Subgroups — C₃×#22549227 #37566539

Order 24318.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16860996	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#22549227	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₁₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₉₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#16860996	C₂×C₃	1	3	yes	complemented
6	C₃×D₁₉₃⋊C₃	—	7	1	no	maximal, Hall
7	C₇×D₁₉₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉₃⋊C₃	—	7	1	no	Hall
9	C₇×C₁₉₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₉₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	D₁₉₃⋊C₃	—	7	3	no	—
12	C₃×C₁₉₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₁₉₃⋊C₃	—	7	3	no	—
14	D₁₉₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₁₉₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×ΓL(1,𝔽₈)	—	193	1	no	maximal, Hall
17	C₃×ΓL(1,𝔽₈)	—	193	1	no	Hall
18	C₂×C₃×C₇	—	579	1	no	—
19	C₂×ΓL(1,𝔽₈)	—	193	3	no	—
20	C₃×C₇	D₁₉₃⋊C₃	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)	—	193	3	no	—
22	C₂×C₃²	—	1351	1	no	Hall
23	C₂×C₇	—	579	1	no	Hall
24	C₃²	—	1351	1	no	Sylow
25	C₇	C₃×D₁₉₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	579	1	no	—
27	C₂×C₃	—	1351	3	no	—
28	C₃	—	1351	3	no	—
29	C₃	#22549227	1	1	yes	characteristic, direct product factor
30	C₂	—	579	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#22549227
commutator, cosocle, hypocenter	C₇×C₁₉₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉₃	C₂×C₃
LCS	G ▷ C₇×C₁₉₃
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.