Group #20249053 — subgroups

Subgroups — #20249053

Order 6016.

444 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 141 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	#15689059	C₂	1	2	yes	maximal
2	#15689035	C₂	1	2	yes	maximal
3	#15689027	C₂	1	4	yes	maximal, complemented
4	#15689010	C₂	1	4	yes	maximal, complemented
5	C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
6	C₄₇×#381	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₉₄	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₄₇⋊#95	C₂²	1	2	yes	—
15	C₄₇⋊#95	C₂²	1	4	yes	—
16	C₄₇⋊#95	C₂²	1	2	yes	—
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	#95×C₄₇	C₂²	1	4	yes	—
21	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₇	—	4	1	no	—
23	C₂²×C₄×C₄₇	—	4	1	no	—
24	C₂²×C₄×C₄₇	Q₈	1	4	yes	complemented
25	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
28	C₂²×Dic₄₇	C₂³	1	4	yes	—
29	C₂²×Dic₄₇	C₂³	1	4	yes	—
30	C₂×Dic₉₄	—	2	8	no	—
31	C₂×Dic₉₄	—	4	2	no	—
32	C₂²⋊C₄×C₄₇	—	4	1	no	—
33	C₂²⋊C₄×C₄₇	—	4	1	no	—
34	C₂²⋊Dic₄₇	—	2	8	no	—
35	C₄⋊Dic₄₇	—	4	2	no	—
36	Dic₄₇⋊C₄	—	2	8	no	—
37	C₄×Dic₄₇	—	4	2	no	—
38	C₄×Dic₄₇	—	4	2	no	—
39	C₂³×C₄₇	—	2	4	no	—
40	C₂³×C₄₇	—	2	1	no	—
41	C₂³×C₄₇	—	2	1	no	—
42	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
43	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₄₇	—	2	2	no	—
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×C₄×C₄₇	—	2	4	no	—
48	C₂×C₄×C₄₇	—	2	2	no	—
49	C₂×C₄×C₄₇	—	2	2	no	—
50	C₂×C₄×C₄₇	—	4	4	no	—
51	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
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	C₂×Dic₄₇	—	2	4	no	—
57	C₂×Dic₄₇	#41	1	8	yes	—
58	Dic₉₄	—	4	8	no	—
59	C₂²×C₄₇	—	2	4	no	—
60	C₂²×C₄₇	—	2	2	no	—
61	C₂²×C₄₇	—	4	2	no	—
62	C₂²×C₄₇	—	4	2	no	—
63	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
64	C₂²×C₄₇	C₂×#41	1	4	yes	—
65	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
67	C₄×C₄₇	—	2	4	no	—
68	C₄×C₄₇	—	4	2	no	—
69	C₄×C₄₇	—	4	2	no	—
70	Dic₄₇	—	2	8	no	—
71	Dic₄₇	—	4	4	no	—
72	#2607	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	—	4	2	no	—
74	C₂×C₄₇	#533	1	2	yes	—
75	C₂×C₄₇	#543	1	1	yes	characteristic
76	C₂×C₄₇	#551	1	2	yes	—
77	C₂×C₄₇	#559	1	2	yes	—
78	#399	—	47	2	no	—
79	#393	—	47	2	no	—
80	#391	—	47	4	no	—
81	#387	—	47	4	no	—
82	#381	D₄₇	1	1	yes	characteristic
83	C₄×C₂²⋊C₄	—	47	2	no	—
84	C₄₇	#2607	1	1	yes	characteristic, complemented, Sylow
85	C₂²×Q₈	—	47	2	no	—
86	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	47	4	no	—
88	C₂×C₄⋊C₄	—	47	2	no	—
89	C₂×C₂²⋊C₄	—	47	4	no	—
90	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
91	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
92	C₂×C₄²	—	47	2	no	—
93	C₂×C₄²	—	47	2	no	—
94	#95	—	47	4	no	—
95	#95	—	47	2	no	—
96	#95	—	47	4	no	—
97	#95	—	47	2	no	—
98	#95	C₂×D₄₇	1	4	yes	—
99	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
100	C₂×Q₈	—	94	8	no	—
101	C₂×Q₈	—	188	2	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	—	4	1	no	—
104	C₂²×C₄	—	47	4	no	—
105	C₂²×C₄	—	47	4	no	—
106	C₂²×C₄	Dic₉₄	1	4	yes	complemented
107	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
108	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
110	C₄⋊C₄	—	94	8	no	—
111	C₄⋊C₄	—	188	2	no	—
112	C₂²⋊C₄	—	4	1	no	—
113	C₂²⋊C₄	—	4	1	no	—
114	C₂²⋊C₄	—	94	8	no	—
115	C₄²	—	188	2	no	—
116	C₄²	—	188	2	no	—
117	C₂³	—	2	4	no	—
118	C₂³	—	2	1	no	—
119	C₂³	—	2	1	no	—
120	C₂³	C₂×Dic₉₄	1	2	yes	—
121	C₂³	C₂³×D₄₇	1	1	yes	characteristic
122	Q₈	—	188	8	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	47	8	no	—
131	C₂×C₄	—	94	4	no	—
132	C₂×C₄	—	94	4	no	—
133	C₂×C₄	—	94	4	no	—
134	C₂×C₄	—	94	4	no	—
135	C₂×C₄	—	94	4	no	—
136	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
137	C₂²	—	2	2	no	—
138	C₂²	—	2	4	no	—
139	C₂²	—	4	2	no	—
140	C₂²	—	4	2	no	—
141	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
142	C₂²	#41×D₄₇	1	4	yes	—
143	C₂²	#13094069	1	1	yes	characteristic
144	C₂²	#13094069	1	1	yes	characteristic
145	C₄	—	2	4	no	—
146	C₄	—	4	2	no	—
147	C₄	—	4	2	no	—
148	C₄	—	94	8	no	—
149	C₄	—	188	4	no	—
150	C₂	—	4	2	no	—
151	C₂	#15689676	1	2	yes	—
152	C₂	#15689749	1	1	yes	characteristic
153	C₂	#15689801	1	2	yes	—
154	C₂	#15689857	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689059

