Group #20242880 — subgroups

Subgroups — #20242880

Order 6016.

152 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689502	C₂	1	1	yes	maximal, characteristic
2	#15689408	C₂	1	1	yes	maximal, characteristic
3	#15689254	C₂	1	1	yes	maximal, characteristic
4	#15688873	C₂	1	1	yes	maximal, characteristic
5	#15688869	C₂	1	1	yes	maximal, characteristic
6	#15688868	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#475	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625337	—	2	1	no	—
9	C₂×#10625337	—	2	1	no	—
10	#13094024	C₂²	1	1	yes	characteristic
11	#13093955	—	2	1	no	—
12	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
13	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	#13093948	—	2	1	no	—
16	#13093935	—	2	1	no	—
17	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	#106×C₄₇	—	2	1	no	—
21	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	#103×C₄₇	—	2	1	no	—
23	C₂×Q₈×C₄₇	—	2	1	no	—
24	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
25	C₂×Dic₉₄	—	2	1	no	—
26	C₂×C₈×C₄₇	—	2	1	no	—
27	C₄⋊C₄×C₄₇	—	2	1	no	—
28	C₄⋊C₄×C₄₇	—	2	1	no	—
29	C₄⋊C₄×C₄₇	—	2	1	no	—
30	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
31	C₄²×C₄₇	—	2	1	no	—
32	C₄²×C₄₇	C₂³	1	1	yes	characteristic
33	#10625337	—	4	2	no	—
34	#10625337	—	4	2	no	—
35	C₄⋊Dic₄₇	—	2	1	no	—
36	C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄₇⋊C₈	—	2	1	no	—
38	C₂×C₄₇⋊C₈	—	2	1	no	—
39	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
40	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
41	Q₈×C₄₇	—	2	1	no	—
42	Q₈×C₄₇	—	2	1	no	—
43	Q₈×C₄₇	—	4	1	no	—
44	Q₈×C₄₇	—	4	1	no	—
45	C₂×C₄×C₄₇	—	2	1	no	—
46	C₂×C₄×C₄₇	—	2	1	no	—
47	C₂×C₄×C₄₇	—	4	1	no	—
48	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂×Dic₄₇	—	4	1	no	—
52	Dic₉₄	—	4	1	no	—
53	Dic₉₄	—	4	1	no	—
54	C₈×C₄₇	—	4	1	no	—
55	C₄₇⋊C₈	—	2	1	no	—
56	C₄₇⋊C₈	—	4	1	no	—
57	C₄₇⋊C₈	—	4	1	no	—
58	C₄₇⋊C₈	SD₁₆	1	2	yes	—
59	C₂²×C₄₇	#121	1	1	yes	characteristic
60	C₄×C₄₇	—	2	1	no	—
61	C₄×C₄₇	—	4	1	no	—
62	C₄×C₄₇	—	4	1	no	—
63	C₄×C₄₇	—	8	1	no	—
64	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
65	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₄×C₄₇	#137	1	1	yes	characteristic
67	C₄×C₄₇	#137	1	1	yes	characteristic
68	Dic₄₇	—	8	1	no	—
69	#1690	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	#460	1	1	yes	characteristic
71	C₂×C₄₇	#470	1	1	yes	characteristic
72	C₂×C₄₇	#473	1	1	yes	characteristic
73	#494	—	47	1	no	—
74	#475	—	47	1	no	—
75	#475	D₄₇	1	1	yes	characteristic
76	#446	—	47	1	no	—
77	#334	—	47	1	no	—
78	#332	—	47	1	no	—
79	#332	—	47	1	no	—
80	C₄₇	#1690	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₁₆	—	94	1	no	—
82	C₂×Q₁₆	—	94	1	no	—
83	C₄⋊Q₈	—	47	1	no	—
84	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
85	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
86	#106	—	2	1	no	—
87	#106	—	94	1	no	—
88	C₄⋊C₈	—	47	1	no	—
89	C₄⋊C₈	—	47	1	no	—
90	C₄⋊C₈	—	94	1	no	—
91	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
92	#103	—	2	1	no	—
93	#103	—	94	1	no	—
94	#97	—	94	1	no	—
95	C₄×C₈	—	47	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	94	1	no	—
98	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
99	Q₁₆	—	188	2	no	—
100	Q₁₆	—	188	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	47	1	no	—
103	C₂×C₈	—	47	1	no	—
104	C₂×C₈	—	94	1	no	—
105	C₂×C₈	—	94	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	94	1	no	—
110	C₄⋊C₄	—	94	1	no	—
111	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
112	C₄²	—	2	1	no	—
113	C₄²	C₂²×D₄₇	1	1	yes	characteristic
114	Q₈	—	2	1	no	—
115	Q₈	—	2	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	188	1	no	—
119	Q₈	—	188	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	188	1	no	—
124	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
125	C₂×C₄	#10625352	1	1	yes	characteristic
126	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
127	C₈	—	4	1	no	—
128	C₈	—	47	2	no	—
129	C₈	—	94	1	no	—
130	C₈	—	188	1	no	—
131	C₈	—	188	1	no	—
132	C₂²	#13093996	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	4	1	no	—
135	C₄	—	4	1	no	—
136	C₄	—	8	1	no	—
137	C₄	—	376	1	no	—
138	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
139	C₄	#13094051	1	1	yes	characteristic
140	C₄	#13094054	1	1	yes	characteristic
141	C₄	#13094055	1	1	yes	characteristic
142	C₂	#15689321	1	1	yes	characteristic
143	C₂	#15689379	1	1	yes	characteristic
144	C₂	#15689396	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689502

C₂

yes

maximal, characteristic

#15689408

C₂

yes

maximal, characteristic

#15689254

C₂

yes

maximal, characteristic

#15688873

C₂

yes

maximal, characteristic

#15688869

C₂

yes

maximal, characteristic

#15688868

C₂

yes

maximal, characteristic

C₄₇×#475

C₂

yes

maximal, characteristic

C₂×#10625337

—

C₂×#10625337

—

#13094024

C₂²

yes

characteristic

#13093955

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

#13093948

—

#13093935

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₂²

yes

characteristic

#106×C₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

#103×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625337

—

#10625337

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

SD₁₆

yes

—

C₂²×C₄₇

#121

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

D₄₇

yes

—

—

—

—

C₄₇

#1690

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

C₄×Q₈

C₂×D₄₇

yes

characteristic

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

—

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₄₇

yes

characteristic

Q₁₆

—

188

—

100

Q₁₆

—

188

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

112

C₄²

—

113

C₄²

C₂²×D₄₇

yes

characteristic

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

188

—

119

Q₈

—

188

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

188

—

124

C₂×C₄

D₄×D₄₇

yes

characteristic

125

C₂×C₄

#10625352

yes

characteristic

126

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

188

—

131

C₈

—

188

—

132

C₂²

#13093996

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

376

—

138

C₄

SD₁₆×D₄₇

yes

characteristic

139

C₄

#13094051

yes

characteristic

140

C₄

#13094054

yes

characteristic

141

C₄

#13094055

yes

characteristic

142

C₂

#15689321

yes

characteristic

143

C₂

#15689379

yes

characteristic

144

C₂

#15689396

yes

characteristic

	subgroup	G/H
center	C₂²	#13093996
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#475	C₂
socle	C₂²×C₄₇	#121
hypercenter	#475	D₄₇
hypocenter	C₄₇	#1690
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

#13093996

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#475

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
80. C₄₇	#1690	semidirect

H ≅ G/N

type

80. C₄₇

#1690

semidirect

Subgroups — #20242880

Conjugacy classes of subgroups

Complements