Subgroups — C₃⋊#22552248 #38735786

Order 24966.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16861932	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#22552248	—	3	1	no	maximal
3	C₇₃×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#16861932	—	2	1	no	—
6	#16861932	D₃	1	1	yes	characteristic, complemented
7	D₁₉×C₇₃	—	3	1	no	Hall
8	C₁₉×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	D₃×C₇₃⋊C₃	—	19	1	no	maximal, Hall
10	C₃×C₇₃⋊C₃	—	19	1	no	Hall
11	D₃×C₇₃	—	19	1	no	—
12	C₂×C₇₃⋊C₃	—	57	1	no	—
13	C₃⋊(D₁₉⋊C₃)	—	73	1	no	maximal, Hall
14	C₃×C₇₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
15	C₇₃⋊C₃	—	19	1	no	—
16	C₇₃⋊C₃	—	38	1	no	—
17	C₃×C₁₉⋊C₃	—	73	1	no	Hall
18	C₂×C₇₃	—	57	1	no	Hall
19	D₅₇	C₇₃⋊C₃	1	1	yes	characteristic, complemented
20	D₁₉⋊C₃	—	219	1	no	—
21	C₇₃	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₉	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented
23	C₁₉⋊C₃	—	73	1	no	—
24	C₁₉⋊C₃	—	146	1	no	—
25	D₁₉	—	3	1	no	Hall
26	C₁₉	D₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1387	1	no	Hall
28	C₃²	—	1387	1	no	Sylow
29	C₂×C₃	—	4161	1	no	—
30	D₃	—	19	1	no	—
31	C₃	—	1387	1	no	—
32	C₃	—	2774	1	no	—
33	C₃	#22552248	1	1	yes	characteristic, complemented
34	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₁₉×C₇₃
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.