Subgroups — C₃²×D₁₀₀₁ #31825093

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₀₀₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	4	yes	complemented
4	C₃²×D₁₄₃	—	7	1	no	maximal, Hall
5	D₁₀₀₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×D₉₁	—	11	1	no	maximal, Hall
7	C₃²×D₇₇	—	13	1	no	maximal, Hall
8	C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₄₃	—	7	4	no	—
11	C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₉₁	—	11	4	no	—
14	C₃×D₇₇	—	13	4	no	—
15	C₃×C₁₁×C₁₃	C₃×D₇	1	4	yes	complemented
16	D₁₄₃	—	7	1	no	Hall
17	C₃×C₇×C₁₃	C₃×D₁₁	1	4	yes	complemented
18	C₃²×D₁₃	—	77	1	no	Hall
19	C₃×C₇×C₁₁	C₃×D₁₃	1	4	yes	complemented
20	C₃²×D₁₁	—	91	1	no	Hall
21	D₉₁	—	11	1	no	Hall
22	D₇₇	—	13	1	no	Hall
23	C₁₁×C₁₃	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
24	C₃²×D₇	—	143	1	no	Hall
25	C₃²×C₁₃	D₇₇	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₁₁	D₉₁	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃×D₁₃	—	77	4	no	—
29	C₇×C₁₁	C₃²×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₁	—	91	4	no	—
31	C₃²×C₇	D₁₄₃	1	1	yes	characteristic, complemented, Hall
32	C₃×D₇	—	143	4	no	—
33	C₃×C₁₃	C₃×D₇₇	1	4	yes	complemented
34	C₃×C₁₁	C₃×D₉₁	1	4	yes	complemented
35	D₁₃	—	77	1	no	Hall
36	D₁₁	—	91	1	no	Hall
37	C₃×C₇	C₃×D₁₄₃	1	4	yes	complemented
38	C₂×C₃²	—	1001	1	no	Hall
39	D₇	—	143	1	no	Hall
40	C₁₃	C₃²×D₇₇	1	1	yes	characteristic, complemented, Sylow
41	C₁₁	C₃²×D₉₁	1	1	yes	characteristic, complemented, Sylow
42	C₃²	D₁₀₀₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₃²×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	1001	4	no	—
45	C₃	C₃×D₁₀₀₁	1	4	yes	direct product factor
46	C₂	—	1001	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₀₀₁
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₃×D₁₀₀₁	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
5. D₁₀₀₁	C₃²	direct (N × H)
8. C₃²×C₁₁×C₁₃	D₇	semidirect
9. C₇×C₁₁×C₁₃	C₂×C₃²	semidirect
11. C₃²×C₇×C₁₃	D₁₁	semidirect
12. C₃²×C₇×C₁₁	D₁₃	semidirect
15. C₃×C₁₁×C₁₃	C₃×D₇	semidirect
17. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
19. C₃×C₇×C₁₁	C₃×D₁₃	semidirect
23. C₁₁×C₁₃	C₃²×D₇	semidirect
25. C₃²×C₁₃	D₇₇	semidirect
26. C₃²×C₁₁	D₉₁	semidirect
27. C₇×C₁₃	C₃²×D₁₁	semidirect
29. C₇×C₁₁	C₃²×D₁₃	semidirect
31. C₃²×C₇	D₁₄₃	semidirect
33. C₃×C₁₃	C₃×D₇₇	semidirect
34. C₃×C₁₁	C₃×D₉₁	semidirect
37. C₃×C₇	C₃×D₁₄₃	semidirect
40. C₁₃	C₃²×D₇₇	semidirect
41. C₁₁	C₃²×D₉₁	semidirect
42. C₃²	D₁₀₀₁	direct (N × H)
43. C₇	C₃²×D₁₄₃	semidirect
45. C₃	C₃×D₁₀₀₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₃	2
C₃×D₁₀₀₁	3
C₃²×D₁₄₃	7
C₃²×D₉₁	11
C₃²×D₇₇	13

Subgroups — C32×D1001 #31825093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₁₀₀₁ #31825093