Group #20243504 — subgroups

Subgroups — #20243504

Order 6016.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688877	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₄₇	C₄	1	2	yes	—
8	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
10	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₇	—	2	2	no	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
18	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	4	no	—
21	C₄²×C₄₇	D₄	1	2	yes	—
22	C₄²×C₄₇	Q₈	1	2	yes	—
23	C₄×Dic₄₇	—	2	2	no	—
24	C₄×Dic₄₇	—	2	2	no	—
25	C₄×Dic₄₇	—	2	2	no	—
26	C₄×Dic₄₇	—	2	4	no	—
27	C₄×Dic₄₇	C₈	1	4	yes	complemented
28	C₂×C₄₇⋊C₈	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	4	no	—
30	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	2	2	no	—
32	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₄₇	M₁₆	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	C₂×C₄×C₄₇	#41	1	2	yes	—
40	C₂×Dic₄₇	—	2	2	no	—
41	C₂×Dic₄₇	—	2	2	no	—
42	C₂×Dic₄₇	—	2	2	no	—
43	C₂×Dic₄₇	—	2	2	no	—
44	C₂×Dic₄₇	C₂×C₈	1	4	yes	—
45	C₂×Dic₄₇	M₁₆	1	4	yes	—
46	C₈×C₄₇	—	4	2	no	—
47	C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂²×C₄₇	#117	1	2	yes	—
50	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
51	C₂²×C₄₇	C₂×M₁₆	1	2	yes	—
52	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
53	C₄×C₄₇	—	2	2	no	—
54	C₄×C₄₇	C₄⋊C₈	1	4	yes	—
55	C₄×C₄₇	#124	1	1	yes	characteristic
56	C₄×C₄₇	#124	1	1	yes	characteristic
57	C₄×C₄₇	#125	1	2	yes	—
58	Dic₄₇	—	2	4	no	—
59	Dic₄₇	—	2	4	no	—
60	#1831	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	#382	1	1	yes	characteristic
62	C₂×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
63	C₂×C₄₇	#423	1	1	yes	characteristic
64	C₂×C₄₇	#431	1	2	yes	—
65	C₂×C₄₇	#432	1	2	yes	—
66	C₂×C₄⋊C₈	—	47	1	no	—
67	C₂×C₄⋊C₈	D₄₇	1	1	yes	characteristic
68	C₄³	—	47	1	no	—
69	#336	—	47	4	no	—
70	C₄₇	#1831	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	47	2	no	—
72	C₂²×C₈	C₂×D₄₇	1	2	yes	—
73	C₂×C₄²	—	47	1	no	—
74	C₂×C₄²	—	47	2	no	—
75	C₂×C₄²	—	47	1	no	—
76	C₂×C₄²	—	47	2	no	—
77	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
78	C₄⋊C₈	—	2	2	no	—
79	C₄⋊C₈	—	94	2	no	—
80	C₂²×C₄	—	47	2	no	—
81	C₂²×C₄	—	47	2	no	—
82	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
83	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
84	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
85	C₂×C₈	—	2	4	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	94	4	no	—
88	C₂×C₈	—	94	2	no	—
89	C₄²	—	47	4	no	—
90	C₄²	—	94	4	no	—
91	C₄²	—	94	2	no	—
92	C₄²	—	94	2	no	—
93	C₄²	—	94	2	no	—
94	C₄²	Dic₉₄	1	2	yes	—
95	C₄²	C₂²⋊D₄₇	1	2	yes	—
96	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	47	4	no	—
99	C₂×C₄	—	47	4	no	—
100	C₂×C₄	—	94	2	no	—
101	C₂×C₄	—	94	2	no	—
102	C₂×C₄	—	94	2	no	—
103	C₂×C₄	—	94	2	no	—
104	C₂×C₄	C₈×D₄₇	1	2	yes	—
105	C₂×C₄	#10625324	1	2	yes	—
106	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
107	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
108	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
109	C₂×C₄	#10625352	1	2	yes	—
110	C₂×C₄	#10625354	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
112	C₈	—	4	2	no	—
113	C₈	—	188	2	no	—
114	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
115	C₂²	#13093982	1	2	yes	—
116	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
117	C₂²	M₁₆×D₄₇	1	2	yes	—
118	C₂²	C₂×#10625324	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	94	4	no	—
121	C₄	—	94	4	no	—
122	C₄	Dic₄₇⋊C₈	1	4	yes	—
123	C₄	#13094011	1	1	yes	characteristic
124	C₄	#13094013	1	1	yes	characteristic
125	C₄	#13094015	1	2	yes	—
126	C₂	#15688988	1	1	yes	characteristic
127	C₂	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
128	C₂	#15689146	1	1	yes	characteristic
129	C₂	#15689175	1	2	yes	—
130	C₂	#15689179	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal

C₂×C₄⋊C₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₈

yes

complemented

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄⋊C₈

yes

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₄⋊C₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#432

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₄₇

yes

characteristic

C₄³

—

#336

—

C₄₇

#1831

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₉₄

yes

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₈×D₄₇

yes

—

105

C₂×C₄

#10625324

yes

—

106

C₂×C₄

Dic₄₇⋊C₄

yes

—

107

C₂×C₄

Dic₄₇⋊C₄

yes

—

108

C₂×C₄

C₂×Dic₉₄

yes

characteristic

109

C₂×C₄

#10625352

yes

—

110

C₂×C₄

#10625354

yes

—

111

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

112

C₈

—

113

C₈

—

188

—

114

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

115

C₂²

#13093982

yes

—

116

C₂²

C₂×C₈×D₄₇

yes

characteristic

117

C₂²

M₁₆×D₄₇

yes

—

118

C₂²

C₂×#10625324

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

Dic₄₇⋊C₈

yes

—

123

C₄

#13094011

yes

characteristic

124

C₄

#13094013

yes

characteristic

125

C₄

#13094015

yes

—

126

C₂

#15688988

yes

characteristic

127

C₂

C₂×Dic₄₇⋊C₈

yes

characteristic

128

C₂

#15689146

yes

characteristic

129

C₂

#15689175

yes

—

130

C₂

#15689179

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₈
Fitting	C₂×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#1831
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂²×C₈

Fitting

C₂×C₄⋊C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂×C₄⋊C₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
27. C₄×Dic₄₇	C₈	semidirect
70. C₄₇	#1831	semidirect

H ≅ G/N

type

27. C₄×Dic₄₇

C₈

semidirect

70. C₄₇

#1831

semidirect

Subgroups — #20243504

Conjugacy classes of subgroups

Complements