Group #22589892 — subgroups

Subgroups — #22589892

Order 9088.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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	#17986027	C₂	1	2	yes	maximal, complemented
2	#17986015	C₂	1	2	yes	maximal
3	#17985967	C₂	1	1	yes	maximal, characteristic
4	#17985756	C₂	1	1	yes	maximal, characteristic, complemented
5	#430×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11765865	C₂²	1	1	yes	characteristic
7	C₂²×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
8	#14556087	C₂²	1	2	yes	—
9	Dic₇₁⋊C₈	—	2	4	no	—
10	#14556054	—	2	4	no	—
11	(C₂×D₇₁)⋊C₈	—	2	2	no	—
12	C₂×M₁₆×C₇₁	C₂²	1	2	yes	—
13	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	#108×C₇₁	—	2	2	no	—
15	#11765865	—	2	2	no	—
16	#11765865	—	2	2	no	—
17	C₂×Dic₁₄₂	Q₈	1	1	yes	characteristic
18	C₂×D₂₈₄	Q₈	1	1	yes	characteristic
19	C₂×C₂²⋊D₇₁	—	2	1	no	—
20	C₂×C₄×D₇₁	—	2	1	no	—
21	C₂×C₇₁⋊C₈	—	2	1	no	—
22	C₂×C₇₁⋊C₈	—	2	2	no	—
23	C₄⋊Dic₇₁	—	2	2	no	—
24	C₂²⋊Dic₇₁	—	2	2	no	—
25	C₄×Dic₇₁	D₄	1	4	yes	—
26	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
27	M₁₆×C₇₁	—	2	2	no	—
28	M₁₆×C₇₁	—	2	2	no	—
29	M₁₆×C₇₁	—	2	2	no	—
30	C₂×C₈×C₇₁	—	2	2	no	—
31	C₂×C₈×C₇₁	D₄	1	2	yes	—
32	C₂³×C₇₁	#41	1	1	yes	characteristic
33	C₂²×D₇₁	—	2	1	no	—
34	C₂×C₄×C₇₁	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₇₁	#41	1	2	yes	—
38	C₂²⋊D₇₁	—	4	2	no	—
39	C₂×Dic₇₁	—	2	1	no	—
40	C₂×Dic₇₁	—	2	4	no	—
41	D₂₈₄	—	2	2	no	—
42	C₄×D₇₁	—	4	1	no	—
43	C₄×D₇₁	—	4	1	no	—
44	Dic₁₄₂	—	2	2	no	—
45	C₈×C₇₁	—	2	2	no	—
46	C₈×C₇₁	—	4	2	no	—
47	C₇₁⋊C₈	—	4	1	no	—
48	C₂²×C₇₁	—	4	1	no	—
49	C₂²×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₇₁	#123	1	2	yes	—
51	C₂×D₇₁	—	4	2	no	—
52	C₂×D₇₁	—	4	1	no	—
53	C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
54	C₄×C₇₁	#123	1	1	yes	characteristic
55	C₄×C₇₁	#127	1	1	yes	characteristic
56	Dic₇₁	—	4	4	no	—
57	Dic₇₁	—	4	1	no	—
58	C₂×C₇₁	—	2	2	no	—
59	C₂×C₇₁	—	2	1	no	—
60	C₂×C₇₁	#399	1	1	yes	characteristic
61	D₇₁	—	8	1	no	—
62	#2098	—	71	1	no	maximal, Sylow
63	C₇₁	#2098	1	1	yes	characteristic, complemented, Sylow
64	#430	D₇₁	1	1	yes	characteristic, complemented
65	#424	—	71	2	no	—
66	#421	—	71	2	no	—
67	#408	—	71	1	no	—
68	H(3,ℤ/4)	—	71	1	no	—
69	C₂×#41	—	71	1	no	—
70	C₂×M₁₆	C₂×D₇₁	1	2	yes	—
71	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
72	C₂²×C₈	—	71	1	no	—
73	#117	—	71	2	no	—
74	#108	—	2	2	no	—
75	C₄⋊C₈	—	142	4	no	—
76	#104	—	142	4	no	—
77	C₂²⋊C₈	—	142	2	no	—
78	#41	—	142	2	no	—
79	#41	—	142	2	no	—
80	C₂×Q₈	—	71	1	no	—
81	C₂×D₄	—	71	1	no	—
82	C₂×D₄	—	142	1	no	—
83	C₂²×C₄	—	142	1	no	—
84	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	142	2	no	—
90	C₂×C₈	—	142	1	no	—
91	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
92	C₄⋊C₄	—	142	2	no	—
93	C₂²⋊C₄	—	142	2	no	—
94	C₄²	—	71	4	no	—
95	C₂³	—	142	1	no	—
96	C₂³	#11765866	1	1	yes	characteristic
97	Q₈	—	142	2	no	—
98	D₄	—	284	2	no	—
99	D₄	—	142	2	no	—
100	C₂×C₄	—	284	1	no	—
101	C₂×C₄	—	284	1	no	—
102	C₂×C₄	—	142	1	no	—
103	C₂×C₄	—	142	4	no	—
104	C₂×C₄	D₄×D₇₁	1	2	yes	—
105	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₇₁	1	1	yes	characteristic
107	C₂×C₄	#11765865	1	2	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	4	2	no	—
110	C₈	—	284	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	284	2	no	—
113	C₂²	—	284	1	no	—
114	C₂²	#14556104	1	1	yes	characteristic
115	C₂²	#14556113	1	2	yes	—
116	C₄	—	284	4	no	—
117	C₄	—	284	1	no	—
118	C₄	#14556106	1	2	yes	—
119	C₄	#14556111	1	1	yes	characteristic
120	C₄	#14556124	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	568	1	no	—
124	C₂	#17985934	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986027

