Group #20244208 — subgroups

Subgroups — #20244208

Order 6016.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093949	C₂	1	4	yes	maximal
3	#15688989	C₂	1	1	yes	maximal, characteristic
4	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₉₄	C₂²	1	2	yes	—
6	#13094024	—	2	2	no	—
7	#13094024	C₄	1	4	yes	complemented
8	C₂×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	#13093949	—	2	8	no	—
11	C₄₇⋊#95	—	2	2	no	—
12	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	#97×C₄₇	—	2	2	no	—
15	C₂²×C₄×C₄₇	D₄	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	2	no	—
18	C₂²×Dic₄₇	—	2	2	no	—
19	C₂×Dic₉₄	—	2	4	no	—
20	C₂×Dic₉₄	—	2	4	no	—
21	C₂×Dic₉₄	—	2	2	no	—
22	C₂×Dic₉₄	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₂×C₈×C₄₇	—	2	2	no	—
25	C₂×C₈×C₄₇	D₄	1	4	yes	—
26	C₄²×C₄₇	C₂×C₄	1	2	yes	—
27	C₄²×C₄₇	D₄	1	2	yes	—
28	C₄⋊Dic₄₇	—	2	8	no	—
29	C₄⋊Dic₄₇	—	2	4	no	—
30	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	2	4	no	—
32	C₂×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	#41	1	2	yes	—
37	C₂×Dic₄₇	—	2	4	no	—
38	C₂×Dic₄₇	—	4	2	no	—
39	C₂×Dic₄₇	—	4	2	no	—
40	C₂×Dic₄₇	—	4	2	no	—
41	C₂×Dic₄₇	—	4	4	no	—
42	Dic₉₄	—	2	8	no	—
43	Dic₉₄	—	4	4	no	—
44	C₈×C₄₇	—	2	4	no	—
45	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄₇	#124	1	1	yes	characteristic
47	C₂²×C₄₇	#127	1	1	yes	characteristic
48	C₂²×C₄₇	#137	1	4	yes	—
49	C₄×C₄₇	—	2	4	no	—
50	C₄×C₄₇	C₄×D₄	1	2	yes	—
51	C₄×C₄₇	#121	1	2	yes	—
52	Dic₄₇	—	4	4	no	—
53	Dic₄₇	—	8	2	no	—
54	#1960	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	#390	1	1	yes	characteristic
56	C₂×C₄₇	#419	1	2	yes	—
57	C₂×C₄₇	#491	1	2	yes	—
58	C₂×C₄₇	#497	1	2	yes	—
59	C₂×C₄⋊Q₈	—	47	1	no	—
60	C₂×#103	—	47	4	no	—
61	C₂×#97	D₄₇	1	1	yes	characteristic
62	#382	—	47	1	no	—
63	C₄₇	#1960	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	47	2	no	—
65	C₂²×C₈	C₂×D₄₇	1	2	yes	—
66	C₄⋊Q₈	—	47	4	no	—
67	C₄⋊Q₈	—	94	2	no	—
68	C₂×C₄⋊C₄	—	47	2	no	—
69	C₂×C₄⋊C₄	—	94	2	no	—
70	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
71	#103	—	94	8	no	—
72	#97	—	2	2	no	—
73	#95	—	94	2	no	—
74	C₂×Q₈	—	47	4	no	—
75	C₂×Q₈	—	94	2	no	—
76	C₂×Q₈	—	94	4	no	—
77	C₂×Q₈	—	94	4	no	—
78	C₂²×C₄	—	94	2	no	—
79	C₂²×C₄	—	94	2	no	—
80	C₂²×C₄	D₁₈₈	1	2	yes	—
81	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	D₁₈₈	1	4	yes	—
85	C₄⋊C₄	—	94	8	no	—
86	C₄⋊C₄	—	94	4	no	—
87	C₄²	C₄×D₄₇	1	2	yes	—
88	C₄²	C₂²⋊D₄₇	1	2	yes	—
89	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
90	Q₈	—	94	8	no	—
91	Q₈	—	188	4	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	94	4	no	—
94	C₂×C₄	—	188	2	no	—
95	C₂×C₄	—	188	4	no	—
96	C₂×C₄	—	188	2	no	—
97	C₂×C₄	—	188	2	no	—
98	C₂×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
99	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
100	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
101	C₂×C₄	#10625350	1	2	yes	—
102	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
105	C₂²	#13094012	1	1	yes	characteristic
106	C₂²	#13094021	1	1	yes	characteristic
107	C₂²	#13094057	1	4	yes	—
108	C₄	—	2	4	no	—
109	C₄	—	376	2	no	—
110	C₄	—	188	4	no	—
111	C₄	C₄×D₁₈₈	1	2	yes	—
112	C₄	#13093998	1	2	yes	—
113	C₂	#15689025	1	1	yes	characteristic
114	C₂	#15689133	1	2	yes	—
115	C₂	#15689492	1	2	yes	—
116	C₂	#15689517	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094024

C₂

yes

maximal, characteristic

C₂×#13093949

C₂

yes

maximal

#15688989

C₂

yes

maximal, characteristic

C₂×#97×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

#13094024

—

#13094024

C₄

yes

complemented

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093949

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

C₄×C₄₇

#121

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#491

yes

—

C₂×C₄₇

#497

yes

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

D₄₇

yes

characteristic

#382

—

C₄₇

#1960

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₄₇

yes

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂×D₁₈₈

yes

characteristic

Q₈

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

100

C₂×C₄

C₂×D₁₈₈

yes

—

101

C₂×C₄

#10625350

yes

—

102

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

103

C₈

—

104

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

105

C₂²

#13094012

yes

characteristic

106

C₂²

#13094021

yes

characteristic

107

C₂²

#13094057

yes

—

108

C₄

—

109

C₄

—

376

—

110

C₄

—

188

—

111

C₄

C₄×D₁₈₈

yes

—

112

C₄

#13093998

yes

—

113

C₂

#15689025

yes

characteristic

114

C₂

#15689133

yes

—

115

C₂

#15689492

yes

—

116

C₂

#15689517

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	#1960
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#97×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×#97

D₄₇

hypocenter

C₄₇

#1960

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
7. #13094024	C₄	semidirect
63. C₄₇	#1960	semidirect

H ≅ G/N

type

7. #13094024

C₄

semidirect

63. C₄₇

#1960

semidirect

Subgroups — #20244208

Conjugacy classes of subgroups

Complements