Group #22627097 — subgroups

Subgroups — C₂×#17989684 #22627097

Order 9344.

272 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11924040	C₂	1	2	yes	maximal, complemented
2	#17989684	C₂	1	4	yes	maximal, direct product factor
3	C₂²×#11924036	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924040	—	2	4	no	—
5	C₂×#11924040	C₂²	1	4	yes	complemented
6	C₂×#11924036	—	2	4	no	—
7	C₂×#11924036	C₄	1	2	yes	—
8	C₂×#11924036	C₂²	1	2	yes	—
9	C₂²×#10596833	C₄	1	1	yes	characteristic
10	C₂²×#10596833	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₇₃	C₄	1	1	yes	characteristic
12	#11924040	—	2	4	no	—
13	#11924036	—	2	4	no	—
14	#11924036	—	2	4	no	—
15	C₂×#10596833	—	2	2	no	—
16	C₂×#10596833	C₂×C₄	1	2	yes	—
17	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596833	D₄	1	4	yes	—
19	C₂×#10596833	C₂³	1	1	yes	characteristic
20	C₂³×D₇₃	C₈	1	1	yes	characteristic
21	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₇₃	—	2	2	no	—
23	C₂×C₄×D₇₃	—	2	2	no	—
24	C₂×C₄×D₇₃	C₈	1	2	yes	—
25	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
27	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂²×D₇₃	—	2	2	no	—
29	C₂²×D₇₃	—	2	2	no	—
30	C₂²×D₇₃	C₁₆	1	4	yes	complemented
31	C₂²×D₇₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
34	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
35	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₃	M₁₆	1	2	yes	—
37	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₄×D₇₃	—	2	4	no	—
39	C₄×D₇₃	—	2	2	no	—
40	C₄×D₇₃	—	2	2	no	—
41	#10596833	—	2	2	no	—
42	#10596833	C₂²⋊C₄	1	2	yes	—
43	#10596833	C₂×D₄	1	2	yes	—
44	C₂²×C₇₃	C₂²⋊C₈	1	2	yes	—
45	C₂²×C₇₃	C₂×C₁₆	1	2	yes	—
46	C₂²×C₇₃	M₃₂	1	2	yes	—
47	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
48	C₂×D₇₃	—	2	8	no	—
49	C₂×D₇₃	—	2	2	no	—
50	C₂×D₇₃	—	2	2	no	—
51	C₂×D₇₃	C₂×C₁₆	1	4	yes	complemented
52	C₄×C₇₃	—	2	2	no	—
53	Dic₇₃	C₂²⋊C₈	1	2	yes	—
54	Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
56	C₂×C₇₃	C₂²⋊C₁₆	1	4	yes	complemented
57	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
58	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
59	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
60	D₇₃	—	2	4	no	—
61	C₂×C₂²⋊C₁₆	—	73	1	no	maximal, Sylow
62	C₇₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
63	C₂³×C₈	—	73	1	no	—
64	C₂²×C₁₆	—	73	2	no	—
65	C₂²⋊C₁₆	—	73	4	no	—
66	C₂³×C₄	—	73	1	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂²×C₈	—	73	2	no	—
70	C₂²×C₈	—	73	2	no	—
71	C₂²×C₈	—	146	4	no	—
72	C₂×C₁₆	—	73	4	no	—
73	C₂×C₁₆	—	146	4	no	—
74	C₂⁴	—	73	1	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	—	73	2	no	—
78	C₂²×C₄	—	146	2	no	—
79	C₂²×C₄	—	146	2	no	—
80	C₂²×C₄	#10596842	1	1	yes	characteristic
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	4	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	2	no	—
85	C₂×C₈	—	146	4	no	—
86	C₂×C₈	—	146	4	no	—
87	C₂×C₈	—	146	2	no	—
88	C₁₆	—	146	4	no	—
89	C₂³	—	73	4	no	—
90	C₂³	—	73	2	no	—
91	C₂³	—	146	2	no	—
92	C₂³	—	146	2	no	—
93	C₂³	C₂×#10596842	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	73	2	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	—	146	4	no	—
101	C₂×C₄	—	146	2	no	—
102	C₂×C₄	C₂×#10596842	1	2	yes	—
103	C₈	—	73	2	no	—
104	C₈	—	73	2	no	—
105	C₈	—	146	2	no	—
106	C₂²	—	73	4	no	—
107	C₂²	—	146	8	no	—
108	C₂²	—	146	2	no	—
109	C₂²	—	146	2	no	—
110	C₂²	C₂²⋊#10596842	1	2	yes	—
111	C₂²	#14556686	1	2	yes	—
112	C₂²	#14556688	1	2	yes	—
113	C₂²	C₂²×#10596842	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	73	1	no	—
116	C₄	—	73	2	no	—
117	C₄	—	73	1	no	—
118	C₂	—	146	4	no	—
119	C₂	#17989684	1	4	yes	direct product factor
120	C₂	C₂×C₂²⋊#10596842	1	1	yes	characteristic
121	C₂	C₂×#14556686	1	1	yes	characteristic
122	C₂	C₂×#14556688	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924040

