Group #20252473 — subgroups

Subgroups — #20252473

Order 6016.

356 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 217 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	#15689254	C₂	1	8	yes	maximal, complemented
2	#15689180	C₂	1	4	yes	maximal
3	#15689176	C₂	1	2	yes	maximal
4	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
6	C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
7	C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
8	#13093935	C₂²	1	8	yes	—
9	C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
10	C₂²×Q₈×C₄₇	C₄	1	1	yes	characteristic
11	C₄×Q₈×C₄₇	C₄	1	4	yes	—
12	C₄×Q₈×C₄₇	C₂²	1	4	yes	—
13	C₂×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
14	C₂×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
15	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
17	C₂×Q₈×C₄₇	—	2	4	no	—
18	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
25	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
26	C₄²×C₄₇	C₂×C₄	1	4	yes	—
27	C₄²×C₄₇	C₂×C₄	1	2	yes	—
28	C₄²×C₄₇	C₂³	1	2	yes	—
29	C₄²×C₄₇	C₂³	1	4	yes	—
30	C₂×C₄₇⋊C₈	C₂³	1	8	yes	—
31	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	Q₈×C₄₇	—	2	8	no	—
33	C₂×C₄×C₄₇	—	2	4	no	—
34	C₂×C₄×C₄₇	—	2	2	no	—
35	C₂×C₄×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	—	4	2	no	—
37	C₂×C₄×C₄₇	M₁₆	1	4	yes	—
38	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
41	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
42	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
44	C₄₇⋊C₈	—	2	8	no	—
45	C₂²×C₄₇	—	2	1	no	—
46	C₂²×C₄₇	—	2	1	no	—
47	C₂²×C₄₇	C₂×M₁₆	1	2	yes	—
48	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	—	2	4	no	—
51	C₄×C₄₇	—	2	2	no	—
52	C₄×C₄₇	—	2	4	no	—
53	C₄×C₄₇	C₂×M₁₆	1	4	yes	—
54	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
55	#2983	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	—	2	2	no	—
57	C₂×C₄₇	#519	1	1	yes	characteristic
58	C₂×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
59	C₂×C₄₇	#568	1	1	yes	characteristic
60	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic
61	#446	—	47	8	no	—
62	#432	—	47	4	no	—
63	#431	—	47	2	no	—
64	C₄₇	#2983	1	1	yes	characteristic, complemented, Sylow
65	C₂²×Q₈	Dic₄₇	1	1	yes	characteristic
66	C₄×Q₈	Dic₄₇	1	4	yes	—
67	C₄×Q₈	C₂×D₄₇	1	4	yes	—
68	C₂×C₄⋊C₄	Dic₄₇	1	2	yes	—
69	C₂×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
70	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
71	C₂×C₄²	C₂×D₄₇	1	2	yes	—
72	C₄⋊C₈	—	47	4	no	—
73	C₄⋊C₈	—	47	8	no	—
74	C₂²⋊C₈	—	47	4	no	—
75	#97	—	47	8	no	—
76	C₄×C₈	—	47	4	no	—
77	C₂×Q₈	—	2	4	no	—
78	C₂×Q₈	C₂×Dic₄₇	1	4	yes	—
79	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
80	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
81	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
82	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
83	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
84	C₂×C₈	—	47	8	no	—
85	C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
86	C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
87	C₄²	C₂×Dic₄₇	1	4	yes	—
88	C₄²	C₂×Dic₄₇	1	2	yes	—
89	C₄²	C₂²×D₄₇	1	2	yes	—
90	C₄²	C₂²×D₄₇	1	4	yes	—
91	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
92	Q₈	—	2	8	no	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	#10625329	1	4	yes	—
98	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
100	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
101	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
102	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
103	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
104	C₈	—	94	8	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	C₂×#10625329	1	2	yes	—
108	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	2	4	no	—
111	C₄	—	2	2	no	—
112	C₄	—	2	4	no	—
113	C₄	C₂×#10625329	1	4	yes	—
114	C₄	#13094072	1	2	yes	—
115	C₂	—	2	2	no	—
116	C₂	#15689601	1	1	yes	characteristic
117	C₂	C₂²×#10625329	1	1	yes	characteristic
118	C₂	#15689890	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689254

C₂

yes

maximal, complemented

#15689180

C₂

yes

maximal

#15689176

C₂

yes

maximal

C₂×C₄×Q₈×C₄₇

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂²⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093935

C₂²

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

—

C₂²×Q₈×C₄₇

C₄

yes

characteristic

C₄×Q₈×C₄₇

C₄

yes

—

C₄×Q₈×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₄

yes

—

C₂×C₄⋊C₄×C₄₇

C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×M₁₆

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×M₁₆

yes

—

C₄×C₄₇

2₋¹⁺⁴

yes

—

#2983

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#519

yes

characteristic

C₂×C₄₇

C₂²×M₁₆

yes

characteristic

C₂×C₄₇

#568

yes

characteristic

C₂×C₄×Q₈

D₄₇

yes

—

—

—

C₄₇

#2983

yes

characteristic, complemented, Sylow

C₂²×Q₈

Dic₄₇

yes

characteristic

C₄×Q₈

Dic₄₇

yes

—

C₄×Q₈

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

Dic₄₇

yes

—

C₂×C₄⋊C₄

Dic₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₄²

C₂²×D₄₇

yes

—

C₄²

C₂²×D₄₇

yes

—

C₂³

C₂²×Dic₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10625329

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

—

100

C₂×C₄

C₂²×Dic₄₇

yes

—

101

C₂×C₄

C₂²×Dic₄₇

yes

—

102

C₂×C₄

C₂²×Dic₄₇

yes

—

103

C₂×C₄

C₂³×D₄₇

yes

characteristic

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×#10625329

yes

—

108

C₂²

C₂³×Dic₄₇

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₂×#10625329

yes

—

114

C₄

#13094072

yes

—

115

C₂

—

116

C₂

#15689601

yes

characteristic

117

C₂

C₂²×#10625329

yes

characteristic

118

C₂

#15689890

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×C₄×Q₈×C₄₇	C₂
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	#2983
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₇

commutator, socle

C₂²×C₄₇

C₂³×C₄

Fitting

C₂×C₄×Q₈×C₄₇

C₂

hypercenter

C₂×C₄×Q₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
1. #15689254	C₂	semidirect
64. C₄₇	#2983	semidirect

H ≅ G/N

type

1. #15689254

C₂

semidirect

64. C₄₇

#2983

semidirect

Subgroups — #20252473

Conjugacy classes of subgroups

Complements