Group #20244942 — subgroups

Subgroups — #20244942

Order 6016.

210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 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	#15689172	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689150	C₂	1	2	yes	maximal, complemented
3	#15689141	C₂	1	2	yes	maximal
4	#15689091	C₂	1	1	yes	maximal, characteristic
5	C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	C₂²	1	1	yes	characteristic
7	C₂×#10625329	C₂²	1	2	yes	—
8	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	#13093960	—	2	2	no	—
10	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
11	#13093952	—	2	4	no	—
12	(C₂×D₄₇)⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	#117×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₄₇	—	2	1	no	—
17	#10625350	—	2	2	no	—
18	#10625350	—	2	2	no	—
19	C₂×D₁₈₈	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₄₇	—	2	1	no	—
21	C₂×Dic₉₄	Q₈	1	1	yes	characteristic
22	M₁₆×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	D₄	1	2	yes	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₂²⋊C₄×C₄₇	—	2	2	no	—
26	C₄²×C₄₇	D₄	1	4	yes	—
27	#10625329	—	2	2	no	—
28	#10625329	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	1	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	2	no	—
32	C₂³×C₄₇	#41	1	1	yes	characteristic
33	C₂²×D₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	—	2	4	no	—
35	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₄₇	#41	1	2	yes	—
39	C₂²⋊D₄₇	—	4	2	no	—
40	C₂×Dic₄₇	—	2	1	no	—
41	D₁₈₈	—	2	2	no	—
42	C₄×D₄₇	—	4	1	no	—
43	C₄×D₄₇	—	4	1	no	—
44	Dic₉₄	—	2	2	no	—
45	C₈×C₄₇	—	2	2	no	—
46	C₄₇⋊C₈	—	4	1	no	—
47	C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇	—	4	1	no	—
49	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₇	#123	1	2	yes	—
51	C₂×D₄₇	—	4	2	no	—
52	C₂×D₄₇	—	4	1	no	—
53	C₄×C₄₇	—	4	4	no	—
54	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
55	C₄×C₄₇	#123	1	1	yes	characteristic
56	C₄×C₄₇	#127	1	1	yes	characteristic
57	Dic₄₇	—	4	1	no	—
58	#2098	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	2	2	no	—
60	C₂×C₄₇	—	2	1	no	—
61	C₂×C₄₇	#399	1	1	yes	characteristic
62	D₄₇	—	8	1	no	—
63	#430	—	47	1	no	—
64	#424	—	47	2	no	—
65	#421	—	47	2	no	—
66	#408	—	47	1	no	—
67	H(3,ℤ/4)	D₄₇	1	1	yes	characteristic, complemented
68	C₄₇	#2098	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	—	47	1	no	—
70	C₂×M₁₆	—	47	2	no	—
71	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
72	C₂²×C₈	—	47	1	no	—
73	#117	C₂×D₄₇	1	2	yes	—
74	#108	—	94	2	no	—
75	C₄⋊C₈	—	94	4	no	—
76	#104	—	94	4	no	—
77	C₂²⋊C₈	—	94	2	no	—
78	#41	—	94	2	no	—
79	#41	—	94	2	no	—
80	C₂×Q₈	—	47	1	no	—
81	C₂×D₄	—	47	1	no	—
82	C₂×D₄	—	94	1	no	—
83	C₂²×C₄	—	94	1	no	—
84	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	94	2	no	—
87	M₁₆	—	94	2	no	—
88	C₂×C₈	—	94	1	no	—
89	C₂×C₈	—	94	2	no	—
90	C₂×C₈	—	94	2	no	—
91	C₂×C₈	D₁₈₈	1	2	yes	—
92	C₄⋊C₄	—	2	2	no	—
93	C₂²⋊C₄	—	2	2	no	—
94	C₄²	D₁₈₈	1	4	yes	—
95	C₂³	—	94	1	no	—
96	C₂³	#10625352	1	1	yes	characteristic
97	Q₈	—	94	2	no	—
98	D₄	—	94	2	no	—
99	D₄	—	188	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	94	1	no	—
102	C₂×C₄	—	188	1	no	—
103	C₂×C₄	—	188	1	no	—
104	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
105	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
106	C₂×C₄	#10625352	1	2	yes	—
107	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	188	1	no	—
110	C₈	—	188	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	188	2	no	—
113	C₂²	—	188	1	no	—
114	C₂²	#13094004	1	1	yes	characteristic
115	C₂²	#13094008	1	2	yes	—
116	C₄	—	4	4	no	—
117	C₄	—	188	1	no	—
118	C₄	#13094004	1	2	yes	—
119	C₄	#13094008	1	1	yes	characteristic
120	C₄	#13094021	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	376	1	no	—
124	C₂	#15689060	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689172

C₂

yes

maximal, characteristic, complemented

#15689150

C₂

yes

maximal, complemented

#15689141

C₂

yes

maximal

#15689091

C₂

yes

maximal, characteristic

C₄₇×H(3,ℤ/4)

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13093960

—

C₄⋊(C₄₇⋊C₈)

—

#13093952

—

(C₂×D₄₇)⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

Q₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

Q₈

yes

characteristic

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

#123

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#2098

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#399

yes

characteristic

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2098

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

#117

C₂×D₄₇

yes

—

#108

—

C₄⋊C₈

—

#104

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₁₈₈

yes

—

C₂³

—

C₂³

#10625352

yes

characteristic

Q₈

—

D₄

—

D₄

—

188

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

188

—

103

C₂×C₄

—

188

—

104

C₂×C₄

C₂×D₁₈₈

yes

—

105

C₂×C₄

C₂×D₁₈₈

yes

characteristic

106

C₂×C₄

#10625352

yes

—

107

C₂×C₄

Q₈×D₄₇

yes

characteristic

108

C₈

—

109

C₈

—

188

—

110

C₈

—

188

—

111

C₂²

—

112

C₂²

—

188

—

113

C₂²

—

188

—

114

C₂²

#13094004

yes

characteristic

115

C₂²

#13094008

yes

—

116

C₄

—

117

C₄

—

188

—

118

C₄

#13094004

yes

—

119

C₄

#13094008

yes

characteristic

120

C₄

#13094021

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

376

—

124

C₂

#15689060

yes

characteristic

	subgroup	G/H
center	C₄	#13094021
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×H(3,ℤ/4)	C₂
socle	C₂×C₄₇	#399
hypercenter	H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#2098
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#13094021

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×H(3,ℤ/4)

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
1. #15689172	C₂	semidirect
2. #15689150	C₂	semidirect
5. C₄₇×H(3,ℤ/4)	C₂	semidirect
67. H(3,ℤ/4)	D₄₇	semidirect
68. C₄₇	#2098	semidirect

H ≅ G/N

type

1. #15689172

C₂

semidirect

2. #15689150

C₂

semidirect

5. C₄₇×H(3,ℤ/4)

C₂

semidirect

67. H(3,ℤ/4)

D₄₇

semidirect

68. C₄₇

#2098

semidirect

Subgroups — #20244942

Conjugacy classes of subgroups

Complements