Subgroups — Dic₇₈₄₃ #44535872

Order 31372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₂₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₃×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₁₃	—	11	1	no	maximal, Hall
4	C₂×C₂₃×C₃₁	D₁₁	1	1	yes	characteristic
5	Dic₃₄₁	—	23	1	no	maximal, Hall
6	Dic₂₅₃	—	31	1	no	maximal, Hall
7	C₂₃×C₃₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₃₁	D₂₃	1	1	yes	characteristic
9	C₂×C₁₁×C₂₃	D₃₁	1	1	yes	characteristic
10	C₁₁×C₃₁	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₂₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
12	Dic₃₁	—	253	1	no	Hall
13	Dic₂₃	—	341	1	no	Hall
14	C₂×C₃₁	D₂₅₃	1	1	yes	characteristic
15	C₂×C₂₃	D₃₄₁	1	1	yes	characteristic
16	Dic₁₁	—	713	1	no	Hall
17	C₃₁	Dic₂₅₃	1	1	yes	characteristic, complemented, Sylow
18	C₂₃	Dic₃₄₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₁	D₇₁₃	1	1	yes	characteristic
20	C₁₁	Dic₇₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	7843	1	no	Sylow
22	C₂	D₇₈₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₄₃
commutator, hypocenter	C₁₁×C₂₃×C₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₂₃×C₃₁	C₂
LCS	G ▷ C₁₁×C₂₃×C₃₁
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.