Group #22590137 — subgroups

Subgroups — #22590137

Order 9088.

160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄×C₈×D₇₁	C₂	1	1	yes	maximal, characteristic
2	Dic₇₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₇₁)⋊C₁₆	C₂	1	2	yes	maximal
4	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₁	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₁	C₂²	1	1	yes	characteristic
8	C₄²×D₇₁	C₄	1	1	yes	characteristic
9	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
10	C₄×C₇₁⋊C₈	C₄	1	1	yes	characteristic
11	C₈×Dic₇₁	C₄	1	1	yes	characteristic
12	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
14	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₇₁	C₈	1	1	yes	characteristic
16	C₂×C₄×D₇₁	C₈	1	1	yes	characteristic
17	C₂×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
20	C₈×D₇₁	—	2	2	no	—
21	C₈×D₇₁	—	2	2	no	—
22	C₄×Dic₇₁	C₈	1	1	yes	characteristic
23	C₄×Dic₇₁	C₈	1	1	yes	characteristic
24	C₄×Dic₇₁	C₂×C₄	1	1	yes	characteristic
25	C₇₁⋊C₁₆	—	2	2	no	—
26	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
28	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
29	C₁₆×C₇₁	—	2	2	no	—
30	C₂²×D₇₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₁	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₇₁	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₇₁	C₂×C₈	1	1	yes	characteristic
37	C₄×D₇₁	—	2	2	no	—
38	C₄×D₇₁	—	2	1	no	—
39	C₄×D₇₁	—	2	1	no	—
40	C₄×D₇₁	C₁₆	1	4	yes	complemented
41	C₈×C₇₁	M₁₆	1	2	yes	—
42	C₈×C₇₁	#41	1	2	yes	—
43	C₇₁⋊C₈	—	2	1	no	—
44	C₇₁⋊C₈	—	2	1	no	—
45	C₂²×C₇₁	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₇₁	—	2	1	no	—
47	C₂×D₇₁	—	2	1	no	—
48	C₂×D₇₁	C₂×C₁₆	1	2	yes	—
49	C₄×C₇₁	C₂×C₁₆	1	2	yes	—
50	C₄×C₇₁	M₃₂	1	2	yes	—
51	C₄×C₇₁	#117	1	1	yes	characteristic
52	C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
53	Dic₇₁	—	2	1	no	—
54	Dic₇₁	—	2	1	no	—
55	Dic₇₁	C₂×C₁₆	1	2	yes	—
56	C₂×C₇₁	#431	1	1	yes	characteristic
57	C₂×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
58	C₂×C₇₁	C₂×M₃₂	1	1	yes	characteristic
59	D₇₁	—	2	2	no	—
60	#2162	—	71	1	no	maximal, Sylow
61	C₇₁	#2162	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₄×C₈	—	71	1	no	—
63	C₄⋊C₁₆	—	71	2	no	—
64	C₂²⋊C₁₆	—	71	2	no	—
65	C₄×C₁₆	—	71	1	no	—
66	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
67	C₂²×C₈	—	71	1	no	—
68	C₂²×C₈	—	71	1	no	—
69	C₂×C₄²	—	71	1	no	—
70	C₂×C₁₆	—	71	2	no	—
71	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
72	C₄×C₈	—	71	1	no	—
73	C₄×C₈	—	71	1	no	—
74	C₄×C₈	—	71	1	no	—
75	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
76	C₂²×C₄	—	71	1	no	—
77	C₂²×C₄	—	71	1	no	—
78	C₂²×C₄	—	71	1	no	—
79	C₂×C₈	—	71	1	no	—
80	C₂×C₈	—	71	1	no	—
81	C₂×C₈	—	142	2	no	—
82	C₂×C₈	—	142	2	no	—
83	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
85	C₄²	—	71	1	no	—
86	C₄²	—	71	1	no	—
87	C₄²	—	71	1	no	—
88	C₄²	C₄×D₇₁	1	1	yes	characteristic
89	C₁₆	—	2	2	no	—
90	C₁₆	—	142	2	no	—
91	C₂³	—	71	1	no	—
92	C₂×C₄	—	71	1	no	—
93	C₂×C₄	—	71	4	no	—
94	C₂×C₄	—	71	1	no	—
95	C₂×C₄	—	71	1	no	—
96	C₂×C₄	—	142	2	no	—
97	C₂×C₄	—	142	1	no	—
98	C₂×C₄	—	142	1	no	—
99	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
100	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
102	C₈	—	142	1	no	—
103	C₈	—	142	1	no	—
104	C₈	#11765848	1	2	yes	—
105	C₈	#11765865	1	2	yes	—
106	C₂²	—	71	2	no	—
107	C₂²	—	142	1	no	—
108	C₂²	—	142	1	no	—
109	C₂²	C₂×C₈×D₇₁	1	1	yes	characteristic
110	C₄	—	71	2	no	—
111	C₄	—	142	1	no	—
112	C₄	—	142	1	no	—
113	C₄	C₁₆×D₇₁	1	2	yes	—
114	C₄	#14556067	1	2	yes	—
115	C₄	#14556085	1	1	yes	characteristic
116	C₄	C₂×#11765848	1	1	yes	characteristic
117	C₂	—	142	2	no	—
118	C₂	#17986050	1	1	yes	characteristic
119	C₂	C₂×C₁₆×D₇₁	1	1	yes	characteristic
120	C₂	C₂×#14556067	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₇₁

