Group #22589130 — subgroups

Subgroups — #22589130

Order 9088.

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

normal subgroups only

This group has 184 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	#17986047	C₂	1	2	yes	maximal
2	C₂×#14556064	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556064	C₂	1	1	yes	maximal, characteristic
4	#17985769	C₂	1	2	yes	maximal
5	#405×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	C₂²	1	2	yes	—
7	C₂×#11765849	C₂²	1	2	yes	—
8	#14556064	—	2	1	no	—
9	#14556064	—	2	1	no	—
10	#14556064	C₄	1	4	yes	complemented
11	#14556063	—	2	4	no	—
12	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	#117×C₇₁	C₂²	1	1	yes	characteristic
15	#97×C₇₁	—	2	1	no	—
16	C₄×C₈×C₇₁	—	2	1	no	—
17	#11765849	—	2	2	no	—
18	#11765849	—	2	2	no	—
19	#11765849	—	2	2	no	—
20	#11765849	C₂×C₄	1	4	yes	—
21	C₂×C₇₁⋊C₈	—	2	2	no	—
22	C₂×C₇₁⋊C₈	—	2	2	no	—
23	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
24	M₁₆×C₇₁	—	2	1	no	—
25	M₁₆×C₇₁	D₄	1	2	yes	—
26	C₂×C₈×C₇₁	—	2	1	no	—
27	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
28	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
30	C₂×C₈×C₇₁	Q₈	1	2	yes	—
31	C₄⋊C₄×C₇₁	—	2	1	no	—
32	C₂²⋊C₄×C₇₁	Q₈	1	2	yes	—
33	C₄²×C₇₁	—	2	1	no	—
34	C₂³×C₇₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₁	—	2	2	no	—
36	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
41	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
42	C₈×C₇₁	—	2	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	—	4	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	—	4	2	no	—
52	C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
54	C₄×C₇₁	#121	1	1	yes	characteristic
55	C₄×C₇₁	#125	1	1	yes	characteristic
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	—	71	1	no	—
65	#405	D₇₁	1	1	yes	characteristic
66	#344	—	71	2	no	—
67	C₂×M₁₆	—	71	2	no	—
68	C₂×M₁₆	—	71	2	no	—
69	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
71	#117	C₂×D₇₁	1	1	yes	characteristic
72	#108	—	71	4	no	—
73	#108	—	142	4	no	—
74	#108	—	142	1	no	—
75	#108	—	142	1	no	—
76	#97	—	2	1	no	—
77	C₄×C₈	—	2	1	no	—
78	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
79	M₁₆	—	2	1	no	—
80	M₁₆	—	71	4	no	—
81	M₁₆	—	142	2	no	—
82	M₁₆	—	142	2	no	—
83	M₁₆	—	142	2	no	—
84	M₁₆	D₂₈₄	1	2	yes	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	142	2	no	—
87	C₂×C₈	—	142	2	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	—	2	1	no	—
93	C₂²⋊C₄	Dic₁₄₂	1	2	yes	—
94	C₄²	—	2	1	no	—
95	C₂³	C₂×Dic₁₄₂	1	1	yes	characteristic
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
99	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
100	C₂×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
101	C₂×C₄	#11765865	1	1	yes	characteristic
102	C₂×C₄	#11765865	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	284	2	no	—
105	C₈	—	142	4	no	—
106	C₈	Dic₇₁⋊C₄	1	2	yes	—
107	C₈	Dic₇₁⋊C₄	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	C₄×Dic₁₄₂	1	1	yes	characteristic
110	C₂²	#14556107	1	1	yes	characteristic
111	C₂²	#14556128	1	1	yes	characteristic
112	C₄	—	4	2	no	—
113	C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
114	C₄	C₄×D₂₈₄	1	1	yes	characteristic
115	C₄	#14556102	1	1	yes	characteristic
116	C₄	#14556120	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#17985897	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986047

C₂

yes

maximal

C₂×#14556064

C₂

yes

maximal, characteristic

C₂×#14556064

C₂

yes

maximal, characteristic

#17985769

C₂

yes

maximal

#405×C₇₁

C₂

yes

maximal, characteristic

C₂×#11765849

C₂²

yes

—

C₂×#11765849

C₂²

yes

—

#14556064

—

#14556064

—

#14556064

C₄

yes

complemented

#14556063

—

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

C₂²×C₈×C₇₁

C₂²

yes

characteristic

#117×C₇₁

C₂²

yes

characteristic

#97×C₇₁

—

C₄×C₈×C₇₁

—

—

—

—

C₂×C₄

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

D₄

yes

—

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

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

Q₈

yes

—

C₄²×C₇₁

—

C₂³×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₁

—

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

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

—

C₄×C₇₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₁

C₄×D₄

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

—

—

—

D₇₁

yes

characteristic

#344

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

C₂²×C₈

C₂×D₇₁

yes

characteristic

#117

C₂×D₇₁

yes

characteristic

#108

—

#108

—

142

—

#108

—

142

—

#108

—

142

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

142

—

M₁₆

—

142

—

M₁₆

—

142

—

M₁₆

D₂₈₄

yes

—

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

—

C₂²⋊C₄

Dic₁₄₂

yes

—

C₄²

—

C₂³

C₂×Dic₁₄₂

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

100

C₂×C₄

C₂×Dic₁₄₂

yes

characteristic

101

C₂×C₄

#11765865

yes

characteristic

102

C₂×C₄

#11765865

yes

characteristic

103

C₈

—

104

C₈

—

284

—

105

C₈

—

142

—

106

C₈

Dic₇₁⋊C₄

yes

—

107

C₈

Dic₇₁⋊C₄

yes

—

108

C₂²

—

109

C₂²

C₄×Dic₁₄₂

yes

characteristic

110

C₂²

#14556107

yes

characteristic

111

C₂²

#14556128

yes

characteristic

112

C₄

—

113

C₄

C₂×Dic₇₁⋊C₄

yes

characteristic

114

C₄

C₄×D₂₈₄

yes

characteristic

115

C₄

#14556102

yes

characteristic

116

C₄

#14556120

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#17985897

yes

characteristic

	subgroup	G/H
center	C₄	#14556102
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#405×C₇₁	C₂
socle	C₂×C₇₁	#389
hypercenter	#405	D₇₁
hypocenter	C₇₁	#1953
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

subgroup

G/H

center

C₄

#14556102

commutator

C₂×C₄×C₇₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

#405×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

N	H ≅ G/N	type
10. #14556064	C₄	semidirect
61. C₇₁	#1953	semidirect

H ≅ G/N

type

10. #14556064

C₄

semidirect

61. C₇₁

#1953

semidirect

Subgroups — #22589130

Conjugacy classes of subgroups

Complements