Subgroups — D₁₁₉₉₇ #37562004

Order 23994.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₉₉₉	—	3	1	no	maximal
3	C₃×C₃₁×C₄₃	D₃	1	1	yes	characteristic
4	D₁₃₃₃	—	9	1	no	Hall
5	C₃₁×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
6	D₃₈₇	—	31	1	no	maximal, Hall
7	D₂₇₉	—	43	1	no	maximal, Hall
8	C₉×C₄₃	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₉×C₃₁	D₄₃	1	1	yes	characteristic, complemented, Hall
10	D₁₂₉	—	93	1	no	—
11	D₉₃	—	129	1	no	—
12	C₃×C₄₃	D₉₃	1	1	yes	characteristic
13	C₃×C₃₁	D₁₂₉	1	1	yes	characteristic
14	D₄₃	—	279	1	no	Hall
15	D₃₁	—	387	1	no	Hall
16	C₄₃	D₂₇₉	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	D₃₈₇	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	1333	1	no	Hall
19	C₉	D₁₃₃₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3999	1	no	—
21	C₃	D₃₉₉₉	1	1	yes	characteristic
22	C₂	—	11997	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₃₁×C₄₃	C₂
Frattini	C₃	D₃₉₉₉
socle	C₃×C₃₁×C₄₃	D₃
LCS	G ▷ C₉×C₃₁×C₄₃
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.