Group #20243517 — subgroups

Subgroups — #20243517

Order 6016.

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

normal subgroups only

This group has 216 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×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688988	C₂	1	2	yes	maximal
3	#15688886	C₂	1	1	yes	maximal, characteristic
4	#15688885	C₂	1	2	yes	maximal
5	C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₈×Dic₄₇	C₄	1	4	yes	complemented
10	C₄₇⋊#95	—	2	2	no	—
11	C₄₇⋊#95	—	2	2	no	—
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×C₄₇	—	2	2	no	—
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₇	—	2	2	no	—
17	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
18	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
26	C₄×Dic₄₇	Q₈	1	2	yes	—
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	4	2	no	—
31	C₂×C₄×C₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	—	4	2	no	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	2	yes	—
36	C₂×C₄×C₄₇	#41	1	2	yes	—
37	C₂×Dic₄₇	—	2	1	no	—
38	C₂×Dic₄₇	—	2	2	no	—
39	C₂×Dic₄₇	—	2	1	no	—
40	C₂×Dic₄₇	—	4	2	no	—
41	C₂×Dic₄₇	—	4	2	no	—
42	C₂×Dic₄₇	—	4	2	no	—
43	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
45	C₈×C₄₇	—	2	2	no	—
46	C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₄₇	#124	1	2	yes	—
49	C₂²×C₄₇	#135	1	1	yes	characteristic
50	C₂²×C₄₇	#135	1	2	yes	—
51	C₂²×C₄₇	#135	1	1	yes	characteristic
52	C₄×C₄₇	—	8	2	no	—
53	C₄×C₄₇	#117	1	1	yes	characteristic
54	C₄×C₄₇	#117	1	1	yes	characteristic
55	C₄×C₄₇	#125	1	2	yes	—
56	Dic₄₇	—	2	2	no	—
57	Dic₄₇	—	2	2	no	—
58	Dic₄₇	—	8	2	no	—
59	#1835	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	#382	1	1	yes	characteristic
61	C₂×C₄₇	#427	1	1	yes	characteristic
62	C₂×C₄₇	#427	1	1	yes	characteristic
63	C₂×C₄₇	#488	1	2	yes	—
64	C₂×C₄₇	#488	1	2	yes	—
65	C₂×C₄×C₈	—	47	1	no	—
66	#382	—	47	2	no	—
67	#340	—	47	1	no	—
68	#340	—	47	2	no	—
69	#340	D₄₇	1	1	yes	characteristic
70	C₄₇	#1835	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	47	1	no	—
72	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
73	C₂×C₄⋊C₄	—	47	2	no	—
74	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
75	C₂×C₄²	—	47	1	no	—
76	C₄×C₈	—	47	4	no	—
77	#95	—	94	2	no	—
78	#95	—	94	2	no	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	47	1	no	—
81	C₂²×C₄	—	47	1	no	—
82	C₂²×C₄	—	94	2	no	—
83	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	47	2	no	—
86	C₂×C₈	—	94	2	no	—
87	C₂×C₈	C₄×D₄₇	1	2	yes	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	94	2	no	—
91	C₄⋊C₄	—	94	2	no	—
92	C₄²	—	47	2	no	—
93	C₄²	—	47	2	no	—
94	C₂³	D₄×D₄₇	1	1	yes	characteristic
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	47	2	no	—
99	C₂×C₄	—	47	2	no	—
100	C₂×C₄	—	94	1	no	—
101	C₂×C₄	—	94	2	no	—
102	C₂×C₄	—	94	1	no	—
103	C₂×C₄	—	188	2	no	—
104	C₂×C₄	—	188	2	no	—
105	C₂×C₄	—	188	2	no	—
106	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
107	C₂×C₄	#10625350	1	2	yes	—
108	C₂×C₄	#10625352	1	2	yes	—
109	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	94	2	no	—
112	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
113	C₂²	#13094010	1	2	yes	—
114	C₂²	#13094043	1	1	yes	characteristic
115	C₂²	#13094045	1	2	yes	—
116	C₂²	#13094047	1	1	yes	characteristic
117	C₄	—	8	2	no	—
118	C₄	—	94	2	no	—
119	C₄	—	94	2	no	—
120	C₄	—	376	2	no	—
121	C₄	#13093980	1	1	yes	characteristic
122	C₄	#13093981	1	1	yes	characteristic
123	C₄	#13094014	1	2	yes	—
124	C₂	#15688987	1	1	yes	characteristic
125	C₂	#15689158	1	1	yes	characteristic
126	C₂	#15689160	1	1	yes	characteristic
127	C₂	#15689476	1	2	yes	—
128	C₂	#15689479	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688988

C₂

yes

maximal

#15688886

C₂

yes

maximal, characteristic

#15688885

C₂

yes

maximal

C₄₇×#340

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₈×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

#135

yes

characteristic

C₂²×C₄₇

#135

yes

—

C₂²×C₄₇

#135

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#488

yes

—

C₂×C₄×C₈

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1835

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₄×C₈

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

D₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

188

—

104

C₂×C₄

—

188

—

105

C₂×C₄

—

188

—

106

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

107

C₂×C₄

#10625350

yes

—

108

C₂×C₄

#10625352

yes

—

109

C₂×C₄

Q₈×D₄₇

yes

characteristic

110

C₈

—

111

C₈

—

112

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

113

C₂²

#13094010

yes

—

114

C₂²

#13094043

yes

characteristic

115

C₂²

#13094045

yes

—

116

C₂²

#13094047

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

376

—

121

C₄

#13093980

yes

characteristic

122

C₄

#13093981

yes

characteristic

123

C₄

#13094014

yes

—

124

C₂

#15688987

yes

characteristic

125

C₂

#15689158

yes

characteristic

126

C₂

#15689160

yes

characteristic

127

C₂

#15689476

yes

—

128

C₂

#15689479

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#340	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#340	D₄₇
hypocenter	C₄₇	#1835
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#340

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
9. C₈×Dic₄₇	C₄	semidirect
70. C₄₇	#1835	semidirect

H ≅ G/N

type

9. C₈×Dic₄₇

C₄

semidirect

70. C₄₇

#1835

semidirect

Subgroups — #20243517

Conjugacy classes of subgroups

Complements