Subgroups — C₃×C₇×D₇₆₇ #44567254

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₆₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×D₅₉	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	D₇₆₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₅₉	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅₉	—	13	1	no	Hall
10	C₁₃×C₅₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×D₁₃	—	59	1	no	maximal, Hall
12	C₇×C₅₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅₉	—	13	1	no	Hall
14	C₃×C₇×C₁₃	D₅₉	1	1	yes	characteristic, complemented, Hall
15	C₇×D₁₃	—	59	1	no	Hall
16	C₃×C₅₉	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
17	D₅₉	—	13	1	no	Hall
18	C₇×C₁₃	C₃×D₅₉	1	1	yes	characteristic, complemented, Hall
19	C₃×D₁₃	—	59	1	no	Hall
20	C₅₉	C₃×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₇	—	767	1	no	Hall
22	C₃×C₁₃	C₇×D₅₉	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	59	1	no	Hall
24	C₃×C₇	D₇₆₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	767	1	no	Hall
26	C₁₃	C₃×C₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₇₆₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	767	1	no	Hall
29	C₃	C₇×D₇₆₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	767	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇₆₇
commutator, cosocle, hypocenter	C₁₃×C₅₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₅₉	C₂
LCS	G ▷ C₁₃×C₅₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₅₉	C₂	semidirect
2. C₇×D₇₆₇	C₃	direct (N × H)
3. C₇×C₁₃×C₅₉	C₂×C₃	semidirect
4. C₃×D₇₆₇	C₇	direct (N × H)
6. C₃×C₁₃×C₅₉	C₂×C₇	semidirect
7. D₇₆₇	C₃×C₇	direct (N × H)
8. C₃×C₇×C₅₉	D₁₃	semidirect
10. C₁₃×C₅₉	C₂×C₃×C₇	semidirect
12. C₇×C₅₉	C₃×D₁₃	semidirect
14. C₃×C₇×C₁₃	D₅₉	semidirect
16. C₃×C₅₉	C₇×D₁₃	semidirect
18. C₇×C₁₃	C₃×D₅₉	semidirect
20. C₅₉	C₃×C₇×D₁₃	semidirect
22. C₃×C₁₃	C₇×D₅₉	semidirect
24. C₃×C₇	D₇₆₇	direct (N × H)
26. C₁₃	C₃×C₇×D₅₉	semidirect
27. C₇	C₃×D₇₆₇	direct (N × H)
29. C₃	C₇×D₇₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₅₉	2
C₇×D₇₆₇	3
C₃×D₇₆₇	7
C₃×C₇×D₅₉	13
C₃×C₇×D₁₃	59

Subgroups — C3×C7×D767 #44567254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₇₆₇ #44567254