Subgroups — C₃⋊(C₃⋊#16814857) #45685897

Order 33300.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16814857	—	3	4	no	maximal
3	C₃²×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#10625194)	—	5	1	no	maximal
5	C₃×C₂₅×D₃₇	D₃	1	4	yes	—
6	#16814857	—	9	1	no	Hall
7	C₃²×C₅×D₃₇	D₅	1	1	yes	characteristic
8	C₃×C₂₅×C₃₇	Dic₃	1	4	yes	complemented
9	C₃⋊#10625194	—	15	4	no	—
10	C₂₅×D₃₇	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₃₇	Dic₅	1	1	yes	characteristic
12	C₃⋊(C₃⋊#3866)	—	25	1	no	Hall
13	C₃×C₅×D₃₇	D₁₅	1	4	yes	—
14	C₂₅×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊Dic₇₅	—	37	1	no	maximal, Hall
16	#10625194	—	45	1	no	—
17	C₃²×D₃₇	D₂₅	1	1	yes	characteristic
18	C₃×C₅×C₃₇	Dic₁₅	1	4	yes	—
19	C₂×C₃²×C₂₅	—	37	1	no	—
20	C₃⋊#3866	—	75	4	no	—
21	C₅×D₃₇	C₃⋊D₁₅	1	1	yes	characteristic
22	C₃²×C₃₇	Dic₂₅	1	1	yes	characteristic, complemented, Hall
23	Dic₇₅	—	111	4	no	—
24	C₃²×C₂₅	#3866	1	1	yes	characteristic, complemented, Hall
25	C₃×D₃₇	D₇₅	1	4	yes	—
26	C₅×C₃₇	C₃⋊Dic₁₅	1	1	yes	characteristic
27	C₃⋊Dic₁₅	—	185	1	no	—
28	C₂×C₃×C₂₅	—	37	4	no	—
29	#3866	—	225	1	no	Hall
30	C₃×C₃₇	Dic₇₅	1	4	yes	complemented
31	Dic₂₅	—	333	1	no	Hall
32	C₂×C₃²×C₅	—	37	1	no	—
33	C₃×C₂₅	C₃⋊#3866	1	4	yes	complemented
34	D₃₇	C₃⋊D₇₅	1	1	yes	characteristic
35	Dic₁₅	—	555	4	no	—
36	C₂×C₂₅	—	37	1	no	—
37	C₃²×C₅	#10625194	1	1	yes	characteristic
38	C₃₇	C₃⋊Dic₇₅	1	1	yes	characteristic, complemented, Sylow
39	C₃⋊Dic₃	—	925	1	no	Hall
40	C₂×C₃×C₅	—	37	4	no	—
41	C₂₅	C₃⋊(C₃⋊#3866)	1	1	yes	characteristic, complemented, Sylow
42	Dic₅	—	1665	1	no	—
43	C₂×C₃²	—	37	1	no	—
44	C₃×C₅	C₃⋊#10625194	1	4	yes	—
45	Dic₃	—	2775	4	no	—
46	C₂×C₅	—	37	1	no	—
47	C₃²	#16814857	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	37	4	no	—
49	C₅	C₃⋊(C₃⋊#10625194)	1	1	yes	characteristic
50	C₄	—	8325	1	no	Sylow
51	C₃	C₃⋊#16814857	1	4	yes	complemented
52	C₂	—	37	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₅×C₃₇	C₄
Frattini	C₅	C₃⋊(C₃⋊#10625194)
socle	C₃²×C₅×C₃₇	Dic₅
prime radical	C₃²×C₅×D₃₇	D₅
cosocle	C₃²×C₂₅×D₃₇	C₂
LCS	G ▷ C₃²×C₂₅×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₂₅×C₃₇	C₄	semidirect
8. C₃×C₂₅×C₃₇	Dic₃	semidirect
14. C₂₅×C₃₇	C₃⋊Dic₃	semidirect
22. C₃²×C₃₇	Dic₂₅	semidirect
24. C₃²×C₂₅	#3866	semidirect
30. C₃×C₃₇	Dic₇₅	semidirect
33. C₃×C₂₅	C₃⋊#3866	semidirect
38. C₃₇	C₃⋊Dic₇₅	semidirect
41. C₂₅	C₃⋊(C₃⋊#3866)	semidirect
47. C₃²	#16814857	semidirect
51. C₃	C₃⋊#16814857	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂₅×D₃₇	2
C₃⋊#16814857	3
C₃⋊(C₃⋊#10625194)	5
C₃⋊Dic₇₅	37

Subgroups — C3⋊(C3⋊#16814857) #45685897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊#16814857) #45685897