Group #20246686 — subgroups

Subgroups — #20246686

Order 6016.

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

normal subgroups only

This group has 432 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	C₄₇⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689064	C₂	1	3	yes	maximal, complemented
3	#15689052	C₂	1	3	yes	maximal
4	#15689047	C₂	1	1	yes	maximal, characteristic
5	C₄×Dic₄₇⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₄×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal
7	C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
11	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
13	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
14	C₄₇⋊#95	C₂²	1	3	yes	—
15	C₄₇⋊#95	C₂²	1	3	yes	—
16	C₄₇⋊#95	C₂²	1	3	yes	—
17	C₄₇⋊#95	C₂²	1	3	yes	—
18	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
19	#95×C₄₇	C₂²	1	1	yes	characteristic
20	#95×C₄₇	C₂²	1	3	yes	—
21	C₂³×D₄₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂³	1	3	yes	—
27	C₂²×Dic₄₇	C₂³	1	3	yes	—
28	C₂×C₄×D₄₇	—	2	6	no	—
29	C₄²×C₄₇	—	2	6	no	—
30	(C₂×D₄₇)⋊C₄	—	2	6	no	—
31	(C₂×D₄₇)⋊C₄	—	2	6	no	—
32	Dic₄₇⋊C₄	—	2	6	no	—
33	Dic₄₇⋊C₄	—	2	6	no	—
34	C₄×Dic₄₇	—	2	6	no	—
35	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
36	C₂²×D₄₇	—	2	3	no	—
37	C₂²×D₄₇	—	2	3	no	—
38	C₂²×D₄₇	#41	1	2	yes	—
39	C₂×C₄×C₄₇	—	2	3	no	—
40	C₂×C₄×C₄₇	—	2	3	no	—
41	C₂×C₄×C₄₇	—	2	3	no	—
42	C₂×C₄×C₄₇	—	2	3	no	—
43	C₂×C₄×C₄₇	—	2	3	no	—
44	C₂×C₄×C₄₇	—	2	3	no	—
45	C₂×C₄×C₄₇	#41	1	6	yes	—
46	C₂×Dic₄₇	—	2	3	no	—
47	C₂×Dic₄₇	—	2	3	no	—
48	C₂×Dic₄₇	—	2	3	no	—
49	C₂×Dic₄₇	—	2	3	no	—
50	C₂×Dic₄₇	—	2	3	no	—
51	C₂×Dic₄₇	—	2	3	no	—
52	C₂×Dic₄₇	#41	1	6	yes	—
53	C₄×D₄₇	—	4	4	no	—
54	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
55	C₂²×C₄₇	C₂×#41	1	3	yes	—
56	C₂²×C₄₇	C₂×#41	1	3	yes	—
57	C₂×D₄₇	—	2	6	no	—
58	C₂×D₄₇	—	4	1	no	—
59	C₂×D₄₇	—	4	3	no	—
60	C₄×C₄₇	—	4	3	no	—
61	C₄×C₄₇	—	4	3	no	—
62	C₄×C₄₇	#126	1	4	yes	—
63	Dic₄₇	—	2	6	no	—
64	Dic₄₇	—	4	1	no	—
65	Dic₄₇	—	4	3	no	—
66	#2401	—	47	1	no	maximal, Sylow
67	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
68	C₂×C₄₇	#529	1	3	yes	—
69	C₂×C₄₇	#529	1	3	yes	—
70	D₄₇	—	4	2	no	—
71	#401	—	47	1	no	—
72	#400	—	47	3	no	—
73	#397	—	47	3	no	—
74	#396	—	47	1	no	—
75	C₄×C₄⋊C₄	—	47	3	no	—
76	C₄×C₂²⋊C₄	—	47	3	no	—
77	#376	D₄₇	1	1	yes	characteristic, complemented
78	C₄₇	#2401	1	1	yes	characteristic, complemented, Sylow
79	C₂³×C₄	—	47	1	no	—
80	C₂×C₄⋊C₄	—	47	3	no	—
81	C₂×C₄⋊C₄	—	47	3	no	—
82	C₂×C₂²⋊C₄	—	47	3	no	—
83	C₂×C₂²⋊C₄	—	47	3	no	—
84	C₂×C₄²	—	47	3	no	—
85	C₂×C₄²	C₂×D₄₇	1	3	yes	—
86	#95	—	47	3	no	—
87	#95	—	47	3	no	—
88	#95	—	47	3	no	—
89	#95	—	47	3	no	—
90	#95	C₂×D₄₇	1	1	yes	characteristic
91	#95	C₂×D₄₇	1	3	yes	—
92	C₂⁴	—	47	1	no	—
93	C₂²×C₄	—	47	3	no	—
94	C₂²×C₄	—	47	1	no	—
95	C₂²×C₄	—	47	3	no	—
96	C₂²×C₄	—	94	6	no	—
97	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
98	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
99	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
100	C₄⋊C₄	—	94	6	no	—
101	C₄⋊C₄	—	94	6	no	—
102	C₂²⋊C₄	—	94	6	no	—
103	C₂²⋊C₄	—	94	6	no	—
104	C₄²	—	2	6	no	—
105	C₄²	—	94	6	no	—
106	C₂³	—	47	2	no	—
107	C₂³	—	94	3	no	—
108	C₂³	—	94	3	no	—
109	C₂³	C₂³×D₄₇	1	1	yes	characteristic
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	3	no	—
116	C₂×C₄	—	47	6	no	—
117	C₂×C₄	—	94	3	no	—
118	C₂×C₄	—	94	3	no	—
119	C₂×C₄	—	94	3	no	—
120	C₂×C₄	—	94	3	no	—
121	C₂×C₄	—	94	3	no	—
122	C₂×C₄	—	94	3	no	—
123	C₂×C₄	—	188	4	no	—
124	C₂×C₄	#10625350	1	6	yes	—
125	C₂²	—	94	6	no	—
126	C₂²	—	188	1	no	—
127	C₂²	—	188	3	no	—
128	C₂²	#41×D₄₇	1	3	yes	—
129	C₂²	#41×D₄₇	1	1	yes	characteristic
130	C₂²	C₂×#10625350	1	3	yes	—
131	C₄	—	4	3	no	—
132	C₄	—	4	3	no	—
133	C₄	—	94	6	no	—
134	C₄	—	188	1	no	—
135	C₄	—	188	3	no	—
136	C₄	#13094018	1	4	yes	—
137	C₂	—	188	2	no	—
138	C₂	C₂×#13094018	1	1	yes	characteristic
139	C₂	#15689651	1	3	yes	—
140	C₂	#15689651	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇⋊#401

