Subgroups — D₁₆₁₀₇ #44567266

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₃₆₉	—	3	1	no	maximal, Hall
3	C₇×C₁₃×C₅₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₃₀₁	—	7	1	no	maximal, Hall
5	D₁₂₃₉	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₅₉	D₇	1	1	yes	characteristic, complemented, Hall
7	D₇₆₇	—	21	1	no	Hall
8	C₃×C₇×C₅₉	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₄₁₃	—	39	1	no	Hall
10	C₁₃×C₅₉	D₂₁	1	1	yes	characteristic, complemented, Hall
11	D₂₇₃	—	59	1	no	maximal, Hall
12	C₇×C₅₉	D₃₉	1	1	yes	characteristic, complemented, Hall
13	D₁₇₇	—	91	1	no	Hall
14	C₃×C₇×C₁₃	D₅₉	1	1	yes	characteristic, complemented, Hall
15	D₉₁	—	177	1	no	Hall
16	C₃×C₅₉	D₉₁	1	1	yes	characteristic, complemented, Hall
17	D₅₉	—	273	1	no	Hall
18	C₇×C₁₃	D₁₇₇	1	1	yes	characteristic, complemented, Hall
19	D₃₉	—	413	1	no	Hall
20	C₅₉	D₂₇₃	1	1	yes	characteristic, complemented, Sylow
21	D₂₁	—	767	1	no	Hall
22	C₃×C₁₃	D₄₁₃	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	1239	1	no	Hall
24	C₃×C₇	D₇₆₇	1	1	yes	characteristic, complemented, Hall
25	D₇	—	2301	1	no	Hall
26	C₁₃	D₁₂₃₉	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₂₃₀₁	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	5369	1	no	Hall
29	C₃	D₅₃₆₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	16107	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₅₉	C₂
LCS	G ▷ C₃×C₇×C₁₃×C₅₉
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.