Subgroups — #21440991⋊C₃ #37551264

Order 23244.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₃)⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#21440991	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₉₃₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₄₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10597010	—	13	1	no	maximal, Hall
7	C₃×D₁₄₉	—	13	1	no	—
8	#10597010	—	13	1	no	Hall
9	C₃×C₁₄₉	—	52	1	no	Hall
10	D₁₄₉	—	13	1	no	—
11	AGL(1,𝔽₁₃)	—	149	1	no	maximal, Hall
12	C₁₄₉	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
13	D₁₃⋊C₃	—	149	1	no	—
14	#261	—	149	1	no	Hall
15	C₁₃⋊C₃	#10597010	1	1	yes	characteristic, complemented, Hall
16	D₁₃	—	149	1	no	—
17	C₁₃	C₃×#10597010	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1937	1	no	Hall
19	C₂×C₃	—	1937	1	no	—
20	C₄	—	1937	1	no	Sylow
21	C₃	—	52	1	no	Sylow
22	C₂	—	1937	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₄₉	C₃×C₄
prime radical	(C₁₃⋊C₃)⋊D₁₄₉	C₂
cosocle	D₁₉₃₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₄₉
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.