Group #22590105 — subgroups

Subgroups — #22590105

Order 9088.

152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556068	C₂	1	1	yes	maximal, characteristic
2	#17985954	C₂	1	1	yes	maximal, characteristic
3	#17985819	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11765849	C₄	1	1	yes	characteristic
6	#14556087	C₄	1	1	yes	characteristic
7	#14556068	—	2	1	no	—
8	#14556068	C₂²	1	2	yes	—
9	C₂×C₇₁⋊C₁₆	—	2	1	no	—
10	#14556038	C₄	1	2	yes	—
11	C₈×Dic₇₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
13	M₃₂×C₇₁	—	2	1	no	—
14	M₃₂×C₇₁	C₂²	1	2	yes	—
15	C₂×C₁₆×C₇₁	—	2	1	no	—
16	#11765849	C₈	1	2	yes	—
17	#11765849	C₈	1	2	yes	—
18	C₂×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
19	C₄⋊Dic₇₁	—	2	1	no	—
20	C₂²⋊Dic₇₁	—	2	1	no	—
21	C₄×Dic₇₁	C₂×C₄	1	2	yes	—
22	C₇₁⋊C₁₆	—	2	2	no	—
23	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
29	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
30	C₁₆×C₇₁	—	2	2	no	—
31	C₂³×C₇₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₇₁	—	2	2	no	—
39	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
42	C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
43	C₇₁⋊C₈	C₂×C₈	1	4	yes	—
44	C₂²×C₇₁	—	4	1	no	—
45	C₂²×C₇₁	C₄⋊C₈	1	1	yes	characteristic
46	C₂²×C₇₁	C₄⋊C₈	1	1	yes	characteristic
47	C₂²×C₇₁	C₂×M₁₆	1	1	yes	characteristic
48	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
49	C₄×C₇₁	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
52	Dic₇₁	—	4	2	no	—
53	C₂×C₇₁	—	2	1	no	—
54	C₂×C₇₁	—	2	1	no	—
55	C₂×C₇₁	—	2	1	no	—
56	C₂×C₇₁	C₂×C₄⋊C₈	1	1	yes	characteristic
57	#2153	—	71	1	no	maximal, Sylow
58	C₇₁	#2153	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₃₂	—	71	1	no	—
60	C₂×M₃₂	D₇₁	1	1	yes	characteristic
61	#405	—	71	1	no	—
62	#364	—	71	4	no	—
63	C₂×M₁₆	—	71	1	no	—
64	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
65	#117	—	71	1	no	—
66	M₃₂	—	2	1	no	—
67	M₃₂	—	71	2	no	—
68	M₃₂	—	142	1	no	—
69	M₃₂	C₂×D₇₁	1	2	yes	—
70	C₂×C₁₆	—	2	1	no	—
71	C₂×C₁₆	—	142	1	no	—
72	#97	—	71	2	no	—
73	C₄×C₈	—	71	2	no	—
74	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
75	M₁₆	—	71	2	no	—
76	M₁₆	—	71	2	no	—
77	C₂×C₈	—	71	2	no	—
78	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
79	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
80	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
84	C₄⋊C₄	—	142	1	no	—
85	C₂²⋊C₄	—	142	1	no	—
86	C₄²	—	71	2	no	—
87	C₁₆	—	2	2	no	—
88	C₁₆	—	142	2	no	—
89	C₂³	#11765848	1	1	yes	characteristic
90	C₂×C₄	—	142	2	no	—
91	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
92	C₂×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
93	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
94	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
95	C₂×C₄	#11765848	1	1	yes	characteristic
96	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
97	C₈	—	71	4	no	—
98	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
99	C₈	Dic₇₁⋊C₄	1	1	yes	characteristic
100	C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
101	C₈	C₂×Dic₁₄₂	1	1	yes	characteristic
102	C₂²	—	4	1	no	—
103	C₂²	Dic₇₁⋊C₈	1	1	yes	characteristic
104	C₂²	Dic₇₁⋊C₈	1	1	yes	characteristic
105	C₂²	C₂×#11765848	1	1	yes	characteristic
106	C₄	—	284	2	no	—
107	C₄	Dic₇₁⋊C₈	1	1	yes	characteristic
108	C₄	Dic₇₁⋊C₈	1	1	yes	characteristic
109	C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
110	C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	C₂×Dic₇₁⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556068

