Group #20245702 — subgroups

Subgroups — #20245702

Order 6016.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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	#15689556	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688960	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688958	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×SD₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#13094047	—	2	1	no	—
9	D₈×D₄₇	—	2	1	no	—
10	#13093967	—	2	1	no	—
11	D₇₅₂	C₂²	1	1	yes	characteristic
12	D₇₅₂	C₂²	1	1	yes	characteristic, complemented
13	#13093965	—	2	1	no	—
14	C₁₆×D₄₇	C₂²	1	1	yes	characteristic
15	C₄₇⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
16	Q₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
17	D₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
19	#10625354	—	4	1	no	—
20	D₄×D₄₇	—	4	1	no	—
21	Q₁₆×C₄₇	—	2	1	no	—
22	D₈×C₄₇	—	2	1	no	—
23	#10625336	—	4	1	no	—
24	#10625334	—	4	1	no	—
25	D₃₇₆	—	2	1	no	—
26	D₃₇₆	—	2	1	no	—
27	C₈×D₄₇	D₄	1	1	yes	characteristic
28	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
29	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
30	C₂²×D₄₇	—	8	1	no	—
31	Q₈×C₄₇	—	4	1	no	—
32	D₄×C₄₇	—	4	1	no	—
33	C₂²⋊D₄₇	—	8	1	no	—
34	D₁₈₈	—	4	1	no	—
35	D₁₈₈	—	4	1	no	—
36	D₁₈₈	—	8	1	no	—
37	C₄×D₄₇	—	8	1	no	—
38	C₄×D₄₇	D₈	1	1	yes	characteristic
39	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
40	C₄₇⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₄₇	—	8	1	no	—
42	C₂×D₄₇	—	8	1	no	—
43	C₂×D₄₇	—	8	1	no	—
44	C₂×D₄₇	—	16	2	no	—
45	C₂×D₄₇	D₁₆	1	1	yes	characteristic
46	C₄×C₄₇	—	8	1	no	—
47	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
48	Dic₄₇	D₁₆	1	1	yes	characteristic
49	#2263	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	—	16	1	no	—
51	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
52	D₄₇	—	2	1	no	—
53	D₄₇	—	16	1	no	—
54	D₄₇	—	16	1	no	—
55	#508	—	47	1	no	—
56	C₂×D₁₆	—	47	1	no	—
57	SD₆₄	—	47	1	no	—
58	SD₆₄	D₄₇	1	1	yes	characteristic, complemented
59	D₃₂	—	47	1	no	—
60	D₃₂	—	47	1	no	—
61	M₆₄	—	47	1	no	—
62	C₄₇	#2263	1	1	yes	characteristic, complemented, Sylow
63	#135	—	94	1	no	—
64	C₂×D₈	—	94	1	no	—
65	Q₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
66	SD₃₂	—	94	1	no	—
67	D₁₆	—	47	1	no	—
68	D₁₆	—	47	1	no	—
69	D₁₆	—	94	1	no	—
70	D₁₆	C₂×D₄₇	1	1	yes	characteristic
71	C₂×C₁₆	—	47	1	no	—
72	C₃₂	—	47	1	no	—
73	C₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
74	#41	—	188	1	no	—
75	C₂×D₄	—	188	1	no	—
76	Q₁₆	—	2	1	no	—
77	SD₁₆	—	188	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	94	1	no	—
80	D₈	—	94	1	no	—
81	D₈	—	188	1	no	—
82	C₂×C₈	—	47	1	no	—
83	C₁₆	—	47	1	no	—
84	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
85	C₂³	—	376	1	no	—
86	Q₈	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	376	1	no	—
89	D₄	—	376	1	no	—
90	D₄	—	188	1	no	—
91	D₄	—	188	1	no	—
92	C₂×C₄	—	47	1	no	—
93	C₂×C₄	—	376	1	no	—
94	C₈	—	47	1	no	—
95	C₈	D₄×D₄₇	1	1	yes	characteristic
96	C₂²	—	8	1	no	—
97	C₂²	—	47	1	no	—
98	C₂²	—	376	1	no	—
99	C₂²	—	376	1	no	—
100	C₂²	—	752	2	no	—
101	C₄	—	8	1	no	—
102	C₄	—	47	1	no	—
103	C₄	D₈×D₄₇	1	1	yes	characteristic
104	C₂	—	16	1	no	—
105	C₂	—	94	1	no	—
106	C₂	—	752	1	no	—
107	C₂	—	752	1	no	—
108	C₂	D₁₆×D₄₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689556

