Finite Group Databasebeta

← C₂×#31772447 #46829482

Subgroups — C₂×#31772447 #46829482

Order 34602.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772447	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇₃×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇₉⋊C₃	—	73	1	no	maximal, Hall
5	C₂×C₇₃⋊C₃	—	79	1	no	maximal, Hall
6	C₇₉⋊C₃	—	73	1	no	Hall
7	C₇₃⋊C₃	—	79	1	no	Hall
8	C₂×C₇₉	C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇₃	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₇₉	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
11	C₇₃	C₂×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	5767	1	no	Hall
13	C₃	—	5767	1	no	Sylow
14	C₂	#31772447	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	#31772447
commutator, cosocle, hypocenter	C₇₃×C₇₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇₃×C₇₉	C₃
LCS	G ▷ C₇₃×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #31772447	C₂	direct (N × H)
2. C₂×C₇₃×C₇₉	C₃	semidirect
3. C₇₃×C₇₉	C₂×C₃	semidirect
8. C₂×C₇₉	C₇₃⋊C₃	semidirect
9. C₂×C₇₃	C₇₉⋊C₃	semidirect
10. C₇₉	C₂×C₇₃⋊C₃	semidirect
11. C₇₃	C₂×C₇₉⋊C₃	semidirect
14. C₂	#31772447	direct (N × H)

Maximal subgroups

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

subgroup	index
#31772447	2
C₂×C₇₃×C₇₉	3
C₂×C₇₉⋊C₃	73
C₂×C₇₃⋊C₃	79