Group #20245545 — subgroups

Subgroups — #20245545

Order 6016.

136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
2	#15688950	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688924	C₂	1	1	yes	maximal, characteristic
6	#15688924	C₂	1	1	yes	maximal, characteristic
7	C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
8	#13094016	—	2	1	no	—
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093956	—	2	1	no	—
14	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄×D₄×C₄₇	—	2	1	no	—
16	#107×C₄₇	C₂²	1	1	yes	characteristic
17	#102×C₄₇	—	2	1	no	—
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₇	—	2	1	no	—
20	C₂²×C₄×C₄₇	—	4	1	no	—
21	D₈×C₄₇	—	2	1	no	—
22	D₈×C₄₇	Q₈	1	2	yes	—
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₇	—	2	1	no	—
26	C₂²⋊C₄×C₄₇	—	4	1	no	—
27	C₄²×C₄₇	D₄	1	1	yes	characteristic
28	C₄⋊Dic₄₇	—	2	1	no	—
29	C₄⋊Dic₄₇	—	2	1	no	—
30	Dic₄₇⋊C₄	—	4	1	no	—
31	Dic₄₇⋊C₄	—	4	1	no	—
32	C₄₇⋊C₁₆	—	2	1	no	—
33	C₄₇⋊C₁₆	—	2	1	no	—
34	C₂³×C₄₇	—	4	1	no	—
35	D₄×C₄₇	—	2	2	no	—
36	D₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	—	8	2	no	—
39	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₄₇	—	4	1	no	—
43	C₂×Dic₄₇	—	4	1	no	—
44	C₈×C₄₇	—	2	1	no	—
45	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
46	C₈×C₄₇	#41	1	1	yes	characteristic
47	C₂²×C₄₇	—	4	2	no	—
48	C₂²×C₄₇	—	8	1	no	—
49	C₂²×C₄₇	—	8	1	no	—
50	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	2	1	no	—
53	C₄×C₄₇	—	8	1	no	—
54	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
55	C₄×C₄₇	#137	1	1	yes	characteristic
56	Dic₄₇	—	8	1	no	—
57	Dic₄₇	—	8	1	no	—
58	#2228	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	8	2	no	—
60	C₂×C₄₇	#474	1	1	yes	characteristic
61	C₂×C₄₇	#508	1	1	yes	characteristic
62	C₂×C₄₇	#509	1	1	yes	characteristic
63	#499	—	47	1	no	—
64	C₄×D₈	D₄₇	1	1	yes	characteristic
65	#367	—	47	1	no	—
66	#366	—	47	1	no	—
67	C₄⋊C₁₆	—	47	1	no	—
68	#357	—	47	1	no	—
69	#357	—	47	1	no	—
70	C₄₇	#2228	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
72	#125	—	94	1	no	—
73	C₄×D₄	—	2	1	no	—
74	C₂×C₁₆	—	47	1	no	—
75	C₂×C₁₆	—	47	1	no	—
76	#107	—	47	1	no	—
77	#107	—	47	1	no	—
78	#107	C₂×D₄₇	1	1	yes	characteristic
79	#106	—	94	1	no	—
80	#102	—	2	1	no	—
81	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
82	C₂×D₄	—	2	1	no	—
83	C₂²×C₄	—	4	1	no	—
84	D₈	—	2	1	no	—
85	D₈	Dic₉₄	1	2	yes	—
86	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	94	1	no	—
90	C₄⋊C₄	—	94	1	no	—
91	C₄⋊C₄	—	188	1	no	—
92	C₄⋊C₄	—	188	1	no	—
93	C₂²⋊C₄	—	4	1	no	—
94	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
95	C₁₆	—	94	1	no	—
96	C₁₆	—	94	1	no	—
97	C₂³	—	4	1	no	—
98	D₄	—	2	2	no	—
99	D₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	8	2	no	—
102	C₂×C₄	—	188	1	no	—
103	C₂×C₄	—	188	1	no	—
104	C₂×C₄	#10625334	1	1	yes	characteristic
105	C₂×C₄	#10625334	1	1	yes	characteristic
106	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	C₂×Dic₉₄	1	1	yes	characteristic
109	C₈	#10625350	1	1	yes	characteristic
110	C₂²	—	4	2	no	—
111	C₂²	—	8	1	no	—
112	C₂²	—	8	1	no	—
113	C₂²	C₂×#10625334	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	8	1	no	—
117	C₄	—	376	1	no	—
118	C₄	—	376	1	no	—
119	C₄	#13094003	1	1	yes	characteristic
120	C₄	#13094054	1	1	yes	characteristic
121	C₂	—	8	2	no	—
122	C₂	#15689403	1	1	yes	characteristic
123	C₂	#15689553	1	1	yes	characteristic
124	C₂	#15689559	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689525

C₂

yes

maximal, characteristic, complemented

#15688950

C₂

yes

maximal, characteristic, complemented

#15688948

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#15688924

C₂

yes

maximal, characteristic

#15688924

C₂

yes

maximal, characteristic

C₄×D₈×C₄₇

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093956

—

C₂×D₈×C₄₇

C₂²

yes

characteristic

C₄×D₄×C₄₇

—

#107×C₄₇

C₂²

yes

characteristic

#102×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2228

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×D₈

D₄₇

yes

characteristic

#367

—

#366

—

C₄⋊C₁₆

—

#357

—

#357

—

C₄₇

#2228

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₇

yes

characteristic

#125

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₄₇

yes

characteristic

#106

—

#102

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

Dic₉₄

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

188

—

103

C₂×C₄

—

188

—

104

C₂×C₄

#10625334

yes

characteristic

105

C₂×C₄

#10625334

yes

characteristic

106

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

107

C₈

—

108

C₈

C₂×Dic₉₄

yes

characteristic

109

C₈

#10625350

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×#10625334

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

376

—

118

C₄

—

376

—

119

C₄

#13094003

yes

characteristic

120

C₄

#13094054

yes

characteristic

121

C₂

—

122

C₂

#15689403

yes

characteristic

123

C₂

#15689553

yes

characteristic

124

C₂

#15689559

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×D₈	D₄₇
hypocenter	C₄₇	#2228
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×D₈×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄×D₈

D₄₇

hypocenter

C₄₇

#2228

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. #15689525	C₂	semidirect
2. #15688950	C₂	semidirect
3. #15688948	C₂	semidirect
4. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
70. C₄₇	#2228	semidirect

H ≅ G/N

type

1. #15689525

C₂

semidirect

2. #15688950

C₂

semidirect

3. #15688948

C₂

semidirect

4. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

70. C₄₇

#2228

semidirect

Subgroups — #20245545

Conjugacy classes of subgroups

Complements