Group #20244904 — subgroups

Subgroups — #20244904

Order 6016.

222 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 65 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	#15689171	C₂	1	2	yes	maximal, complemented
3	#15689087	C₂	1	2	yes	maximal
4	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#407	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂×#10625329	C₂²	1	2	yes	—
8	#13093960	—	2	2	no	—
9	#13093959	—	2	4	no	—
10	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
11	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²⋊C₈×C₄₇	—	2	2	no	—
15	C₂⁴×C₄₇	Q₈	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	—	2	2	no	—
17	C₂²×C₄×C₄₇	—	2	1	no	—
18	C₂²×C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄×C₄₇	—	2	2	no	—
20	C₂²×C₄×C₄₇	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₄₇	—	2	2	no	—
23	M₁₆×C₄₇	—	2	2	no	—
24	C₂×C₈×C₄₇	—	2	1	no	—
25	C₂×C₈×C₄₇	D₄	1	2	yes	—
26	#10625329	—	2	2	no	—
27	#10625329	—	2	2	no	—
28	#10625329	—	2	2	no	—
29	#10625329	—	2	2	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
32	C₂³×C₄₇	—	2	2	no	—
33	C₂³×C₄₇	—	2	1	no	—
34	C₂³×C₄₇	—	4	2	no	—
35	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	1	no	—
38	C₂×C₄×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	—	4	2	no	—
40	C₂×C₄×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
44	C₂×C₄×C₄₇	#41	1	2	yes	—
45	C₈×C₄₇	—	2	2	no	—
46	C₈×C₄₇	—	4	1	no	—
47	C₄₇⋊C₈	—	2	4	no	—
48	C₄₇⋊C₈	—	4	2	no	—
49	C₂²×C₄₇	—	2	4	no	—
50	C₂²×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	—	4	1	no	—
52	C₂²×C₄₇	—	4	2	no	—
53	C₂²×C₄₇	—	4	1	no	—
54	C₂²×C₄₇	—	4	1	no	—
55	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
56	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
57	C₄×C₄₇	—	4	1	no	—
58	C₄×C₄₇	#123	1	1	yes	characteristic
59	C₄×C₄₇	#123	1	2	yes	—
60	C₄×C₄₇	#127	1	1	yes	characteristic
61	#2091	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	—	2	2	no	—
63	C₂×C₄₇	—	2	1	no	—
64	C₂×C₄₇	—	4	2	no	—
65	C₂×C₄₇	#399	1	1	yes	characteristic
66	#430	—	47	2	no	—
67	#430	—	47	1	no	—
68	#407	—	47	2	no	—
69	#407	D₄₇	1	1	yes	characteristic
70	#338	—	47	1	no	—
71	C₄₇	#2091	1	1	yes	characteristic, complemented, Sylow
72	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
73	C₂×M₁₆	—	47	2	no	—
74	C₂×M₁₆	—	47	2	no	—
75	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
76	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
77	#108	—	94	4	no	—
78	#108	—	94	2	no	—
79	C₂²⋊C₈	—	2	2	no	—
80	C₂²⋊C₈	—	94	4	no	—
81	C₂⁴	Dic₉₄	1	1	yes	characteristic
82	C₂²×C₄	—	2	1	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	Dic₉₄	1	1	yes	characteristic
87	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
88	M₁₆	—	2	2	no	—
89	M₁₆	—	2	2	no	—
90	M₁₆	—	94	2	no	—
91	M₁₆	—	94	2	no	—
92	M₁₆	—	94	2	no	—
93	M₁₆	—	94	2	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	47	4	no	—
96	C₂×C₈	—	94	2	no	—
97	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	1	no	—
100	C₂³	—	4	2	no	—
101	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	#10625350	1	1	yes	characteristic
108	C₂×C₄	D₄×D₄₇	1	2	yes	—
109	C₂×C₄	#10625352	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	1	no	—
113	C₈	—	94	4	no	—
114	C₈	—	188	2	no	—
115	C₂²	—	2	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	4	1	no	—
118	C₂²	—	4	2	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#13094001	1	2	yes	—
122	C₂²	#13094003	1	1	yes	characteristic
123	C₄	—	4	1	no	—
124	C₄	#13094005	1	1	yes	characteristic
125	C₄	#13094006	1	2	yes	—
126	C₄	#13094020	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#15689059	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689172

C₂

yes

maximal, characteristic, complemented

#15689171

C₂

yes

maximal, complemented

#15689087

C₂

yes

maximal

C₄₇⋊#338

C₂

yes

maximal, characteristic, complemented

C₄₇×#407

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂×#10625329

C₂²

yes

—

#13093960

—

#13093959

—

C₂²⋊(C₄₇⋊C₈)

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

—

—

—

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#123

yes

characteristic

C₄×C₄₇

#123

yes

—

C₄×C₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

D₄₇

yes

characteristic

#338

—

C₄₇

#2091

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

Dic₉₄

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×Dic₉₄

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#10625350

yes

characteristic

108

C₂×C₄

D₄×D₄₇

yes

—

109

C₂×C₄

#10625352

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

188

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#13094001

yes

—

122

C₂²

#13094003

yes

characteristic

123

C₄

—

124

C₄

#13094005

yes

characteristic

125

C₄

#13094006

yes

—

126

C₄

#13094020

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#15689059

yes

characteristic

	subgroup	G/H
center	C₄	#13094020
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#407	C₂
socle	C₂×C₄₇	#399
hypercenter	#407	D₄₇
hypocenter	C₄₇	#2091
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

subgroup

G/H

center

C₄

#13094020

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#407

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #407

N	H ≅ G/N	type
1. #15689172	C₂	semidirect
2. #15689171	C₂	semidirect
4. C₄₇⋊#338	C₂	semidirect
71. C₄₇	#2091	semidirect

H ≅ G/N

type

1. #15689172

C₂

semidirect

2. #15689171

C₂

semidirect

4. C₄₇⋊#338

C₂

semidirect

71. C₄₇

#2091

semidirect

Subgroups — #20244904

Conjugacy classes of subgroups

Complements