C₂

yes

maximal, characteristic

Dic₇₁⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₇₁)⋊C₁₆

C₂

yes

maximal

C₄×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₁

C₄

yes

characteristic

C₂×C₈×D₇₁

C₂²

yes

characteristic

C₄²×D₇₁

C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

—

C₄×C₇₁⋊C₈

C₄

yes

characteristic

C₈×Dic₇₁

C₄

yes

characteristic

C₈×Dic₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₄×D₇₁

C₈

yes

characteristic

C₂×C₄×D₇₁

C₈

yes

characteristic

C₂×C₄×D₇₁

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₈×D₇₁

—

C₈×D₇₁

—

C₄×Dic₇₁

C₈

yes

characteristic

C₄×Dic₇₁

C₈

yes

characteristic

C₄×Dic₇₁

C₂×C₄

yes

characteristic

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂²×D₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

characteristic

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

C₁₆

yes

complemented

C₈×C₇₁

M₁₆

yes

—

C₈×C₇₁

#41

yes

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

C₂²×C₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

C₂×C₁₆

yes

—

C₄×C₇₁

C₂×C₁₆

yes

—

C₄×C₇₁

M₃₂

yes

—

C₄×C₇₁

#117

yes

characteristic

C₄×C₇₁

C₂×M₁₆

yes

characteristic

Dic₇₁

—

Dic₇₁

—

Dic₇₁

C₂×C₁₆

yes

—

C₂×C₇₁

#431

yes

characteristic

C₂×C₇₁

C₂²×C₁₆

yes

characteristic

C₂×C₇₁

C₂×M₃₂

yes

characteristic

D₇₁

—

#2162

—

maximal, Sylow

C₇₁

#2162

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

142

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

C₈×D₇₁

yes

characteristic

100

C₂×C₄

C₈×D₇₁

yes

characteristic

101

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

102

C₈

—

142

—

103

C₈

—

142

—

104

C₈

#11765848

yes

—

105

C₈

#11765865

yes

—

106

C₂²

—

107

C₂²

—

142

—

108

C₂²

—

142

—

109

C₂²

C₂×C₈×D₇₁

yes

characteristic

110

C₄

—

111

C₄

—

142

—

112

C₄

—

142

—

113

C₄

C₁₆×D₇₁

yes

—

114

C₄

#14556067

yes

—

115

C₄

#14556085

yes

characteristic

116

C₄

C₂×#11765848

yes

characteristic

117

C₂

—

142

—

118

C₂

#17986050

yes

characteristic

119

C₂

C₂×C₁₆×D₇₁

yes

characteristic

120

C₂

C₂×#14556067

yes

characteristic

	subgroup	G/H
center	C₄×C₈	C₂×D₇₁
commutator	C₂×C₇₁	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	#2162
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₄×C₈

C₂×D₇₁

commutator

C₂×C₇₁

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²×C₈

hypercenter

C₄×C₁₆

D₇₁

C₇₁

G ▷ C₂×C₇₁ ▷ C₇₁

C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. Dic₇₁⋊C₁₆	C₂	semidirect
4. C₄×C₇₁⋊C₁₆	C₂	semidirect
5. C₄×C₁₆×C₇₁	C₂	semidirect
40. C₄×D₇₁	C₁₆	semidirect
61. C₇₁	#2162	semidirect
66. C₄×C₁₆	D₇₁	semidirect

H ≅ G/N

type

2. Dic₇₁⋊C₁₆

C₂

semidirect

4. C₄×C₇₁⋊C₁₆

C₂

semidirect

5. C₄×C₁₆×C₇₁

C₂

semidirect

40. C₄×D₇₁

C₁₆

semidirect

61. C₇₁

#2162

semidirect

66. C₄×C₁₆

D₇₁

semidirect

Subgroups — #22590137

Conjugacy classes of subgroups

Complements