Subgroups — #46852257

Order 34788.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22576354	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₂₂₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#22576354	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₂₂₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₂₂₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₂₂₃⋊C₃)⋊C₄	—	13	1	no	maximal, Hall
7	C₂×C₂₂₃⋊C₃	—	13	1	no	—
8	Dic₂₂₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
9	C₂₂₃⋊C₃	—	13	1	no	Hall
10	C₂×C₂₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
11	C₂₂₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₁₃⋊C₃	—	223	1	no	maximal, Hall
13	C₂×C₁₃⋊C₃	—	223	1	no	—
14	C₄×C₁₃	—	223	1	no	Hall
15	C₁₃⋊C₃	—	223	1	no	Hall
16	C₂×C₁₃	D₂₂₃⋊C₃	1	1	yes	characteristic
17	C₁₃	(C₂₂₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2899	1	no	Hall
19	C₂×C₃	—	2899	1	no	—
20	C₄	—	223	1	no	Sylow
21	C₃	—	2899	1	no	Sylow
22	C₂	#31775051	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#31775051
commutator, hypocenter	C₁₃×C₂₂₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃×C₂₂₃	C₂×C₃
prime radical	C₂×#22576354	C₂
LCS	G ▷ C₁₃×C₂₂₃
UCS	C₁ ◁ C₂

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.