Subgroups — C₃⋊D₃×D₂₉₉ #24924562

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₈₉₇	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₂₃	C₂	semidirect
3. C₃²×D₂₉₉	C₂	semidirect
5. C₃²×C₁₃×C₂₃	C₂²	semidirect
8. C₃×D₂₉₉	D₃	semidirect
10. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
14. D₂₉₉	C₃⋊D₃	direct (N × H)
17. C₃⋊D₃×C₂₃	D₁₃	semidirect
19. C₁₃×C₂₃	C₂×C₃⋊D₃	semidirect
22. C₁₃×C₃⋊D₃	D₂₃	semidirect
24. C₃²×C₂₃	C₂×D₁₃	semidirect
29. C₃²×C₁₃	C₂×D₂₃	semidirect
34. C₃×C₂₃	D₃×D₁₃	semidirect
39. C₃×C₁₃	D₃×D₂₃	semidirect
44. C₂₃	C₃⋊D₃×D₁₃	semidirect
47. C₃⋊D₃	D₂₉₉	direct (N × H)
48. C₁₃	C₃⋊D₃×D₂₃	semidirect
50. C₃²	C₂×D₂₉₉	semidirect
55. C₃	D₃×D₂₉₉	semidirect

Subgroups — C3⋊D3×D299 #24924562

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊D₃×D₂₉₉ #24924562