Subgroups — C₃×C₇²×D₈₉ #39908607

Order 26166.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₈₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₈₉	C₇	1	8	yes	maximal, direct product factor
5	C₃×C₇×C₈₉	C₂×C₇	1	8	yes	complemented
6	C₇×D₈₉	C₃×C₇	1	8	yes	direct product factor
7	C₇×C₈₉	C₂×C₃×C₇	1	8	yes	complemented
8	C₃×D₈₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇²	—	89	1	no	maximal, Hall
10	C₃×C₈₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
11	D₈₉	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇²	D₈₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇²	—	89	1	no	Hall
14	C₈₉	C₂×C₃×C₇²	1	1	yes	characteristic, complemented, Sylow
15	C₇²	C₃×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₇	—	89	8	no	—
17	C₃×C₇	C₇×D₈₉	1	8	yes	direct product factor
18	C₂×C₇	—	89	8	no	—
19	C₇	C₃×C₇×D₈₉	1	8	yes	direct product factor
20	C₂×C₃	—	89	1	no	Hall
21	C₃	C₇²×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	89	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇²	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂×C₃×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₃×C₇²

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

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