Subgroups — C₁₃×C₁₃⋊C₃×D₃₃ #45689599

Order 33462.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₃₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×D₁₁×C₁₃⋊C₃	—	3	1	no	maximal
4	C₁₁×C₁₃×C₁₃⋊C₃	—	2	1	no	—
5	C₁₁×C₁₃×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₁×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃²×D₁₁	—	3	1	no	Hall
8	D₃×C₁₃×C₁₃⋊C₃	—	11	1	no	maximal, Hall
9	C₃×C₁₃×D₃₃	—	13	1	no	maximal
10	C₁₃⋊C₃×D₃₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
11	C₁₁×C₁₃²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₁×C₁₃	—	13	1	no	—
14	C₃×C₁₁×C₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
15	D₃×C₁₃²	—	11	1	no	—
16	C₂×C₁₃×C₁₃⋊C₃	—	33	1	no	—
17	C₁₃×D₃₃	—	3	4	no	—
18	C₁₃×D₃₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
19	C₁₃×D₃₃	C₃×C₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×D₁₁	—	39	1	no	—
21	D₁₁×C₁₃⋊C₃	—	3	1	no	—
22	C₃×C₁₃²	C₃×D₁₁	1	1	yes	characteristic, complemented
23	C₁₃×C₁₃⋊C₃	—	2	1	no	—
24	C₁₃×C₁₃⋊C₃	D₃₃	1	1	yes	characteristic, direct product factor
25	C₃×C₁₁×C₁₃	—	3	4	no	—
26	C₃×C₁₁×C₁₃	—	13	1	no	—
27	C₃×C₁₁×C₁₃	—	26	1	no	—
28	C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
29	C₃×C₁₁×C₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₁₁×C₁₃⋊C₃	—	2	1	no	—
31	C₁₁×C₁₃⋊C₃	D₃×C₁₃	1	1	yes	characteristic, complemented
32	C₂×C₁₃²	—	33	1	no	Hall
33	C₁₃×D₁₁	—	3	1	no	—
34	C₁₃×D₁₁	—	3	1	no	—
35	C₁₃×D₁₁	—	9	4	no	—
36	C₃×D₃×C₁₃	—	143	1	no	—
37	D₃×C₁₃⋊C₃	—	11	1	no	—
38	C₃×D₃₃	—	13	1	no	Hall
39	C₁₃²	C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
40	C₁₁×C₁₃	—	3	4	no	—
41	C₁₁×C₁₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
42	C₁₁×C₁₃	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
43	C₃²×C₁₃	—	13	1	no	—
44	C₃×C₁₃⋊C₃	C₁₃×D₁₁	1	1	yes	characteristic, complemented
45	C₃²×C₁₁	—	13	1	no	Hall
46	C₂×C₃×C₁₃	—	429	1	no	—
47	D₃×C₁₃	—	11	1	no	—
48	D₃×C₁₃	—	11	1	no	—
49	D₃×C₁₃	—	33	4	no	—
50	C₂×C₁₃⋊C₃	—	33	1	no	—
51	D₃₃	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
52	C₃×D₁₁	—	39	1	no	—
53	C₃×C₁₃	—	3	4	no	—
54	C₃×C₁₃	—	13	1	no	—
55	C₃×C₁₃	—	26	1	no	—
56	C₃×C₁₃	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented
58	C₁₃⋊C₃	—	2	1	no	—
59	C₁₃⋊C₃	C₁₃×D₃₃	1	1	yes	characteristic, direct product factor
60	C₃×C₁₁	—	13	1	no	—
61	C₃×C₁₁	—	26	1	no	—
62	C₃×C₁₁	C₂×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
63	C₂×C₁₃	—	33	1	no	—
64	C₂×C₁₃	—	33	1	no	—
65	C₂×C₁₃	—	99	4	no	—
66	D₁₁	—	3	1	no	Hall
67	C₃×D₃	—	143	1	no	Hall
68	C₁₃	—	3	4	no	—
69	C₁₃	C₁₃⋊C₃×D₃₃	1	1	yes	characteristic, direct product factor
70	C₁₃	C₃×C₁₃×D₃₃	1	1	yes	characteristic, complemented
71	C₁₁	D₃×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
72	C₃²	—	13	1	no	Sylow
73	C₂×C₃	—	429	1	no	—
74	D₃	—	11	1	no	—
75	C₃	—	13	1	no	—
76	C₃	—	26	1	no	—
77	C₃	C₁₃×D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
78	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₁₃⋊C₃×D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₃	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃²	C₂×C₃
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₁₃⋊C₃	C₂	semidirect
2. C₁₃²×D₃₃	C₃	semidirect
5. C₁₁×C₁₃×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₁₁×C₁₃²	C₂×C₃	semidirect
10. C₁₃⋊C₃×D₃₃	C₁₃	direct (N × H)
11. C₁₁×C₁₃²	C₃×D₃	semidirect
12. C₃×C₁₃×C₁₃⋊C₃	D₁₁	semidirect
14. C₃×C₁₁×C₁₃⋊C₃	C₂×C₁₃	semidirect
18. C₁₃×D₃₃	C₁₃⋊C₃	direct (N × H)
19. C₁₃×D₃₃	C₃×C₁₃	semidirect
22. C₃×C₁₃²	C₃×D₁₁	semidirect
24. C₁₃×C₁₃⋊C₃	D₃₃	direct (N × H)
28. C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	semidirect
29. C₃×C₁₁×C₁₃	C₂×C₃×C₁₃	semidirect
31. C₁₁×C₁₃⋊C₃	D₃×C₁₃	semidirect
39. C₁₃²	C₃×D₃₃	semidirect
41. C₁₁×C₁₃	D₃×C₁₃⋊C₃	semidirect
42. C₁₁×C₁₃	C₃×D₃×C₁₃	semidirect
44. C₃×C₁₃⋊C₃	C₁₃×D₁₁	semidirect
51. D₃₃	C₁₃×C₁₃⋊C₃	direct (N × H)
56. C₃×C₁₃	D₁₁×C₁₃⋊C₃	semidirect
57. C₃×C₁₃	C₃×C₁₃×D₁₁	semidirect
59. C₁₃⋊C₃	C₁₃×D₃₃	direct (N × H)
62. C₃×C₁₁	C₂×C₁₃×C₁₃⋊C₃	semidirect
69. C₁₃	C₁₃⋊C₃×D₃₃	direct (N × H)
70. C₁₃	C₃×C₁₃×D₃₃	semidirect
71. C₁₁	D₃×C₁₃×C₁₃⋊C₃	semidirect
77. C₃	C₁₃×D₁₁×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×C₁₁×C₁₃×C₁₃⋊C₃	2
C₁₃²×D₃₃	3
C₁₃×D₁₁×C₁₃⋊C₃	3
D₃×C₁₃×C₁₃⋊C₃	11
C₃×C₁₃×D₃₃	13
C₁₃⋊C₃×D₃₃	13

Subgroups — C13×C13⋊C3×D33 #45689599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₃⋊C₃×D₃₃ #45689599