Subgroups — (C₃⋊D₃)⋊D₂₉₉ #24924573

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₈₉₇	C₂	1	2	yes	maximal, complemented
3	D₃×D₂₉₉	—	3	2	no	maximal
4	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₈₉₇	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₂₃	—	3	2	no	—
7	D₃×C₁₃×C₂₃	—	6	1	no	—
8	C₃×D₂₉₉	—	3	2	no	—
9	C₂×D₂₉₉	—	9	1	no	Hall
10	C₃×C₁₃×C₂₃	—	2	1	no	—
11	C₃×C₁₃×C₂₃	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₂₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₂₃	—	9	1	no	—
14	D₂₉₉	—	3	2	no	—
15	(C₃⋊D₃)⋊D₁₃	—	23	1	no	maximal, Hall
16	C₃⋊D₃×C₂₃	D₁₃	1	1	yes	characteristic, complemented
17	C₃×D₆₉	—	13	2	no	—
18	C₁₃×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
19	D₃×D₂₃	—	39	2	no	—
20	C₁₃×C₃⋊D₃	D₂₃	1	1	yes	characteristic, complemented
21	C₃×D₃₉	—	23	2	no	—
22	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₁₃	—	69	2	no	—
24	D₆₉	—	13	2	no	—
25	C₃×D₂₃	—	39	2	no	—
26	D₃×C₂₃	—	3	2	no	—
27	D₃×C₂₃	—	6	1	no	—
28	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₂₃	—	117	1	no	Hall
30	D₃₉	—	23	2	no	—
31	C₃×D₁₃	—	69	2	no	—
32	D₃×C₁₃	—	3	2	no	—
33	D₃×C₁₃	—	6	1	no	—
34	C₃×C₂₃	—	2	1	no	—
35	C₃×C₂₃	D₃×D₁₃	1	2	yes	complemented
36	C₂×D₁₃	—	207	1	no	Hall
37	C₂×C₂₃	—	9	1	no	—
38	D₂₃	—	39	2	no	—
39	C₃×C₁₃	—	2	1	no	—
40	C₃×C₁₃	D₃×D₂₃	1	2	yes	complemented
41	D₃²	—	299	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	D₁₃	—	69	2	no	—
44	C₂₃	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃⋊D₃	D₂₉₉	1	1	yes	characteristic, complemented
46	C₃×D₃	—	299	2	no	—
47	C₁₃	(C₃⋊D₃)⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₃	—	897	2	no	—
49	C₃²	C₂×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	897	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	299	2	no	—
54	C₂²	—	2691	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₂₉₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	897	2	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. C₁₃×C₃⋊D₃×C₂₃	C₂	semidirect
2. C₃×D₈₉₇	C₂	semidirect
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. D₈₉₇	D₃	semidirect
11. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
16. C₃⋊D₃×C₂₃	D₁₃	semidirect
18. C₁₃×C₂₃	D₃²	semidirect
20. C₁₃×C₃⋊D₃	D₂₃	semidirect
22. C₃²×C₂₃	C₂×D₁₃	semidirect
28. C₃²×C₁₃	C₂×D₂₃	semidirect
35. C₃×C₂₃	D₃×D₁₃	semidirect
40. C₃×C₁₃	D₃×D₂₃	semidirect
44. C₂₃	(C₃⋊D₃)⋊D₁₃	semidirect
45. C₃⋊D₃	D₂₉₉	semidirect
47. C₁₃	(C₃⋊D₃)⋊D₂₃	semidirect
49. C₃²	C₂×D₂₉₉	semidirect
56. C₃	D₃×D₂₉₉	semidirect

Subgroups — (C3⋊D3)⋊D299 #24924573

Conjugacy classes of subgroups

Complements

Subgroups — (C₃⋊D₃)⋊D₂₉₉ #24924573