Subgroups — C₃²×D₆₉ #11927872

Order 1242.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₆₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₂₃	—	3	1	no	maximal
4	C₃²×C₂₃	—	2	4	no	—
5	C₃²×C₂₃	D₃	1	1	yes	characteristic, complemented
6	C₃²×C₂₃	C₂×C₃	1	4	yes	complemented
7	D₆₉	C₃²	1	1	yes	characteristic, direct product factor
8	C₃×D₂₃	—	3	4	no	—
9	C₃×C₂₃	—	2	4	no	—
10	C₃×C₂₃	C₃×D₃	1	4	yes	complemented
11	C₃×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
12	C₃²×D₃	—	23	1	no	maximal, Hall
13	D₂₃	—	3	1	no	Hall
14	C₃³	D₂₃	1	1	yes	characteristic, complemented, Sylow
15	C₂₃	C₃²×D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃²	—	69	1	no	—
17	C₃×D₃	—	23	4	no	—
18	C₃²	—	2	4	no	—
19	C₃²	C₃×D₂₃	1	4	yes	complemented
20	C₃²	D₆₉	1	1	yes	characteristic, direct product factor
21	C₂×C₃	—	69	4	no	—
22	D₃	—	23	1	no	—
23	C₃	—	2	4	no	—
24	C₃	C₃²×D₂₃	1	1	yes	characteristic, complemented
25	C₃	C₃×D₆₉	1	4	yes	direct product factor
26	C₂	—	69	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₆₉
commutator, cosocle, hypocenter	C₃×C₂₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₂₃	C₂
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₃²

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.