Subgroups — C₇×C₁₁×C₃⋊D₃₃ #29503903

Order 15246.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₁×D₃₃	—	3	4	no	maximal
3	C₃×C₇×C₁₁²	D₃	1	4	yes	complemented
4	C₁₁×C₃⋊D₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₁×D₁₁	—	9	1	no	Hall
6	C₇×C₃⋊D₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
7	C₇×C₁₁×C₃⋊D₃	—	11	1	no	maximal
8	C₃²×C₁₁²	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₃₃	—	3	4	no	—
11	C₃²×C₇×C₁₁	—	2	5	no	—
12	C₃²×C₇×C₁₁	D₁₁	1	1	yes	characteristic, complemented
13	C₃²×C₇×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₇×D₃₃	—	3	4	no	—
15	D₃×C₇×C₁₁	—	33	4	no	—
16	C₃×C₁₁²	D₃×C₇	1	4	yes	complemented
17	C₁₁×D₁₁	—	9	1	no	Hall
18	C₃×C₇×C₁₁	—	2	20	no	—
19	C₃×C₇×C₁₁	D₃×C₁₁	1	4	yes	complemented
20	C₃×C₇×C₁₁	D₃₃	1	4	yes	complemented
21	C₃⋊D₃₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor
22	C₁₁×C₃⋊D₃	—	11	1	no	—
23	C₂×C₇×C₁₁	—	99	1	no	—
24	C₇×D₁₁	—	9	1	no	—
25	C₇×C₃⋊D₃	—	11	1	no	Hall
26	C₁₁²	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
27	C₃²×C₁₁	—	2	5	no	—
28	C₃²×C₁₁	C₇×D₁₁	1	1	yes	characteristic, complemented
29	C₃²×C₁₁	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
30	C₇×C₁₁	—	2	5	no	—
31	C₇×C₁₁	C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented
32	C₇×C₁₁	C₃⋊D₃₃	1	1	yes	characteristic, direct product factor
33	D₃₃	—	3	4	no	—
34	D₃×C₁₁	—	33	4	no	—
35	C₃²×C₇	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
36	D₃×C₇	—	33	4	no	—
37	C₃×C₁₁	—	2	20	no	—
38	C₃×C₁₁	D₃×C₇×C₁₁	1	4	yes	complemented
39	C₃×C₁₁	C₇×D₃₃	1	4	yes	complemented
40	C₂×C₁₁	—	99	1	no	—
41	D₁₁	—	9	1	no	—
42	C₃×C₇	C₁₁×D₃₃	1	4	yes	complemented
43	C₃⋊D₃	—	11	1	no	Hall
44	C₂×C₇	—	99	1	no	Hall
45	C₁₁	—	2	5	no	—
46	C₁₁	C₇×C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented
47	C₁₁	C₇×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor
48	C₃²	C₇×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₇	C₁₁×C₃⋊D₃₃	1	1	yes	characteristic, direct product factor, Sylow
50	D₃	—	33	4	no	—
51	C₃	C₇×C₁₁×D₃₃	1	4	yes	complemented
52	C₂	—	99	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁²	C₂	semidirect
3. C₃×C₇×C₁₁²	D₃	semidirect
4. C₁₁×C₃⋊D₃₃	C₇	direct (N × H)
6. C₇×C₃⋊D₃₃	C₁₁	direct (N × H)
8. C₃²×C₁₁²	C₂×C₇	semidirect
9. C₇×C₁₁²	C₃⋊D₃	semidirect
12. C₃²×C₇×C₁₁	D₁₁	semidirect
13. C₃²×C₇×C₁₁	C₂×C₁₁	semidirect
16. C₃×C₁₁²	D₃×C₇	semidirect
19. C₃×C₇×C₁₁	D₃×C₁₁	semidirect
20. C₃×C₇×C₁₁	D₃₃	semidirect
21. C₃⋊D₃₃	C₇×C₁₁	direct (N × H)
26. C₁₁²	C₇×C₃⋊D₃	semidirect
28. C₃²×C₁₁	C₇×D₁₁	semidirect
29. C₃²×C₁₁	C₂×C₇×C₁₁	semidirect
31. C₇×C₁₁	C₁₁×C₃⋊D₃	semidirect
32. C₇×C₁₁	C₃⋊D₃₃	direct (N × H)
35. C₃²×C₇	C₁₁×D₁₁	semidirect
38. C₃×C₁₁	D₃×C₇×C₁₁	semidirect
39. C₃×C₁₁	C₇×D₃₃	semidirect
42. C₃×C₇	C₁₁×D₃₃	semidirect
46. C₁₁	C₇×C₁₁×C₃⋊D₃	semidirect
47. C₁₁	C₇×C₃⋊D₃₃	direct (N × H)
48. C₃²	C₇×C₁₁×D₁₁	semidirect
49. C₇	C₁₁×C₃⋊D₃₃	direct (N × H)
51. C₃	C₇×C₁₁×D₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁²	2
C₇×C₁₁×D₃₃	3
C₁₁×C₃⋊D₃₃	7
C₇×C₃⋊D₃₃	11
C₇×C₁₁×C₃⋊D₃	11

Subgroups — C7×C11×C3⋊D33 #29503903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×C₃⋊D₃₃ #29503903