Subgroups — (C₃⋊D₃)⋊D₂₄₇ #22580374

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₇₄₁	C₂	1	2	yes	maximal, complemented
3	D₃×D₂₄₇	—	3	2	no	maximal
4	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇₄₁	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₁₉	—	3	2	no	—
7	D₃×C₁₃×C₁₉	—	6	1	no	—
8	C₃×D₂₄₇	—	3	2	no	—
9	C₂×D₂₄₇	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	—	2	1	no	—
11	C₃×C₁₃×C₁₉	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₁₉	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₁₉	—	9	1	no	—
14	D₂₄₇	—	3	2	no	—
15	(C₃⋊D₃)⋊D₁₃	—	19	1	no	maximal, Hall
16	C₃⋊D₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
17	C₃×D₅₇	—	13	2	no	—
18	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₃⋊D₃	D₁₉	1	1	yes	characteristic, complemented
20	C₃×D₃₉	—	19	2	no	—
21	D₃×D₁₉	—	39	2	no	—
22	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₁₃	—	57	2	no	—
24	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	D₅₇	—	13	2	no	—
26	C₃×D₁₉	—	39	2	no	—
27	D₃×C₁₉	—	3	2	no	—
28	D₃×C₁₉	—	6	1	no	—
29	D₃₉	—	19	2	no	—
30	C₃×D₁₃	—	57	2	no	—
31	D₃×C₁₃	—	3	2	no	—
32	D₃×C₁₃	—	6	1	no	—
33	C₂×D₁₉	—	117	1	no	Hall
34	C₃×C₁₉	—	2	1	no	—
35	C₃×C₁₉	D₃×D₁₃	1	2	yes	complemented
36	C₂×D₁₃	—	171	1	no	Hall
37	C₃×C₁₃	—	2	1	no	—
38	C₃×C₁₃	D₃×D₁₉	1	2	yes	complemented
39	C₂×C₁₉	—	9	1	no	—
40	D₁₉	—	39	2	no	—
41	D₃²	—	247	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	D₁₃	—	57	2	no	—
44	C₁₉	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃⋊D₃	D₂₄₇	1	1	yes	characteristic, complemented
46	C₃×D₃	—	247	2	no	—
47	C₁₃	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₃	—	741	2	no	—
49	C₃²	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	741	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	247	2	no	—
54	C₂²	—	2223	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₂₄₇	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	741	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
2. C₃×D₇₄₁	C₂	semidirect
4. C₃²×C₁₃×C₁₉	C₂²	semidirect
5. D₇₄₁	D₃	semidirect
11. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
16. C₃⋊D₃×C₁₉	D₁₃	semidirect
18. C₁₃×C₁₉	D₃²	semidirect
19. C₁₃×C₃⋊D₃	D₁₉	semidirect
22. C₃²×C₁₉	C₂×D₁₃	semidirect
24. C₃²×C₁₃	C₂×D₁₉	semidirect
35. C₃×C₁₉	D₃×D₁₃	semidirect
38. C₃×C₁₃	D₃×D₁₉	semidirect
44. C₁₉	(C₃⋊D₃)⋊D₁₃	semidirect
45. C₃⋊D₃	D₂₄₇	semidirect
47. C₁₃	(C₃⋊D₃)⋊D₁₉	semidirect
49. C₃²	C₂×D₂₄₇	semidirect
56. C₃	D₃×D₂₄₇	semidirect

Subgroups — (C3⋊D3)⋊D247 #22580374

Conjugacy classes of subgroups

Complements

Subgroups — (C₃⋊D₃)⋊D₂₄₇ #22580374