Group #20245236 — subgroups

Subgroups — C₄×D₇₅₂ #20245236

Order 6016.

174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₄×D₃₇₆	C₂	1	2	yes	maximal, complemented
3	#15688949	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688925	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃₇₆	C₂²	1	2	yes	—
7	C₄×D₁₈₈	—	2	2	no	—
8	D₇₅₂	C₄	1	4	yes	direct product factor
9	#13093958	C₂²	1	2	yes	—
10	#13093946	—	2	2	no	—
11	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₁₈₈	—	2	2	no	—
15	C₂×C₄×D₄₇	—	4	2	no	—
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄²×C₄₇	D₄	1	1	yes	characteristic
19	(C₂×D₄₇)⋊C₄	—	4	2	no	—
20	C₄⋊Dic₄₇	—	2	2	no	—
21	D₃₇₆	—	2	2	no	—
22	D₃₇₆	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₄₇	—	2	1	no	—
24	C₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
25	C₂²×D₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
27	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₇	—	4	2	no	—
30	D₁₈₈	—	2	4	no	—
31	D₁₈₈	—	4	2	no	—
32	C₄×D₄₇	—	8	4	no	—
33	C₈×C₄₇	—	2	1	no	—
34	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₇	#41	1	1	yes	characteristic
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	—	2	1	no	—
41	C₄×C₄₇	D₁₆	1	2	yes	complemented
42	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
43	C₄×C₄₇	#135	1	1	yes	characteristic
44	Dic₄₇	—	8	2	no	—
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	—	47	1	no	—
53	#357	—	47	2	no	—
54	C₄×C₁₆	D₄₇	1	1	yes	characteristic, complemented
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	C₂×D₄₇	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
61	#107	—	47	2	no	—
62	#102	—	94	2	no	—
63	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
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	D₁₈₈	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
70	C₄⋊C₄	—	94	2	no	—
71	C₂²⋊C₄	—	188	2	no	—
72	C₄²	D₁₈₈	1	1	yes	characteristic
73	C₁₆	—	2	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	—	376	4	no	—
79	C₂×C₄	—	188	2	no	—
80	C₂×C₄	D₃₇₆	1	1	yes	characteristic
81	C₂×C₄	D₃₇₆	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
85	C₈	#10625350	1	1	yes	characteristic
86	C₂²	—	376	2	no	—
87	C₂²	—	376	2	no	—
88	C₂²	—	188	4	no	—
89	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	376	2	no	—
92	C₄	D₇₅₂	1	2	yes	direct product factor
93	C₄	C₄×D₁₈₈	1	1	yes	characteristic
94	C₄	#13094046	1	1	yes	characteristic
95	C₂	—	376	4	no	—
96	C₂	C₄×D₃₇₆	1	1	yes	characteristic
97	C₂	C₂×D₇₅₂	1	1	yes	characteristic
98	C₂	#15689555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₇₅₂

C₂

yes

maximal, characteristic

C₄×D₃₇₆

C₂

yes

maximal, complemented

#15688949

C₂

yes

maximal, characteristic, complemented

#15688925

C₂

yes

maximal, complemented

C₄×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

—

C₄×D₁₈₈

—

D₇₅₂

C₄

yes

direct product factor

#13093958

C₂²

yes

—

#13093946

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

D₃₇₆

—

D₃₇₆

C₂×C₄

yes

complemented

C₁₆×C₄₇

—

C₁₆×C₄₇

C₂×C₄

yes

complemented

C₂²×D₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

D₁₆

yes

complemented

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

#135

yes

characteristic

Dic₄₇

—

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

—

#357

—

C₄×C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₄×D₄

—

D₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#102

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

188

—

D₈

—

D₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

C₁₆

C₄×D₄₇

yes

complemented

C₂³

—

188

—

D₄

—

D₄

—

188

—

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

—

C₈

C₂×C₄×D₄₇

yes

characteristic

C₈

#10625350

yes

characteristic

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

188

—

C₂²

C₂×D₃₇₆

yes

characteristic

C₄

—

C₄

—

376

—

C₄

D₇₅₂

yes

direct product factor

C₄

C₄×D₁₈₈

yes

characteristic

C₄

#13094046

yes

characteristic

C₂

—

376

—

C₂

C₄×D₃₇₆

yes

characteristic

C₂

C₂×D₇₅₂

yes

characteristic

C₂

#15689555

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₃₇₆
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	C₄×D₁₆
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₄

D₃₇₆

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×C₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄×C₁₆

D₄₇

hypocenter

C₄₇

C₄×D₁₆

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄×D₃₇₆	C₂	semidirect
3. #15688949	C₂	semidirect
4. #15688925	C₂	semidirect
5. C₄×C₁₆×C₄₇	C₂	semidirect
8. D₇₅₂	C₄	direct (N × H)
22. D₃₇₆	C₂×C₄	semidirect
24. C₁₆×C₄₇	C₂×C₄	semidirect
41. C₄×C₄₇	D₁₆	semidirect
54. C₄×C₁₆	D₄₇	semidirect
55. C₄₇	C₄×D₁₆	semidirect
74. C₁₆	C₄×D₄₇	semidirect
92. C₄	D₇₅₂	direct (N × H)

H ≅ G/N

type

2. C₄×D₃₇₆

C₂

semidirect

3. #15688949

C₂

semidirect

4. #15688925

C₂

semidirect

5. C₄×C₁₆×C₄₇

C₂

semidirect

8. D₇₅₂

C₄

direct (N × H)

22. D₃₇₆

C₂×C₄

semidirect

24. C₁₆×C₄₇

C₂×C₄

semidirect

41. C₄×C₄₇

D₁₆

semidirect

54. C₄×C₁₆

D₄₇

semidirect

55. C₄₇

C₄×D₁₆

semidirect

74. C₁₆

C₄×D₄₇

semidirect

92. C₄

D₇₅₂

direct (N × H)

Subgroups — C₄×D₇₅₂ #20245236

Conjugacy classes of subgroups

Complements

Subgroups — C4×D752 #20245236

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₇₅₂ #20245236