Group #20242901 — subgroups

Subgroups — #20242901

Order 6016.

166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689528	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689328	C₂	1	2	yes	maximal
3	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688868	C₂	1	2	yes	maximal, complemented
5	C₄₇×#436	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625335	—	2	2	no	—
7	#13094024	C₂²	1	2	yes	—
8	#13093958	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093947	—	2	2	no	—
12	C₂×M₁₆×C₄₇	—	2	1	no	—
13	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	—	2	1	no	—
19	C₂×Dic₉₄	—	2	2	no	—
20	M₁₆×C₄₇	—	4	2	no	—
21	C₂×C₈×C₄₇	—	2	1	no	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
25	C₂²⋊C₄×C₄₇	—	2	1	no	—
26	C₄²×C₄₇	C₂³	1	1	yes	characteristic
27	#10625335	—	4	4	no	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂³×C₄₇	—	2	1	no	—
32	D₄×C₄₇	—	2	2	no	—
33	C₂×C₄×C₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	—	4	1	no	—
35	C₂×C₄×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
39	C₂×Dic₄₇	—	4	2	no	—
40	Dic₉₄	—	4	2	no	—
41	Dic₉₄	—	4	2	no	—
42	C₈×C₄₇	—	2	1	no	—
43	C₈×C₄₇	—	4	1	no	—
44	C₈×C₄₇	SD₁₆	1	2	yes	complemented
45	C₄₇⋊C₈	—	4	2	no	—
46	C₂²×C₄₇	—	4	1	no	—
47	C₂²×C₄₇	—	4	1	no	—
48	C₂²×C₄₇	—	4	1	no	—
49	C₂²×C₄₇	#121	1	1	yes	characteristic
50	C₄×C₄₇	—	2	1	no	—
51	C₄×C₄₇	—	4	1	no	—
52	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
53	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
54	C₄×C₄₇	#137	1	1	yes	characteristic
55	Dic₄₇	—	8	2	no	—
56	#1693	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	—	8	1	no	—
58	C₂×C₄₇	#461	1	1	yes	characteristic
59	C₂×C₄₇	#469	1	1	yes	characteristic
60	C₂×C₄₇	#473	1	1	yes	characteristic
61	#500	—	47	1	no	—
62	#461	—	47	2	no	—
63	#436	D₄₇	1	1	yes	characteristic
64	#334	—	47	1	no	—
65	#332	—	47	2	no	—
66	C₄₇	#1693	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	94	2	no	—
68	C₂×M₁₆	—	2	1	no	—
69	C₄⋊Q₈	—	47	2	no	—
70	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
71	#107	—	94	1	no	—
72	#107	—	94	1	no	—
73	C₄⋊C₈	—	47	2	no	—
74	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
75	#103	—	94	2	no	—
76	C₂²⋊C₈	—	2	1	no	—
77	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂×Q₈	—	94	2	no	—
79	C₂×D₄	D₁₈₈	1	1	yes	characteristic
80	C₂²×C₄	—	2	1	no	—
81	SD₁₆	—	188	4	no	—
82	M₁₆	—	4	2	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	94	2	no	—
85	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
87	C₄⋊C₄	—	94	2	no	—
88	C₄⋊C₄	—	94	2	no	—
89	C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
90	C₂²⋊C₄	—	2	1	no	—
91	C₄²	C₂²×D₄₇	1	1	yes	characteristic
92	C₂³	—	2	1	no	—
93	Q₈	—	188	2	no	—
94	Q₈	—	188	2	no	—
95	D₄	—	2	2	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	188	2	no	—
100	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
101	C₂×C₄	#10625350	1	1	yes	characteristic
102	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	4	1	no	—
105	C₈	—	188	2	no	—
106	C₈	#10625335	1	2	yes	complemented
107	C₂²	—	4	1	no	—
108	C₂²	—	4	1	no	—
109	C₂²	—	4	1	no	—
110	C₂²	#13093998	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	4	1	no	—
113	C₄	—	376	2	no	—
114	C₄	C₂×#10625335	1	1	yes	characteristic
115	C₄	#13094052	1	2	yes	—
116	C₄	#13094054	1	1	yes	characteristic
117	C₂	—	8	1	no	—
118	C₂	#15689328	1	1	yes	characteristic
119	C₂	#15689376	1	1	yes	characteristic
120	C₂	#15689398	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic, complemented

#15689328

C₂

yes

maximal

#15688874

C₂

yes

maximal, characteristic, complemented

#15688868

C₂

yes

maximal, complemented

C₄₇×#436

C₂

yes

maximal, characteristic

C₂×#10625335

—

#13094024

C₂²

yes

—

#13093958

—

#13093958

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093947

—

C₂×M₁₆×C₄₇

—

C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

SD₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

#1693

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#334

—

#332

—

C₄₇

#1693

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₄₇

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

characteristic

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

D₁₈₈

yes

characteristic

C₂²×C₄

—

SD₁₆

—

188

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₈₈

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

100

C₂×C₄

C₂×D₁₈₈

yes

characteristic

101

C₂×C₄

#10625350

yes

characteristic

102

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

188

—

106

C₈

#10625335

yes

complemented

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

#13093998

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

376

—

114

C₄

C₂×#10625335

yes

characteristic

115

C₄

#13094052

yes

—

116

C₄

#13094054

yes

characteristic

117

C₂

—

118

C₂

#15689328

yes

characteristic

119

C₂

#15689376

yes

characteristic

120

C₂

#15689398

yes

characteristic

	subgroup	G/H
center	C₂²	#13093998
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#436	C₂
socle	C₂²×C₄₇	#121
hypercenter	#436	D₄₇
hypocenter	C₄₇	#1693
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #436

subgroup

G/H

center

C₂²

#13093998

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#436

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #436

N	H ≅ G/N	type
1. #15689528	C₂	semidirect
3. #15688874	C₂	semidirect
4. #15688868	C₂	semidirect
44. C₈×C₄₇	SD₁₆	semidirect
66. C₄₇	#1693	semidirect
106. C₈	#10625335	semidirect

H ≅ G/N

type

1. #15689528

C₂

semidirect

3. #15688874

C₂

semidirect

4. #15688868

C₂

semidirect

44. C₈×C₄₇

SD₁₆

semidirect

66. C₄₇

#1693

semidirect

106. C₈

#10625335

semidirect

Subgroups — #20242901

Conjugacy classes of subgroups

Complements