Subgroups — C₃⋊#26044451 #47977331

Order 35322.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19154637	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26044451	—	3	1	no	maximal, Hall
3	#19154637	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉×D₈₇	—	7	1	no	maximal, Hall
5	C₃×C₂₉²	D₇	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₂₉	—	21	1	no	Hall
7	C₂₉²	D₂₁	1	1	yes	characteristic, complemented, Sylow
8	C₃×C₂₉⋊C₇	—	58	1	no	—
9	C₂₉⋊C₇	—	58	1	no	—
10	D₈₇	—	7	1	no	—
11	D₃×C₂₉	—	203	1	no	—
12	C₃×C₂₉	—	2	1	no	—
13	C₃×C₂₉	—	7	1	no	—
14	C₃×C₂₉	—	7	1	no	—
15	C₃×C₂₉	—	14	1	no	—
16	C₂×C₂₉	—	609	1	no	—
17	D₂₉	—	21	1	no	—
18	D₂₁	—	841	1	no	maximal, Hall
19	C₂₉	—	2	1	no	—
20	C₂₉	—	7	1	no	—
21	C₂₉	—	7	1	no	—
22	C₂₉	—	14	1	no	—
23	C₃×C₇	—	841	1	no	Hall
24	D₇	—	2523	1	no	Hall
25	C₇	—	841	1	no	Sylow
26	D₃	—	203	1	no	Hall
27	C₃	#26044451	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	609	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×#19154637	C₂
Fitting, socle	C₃×C₂₉²	D₇
LCS	G ▷ C₃×#19154637
UCS	C₁

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.