Group #20253899 — subgroups

Subgroups — #20253899

Order 6016.

356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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	#15689678	C₂	1	2	yes	maximal
2	#15689528	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689524	C₂	1	4	yes	maximal, complemented
4	#15689519	C₂	1	2	yes	maximal, complemented
5	#15689160	C₂	1	4	yes	maximal
6	C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄₇	C₂²	1	2	yes	—
9	#13094024	C₂²	1	2	yes	—
10	#13094015	C₂²	1	4	yes	—
11	#13094004	—	2	2	no	—
12	#13094000	—	2	2	no	—
13	Q₈×Dic₄₇	—	2	2	no	—
14	#13093989	—	2	2	no	—
15	#13093982	C₂²	1	4	yes	—
16	C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#13093958	C₂²	1	4	yes	—
18	#13093955	C₂²	1	8	yes	—
19	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	#107×C₄₇	C₂²	1	4	yes	—
23	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
26	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₄	—	2	2	no	—
29	C₂×C₈×C₄₇	C₂³	1	2	yes	—
30	C₄⋊C₄×C₄₇	—	2	2	no	—
31	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
32	C₄²×C₄₇	C₂³	1	1	yes	characteristic
33	(C₂×D₄₇)⋊C₄	—	2	4	no	—
34	C₄⋊Dic₄₇	—	2	2	no	—
35	C₄⋊Dic₄₇	—	2	4	no	—
36	C₄⋊Dic₄₇	C₂³	1	4	yes	—
37	Dic₄₇⋊C₄	—	2	4	no	—
38	C₄×Dic₄₇	—	2	4	no	—
39	C₄×Dic₄₇	D₄	1	1	yes	characteristic
40	C₄×Dic₄₇	D₄	1	1	yes	characteristic
41	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
42	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₈×D₄₇	Q₈	1	8	yes	complemented
44	C₂²×D₄₇	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₄₇	—	4	4	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₄₇	—	2	4	no	—
51	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₄₇	C₂×D₄	1	1	yes	characteristic
54	C₄×D₄₇	—	2	2	no	—
55	C₄×D₄₇	—	2	2	no	—
56	C₄×D₄₇	C₂×Q₈	1	4	yes	—
57	Dic₉₄	—	4	4	no	—
58	C₈×C₄₇	C₂×Q₈	1	4	yes	—
59	C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
60	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
61	C₂×D₄₇	—	2	1	no	—
62	C₂×D₄₇	—	2	1	no	—
63	C₂×D₄₇	C₄⋊Q₈	1	2	yes	—
64	C₄×C₄₇	—	4	4	no	—
65	C₄×C₄₇	#135	1	2	yes	—
66	C₄×C₄₇	#135	1	2	yes	—
67	C₄×C₄₇	C₂²×Q₈	1	2	yes	—
68	Dic₄₇	—	2	1	no	—
69	Dic₄₇	—	2	1	no	—
70	Dic₄₇	—	4	4	no	—
71	Dic₄₇	C₄⋊Q₈	1	2	yes	—
72	#3160	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
75	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
76	D₄₇	—	2	2	no	—
77	#533	—	47	2	no	—
78	#500	—	47	1	no	—
79	#500	D₄₇	1	1	yes	characteristic, complemented
80	#499	—	47	4	no	—
81	#498	—	47	2	no	—
82	#427	—	47	4	no	—
83	C₂×C₄×C₈	—	47	1	no	—
84	C₄₇	#3160	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₈	—	47	2	no	—
86	C₄⋊Q₈	—	47	2	no	—
87	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
88	#125	—	47	4	no	—
89	C₂²⋊Q₈	—	94	2	no	—
90	C₂²⋊Q₈	—	94	2	no	—
91	C₄×Q₈	—	94	2	no	—
92	C₄×Q₈	—	94	2	no	—
93	#117	—	47	4	no	—
94	C₂×C₄²	—	47	1	no	—
95	#107	—	47	4	no	—
96	#107	C₂×D₄₇	1	4	yes	—
97	#106	—	47	8	no	—
98	C₄×C₈	—	47	2	no	—
99	C₄×C₈	—	47	1	no	—
100	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	94	2	no	—
103	C₂²×C₄	—	47	1	no	—
104	C₂²×C₄	—	47	1	no	—
105	C₂²×C₄	—	47	1	no	—
106	C₂×C₈	—	47	2	no	—
107	C₂×C₈	—	47	8	no	—
108	C₂×C₈	C₂²×D₄₇	1	2	yes	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	47	4	no	—
111	C₄⋊C₄	—	94	4	no	—
112	C₄⋊C₄	—	94	4	no	—
113	C₄⋊C₄	—	94	2	no	—
114	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
115	C₂²⋊C₄	—	94	4	no	—
116	C₄²	—	47	1	no	—
117	C₄²	—	47	1	no	—
118	C₄²	—	47	1	no	—
119	C₄²	—	94	4	no	—
120	C₄²	C₂²×D₄₇	1	1	yes	characteristic
121	C₂³	—	47	1	no	—
122	Q₈	—	4	4	no	—
123	Q₈	—	188	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	47	1	no	—
126	C₂×C₄	—	47	4	no	—
127	C₂×C₄	—	47	1	no	—
128	C₂×C₄	—	47	1	no	—
129	C₂×C₄	—	94	2	no	—
130	C₂×C₄	—	94	2	no	—
131	C₂×C₄	—	94	4	no	—
132	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
133	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
135	C₈	—	47	4	no	—
136	C₈	Q₈×D₄₇	1	4	yes	—
137	C₂²	—	47	2	no	—
138	C₂²	—	94	1	no	—
139	C₂²	—	94	1	no	—
140	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
141	C₄	—	4	4	no	—
142	C₄	—	47	2	no	—
143	C₄	—	94	1	no	—
144	C₄	—	94	1	no	—
145	C₄	—	188	4	no	—
146	C₄	#13094043	1	2	yes	—
147	C₄	#13094047	1	2	yes	—
148	C₄	C₂×Q₈×D₄₇	1	2	yes	—
149	C₂	—	94	2	no	—
150	C₂	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
151	C₂	C₂×#13094043	1	1	yes	characteristic
152	C₂	C₂×#13094047	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689678

