Subgroups — C₃⋊#22549231 #37566549

Order 24318.

36 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	#22549231	—	3	1	no	maximal
3	D₂₁×C₁₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₉₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#16860996	—	2	1	no	—
6	#16860996	D₃	1	1	yes	characteristic, complemented
7	D₃×C₁₉₃⋊C₃	—	7	1	no	maximal, Hall
8	D₇×C₁₉₃	—	3	1	no	Hall
9	C₃×C₁₉₃⋊C₃	—	7	1	no	Hall
10	C₇×C₁₉₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₉₃	—	7	1	no	—
12	C₂×C₁₉₃⋊C₃	—	21	1	no	—
13	C₃×C₁₉₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
14	C₁₉₃⋊C₃	—	7	1	no	—
15	C₁₉₃⋊C₃	—	14	1	no	—
16	C₂×C₁₉₃	—	21	1	no	Hall
17	C₁₉₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊AGL(1,𝔽₇)	—	193	1	no	maximal, Hall
19	C₃×ΓL(1,𝔽₈)	—	193	1	no	Hall
20	D₂₁	C₁₉₃⋊C₃	1	1	yes	characteristic, complemented
21	AGL(1,𝔽₇)	—	579	1	no	—
22	C₃×C₇	C₂×C₁₉₃⋊C₃	1	1	yes	characteristic, complemented
23	ΓL(1,𝔽₈)	—	386	1	no	—
24	ΓL(1,𝔽₈)	—	193	1	no	—
25	C₃×D₃	—	1351	1	no	Hall
26	D₇	—	3	1	no	Hall
27	C₃²	—	1351	1	no	Sylow
28	C₇	D₃×C₁₉₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	4053	1	no	—
30	D₃	—	7	1	no	—
31	C₃	—	1351	1	no	—
32	C₃	—	2702	1	no	—
33	C₃	#22549231	1	1	yes	characteristic, complemented
34	C₂	—	21	1	no	Sylow

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