Group #20245234 — subgroups

Subgroups — #20245234

Order 6016.

174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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×D₇₅₂	C₂	1	1	yes	maximal, characteristic
2	#15689205	C₂	1	2	yes	maximal, complemented
3	#15688923	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	#13093986	—	2	2	no	—
8	D₇₅₂	C₄	1	4	yes	complemented
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13093944	—	2	2	no	—
11	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	#107×C₄₇	C₂²	1	2	yes	—
14	C₂×D₁₈₈	—	2	2	no	—
15	C₂×C₄×D₄₇	—	4	2	no	—
16	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₄₇	—	2	2	no	—
18	(C₂×D₄₇)⋊C₄	—	4	2	no	—
19	C₄×Dic₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
21	D₃₇₆	—	2	2	no	—
22	D₃₇₆	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
24	C₄₇⋊C₁₆	—	2	1	no	—
25	C₂²×D₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₄₇	D₈	1	1	yes	characteristic
29	C₂×Dic₄₇	D₈	1	1	yes	characteristic
30	D₁₈₈	—	2	4	no	—
31	D₁₈₈	—	4	2	no	—
32	C₄×D₄₇	—	8	4	no	—
33	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₄₇	#41	1	1	yes	characteristic
35	C₄₇⋊C₈	—	2	1	no	—
36	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
37	C₂×D₄₇	—	4	4	no	—
38	C₂×D₄₇	—	8	2	no	—
39	C₂×D₄₇	—	8	2	no	—
40	C₄×C₄₇	—	8	2	no	—
41	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₇	#135	1	1	yes	characteristic
43	Dic₄₇	—	2	1	no	—
44	Dic₄₇	D₁₆	1	2	yes	complemented
45	C₄×D₁₆	—	47	1	no	maximal, Sylow
46	C₂×C₄₇	C₄×D₈	1	1	yes	characteristic
47	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
48	C₂×C₄₇	#508	1	1	yes	characteristic
49	D₄₇	—	8	4	no	—
50	C₂×D₁₆	—	47	1	no	—
51	C₄×D₈	—	47	2	no	—
52	#366	D₄₇	1	1	yes	characteristic, complemented
53	#357	—	47	2	no	—
54	C₄×C₁₆	—	47	1	no	—
55	C₄₇	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	47	2	no	—
57	C₄×D₄	—	94	2	no	—
58	D₁₆	—	47	4	no	—
59	C₂×C₁₆	—	47	1	no	—
60	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
61	#107	C₂×D₄₇	1	2	yes	—
62	#102	—	94	2	no	—
63	C₄×C₈	—	47	1	no	—
64	C₂×D₄	—	94	2	no	—
65	C₂²×C₄	—	188	2	no	—
66	D₈	—	47	4	no	—
67	D₈	—	94	2	no	—
68	C₂×C₈	—	47	1	no	—
69	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
70	C₄⋊C₄	—	2	2	no	—
71	C₂²⋊C₄	—	188	2	no	—
72	C₄²	—	47	1	no	—
73	C₁₆	—	94	1	no	—
74	C₁₆	C₄×D₄₇	1	2	yes	complemented
75	C₂³	—	188	2	no	—
76	D₄	—	94	4	no	—
77	D₄	—	188	2	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	47	1	no	—
80	C₂×C₄	—	47	1	no	—
81	C₂×C₄	—	376	4	no	—
82	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
83	C₈	—	94	1	no	—
84	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
85	C₈	#10625354	1	1	yes	characteristic
86	C₂²	—	376	2	no	—
87	C₂²	—	376	2	no	—
88	C₂²	—	188	4	no	—
89	C₂²	D₈×D₄₇	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	47	2	no	—
92	C₄	—	94	1	no	—
93	C₄	#13093986	1	1	yes	characteristic
94	C₄	#13094047	1	1	yes	characteristic
95	C₂	—	376	4	no	—
96	C₂	#15689205	1	1	yes	characteristic
97	C₂	D₁₆×D₄₇	1	1	yes	characteristic
98	C₂	#15689556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₇₅₂

C₂

yes

maximal, characteristic

#15689205

C₂

yes

maximal, complemented

#15688923

C₂

yes

maximal, complemented

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×#366

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

—

#13093986

—

D₇₅₂

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093944

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

C₂×C₄

yes

complemented

C₁₆×C₄₇

C₂×C₄

yes

complemented

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

#135

yes

characteristic

Dic₄₇

—

Dic₄₇

D₁₆

yes

complemented

C₄×D₁₆

—

maximal, Sylow

C₂×C₄₇

C₄×D₈

yes

characteristic

C₂×C₄₇

C₂×D₁₆

yes

characteristic

C₂×C₄₇

#508

yes

characteristic

D₄₇

—

C₂×D₁₆

—

C₄×D₈

—

#366

D₄₇

yes

characteristic, complemented

#357

—

C₄×C₁₆

—

C₄₇

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₄×D₄

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

C₂×D₄₇

yes

—

#102

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

188

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

—

C₁₆

—

C₁₆

C₄×D₄₇

yes

complemented

C₂³

—

188

—

D₄

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

C₂×C₄×D₄₇

yes

characteristic

C₈

#10625354

yes

characteristic

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

188

—

C₂²

D₈×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

376

—

C₂

#15689205

yes

characteristic

C₂

D₁₆×D₄₇

yes

characteristic

C₂

#15689556

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#366	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#366	D₄₇
hypocenter	C₄₇	C₄×D₁₆
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#366

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

#366

D₄₇

hypocenter

C₄₇

C₄×D₁₆

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
2. #15689205	C₂	semidirect
3. #15688923	C₂	semidirect
4. C₁₆×Dic₄₇	C₂	semidirect
5. C₄₇×#366	C₂	semidirect
8. D₇₅₂	C₄	semidirect
22. D₃₇₆	C₂×C₄	semidirect
23. C₁₆×C₄₇	C₂×C₄	semidirect
44. Dic₄₇	D₁₆	semidirect
52. #366	D₄₇	semidirect
55. C₄₇	C₄×D₁₆	semidirect
74. C₁₆	C₄×D₄₇	semidirect

H ≅ G/N

type

2. #15689205

C₂

semidirect

3. #15688923

C₂

semidirect

4. C₁₆×Dic₄₇

C₂

semidirect

5. C₄₇×#366

C₂

semidirect

8. D₇₅₂

C₄

semidirect

22. D₃₇₆

C₂×C₄

semidirect

23. C₁₆×C₄₇

C₂×C₄

semidirect

44. Dic₄₇

D₁₆

semidirect

52. #366

D₄₇

semidirect

55. C₄₇

C₄×D₁₆

semidirect

74. C₁₆

C₄×D₄₇

semidirect

Subgroups — #20245234

Conjugacy classes of subgroups

Complements