Group #20244966 — subgroups

Subgroups — #20244966

Order 6016.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#15689171	C₂	1	1	yes	maximal, characteristic
2	#15689147	C₂	1	1	yes	maximal, characteristic
3	#15688894	C₂	1	1	yes	maximal, characteristic
4	#15688893	C₂	1	1	yes	maximal, characteristic
5	#15688883	C₂	1	1	yes	maximal, characteristic
6	#15688879	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625329	C₂²	1	1	yes	characteristic
9	C₂×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#10625329	C₂²	1	1	yes	characteristic
11	#13093983	C₂²	1	1	yes	characteristic
12	#13093959	—	2	2	no	—
13	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
14	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	#117×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	—	2	1	no	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	M₁₆×C₄₇	—	2	1	no	—
20	M₁₆×C₄₇	—	2	1	no	—
21	C₂×C₈×C₄₇	—	2	1	no	—
22	C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₂²⋊C₄×C₄₇	—	2	1	no	—
24	C₄²×C₄₇	—	2	1	no	—
25	C₄²×C₄₇	—	2	1	no	—
26	C₄²×C₄₇	Q₈	1	1	yes	characteristic
27	C₄²×C₄₇	Q₈	1	1	yes	characteristic
28	C₂²⋊Dic₄₇	—	2	1	no	—
29	C₄⋊Dic₄₇	—	2	1	no	—
30	C₄×Dic₄₇	—	2	1	no	—
31	#10625329	—	2	1	no	—
32	#10625329	—	2	1	no	—
33	#10625329	—	2	1	no	—
34	#10625329	—	2	1	no	—
35	#10625329	—	2	1	no	—
36	#10625329	—	2	1	no	—
37	C₂×C₄₇⋊C₈	—	2	1	no	—
38	C₂×C₄₇⋊C₈	—	2	1	no	—
39	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
40	C₂³×C₄₇	#41	1	1	yes	characteristic
41	C₂×C₄×C₄₇	—	2	1	no	—
42	C₂×C₄×C₄₇	—	2	1	no	—
43	C₂×C₄×C₄₇	—	4	2	no	—
44	C₂×C₄×C₄₇	—	4	1	no	—
45	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
48	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
49	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
50	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂×Dic₄₇	—	4	1	no	—
52	C₈×C₄₇	—	4	1	no	—
53	C₄₇⋊C₈	—	2	2	no	—
54	C₄₇⋊C₈	—	4	1	no	—
55	C₄₇⋊C₈	—	4	1	no	—
56	C₂²×C₄₇	—	4	1	no	—
57	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂²×C₄₇	#126	1	1	yes	characteristic
59	C₂²×C₄₇	#126	1	1	yes	characteristic
60	C₄×C₄₇	—	2	2	no	—
61	C₄×C₄₇	—	4	1	no	—
62	C₄×C₄₇	—	8	1	no	—
63	C₄×C₄₇	#123	1	1	yes	characteristic
64	C₄×C₄₇	#124	1	1	yes	characteristic
65	C₄×C₄₇	#125	1	1	yes	characteristic
66	C₄×C₄₇	#125	1	1	yes	characteristic
67	Dic₄₇	—	8	1	no	—
68	#2102	—	47	1	no	maximal, Sylow
69	C₂×C₄₇	—	2	1	no	—
70	C₂×C₄₇	—	2	1	no	—
71	C₂×C₄₇	—	2	1	no	—
72	C₂×C₄₇	#400	1	1	yes	characteristic
73	#430	—	47	1	no	—
74	#423	—	47	1	no	—
75	#344	—	47	1	no	—
76	#344	—	47	1	no	—
77	#339	—	47	1	no	—
78	#339	D₄₇	1	1	yes	characteristic
79	H(3,ℤ/4)	—	47	1	no	—
80	C₄₇	#2102	1	1	yes	characteristic, complemented, Sylow
81	C₂×M₁₆	—	47	1	no	—
82	C₂×M₁₆	—	47	1	no	—
83	C₂×M₁₆	—	47	1	no	—
84	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
85	#117	—	47	1	no	—
86	#117	C₂×D₄₇	1	1	yes	characteristic
87	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
88	#108	—	94	2	no	—
89	C₄⋊C₈	—	94	2	no	—
90	C₂²×C₄	—	2	1	no	—
91	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
92	M₁₆	—	2	1	no	—
93	M₁₆	—	2	1	no	—
94	M₁₆	—	94	1	no	—
95	M₁₆	—	94	1	no	—
96	M₁₆	—	94	1	no	—
97	M₁₆	—	94	1	no	—
98	M₁₆	—	94	1	no	—
99	M₁₆	—	94	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	47	2	no	—
102	C₂×C₈	—	94	1	no	—
103	C₂×C₈	—	94	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	94	1	no	—
106	C₂²⋊C₄	—	2	1	no	—
107	C₂²⋊C₄	—	94	1	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	94	1	no	—
111	C₄²	Dic₉₄	1	1	yes	characteristic
112	C₄²	Dic₉₄	1	1	yes	characteristic
113	C₂³	#10625352	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	188	1	no	—
119	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
120	C₂×C₄	#10625350	1	1	yes	characteristic
121	C₂×C₄	#10625350	1	1	yes	characteristic
122	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
123	C₂×C₄	#10625352	1	1	yes	characteristic
124	C₂×C₄	#10625354	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	94	2	no	—
127	C₈	—	188	1	no	—
128	C₈	—	188	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	#13094001	1	1	yes	characteristic
131	C₂²	#13094017	1	1	yes	characteristic
132	C₂²	#13094019	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	4	1	no	—
135	C₄	—	8	1	no	—
136	C₄	—	376	1	no	—
137	C₄	#13094009	1	1	yes	characteristic
138	C₄	#13094010	1	1	yes	characteristic
139	C₄	#13094015	1	1	yes	characteristic
140	C₄	#13094016	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#15689065	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689171

