Group #22627091 — subgroups

Subgroups — #64408⋊M₃₂ #22627091

Order 9344.

196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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	#17989706	C₂	1	2	yes	maximal
2	#17989682	C₂	1	2	yes	maximal, complemented
3	#64408⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
5	#14556688	C₄	1	4	yes	complemented
6	#14556687	C₄	1	4	yes	complemented
7	#14556686	C₂²	1	4	yes	—
8	C₂×#11924036	C₂²	1	1	yes	characteristic
9	C₂×C₄×#64408	C₄	1	1	yes	characteristic
10	C₈×#64408	C₄	1	1	yes	characteristic
11	C₈×#64408	C₄	1	1	yes	characteristic
12	C₈×#64408	C₂²	1	1	yes	characteristic
13	C₈×#64408	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
15	#11924040	C₂×C₄	1	8	yes	complemented
16	C₂²×#64408	C₈	1	2	yes	—
17	#11924036	C₂×C₄	1	1	yes	characteristic
18	#11924036	C₂×C₄	1	2	yes	—
19	#11924036	C₂³	1	1	yes	characteristic
20	C₂×#10596833	C₂×C₄	1	2	yes	—
21	C₄×#64408	C₈	1	2	yes	—
22	C₄×#64408	C₂×C₄	1	1	yes	characteristic
23	C₄×#64408	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×#10596831	C₈	1	1	yes	characteristic
26	C₈×D₇₃	C₈	1	1	yes	characteristic
27	C₈×D₇₃	C₈	1	1	yes	characteristic
28	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
29	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
31	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×#64408	—	2	4	no	—
33	C₂×#64408	C₂×C₈	1	2	yes	—
34	C₂×#64408	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
37	C₄×D₇₃	C₄²	1	1	yes	characteristic
38	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
39	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
40	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
41	#10596833	C₄²	1	2	yes	—
42	#10596833	C₂²×C₄	1	2	yes	—
43	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
44	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
45	#10596831	C₂×C₈	1	1	yes	characteristic
46	#10596831	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
48	C₂×D₇₃	—	2	2	no	—
49	C₂×D₇₃	C₄×C₈	1	1	yes	characteristic
50	C₂×D₇₃	C₂²×C₈	1	1	yes	characteristic
51	#64408	—	2	2	no	—
52	#64408	M₃₂	1	4	yes	complemented
53	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
54	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
55	Dic₇₃	C₄×C₈	1	1	yes	characteristic
56	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₇₃	—	2	1	no	—
58	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
59	D₇₃	—	2	1	no	—
60	D₇₃	C₂×M₃₂	1	2	yes	—
61	C₄×M₃₂	—	73	1	no	maximal, Sylow
62	C₇₃	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	73	2	no	—
64	C₂×C₄×C₈	—	73	1	no	—
65	#346	—	73	2	no	—
66	C₄×C₁₆	—	73	2	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂×C₄²	—	73	1	no	—
70	M₃₂	—	73	4	no	—
71	M₃₂	—	73	4	no	—
72	C₂×C₁₆	—	73	4	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₄×C₈	—	73	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	73	2	no	—
79	C₂×C₈	—	73	2	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	2	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	1	no	—
87	C₂×C₈	—	73	1	no	—
88	C₂×C₈	#10596842	1	1	yes	characteristic
89	C₄²	—	73	2	no	—
90	C₄²	—	73	1	no	—
91	C₄²	—	73	1	no	—
92	C₁₆	—	73	8	no	—
93	C₂³	—	73	1	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	146	4	no	—
102	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
103	C₈	—	73	2	no	—
104	C₈	—	73	2	no	—
105	C₈	—	73	1	no	—
106	C₈	—	73	1	no	—
107	C₈	C₂×#10596842	1	1	yes	characteristic
108	C₈	C₂×#10596842	1	1	yes	characteristic
109	C₂²	—	73	1	no	—
110	C₂²	—	73	1	no	—
111	C₂²	—	146	2	no	—
112	C₂²	C₄×#10596842	1	1	yes	characteristic
113	C₄	—	73	4	no	—
114	C₄	—	73	1	no	—
115	C₄	—	73	1	no	—
116	C₄	—	146	2	no	—
117	C₄	C₄×#10596842	1	1	yes	characteristic
118	C₄	C₂²×#10596842	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	73	2	no	—
121	C₂	—	146	1	no	—
122	C₂	C₂×C₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989706

