C₂²×#92418	C₄	1	2	yes	—
9	C₂²×#92418	C₂²	1	2	yes	—
10	C₂²×#92418	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₆₁	C₄	1	1	yes	characteristic
12	C₂⁴×C₆₁	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	—	2	2	no	—
14	C₂²×C₄×C₆₁	—	2	2	no	—
15	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₈	1	2	yes	—
17	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#92418	—	2	2	no	—
20	C₂×#92418	—	2	4	no	—
21	C₂×#92418	—	2	4	no	—
22	C₂×#92418	C₂×C₄	1	2	yes	—
23	C₂×#92418	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	D₄	1	4	yes	—
25	C₂×#92418	C₂³	1	1	yes	characteristic
26	#11758187	—	2	4	no	—
27	C₂³×C₆₁	—	2	2	no	—
28	C₂³×C₆₁	—	2	2	no	—
29	C₂³×C₆₁	C₁₆	1	4	yes	complemented
30	C₂³×C₆₁	C₂×C₈	1	2	yes	—
31	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	2	no	—
33	C₂×C₄×C₆₁	—	2	4	no	—
34	C₂×C₄×C₆₁	—	2	2	no	—
35	C₂×C₄×C₆₁	—	2	2	no	—
36	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
40	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
41	#92418	—	2	2	no	—
42	#92418	C₂²⋊C₄	1	2	yes	—
43	#92418	C₂×D₄	1	2	yes	—
44	C₂²×C₆₁	—	2	8	no	—
45	C₂²×C₆₁	—	2	2	no	—
46	C₂²×C₆₁	—	2	2	no	—
47	C₂²×C₆₁	C₂²⋊C₈	1	2	yes	—
48	C₂²×C₆₁	C₂×C₁₆	1	2	yes	—
49	C₂²×C₆₁	C₂×C₁₆	1	4	yes	complemented
50	C₂²×C₆₁	M₃₂	1	2	yes	—
51	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
52	C₄×C₆₁	—	2	2	no	—
53	C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
54	C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
56	C₂×C₂²⋊C₁₆	—	61	1	no	maximal, Sylow
57	C₂×C₆₁	—	2	4	no	—
58	C₂×C₆₁	C₂²⋊C₁₆	1	4	yes	complemented
59	C₂×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
60	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
61	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
62	C₂³×C₈	—	61	1	no	—
63	C₂²×C₁₆	—	61	2	no	—
64	C₂²⋊C₁₆	—	61	4	no	—
65	C₆₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
66	C₂³×C₄	#6923	1	1	yes	characteristic
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	—	61	2	no	—
69	C₂²×C₈	—	61	2	no	—
70	C₂²×C₈	—	61	1	no	—
71	C₂²×C₈	—	122	4	no	—
72	C₂×C₁₆	—	61	4	no	—
73	C₂×C₁₆	—	122	4	no	—
74	C₂⁴	#92420	1	1	yes	characteristic
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	—	2	2	no	—
77	C₂²×C₄	#92420	1	1	yes	characteristic
78	C₂²×C₄	#92420	1	2	yes	—
79	C₂²×C₄	C₂×#6923	1	2	yes	—
80	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
81	C₂×C₈	—	61	4	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	122	4	no	—
86	C₂×C₈	—	122	4	no	—
87	C₂×C₈	—	122	2	no	—
88	C₁₆	—	122	4	no	—
89	C₂³	—	2	2	no	—
90	C₂³	—	2	2	no	—
91	C₂³	#11758187	1	4	yes	complemented
92	C₂³	C₂×#92420	1	2	yes	—
93	C₂³	C₂×#92420	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	C₂×#92420	1	2	yes	—
99	C₂×C₄	C₂×#92420	1	1	yes	characteristic
100	C₂×C₄	#11758217	1	2	yes	—
101	C₂×C₄	C₂²⋊#6923	1	2	yes	—
102	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
103	C₈	—	61	2	no	—
104	C₈	—	61	2	no	—
105	C₈	—	122	2	no	—
106	C₂²	—	2	2	no	—
107	C₂²	—	2	2	no	—
108	C₂²	—	2	8	no	—
109	C₂²	C₂²⋊#92420	1	2	yes	—
110	C₂²	C₂×#11758187	1	2	yes	—
111	C₂²	C₂×#11758187	1	4	yes	complemented
112	C₂²	#14519851	1	2	yes	—
113	C₂²	C₂²×#92420	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	C₂²⋊#92420	1	2	yes	—
116	C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
117	C₄	C₂×#11758217	1	1	yes	characteristic
118	C₂	—	2	4	no	—
119	C₂	C₂²⋊#11758187	1	4	yes	direct product factor
120	C₂	C₂×C₂²⋊#92420	1	1	yes	characteristic
121	C₂	C₂²×#11758187	1	1	yes	characteristic
122	C₂	C₂×#14519851	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758187

