Group #20255192 — subgroups

Subgroups — #20255192

Order 6016.

444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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	#15689936	C₂	1	4	yes	maximal, complemented
2	#15689395	C₂	1	4	yes	maximal, complemented
3	#15689305	C₂	1	4	yes	maximal, complemented
4	#15689241	C₂	1	2	yes	maximal, complemented
5	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094072	C₂²	1	4	yes	—
7	#13094056	—	2	8	no	—
8	#13094055	C₂²	1	8	yes	—
9	#13094047	—	2	4	no	—
10	#13094046	C₂²	1	2	yes	—
11	Q₁₆×D₄₇	—	2	4	no	—
12	#13094030	C₂²	1	4	yes	—
13	#13093960	C₂²	1	2	yes	—
14	#13093952	C₂²	1	4	yes	—
15	#13093943	C₂²	1	4	yes	—
16	C₂×Q₁₆×C₄₇	C₂²	1	4	yes	—
17	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
20	#10625354	—	2	8	no	—
21	Q₈×D₄₇	—	2	8	no	—
22	#10625350	—	4	4	no	—
23	#10625350	C₂³	1	4	yes	—
24	Q₁₆×C₄₇	—	2	4	no	—
25	Q₁₆×C₄₇	—	2	4	no	—
26	C₂×C₈×C₄₇	C₂³	1	2	yes	—
27	C₄⋊C₄×C₄₇	—	4	2	no	—
28	C₄²×C₄₇	C₂³	1	1	yes	characteristic
29	#10625337	—	2	8	no	—
30	#10625336	—	2	8	no	—
31	#10625329	C₂³	1	4	yes	—
32	Dic₁₈₈	D₄	1	2	yes	—
33	D₃₇₆	D₄	1	2	yes	—
34	#10625325	D₄	1	4	yes	—
35	#10625324	—	2	4	no	—
36	C₈×D₄₇	—	2	4	no	—
37	Q₈×C₄₇	—	2	8	no	—
38	C₂×C₄×C₄₇	—	2	1	no	—
39	C₂×C₄×C₄₇	—	2	4	no	—
40	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
41	C₂²⋊D₄₇	—	2	4	no	—
42	D₁₈₈	—	4	4	no	—
43	D₁₈₈	C₂×D₄	1	4	yes	—
44	C₄×D₄₇	—	2	4	no	—
45	C₄×D₄₇	—	4	8	no	—
46	Dic₉₄	—	4	4	no	—
47	Dic₉₄	C₂×D₄	1	4	yes	—
48	C₈×C₄₇	C₂×D₄	1	2	yes	—
49	C₈×C₄₇	C₂×D₄	1	2	yes	—
50	C₄₇⋊C₈	—	2	4	no	—
51	C₂²×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
52	C₂×D₄₇	—	2	4	no	—
53	C₄×C₄₇	—	2	2	no	—
54	C₄×C₄₇	—	4	4	no	—
55	C₄×C₄₇	C₂²×D₄	1	2	yes	—
56	Dic₄₇	—	2	4	no	—
57	#3293	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	—	2	1	no	—
59	C₂×C₄₇	D₄²	1	1	yes	characteristic
60	D₄₇	—	4	4	no	—
61	#578	—	47	4	no	—
62	#494	D₄₇	1	1	yes	characteristic, complemented
63	#473	—	47	4	no	—
64	#456	—	47	4	no	—
65	#443	—	47	2	no	—
66	C₄₇	#3293	1	1	yes	characteristic, complemented, Sylow
67	2₋¹⁺⁴	—	47	4	no	—
68	#137	—	47	8	no	—
69	#137	—	94	8	no	—
70	#135	—	47	2	no	—
71	#135	—	94	4	no	—
72	C₂×Q₁₆	—	94	4	no	—
73	C₂×Q₁₆	C₂×D₄₇	1	4	yes	—
74	#131	—	47	4	no	—
75	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
76	#108	—	47	2	no	—
77	#104	—	47	4	no	—
78	#101	—	47	4	no	—
79	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
80	#41	—	47	4	no	—
81	#41	—	94	8	no	—
82	#41	—	188	4	no	—
83	C₂×Q₈	—	94	8	no	—
84	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
85	Q₁₆	—	2	4	no	—
86	Q₁₆	—	2	4	no	—
87	Q₁₆	—	47	2	no	—
88	Q₁₆	—	94	8	no	—
89	SD₁₆	—	47	4	no	—
90	SD₁₆	—	94	8	no	—
91	D₈	—	47	2	no	—
92	M₁₆	—	47	4	no	—
93	M₁₆	—	94	4	no	—
94	C₂×C₈	—	94	4	no	—
95	C₂×C₈	C₂²×D₄₇	1	2	yes	—
96	C₄⋊C₄	—	4	2	no	—
97	C₄²	C₂²×D₄₇	1	1	yes	characteristic
98	Q₈	—	2	8	no	—
99	Q₈	—	47	4	no	—
100	Q₈	—	188	4	no	—
101	D₄	—	47	4	no	—
102	D₄	—	94	4	no	—
103	D₄	—	188	4	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	94	4	no	—
107	C₂×C₄	—	188	8	no	—
108	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
109	C₈	—	94	4	no	—
110	C₈	D₄×D₄₇	1	2	yes	—
111	C₈	D₄×D₄₇	1	2	yes	—
112	C₂²	—	94	4	no	—
113	C₂²	#13094069	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	—	94	4	no	—
117	C₄	C₂×D₄×D₄₇	1	2	yes	—
118	C₂	—	2	1	no	—
119	C₂	—	188	4	no	—
120	C₂	#15689758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689936

