Group #20243463 — subgroups

Subgroups — #20243463

Order 6016.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13093983	C₂	1	1	yes	maximal, characteristic
2	#15688986	C₂	1	1	yes	maximal, characteristic
3	#15688889	C₂	1	4	yes	maximal
4	C₄₇×#381	C₂	1	1	yes	maximal, characteristic
5	#13093983	—	2	2	no	—
6	#13093983	—	2	2	no	—
7	C₂×C₄⋊Dic₄₇	C₄	1	2	yes	complemented
8	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×C₄×Dic₄₇	C₄	1	2	yes	complemented
11	C₄₇⋊#95	—	2	2	no	—
12	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
14	#95×C₄₇	—	2	2	no	—
15	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	—	2	4	no	—
17	C₂²×C₄×C₄₇	—	2	2	no	—
18	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	D₄	1	2	yes	—
21	C₂²×C₄×C₄₇	D₄	1	2	yes	—
22	C₂²×Dic₄₇	—	2	2	no	—
23	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
24	C₂²⋊C₄×C₄₇	—	2	4	no	—
25	C₂²⋊Dic₄₇	—	2	2	no	—
26	C₂²⋊Dic₄₇	—	2	2	no	—
27	C₂²⋊Dic₄₇	—	2	4	no	—
28	C₄⋊Dic₄₇	—	2	4	no	—
29	C₄×Dic₄₇	—	2	4	no	—
30	C₂³×C₄₇	—	4	2	no	—
31	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂³×C₄₇	#41	1	4	yes	—
35	C₂×C₄×C₄₇	—	2	2	no	—
36	C₂×C₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	4	no	—
38	C₂×C₄×C₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇	—	4	4	no	—
40	C₂×C₄×C₄₇	—	4	2	no	—
41	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
43	C₂×Dic₄₇	—	2	4	no	—
44	C₂×Dic₄₇	—	4	4	no	—
45	C₂×Dic₄₇	—	4	4	no	—
46	C₂×Dic₄₇	—	4	2	no	—
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	—	2	2	no	—
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	—	4	4	no	—
51	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄₇	#117	1	2	yes	—
53	C₂²×C₄₇	#123	1	2	yes	—
54	C₂²×C₄₇	#123	1	2	yes	—
55	C₄×C₄₇	—	2	2	no	—
56	C₄×C₄₇	—	2	2	no	—
57	C₄×C₄₇	—	8	2	no	—
58	Dic₄₇	—	4	4	no	—
59	Dic₄₇	—	8	2	no	—
60	#1820	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	—	2	2	no	—
62	C₂×C₄₇	—	2	2	no	—
63	C₂×C₄₇	—	2	2	no	—
64	C₂×C₄₇	#381	1	1	yes	characteristic
65	C₂×C₄₇	#410	1	2	yes	—
66	C₂×#117	—	47	1	no	—
67	#381	—	47	1	no	—
68	#381	D₄₇	1	1	yes	characteristic
69	#342	—	47	4	no	—
70	C₄₇	#1820	1	1	yes	characteristic, complemented, Sylow
71	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
72	#117	—	94	2	no	—
73	#117	—	94	2	no	—
74	C₂×C₄⋊C₄	—	47	2	no	—
75	C₂×C₂²⋊C₄	—	47	2	no	—
76	C₂×C₂²⋊C₄	—	47	2	no	—
77	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
78	C₂×C₄²	—	47	2	no	—
79	#95	—	2	2	no	—
80	#95	—	94	2	no	—
81	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
82	C₂²×C₄	—	2	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	47	4	no	—
85	C₂²×C₄	—	94	2	no	—
86	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
88	C₂²×C₄	D₁₈₈	1	2	yes	—
89	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
90	C₄⋊C₄	—	94	4	no	—
91	C₂²⋊C₄	—	2	4	no	—
92	C₂²⋊C₄	—	94	2	no	—
93	C₂²⋊C₄	—	94	2	no	—
94	C₂²⋊C₄	—	94	4	no	—
95	C₄²	—	94	4	no	—
96	C₂³	—	4	2	no	—
97	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
98	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
99	C₂³	#10625352	1	4	yes	—
100	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	94	4	no	—
108	C₂×C₄	—	188	4	no	—
109	C₂×C₄	—	188	2	no	—
110	C₂×C₄	—	188	4	no	—
111	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
112	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	4	no	—
117	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
118	C₂²	#13093980	1	2	yes	—
119	C₂²	#13094005	1	2	yes	—
120	C₂²	#13094008	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	2	2	no	—
123	C₄	—	8	2	no	—
124	C₄	—	376	2	no	—
125	C₄	—	188	4	no	—
126	C₂	—	2	2	no	—
127	C₂	—	2	2	no	—
128	C₂	—	2	2	no	—
129	C₂	#15688984	1	1	yes	characteristic
130	C₂	#15689096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093983

C₂

yes

maximal, characteristic

#15688986

C₂

yes

maximal, characteristic

#15688889

C₂

yes

maximal

C₄₇×#381

C₂

yes

maximal, characteristic

#13093983

—

#13093983

—

C₂×C₄⋊Dic₄₇

C₄

yes

complemented

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂³×C₄₇

#41

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#123

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#1820

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#381

yes

characteristic

C₂×C₄₇

#410

yes

—

C₂×#117

—

#381

—

#381

D₄₇

yes

characteristic

#342

—

C₄₇

#1820

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

#95

—

#95

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂×C₄×D₄₇

yes

characteristic

C₂³

C₂×D₁₈₈

yes

characteristic

C₂³

#10625352

yes

—

100

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

188

—

109

C₂×C₄

—

188

—

110

C₂×C₄

—

188

—

111

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

112

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

118

C₂²

#13093980

yes

—

119

C₂²

#13094005

yes

—

120

C₂²

#13094008

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

376

—

125

C₄

—

188

—

126

C₂

—

127

C₂

—

128

C₂

—

129

C₂

#15688984

yes

characteristic

130

C₂

#15689096

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂⁴	C₂²×D₄₇
Fitting	C₄₇×#381	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	#381	D₄₇
hypocenter	C₄₇	#1820
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

subgroup

G/H

center

C₂²

C₂×(C₂×D₄₇)⋊C₄

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂⁴

C₂²×D₄₇

Fitting

C₄₇×#381

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

N	H ≅ G/N	type
7. C₂×C₄⋊Dic₄₇	C₄	semidirect
10. C₂×C₄×Dic₄₇	C₄	semidirect
70. C₄₇	#1820	semidirect

H ≅ G/N

type

7. C₂×C₄⋊Dic₄₇

C₄

semidirect

10. C₂×C₄×Dic₄₇

C₄

semidirect

70. C₄₇

#1820

semidirect

Subgroups — #20243463

Conjugacy classes of subgroups

Complements