Group #20243312 — subgroups

Subgroups — #20243312

Order 6016.

564 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13093943	C₂	1	4	yes	maximal, complemented
2	#15689087	C₂	1	2	yes	maximal
3	C₂³×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	C₂²	1	4	yes	—
5	#13093943	—	2	8	no	—
6	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
7	C₂²×Q₈×C₄₇	—	2	8	no	—
8	C₂²×Q₈×C₄₇	—	2	4	no	—
9	C₂²×Q₈×C₄₇	C₄	1	2	yes	—
10	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
11	C₂³×C₄×C₄₇	C₄	1	2	yes	—
12	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Q₈×C₄₇	—	2	32	no	—
15	C₂×Q₈×C₄₇	—	2	8	no	—
16	C₂×Q₈×C₄₇	—	2	4	no	—
17	C₂×Q₈×C₄₇	—	2	4	no	—
18	C₂×Q₈×C₄₇	—	2	4	no	—
19	C₂×Q₈×C₄₇	D₄	1	8	yes	—
20	C₂²×C₄×C₄₇	—	2	4	no	—
21	C₂²×C₄×C₄₇	—	2	8	no	—
22	C₂²×C₄×C₄₇	—	2	4	no	—
23	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	D₄	1	4	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	#10625329	—	2	8	no	—
28	C₂×C₄₇⋊C₈	—	2	4	no	—
29	C₂³×C₄₇	—	2	4	no	—
30	C₂³×C₄₇	—	2	2	no	—
31	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
32	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	Q₈×C₄₇	—	2	16	no	—
34	Q₈×C₄₇	—	2	16	no	—
35	C₂×C₄×C₄₇	—	2	16	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇	—	2	8	no	—
40	C₂×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
41	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
44	C₄₇⋊C₈	—	4	4	no	—
45	C₂²×C₄₇	—	2	8	no	—
46	C₂²×C₄₇	—	2	2	no	—
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	—	2	2	no	—
49	C₂²×C₄₇	#101	1	4	yes	complemented
50	C₂²×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₄₇	—	2	8	no	—
53	C₄×C₄₇	—	2	2	no	—
54	C₄×C₄₇	#120	1	4	yes	—
55	#1784	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	—	2	4	no	—
57	C₂×C₄₇	—	2	2	no	—
58	C₂×C₄₇	#379	1	1	yes	characteristic
59	C₂×C₄₇	C₂×#101	1	2	yes	—
60	C₂³×Q₈	D₄₇	1	1	yes	characteristic
61	C₂×#101	—	47	4	no	—
62	#407	—	47	2	no	—
63	C₄₇	#1784	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	2	8	no	—
65	C₂²×Q₈	—	2	4	no	—
66	C₂²×Q₈	Dic₄₇	1	2	yes	—
67	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
68	C₂³×C₄	Dic₄₇	1	2	yes	—
69	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
70	C₂×M₁₆	—	47	4	no	—
71	#101	—	94	8	no	—
72	C₂²⋊C₈	—	94	4	no	—
73	C₂⁴	C₂×Dic₄₇	1	1	yes	characteristic
74	C₂×Q₈	—	2	32	no	—
75	C₂×Q₈	—	2	8	no	—
76	C₂×Q₈	—	2	4	no	—
77	C₂×Q₈	—	2	4	no	—
78	C₂×Q₈	—	2	4	no	—
79	C₂×Q₈	C₂²⋊D₄₇	1	8	yes	—
80	C₂²×C₄	—	2	4	no	—
81	C₂²×C₄	—	2	8	no	—
82	C₂²×C₄	—	2	4	no	—
83	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
84	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
85	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
86	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
87	M₁₆	—	94	8	no	—
88	C₂×C₈	—	94	4	no	—
89	C₂³	—	2	4	no	—
90	C₂³	—	2	2	no	—
91	C₂³	C₂²⋊Dic₄₇	1	2	yes	—
92	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
93	Q₈	—	2	16	no	—
94	Q₈	—	2	16	no	—
95	C₂×C₄	—	2	16	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	—	2	8	no	—
100	C₂×C₄	C₂²⋊Dic₄₇	1	8	yes	—
101	C₂×C₄	C₂²⋊Dic₄₇	1	2	yes	—
102	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
103	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
104	C₈	—	188	4	no	—
105	C₂²	—	2	8	no	—
106	C₂²	—	2	2	no	—
107	C₂²	—	2	2	no	—
108	C₂²	—	2	2	no	—
109	C₂²	#13093943	1	4	yes	complemented
110	C₂²	C₂×C₂²⋊Dic₄₇	1	2	yes	—
111	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
112	C₄	—	2	8	no	—
113	C₄	—	2	2	no	—
114	C₄	#13093993	1	4	yes	—
115	C₂	—	2	4	no	—
116	C₂	—	2	2	no	—
117	C₂	#15688979	1	1	yes	characteristic
118	C₂	C₂×#13093943	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093943

C₂

yes

maximal, complemented

#15689087

C₂

yes

maximal

C₂³×Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

#13093943

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

C₄

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₄

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×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×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#101

yes

complemented

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#120

yes

—

#1784

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#379

yes

characteristic

C₂×C₄₇

C₂×#101

yes

—

C₂³×Q₈

D₄₇

yes

characteristic

C₂×#101

—

#407

—

C₄₇

#1784

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

Dic₄₇

yes

—

C₂²×Q₈

C₂×D₄₇

yes

—

C₂³×C₄

Dic₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

#101

—

C₂²⋊C₈

—

C₂⁴

C₂×Dic₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₄₇

yes

—

C₂³

C₂²×Dic₄₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂²⋊Dic₄₇

yes

—

101

C₂×C₄

C₂²⋊Dic₄₇

yes

—

102

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

103

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

104

C₈

—

188

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

#13093943

yes

complemented

110

C₂²

C₂×C₂²⋊Dic₄₇

yes

—

111

C₂²

C₂×C₂²⋊Dic₄₇

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#13093993

yes

—

115

C₂

—

116

C₂

—

117

C₂

#15688979

yes

characteristic

118

C₂

C₂×#13093943

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂³×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂³×Q₈	D₄₇
hypocenter	C₄₇	#1784
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂³×Q₈×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

hypercenter

C₂³×Q₈

D₄₇

hypocenter

C₄₇

#1784

LCS

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×Q₈

N	H ≅ G/N	type
1. C₂×#13093943	C₂	semidirect
49. C₂²×C₄₇	#101	semidirect
63. C₄₇	#1784	semidirect
109. C₂²	#13093943	semidirect

H ≅ G/N

type

1. C₂×#13093943

C₂

semidirect

49. C₂²×C₄₇

#101

semidirect

63. C₄₇

#1784

semidirect

109. C₂²

#13093943

semidirect

Subgroups — #20243312

Conjugacy classes of subgroups

Complements