Group #22589128 — subgroups

Subgroups — #22589128

Order 9088.

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

normal subgroups only

This group has 184 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	#17986047	C₂	1	2	yes	maximal
2	C₂×#14556064	C₂	1	1	yes	maximal, characteristic
3	#17985954	C₂	1	1	yes	maximal, characteristic
4	#17985770	C₂	1	2	yes	maximal
5	C₂×#108×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	C₂²	1	2	yes	—
7	C₂×#11765849	C₂²	1	1	yes	characteristic
8	#14556087	C₂²	1	1	yes	characteristic
9	#14556064	C₄	1	4	yes	complemented
10	#14556063	—	2	4	no	—
11	#14556038	—	2	1	no	—
12	C₈×Dic₇₁	—	2	1	no	—
13	C₂×M₁₆×C₇₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	#108×C₇₁	—	2	1	no	—
16	#108×C₇₁	—	2	1	no	—
17	#11765849	—	2	1	no	—
18	#11765849	—	2	2	no	—
19	#11765849	C₂×C₄	1	4	yes	—
20	#11765849	D₄	1	2	yes	—
21	C₂×C₇₁⋊C₈	—	2	1	no	—
22	C₂×C₇₁⋊C₈	—	2	2	no	—
23	C₄⋊Dic₇₁	—	2	1	no	—
24	C₂²⋊Dic₇₁	Q₈	1	2	yes	—
25	C₄×Dic₇₁	—	2	1	no	—
26	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
27	M₁₆×C₇₁	—	2	2	no	—
28	M₁₆×C₇₁	—	2	2	no	—
29	C₂×C₈×C₇₁	—	2	2	no	—
30	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₁	Q₈	1	2	yes	—
34	C₂³×C₇₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
40	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
41	C₂×Dic₇₁	—	2	2	no	—
42	C₈×C₇₁	—	4	2	no	—
43	C₈×C₇₁	C₄⋊C₄	1	2	yes	—
44	C₈×C₇₁	C₄⋊C₄	1	2	yes	—
45	C₇₁⋊C₈	—	2	4	no	—
46	C₇₁⋊C₈	—	2	2	no	—
47	C₂²×C₇₁	—	4	1	no	—
48	C₂²×C₇₁	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
53	C₄×C₇₁	#121	1	1	yes	characteristic
54	C₄×C₇₁	#125	1	1	yes	characteristic
55	Dic₇₁	—	4	2	no	—
56	C₂×C₇₁	—	2	1	no	—
57	C₂×C₇₁	—	2	1	no	—
58	C₂×C₇₁	—	2	1	no	—
59	C₂×C₇₁	#389	1	1	yes	characteristic
60	#1953	—	71	1	no	maximal, Sylow
61	C₇₁	#1953	1	1	yes	characteristic, complemented, Sylow
62	#430	—	71	2	no	—
63	C₂×#108	—	71	1	no	—
64	C₂×#108	D₇₁	1	1	yes	characteristic
65	#405	—	71	1	no	—
66	#344	—	71	2	no	—
67	C₂×M₁₆	—	71	2	no	—
68	C₂×M₁₆	—	71	1	no	—
69	C₂×M₁₆	C₂×D₇₁	1	2	yes	—
70	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
71	#117	—	71	1	no	—
72	#108	—	2	1	no	—
73	#108	—	2	1	no	—
74	#108	—	71	4	no	—
75	#108	—	142	4	no	—
76	#97	—	142	1	no	—
77	C₄×C₈	—	142	1	no	—
78	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	2	2	no	—
81	M₁₆	—	71	4	no	—
82	M₁₆	—	71	2	no	—
83	M₁₆	—	142	1	no	—
84	M₁₆	—	142	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	142	2	no	—
87	C₂×C₈	—	142	1	no	—
88	C₂×C₈	Dic₁₄₂	1	2	yes	—
89	C₂×C₈	C₄×D₇₁	1	2	yes	—
90	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
91	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
92	C₄⋊C₄	—	142	1	no	—
93	C₂²⋊C₄	—	71	2	no	—
94	C₄²	—	142	1	no	—
95	C₂³	Q₈×D₇₁	1	1	yes	characteristic
96	C₂×C₄	—	142	2	no	—
97	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
98	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
100	C₂×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
101	C₂×C₄	#11765864	1	1	yes	characteristic
102	C₂×C₄	#11765866	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	142	4	no	—
105	C₈	—	142	2	no	—
106	C₈	Dic₇₁⋊C₄	1	2	yes	—
107	C₈	Dic₇₁⋊C₄	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#14556093	1	1	yes	characteristic
110	C₂²	#14556104	1	1	yes	characteristic
111	C₂²	#14556127	1	1	yes	characteristic
112	C₄	—	284	2	no	—
113	C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
114	C₄	#14556090	1	1	yes	characteristic
115	C₄	#14556099	1	1	yes	characteristic
116	C₄	#14556119	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#17985895	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986047