C₂

yes

maximal, characteristic, complemented

D₁₆×D₄₇

C₂

yes

maximal, characteristic, complemented

#15688960

C₂

yes

maximal, characteristic, complemented

D₁₅₀₄

C₂

yes

maximal, characteristic, complemented

#15688958

C₂

yes

maximal, characteristic, complemented

#15688956

C₂

yes

maximal, characteristic, complemented

C₄₇×SD₆₄

C₂

yes

maximal, characteristic, complemented

#13094047

—

D₈×D₄₇

—

#13093967

—

D₇₅₂

C₂²

yes

characteristic

D₇₅₂

C₂²

yes

characteristic, complemented

#13093965

—

C₁₆×D₄₇

C₂²

yes

characteristic

C₄₇⋊C₃₂

C₂²

yes

characteristic, complemented

Q₃₂×C₄₇

C₂²

yes

characteristic, complemented

D₁₆×C₄₇

C₂²

yes

characteristic

C₃₂×C₄₇

C₂²

yes

characteristic, complemented

#10625354

—

D₄×D₄₇

—

Q₁₆×C₄₇

—

D₈×C₄₇

—

#10625336

—

#10625334

—

D₃₇₆

—

D₃₇₆

—

C₈×D₄₇

D₄

yes

characteristic

C₁₆×C₄₇

C₂³

yes

characteristic

C₄₇⋊C₁₆

D₄

yes

characteristic

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

C₂²⋊D₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

D₈

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₂²×C₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

D₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

D₁₆

yes

characteristic

#2263

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×D₁₆

yes

characteristic

D₄₇

—

D₄₇

—

D₄₇

—

#508

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

D₄₇

yes

characteristic, complemented

D₃₂

—

D₃₂

—

M₆₄

—

C₄₇

#2263

yes

characteristic, complemented, Sylow

#135

—

C₂×D₈

—

Q₃₂

C₂×D₄₇

yes

characteristic, complemented

SD₃₂

—

D₁₆

—

D₁₆

—

D₁₆

—

D₁₆

C₂×D₄₇

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₄₇

yes

characteristic, complemented

#41

—

188

—

C₂×D₄

—

188

—

Q₁₆

—

SD₁₆

—

188

—

D₈

—

D₈

—

D₈

—

D₈

—

188

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₄₇

yes

characteristic

C₂³

—

376

—

Q₈

—

D₄

—

D₄

—

376

—

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

376

—

C₈

—

C₈

D₄×D₄₇

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

376

—

C₂²

—

376

—

100

C₂²

—

752

—

101

C₄

—

102

C₄

—

103

C₄

D₈×D₄₇

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

—

752

—

107

C₂

—

752

—

108

C₂

D₁₆×D₄₇

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₇
commutator	C₁₆×C₄₇	C₂³
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₄₇×SD₆₄	C₂
socle	C₂×C₄₇	C₂×D₁₆
hypercenter	SD₆₄	D₄₇
hypocenter	C₄₇	#2263
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₄₇

commutator

C₁₆×C₄₇

C₂³

Frattini

C₁₆

C₂²×D₄₇

Fitting

C₄₇×SD₆₄

C₂

socle

C₂×C₄₇

C₂×D₁₆

hypercenter

SD₆₄

D₄₇

hypocenter

C₄₇

#2263

LCS

G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. #15689556	C₂	semidirect
2. D₁₆×D₄₇	C₂	semidirect
3. #15688960	C₂	semidirect
4. D₁₅₀₄	C₂	semidirect
5. #15688958	C₂	semidirect
6. #15688956	C₂	semidirect
7. C₄₇×SD₆₄	C₂	semidirect
12. D₇₅₂	C₂²	semidirect
15. C₄₇⋊C₃₂	C₂²	semidirect
16. Q₃₂×C₄₇	C₂²	semidirect
18. C₃₂×C₄₇	C₂²	semidirect
58. SD₆₄	D₄₇	semidirect
62. C₄₇	#2263	semidirect
65. Q₃₂	C₂×D₄₇	semidirect
73. C₃₂	C₂×D₄₇	semidirect

H ≅ G/N

type

1. #15689556

C₂

semidirect

2. D₁₆×D₄₇

C₂

semidirect

3. #15688960

C₂

semidirect

4. D₁₅₀₄

C₂

semidirect

5. #15688958

C₂

semidirect

6. #15688956

C₂

semidirect

7. C₄₇×SD₆₄

C₂

semidirect

12. D₇₅₂

C₂²

semidirect

15. C₄₇⋊C₃₂

C₂²

semidirect

16. Q₃₂×C₄₇

C₂²

semidirect

18. C₃₂×C₄₇

C₂²

semidirect

58. SD₆₄

D₄₇

semidirect

62. C₄₇

#2263

semidirect

65. Q₃₂

C₂×D₄₇

semidirect

73. C₃₂

C₂×D₄₇

semidirect

Subgroups — #20245702

Conjugacy classes of subgroups

Complements