Subgroups — D₃₃×#92788 #45689603

Order 33462.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×#92788	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃²×D₃₃	C₃	1	1	yes	maximal, characteristic, complemented
3	D₁₁×#92788	—	3	1	no	maximal
4	C₁₁×#92788	—	2	1	no	—
5	C₁₁×#92788	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×#92788	—	11	1	no	maximal, Hall
9	C₁₃⋊C₃×D₃₃	—	13	14	no	maximal
10	C₁₁×C₁₃²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×#92788	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃⋊C₃	—	13	14	no	—
13	D₃×C₁₃²	—	11	1	no	—
14	C₂×#92788	—	33	1	no	—
15	C₁₃×D₃₃	C₁₃⋊C₃	1	14	yes	complemented
16	D₁₁×C₁₃⋊C₃	—	39	14	no	—
17	C₃×C₁₃²	C₃×D₁₁	1	1	yes	characteristic, complemented
18	#92788	—	2	1	no	—
19	#92788	D₃₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	1	14	yes	complemented
21	C₁₁×C₁₃⋊C₃	—	13	14	no	—
22	C₁₁×C₁₃⋊C₃	—	26	14	no	—
23	C₂×C₁₃²	—	33	1	no	Hall
24	C₁₃×D₁₁	—	3	14	no	—
25	D₃×C₁₃⋊C₃	—	143	14	no	—
26	C₃×D₃₃	—	169	1	no	Hall
27	C₁₃²	C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
28	C₁₁×C₁₃	D₃×C₁₃⋊C₃	1	14	yes	complemented
29	C₃×C₁₃⋊C₃	—	13	14	no	—
30	C₃²×C₁₁	—	169	1	no	Hall
31	D₃×C₁₃	—	11	14	no	—
32	C₂×C₁₃⋊C₃	—	429	14	no	—
33	D₃₃	#92788	1	1	yes	characteristic, direct product factor
34	C₃×D₁₁	—	507	1	no	—
35	C₃×C₁₃	D₁₁×C₁₃⋊C₃	1	14	yes	complemented
36	C₁₃⋊C₃	—	13	14	no	—
37	C₁₃⋊C₃	—	26	14	no	—
38	C₃×C₁₁	—	338	1	no	—
39	C₃×C₁₁	—	169	1	no	—
40	C₃×C₁₁	C₂×#92788	1	1	yes	characteristic, complemented
41	C₂×C₁₃	—	33	14	no	—
42	D₁₁	—	3	1	no	Hall
43	C₃×D₃	—	1859	1	no	Hall
44	C₁₃	C₁₃⋊C₃×D₃₃	1	14	yes	complemented
45	C₁₁	D₃×#92788	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	169	1	no	Sylow
47	C₂×C₃	—	5577	1	no	—
48	D₃	—	11	1	no	—
49	C₃	—	338	1	no	—
50	C₃	—	169	1	no	—
51	C₃	D₁₁×#92788	1	1	yes	characteristic, complemented
52	C₂	—	33	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×#92788	C₂	semidirect
2. C₁₃²×D₃₃	C₃	semidirect
5. C₁₁×#92788	D₃	semidirect
6. C₃×C₁₁×C₁₃²	C₂×C₃	semidirect
10. C₁₁×C₁₃²	C₃×D₃	semidirect
11. C₃×#92788	D₁₁	semidirect
15. C₁₃×D₃₃	C₁₃⋊C₃	semidirect
17. C₃×C₁₃²	C₃×D₁₁	semidirect
19. #92788	D₃₃	direct (N × H)
20. C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	semidirect
27. C₁₃²	C₃×D₃₃	semidirect
28. C₁₁×C₁₃	D₃×C₁₃⋊C₃	semidirect
33. D₃₃	#92788	direct (N × H)
35. C₃×C₁₃	D₁₁×C₁₃⋊C₃	semidirect
40. C₃×C₁₁	C₂×#92788	semidirect
44. C₁₃	C₁₃⋊C₃×D₃₃	semidirect
45. C₁₁	D₃×#92788	semidirect
51. C₃	D₁₁×#92788	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁×#92788	2
C₁₃²×D₃₃	3
D₁₁×#92788	3
D₃×#92788	11
C₁₃⋊C₃×D₃₃	13

Subgroups — D33×#92788 #45689603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃×#92788 #45689603