Subgroups — C₃×#24924362 #44567166

Order 32193.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24924362	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₇²×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#13095276	—	7	8	no	maximal
4	C₇²×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₇₃	ΓL(1,𝔽₈)	1	8	yes	complemented
6	#13095276	—	7	24	no	—
7	C₃×C₇₃⋊C₃	—	49	1	no	Hall
8	C₇×C₇₃	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
9	C₃×#3861	—	73	1	no	maximal, Hall
10	C₃×C₇₃	#3861	1	1	yes	characteristic, complemented
11	C₇₃⋊C₃	—	49	3	no	—
12	C₃×C₇²	C₇₃⋊C₃	1	1	yes	characteristic, complemented
13	#3861	—	73	3	no	—
14	C₇₃	C₃×#3861	1	1	yes	characteristic, complemented, Sylow
15	C₃×ΓL(1,𝔽₈)	—	511	8	no	—
16	C₇²	C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₇	#13095276	1	8	yes	complemented
18	ΓL(1,𝔽₈)	—	511	24	no	—
19	C₃²	—	3577	1	no	Sylow
20	C₇	C₃×#13095276	1	8	yes	complemented
21	C₃	—	3577	3	no	—
22	C₃	#24924362	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	#24924362
commutator, cosocle, hypocenter	C₇²×C₇₃	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₇₃	C₃
LCS	G ▷ C₇²×C₇₃
UCS	C₁ ◁ C₃

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.