Subgroups — C₂×C₁₇×D₃₂₉ #36375401

Order 22372.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₃₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×D₄₇	—	7	1	no	maximal, Hall
5	C₂×C₁₇×C₄₇	D₇	1	1	yes	characteristic, complemented
6	C₁₇×D₄₇	—	7	2	no	—
7	C₂×D₃₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₄₇	C₂×C₁₇	1	1	yes	characteristic, complemented
10	D₃₂₉	C₂×C₁₇	1	2	yes	direct product factor
11	C₂×D₇×C₁₇	—	47	1	no	maximal, Hall
12	C₇×C₄₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₇	D₄₇	1	1	yes	characteristic, complemented
14	D₇×C₁₇	—	47	2	no	—
15	C₂×D₄₇	—	7	1	no	Hall
16	C₇×C₁₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₇	D₇×C₁₇	1	1	yes	characteristic, complemented
18	D₄₇	—	7	2	no	—
19	C₂²×C₁₇	—	329	1	no	Hall
20	C₄₇	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	—	329	2	no	—
22	C₂×C₁₇	D₃₂₉	1	1	yes	characteristic, direct product factor
23	C₂×D₇	—	47	1	no	Hall
24	C₁₇	C₂×D₃₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	C₁₇×D₄₇	1	1	yes	characteristic, complemented
26	D₇	—	47	2	no	—
27	C₇	C₂×C₁₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	329	1	no	Sylow
29	C₂	—	329	2	no	—
30	C₂	C₁₇×D₃₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₃₂₉
commutator, cosocle, hypocenter	C₇×C₄₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇×C₄₇	C₂
LCS	G ▷ C₇×C₄₇
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₃₂₉	C₂	direct (N × H)
2. C₂×C₇×C₁₇×C₄₇	C₂	semidirect
3. C₇×C₁₇×C₄₇	C₂²	semidirect
5. C₂×C₁₇×C₄₇	D₇	semidirect
7. C₂×D₃₂₉	C₁₇	direct (N × H)
8. C₁₇×C₄₇	C₂×D₇	semidirect
9. C₂×C₇×C₄₇	C₂×C₁₇	semidirect
10. D₃₂₉	C₂×C₁₇	direct (N × H)
12. C₇×C₄₇	C₂²×C₁₇	semidirect
13. C₂×C₇×C₁₇	D₄₇	semidirect
16. C₇×C₁₇	C₂×D₄₇	semidirect
17. C₂×C₄₇	D₇×C₁₇	semidirect
20. C₄₇	C₂×D₇×C₁₇	semidirect
22. C₂×C₁₇	D₃₂₉	direct (N × H)
24. C₁₇	C₂×D₃₂₉	direct (N × H)
25. C₂×C₇	C₁₇×D₄₇	semidirect
27. C₇	C₂×C₁₇×D₄₇	semidirect
30. C₂	C₁₇×D₃₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×D₃₂₉	2
C₂×C₇×C₁₇×C₄₇	2
C₂×C₁₇×D₄₇	7
C₂×D₃₂₉	17
C₂×D₇×C₁₇	47

Subgroups — C2×C17×D329 #36375401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₃₂₉ #36375401