C₂

yes

maximal

#17989682

C₂

yes

maximal, complemented

#64408⋊C₁₆

C₂

yes

maximal, complemented

C₂×C₈×#64408

C₂

yes

maximal, characteristic

#14556688

C₄

yes

complemented

#14556687

C₄

yes

complemented

#14556686

C₂²

yes

—

C₂×#11924036

C₂²

yes

characteristic

C₂×C₄×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₄

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

#11924040

C₂×C₄

yes

complemented

C₂²×#64408

C₈

yes

—

#11924036

C₂×C₄

yes

characteristic

#11924036

C₂×C₄

yes

—

#11924036

C₂³

yes

characteristic

C₂×#10596833

C₂×C₄

yes

—

C₄×#64408

C₈

yes

—

C₄×#64408

C₂×C₄

yes

characteristic

C₄×#64408

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic

C₈×D₇₃

C₈

yes

characteristic

C₈×D₇₃

C₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×#64408

—

C₂×#64408

C₂×C₈

yes

—

C₂×#64408

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₄²

yes

—

#10596833

C₂²×C₄

yes

—

C₈×C₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₂²×C₈

yes

characteristic

#64408

—

#64408

M₃₂

yes

complemented

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×C₈

yes

characteristic

Dic₇₃

C₂×C₄²

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

D₇₃

—

D₇₃

C₂×M₃₂

yes

—

C₄×M₃₂

—

maximal, Sylow

C₇₃

C₄×M₃₂

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10596842

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

146

—

102

C₂×C₄

C₂×#10596842

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

C₂×#10596842

yes

characteristic

108

C₈

C₂×#10596842

yes

characteristic

109

C₂²

—

110

C₂²

—

111

C₂²

—

146

—

112

C₂²

C₄×#10596842

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

146

—

117

C₄

C₄×#10596842

yes

characteristic

118

C₄

C₂²×#10596842

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

146

—

122

C₂

C₂×C₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₈	C₂×#10596842
commutator, socle	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₄	C₂²×#10596842
Fitting	C₂×C₈×C₇₃	C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	C₄×M₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈

subgroup

G/H

center

C₈

C₂×#10596842

commutator, socle

C₂×C₇₃

C₂×C₄×C₈

Frattini

C₄

C₂²×#10596842

Fitting

C₂×C₈×C₇₃

C₈

hypercenter

C₂×C₈

#10596842

hypocenter

C₇₃

C₄×M₃₂

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈

N	H ≅ G/N	type
2. #17989682	C₂	semidirect
3. #64408⋊C₁₆	C₂	semidirect
5. #14556688	C₄	semidirect
6. #14556687	C₄	semidirect
15. #11924040	C₂×C₄	semidirect
52. #64408	M₃₂	semidirect
62. C₇₃	C₄×M₃₂	semidirect

H ≅ G/N

type

2. #17989682

C₂

semidirect

3. #64408⋊C₁₆

C₂

semidirect

5. #14556688

C₄

semidirect

6. #14556687

C₄

semidirect

15. #11924040

C₂×C₄

semidirect

52. #64408

M₃₂

semidirect

62. C₇₃

C₄×M₃₂

semidirect

Subgroups — #64408⋊M₃₂ #22627091

Conjugacy classes of subgroups

Complements

Subgroups — #64408⋊M32 #22627091

Conjugacy classes of subgroups

Complements

Subgroups — #64408⋊M₃₂ #22627091