Group #20249358 — subgroups

Subgroups — #20249358

Order 6016.

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

normal subgroups only

This group has 436 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, complemented
2	#15689057	C₂	1	4	yes	maximal, complemented
3	#15688996	C₂	1	4	yes	maximal
4	#15688983	C₂	1	2	yes	maximal
5	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
11	C₄₇⋊#95	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	4	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
15	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	#95×C₄₇	C₂²	1	4	yes	—
17	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	—	2	4	no	—
19	C₂²×C₄×C₄₇	—	4	2	no	—
20	C₂²×C₄×C₄₇	—	4	2	no	—
21	C₂²×C₄×C₄₇	—	4	2	no	—
22	C₂²×C₄×C₄₇	Q₈	1	4	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
25	C₂²×Dic₄₇	C₂³	1	4	yes	—
26	C₂²×Dic₄₇	C₂³	1	4	yes	—
27	C₂²⋊Dic₄₇	—	2	8	no	—
28	C₄⋊Dic₄₇	—	4	2	no	—
29	C₄⋊Dic₄₇	—	4	2	no	—
30	Dic₄₇⋊C₄	—	4	4	no	—
31	Dic₄₇⋊C₄	—	4	4	no	—
32	C₂³×C₄₇	—	2	1	no	—
33	C₂³×C₄₇	—	2	2	no	—
34	C₂³×C₄₇	—	2	1	no	—
35	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
36	C₂³×C₄₇	#41	1	4	yes	—
37	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	—	2	2	no	—
40	C₂×C₄×C₄₇	—	2	4	no	—
41	C₂×C₄×C₄₇	—	2	4	no	—
42	C₂×C₄×C₄₇	—	2	4	no	—
43	C₂×C₄×C₄₇	—	4	4	no	—
44	C₂×C₄×C₄₇	—	4	8	no	—
45	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
46	C₂×Dic₄₇	—	2	4	no	—
47	C₂×Dic₄₇	—	2	4	no	—
48	C₂×Dic₄₇	—	2	4	no	—
49	C₂×Dic₄₇	—	2	4	no	—
50	C₂×Dic₄₇	—	2	4	no	—
51	C₂×Dic₄₇	—	2	4	no	—
52	C₂²×C₄₇	—	2	4	no	—
53	C₂²×C₄₇	—	2	4	no	—
54	C₂²×C₄₇	—	2	2	no	—
55	C₂²×C₄₇	—	2	2	no	—
56	C₂²×C₄₇	#125	1	4	yes	—
57	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
58	C₂²×C₄₇	C₂×#41	1	2	yes	—
59	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
60	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
61	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
62	C₄×C₄₇	—	2	4	no	—
63	C₄×C₄₇	—	4	4	no	—
64	Dic₄₇	—	4	4	no	—
65	Dic₄₇	—	4	4	no	—
66	#2646	—	47	1	no	maximal, Sylow
67	C₂×C₄₇	—	2	4	no	—
68	C₂×C₄₇	C₂×#125	1	1	yes	characteristic
69	C₂×C₄₇	#538	1	2	yes	—
70	C₂×C₄₇	#539	1	2	yes	—
71	C₂×C₄₇	#543	1	1	yes	characteristic
72	C₂×C₄₇	#544	1	1	yes	characteristic
73	#400	—	47	4	no	—
74	#398	—	47	4	no	—
75	#385	—	47	4	no	—
76	#380	—	47	2	no	—
77	C₂×#95	D₄₇	1	1	yes	characteristic
78	C₄₇	#2646	1	1	yes	characteristic, complemented, Sylow
79	C₂³×C₄	C₂×D₄₇	1	2	yes	—
80	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
81	C₂×C₄⋊C₄	—	47	4	no	—
82	C₂×C₄⋊C₄	—	47	4	no	—
83	C₂×C₄⋊C₄	—	47	2	no	—
84	C₂×C₄⋊C₄	—	47	2	no	—
85	C₂×C₂²⋊C₄	—	47	4	no	—
86	#95	—	47	4	no	—
87	#95	—	47	4	no	—
88	#95	—	47	4	no	—
89	#95	C₂×D₄₇	1	4	yes	—
90	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
91	C₂²×C₄	—	2	4	no	—
92	C₂²×C₄	—	4	2	no	—
93	C₂²×C₄	—	4	2	no	—
94	C₂²×C₄	—	4	2	no	—
95	C₂²×C₄	—	47	4	no	—
96	C₂²×C₄	—	47	4	no	—
97	C₂²×C₄	Dic₉₄	1	4	yes	—
98	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
99	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
100	C₄⋊C₄	—	188	4	no	—
101	C₄⋊C₄	—	188	4	no	—
102	C₄⋊C₄	—	188	2	no	—
103	C₄⋊C₄	—	188	2	no	—
104	C₂²⋊C₄	—	94	8	no	—
105	C₂³	—	2	2	no	—
106	C₂³	—	2	1	no	—
107	C₂³	—	2	1	no	—
108	C₂³	C₂×Dic₉₄	1	2	yes	—
109	C₂³	#10625350	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	4	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	8	no	—
118	C₂×C₄	—	94	4	no	—
119	C₂×C₄	—	94	4	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	C₂×Dic₉₄	1	4	yes	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	2	4	no	—
128	C₂²	—	2	4	no	—
129	C₂²	#13094016	1	4	yes	—
130	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
131	C₂²	C₂×#10625350	1	2	yes	—
132	C₂²	#13094069	1	2	yes	—
133	C₂²	#13094069	1	1	yes	characteristic
134	C₂²	#13094072	1	1	yes	characteristic
135	C₄	—	2	4	no	—
136	C₄	—	4	4	no	—
137	C₄	—	188	4	no	—
138	C₄	—	188	4	no	—
139	C₂	—	2	4	no	—
140	C₂	C₂×#13094016	1	1	yes	characteristic
141	C₂	#15689711	1	2	yes	—
142	C₂	#15689720	1	2	yes	—
143	C₂	#15689749	1	1	yes	characteristic
144	C₂	#15689754	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689065