C₂

yes

maximal, complemented

#17986015

C₂

yes

maximal

#17985967

C₂

yes

maximal, characteristic

#17985756

C₂

yes

maximal, characteristic, complemented

#430×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#11765865

C₂²

yes

characteristic

C₂²×C₇₁⋊C₈

C₂²

yes

characteristic

#14556087

C₂²

yes

—

Dic₇₁⋊C₈

—

#14556054

—

(C₂×D₇₁)⋊C₈

—

C₂×M₁₆×C₇₁

C₂²

yes

—

C₂×M₁₆×C₇₁

C₂²

yes

characteristic

#108×C₇₁

—

#11765865

—

#11765865

—

C₂×Dic₁₄₂

Q₈

yes

characteristic

C₂×D₂₈₄

Q₈

yes

characteristic

C₂×C₂²⋊D₇₁

—

C₂×C₄×D₇₁

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

D₄

yes

—

C₂²×C₄×C₇₁

C₂³

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

—

C₂³×C₇₁

#41

yes

characteristic

C₂²×D₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₁

#41

yes

—

C₂²⋊D₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₇₁

#123

yes

—

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

C₂²⋊Q₈

yes

—

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#399

yes

characteristic

D₇₁

—

#2098

—

maximal, Sylow

C₇₁

#2098

yes

characteristic, complemented, Sylow

#430

D₇₁

yes

characteristic, complemented

—

—

—

—

C₂×#41

—

C₂×M₁₆

C₂×D₇₁

yes

—

C₂×M₁₆

C₂×D₇₁

yes

characteristic

C₂²×C₈

—

#117

—

#108

—

C₄⋊C₈

—

142

—

#104

—

142

—

C₂²⋊C₈

—

142

—

#41

—

142

—

#41

—

142

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

142

—

C₂²×C₄

—

142

—

C₂²×C₄

C₂²×D₇₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₂²⋊D₇₁

yes

—

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

142

—

C₄²

—

C₂³

—

142

—

C₂³

#11765866

yes

characteristic

Q₈

—

142

—

D₄

—

284

—

D₄

—

142

—

100

C₂×C₄

—

284

—

101

C₂×C₄

—

284

—

102

C₂×C₄

—

142

—

103

C₂×C₄

—

142

—

104

C₂×C₄

D₄×D₇₁

yes

—

105

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

106

C₂×C₄

Q₈×D₇₁

yes

characteristic

107

C₂×C₄

#11765865

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

284

—

111

C₂²

—

112

C₂²

—

284

—

113

C₂²

—

284

—

114

C₂²

#14556104

yes

characteristic

115

C₂²

#14556113

yes

—

116

C₄

—

284

—

117

C₄

—

284

—

118

C₄

#14556106

yes

—

119

C₄

#14556111

yes

characteristic

120

C₄

#14556124

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

568

—

124

C₂

#17985934

yes

characteristic

	subgroup	G/H
center	C₄	#14556124
commutator	C₂²×C₄×C₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#430×C₇₁	C₂
socle	C₂×C₇₁	#399
hypercenter	#430	D₇₁
hypocenter	C₇₁	#2098
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

#14556124

commutator

C₂²×C₄×C₇₁

C₂³

Frattini

C₂²×C₄

C₂²×D₇₁

Fitting

#430×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
1. #17986027	C₂	semidirect
4. #17985756	C₂	semidirect
5. #430×C₇₁	C₂	semidirect
63. C₇₁	#2098	semidirect
64. #430	D₇₁	semidirect

H ≅ G/N

type

1. #17986027

C₂

semidirect

4. #17985756

C₂

semidirect

5. #430×C₇₁

C₂

semidirect

63. C₇₁

#2098

semidirect

64. #430

D₇₁

semidirect

Subgroups — #22589892

Conjugacy classes of subgroups

Complements