Finite Group Databasebeta

← C₂×C₆₇×D₈₉ #37558749

Subgroups — C₂×C₆₇×D₈₉ #37558749

Order 23852.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×D₈₉	C₂	1	2	yes	maximal, direct product factor
3	C₆₇×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₈₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₆₇	—	89	1	no	maximal, Hall
6	C₂×C₈₉	C₂×C₆₇	1	1	yes	characteristic, complemented
7	D₈₉	C₂×C₆₇	1	2	yes	direct product factor
8	C₂×C₆₇	—	89	2	no	—
9	C₂×C₆₇	D₈₉	1	1	yes	characteristic, direct product factor
10	C₈₉	C₂²×C₆₇	1	1	yes	characteristic, complemented, Sylow
11	C₆₇	C₂×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²	—	89	1	no	Sylow
13	C₂	—	89	2	no	—
14	C₂	C₆₇×D₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₆₇	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂²×C₆₇
Frattini	C₁	G
Fitting, socle	C₂×C₆₇×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₇×C₈₉	C₂	semidirect
2. C₆₇×D₈₉	C₂	direct (N × H)
3. C₆₇×C₈₉	C₂²	semidirect
4. C₂×D₈₉	C₆₇	direct (N × H)
6. C₂×C₈₉	C₂×C₆₇	semidirect
7. D₈₉	C₂×C₆₇	direct (N × H)
9. C₂×C₆₇	D₈₉	direct (N × H)
10. C₈₉	C₂²×C₆₇	semidirect
11. C₆₇	C₂×D₈₉	direct (N × H)
14. C₂	C₆₇×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₇×C₈₉	2
C₆₇×D₈₉	2
C₂×D₈₉	67
C₂²×C₆₇	89