Group #20242878 — subgroups

Subgroups — #20242878

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	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689404	C₂	1	2	yes	maximal
3	#15689202	C₂	1	1	yes	maximal, characteristic
4	#15688868	C₂	1	2	yes	maximal, complemented
5	C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₈₈	—	2	1	no	—
7	C₂×Dic₁₈₈	—	2	1	no	—
8	C₂×#10625324	—	2	1	no	—
9	#13094024	C₂²	1	2	yes	—
10	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
11	#13093958	—	2	2	no	—
12	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	#13093946	—	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	Dic₁₈₈	—	4	2	no	—
30	Dic₁₈₈	—	4	2	no	—
31	#10625324	—	4	2	no	—
32	C₂²×D₄₇	—	2	1	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
36	C₂×Dic₄₇	—	2	1	no	—
37	C₂×Dic₄₇	—	4	2	no	—
38	D₁₈₈	—	2	2	no	—
39	C₄×D₄₇	—	4	1	no	—
40	C₄×D₄₇	—	4	1	no	—
41	Dic₉₄	—	4	2	no	—
42	Dic₉₄	—	4	2	no	—
43	C₈×C₄₇	—	2	1	no	—
44	C₈×C₄₇	—	4	2	no	—
45	C₈×C₄₇	D₈	1	2	yes	—
46	C₄₇⋊C₈	—	4	1	no	—
47	C₂²×C₄₇	#121	1	1	yes	characteristic
48	C₂×D₄₇	—	4	1	no	—
49	C₂×D₄₇	—	4	1	no	—
50	C₂×D₄₇	—	4	1	no	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
53	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₄×C₄₇	#137	1	2	yes	—
55	Dic₄₇	—	4	1	no	—
56	Dic₄₇	—	8	2	no	—
57	#1689	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	#459	1	1	yes	characteristic
59	C₂×C₄₇	#470	1	1	yes	characteristic
60	C₂×C₄₇	#473	1	1	yes	characteristic
61	D₄₇	—	8	1	no	—
62	#494	—	47	1	no	—
63	#474	—	47	2	no	—
64	#436	—	47	1	no	—
65	#334	D₄₇	1	1	yes	characteristic, complemented
66	#332	—	47	2	no	—
67	C₄₇	#1689	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	—	94	1	no	—
69	C₂×Q₁₆	—	94	1	no	—
70	C₂×M₁₆	—	94	1	no	—
71	C₄⋊Q₈	—	47	2	no	—
72	C₄×D₄	—	47	1	no	—
73	#107	—	94	2	no	—
74	C₄⋊C₈	—	47	1	no	—
75	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
76	#102	—	94	2	no	—
77	C₂²⋊C₈	—	94	1	no	—
78	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
79	C₂×Q₈	—	94	2	no	—
80	C₂×D₄	—	47	1	no	—
81	C₂²×C₄	—	94	1	no	—
82	Q₁₆	—	188	2	no	—
83	Q₁₆	—	188	2	no	—
84	M₁₆	—	188	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	94	1	no	—
87	C₂×C₈	D₁₈₈	1	1	yes	characteristic
88	C₂×C₈	D₁₈₈	1	1	yes	characteristic
89	C₄⋊C₄	—	47	1	no	—
90	C₄⋊C₄	—	94	2	no	—
91	C₄⋊C₄	—	94	2	no	—
92	C₂²⋊C₄	—	94	1	no	—
93	C₄²	C₂²×D₄₇	1	1	yes	characteristic
94	C₂³	—	94	1	no	—
95	Q₈	—	188	2	no	—
96	Q₈	—	188	2	no	—
97	D₄	—	94	2	no	—
98	C₂×C₄	—	94	1	no	—
99	C₂×C₄	—	188	2	no	—
100	C₂×C₄	—	188	1	no	—
101	C₂×C₄	—	188	1	no	—
102	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
103	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
104	C₂×C₄	#10625354	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	4	2	no	—
107	C₈	—	188	1	no	—
108	C₈	D₃₇₆	1	2	yes	—
109	C₂²	—	188	1	no	—
110	C₂²	—	188	1	no	—
111	C₂²	—	188	1	no	—
112	C₂²	#13093999	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	376	2	no	—
115	C₄	—	188	1	no	—
116	C₄	C₂×D₃₇₆	1	1	yes	characteristic
117	C₄	#13094052	1	1	yes	characteristic
118	C₄	#13094053	1	2	yes	—
119	C₂	—	376	1	no	—
120	C₂	#15689319	1	1	yes	characteristic
121	C₂	#15689382	1	1	yes	characteristic
122	C₂	#15689399	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689503

C₂

yes

maximal, characteristic, complemented

#15689404

C₂

yes

maximal

#15689202

C₂

yes

maximal, characteristic

#15688868

C₂

yes

maximal, complemented

C₄₇×#334

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×#10625324

—

#13094024

C₂²

yes

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093958

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

#13093946

—

(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

—

Dic₁₈₈

—

Dic₁₈₈

—

#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

D₈

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×D₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

#332

—

C₄₇

#1689

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

Q₁₆

—

188

—

Q₁₆

—

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

—

100

C₂×C₄

—

188

—

101

C₂×C₄

—

188

—

102

C₂×C₄

C₂×D₁₈₈

yes

characteristic

103

C₂×C₄

D₄×D₄₇

yes

characteristic

104

C₂×C₄

#10625354

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

188

—

108

C₈

D₃₇₆

yes

—

109

C₂²

—

188

—

110

C₂²

—

188

—

111

C₂²

—

188

—

112

C₂²

#13093999

yes

characteristic

113

C₄

—

114

C₄

—

376

—

115

C₄

—

188

—

116

C₄

C₂×D₃₇₆

yes

characteristic

117

C₄

#13094052

yes

characteristic

118

C₄

#13094053

yes

—

119

C₂

—

376

—

120

C₂

#15689319

yes

characteristic

121

C₂

#15689382

yes

characteristic

122

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	#1689
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. #15689503	C₂	semidirect
4. #15688868	C₂	semidirect
5. C₄₇×#334	C₂	semidirect
65. #334	D₄₇	semidirect
67. C₄₇	#1689	semidirect

H ≅ G/N

type

1. #15689503

C₂

semidirect

4. #15688868

C₂

semidirect

5. C₄₇×#334

C₂

semidirect

65. #334

D₄₇

semidirect

67. C₄₇

#1689

semidirect

Subgroups — #20242878

Conjugacy classes of subgroups

Complements