C₂

yes

maximal

#15689528

C₂

yes

maximal, characteristic, complemented

#15689524

C₂

yes

maximal, complemented

#15689519

C₂

yes

maximal, complemented

#15689160

C₂

yes

maximal

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic

C₄₇×#500

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₂²

yes

—

#13094024

C₂²

yes

—

#13094015

C₂²

yes

—

#13094004

—

#13094000

—

Q₈×Dic₄₇

—

#13093989

—

#13093982

C₂²

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093958

C₂²

yes

—

#13093955

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

#107×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×C₄×D₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

C₂³

yes

characteristic

C₂×C₄₇⋊C₈

C₂³

yes

—

C₈×D₄₇

Q₈

yes

complemented

C₂²×D₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

C₂×D₄

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

C₂×Q₈

yes

—

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

—

C₄₇⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

C₂²×Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₄⋊Q₈

yes

—

#3160

—

maximal, Sylow

C₂×C₄₇

C₂×C₄⋊Q₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#533

—

#500

—

#500

D₄₇

yes

characteristic, complemented

#499

—

#498

—

#427

—

C₂×C₄×C₈

—

C₄₇

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#107

C₂×D₄₇

yes

—

#106

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₂×D₄₇

yes

characteristic

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₇

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²×D₄₇

yes

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₂²×D₄₇

yes

characteristic

121

C₂³

—

122

Q₈

—

123

Q₈

—

188

—

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

D₄×D₄₇

yes

characteristic

133

C₂×C₄

D₄×D₄₇

yes

characteristic

134

C₂×C₄

C₂³×D₄₇

yes

characteristic

135

C₈

—

136

C₈

Q₈×D₄₇

yes

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×D₄×D₄₇

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

188

—

146

C₄

#13094043

yes

—

147

C₄

#13094047

yes

—

148

C₄

C₂×Q₈×D₄₇

yes

—

149

C₂

—

150

C₂

C₄⋊Q₈×D₄₇

yes

characteristic

151

C₂

C₂×#13094043

yes

characteristic

152

C₂

C₂×#13094047

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#500	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#500	D₄₇
hypocenter	C₄₇	#3160
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#500

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
2. #15689528	C₂	semidirect
3. #15689524	C₂	semidirect
4. #15689519	C₂	semidirect
7. C₄₇×#500	C₂	semidirect
43. C₈×D₄₇	Q₈	semidirect
79. #500	D₄₇	semidirect
84. C₄₇	#3160	semidirect

H ≅ G/N

type

2. #15689528

C₂

semidirect

3. #15689524

C₂

semidirect

4. #15689519

C₂

semidirect

7. C₄₇×#500

C₂

semidirect

43. C₈×D₄₇

Q₈

semidirect

79. #500

D₄₇

semidirect

84. C₄₇

#3160

semidirect

Subgroups — #20253899

Conjugacy classes of subgroups

Complements