Subgroups — C₂×C₃⋊D₈₉₇ #24924583

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₈₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈₉₇	—	3	4	no	maximal
4	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	D₃	1	4	yes	complemented
6	D₈₉₇	—	3	8	no	—
7	C₂×D₂₉₉	—	9	1	no	Hall
8	C₃×C₁₃×C₂₃	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₆₉	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
11	D₂₉₉	—	9	2	no	—
12	C₂×C₃⋊D₃₉	—	23	1	no	maximal, Hall
13	C₂×C₃²×C₂₃	D₁₃	1	1	yes	characteristic, complemented
14	C₃⋊D₆₉	—	13	2	no	—
15	C₁₃×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₆₉	—	39	4	no	—
17	C₂×C₃²×C₁₃	D₂₃	1	1	yes	characteristic, complemented
18	C₃⋊D₃₉	—	23	2	no	—
19	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₉	—	69	4	no	—
21	C₂×C₃×C₂₃	D₃₉	1	4	yes	complemented
22	D₆₉	—	39	8	no	—
23	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₂₃	—	117	1	no	Hall
25	C₂×C₃×C₁₃	D₆₉	1	4	yes	complemented
26	D₃₉	—	69	8	no	—
27	C₃×C₂₃	C₂×D₃₉	1	4	yes	complemented
28	C₂×D₁₃	—	207	1	no	Hall
29	C₂×C₂₃	C₃⋊D₃₉	1	1	yes	characteristic, complemented
30	D₂₃	—	117	2	no	—
31	C₃×C₁₃	C₂×D₆₉	1	4	yes	complemented
32	C₂×C₃⋊D₃	—	299	1	no	Hall
33	C₂×C₁₃	C₃⋊D₆₉	1	1	yes	characteristic, complemented
34	D₁₃	—	207	2	no	—
35	C₂₃	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	D₂₉₉	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	299	2	no	—
38	C₁₃	C₂×C₃⋊D₆₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	897	4	no	—
40	C₃²	C₂×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₈₉₇	1	4	yes	complemented
42	D₃	—	897	8	no	—
43	C₂²	—	2691	1	no	Sylow
44	C₃	C₂×D₈₉₇	1	4	yes	complemented
45	C₂	—	2691	2	no	—
46	C₂	C₃⋊D₈₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₈₉₇
commutator, cosocle, hypocenter	C₃²×C₁₃×C₂₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₃²×C₁₃×C₂₃
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃⋊D₈₉₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. C₂×C₃×C₁₃×C₂₃	D₃	semidirect
8. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
10. C₂×C₁₃×C₂₃	C₃⋊D₃	semidirect
13. C₂×C₃²×C₂₃	D₁₃	semidirect
15. C₁₃×C₂₃	C₂×C₃⋊D₃	semidirect
17. C₂×C₃²×C₁₃	D₂₃	semidirect
19. C₃²×C₂₃	C₂×D₁₃	semidirect
21. C₂×C₃×C₂₃	D₃₉	semidirect
23. C₃²×C₁₃	C₂×D₂₃	semidirect
25. C₂×C₃×C₁₃	D₆₉	semidirect
27. C₃×C₂₃	C₂×D₃₉	semidirect
29. C₂×C₂₃	C₃⋊D₃₉	semidirect
31. C₃×C₁₃	C₂×D₆₉	semidirect
33. C₂×C₁₃	C₃⋊D₆₉	semidirect
35. C₂₃	C₂×C₃⋊D₃₉	semidirect
36. C₂×C₃²	D₂₉₉	semidirect
38. C₁₃	C₂×C₃⋊D₆₉	semidirect
40. C₃²	C₂×D₂₉₉	semidirect
41. C₂×C₃	D₈₉₇	semidirect
44. C₃	C₂×D₈₉₇	semidirect
46. C₂	C₃⋊D₈₉₇	direct (N × H)

Subgroups — C2×C3⋊D897 #24924583

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊D₈₉₇ #24924583