Group #20268591 — subgroups

Subgroups — #20268591

Order 6592.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#13110105	C₂	1	2	yes	maximal, complemented
2	#15693054	C₂	1	4	yes	maximal, complemented
3	#15693049	C₂	1	4	yes	maximal, complemented
4	#15693043	C₂	1	4	yes	maximal, complemented
5	C₂×M₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13110105	—	2	2	no	—
7	#13110105	—	2	2	no	—
8	#13110105	C₂²	1	4	yes	—
9	#13110105	C₂²	1	4	yes	complemented
10	C₂×Dic₂₀₆	C₂²	1	2	yes	complemented
11	C₂×D₄₁₂	C₂²	1	2	yes	complemented
12	C₂×C₂²⋊D₁₀₃	—	2	2	no	—
13	C₂×C₄×D₁₀₃	—	2	2	no	—
14	Dic₄₁₂	C₂²	1	4	yes	complemented
15	#13110094	C₂²	1	8	yes	complemented
16	D₈₂₄	C₂²	1	4	yes	complemented
17	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	M₁₆×C₁₀₃	C₂²	1	4	yes	complemented
19	C₂×C₈×C₁₀₃	C₂²	1	2	yes	complemented
20	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
21	C₂²×D₁₀₃	—	2	2	no	—
22	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
23	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₀₃	C₂³	1	2	yes	—
26	C₂²⋊D₁₀₃	—	2	4	no	—
27	C₂²⋊D₁₀₃	—	2	4	no	—
28	C₂×Dic₁₀₃	—	2	2	no	—
29	D₄₁₂	—	2	2	no	—
30	D₄₁₂	C₂³	1	4	yes	—
31	C₄×D₁₀₃	—	2	4	no	—
32	C₄×D₁₀₃	—	2	4	no	—
33	Dic₂₀₆	—	2	2	no	—
34	Dic₂₀₆	C₂³	1	4	yes	—
35	C₈×C₁₀₃	C₂³	1	4	yes	—
36	C₂²×C₁₀₃	—	4	1	no	—
37	C₂²×C₁₀₃	C₂×D₄	1	2	yes	—
38	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
39	C₂×D₁₀₃	—	2	4	no	—
40	C₂×D₁₀₃	—	4	4	no	—
41	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
42	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
43	C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
44	Dic₁₀₃	—	2	4	no	—
45	C₂×C₁₀₃	—	2	2	no	—
46	C₂×C₁₀₃	—	2	1	no	—
47	C₂×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
48	D₁₀₃	—	4	4	no	—
49	C₁₀₃	#575	1	1	yes	characteristic, complemented, Sylow
50	#575	—	103	1	no	maximal, Sylow
51	C₂×#41	—	103	2	no	—
52	#137	—	103	4	no	—
53	AGL(1,ℤ/8)	—	103	4	no	—
54	#135	—	103	4	no	—
55	C₂×M₁₆	D₁₀₃	1	1	yes	characteristic, complemented
56	#41	—	103	4	no	—
57	#41	—	103	4	no	—
58	#41	—	206	2	no	—
59	#41	—	206	2	no	—
60	C₂×Q₈	—	103	2	no	—
61	C₂×D₄	—	103	2	no	—
62	C₂×D₄	—	206	2	no	—
63	C₂²×C₄	—	206	2	no	—
64	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
65	Q₁₆	—	103	4	no	—
66	SD₁₆	—	103	8	no	—
67	D₈	—	103	4	no	—
68	M₁₆	C₂×D₁₀₃	1	4	yes	complemented
69	C₂×C₈	C₂×D₁₀₃	1	2	yes	complemented
70	C₂³	—	206	2	no	—
71	C₂³	D₄₁₂	1	1	yes	characteristic
72	Q₈	—	103	4	no	—
73	Q₈	—	206	2	no	—
74	D₄	—	103	4	no	—
75	D₄	—	206	4	no	—
76	D₄	—	206	4	no	—
77	D₄	—	206	2	no	—
78	C₂×C₄	—	206	2	no	—
79	C₂×C₄	—	206	4	no	—
80	C₂×C₄	—	206	4	no	—
81	C₂×C₄	D₄₁₂	1	1	yes	characteristic
82	C₂×C₄	D₄₁₂	1	2	yes	—
83	C₂×C₄	C₂²×D₁₀₃	1	2	yes	—
84	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
85	C₈	C₂²×D₁₀₃	1	4	yes	—
86	C₂²	—	4	1	no	—
87	C₂²	—	412	4	no	—
88	C₂²	—	206	4	no	—
89	C₂²	C₂×D₄₁₂	1	2	yes	—
90	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
91	C₄	—	206	4	no	—
92	C₄	C₂×D₄₁₂	1	2	yes	—
93	C₄	C₂×D₄₁₂	1	1	yes	characteristic
94	C₄	C₂³×D₁₀₃	1	1	yes	characteristic
95	C₂	—	2	2	no	—
96	C₂	—	2	1	no	—
97	C₂	—	412	4	no	—
98	C₂	C₂²×D₄₁₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110105

