Group #20245543 — subgroups

Subgroups — #20245543

Order 6016.

136 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 49 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	#15689524	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688950	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688949	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688924	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#357	C₂	1	1	yes	maximal, characteristic
8	#13094015	—	2	1	no	—
9	D₄×Dic₄₇	—	2	1	no	—
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093955	—	2	1	no	—
14	#13093945	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₇	—	2	1	no	—
20	C₂²×Dic₄₇	—	4	1	no	—
21	D₈×C₄₇	—	2	1	no	—
22	D₈×C₄₇	Q₈	1	2	yes	—
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₂²⋊Dic₄₇	—	4	1	no	—
26	C₄⋊Dic₄₇	—	2	1	no	—
27	C₄⋊Dic₄₇	—	2	1	no	—
28	C₄⋊Dic₄₇	—	4	1	no	—
29	Dic₄₇⋊C₄	—	4	1	no	—
30	C₄×Dic₄₇	D₄	1	1	yes	characteristic
31	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
32	C₁₆×C₄₇	—	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	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₇	—	4	1	no	—
40	C₂×Dic₄₇	—	4	1	no	—
41	C₂×Dic₄₇	—	8	2	no	—
42	C₂×Dic₄₇	D₈	1	1	yes	characteristic
43	C₂×Dic₄₇	D₈	1	1	yes	characteristic
44	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₇	#41	1	1	yes	characteristic
46	C₄₇⋊C₈	—	2	1	no	—
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	—	8	1	no	—
52	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
53	C₄×C₄₇	#137	1	1	yes	characteristic
54	Dic₄₇	—	2	1	no	—
55	Dic₄₇	—	2	1	no	—
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	—	47	1	no	—
65	#367	—	47	1	no	—
66	#366	—	47	1	no	—
67	C₄⋊C₁₆	—	47	1	no	—
68	#357	—	47	1	no	—
69	#357	D₄₇	1	1	yes	characteristic
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	—	94	1	no	—
74	C₂×C₁₆	—	47	1	no	—
75	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
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	—	94	1	no	—
81	C₄×C₈	—	47	1	no	—
82	C₂×D₄	—	2	1	no	—
83	C₂²×C₄	—	188	1	no	—
84	D₈	—	2	1	no	—
85	D₈	Dic₉₄	1	2	yes	—
86	C₂×C₈	—	47	1	no	—
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	—	188	1	no	—
94	C₄²	—	47	1	no	—
95	C₁₆	—	2	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	—	47	1	no	—
102	C₂×C₄	—	47	1	no	—
103	C₂×C₄	—	376	2	no	—
104	C₂×C₄	—	188	1	no	—
105	C₂×C₄	—	188	1	no	—
106	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
107	C₈	—	94	1	no	—
108	C₈	C₂×Dic₉₄	1	1	yes	characteristic
109	C₈	#10625352	1	1	yes	characteristic
110	C₂²	—	4	2	no	—
111	C₂²	—	8	1	no	—
112	C₂²	—	8	1	no	—
113	C₂²	D₈×D₄₇	1	1	yes	characteristic
114	C₄	—	8	1	no	—
115	C₄	—	94	1	no	—
116	C₄	—	94	1	no	—
117	C₄	—	376	1	no	—
118	C₄	—	376	1	no	—
119	C₄	#13094001	1	1	yes	characteristic
120	C₄	#13094053	1	1	yes	characteristic
121	C₂	—	8	2	no	—
122	C₂	#15689401	1	1	yes	characteristic
123	C₂	#15689552	1	1	yes	characteristic
124	C₂	#15689560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689524

C₂

yes

maximal, characteristic, complemented

D₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688950

C₂

yes

maximal, characteristic, complemented

#15688949

C₂

yes

maximal, characteristic, complemented

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#15688924

C₂

yes

maximal, characteristic

C₄₇×#357

C₂

yes

maximal, characteristic

#13094015

—

D₄×Dic₄₇

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093955

—

#13093945

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×D₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂²×Dic₄₇

—

D₈×C₄₇

—

D₈×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2228

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×D₈

—

#367

—

#366

—

C₄⋊C₁₆

—

#357

—

#357

D₄₇

yes

characteristic

C₄₇

#2228

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₇

yes

characteristic

#125

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

characteristic

#106

—

#102

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

188

—

D₈

—

D₈

Dic₉₄

yes

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

376

—

104

C₂×C₄

—

188

—

105

C₂×C₄

—

188

—

106

C₂×C₄

D₄×D₄₇

yes

characteristic

107

C₈

—

108

C₈

C₂×Dic₉₄

yes

characteristic

109

C₈

#10625352

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

D₈×D₄₇

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

376

—

118

C₄

—

376

—

119

C₄

#13094001

yes

characteristic

120

C₄

#13094053

yes

characteristic

121

C₂

—

122

C₂

#15689401

yes

characteristic

123

C₂

#15689552

yes

characteristic

124

C₂

#15689560

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#357	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#357	D₄₇
hypocenter	C₄₇	#2228
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#357

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #15689524	C₂	semidirect
3. #15688950	C₂	semidirect
4. #15688949	C₂	semidirect
5. Dic₄₇⋊C₁₆	C₂	semidirect
70. C₄₇	#2228	semidirect

H ≅ G/N

type

1. #15689524

C₂

semidirect

3. #15688950

C₂

semidirect

4. #15688949

C₂

semidirect

5. Dic₄₇⋊C₁₆

C₂

semidirect

70. C₄₇

#2228

semidirect

Subgroups — #20245543

Conjugacy classes of subgroups

Complements