C₂

yes

maximal, complemented

#17989684

C₂

yes

maximal, direct product factor

C₂²×#11924036

C₂

yes

maximal, characteristic

C₂×#11924040

—

C₂×#11924040

C₂²

yes

complemented

C₂×#11924036

—

C₂×#11924036

C₄

yes

—

C₂×#11924036

C₂²

yes

—

C₂²×#10596833

C₄

yes

characteristic

C₂²×#10596833

C₂²

yes

characteristic

C₂²×C₄×D₇₃

C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

D₄

yes

—

C₂×#10596833

C₂³

yes

characteristic

C₂³×D₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₈

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

C₁₆

yes

complemented

C₂²×D₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

M₁₆

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

#10596833

—

#10596833

C₂²⋊C₄

yes

—

#10596833

C₂×D₄

yes

—

C₂²×C₇₃

C₂²⋊C₈

yes

—

C₂²×C₇₃

C₂×C₁₆

yes

—

C₂²×C₇₃

M₃₂

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₁₆

yes

complemented

C₄×C₇₃

—

Dic₇₃

C₂²⋊C₈

yes

—

Dic₇₃

C₂×C₂²⋊C₄

yes

characteristic

Dic₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

C₂²⋊C₁₆

yes

complemented

C₂×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₇₃

C₂²×C₁₆

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

characteristic

D₇₃

—

C₂×C₂²⋊C₁₆

—

maximal, Sylow

C₇₃

C₂×C₂²⋊C₁₆

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₁₆

—

146

—

C₂³

—

C₂³

—

C₂³

—

146

—

C₂³

—

146

—

C₂³

C₂×#10596842

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

C₂×#10596842

yes

—

103

C₈

—

104

C₈

—

105

C₈

—

146

—

106

C₂²

—

107

C₂²

—

146

—

108

C₂²

—

146

—

109

C₂²

—

146

—

110

C₂²

C₂²⋊#10596842

yes

—

111

C₂²

#14556686

yes

—

112

C₂²

#14556688

yes

—

113

C₂²

C₂²×#10596842

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₂

—

146

—

119

C₂

#17989684

yes

direct product factor

120

C₂

C₂×C₂²⋊#10596842

yes

characteristic

121

C₂

C₂×#14556686

yes

characteristic

122

C₂

C₂×#14556688

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#10596842
commutator	C₂×C₇₃	C₂²×C₁₆
Frattini	C₂²	C₂²×#10596842
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂³×C₇₃	C₂×C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	C₂×C₂²⋊C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

subgroup

G/H

center

C₂³

C₂×#10596842

commutator

C₂×C₇₃

C₂²×C₁₆

Frattini

C₂²

C₂²×#10596842

Fitting

C₂²×C₄×C₇₃

C₈

socle

C₂³×C₇₃

C₂×C₈

hypercenter

C₂²×C₄

#10596842

hypocenter

C₇₃

C₂×C₂²⋊C₁₆

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄

N	H ≅ G/N	type
1. C₂²×#11924040	C₂	semidirect
2. #17989684	C₂	direct (N × H)
5. C₂×#11924040	C₂²	semidirect
30. C₂²×D₇₃	C₁₆	semidirect
51. C₂×D₇₃	C₂×C₁₆	semidirect
56. C₂×C₇₃	C₂²⋊C₁₆	semidirect
62. C₇₃	C₂×C₂²⋊C₁₆	semidirect
119. C₂	#17989684	direct (N × H)

H ≅ G/N

type

1. C₂²×#11924040

C₂

semidirect

2. #17989684

C₂

direct (N × H)

5. C₂×#11924040

C₂²

semidirect

30. C₂²×D₇₃

C₁₆

semidirect

51. C₂×D₇₃

C₂×C₁₆

semidirect

56. C₂×C₇₃

C₂²⋊C₁₆

semidirect

62. C₇₃

C₂×C₂²⋊C₁₆

semidirect

119. C₂

#17989684

direct (N × H)

Subgroups — C₂×#17989684 #22627097

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989684 #22627097

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989684 #22627097