Group #20244926 — subgroups

Subgroups — #20244926

Order 6016.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13093957	C₂	1	2	yes	maximal
2	C₂×#13093948	C₂	1	2	yes	maximal
3	#15688993	C₂	1	1	yes	maximal, characteristic
4	#15688878	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₇	—	2	2	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	#13093957	—	2	4	no	—
10	#13093948	—	2	4	no	—
11	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	#95×C₄₇	—	2	2	no	—
15	C₂×Q₈×C₄₇	—	2	1	no	—
16	C₂×Q₈×C₄₇	—	2	2	no	—
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×Q₈×C₄₇	Q₈	1	2	yes	—
19	C₂²×C₄×C₄₇	—	2	1	no	—
20	C₂²×C₄×C₄₇	—	2	1	no	—
21	C₂²×C₄×C₄₇	D₄	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂²×Dic₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄²×C₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	2	2	no	—
27	C₄⋊Dic₄₇	—	2	2	no	—
28	C₄⋊Dic₄₇	—	4	4	no	—
29	C₂×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
32	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₄₇	—	2	4	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	—	4	2	no	—
42	C₂×C₄×C₄₇	Q₁₆	1	4	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
46	C₂×C₄×C₄₇	#41	1	2	yes	—
47	C₂×Dic₄₇	—	4	2	no	—
48	C₂×Dic₄₇	—	4	4	no	—
49	C₄₇⋊C₈	—	2	4	no	—
50	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₄₇	#123	1	1	yes	characteristic
52	C₂²×C₄₇	#127	1	1	yes	characteristic
53	C₂²×C₄₇	C₂×Q₁₆	1	2	yes	—
54	C₂²×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
55	C₄×C₄₇	—	2	4	no	—
56	C₄×C₄₇	—	4	2	no	—
57	C₄×C₄₇	—	8	1	no	—
58	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₄₇	#123	1	2	yes	—
60	Dic₄₇	—	8	2	no	—
61	#2095	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	#399	1	1	yes	characteristic
63	C₂×C₄₇	#477	1	2	yes	—
64	C₂×C₄₇	#484	1	2	yes	—
65	C₂×C₄₇	#494	1	1	yes	characteristic
66	C₂×C₄₇	#496	1	1	yes	characteristic
67	C₂×#107	—	47	2	no	—
68	C₂×#103	—	47	2	no	—
69	#391	D₄₇	1	1	yes	characteristic
70	#384	—	47	1	no	—
71	#336	—	47	1	no	—
72	C₄₇	#2095	1	1	yes	characteristic, complemented, Sylow
73	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
74	C₂²×C₈	—	47	2	no	—
75	C₂×C₄⋊C₄	—	47	2	no	—
76	C₂×C₄⋊C₄	—	94	2	no	—
77	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
79	#107	—	94	4	no	—
80	#103	—	94	4	no	—
81	#95	—	2	2	no	—
82	C₂×Q₈	—	2	1	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	Dic₉₄	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	94	2	no	—
89	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
91	C₂×C₈	—	47	4	no	—
92	C₂×C₈	—	94	2	no	—
93	C₂×C₈	—	94	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	94	2	no	—
96	C₄⋊C₄	—	94	2	no	—
97	C₄⋊C₄	—	188	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	188	2	no	—
110	C₂×C₄	—	188	4	no	—
111	C₂×C₄	#10625337	1	4	yes	—
112	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
113	C₂×C₄	#10625350	1	1	yes	characteristic
114	C₂×C₄	D₄×D₄₇	1	2	yes	—
115	C₂×C₄	#10625352	1	2	yes	—
116	C₈	—	94	4	no	—
117	C₂²	#13094003	1	1	yes	characteristic
118	C₂²	#13094005	1	1	yes	characteristic
119	C₂²	#13094020	1	1	yes	characteristic
120	C₂²	C₂×#10625337	1	2	yes	—
121	C₂²	#13094049	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	1	no	—
125	C₄	—	376	2	no	—
126	C₄	#13094001	1	2	yes	—
127	C₄	#13094006	1	2	yes	—
128	C₂	#15689059	1	1	yes	characteristic
129	C₂	#15689418	1	2	yes	—
130	C₂	#15689456	1	2	yes	—
131	C₂	#15689502	1	1	yes	characteristic
132	C₂	#15689513	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093957

C₂

yes

maximal

C₂×#13093948

C₂

yes

maximal

#15688993

C₂

yes

maximal, characteristic

#15688878

C₂

yes

maximal, characteristic

C₄₇×#391

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093957

—

#13093948

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×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

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²⋊Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×Q₁₆

yes

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

#123

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#484

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#384

—

#336

—

C₄₇

#2095

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₉₄

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄²

—

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

188

—

110

C₂×C₄

—

188

—

111

C₂×C₄

#10625337

yes

—

112

C₂×C₄

C₂×Dic₉₄

yes

characteristic

113

C₂×C₄

#10625350

yes

characteristic

114

C₂×C₄

D₄×D₄₇

yes

—

115

C₂×C₄

#10625352

yes

—

116

C₈

—

117

C₂²

#13094003

yes

characteristic

118

C₂²

#13094005

yes

characteristic

119

C₂²

#13094020

yes

characteristic

120

C₂²

C₂×#10625337

yes

—

121

C₂²

#13094049

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

376

—

126

C₄

#13094001

yes

—

127

C₄

#13094006

yes

—

128

C₂

#15689059

yes

characteristic

129

C₂

#15689418

yes

—

130

C₂

#15689456

yes

—

131

C₂

#15689502

yes

characteristic

132

C₂

#15689513

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#391	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#391	D₄₇
hypocenter	C₄₇	#2095
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#391

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
72. C₄₇	#2095	semidirect

H ≅ G/N

type

72. C₄₇

#2095

semidirect

Subgroups — #20244926

Conjugacy classes of subgroups

Complements