C₂

yes

maximal, complemented

#15689057

C₂

yes

maximal, complemented

#15688996

C₂

yes

maximal

#15688983

C₂

yes

maximal

C₂×#95×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

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×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#125

yes

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2646

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#125

yes

characteristic

C₂×C₄₇

#538

yes

—

C₂×C₄₇

#539

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

C₂×#95

D₄₇

yes

characteristic

C₄₇

#2646

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₄₇

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

100

C₄⋊C₄

—

188

—

101

C₄⋊C₄

—

188

—

102

C₄⋊C₄

—

188

—

103

C₄⋊C₄

—

188

—

104

C₂²⋊C₄

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂×Dic₉₄

yes

—

109

C₂³

#10625350

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

C₂×Dic₉₄

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#13094016

yes

—

130

C₂²

C₂²×Dic₉₄

yes

characteristic

131

C₂²

C₂×#10625350

yes

—

132

C₂²

#13094069

yes

—

133

C₂²

#13094069

yes

characteristic

134

C₂²

#13094072

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

188

—

138

C₄

—

188

—

139

C₂

—

140

C₂

C₂×#13094016

yes

characteristic

141

C₂

#15689711

yes

—

142

C₂

#15689720

yes

—

143

C₂

#15689749

yes

characteristic

144

C₂

#15689754

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#95×C₄₇	C₂
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#2646
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#95×C₄₇

C₂

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
1. #15689065	C₂	semidirect
2. #15689057	C₂	semidirect
78. C₄₇	#2646	semidirect

H ≅ G/N

type

1. #15689065

C₂

semidirect

2. #15689057

C₂

semidirect

78. C₄₇

#2646

semidirect

Subgroups — #20249358

Conjugacy classes of subgroups

Complements