Subgroups — C₃×C₁₁²×D₂₁ #29503907

Order 15246.

252 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	C₁₁²×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁²×D₇	—	3	1	no	maximal
4	C₃×C₇×C₁₁²	—	2	1	no	—
5	C₃×C₇×C₁₁²	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₃×C₁₁²	—	7	1	no	maximal, Hall
8	C₁₁²×D₇	—	3	1	no	Hall
9	C₃×C₁₁×D₂₁	C₁₁	1	12	yes	maximal, direct product factor
10	C₃²×C₁₁²	D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₁²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₁²	—	21	1	no	—
13	D₃×C₁₁²	—	7	1	no	—
14	C₃²×C₇×C₁₁	C₂×C₁₁	1	12	yes	complemented
15	C₁₁×D₂₁	C₃×C₁₁	1	12	yes	direct product factor
16	C₃×C₁₁×D₇	—	3	12	no	—
17	C₃×C₁₁²	—	2	1	no	—
18	C₃×C₁₁²	C₃×D₇	1	1	yes	characteristic, complemented
19	C₃×C₁₁²	D₂₁	1	1	yes	characteristic, direct product factor
20	C₂×C₁₁²	—	21	1	no	Hall
21	C₃×C₇×C₁₁	—	2	12	no	—
22	C₃×C₇×C₁₁	D₃×C₁₁	1	12	yes	complemented
23	C₃×C₇×C₁₁	C₂×C₃×C₁₁	1	12	yes	complemented
24	C₃×D₃×C₁₁	—	7	12	no	—
25	C₁₁×D₇	—	3	12	no	—
26	C₃×D₂₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
27	C₁₁²	C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₃²×C₁₁	C₁₁×D₇	1	12	yes	complemented
29	C₇×C₁₁	C₃×D₃×C₁₁	1	12	yes	complemented
30	C₂×C₃×C₁₁	—	21	12	no	—
31	D₃×C₁₁	—	7	12	no	—
32	C₃²×C₇	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
33	D₂₁	C₃×C₁₁²	1	1	yes	characteristic, direct product factor
34	C₃×D₇	—	3	1	no	—
35	C₃×C₁₁	—	2	12	no	—
36	C₃×C₁₁	C₃×C₁₁×D₇	1	12	yes	complemented
37	C₃×C₁₁	C₁₁×D₂₁	1	12	yes	direct product factor
38	C₂×C₁₁	—	21	12	no	—
39	C₃×C₇	—	2	1	no	—
40	C₃×C₇	D₃×C₁₁²	1	1	yes	characteristic, complemented
41	C₃×C₇	C₂×C₃×C₁₁²	1	1	yes	characteristic, complemented
42	C₃×D₃	—	7	1	no	Hall
43	D₇	—	3	1	no	Hall
44	C₁₁	C₃×C₁₁×D₂₁	1	12	yes	direct product factor
45	C₃²	C₁₁²×D₇	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×D₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	21	1	no	—
48	D₃	—	7	1	no	—
49	C₃	—	2	1	no	—
50	C₃	C₃×C₁₁²×D₇	1	1	yes	characteristic, complemented
51	C₃	C₁₁²×D₂₁	1	1	yes	characteristic, direct product factor
52	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁²	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁²	C₂	semidirect
2. C₁₁²×D₂₁	C₃	direct (N × H)
5. C₃×C₇×C₁₁²	D₃	semidirect
6. C₃×C₇×C₁₁²	C₂×C₃	semidirect
9. C₃×C₁₁×D₂₁	C₁₁	direct (N × H)
10. C₃²×C₁₁²	D₇	semidirect
11. C₇×C₁₁²	C₃×D₃	semidirect
14. C₃²×C₇×C₁₁	C₂×C₁₁	semidirect
15. C₁₁×D₂₁	C₃×C₁₁	direct (N × H)
18. C₃×C₁₁²	C₃×D₇	semidirect
19. C₃×C₁₁²	D₂₁	direct (N × H)
22. C₃×C₇×C₁₁	D₃×C₁₁	semidirect
23. C₃×C₇×C₁₁	C₂×C₃×C₁₁	semidirect
26. C₃×D₂₁	C₁₁²	direct (N × H)
27. C₁₁²	C₃×D₂₁	direct (N × H)
28. C₃²×C₁₁	C₁₁×D₇	semidirect
29. C₇×C₁₁	C₃×D₃×C₁₁	semidirect
32. C₃²×C₇	C₂×C₁₁²	semidirect
33. D₂₁	C₃×C₁₁²	direct (N × H)
36. C₃×C₁₁	C₃×C₁₁×D₇	semidirect
37. C₃×C₁₁	C₁₁×D₂₁	direct (N × H)
40. C₃×C₇	D₃×C₁₁²	semidirect
41. C₃×C₇	C₂×C₃×C₁₁²	semidirect
44. C₁₁	C₃×C₁₁×D₂₁	direct (N × H)
45. C₃²	C₁₁²×D₇	semidirect
46. C₇	C₃×D₃×C₁₁²	semidirect
50. C₃	C₃×C₁₁²×D₇	semidirect
51. C₃	C₁₁²×D₂₁	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×C₁₁²	2
C₁₁²×D₂₁	3
C₃×C₁₁²×D₇	3
C₃×D₃×C₁₁²	7
C₃×C₁₁×D₂₁	11

Subgroups — C3×C112×D21 #29503907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁²×D₂₁ #29503907