C₂

yes

maximal

C₂×#14556064

C₂

yes

maximal, characteristic

#17985954

C₂

yes

maximal, characteristic

#17985770

C₂

yes

maximal

C₂×#108×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₂²

yes

—

C₂×#11765849

C₂²

yes

characteristic

#14556087

C₂²

yes

characteristic

#14556064

C₄

yes

complemented

#14556063

—

#14556038

—

C₈×Dic₇₁

—

C₂×M₁₆×C₇₁

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

#108×C₇₁

—

#108×C₇₁

—

#11765849

—

#11765849

—

#11765849

C₂×C₄

yes

—

#11765849

D₄

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

Q₈

yes

—

C₄×Dic₇₁

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂×C₄

yes

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

Q₈

yes

—

C₂³×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₈

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

C₄⋊C₄

yes

—

C₈×C₇₁

C₄⋊C₄

yes

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₄×Q₈

yes

characteristic

C₂²×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₁

C₄⋊Q₈

yes

characteristic

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₄×D₄

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

#430

—

C₂×#108

—

C₂×#108

D₇₁

yes

characteristic

#405

—

#344

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₁

yes

—

C₂²×C₈

C₂×D₇₁

yes

—

—

—

—

—

142

—

#97

—

142

—

C₄×C₈

—

142

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

142

—

M₁₆

—

142

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

Dic₁₄₂

yes

—

C₂×C₈

C₄×D₇₁

yes

—

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

C₄²

—

142

—

C₂³

Q₈×D₇₁

yes

characteristic

C₂×C₄

—

142

—

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₂×C₄

D₄×D₇₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

100

C₂×C₄

C₂×Dic₁₄₂

yes

characteristic

101

C₂×C₄

#11765864

yes

characteristic

102

C₂×C₄

#11765866

yes

characteristic

103

C₈

—

104

C₈

—

142

—

105

C₈

—

142

—

106

C₈

Dic₇₁⋊C₄

yes

—

107

C₈

Dic₇₁⋊C₄

yes

—

108

C₂²

—

109

C₂²

#14556093

yes

characteristic

110

C₂²

#14556104

yes

characteristic

111

C₂²

#14556127

yes

characteristic

112

C₄

—

284

—

113

C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

114

C₄

#14556090

yes

characteristic

115

C₄

#14556099

yes

characteristic

116

C₄

#14556119

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#17985895

yes

characteristic

	subgroup	G/H
center	C₄	#14556099
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	C₂×#108×C₇₁	C₂
socle	C₂×C₇₁	#389
hypercenter	C₂×#108	D₇₁
hypocenter	C₇₁	#1953
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#14556099

commutator

C₂×C₄×C₇₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

C₂×#108×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
9. #14556064	C₄	semidirect
61. C₇₁	#1953	semidirect

H ≅ G/N

type

9. #14556064

C₄

semidirect

61. C₇₁

#1953

semidirect

Subgroups — #22589128

Conjugacy classes of subgroups

Complements