Group #20242902 — subgroups

Subgroups — #20242902

Order 6016.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	#15689528	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689329	C₂	1	2	yes	maximal
3	#15689202	C₂	1	1	yes	maximal, characteristic
4	#15688870	C₂	1	2	yes	maximal, complemented
5	C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625325	—	2	2	no	—
7	C₂×#10625324	—	2	1	no	—
8	#13094024	C₂²	1	2	yes	—
9	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	#13093958	—	2	1	no	—
11	#13093958	—	2	1	no	—
12	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	#13093949	—	2	2	no	—
14	(C₂×D₄₇)⋊C₈	—	2	1	no	—
15	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×D₁₈₈	D₄	1	1	yes	characteristic
18	C₂×C₄×D₄₇	—	2	1	no	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₄²×C₄₇	C₂³	1	1	yes	characteristic
24	(C₂×D₄₇)⋊C₄	—	2	1	no	—
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	2	2	no	—
27	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
28	C₂×C₄₇⋊C₈	—	2	1	no	—
29	#10625325	—	4	4	no	—
30	#10625324	—	4	2	no	—
31	C₂²×D₄₇	—	2	1	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
35	C₂×Dic₄₇	—	2	1	no	—
36	C₂×Dic₄₇	—	4	2	no	—
37	D₁₈₈	—	2	2	no	—
38	C₄×D₄₇	—	4	1	no	—
39	C₄×D₄₇	—	4	1	no	—
40	Dic₉₄	—	4	2	no	—
41	Dic₉₄	—	4	2	no	—
42	C₈×C₄₇	—	2	1	no	—
43	C₈×C₄₇	—	4	2	no	—
44	C₈×C₄₇	SD₁₆	1	2	yes	complemented
45	C₄₇⋊C₈	—	4	1	no	—
46	C₂²×C₄₇	#121	1	1	yes	characteristic
47	C₂×D₄₇	—	4	1	no	—
48	C₂×D₄₇	—	4	1	no	—
49	C₂×D₄₇	—	4	1	no	—
50	C₄×C₄₇	—	2	1	no	—
51	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
52	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
53	C₄×C₄₇	#137	1	1	yes	characteristic
54	Dic₄₇	—	4	1	no	—
55	Dic₄₇	—	8	2	no	—
56	#1693	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	#461	1	1	yes	characteristic
58	C₂×C₄₇	#469	1	1	yes	characteristic
59	C₂×C₄₇	#473	1	1	yes	characteristic
60	D₄₇	—	8	1	no	—
61	#500	—	47	1	no	—
62	#461	—	47	2	no	—
63	#436	—	47	1	no	—
64	#334	D₄₇	1	1	yes	characteristic, complemented
65	#332	—	47	2	no	—
66	C₄₇	#1693	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	94	2	no	—
68	C₂×M₁₆	—	94	1	no	—
69	C₄⋊Q₈	—	47	2	no	—
70	C₄×D₄	—	47	1	no	—
71	#107	—	94	1	no	—
72	#107	—	94	1	no	—
73	C₄⋊C₈	—	47	1	no	—
74	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
75	#103	—	94	2	no	—
76	C₂²⋊C₈	—	94	1	no	—
77	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂×Q₈	—	94	2	no	—
79	C₂×D₄	—	47	1	no	—
80	C₂²×C₄	—	94	1	no	—
81	SD₁₆	—	188	4	no	—
82	M₁₆	—	188	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	94	1	no	—
85	C₂×C₈	D₁₈₈	1	1	yes	characteristic
86	C₂×C₈	D₁₈₈	1	1	yes	characteristic
87	C₄⋊C₄	—	47	1	no	—
88	C₄⋊C₄	—	94	2	no	—
89	C₄⋊C₄	—	94	2	no	—
90	C₂²⋊C₄	—	94	1	no	—
91	C₄²	C₂²×D₄₇	1	1	yes	characteristic
92	C₂³	—	94	1	no	—
93	Q₈	—	188	2	no	—
94	Q₈	—	188	2	no	—
95	D₄	—	94	2	no	—
96	C₂×C₄	—	94	1	no	—
97	C₂×C₄	—	188	2	no	—
98	C₂×C₄	—	188	1	no	—
99	C₂×C₄	—	188	1	no	—
100	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
101	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
102	C₂×C₄	#10625354	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	4	2	no	—
105	C₈	—	188	1	no	—
106	C₈	#10625325	1	2	yes	complemented
107	C₂²	—	188	1	no	—
108	C₂²	—	188	1	no	—
109	C₂²	—	188	1	no	—
110	C₂²	#13093999	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	376	2	no	—
113	C₄	—	188	1	no	—
114	C₄	C₂×#10625325	1	1	yes	characteristic
115	C₄	#13094051	1	2	yes	—
116	C₄	#13094057	1	1	yes	characteristic
117	C₂	—	376	1	no	—
118	C₂	#15689329	1	1	yes	characteristic
119	C₂	#15689377	1	1	yes	characteristic
120	C₂	#15689399	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic, complemented

#15689329

C₂

yes

maximal

#15689202

C₂

yes

maximal, characteristic

#15688870

C₂

yes

maximal, complemented

C₄₇×#334

C₂

yes

maximal, characteristic, complemented

C₂×#10625325

—

C₂×#10625324

—

#13094024

C₂²

yes

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093958

—

#13093958

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

#13093949

—

(C₂×D₄₇)⋊C₈

—

C₄⋊C₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

D₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

—

#10625325

—

#10625324

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

SD₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

#332

—

C₄₇

#1693

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

SD₁₆

—

188

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

100

C₂×C₄

C₂×D₁₈₈

yes

characteristic

101

C₂×C₄

D₄×D₄₇

yes

characteristic

102

C₂×C₄

#10625354

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

188

—

106

C₈

#10625325

yes

complemented

107

C₂²

—

188

—

108

C₂²

—

188

—

109

C₂²

—

188

—

110

C₂²

#13093999

yes

characteristic

111

C₄

—

112

C₄

—

376

—

113

C₄

—

188

—

114

C₄

C₂×#10625325

yes

characteristic

115

C₄

#13094051

yes

—

116

C₄

#13094057

yes

characteristic

117

C₂

—

376

—

118

C₂

#15689329

yes

characteristic

119

C₂

#15689377

yes

characteristic

120

C₂

#15689399

yes

characteristic

	subgroup	G/H
center	C₂²	#13093999
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#334	C₂
socle	C₂²×C₄₇	#121
hypercenter	#334	D₄₇
hypocenter	C₄₇	#1693
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13093999

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#334

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #15689528	C₂	semidirect
4. #15688870	C₂	semidirect
5. C₄₇×#334	C₂	semidirect
44. C₈×C₄₇	SD₁₆	semidirect
64. #334	D₄₇	semidirect
66. C₄₇	#1693	semidirect
106. C₈	#10625325	semidirect

H ≅ G/N

type

1. #15689528

C₂

semidirect

4. #15688870

C₂

semidirect

5. C₄₇×#334

C₂

semidirect

44. C₈×C₄₇

SD₁₆

semidirect

64. #334

D₄₇

semidirect

66. C₄₇

#1693

semidirect

106. C₈

#10625325

semidirect

Subgroups — #20242902

Conjugacy classes of subgroups

Complements