Group #20244137 — subgroups

Subgroups — #20244137

Order 6016.

208 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 97 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	1	yes	maximal, characteristic
2	#15689150	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15688882	C₂	1	2	yes	maximal
5	C₄₇×#427	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	#13093960	—	2	2	no	—
10	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
11	C₈×Dic₄₇	—	2	2	no	—
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	#117×C₄₇	C₂²	1	2	yes	—
14	#107×C₄₇	C₄	1	2	yes	complemented
15	#106×C₄₇	C₄	1	2	yes	complemented
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	1	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	2	yes	—
21	C₂×C₈×C₄₇	Q₈	1	2	yes	—
22	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
23	C₂²⋊C₄×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	—	2	2	no	—
25	C₄×Dic₄₇	—	2	1	no	—
26	C₄×Dic₄₇	Q₈	1	2	yes	—
27	#10625329	—	2	2	no	—
28	#10625329	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	1	no	—
30	C₂×C₄₇⋊C₈	—	2	1	no	—
31	C₂×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
33	C₂³×C₄₇	#41	1	1	yes	characteristic
34	C₂×C₄×C₄₇	—	2	4	no	—
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	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	2	2	no	—
43	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
44	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
45	C₄₇⋊C₈	—	2	2	no	—
46	C₄₇⋊C₈	—	4	2	no	—
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₇	#125	1	1	yes	characteristic
51	C₄×C₄₇	—	4	4	no	—
52	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
54	C₄×C₄₇	#121	1	1	yes	characteristic
55	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₄₇	—	2	4	no	—
57	#1945	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	—	2	1	no	—
60	C₂×C₄₇	#389	1	1	yes	characteristic
61	C₂×C₄₇	#443	1	2	yes	—
62	C₂×#108	—	47	1	no	—
63	#427	D₄₇	1	1	yes	characteristic
64	#424	—	47	2	no	—
65	C₂×C₄×C₈	—	47	1	no	—
66	#339	—	47	2	no	—
67	C₄₇	#1945	1	1	yes	characteristic, complemented, Sylow
68	C₂×M₁₆	—	47	2	no	—
69	C₂²×C₈	—	47	1	no	—
70	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
71	#117	C₂×D₄₇	1	2	yes	—
72	C₂×C₄²	—	47	1	no	—
73	#108	—	94	2	no	—
74	#107	Dic₄₇	1	2	yes	complemented
75	#106	Dic₄₇	1	2	yes	complemented
76	C₄⋊C₈	—	94	4	no	—
77	C₄×C₈	—	94	2	no	—
78	C₂²×C₄	—	94	1	no	—
79	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
80	M₁₆	—	94	2	no	—
81	M₁₆	—	94	2	no	—
82	C₂×C₈	—	47	2	no	—
83	C₂×C₈	—	94	1	no	—
84	C₂×C₈	—	94	1	no	—
85	C₂×C₈	—	94	2	no	—
86	C₂×C₈	Dic₉₄	1	2	yes	—
87	C₂×C₈	D₁₈₈	1	2	yes	—
88	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
89	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
90	C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
91	C₂²⋊C₄	—	2	2	no	—
92	C₄²	—	2	2	no	—
93	C₄²	—	47	2	no	—
94	C₄²	—	94	1	no	—
95	C₂³	#10625352	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	94	4	no	—
98	C₂×C₄	—	94	2	no	—
99	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
100	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
101	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
102	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
103	C₂×C₄	#10625354	1	1	yes	characteristic
104	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
105	C₈	—	94	2	no	—
106	C₈	—	188	2	no	—
107	C₈	C₄⋊Dic₄₇	1	2	yes	—
108	C₈	C₄⋊Dic₄₇	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	D₄×Dic₄₇	1	1	yes	characteristic
111	C₂²	#13094004	1	1	yes	characteristic
112	C₂²	#13094015	1	1	yes	characteristic
113	C₄	—	4	4	no	—
114	C₄	—	94	4	no	—
115	C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
116	C₄	Q₈×Dic₄₇	1	1	yes	characteristic
117	C₄	#13093999	1	1	yes	characteristic
118	C₄	#13094023	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#15689022	1	1	yes	characteristic
122	C₂	#15689240	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093960

C₂

yes

maximal, characteristic

#15689150

C₂

yes

maximal

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688882

C₂

yes

maximal

C₄₇×#427

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093960

—

C₄⋊(C₄₇⋊C₈)

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

—

#107×C₄₇

C₄

yes

complemented

#106×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

Q₈

yes

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

Q₈

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

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

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

#125

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₄×Q₈

yes

characteristic

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

Dic₄₇

—

#1945

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#389

yes

characteristic

C₂×C₄₇

#443

yes

—

C₂×#108

—

#427

D₄₇

yes

characteristic

#424

—

C₂×C₄×C₈

—

#339

—

C₄₇

#1945

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

C₂×D₄₇

yes

—

C₂×C₄²

—

#108

—

#107

Dic₄₇

yes

complemented

#106

Dic₄₇

yes

complemented

C₄⋊C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

D₁₈₈

yes

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#10625352

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

characteristic

100

C₂×C₄

C₂×D₁₈₈

yes

characteristic

101

C₂×C₄

D₄×D₄₇

yes

characteristic

102

C₂×C₄

Q₈×D₄₇

yes

characteristic

103

C₂×C₄

#10625354

yes

characteristic

104

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

105

C₈

—

106

C₈

—

188

—

107

C₈

C₄⋊Dic₄₇

yes

—

108

C₈

C₄⋊Dic₄₇

yes

—

109

C₂²

—

110

C₂²

D₄×Dic₄₇

yes

characteristic

111

C₂²

#13094004

yes

characteristic

112

C₂²

#13094015

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

116

C₄

Q₈×Dic₄₇

yes

characteristic

117

C₄

#13093999

yes

characteristic

118

C₄

#13094023

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#15689022

yes

characteristic

122

C₂

#15689240

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#427	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	#427	D₄₇
hypocenter	C₄₇	#1945
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#427

C₂

socle

C₂²×C₄₇

C₄×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
14. #107×C₄₇	C₄	semidirect
15. #106×C₄₇	C₄	semidirect
67. C₄₇	#1945	semidirect
74. #107	Dic₄₇	semidirect
75. #106	Dic₄₇	semidirect

H ≅ G/N

type

14. #107×C₄₇

C₄

semidirect

15. #106×C₄₇

C₄

semidirect

67. C₄₇

#1945

semidirect

74. #107

Dic₄₇

semidirect

75. #106

Dic₄₇

semidirect

Subgroups — #20244137

Conjugacy classes of subgroups

Complements