C₂

yes

maximal, complemented

C₂²⋊#11758187

C₂

yes

maximal, direct product factor

C₂³×#92418

C₂

yes

maximal, characteristic

C₂×#11758187

—

C₂×#11758187

C₂²

yes

complemented

C₂²×#92418

—

C₂²×#92418

C₄

yes

characteristic

C₂²×#92418

C₄

yes

—

C₂²×#92418

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂³×C₄×C₆₁

C₄

yes

characteristic

C₂⁴×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₈

yes

—

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

C₂³

yes

characteristic

#11758187

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₁₆

yes

complemented

C₂³×C₆₁

C₂×C₈

yes

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×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

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

—

C₂²×C₆₁

C₂×C₁₆

yes

—

C₂²×C₆₁

C₂×C₁₆

yes

complemented

C₂²×C₆₁

M₃₂

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

C₂×C₂²⋊C₁₆

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂²⋊C₁₆

yes

complemented

C₂×C₆₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂³×C₈

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₆₁

C₂×C₂²⋊C₁₆

yes

characteristic, complemented, Sylow

C₂³×C₄

#6923

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂⁴

#92420

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#92420

yes

characteristic

C₂²×C₄

#92420

yes

—

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₁₆

—

122

—

C₂³

—

C₂³

—

C₂³

#11758187

yes

complemented

C₂³

C₂×#92420

yes

—

C₂³

C₂×#92420

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#92420

yes

—

C₂×C₄

C₂×#92420

yes

characteristic

100

C₂×C₄

#11758217

yes

—

101

C₂×C₄

C₂²⋊#6923

yes

—

102

C₂×C₄

C₂²×#6923

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

122

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂²⋊#92420

yes

—

110

C₂²

C₂×#11758187

yes

—

111

C₂²

C₂×#11758187

yes

complemented

112

C₂²

#14519851

yes

—

113

C₂²

C₂²×#92420

yes

characteristic

114

C₄

—

115

C₄

C₂²⋊#92420

yes

—

116

C₄

C₂×C₂²⋊#6923

yes

characteristic

117

C₄

C₂×#11758217

yes

characteristic

118

C₂

—

119

C₂

C₂²⋊#11758187

yes

direct product factor

120

C₂

C₂×C₂²⋊#92420

yes

characteristic

121

C₂

C₂²×#11758187

yes

characteristic

122

C₂

C₂×#14519851

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#6923
commutator	C₂×C₆₁	C₂²×C₁₆
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂³×C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂×C₈
hypercenter	C₂³×C₄	#6923
hypocenter	C₆₁	C₂×C₂²⋊C₁₆
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

subgroup

G/H

center

C₂²×C₄

C₂×#6923

commutator

C₂×C₆₁

C₂²×C₁₆

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂³×C₄×C₆₁

C₄

socle

C₂³×C₆₁

C₂×C₈

hypercenter

C₂³×C₄

#6923

hypocenter

C₆₁

C₂×C₂²⋊C₁₆

LCS

G ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

N	H ≅ G/N	type
1. C₂²×#11758187	C₂	semidirect
2. C₂²⋊#11758187	C₂	direct (N × H)
5. C₂×#11758187	C₂²	semidirect
29. C₂³×C₆₁	C₁₆	semidirect
49. C₂²×C₆₁	C₂×C₁₆	semidirect
58. C₂×C₆₁	C₂²⋊C₁₆	semidirect
65. C₆₁	C₂×C₂²⋊C₁₆	semidirect
91. C₂³	#11758187	semidirect
111. C₂²	C₂×#11758187	semidirect
119. C₂	C₂²⋊#11758187	direct (N × H)

H ≅ G/N

type

1. C₂²×#11758187

C₂

semidirect

2. C₂²⋊#11758187

C₂

direct (N × H)

5. C₂×#11758187

C₂²

semidirect

29. C₂³×C₆₁

C₁₆

semidirect

49. C₂²×C₆₁

C₂×C₁₆

semidirect

58. C₂×C₆₁

C₂²⋊C₁₆

semidirect

65. C₆₁

C₂×C₂²⋊C₁₆

semidirect

91. C₂³

#11758187

semidirect

111. C₂²

C₂×#11758187

semidirect

119. C₂

C₂²⋊#11758187

direct (N × H)

Subgroups — C₂×C₂²⋊#11758187 #21462043

Conjugacy classes of subgroups

Complements

Subgroups — C2×C22⋊#11758187 #21462043

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂²⋊#11758187 #21462043