Group #20241270 — subgroups

Subgroups — #20241270

Order 6016.

180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13093935	C₂	1	1	yes	maximal, characteristic
2	#15688989	C₂	1	1	yes	maximal, characteristic
3	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	—	2	1	no	—
5	C₂×C₄⋊Dic₄₇	C₄	1	2	yes	—
6	#13093935	—	2	1	no	—
7	#13093935	C₄	1	2	yes	complemented
8	C₄₇⋊#95	—	2	1	no	—
9	C₄₇⋊#95	—	2	1	no	—
10	C₂²×C₈×C₄₇	—	2	1	no	—
11	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	#97×C₄₇	—	2	1	no	—
13	#97×C₄₇	C₄	1	2	yes	complemented
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	—	2	4	no	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₄₇	D₄	1	1	yes	characteristic
23	C₄²×C₄₇	Q₈	1	1	yes	characteristic
24	C₄⋊Dic₄₇	—	4	2	no	—
25	C₂×C₄₇⋊C₈	—	2	4	no	—
26	C₂×C₄₇⋊C₈	—	2	2	no	—
27	C₂³×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	—	2	2	no	—
32	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₄₇	—	4	2	no	—
39	C₂×Dic₄₇	—	4	2	no	—
40	C₂×Dic₄₇	—	4	2	no	—
41	C₈×C₄₇	—	2	4	no	—
42	C₄₇⋊C₈	—	2	4	no	—
43	C₂²×C₄₇	#95	1	1	yes	characteristic
44	C₂²×C₄₇	#100	1	1	yes	characteristic
45	C₂²×C₄₇	#101	1	1	yes	characteristic
46	C₂²×C₄₇	#104	1	2	yes	—
47	C₂²×C₄₇	#104	1	2	yes	—
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	—	2	1	no	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	2	1	no	—
53	C₄×C₄₇	—	2	1	no	—
54	Dic₄₇	—	8	2	no	—
55	#1295	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	#329	1	2	yes	—
57	C₂×C₄₇	#330	1	2	yes	—
58	C₂×C₄₇	#339	1	1	yes	characteristic
59	C₂×C₄₇	#339	1	1	yes	characteristic
60	C₂×C₄₇	#343	1	1	yes	characteristic
61	C₂×#97	—	47	1	no	—
62	C₂×#97	D₄₇	1	1	yes	characteristic
63	#382	—	47	1	no	—
64	C₄₇	#1295	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₈	—	2	1	no	—
66	C₂²×C₈	—	94	1	no	—
67	C₂×C₄⋊C₄	—	47	2	no	—
68	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
69	#97	—	2	1	no	—
70	#97	—	47	2	no	—
71	#97	—	94	1	no	—
72	#97	Dic₄₇	1	2	yes	complemented
73	#95	—	94	1	no	—
74	#95	—	94	1	no	—
75	C₂²×C₄	—	94	2	no	—
76	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
77	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
78	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	94	4	no	—
82	C₂×C₈	—	94	2	no	—
83	C₄⋊C₄	—	188	2	no	—
84	C₄²	Dic₉₄	1	1	yes	characteristic
85	C₄²	C₄×D₄₇	1	1	yes	characteristic
86	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
87	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
88	C₂³	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	188	2	no	—
94	C₂×C₄	—	188	2	no	—
95	C₂×C₄	—	188	2	no	—
96	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
97	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
98	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
99	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
100	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
101	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
102	C₈	—	2	4	no	—
103	C₈	—	94	4	no	—
104	C₂²	C₄₇⋊#95	1	1	yes	characteristic
105	C₂²	#13093940	1	1	yes	characteristic
106	C₂²	#13093942	1	1	yes	characteristic
107	C₂²	#13093950	1	2	yes	—
108	C₂²	#13093952	1	2	yes	—
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	376	2	no	—
116	C₂	#15688862	1	2	yes	—
117	C₂	#15688864	1	2	yes	—
118	C₂	#15688883	1	1	yes	characteristic
119	C₂	#15688884	1	1	yes	characteristic
120	C₂	#15688891	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093935

C₂

yes

maximal, characteristic

#15688989

C₂

yes

maximal, characteristic

C₂×#97×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

—

C₂×C₄⋊Dic₄₇

C₄

yes

—

#13093935

—

#13093935

C₄

yes

complemented

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

—

#97×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

Q₈

yes

characteristic

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#104

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#1295

—

maximal, Sylow

C₂×C₄₇

#329

yes

—

C₂×C₄₇

#330

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×#97

—

C₂×#97

D₄₇

yes

characteristic

#382

—

C₄₇

#1295

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

Dic₄₇

yes

complemented

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

188

—

C₄²

Dic₉₄

yes

characteristic

C₄²

C₄×D₄₇

yes

characteristic

C₄²

C₂×Dic₄₇

yes

characteristic

C₄²

C₂²⋊D₄₇

yes

characteristic

C₂³

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₄₇

yes

characteristic

100

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

101

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

102

C₈

—

103

C₈

—

104

C₂²

C₄₇⋊#95

yes

characteristic

105

C₂²

#13093940

yes

characteristic

106

C₂²

#13093942

yes

characteristic

107

C₂²

#13093950

yes

—

108

C₂²

#13093952

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

376

—

116

C₂

#15688862

yes

—

117

C₂

#15688864

yes

—

118

C₂

#15688883

yes

characteristic

119

C₂

#15688884

yes

characteristic

120

C₂

#15688891

yes

characteristic

	subgroup	G/H
center	C₂³	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₄²
Frattini	C₂×C₄²	C₂×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂²⋊C₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	#1295
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

(C₂×D₄₇)⋊C₄

commutator

C₂×C₄×C₄₇

C₄²

Frattini

C₂×C₄²

C₂×D₄₇

Fitting

C₂×#97×C₄₇

C₂

socle

C₂³×C₄₇

C₂²⋊C₄

hypercenter

C₂×#97

D₄₇

hypocenter

C₄₇

#1295

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
7. #13093935	C₄	semidirect
13. #97×C₄₇	C₄	semidirect
64. C₄₇	#1295	semidirect
72. #97	Dic₄₇	semidirect

H ≅ G/N

type

7. #13093935

C₄

semidirect

13. #97×C₄₇

C₄

semidirect

64. C₄₇

#1295

semidirect

72. #97

Dic₄₇

semidirect

Subgroups — #20241270

Conjugacy classes of subgroups

Complements