Subgroups — C₇×C₁₇×D₉₃ #36348989

Order 22134.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₃₁	—	3	1	no	maximal, Hall
3	C₇×C₁₇×C₃₁	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₉₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₉₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₃₁	—	3	1	no	Hall
8	D₃×C₇×C₁₇	—	31	1	no	maximal, Hall
9	C₃×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₇×C₃₁	D₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₁	—	3	1	no	Hall
12	C₃×C₇×C₁₇	D₃₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₇	—	93	1	no	Hall
14	C₇×C₃₁	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	D₉₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₇	D₉₃	1	1	yes	characteristic, direct product factor, Hall
17	D₃×C₁₇	—	31	1	no	Hall
18	C₃×C₃₁	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
19	D₃₁	—	3	1	no	Hall
20	C₃×C₁₇	C₇×D₃₁	1	1	yes	characteristic, complemented, Hall
21	D₃×C₇	—	31	1	no	Hall
22	C₂×C₁₇	—	93	1	no	Hall
23	C₃₁	D₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₇×D₃₁	1	1	yes	characteristic, complemented, Hall
25	C₁₇	C₇×D₉₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	—	93	1	no	Hall
27	C₇	C₁₇×D₉₃	1	1	yes	characteristic, direct product factor, Sylow
28	D₃	—	31	1	no	Hall
29	C₃	C₇×C₁₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₉₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₃₁	C₂	semidirect
3. C₇×C₁₇×C₃₁	D₃	semidirect
4. C₁₇×D₉₃	C₇	direct (N × H)
5. C₃×C₁₇×C₃₁	C₂×C₇	semidirect
6. C₇×D₉₃	C₁₇	direct (N × H)
9. C₃×C₇×C₃₁	C₂×C₁₇	semidirect
10. C₁₇×C₃₁	D₃×C₇	semidirect
12. C₃×C₇×C₁₇	D₃₁	semidirect
14. C₇×C₃₁	D₃×C₁₇	semidirect
15. D₉₃	C₇×C₁₇	direct (N × H)
16. C₇×C₁₇	D₉₃	direct (N × H)
18. C₃×C₃₁	C₂×C₇×C₁₇	semidirect
20. C₃×C₁₇	C₇×D₃₁	semidirect
23. C₃₁	D₃×C₇×C₁₇	semidirect
24. C₃×C₇	C₁₇×D₃₁	semidirect
25. C₁₇	C₇×D₉₃	direct (N × H)
27. C₇	C₁₇×D₉₃	direct (N × H)
29. C₃	C₇×C₁₇×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇×C₃₁	2
C₇×C₁₇×D₃₁	3
C₁₇×D₉₃	7
C₇×D₉₃	17
D₃×C₇×C₁₇	31

Subgroups — C7×C17×D93 #36348989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₇×D₉₃ #36348989