C₂

yes

maximal, characteristic, complemented

#15689064

C₂

yes

maximal, complemented

#15689052

C₂

yes

maximal

#15689047

C₂

yes

maximal, characteristic

C₄×Dic₄₇⋊C₄

C₂

yes

maximal, complemented

C₄×(C₂×D₄₇)⋊C₄

C₂

yes

maximal

C₄₇×#376

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×C₄×D₄₇

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

#41

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₄×D₄₇

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#529

yes

—

D₄₇

—

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

D₄₇

yes

characteristic, complemented

C₄₇

#2401

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

—

—

C₂×D₄₇

yes

characteristic

#95

C₂×D₄₇

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂³×D₄₇

yes

characteristic

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

188

—

124

C₂×C₄

#10625350

yes

—

125

C₂²

—

126

C₂²

—

188

—

127

C₂²

—

188

—

128

C₂²

#41×D₄₇

yes

—

129

C₂²

#41×D₄₇

yes

characteristic

130

C₂²

C₂×#10625350

yes

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

188

—

135

C₄

—

188

—

136

C₄

#13094018

yes

—

137

C₂

—

188

—

138

C₂

C₂×#13094018

yes

characteristic

139

C₂

#15689651

yes

—

140

C₂

#15689651

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#2401
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₄₇×#376

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
1. C₄₇⋊#401	C₂	semidirect
2. #15689064	C₂	semidirect
5. C₄×Dic₄₇⋊C₄	C₂	semidirect
7. C₄₇×#376	C₂	semidirect
77. #376	D₄₇	semidirect
78. C₄₇	#2401	semidirect

H ≅ G/N

type

1. C₄₇⋊#401

C₂

semidirect

2. #15689064

C₂

semidirect

5. C₄×Dic₄₇⋊C₄

C₂

semidirect

7. C₄₇×#376

C₂

semidirect

77. #376

D₄₇

semidirect

78. C₄₇

#2401

semidirect

Subgroups — #20246686

Conjugacy classes of subgroups

Complements