Subgroups — D₉₄₇₇ #72214739

Order 18954.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁₅₉	—	3	1	no	maximal
2	D₁₀₅₃	—	9	1	no	—
3	C₁₃×C₇₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₂₄₃	D₃	1	1	yes	characteristic
5	D₇₂₉	—	13	1	no	maximal, Hall
6	C₁₃×C₈₁	D₉	1	1	yes	characteristic
7	C₇₂₉	D₁₃	1	1	yes	characteristic, complemented, Sylow
8	D₃₅₁	—	27	1	no	—
9	D₂₄₃	—	39	1	no	—
10	C₁₃×C₂₇	D₂₇	1	1	yes	characteristic
11	C₂₄₃	D₃₉	1	1	yes	characteristic
12	D₁₁₇	—	81	1	no	—
13	D₈₁	—	117	1	no	—
14	C₉×C₁₃	D₈₁	1	1	yes	characteristic
15	C₈₁	D₁₁₇	1	1	yes	characteristic
16	D₃₉	—	243	1	no	—
17	D₂₇	—	351	1	no	—
18	C₃×C₁₃	D₂₄₃	1	1	yes	characteristic
19	C₂₇	D₃₅₁	1	1	yes	characteristic
20	D₁₃	—	729	1	no	Hall
21	D₉	—	1053	1	no	—
22	C₁₃	D₇₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₉	D₁₀₅₃	1	1	yes	characteristic
24	D₃	—	3159	1	no	—
25	C₃	D₃₁₅₉	1	1	yes	characteristic
26	C₂	—	9477	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃×C₇₂₉	C₂
Frattini	C₂₄₃	D₃₉
socle	C₃×C₁₃	D₂₄₃
LCS	G ▷ C₁₃×C₇₂₉
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.