C₂

yes

maximal

#15689035

C₂

yes

maximal

#15689027

C₂

yes

maximal, complemented

#15689010

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal

C₄₇×#381

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

Q₈

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×Q₈

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

#41

yes

—

Dic₉₄

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2607

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#533

yes

—

C₂×C₄₇

#543

yes

characteristic

C₂×C₄₇

#551

yes

—

C₂×C₄₇

#559

yes

—

—

—

—

—

D₄₇

yes

characteristic

C₄×C₂²⋊C₄

—

C₄₇

#2607

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₂²⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

—

—

—

—

C₂×D₄₇

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

100

C₂×Q₈

—

101

C₂×Q₈

—

188

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

Dic₉₄

yes

complemented

107

C₂²×C₄

C₂²×D₄₇

yes

—

108

C₂²×C₄

C₂²×D₄₇

yes

—

109

C₂²×C₄

C₂²×D₄₇

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

188

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

188

—

116

C₄²

—

188

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×Dic₉₄

yes

—

121

C₂³

C₂³×D₄₇

yes

characteristic

122

Q₈

—

188

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×Dic₉₄

yes

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂²×Dic₉₄

yes

characteristic

142

C₂²

#41×D₄₇

yes

—

143

C₂²

#13094069

yes

characteristic

144

C₂²

#13094069

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

188

—

150

C₂

—

151

C₂

#15689676

yes

—

152

C₂

#15689749

yes

characteristic

153

C₂

#15689801

yes

—

154

C₂

#15689857

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#381	C₂
hypercenter	#381	D₄₇
hypocenter	C₄₇	#2607
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#381

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
3. #15689027	C₂	semidirect
4. #15689010	C₂	semidirect
24. C₂²×C₄×C₄₇	Q₈	semidirect
84. C₄₇	#2607	semidirect
106. C₂²×C₄	Dic₉₄	semidirect

H ≅ G/N

type

3. #15689027

C₂

semidirect

4. #15689010

C₂

semidirect

24. C₂²×C₄×C₄₇

Q₈

semidirect

84. C₄₇

#2607

semidirect

106. C₂²×C₄

Dic₉₄

semidirect

Subgroups — #20249053

Conjugacy classes of subgroups

Complements