C₂

yes

maximal, complemented

#15689395

C₂

yes

maximal, complemented

#15689305

C₂

yes

maximal, complemented

#15689241

C₂

yes

maximal, complemented

C₄₇×#494

C₂

yes

maximal, characteristic, complemented

#13094072

C₂²

yes

—

#13094056

—

#13094055

C₂²

yes

—

#13094047

—

#13094046

C₂²

yes

—

Q₁₆×D₄₇

—

#13094030

C₂²

yes

—

#13093960

C₂²

yes

—

#13093952

C₂²

yes

—

#13093943

C₂²

yes

—

C₂×Q₁₆×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

C₂³

yes

—

#10625354

—

Q₈×D₄₇

—

#10625350

—

#10625350

C₂³

yes

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

—

—

C₂³

yes

—

Dic₁₈₈

D₄

yes

—

D₃₇₆

D₄

yes

—

#10625325

D₄

yes

—

#10625324

—

C₈×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²⋊D₄₇

—

D₁₈₈

—

D₁₈₈

C₂×D₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

C₂×D₄

yes

—

C₈×C₄₇

C₂×D₄

yes

—

C₈×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

H(5,𝔽₂)

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²×D₄

yes

—

Dic₄₇

—

#3293

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

D₄²

yes

characteristic

D₄₇

—

#578

—

#494

D₄₇

yes

characteristic, complemented

#473

—

#456

—

#443

—

C₄₇

#3293

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

—

#131

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#108

—

#104

—

#101

—

C₄×C₈

C₂×D₄₇

yes

—

—

—

188

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₇

yes

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

188

—

101

D₄

—

102

D₄

—

103

D₄

—

188

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

188

—

108

C₂×C₄

C₂³×D₄₇

yes

characteristic

109

C₈

—

110

C₈

D₄×D₄₇

yes

—

111

C₈

D₄×D₄₇

yes

—

112

C₂²

—

113

C₂²

#13094069

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×D₄×D₄₇

yes

—

118

C₂

—

119

C₂

—

188

—

120

C₂

#15689758

yes

characteristic

	subgroup	G/H
center	C₂	#15689758
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂×C₄₇	D₄²
hypercenter	#494	D₄₇
hypocenter	C₄₇	#3293
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

subgroup

G/H

center

C₂

#15689758

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#494

C₂

socle

C₂×C₄₇

D₄²

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

N	H ≅ G/N	type
1. #15689936	C₂	semidirect
2. #15689395	C₂	semidirect
3. #15689305	C₂	semidirect
4. #15689241	C₂	semidirect
5. C₄₇×#494	C₂	semidirect
62. #494	D₄₇	semidirect
66. C₄₇	#3293	semidirect

H ≅ G/N

type

1. #15689936

C₂

semidirect

2. #15689395

C₂

semidirect

3. #15689305

C₂

semidirect

4. #15689241

C₂

semidirect

5. C₄₇×#494

C₂

semidirect

62. #494

D₄₇

semidirect

66. C₄₇

#3293

semidirect

Subgroups — #20255192

Conjugacy classes of subgroups

Complements