C₂

yes

maximal, characteristic

#17985954

C₂

yes

maximal, characteristic

#17985819

C₂

yes

maximal, complemented

C₂×M₃₂×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₄

yes

characteristic

#14556087

C₄

yes

characteristic

#14556068

—

#14556068

C₂²

yes

—

C₂×C₇₁⋊C₁₆

—

#14556038

C₄

yes

—

C₈×Dic₇₁

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

—

M₃₂×C₇₁

C₂²

yes

—

C₂×C₁₆×C₇₁

—

#11765849

C₈

yes

—

#11765849

C₈

yes

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

C₂×C₄

yes

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

M₁₆

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

M₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

—

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₄⋊C₄

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

C₂×Q₈

yes

characteristic

C₇₁⋊C₈

C₂×C₈

yes

—

C₂²×C₇₁

—

C₂²×C₇₁

C₄⋊C₈

yes

characteristic

C₂²×C₇₁

C₄⋊C₈

yes

characteristic

C₂²×C₇₁

C₂×M₁₆

yes

characteristic

C₄×C₇₁

C₄⋊C₈

yes

characteristic

C₄×C₇₁

C₄⋊C₈

yes

characteristic

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₂²×C₈

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

C₂×C₄⋊C₈

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

D₇₁

yes

characteristic

#405

—

#364

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

142

—

M₃₂

C₂×D₇₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

142

—

#97

—

C₄×C₈

—

C₂²×C₄

C₄×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

Dic₁₄₂

yes

characteristic

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

142

—

C₄²

—

C₁₆

—

C₁₆

—

142

—

C₂³

#11765848

yes

characteristic

C₂×C₄

—

142

—

C₂×C₄

Dic₇₁⋊C₄

yes

characteristic

C₂×C₄

Dic₇₁⋊C₄

yes

characteristic

C₂×C₄

C₈×D₇₁

yes

characteristic

C₂×C₄

C₈×D₇₁

yes

characteristic

C₂×C₄

#11765848

yes

characteristic

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

C₈

Dic₇₁⋊C₄

yes

characteristic

C₈

Dic₇₁⋊C₄

yes

characteristic

100

C₈

C₂×C₂²⋊D₇₁

yes

characteristic

101

C₈

C₂×Dic₁₄₂

yes

characteristic

102

C₂²

—

103

C₂²

Dic₇₁⋊C₈

yes

characteristic

104

C₂²

Dic₇₁⋊C₈

yes

characteristic

105

C₂²

C₂×#11765848

yes

characteristic

106

C₄

—

284

—

107

C₄

Dic₇₁⋊C₈

yes

characteristic

108

C₄

Dic₇₁⋊C₈

yes

characteristic

109

C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

110

C₄

C₂×C₈×D₇₁

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

—

114

C₂

C₂×Dic₇₁⋊C₈

yes

characteristic

	subgroup	G/H
center	C₈	C₂×C₂²⋊D₇₁
commutator	C₄×C₇₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×M₃₂×C₇₁	C₂
socle	C₂×C₇₁	C₂×C₄⋊C₈
hypercenter	C₂×M₃₂	D₇₁
hypocenter	C₇₁	#2153
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₈

C₂×C₂²⋊D₇₁

commutator

C₄×C₇₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×M₃₂×C₇₁

C₂

socle

C₂×C₇₁

C₂×C₄⋊C₈

hypercenter

C₂×M₃₂

D₇₁

hypocenter

C₇₁

#2153

LCS

G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #17985819	C₂	semidirect
58. C₇₁	#2153	semidirect

H ≅ G/N

type

3. #17985819

C₂

semidirect

58. C₇₁

#2153

semidirect

Subgroups — #22590105

Conjugacy classes of subgroups

Complements