Subgroups — D₂₆₁₁₇ #72289331

Order 52234.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₃₁	—	7	1	no	maximal
3	D₂₀₀₉	—	13	1	no	maximal, Hall
4	C₇×C₁₃×C₄₁	D₇	1	1	yes	characteristic
5	C₄₁×C₄₉	D₁₃	1	1	yes	characteristic, complemented, Hall
6	D₆₃₇	—	41	1	no	maximal, Hall
7	D₅₃₃	—	49	1	no	Hall
8	C₁₃×C₄₉	D₄₁	1	1	yes	characteristic, complemented, Hall
9	D₂₈₇	—	91	1	no	—
10	C₁₃×C₄₁	D₄₉	1	1	yes	characteristic, complemented, Hall
11	C₇×C₄₁	D₉₁	1	1	yes	characteristic
12	D₉₁	—	287	1	no	—
13	D₄₉	—	533	1	no	Hall
14	C₇×C₁₃	D₂₈₇	1	1	yes	characteristic
15	D₄₁	—	637	1	no	Hall
16	C₄₉	D₅₃₃	1	1	yes	characteristic, complemented, Sylow
17	C₄₁	D₆₃₇	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	—	2009	1	no	Hall
19	D₇	—	3731	1	no	—
20	C₁₃	D₂₀₀₉	1	1	yes	characteristic, complemented, Sylow
21	C₇	D₃₇₃₁	1	1	yes	characteristic
22	C₂	—	26117	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃×C₄₁×C₄₉	C₂
Frattini	C₇	D₃₇₃₁
socle	C₇×C₁₃×C₄₁	D₇
LCS	G ▷ C₁₃×C₄₁×C₄₉
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.