Group #20242448 — subgroups

Subgroups — #20242448

Order 6016.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689859	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689499	C₂	1	1	yes	maximal, characteristic
3	#15689324	C₂	1	2	yes	maximal, complemented
4	#15688853	C₂	1	2	yes	maximal, complemented
5	C₄₇×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625325	—	2	2	no	—
7	C₂×#10625334	—	2	2	no	—
8	#13094021	C₂²	1	1	yes	characteristic
9	#13094011	—	2	2	no	—
10	#13094005	—	2	2	no	—
11	C₄×Dic₉₄	C₂²	1	2	yes	—
12	D₄×Dic₄₇	—	2	2	no	—
13	#13093946	—	2	2	no	—
14	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#127×C₄₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×D₄×C₄₇	—	2	2	no	—
18	C₂×D₄×C₄₇	D₄	1	2	yes	—
19	C₂²×Dic₄₇	—	2	2	no	—
20	C₂×D₁₈₈	—	2	2	no	—
21	C₂×D₁₈₈	—	2	1	no	—
22	C₂×Dic₉₄	D₄	1	2	yes	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²⋊Dic₄₇	—	2	4	no	—
26	C₂²⋊Dic₄₇	—	2	2	no	—
27	#10625334	—	4	4	no	—
28	C₄⋊Dic₄₇	D₄	1	2	yes	—
29	Dic₄₇⋊C₄	—	2	2	no	—
30	C₄×Dic₄₇	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	1	no	—
32	#10625325	—	4	4	no	—
33	C₂³×C₄₇	—	2	2	no	—
34	C₂²×D₄₇	—	4	1	no	—
35	D₄×C₄₇	—	4	2	no	—
36	D₄×C₄₇	—	4	2	no	—
37	D₄×C₄₇	—	4	2	no	—
38	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
40	C₂×Dic₄₇	—	2	2	no	—
41	C₂×Dic₄₇	—	2	2	no	—
42	C₂×Dic₄₇	—	8	2	no	—
43	D₁₈₈	—	4	2	no	—
44	D₁₈₈	—	4	2	no	—
45	D₁₈₈	—	4	2	no	—
46	Dic₉₄	—	2	2	no	—
47	Dic₉₄	—	2	2	no	—
48	C₈×C₄₇	—	4	2	no	—
49	C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇	—	4	4	no	—
51	C₂²×C₄₇	—	4	2	no	—
52	C₂²×C₄₇	#120	1	1	yes	characteristic
53	C₂×D₄₇	—	8	2	no	—
54	C₂×D₄₇	—	8	1	no	—
55	C₄×C₄₇	—	2	1	no	—
56	C₄×C₄₇	#135	1	2	yes	—
57	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
58	Dic₄₇	—	4	2	no	—
59	Dic₄₇	—	4	2	no	—
60	#1620	—	47	1	no	maximal, Sylow
61	C₂×C₄₇	—	8	2	no	—
62	C₂×C₄₇	#449	1	2	yes	—
63	C₂×C₄₇	#453	1	1	yes	characteristic
64	D₄₇	—	16	1	no	—
65	#559	—	47	1	no	—
66	#493	—	47	1	no	—
67	#460	—	47	2	no	—
68	#331	D₄₇	1	1	yes	characteristic, complemented
69	Q₈⋊C₈	—	47	2	no	—
70	C₄₇	#1620	1	1	yes	characteristic, complemented, Sylow
71	C₂×SD₁₆	—	94	2	no	—
72	C₂×D₈	—	94	2	no	—
73	#127	—	47	1	no	—
74	#127	C₂×D₄₇	1	1	yes	characteristic
75	#124	—	94	2	no	—
76	#123	—	94	2	no	—
77	C₄×Q₈	—	47	2	no	—
78	C₄×D₄	—	94	2	no	—
79	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
80	#102	—	94	2	no	—
81	C₄×C₈	—	47	1	no	—
82	C₂×Q₈	—	47	2	no	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	94	1	no	—
85	C₂×D₄	—	94	2	no	—
86	C₂×D₄	D₁₈₈	1	2	yes	—
87	C₂²×C₄	—	94	2	no	—
88	SD₁₆	—	188	4	no	—
89	D₈	—	188	4	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	94	1	no	—
92	C₄⋊C₄	—	47	2	no	—
93	C₄⋊C₄	—	94	2	no	—
94	C₂²⋊C₄	—	94	4	no	—
95	C₂²⋊C₄	—	94	2	no	—
96	C₄²	—	94	2	no	—
97	C₄²	C₂²×D₄₇	1	1	yes	characteristic
98	C₂³	—	2	2	no	—
99	C₂³	—	188	1	no	—
100	Q₈	—	94	2	no	—
101	Q₈	—	94	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	188	2	no	—
106	D₄	—	188	2	no	—
107	D₄	—	188	2	no	—
108	C₂×C₄	—	94	2	no	—
109	C₂×C₄	—	94	2	no	—
110	C₂×C₄	—	376	2	no	—
111	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
112	C₂×C₄	D₄×D₄₇	1	2	yes	—
113	C₈	—	4	2	no	—
114	C₈	—	94	2	no	—
115	C₂²	—	4	4	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	376	2	no	—
118	C₂²	—	376	1	no	—
119	C₂²	#13093994	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	188	2	no	—
122	C₄	—	188	2	no	—
123	C₄	#13094045	1	2	yes	—
124	C₄	#13094048	1	2	yes	—
125	C₂	—	8	2	no	—
126	C₂	—	752	1	no	—
127	C₂	#15689269	1	2	yes	—
128	C₂	#15689293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689859

