Group #20249363 — subgroups

Subgroups — #20249363

Order 6016.

360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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	#15689065	C₂	1	4	yes	maximal
2	#15689057	C₂	1	4	yes	maximal
3	#15689021	C₂	1	2	yes	maximal
4	#15689021	C₂	1	2	yes	maximal
5	#15688993	C₂	1	1	yes	maximal, characteristic
6	#15688989	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#376	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₄₇⋊#95	C₂²	1	4	yes	—
15	C₄₇⋊#95	C₂²	1	4	yes	—
16	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	#95×C₄₇	C₂²	1	2	yes	—
20	#95×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂³	1	4	yes	—
27	C₂²×Dic₄₇	C₂³	1	4	yes	—
28	C₄²×C₄₇	—	2	2	no	—
29	C₄²×C₄₇	—	2	2	no	—
30	C₄²×C₄₇	Q₈	1	4	yes	—
31	C₄⋊Dic₄₇	—	2	4	no	—
32	C₄⋊Dic₄₇	—	2	4	no	—
33	C₄⋊Dic₄₇	—	4	4	no	—
34	Dic₄₇⋊C₄	—	4	4	no	—
35	Dic₄₇⋊C₄	—	4	4	no	—
36	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	—	2	1	no	—
40	C₂×C₄×C₄₇	—	2	1	no	—
41	C₂×C₄×C₄₇	—	2	2	no	—
42	C₂×C₄×C₄₇	—	2	2	no	—
43	C₂×C₄×C₄₇	—	2	2	no	—
44	C₂×C₄×C₄₇	—	2	2	no	—
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
47	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₄₇	#41	1	2	yes	—
49	C₂×C₄×C₄₇	#41	1	2	yes	—
50	C₂×Dic₄₇	—	2	4	no	—
51	C₂×Dic₄₇	—	2	4	no	—
52	C₂×Dic₄₇	—	2	4	no	—
53	C₂×Dic₄₇	—	2	4	no	—
54	C₂×Dic₄₇	—	2	4	no	—
55	C₂×Dic₄₇	—	2	4	no	—
56	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
57	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
58	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
59	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
60	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
61	C₄×C₄₇	—	2	4	no	—
62	C₄×C₄₇	—	4	1	no	—
63	C₄×C₄₇	—	4	1	no	—
64	C₄×C₄₇	—	4	2	no	—
65	C₄×C₄₇	#125	1	4	yes	—
66	Dic₄₇	—	4	4	no	—
67	Dic₄₇	—	4	4	no	—
68	#2647	—	47	1	no	maximal, Sylow
69	C₂×C₄₇	C₂×#125	1	1	yes	characteristic
70	C₂×C₄₇	#540	1	1	yes	characteristic
71	C₂×C₄₇	#541	1	1	yes	characteristic
72	C₂×C₄₇	#542	1	2	yes	—
73	C₂×C₄₇	#544	1	2	yes	—
74	#400	—	47	4	no	—
75	#398	—	47	4	no	—
76	#389	—	47	2	no	—
77	#389	—	47	2	no	—
78	#384	—	47	1	no	—
79	#382	—	47	1	no	—
80	#376	D₄₇	1	1	yes	characteristic
81	C₄₇	#2647	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₄⋊C₄	—	47	2	no	—
83	C₂×C₄⋊C₄	—	47	2	no	—
84	C₂×C₄⋊C₄	—	47	4	no	—
85	C₂×C₄⋊C₄	—	47	4	no	—
86	C₂×C₄⋊C₄	—	47	4	no	—
87	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
88	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
89	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
90	#95	—	47	4	no	—
91	#95	—	47	4	no	—
92	#95	—	47	4	no	—
93	#95	C₂×D₄₇	1	2	yes	—
94	#95	C₂×D₄₇	1	2	yes	—
95	C₂²×C₄	—	47	4	no	—
96	C₂²×C₄	—	47	4	no	—
97	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
99	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
101	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
102	C₄⋊C₄	—	94	4	no	—
103	C₄⋊C₄	—	94	4	no	—
104	C₄⋊C₄	—	188	4	no	—
105	C₄⋊C₄	—	188	4	no	—
106	C₄⋊C₄	—	188	4	no	—
107	C₄²	—	2	2	no	—
108	C₄²	—	2	2	no	—
109	C₄²	Dic₉₄	1	4	yes	—
110	C₂³	C₂³×D₄₇	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	94	4	no	—
121	C₂×C₄	—	94	4	no	—
122	C₂×C₄	—	94	4	no	—
123	C₂×C₄	—	94	4	no	—
124	C₂×C₄	—	94	4	no	—
125	C₂×C₄	—	94	4	no	—
126	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
127	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
128	C₂×C₄	#10625350	1	2	yes	—
129	C₂×C₄	#10625350	1	2	yes	—
130	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
131	C₂²	C₂×#10625350	1	1	yes	characteristic
132	C₂²	C₂×#10625350	1	1	yes	characteristic
133	C₂²	#13094070	1	2	yes	—
134	C₂²	#13094071	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	4	2	no	—
139	C₄	—	188	4	no	—
140	C₄	—	188	4	no	—
141	C₄	#13094016	1	4	yes	—
142	C₂	C₂×#13094016	1	1	yes	characteristic
143	C₂	#15689728	1	1	yes	characteristic
144	C₂	#15689735	1	1	yes	characteristic
145	C₂	#15689744	1	2	yes	—
146	C₂	#15689751	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689065

C₂

yes

maximal

#15689057

C₂

yes

maximal

#15689021

C₂

yes

maximal

#15689021

C₂

yes

maximal

#15688993

C₂

yes

maximal, characteristic

#15688989

C₂

yes

maximal, characteristic

C₄₇×#376

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

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

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#125

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#544

yes

—

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2647

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

—

#95

C₂×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

100

C₂²×C₄

C₂²×D₄₇

yes

—

101

C₂²×C₄

C₂²×D₄₇

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

188

—

105

C₄⋊C₄

—

188

—

106

C₄⋊C₄

—

188

—

107

C₄²

—

108

C₄²

—

109

C₄²

Dic₉₄

yes

—

110

C₂³

C₂³×D₄₇

yes

characteristic

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

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₉₄

yes

—

127

C₂×C₄

C₂×Dic₉₄

yes

—

128

C₂×C₄

#10625350

yes

—

129

C₂×C₄

#10625350

yes

—

130

C₂²

C₂²×Dic₉₄

yes

characteristic

131

C₂²

C₂×#10625350

yes

characteristic

132

C₂²

C₂×#10625350

yes

characteristic

133

C₂²

#13094070

yes

—

134

C₂²

#13094071

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

188

—

140

C₄

—

188

—

141

C₄

#13094016

yes

—

142

C₂

C₂×#13094016

yes

characteristic

143

C₂

#15689728

yes

characteristic

144

C₂

#15689735

yes

characteristic

145

C₂

#15689744

yes

—

146

C₂

#15689751

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#2647
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#376

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
81. C₄₇	#2647	semidirect

H ≅ G/N

type

81. C₄₇

#2647

semidirect

Subgroups — #20249363

Conjugacy classes of subgroups

Complements