Subgroups — Dic₈₄₃₇ #46798147

Order 33748.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₆₇	—	11	1	no	maximal, Hall
4	Dic₆₄₉	—	13	1	no	maximal, Hall
5	C₂×C₁₃×C₅₉	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₅₉	D₁₃	1	1	yes	characteristic
7	C₁₃×C₅₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₅₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
9	Dic₁₄₃	—	59	1	no	maximal, Hall
10	C₂×C₁₁×C₁₃	D₅₉	1	1	yes	characteristic
11	Dic₅₉	—	143	1	no	Hall
12	C₁₁×C₁₃	Dic₅₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₉	D₁₄₃	1	1	yes	characteristic
14	C₅₉	Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₃	—	649	1	no	Hall
16	Dic₁₁	—	767	1	no	Hall
17	C₂×C₁₃	D₆₄₉	1	1	yes	characteristic
18	C₂×C₁₁	D₇₆₇	1	1	yes	characteristic
19	C₁₃	Dic₆₄₉	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₇₆₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8437	1	no	Sylow
22	C₂	D₈₄₃₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₄₃₇
commutator, hypocenter	C₁₁×C₁₃×C₅₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₃×C₅₉	C₂
LCS	G ▷ C₁₁×C₁₃×C₅₉
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.