Group #20245268 — subgroups

Subgroups — #20245268

Order 6016.

146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689555	C₂	1	1	yes	maximal, characteristic
2	#15689239	C₂	1	2	yes	maximal, complemented
3	#15688929	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094046	C₂²	1	2	yes	—
7	#13094032	—	2	2	no	—
8	Dic₃₇₆	C₄	1	1	yes	characteristic, complemented
9	#13093969	C₄	1	2	yes	complemented
10	D₇₅₂	C₄	1	1	yes	characteristic, complemented
11	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
12	#13093950	—	2	2	no	—
13	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	#108×C₄₇	C₂²	1	2	yes	—
16	#10625350	—	2	2	no	—
17	M₁₆×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄×Dic₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
21	Dic₁₈₈	C₂×C₄	1	2	yes	—
22	D₃₇₆	C₂×C₄	1	2	yes	—
23	#10625325	—	2	2	no	—
24	#10625324	—	4	2	no	—
25	C₈×D₄₇	—	4	2	no	—
26	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₄₇⋊C₁₆	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂²⋊D₄₇	—	4	2	no	—
31	C₂×Dic₄₇	—	2	1	no	—
32	D₁₈₈	—	2	2	no	—
33	C₄×D₄₇	—	4	2	no	—
34	Dic₉₄	—	2	2	no	—
35	C₈×C₄₇	—	4	2	no	—
36	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₄₇	#41	1	1	yes	characteristic
38	C₄₇⋊C₈	D₈	1	1	yes	characteristic
39	C₄₇⋊C₈	D₈	1	1	yes	characteristic
40	C₂²×C₄₇	#135	1	1	yes	characteristic
41	C₂×D₄₇	—	4	2	no	—
42	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
43	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
44	Dic₄₇	—	2	2	no	—
45	Dic₄₇	—	4	2	no	—
46	#2178	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	—	2	1	no	—
48	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
49	D₄₇	—	8	2	no	—
50	#508	—	47	1	no	—
51	#443	—	47	2	no	—
52	#368	D₄₇	1	1	yes	characteristic, complemented
53	#359	—	47	2	no	—
54	C₄×C₁₆	—	47	1	no	—
55	C₄₇	#2178	1	1	yes	characteristic, complemented, Sylow
56	#135	—	47	2	no	—
57	#131	—	94	2	no	—
58	Q₃₂	—	47	1	no	—
59	SD₃₂	—	47	2	no	—
60	D₁₆	—	47	1	no	—
61	C₂×C₁₆	—	47	1	no	—
62	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
63	#108	C₂×D₄₇	1	2	yes	—
64	#104	—	94	2	no	—
65	C₄×C₈	—	47	1	no	—
66	#41	—	94	2	no	—
67	Q₁₆	—	47	2	no	—
68	SD₁₆	—	94	2	no	—
69	D₈	—	47	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	188	2	no	—
72	C₂×C₈	—	47	1	no	—
73	C₂×C₈	—	188	2	no	—
74	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
75	C₄²	—	47	1	no	—
76	C₁₆	—	94	1	no	—
77	C₁₆	C₄×D₄₇	1	1	yes	characteristic
78	C₁₆	C₄×D₄₇	1	1	yes	characteristic
79	Q₈	—	94	2	no	—
80	D₄	—	94	2	no	—
81	D₄	—	188	2	no	—
82	C₂×C₄	—	94	1	no	—
83	C₂×C₄	—	188	2	no	—
84	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
85	C₈	—	4	2	no	—
86	C₈	—	47	1	no	—
87	C₈	—	47	1	no	—
88	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
89	C₈	#10625354	1	1	yes	characteristic
90	C₂²	—	188	2	no	—
91	C₂²	#13094047	1	1	yes	characteristic
92	C₄	—	94	2	no	—
93	C₄	—	188	2	no	—
94	C₄	#13093986	1	1	yes	characteristic
95	C₄	D₈×D₄₇	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	376	2	no	—
98	C₂	#15689205	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689555

C₂

yes

maximal, characteristic

#15689239

C₂

yes

maximal, complemented

#15688929

C₂

yes

maximal, complemented

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×#368

C₂

yes

maximal, characteristic, complemented

#13094046

C₂²

yes

—

#13094032

—

Dic₃₇₆

C₄

yes

characteristic, complemented

#13093969

C₄

yes

complemented

D₇₅₂

C₄

yes

characteristic, complemented

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093950

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₂²

yes

—

#10625350

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

C₂×C₄

yes

—

D₃₇₆

C₂×C₄

yes

—

#10625325

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

C₂×C₄

yes

characteristic

C₁₆×C₄₇

C₂×C₄

yes

characteristic

C₄₇⋊C₁₆

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₂²×C₄₇

#135

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2178

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₄×D₈

yes

characteristic

D₄₇

—

#508

—

#443

—

#368

D₄₇

yes

characteristic, complemented

#359

—

C₄×C₁₆

—

C₄₇

#2178

yes

characteristic, complemented, Sylow

#135

—

#131

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#108

C₂×D₄₇

yes

—

#104

—

C₄×C₈

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

188

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

C₄×D₄₇

yes

characteristic

C₁₆

C₄×D₄₇

yes

characteristic

Q₈

—

D₄

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

C₂×C₄×D₄₇

yes

characteristic

C₈

#10625354

yes

characteristic

C₂²

—

188

—

C₂²

#13094047

yes

characteristic

C₄

—

C₄

—

188

—

C₄

#13093986

yes

characteristic

C₄

D₈×D₄₇

yes

characteristic

C₂

—

C₂

—

376

—

C₂

#15689205

yes

characteristic

	subgroup	G/H
center	C₄	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#368	C₂
socle	C₂×C₄₇	C₄×D₈
hypercenter	#368	D₄₇
hypocenter	C₄₇	#2178
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

subgroup

G/H

center

C₄

D₈×D₄₇

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#368

C₂

socle

C₂×C₄₇

C₄×D₈

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

N	H ≅ G/N	type
2. #15689239	C₂	semidirect
3. #15688929	C₂	semidirect
4. C₁₆×Dic₄₇	C₂	semidirect
5. C₄₇×#368	C₂	semidirect
8. Dic₃₇₆	C₄	semidirect
9. #13093969	C₄	semidirect
10. D₇₅₂	C₄	semidirect
52. #368	D₄₇	semidirect
55. C₄₇	#2178	semidirect

H ≅ G/N

type

2. #15689239

C₂

semidirect

3. #15688929

C₂

semidirect

4. C₁₆×Dic₄₇

C₂

semidirect

5. C₄₇×#368

C₂

semidirect

8. Dic₃₇₆

C₄

semidirect

9. #13093969

C₄

semidirect

10. D₇₅₂

C₄

semidirect

52. #368

D₄₇

semidirect

55. C₄₇

#2178

semidirect

Subgroups — #20245268

Conjugacy classes of subgroups

Complements