Subgroups — C₃×Dic₂₅₂₇ #44476437

Order 30324.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₃₆₁	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₃₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₃₆₁	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₃₆₁	—	7	1	no	maximal, Hall
6	C₇×C₃₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₃₆₁	D₇	1	1	yes	characteristic
8	C₃×Dic₁₃₃	—	19	1	no	maximal
9	Dic₃₆₁	—	7	1	no	Hall
10	C₃×C₃₆₁	Dic₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₁₉	D₁₉	1	1	yes	characteristic
12	C₂×C₃₆₁	C₃×D₇	1	1	yes	characteristic
13	Dic₁₃₃	—	19	1	no	—
14	C₃×C₇×C₁₉	Dic₁₉	1	1	yes	characteristic
15	C₃₆₁	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic
17	C₃×Dic₁₉	—	133	1	no	—
18	C₇×C₁₉	C₃×Dic₁₉	1	1	yes	characteristic
19	C₂×C₃×C₁₉	D₁₃₃	1	1	yes	characteristic
20	C₃×Dic₇	—	361	1	no	Hall
21	Dic₁₉	—	133	1	no	—
22	C₃×C₁₉	Dic₁₃₃	1	1	yes	characteristic
23	C₂×C₃×C₇	D₃₆₁	1	1	yes	characteristic
24	C₂×C₁₉	C₃×D₁₃₃	1	1	yes	characteristic
25	Dic₇	—	361	1	no	Hall
26	C₃×C₇	Dic₃₆₁	1	1	yes	characteristic, complemented, Hall
27	C₁₉	C₃×Dic₁₃₃	1	1	yes	characteristic
28	C₂×C₇	C₃×D₃₆₁	1	1	yes	characteristic
29	C₃×C₄	—	2527	1	no	Hall
30	C₇	C₃×Dic₃₆₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₅₂₇	1	1	yes	characteristic
32	C₄	—	2527	1	no	Sylow
33	C₃	Dic₂₅₂₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×D₂₅₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₂₇
commutator, hypocenter	C₇×C₃₆₁	C₃×C₄
Frattini	C₂×C₁₉	C₃×D₁₃₃
Fitting	C₂×C₃×C₇×C₃₆₁	C₂
socle, prime radical	C₂×C₃×C₇×C₁₉	D₁₉
cosocle	C₂×C₇×C₃₆₁	C₂×C₃
LCS	G ▷ C₇×C₃₆₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₂₇	C₃	direct (N × H)
3. C₃×C₇×C₃₆₁	C₄	semidirect
6. C₇×C₃₆₁	C₃×C₄	semidirect
10. C₃×C₃₆₁	Dic₇	semidirect
15. C₃₆₁	C₃×Dic₇	semidirect
26. C₃×C₇	Dic₃₆₁	semidirect
30. C₇	C₃×Dic₃₆₁	semidirect
33. C₃	Dic₂₅₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₃₆₁	2
Dic₂₅₂₇	3
C₃×Dic₃₆₁	7
C₃×Dic₁₃₃	19

Subgroups — C3×Dic2527 #44476437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₅₂₇ #44476437