Group #20244176 — subgroups

Subgroups — #20244176

Order 6016.

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

normal subgroups only

This group has 184 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	#15689171	C₂	1	2	yes	maximal
2	C₂×#13093960	C₂	1	1	yes	maximal, characteristic
3	#15689078	C₂	1	1	yes	maximal, characteristic
4	#15688894	C₂	1	2	yes	maximal
5	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂×#10625329	C₂²	1	1	yes	characteristic
8	#13093983	C₂²	1	1	yes	characteristic
9	#13093960	C₄	1	4	yes	complemented
10	#13093959	—	2	4	no	—
11	#13093934	—	2	1	no	—
12	C₈×Dic₄₇	—	2	1	no	—
13	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	#108×C₄₇	—	2	1	no	—
16	#108×C₄₇	—	2	1	no	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	M₁₆×C₄₇	—	2	2	no	—
19	M₁₆×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	Q₈	1	2	yes	—
25	C₂²⋊Dic₄₇	Q₈	1	2	yes	—
26	C₄⋊Dic₄₇	—	2	1	no	—
27	C₄×Dic₄₇	—	2	1	no	—
28	#10625329	—	2	2	no	—
29	#10625329	—	2	1	no	—
30	#10625329	C₂×C₄	1	4	yes	—
31	#10625329	D₄	1	2	yes	—
32	C₂×C₄₇⋊C₈	—	2	1	no	—
33	C₂×C₄₇⋊C₈	—	2	2	no	—
34	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
40	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
41	C₂×Dic₄₇	—	2	2	no	—
42	C₈×C₄₇	—	4	2	no	—
43	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
44	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
45	C₄₇⋊C₈	—	2	4	no	—
46	C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇	—	4	1	no	—
48	C₂²×C₄₇	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
53	C₄×C₄₇	#121	1	1	yes	characteristic
54	C₄×C₄₇	#125	1	1	yes	characteristic
55	Dic₄₇	—	4	2	no	—
56	#1953	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	—	2	1	no	—
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	—	2	1	no	—
60	C₂×C₄₇	#389	1	1	yes	characteristic
61	#430	—	47	2	no	—
62	C₂×#108	—	47	1	no	—
63	C₂×#108	D₄₇	1	1	yes	characteristic
64	#405	—	47	1	no	—
65	#344	—	47	2	no	—
66	C₄₇	#1953	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	47	2	no	—
68	C₂×M₁₆	—	47	1	no	—
69	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
70	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
71	#117	—	47	1	no	—
72	#108	—	2	1	no	—
73	#108	—	2	1	no	—
74	#108	—	47	4	no	—
75	#108	—	94	4	no	—
76	#97	—	94	1	no	—
77	C₄×C₈	—	94	1	no	—
78	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	2	2	no	—
81	M₁₆	—	47	4	no	—
82	M₁₆	—	47	2	no	—
83	M₁₆	—	94	1	no	—
84	M₁₆	—	94	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	94	2	no	—
87	C₂×C₈	—	94	1	no	—
88	C₂×C₈	Dic₉₄	1	2	yes	—
89	C₂×C₈	C₄×D₄₇	1	2	yes	—
90	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
91	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
92	C₄⋊C₄	—	94	1	no	—
93	C₂²⋊C₄	—	47	2	no	—
94	C₄²	—	94	1	no	—
95	C₂³	Q₈×D₄₇	1	1	yes	characteristic
96	C₂×C₄	—	94	2	no	—
97	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
99	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
100	C₂×C₄	#10625352	1	1	yes	characteristic
101	C₂×C₄	#10625354	1	1	yes	characteristic
102	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
103	C₈	—	4	2	no	—
104	C₈	—	94	4	no	—
105	C₈	—	94	2	no	—
106	C₈	Dic₄₇⋊C₄	1	2	yes	—
107	C₈	Dic₄₇⋊C₄	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#13093989	1	1	yes	characteristic
110	C₂²	#13094000	1	1	yes	characteristic
111	C₂²	#13094023	1	1	yes	characteristic
112	C₄	—	188	2	no	—
113	C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
114	C₄	#13093986	1	1	yes	characteristic
115	C₄	#13093995	1	1	yes	characteristic
116	C₄	#13094015	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#15689019	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689171

C₂

yes

maximal

C₂×#13093960

C₂

yes

maximal, characteristic

#15689078

C₂

yes

maximal, characteristic

#15688894

C₂

yes

maximal

C₂×#108×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

#13093960

C₄

yes

complemented

#13093959

—

#13093934

—

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

#108×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

—

C₂²⋊Dic₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

#10625329

C₂×C₄

yes

—

#10625329

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×Q₈

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

C₄⋊Q₈

yes

characteristic

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1953

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#405

—

#344

—

C₄₇

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

—

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

Q₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

characteristic

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

characteristic

100

C₂×C₄

#10625352

yes

characteristic

101

C₂×C₄

#10625354

yes

characteristic

102

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

Dic₄₇⋊C₄

yes

—

107

C₈

Dic₄₇⋊C₄

yes

—

108

C₂²

—

109

C₂²

#13093989

yes

characteristic

110

C₂²

#13094000

yes

characteristic

111

C₂²

#13094023

yes

characteristic

112

C₄

—

188

—

113

C₄

C₂×Dic₄₇⋊C₄

yes

characteristic

114

C₄

#13093986

yes

characteristic

115

C₄

#13093995

yes

characteristic

116

C₄

#13094015

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#15689019

yes

characteristic

	subgroup	G/H
center	C₄	#13093995
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂×C₄₇	#389
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1953
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#13093995

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#108×C₄₇

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
9. #13093960	C₄	semidirect
66. C₄₇	#1953	semidirect

H ≅ G/N

type

9. #13093960

C₄

semidirect

66. C₄₇

#1953

semidirect

Subgroups — #20244176

Conjugacy classes of subgroups

Complements