Group #20243413 — subgroups

Subgroups — #20243413

Order 6016.

336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13093956	C₂	1	2	yes	maximal, complemented
2	#15688983	C₂	1	2	yes	maximal
3	#15688886	C₂	1	2	yes	maximal, complemented
4	C₂³×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
6	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
7	#13093956	—	2	4	no	—
8	C₄₇⋊#95	—	2	2	no	—
9	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₇	—	2	4	no	—
11	C₂²×C₈×C₄₇	C₄	1	4	yes	complemented
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄₇	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	—	2	2	no	—
16	C₂²×C₄×C₄₇	—	2	2	no	—
17	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₇	—	2	4	no	—
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	—	2	8	no	—
24	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₄₇	D₄	1	4	yes	—
27	C₂²⋊Dic₄₇	—	4	4	no	—
28	C₄⋊Dic₄₇	—	2	4	no	—
29	C₄⋊Dic₄₇	—	2	4	no	—
30	C₂³×C₄₇	—	2	2	no	—
31	C₂³×C₄₇	—	2	2	no	—
32	C₂³×C₄₇	C₄⋊C₄	1	2	yes	—
33	C₂³×C₄₇	SD₁₆	1	4	yes	—
34	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	C₂×Dic₄₇	—	4	4	no	—
45	C₂×Dic₄₇	—	4	4	no	—
46	C₂×Dic₄₇	—	4	4	no	—
47	C₈×C₄₇	—	2	2	no	—
48	C₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	—	2	8	no	—
52	C₂²×C₄₇	#106	1	4	yes	complemented
53	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄₇	#121	1	2	yes	—
55	C₂²×C₄₇	C₂×SD₁₆	1	2	yes	—
56	C₂²×C₄₇	#135	1	2	yes	—
57	C₄×C₄₇	—	2	2	no	—
58	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₄₇	#117	1	1	yes	characteristic
60	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
61	Dic₄₇	—	8	4	no	—
62	#1807	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	—	2	4	no	—
64	C₂×C₄₇	#380	1	1	yes	characteristic
65	C₂×C₄₇	C₂×#106	1	1	yes	characteristic
66	C₂×C₄₇	#427	1	1	yes	characteristic
67	C₂×C₄₇	#465	1	4	yes	—
68	C₂³×C₈	D₄₇	1	1	yes	characteristic
69	C₂×#106	—	47	2	no	—
70	#380	—	47	2	no	—
71	#340	—	47	2	no	—
72	C₄₇	#1807	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
74	C₂²×C₈	—	2	4	no	—
75	C₂²×C₈	Dic₄₇	1	4	yes	complemented
76	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
77	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂×C₄⋊C₄	—	47	4	no	—
79	C₂×C₂²⋊C₄	—	94	2	no	—
80	#106	—	94	4	no	—
81	#95	—	94	2	no	—
82	C₂⁴	D₁₈₈	1	1	yes	characteristic
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	94	4	no	—
86	C₂²×C₄	Dic₉₄	1	2	yes	—
87	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
88	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
89	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	2	8	no	—
92	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
93	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
94	C₂×C₈	C₂²⋊D₄₇	1	4	yes	—
95	C₄⋊C₄	—	94	4	no	—
96	C₄⋊C₄	—	94	4	no	—
97	C₂²⋊C₄	—	188	4	no	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	2	no	—
100	C₂³	#10625325	1	4	yes	—
101	C₂³	C₄⋊Dic₄₇	1	2	yes	—
102	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	188	4	no	—
108	C₂×C₄	—	188	4	no	—
109	C₂×C₄	—	188	4	no	—
110	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
111	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
112	C₂×C₄	#10625350	1	2	yes	—
113	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
114	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
115	C₈	—	2	2	no	—
116	C₈	C₂²⋊Dic₄₇	1	4	yes	complemented
117	C₂²	—	2	2	no	—
118	C₂²	—	2	8	no	—
119	C₂²	—	2	2	no	—
120	C₂²	#13093956	1	4	yes	complemented
121	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
122	C₂²	#13093998	1	2	yes	—
123	C₂²	C₂×#10625325	1	2	yes	—
124	C₂²	#13094046	1	2	yes	—
125	C₄	—	2	2	no	—
126	C₄	—	376	4	no	—
127	C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
128	C₄	#13093983	1	1	yes	characteristic
129	C₄	#13094003	1	2	yes	—
130	C₂	—	2	4	no	—
131	C₂	#15688983	1	1	yes	characteristic
132	C₂	C₂×#13093956	1	1	yes	characteristic
133	C₂	#15689161	1	1	yes	characteristic
134	C₂	#15689352	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093956

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal

#15688886

C₂

yes

maximal, complemented

C₂³×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

—

#13093956

—

C₄₇⋊#95

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₄

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

SD₁₆

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

complemented

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#106

yes

complemented

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂×SD₁₆

yes

—

C₂²×C₄₇

#135

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂²⋊Q₈

yes

—

Dic₄₇

—

#1807

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂³×C₈

D₄₇

yes

—

—

—

C₄₇

#1807

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂²×C₈

Dic₄₇

yes

complemented

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#106

—

#95

—

C₂⁴

D₁₈₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₂³

—

C₂³

—

100

C₂³

#10625325

yes

—

101

C₂³

C₄⋊Dic₄₇

yes

—

102

C₂³

C₂×D₁₈₈

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

188

—

108

C₂×C₄

—

188

—

109

C₂×C₄

—

188

—

110

C₂×C₄

C₄⋊Dic₄₇

yes

—

111

C₂×C₄

C₂×Dic₉₄

yes

characteristic

112

C₂×C₄

#10625350

yes

—

113

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

114

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

115

C₈

—

116

C₈

C₂²⋊Dic₄₇

yes

complemented

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

#13093956

yes

complemented

121

C₂²

C₂×C₄⋊Dic₄₇

yes

characteristic

122

C₂²

#13093998

yes

—

123

C₂²

C₂×#10625325

yes

—

124

C₂²

#13094046

yes

—

125

C₄

—

126

C₄

—

376

—

127

C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

128

C₄

#13093983

yes

characteristic

129

C₄

#13094003

yes

—

130

C₂

—

131

C₂

#15688983

yes

characteristic

132

C₂

C₂×#13093956

yes

characteristic

133

C₂

#15689161

yes

characteristic

134

C₂

#15689352

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂³×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂³×C₈	D₄₇
hypocenter	C₄₇	#1807
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂³×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂³×C₈

D₄₇

hypocenter

C₄₇

#1807

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
1. C₂×#13093956	C₂	semidirect
3. #15688886	C₂	semidirect
11. C₂²×C₈×C₄₇	C₄	semidirect
48. C₈×C₄₇	C₂²⋊C₄	semidirect
52. C₂²×C₄₇	#106	semidirect
72. C₄₇	#1807	semidirect
75. C₂²×C₈	Dic₄₇	semidirect
116. C₈	C₂²⋊Dic₄₇	semidirect
120. C₂²	#13093956	semidirect

H ≅ G/N

type

1. C₂×#13093956

C₂

semidirect

3. #15688886

C₂

semidirect

11. C₂²×C₈×C₄₇

C₄

semidirect

48. C₈×C₄₇

C₂²⋊C₄

semidirect

52. C₂²×C₄₇

#106

semidirect

72. C₄₇

#1807

semidirect

75. C₂²×C₈

Dic₄₇

semidirect

116. C₈

C₂²⋊Dic₄₇

semidirect

120. C₂²

#13093956

semidirect

Subgroups — #20243413

Conjugacy classes of subgroups

Complements