Group #20251749 — subgroups

Subgroups — #20251749

Order 6016.

472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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×#13094015	C₂	1	2	yes	maximal
2	#15689022	C₂	1	4	yes	maximal
3	#15689019	C₂	1	4	yes	maximal
4	#15688993	C₂	1	1	yes	maximal, characteristic
5	#15688988	C₂	1	2	yes	maximal
6	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#384	C₂	1	1	yes	maximal, characteristic
8	#13094015	—	2	8	no	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
12	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₄₇⋊#95	C₂²	1	8	yes	—
18	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
20	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
24	C₂²×Dic₄₇	C₂³	1	4	yes	—
25	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₇	C₂³	1	2	yes	—
28	C₄⋊C₄×C₄₇	—	2	4	no	—
29	C₄⋊C₄×C₄₇	—	2	8	no	—
30	C₄²×C₄₇	Q₈	1	4	yes	—
31	C₄⋊Dic₄₇	—	2	4	no	—
32	C₄⋊Dic₄₇	—	2	8	no	—
33	C₄⋊Dic₄₇	—	2	8	no	—
34	Dic₄₇⋊C₄	—	2	8	no	—
35	C₄×Dic₄₇	—	2	4	no	—
36	C₄×Dic₄₇	—	2	4	no	—
37	C₄×Dic₄₇	D₄	1	4	yes	—
38	C₄×Dic₄₇	Q₈	1	4	yes	—
39	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₄₇	—	2	4	no	—
41	C₂×C₄×C₄₇	—	2	8	no	—
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₄₇	#41	1	4	yes	—
47	C₂×C₄×C₄₇	#41	1	4	yes	—
48	C₂×Dic₄₇	—	2	2	no	—
49	C₂×Dic₄₇	—	2	2	no	—
50	C₂×Dic₄₇	—	2	2	no	—
51	C₂×Dic₄₇	—	2	2	no	—
52	C₂×Dic₄₇	—	2	4	no	—
53	C₂×Dic₄₇	—	2	8	no	—
54	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
55	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
56	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
57	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
58	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
59	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
60	C₂²×C₄₇	C₂×#41	1	2	yes	—
61	C₂²×C₄₇	C₂×#41	1	2	yes	—
62	C₄×C₄₇	—	4	4	no	—
63	C₄×C₄₇	#125	1	8	yes	complemented
64	C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
65	Dic₄₇	—	2	2	no	—
66	Dic₄₇	—	2	2	no	—
67	Dic₄₇	—	2	4	no	—
68	Dic₄₇	—	4	4	no	—
69	#2859	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	C₂×#125	1	2	yes	—
71	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄₇	#532	1	1	yes	characteristic
73	C₂×C₄₇	#532	1	1	yes	characteristic
74	C₂×C₄₇	#533	1	2	yes	—
75	C₂×#125	—	47	2	no	—
76	#389	—	47	4	no	—
77	#389	—	47	4	no	—
78	#384	—	47	1	no	—
79	#384	D₄₇	1	1	yes	characteristic
80	#382	—	47	2	no	—
81	C₄³	—	47	1	no	—
82	C₄₇	#2859	1	1	yes	characteristic, complemented, Sylow
83	#125	—	94	8	no	—
84	C₂×C₄⋊C₄	—	47	4	no	—
85	C₂×C₄⋊C₄	—	47	2	no	—
86	C₂×C₄⋊C₄	—	47	4	no	—
87	C₂×C₄⋊C₄	—	47	4	no	—
88	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
89	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
90	C₂×C₄²	—	47	1	no	—
91	C₂×C₄²	—	47	1	no	—
92	C₂×C₄²	—	47	2	no	—
93	C₂×C₄²	—	47	2	no	—
94	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
95	#95	—	47	8	no	—
96	C₂²×C₄	—	47	2	no	—
97	C₂²×C₄	—	47	1	no	—
98	C₂²×C₄	—	47	1	no	—
99	C₂²×C₄	—	47	4	no	—
100	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
101	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	2	8	no	—
105	C₄⋊C₄	—	94	8	no	—
106	C₄⋊C₄	—	94	8	no	—
107	C₄⋊C₄	—	94	4	no	—
108	C₄⋊C₄	—	94	8	no	—
109	C₄²	—	47	4	no	—
110	C₄²	—	47	4	no	—
111	C₄²	—	94	4	no	—
112	C₄²	—	94	4	no	—
113	C₄²	Dic₉₄	1	4	yes	—
114	C₂³	C₂³×D₄₇	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	47	2	no	—
118	C₂×C₄	—	47	2	no	—
119	C₂×C₄	—	47	4	no	—
120	C₂×C₄	—	94	2	no	—
121	C₂×C₄	—	94	2	no	—
122	C₂×C₄	—	94	2	no	—
123	C₂×C₄	—	94	2	no	—
124	C₂×C₄	—	94	4	no	—
125	C₂×C₄	—	94	8	no	—
126	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
127	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
128	C₂×C₄	D₄×D₄₇	1	2	yes	—
129	C₂×C₄	#10625352	1	4	yes	—
130	C₂×C₄	Q₈×D₄₇	1	2	yes	—
131	C₂×C₄	#10625354	1	4	yes	—
132	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
133	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
134	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
135	C₂²	C₂×#10625352	1	2	yes	—
136	C₂²	C₂×#10625354	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	94	2	no	—
139	C₄	—	94	2	no	—
140	C₄	—	94	4	no	—
141	C₄	—	188	4	no	—
142	C₄	#13094015	1	8	yes	complemented
143	C₄	#13094023	1	4	yes	—
144	C₂	C₂×#13094015	1	2	yes	—
145	C₂	C₂×#13094023	1	1	yes	characteristic
146	C₂	#15689671	1	1	yes	characteristic
147	C₂	#15689674	1	1	yes	characteristic
148	C₂	#15689678	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094015

