Group #20245544 — subgroups

Subgroups — #20245544

Order 6016.

136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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	#15689205	C₂	1	1	yes	maximal, characteristic
3	#15688948	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688925	C₂	1	1	yes	maximal, characteristic
6	#15688923	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
9	#13094015	—	2	1	no	—
10	#13093986	—	2	1	no	—
11	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093955	—	2	1	no	—
14	#13093944	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	#107×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×D₁₈₈	—	2	1	no	—
20	C₂×C₄×D₄₇	—	4	1	no	—
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₄⋊C₄×C₄₇	—	2	1	no	—
24	(C₂×D₄₇)⋊C₄	—	4	1	no	—
25	C₄⋊Dic₄₇	—	2	1	no	—
26	C₄⋊Dic₄₇	—	4	1	no	—
27	Dic₄₇⋊C₄	—	4	1	no	—
28	C₄×Dic₄₇	D₄	1	1	yes	characteristic
29	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
30	D₃₇₆	—	2	1	no	—
31	D₃₇₆	Q₈	1	2	yes	—
32	C₁₆×C₄₇	—	2	1	no	—
33	C₄₇⋊C₁₆	—	2	1	no	—
34	C₂²×D₄₇	—	4	1	no	—
35	C₂×C₄×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₇	—	4	1	no	—
39	C₂×Dic₄₇	D₈	1	1	yes	characteristic
40	C₂×Dic₄₇	D₈	1	1	yes	characteristic
41	D₁₈₈	—	2	2	no	—
42	D₁₈₈	—	4	1	no	—
43	C₄×D₄₇	—	8	2	no	—
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	C₂×D₈	1	1	yes	characteristic
48	C₂×D₄₇	—	4	2	no	—
49	C₂×D₄₇	—	8	1	no	—
50	C₂×D₄₇	—	8	1	no	—
51	C₄×C₄₇	—	8	1	no	—
52	C₄×C₄₇	—	8	1	no	—
53	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
54	C₄×C₄₇	#137	1	1	yes	characteristic
55	Dic₄₇	—	2	1	no	—
56	Dic₄₇	—	2	1	no	—
57	Dic₄₇	—	8	1	no	—
58	#2228	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	#474	1	1	yes	characteristic
60	C₂×C₄₇	#508	1	1	yes	characteristic
61	C₂×C₄₇	#509	1	1	yes	characteristic
62	D₄₇	—	8	2	no	—
63	#499	—	47	1	no	—
64	C₄×D₈	—	47	1	no	—
65	#367	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
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	—	94	1	no	—
83	C₂²×C₄	—	188	1	no	—
84	D₈	—	47	2	no	—
85	D₈	—	94	1	no	—
86	C₂×C₈	—	47	1	no	—
87	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	2	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	—	188	1	no	—
98	D₄	—	94	2	no	—
99	D₄	—	188	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	47	1	no	—
103	C₂×C₄	—	47	1	no	—
104	C₂×C₄	—	376	2	no	—
105	C₂×C₄	—	188	1	no	—
106	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
107	C₈	—	94	1	no	—
108	C₈	#10625350	1	1	yes	characteristic
109	C₈	Q₈×D₄₇	1	1	yes	characteristic
110	C₂²	—	376	1	no	—
111	C₂²	—	376	1	no	—
112	C₂²	—	188	2	no	—
113	C₂²	D₈×D₄₇	1	1	yes	characteristic
114	C₄	—	8	1	no	—
115	C₄	—	8	1	no	—
116	C₄	—	94	1	no	—
117	C₄	—	94	1	no	—
118	C₄	—	376	1	no	—
119	C₄	#13094002	1	1	yes	characteristic
120	C₄	#13094056	1	1	yes	characteristic
121	C₂	—	376	2	no	—
122	C₂	#15689402	1	1	yes	characteristic
123	C₂	#15689554	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

#15689205

C₂

yes

maximal, characteristic

#15688948

C₂

yes

maximal, characteristic, complemented

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#15688925

C₂

yes

maximal, characteristic

#15688923

C₂

yes

maximal, characteristic

C₄₇×#367

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

characteristic

#13094015

—

#13093986

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093955

—

#13093944

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

Q₈

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#499

—

C₄×D₈

—

#367

D₄₇

yes

characteristic, complemented

#366

—

C₄⋊C₁₆

—

#357

—

#357

—

C₄₇

#2228

yes

characteristic, complemented, Sylow

C₂×D₈

—

#125

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#107

C₂×D₄₇

yes

characteristic

#107

C₂×D₄₇

yes

characteristic

#106

—

#102

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

188

—

D₈

—

D₈

—

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

—

188

—

D₄

—

D₄

—

188

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

376

—

105

C₂×C₄

—

188

—

106

C₂×C₄

D₄×D₄₇

yes

characteristic

107

C₈

—

108

C₈

#10625350

yes

characteristic

109

C₈

Q₈×D₄₇

yes

characteristic

110

C₂²

—

376

—

111

C₂²

—

376

—

112

C₂²

—

188

—

113

C₂²

D₈×D₄₇

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

376

—

119

C₄

#13094002

yes

characteristic

120

C₄

#13094056

yes

characteristic

121

C₂

—

376

—

122

C₂

#15689402

yes

characteristic

123

C₂

#15689554

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×#367	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#367	D₄₇
hypocenter	C₄₇	#2228
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#367

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

N	H ≅ G/N	type
1. #15689524	C₂	semidirect
3. #15688948	C₂	semidirect
4. Dic₄₇⋊C₁₆	C₂	semidirect
7. C₄₇×#367	C₂	semidirect
65. #367	D₄₇	semidirect
70. C₄₇	#2228	semidirect

H ≅ G/N

type

1. #15689524

C₂

semidirect

3. #15688948

C₂

semidirect

4. Dic₄₇⋊C₁₆

C₂

semidirect

7. C₄₇×#367

C₂

semidirect

65. #367

D₄₇

semidirect

70. C₄₇

#2228

semidirect

Subgroups — #20245544

Conjugacy classes of subgroups

Complements