C₂

yes

maximal, characteristic

#15689147

C₂

yes

maximal, characteristic

#15688894

C₂

yes

maximal, characteristic

#15688893

C₂

yes

maximal, characteristic

#15688883

C₂

yes

maximal, characteristic

#15688879

C₂

yes

maximal, characteristic

C₄₇×#339

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

#13093959

—

C₄⋊(C₄₇⋊C₈)

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

Q₈

yes

characteristic

C₄²×C₄₇

Q₈

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

—

—

—

—

—

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#2102

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

H(3,ℤ/4)

—

C₄₇

#2102

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#117

—

#117

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

#108

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

Dic₉₄

yes

characteristic

112

C₄²

Dic₉₄

yes

characteristic

113

C₂³

#10625352

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

188

—

119

C₂×C₄

C₂×Dic₉₄

yes

characteristic

120

C₂×C₄

#10625350

yes

characteristic

121

C₂×C₄

#10625350

yes

characteristic

122

C₂×C₄

D₄×D₄₇

yes

characteristic

123

C₂×C₄

#10625352

yes

characteristic

124

C₂×C₄

#10625354

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

188

—

128

C₈

—

188

—

129

C₂²

—

130

C₂²

#13094001

yes

characteristic

131

C₂²

#13094017

yes

characteristic

132

C₂²

#13094019

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

376

—

137

C₄

#13094009

yes

characteristic

138

C₄

#13094010

yes

characteristic

139

C₄

#13094015

yes

characteristic

140

C₄

#13094016

yes

characteristic

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

#15689065

yes

characteristic

	subgroup	G/H
center	C₄	#13094010
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#339	C₂
socle	C₂×C₄₇	#400
hypercenter	#339	D₄₇
hypocenter	C₄₇	#2102
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

subgroup

G/H

center

C₄

#13094010

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#339

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

N	H ≅ G/N	type
80. C₄₇	#2102	semidirect

H ≅ G/N

type

80. C₄₇

#2102

semidirect

Subgroups — #20244966

Conjugacy classes of subgroups

Complements