Subgroups — C₃²×Dic₂₁₇ #21462955

Order 7812.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₁₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₃₁	C₂×C₃	1	4	yes	—
5	C₃²×Dic₃₁	—	7	1	no	maximal, Hall
6	Dic₂₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₃₁	C₃×C₄	1	4	yes	complemented
8	C₂×C₃²×C₃₁	D₇	1	1	yes	characteristic
9	C₂×C₇×C₃₁	C₂×C₃²	1	1	yes	characteristic
10	C₃×Dic₃₁	—	7	4	no	—
11	C₃²×C₃₁	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₃²×Dic₇	—	31	1	no	maximal, Hall
13	C₇×C₃₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₃₁	C₃×D₇	1	4	yes	—
15	C₂×C₃²×C₇	D₃₁	1	1	yes	characteristic
16	Dic₃₁	—	7	1	no	Hall
17	C₃×C₃₁	C₃×Dic₇	1	4	yes	complemented
18	C₃×Dic₇	—	31	4	no	—
19	C₃²×C₇	Dic₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	C₃²×D₇	1	1	yes	characteristic
21	C₂×C₃×C₇	C₃×D₃₁	1	4	yes	—
22	C₃²×C₄	—	217	1	no	Hall
23	C₃₁	C₃²×Dic₇	1	1	yes	characteristic, complemented, Sylow
24	Dic₇	—	31	1	no	Hall
25	C₃×C₇	C₃×Dic₃₁	1	4	yes	complemented
26	C₂×C₃²	D₂₁₇	1	1	yes	characteristic
27	C₂×C₇	C₃²×D₃₁	1	1	yes	characteristic
28	C₃×C₄	—	217	4	no	—
29	C₃²	Dic₂₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₃×D₂₁₇	1	4	yes	—
32	C₄	—	217	1	no	Sylow
33	C₃	C₃×Dic₂₁₇	1	4	yes	direct product factor
34	C₂	C₃²×D₂₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₂₁₇
commutator, hypocenter	C₇×C₃₁	C₃²×C₄
Frattini	C₂	C₃²×D₂₁₇
Fitting, socle	C₂×C₃²×C₇×C₃₁	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₂₁₇	C₃	direct (N × H)
3. C₃²×C₇×C₃₁	C₄	semidirect
6. Dic₂₁₇	C₃²	direct (N × H)
7. C₃×C₇×C₃₁	C₃×C₄	semidirect
11. C₃²×C₃₁	Dic₇	semidirect
13. C₇×C₃₁	C₃²×C₄	semidirect
17. C₃×C₃₁	C₃×Dic₇	semidirect
19. C₃²×C₇	Dic₃₁	semidirect
23. C₃₁	C₃²×Dic₇	semidirect
25. C₃×C₇	C₃×Dic₃₁	semidirect
29. C₃²	Dic₂₁₇	direct (N × H)
30. C₇	C₃²×Dic₃₁	semidirect
33. C₃	C₃×Dic₂₁₇	direct (N × H)

Subgroups — C32×Dic217 #21462955

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×Dic₂₁₇ #21462955