Subgroups — (C₃⋊D₃)⋊D₈₉₉ #44569121

Order 32364.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₉₇	C₂	1	2	yes	maximal, complemented
2	C₃⋊D₃×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×D₈₉₉	—	3	2	no	maximal
4	C₃²×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₆₉₇	D₃	1	2	yes	complemented
6	D₃×C₂₉×C₃₁	—	3	2	no	—
7	D₃×C₂₉×C₃₁	—	6	1	no	—
8	C₃×D₈₉₉	—	3	2	no	—
9	C₂×D₈₉₉	—	9	1	no	Hall
10	C₃×C₂₉×C₃₁	—	2	1	no	—
11	C₃×C₂₉×C₃₁	C₂×D₃	1	2	yes	complemented
12	C₂×C₂₉×C₃₁	—	9	1	no	—
13	D₈₉₉	—	3	2	no	—
14	(C₃⋊D₃)⋊D₃₁	—	29	1	no	maximal, Hall
15	(C₃⋊D₃)⋊D₂₉	—	31	1	no	maximal, Hall
16	C₂₉×C₃₁	D₃²	1	1	yes	characteristic, complemented, Hall
17	C₃⋊D₃×C₃₁	D₂₉	1	1	yes	characteristic, complemented
18	C₃×D₉₃	—	29	2	no	—
19	C₃⋊D₃×C₂₉	D₃₁	1	1	yes	characteristic, complemented
20	C₃×D₈₇	—	31	2	no	—
21	D₃×D₃₁	—	87	2	no	—
22	D₃×D₂₉	—	93	2	no	—
23	C₃²×C₃₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₂₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
25	D₉₃	—	29	2	no	—
26	C₃×D₃₁	—	87	2	no	—
27	D₃×C₃₁	—	3	2	no	—
28	D₃×C₃₁	—	6	1	no	—
29	D₈₇	—	31	2	no	—
30	C₃×D₂₉	—	93	2	no	—
31	D₃×C₂₉	—	3	2	no	—
32	D₃×C₂₉	—	6	1	no	—
33	C₂×D₃₁	—	261	1	no	Hall
34	C₂×D₂₉	—	279	1	no	Hall
35	C₃×C₃₁	—	2	1	no	—
36	C₃×C₃₁	D₃×D₂₉	1	2	yes	complemented
37	C₃×C₂₉	—	2	1	no	—
38	C₃×C₂₉	D₃×D₃₁	1	2	yes	complemented
39	C₂×C₃₁	—	9	1	no	—
40	D₃₁	—	87	2	no	—
41	C₂×C₂₉	—	9	1	no	—
42	D₂₉	—	93	2	no	—
43	D₃²	—	899	1	no	Hall
44	C₃₁	(C₃⋊D₃)⋊D₂₉	1	1	yes	characteristic, complemented, Sylow
45	C₂₉	(C₃⋊D₃)⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₃⋊D₃	D₈₉₉	1	1	yes	characteristic, complemented
47	C₃×D₃	—	899	2	no	—
48	C₂×D₃	—	2697	2	no	—
49	C₃²	C₂×D₈₉₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	2697	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	899	2	no	—
54	C₂²	—	8091	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₈₉₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	2697	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉×C₃₁	C₂²
LCS	G ▷ C₃²×C₂₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₆₉₇	C₂	semidirect
2. C₃⋊D₃×C₂₉×C₃₁	C₂	semidirect
4. C₃²×C₂₉×C₃₁	C₂²	semidirect
5. D₂₆₉₇	D₃	semidirect
11. C₃×C₂₉×C₃₁	C₂×D₃	semidirect
16. C₂₉×C₃₁	D₃²	semidirect
17. C₃⋊D₃×C₃₁	D₂₉	semidirect
19. C₃⋊D₃×C₂₉	D₃₁	semidirect
23. C₃²×C₃₁	C₂×D₂₉	semidirect
24. C₃²×C₂₉	C₂×D₃₁	semidirect
36. C₃×C₃₁	D₃×D₂₉	semidirect
38. C₃×C₂₉	D₃×D₃₁	semidirect
44. C₃₁	(C₃⋊D₃)⋊D₂₉	semidirect
45. C₂₉	(C₃⋊D₃)⋊D₃₁	semidirect
46. C₃⋊D₃	D₈₉₉	semidirect
49. C₃²	C₂×D₈₉₉	semidirect
56. C₃	D₃×D₈₉₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₂₆₉₇	2
C₃⋊D₃×C₂₉×C₃₁	2
D₃×D₈₉₉	3
(C₃⋊D₃)⋊D₃₁	29
(C₃⋊D₃)⋊D₂₉	31

Subgroups — (C3⋊D3)⋊D899 #44569121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₈₉₉ #44569121