Subgroups — C₃²×Dic₂₄₇ #22580225

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₄₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	4	yes	—
5	Dic₂₄₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₁₉	C₃×C₄	1	4	yes	complemented
7	C₃²×Dic₁₉	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic
9	C₃²×Dic₁₃	—	19	1	no	maximal, Hall
10	C₂×C₃²×C₁₉	D₁₃	1	1	yes	characteristic
11	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃²×C₁₃	D₁₉	1	1	yes	characteristic
13	C₃×Dic₁₉	—	13	4	no	—
14	C₃²×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₁₃	—	19	4	no	—
16	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	C₃×D₁₃	1	4	yes	—
18	C₂×C₃×C₁₃	C₃×D₁₉	1	4	yes	—
19	Dic₁₉	—	13	1	no	Hall
20	C₃×C₁₉	C₃×Dic₁₃	1	4	yes	complemented
21	Dic₁₃	—	19	1	no	Hall
22	C₃×C₁₃	C₃×Dic₁₉	1	4	yes	complemented
23	C₂×C₁₉	C₃²×D₁₃	1	1	yes	characteristic
24	C₃²×C₄	—	247	1	no	Hall
25	C₂×C₁₃	C₃²×D₁₉	1	1	yes	characteristic
26	C₁₉	C₃²×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	D₂₄₇	1	1	yes	characteristic
28	C₁₃	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	247	4	no	—
30	C₃²	Dic₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×D₂₄₇	1	4	yes	—
32	C₄	—	247	1	no	Sylow
33	C₃	C₃×Dic₂₄₇	1	4	yes	direct product factor
34	C₂	C₃²×D₂₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₂₄₇
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₂	C₃²×D₂₄₇
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₂₄₇	C₃	direct (N × H)
3. C₃²×C₁₃×C₁₉	C₄	semidirect
5. Dic₂₄₇	C₃²	direct (N × H)
6. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₃×C₁₉	C₃²×C₄	semidirect
14. C₃²×C₁₉	Dic₁₃	semidirect
16. C₃²×C₁₃	Dic₁₉	semidirect
20. C₃×C₁₉	C₃×Dic₁₃	semidirect
22. C₃×C₁₃	C₃×Dic₁₉	semidirect
26. C₁₉	C₃²×Dic₁₃	semidirect
28. C₁₃	C₃²×Dic₁₉	semidirect
30. C₃²	Dic₂₄₇	direct (N × H)
33. C₃	C₃×Dic₂₄₇	direct (N × H)

Subgroups — C32×Dic247 #22580225

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×Dic₂₄₇ #22580225