Subgroups — D₈₉₉⋊(C₃⋊D₃) #44569129

Order 32364.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₃²×D₈₉₉	2
C₂₉×C₃⋊D₉₃	2
C₃₁×C₃⋊D₈₇	2
D₈₇⋊D₃₁	3
C₃⋊D₃×D₃₁	29
C₃⋊D₃×D₂₉	31

Subgroups — D899⋊(C3⋊D3) #44569129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈₉₉⋊(C₃⋊D₃) #44569129