Subgroups — #37566521

Order 24318.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131548	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇×C₁₉₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₉₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₉₃⋊C₉	—	7	1	no	maximal, Hall
5	D₇×C₁₉₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉₃⋊C₉	—	7	1	no	Hall
7	C₇×C₁₉₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₉₃	—	21	1	no	—
9	C₃×C₁₉₃	AGL(1,𝔽₇)	1	1	yes	characteristic
10	C₂×C₁₉₃	—	21	1	no	Hall
11	C₁₉₃	D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
12	D₇⋊C₉	—	193	1	no	maximal, Hall
13	C₇⋊C₉	—	193	1	no	Hall
14	C₃×D₇	C₁₉₃⋊C₃	1	1	yes	characteristic
15	C₃×C₇	C₂×C₁₉₃⋊C₃	1	1	yes	characteristic
16	C₂×C₉	—	1351	1	no	Hall
17	D₇	C₁₉₃⋊C₉	1	1	yes	characteristic, complemented, Hall
18	C₉	—	1351	1	no	Sylow
19	C₇	C₂×C₁₉₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	1	no	—
21	C₃	#22549231	1	1	yes	characteristic
22	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#22549231
commutator, hypocenter	C₇×C₁₉₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₉₃	C₂×C₃
prime radical	C₃×D₇×C₁₉₃	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.