C₂

yes

maximal

#15689022

C₂

yes

maximal

#15689019

C₂

yes

maximal

#15688993

C₂

yes

maximal, characteristic

#15688988

C₂

yes

maximal

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

C₄₇×#384

C₂

yes

maximal, characteristic

#13094015

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

#125

yes

complemented

C₄×C₄₇

C₄⋊Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2859

—

maximal, Sylow

C₂×C₄₇

C₂×#125

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

#382

—

C₄³

—

C₄₇

#2859

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₄₇

yes

—

101

C₂²×C₄

C₂²×D₄₇

yes

characteristic

102

C₂²×C₄

C₂²×D₄₇

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

Dic₉₄

yes

—

114

C₂³

C₂³×D₄₇

yes

characteristic

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

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₉₄

yes

—

127

C₂×C₄

C₂×Dic₉₄

yes

—

128

C₂×C₄

D₄×D₄₇

yes

—

129

C₂×C₄

#10625352

yes

—

130

C₂×C₄

Q₈×D₄₇

yes

—

131

C₂×C₄

#10625354

yes

—

132

C₂²

C₂×D₄×D₄₇

yes

characteristic

133

C₂²

C₂×Q₈×D₄₇

yes

characteristic

134

C₂²

C₂²×Dic₉₄

yes

characteristic

135

C₂²

C₂×#10625352

yes

—

136

C₂²

C₂×#10625354

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

188

—

142

C₄

#13094015

yes

complemented

143

C₄

#13094023

yes

—

144

C₂

C₂×#13094015

yes

—

145

C₂

C₂×#13094023

yes

characteristic

146

C₂

#15689671

yes

characteristic

147

C₂

#15689674

yes

characteristic

148

C₂

#15689678

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#384	C₂
hypercenter	#384	D₄₇
hypocenter	C₄₇	#2859
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#384

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
63. C₄×C₄₇	#125	semidirect
82. C₄₇	#2859	semidirect
142. C₄	#13094015	semidirect

H ≅ G/N

type

63. C₄×C₄₇

#125

semidirect

82. C₄₇

#2859

semidirect

142. C₄

#13094015

semidirect

Subgroups — #20251749

Conjugacy classes of subgroups

Complements