Subgroups — C₁₁×C₁₃⋊C₃×D₂₁ #31825070

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₁₃⋊C₃	—	3	1	no	maximal
3	C₁₁×C₁₃×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₁₃⋊C₃	—	2	1	no	—
5	C₇×C₁₁×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₁×C₁₃⋊C₃	—	7	1	no	maximal, Hall
8	C₁₁×C₁₃×D₇	—	3	1	no	Hall
9	C₁₃⋊C₃×D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₁×D₂₁	—	13	1	no	maximal, Hall
11	C₃×C₁₁×C₁₃⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₁₁×C₁₃	—	7	1	no	—
14	C₂×C₁₁×C₁₃⋊C₃	—	21	1	no	—
15	C₃×C₇×C₁₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₁	—	13	1	no	Hall
17	C₁₃×D₂₁	C₃×C₁₁	1	1	yes	characteristic, complemented
18	D₇×C₁₃⋊C₃	—	3	1	no	—
19	C₁₁×D₂₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₁×D₇	—	39	1	no	—
21	C₃×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
22	C₁₁×C₁₃⋊C₃	—	2	1	no	—
23	C₁₁×C₁₃⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁×C₁₃	—	21	1	no	Hall
25	C₃×C₇×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
26	C₇×C₁₃⋊C₃	—	2	1	no	—
27	C₇×C₁₃⋊C₃	D₃×C₁₁	1	1	yes	characteristic, complemented
28	D₃×C₁₃⋊C₃	—	7	1	no	Hall
29	C₃×C₇×C₁₁	—	13	1	no	—
30	C₃×C₇×C₁₁	—	26	1	no	—
31	C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₃×D₃×C₁₁	—	91	1	no	Hall
33	C₁₃×D₇	—	3	1	no	Hall
34	C₁₁×D₇	—	3	1	no	Hall
35	C₁₁×C₁₃	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
36	C₃×D₂₁	—	13	1	no	Hall
37	C₃×C₁₃⋊C₃	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₁₁	—	13	1	no	Hall
39	C₇×C₁₃	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
40	D₃×C₁₃	—	7	1	no	—
41	C₂×C₁₃⋊C₃	—	21	1	no	—
42	C₇×C₁₁	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₁₁	—	273	1	no	—
44	D₃×C₁₁	—	7	1	no	—
45	C₃²×C₇	—	13	1	no	Hall
46	D₂₁	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
47	C₃×D₇	—	39	1	no	—
48	C₃×C₁₃	C₃×C₁₁×D₇	1	1	yes	characteristic, complemented
49	C₁₃⋊C₃	—	2	1	no	—
50	C₁₃⋊C₃	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor
51	C₃×C₁₁	—	13	1	no	—
52	C₃×C₁₁	—	26	1	no	—
53	C₃×C₁₁	D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₁₃	—	21	1	no	Hall
55	C₂×C₁₁	—	21	1	no	Hall
56	C₃×C₇	—	13	1	no	—
57	C₃×C₇	—	26	1	no	—
58	C₃×C₇	C₂×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
59	C₃×D₃	—	91	1	no	Hall
60	D₇	—	3	1	no	Hall
61	C₁₃	C₃×C₁₁×D₂₁	1	1	yes	characteristic, complemented, Sylow
62	C₁₁	C₁₃⋊C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	—	13	1	no	Sylow
64	C₇	D₃×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	273	1	no	—
66	D₃	—	7	1	no	—
67	C₃	—	13	1	no	—
68	C₃	—	26	1	no	—
69	C₃	C₁₁×D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₁₃⋊C₃×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₁₃⋊C₃	C₂	semidirect
3. C₁₁×C₁₃×D₂₁	C₃	semidirect
5. C₇×C₁₁×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
9. C₁₃⋊C₃×D₂₁	C₁₁	direct (N × H)
11. C₃×C₁₁×C₁₃⋊C₃	D₇	semidirect
12. C₇×C₁₁×C₁₃	C₃×D₃	semidirect
15. C₃×C₇×C₁₃⋊C₃	C₂×C₁₁	semidirect
17. C₁₃×D₂₁	C₃×C₁₁	semidirect
19. C₁₁×D₂₁	C₁₃⋊C₃	direct (N × H)
21. C₃×C₁₁×C₁₃	C₃×D₇	semidirect
23. C₁₁×C₁₃⋊C₃	D₂₁	direct (N × H)
25. C₃×C₇×C₁₃	C₂×C₃×C₁₁	semidirect
27. C₇×C₁₃⋊C₃	D₃×C₁₁	semidirect
31. C₃×C₇×C₁₁	C₂×C₁₃⋊C₃	semidirect
35. C₁₁×C₁₃	C₃×D₂₁	semidirect
37. C₃×C₁₃⋊C₃	C₁₁×D₇	semidirect
39. C₇×C₁₃	C₃×D₃×C₁₁	semidirect
42. C₇×C₁₁	D₃×C₁₃⋊C₃	semidirect
46. D₂₁	C₁₁×C₁₃⋊C₃	direct (N × H)
48. C₃×C₁₃	C₃×C₁₁×D₇	semidirect
50. C₁₃⋊C₃	C₁₁×D₂₁	direct (N × H)
53. C₃×C₁₁	D₇×C₁₃⋊C₃	semidirect
58. C₃×C₇	C₂×C₁₁×C₁₃⋊C₃	semidirect
61. C₁₃	C₃×C₁₁×D₂₁	semidirect
62. C₁₁	C₁₃⋊C₃×D₂₁	direct (N × H)
64. C₇	D₃×C₁₁×C₁₃⋊C₃	semidirect
69. C₃	C₁₁×D₇×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×C₁₃⋊C₃	2
C₁₁×D₇×C₁₃⋊C₃	3
C₁₁×C₁₃×D₂₁	3
D₃×C₁₁×C₁₃⋊C₃	7
C₁₃⋊C₃×D₂₁	11
C₃×C₁₁×D₂₁	13

Subgroups — C11×C13⋊C3×D21 #31825070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃⋊C₃×D₂₁ #31825070