Group #20243438 — subgroups

Subgroups — #20243438

Order 6016.

252 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13093960	C₂	1	2	yes	maximal, complemented
2	#15689107	C₂	1	2	yes	maximal
3	C₄₇⋊#338	C₂	1	2	yes	maximal, complemented
4	C₂×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625329	C₂²	1	4	yes	—
6	#13093960	—	2	4	no	—
7	#13093943	—	2	2	no	—
8	#13093941	—	2	2	no	—
9	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
10	#131×C₄₇	—	2	4	no	—
11	C₂×M₁₆×C₄₇	C₄	1	2	yes	—
12	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₇	C₄	1	2	yes	—
14	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	#41×C₄₇	—	2	2	no	—
16	#41×C₄₇	—	2	2	no	—
17	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×D₄×C₄₇	Q₈	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₄₇	—	2	2	no	—
23	M₁₆×C₄₇	—	2	4	no	—
24	C₂×C₈×C₄₇	—	2	4	no	—
25	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₄₇	D₄	1	4	yes	—
29	#10625329	—	2	4	no	—
30	#10625329	—	2	4	no	—
31	C₂×C₄₇⋊C₈	—	2	4	no	—
32	C₂³×C₄₇	C₄⋊C₄	1	2	yes	—
33	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
34	Q₈×C₄₇	—	2	2	no	—
35	D₄×C₄₇	—	2	4	no	—
36	D₄×C₄₇	—	2	2	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	C₈×C₄₇	—	2	2	no	—
45	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
46	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₄₇⋊C₈	—	4	4	no	—
48	C₂²×C₄₇	—	2	2	no	—
49	C₂²×C₄₇	—	4	1	no	—
50	C₂²×C₄₇	—	4	2	no	—
51	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
53	C₄×C₄₇	—	2	2	no	—
54	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₄₇	#117	1	1	yes	characteristic
56	C₄×C₄₇	#121	1	2	yes	—
57	#1813	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	—	2	2	no	—
60	C₂×C₄₇	—	4	2	no	—
61	C₂×C₄₇	#380	1	1	yes	characteristic
62	C₂×#131	D₄₇	1	1	yes	characteristic
63	C₂×#108	—	47	2	no	—
64	#413	—	47	2	no	—
65	#338	—	47	2	no	—
66	C₄₇	#1813	1	1	yes	characteristic, complemented, Sylow
67	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
68	#131	—	2	4	no	—
69	C₂×M₁₆	—	47	4	no	—
70	C₂×M₁₆	Dic₄₇	1	2	yes	—
71	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
72	C₂²×C₈	Dic₄₇	1	2	yes	—
73	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
74	#108	—	94	4	no	—
75	#101	—	94	2	no	—
76	#100	—	94	2	no	—
77	#41	—	2	2	no	—
78	#41	—	2	2	no	—
79	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
80	C₂×D₄	Dic₉₄	1	2	yes	—
81	C₂×D₄	D₁₈₈	1	1	yes	characteristic
82	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
83	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	2	4	no	—
86	M₁₆	—	94	4	no	—
87	M₁₆	—	94	4	no	—
88	C₂×C₈	—	2	4	no	—
89	C₂×C₈	—	94	4	no	—
90	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
91	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
92	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₄₇	1	4	yes	—
94	C₂³	C₄⋊Dic₄₇	1	2	yes	—
95	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
96	Q₈	—	2	2	no	—
97	D₄	—	2	4	no	—
98	D₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
102	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
103	C₂×C₄	#10625350	1	2	yes	—
104	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
105	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
106	C₈	—	2	2	no	—
107	C₈	—	188	4	no	—
108	C₈	C₂²⋊Dic₄₇	1	2	yes	—
109	C₈	C₂²⋊Dic₄₇	1	2	yes	—
110	C₂²	—	2	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	2	no	—
113	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
114	C₂²	#13094003	1	2	yes	—
115	C₄	—	2	2	no	—
116	C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
117	C₄	#13093983	1	1	yes	characteristic
118	C₄	#13093998	1	2	yes	—
119	C₂	—	2	1	no	—
120	C₂	—	2	2	no	—
121	C₂	—	4	2	no	—
122	C₂	#15688983	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093960

C₂

yes

maximal, complemented

#15689107

C₂

yes

maximal

C₄₇⋊#338

C₂

yes

maximal, complemented

C₂×#131×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

#13093960

—

#13093943

—

#13093941

—

C₂×#41×C₄₇

C₂²

yes

characteristic

#131×C₄₇

—

C₂×M₁₆×C₄₇

C₄

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₄

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×D₄×C₄₇

D₄

yes

characteristic

C₂×D₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

#1813

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#380

yes

characteristic

C₂×#131

D₄₇

yes

—

—

—

C₄₇

#1813

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₇

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

Dic₄₇

yes

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

Dic₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

—

—

—

—

—

C₂×Q₈

D₁₈₈

yes

characteristic

C₂×D₄

Dic₉₄

yes

—

C₂×D₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂³

C₄⋊Dic₄₇

yes

—

C₂³

C₂×Dic₉₄

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄⋊Dic₄₇

yes

—

102

C₂×C₄

C₂×D₁₈₈

yes

characteristic

103

C₂×C₄

#10625350

yes

—

104

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

105

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

106

C₈

—

107

C₈

—

188

—

108

C₈

C₂²⋊Dic₄₇

yes

—

109

C₈

C₂²⋊Dic₄₇

yes

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₄⋊Dic₄₇

yes

characteristic

114

C₂²

#13094003

yes

—

115

C₄

—

116

C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

117

C₄

#13093983

yes

characteristic

118

C₄

#13093998

yes

—

119

C₂

—

120

C₂

—

121

C₂

—

122

C₂

#15688983

yes

characteristic

	subgroup	G/H
center	C₄	#13093983
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#131×C₄₇	C₂
socle	C₂×C₄₇	#380
hypercenter	C₂×#131	D₄₇
hypocenter	C₄₇	#1813
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₂×#131

subgroup

G/H

center

C₄

#13093983

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#131×C₄₇

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₂×#131

N	H ≅ G/N	type
1. C₂×#13093960	C₂	semidirect
3. C₄₇⋊#338	C₂	semidirect
66. C₄₇	#1813	semidirect

H ≅ G/N

type

1. C₂×#13093960

C₂

semidirect

3. C₄₇⋊#338

C₂

semidirect

66. C₄₇

#1813

semidirect

Subgroups — #20243438

Conjugacy classes of subgroups

Complements