C₂

yes

maximal, complemented

#15693054

C₂

yes

maximal, complemented

#15693049

C₂

yes

maximal, complemented

#15693043

C₂

yes

maximal, complemented

C₂×M₁₆×C₁₀₃

C₂

yes

maximal, characteristic, complemented

#13110105

—

#13110105

—

#13110105

C₂²

yes

—

#13110105

C₂²

yes

complemented

C₂×Dic₂₀₆

C₂²

yes

complemented

C₂×D₄₁₂

C₂²

yes

complemented

C₂×C₂²⋊D₁₀₃

—

C₂×C₄×D₁₀₃

—

Dic₄₁₂

C₂²

yes

complemented

#13110094

C₂²

yes

complemented

D₈₂₄

C₂²

yes

complemented

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

M₁₆×C₁₀₃

C₂²

yes

complemented

C₂×C₈×C₁₀₃

C₂²

yes

complemented

C₂³×C₁₀₃

D₄

yes

characteristic

C₂²×D₁₀₃

—

C₂×C₄×C₁₀₃

D₄

yes

—

C₂×C₄×C₁₀₃

D₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂×C₄×C₁₀₃

C₂³

yes

—

C₂²⋊D₁₀₃

—

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

—

D₄₁₂

—

D₄₁₂

C₂³

yes

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

Dic₂₀₆

—

Dic₂₀₆

C₂³

yes

—

C₈×C₁₀₃

C₂³

yes

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂×D₄

yes

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

C₂⁴

yes

characteristic

Dic₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

C₂²×D₄

yes

characteristic

D₁₀₃

—

C₁₀₃

#575

yes

characteristic, complemented, Sylow

#575

—

103

maximal, Sylow

C₂×#41

—

103

—

#137

—

103

—

AGL(1,ℤ/8)

—

103

—

#135

—

103

—

C₂×M₁₆

D₁₀₃

yes

characteristic, complemented

#41

—

103

—

#41

—

103

—

#41

—

206

—

#41

—

206

—

C₂×Q₈

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂²×C₄

—

206

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

Q₁₆

—

103

—

SD₁₆

—

103

—

D₈

—

103

—

M₁₆

C₂×D₁₀₃

yes

complemented

C₂×C₈

C₂×D₁₀₃

yes

complemented

C₂³

—

206

—

C₂³

D₄₁₂

yes

characteristic

Q₈

—

103

—

Q₈

—

206

—

D₄

—

103

—

D₄

—

206

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

D₄₁₂

yes

characteristic

C₂×C₄

D₄₁₂

yes

—

C₂×C₄

C₂²×D₁₀₃

yes

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

C₂²×D₁₀₃

yes

—

C₂²

—

C₂²

—

412

—

C₂²

—

206

—

C₂²

C₂×D₄₁₂

yes

—

C₂²

C₂×D₄₁₂

yes

characteristic

C₄

—

206

—

C₄

C₂×D₄₁₂

yes

—

C₄

C₂×D₄₁₂

yes

characteristic

C₄

C₂³×D₁₀₃

yes

characteristic

C₂

—

C₂

—

C₂

—

412

—

C₂

C₂²×D₄₁₂

yes

characteristic

	subgroup	G/H
center	C₄	C₂×D₄₁₂
commutator	C₄×C₁₀₃	C₂⁴
Frattini	C₄	C₂³×D₁₀₃
Fitting	C₂×M₁₆×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂²×D₄
hypercenter	C₂×M₁₆	D₁₀₃
hypocenter	C₁₀₃	#575
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

C₂×D₄₁₂

commutator

C₄×C₁₀₃

C₂⁴

Frattini

C₄

C₂³×D₁₀₃

Fitting

C₂×M₁₆×C₁₀₃

C₂

socle

C₂×C₁₀₃

C₂²×D₄

hypercenter

C₂×M₁₆

D₁₀₃

hypocenter

C₁₀₃

#575

LCS

G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#13110105	C₂	semidirect
2. #15693054	C₂	semidirect
3. #15693049	C₂	semidirect
4. #15693043	C₂	semidirect
5. C₂×M₁₆×C₁₀₃	C₂	semidirect
9. #13110105	C₂²	semidirect
10. C₂×Dic₂₀₆	C₂²	semidirect
11. C₂×D₄₁₂	C₂²	semidirect
14. Dic₄₁₂	C₂²	semidirect
15. #13110094	C₂²	semidirect
16. D₈₂₄	C₂²	semidirect
18. M₁₆×C₁₀₃	C₂²	semidirect
19. C₂×C₈×C₁₀₃	C₂²	semidirect
49. C₁₀₃	#575	semidirect
55. C₂×M₁₆	D₁₀₃	semidirect
68. M₁₆	C₂×D₁₀₃	semidirect
69. C₂×C₈	C₂×D₁₀₃	semidirect

H ≅ G/N

type

1. C₂×#13110105

C₂

semidirect

2. #15693054

C₂

semidirect

3. #15693049

C₂

semidirect

4. #15693043

C₂

semidirect

5. C₂×M₁₆×C₁₀₃

C₂

semidirect

9. #13110105

C₂²

semidirect

10. C₂×Dic₂₀₆

C₂²

semidirect

11. C₂×D₄₁₂

C₂²

semidirect

14. Dic₄₁₂

C₂²

semidirect

15. #13110094

C₂²

semidirect

16. D₈₂₄

C₂²

semidirect

18. M₁₆×C₁₀₃

C₂²

semidirect

19. C₂×C₈×C₁₀₃

C₂²

semidirect

49. C₁₀₃

#575

semidirect

55. C₂×M₁₆

D₁₀₃

semidirect

68. M₁₆

C₂×D₁₀₃

semidirect

69. C₂×C₈

C₂×D₁₀₃

semidirect

Subgroups — #20268591

Conjugacy classes of subgroups

Complements