C₂

yes

maximal, characteristic, complemented

#15689499

C₂

yes

maximal, characteristic

#15689324

C₂

yes

maximal, complemented

#15688853

C₂

yes

maximal, complemented

C₄₇×#331

C₂

yes

maximal, characteristic, complemented

C₂×#10625325

—

C₂×#10625334

—

#13094021

C₂²

yes

characteristic

#13094011

—

#13094005

—

C₄×Dic₉₄

C₂²

yes

—

D₄×Dic₄₇

—

#13093946

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#127×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×Dic₉₄

D₄

yes

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

#10625334

—

C₄⋊Dic₄₇

D₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

#10625325

—

C₂³×C₄₇

—

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#135

yes

—

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

Dic₄₇

—

Dic₄₇

—

#1620

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#449

yes

—

C₂×C₄₇

#453

yes

characteristic

D₄₇

—

—

—

—

D₄₇

yes

characteristic, complemented

Q₈⋊C₈

—

C₄₇

#1620

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

#127

—

#127

C₂×D₄₇

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

C₄⋊C₈

C₂×D₄₇

yes

—

#102

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₁₈₈

yes

—

C₂²×C₄

—

SD₁₆

—

188

—

D₈

—

188

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

C₂³

—

188

—

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

188

—

106

D₄

—

188

—

107

D₄

—

188

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

376

—

111

C₂×C₄

C₂×D₁₈₈

yes

characteristic

112

C₂×C₄

D₄×D₄₇

yes

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

376

—

118

C₂²

—

376

—

119

C₂²

#13093994

yes

characteristic

120

C₄

—

121

C₄

—

188

—

122

C₄

—

188

—

123

C₄

#13094045

yes

—

124

C₄

#13094048

yes

—

125

C₂

—

126

C₂

—

752

—

127

C₂

#15689269

yes

—

128

C₂

#15689293

yes

characteristic

	subgroup	G/H
center	C₂²	#13093994
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#331	C₂
socle	C₂²×C₄₇	#120
hypercenter	#331	D₄₇
hypocenter	C₄₇	#1620
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#13093994

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#331

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
1. #15689859	C₂	semidirect
3. #15689324	C₂	semidirect
4. #15688853	C₂	semidirect
5. C₄₇×#331	C₂	semidirect
68. #331	D₄₇	semidirect
70. C₄₇	#1620	semidirect

H ≅ G/N

type

1. #15689859

C₂

semidirect

3. #15689324

C₂

semidirect

4. #15688853

C₂

semidirect

5. C₄₇×#331

C₂

semidirect

68. #331

D₄₇

semidirect

70. C₄₇

#1620

semidirect

Subgroups — #20242448

Conjugacy classes of subgroups

Complements