Subgroups — C₃×Dic₂₅₉₇ #44528313

Order 31164.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₉×C₅₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄₉×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₉×C₅₃	C₂×C₃	1	1	yes	characteristic
5	C₃×Dic₃₇₁	—	7	1	no	maximal
6	C₄₉×C₅₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₅₃	D₇	1	1	yes	characteristic
8	Dic₃₇₁	—	7	1	no	—
9	C₃×C₇×C₅₃	Dic₇	1	1	yes	characteristic
10	C₂×C₇×C₅₃	C₃×D₇	1	1	yes	characteristic
11	C₃×Dic₅₃	—	49	1	no	Hall
12	C₃×Dic₄₉	—	53	1	no	maximal, Hall
13	C₇×C₅₃	C₃×Dic₇	1	1	yes	characteristic
14	C₂×C₃×C₅₃	D₄₉	1	1	yes	characteristic
15	C₂×C₃×C₄₉	D₅₃	1	1	yes	characteristic
16	Dic₅₃	—	49	1	no	Hall
17	Dic₄₉	—	53	1	no	Hall
18	C₃×C₅₃	Dic₄₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₉	Dic₅₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₃	C₃×D₄₉	1	1	yes	characteristic
21	C₂×C₄₉	C₃×D₅₃	1	1	yes	characteristic
22	C₃×Dic₇	—	371	1	no	—
23	C₅₃	C₃×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
24	C₄₉	C₃×Dic₅₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	D₃₇₁	1	1	yes	characteristic
26	Dic₇	—	371	1	no	—
27	C₃×C₇	Dic₃₇₁	1	1	yes	characteristic
28	C₂×C₇	C₃×D₃₇₁	1	1	yes	characteristic
29	C₃×C₄	—	2597	1	no	Hall
30	C₇	C₃×Dic₃₇₁	1	1	yes	characteristic
31	C₂×C₃	D₂₅₉₇	1	1	yes	characteristic
32	C₄	—	2597	1	no	Sylow
33	C₃	Dic₂₅₉₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×D₂₅₉₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₉₇
commutator, hypocenter	C₄₉×C₅₃	C₃×C₄
Frattini	C₂×C₇	C₃×D₃₇₁
Fitting	C₂×C₃×C₄₉×C₅₃	C₂
socle, prime radical	C₂×C₃×C₇×C₅₃	D₇
cosocle	C₂×C₄₉×C₅₃	C₂×C₃
LCS	G ▷ C₄₉×C₅₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₉₇	C₃	direct (N × H)
3. C₃×C₄₉×C₅₃	C₄	semidirect
6. C₄₉×C₅₃	C₃×C₄	semidirect
18. C₃×C₅₃	Dic₄₉	semidirect
19. C₃×C₄₉	Dic₅₃	semidirect
23. C₅₃	C₃×Dic₄₉	semidirect
24. C₄₉	C₃×Dic₅₃	semidirect
33. C₃	Dic₂₅₉₇	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×C₄₉×C₅₃	2
Dic₂₅₉₇	3
C₃×Dic₃₇₁	7
C₃×Dic₄₉	53

Subgroups — C3×Dic2597 #44528313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₅₉₇ #44528313