Subgroups — C₉⋊#14523821 #34062882

Order 19188.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅₃₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#14523821	—	3	1	no	maximal
3	C₉×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₃₃	D₃	1	1	yes	characteristic
5	#14523821	—	9	1	no	Hall
6	C₃×C₁₃×C₄₁	Dic₃	1	1	yes	characteristic
7	C₉⋊#4223	—	13	1	no	maximal, Hall
8	D₅₃₃	D₉	1	1	yes	characteristic
9	C₉×D₄₁	—	13	1	no	—
10	C₁₃×C₄₁	Dic₉	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#4223	—	39	1	no	—
12	C₉⋊#261	—	41	1	no	maximal, Hall
13	C₉×C₄₁	#261	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₁	—	13	1	no	—
15	C₉×D₁₃	—	41	1	no	—
16	#4223	—	117	1	no	Hall
17	C₃⋊#261	—	123	1	no	—
18	C₃×C₄₁	C₃⋊#261	1	1	yes	characteristic
19	C₉×C₁₃	#4223	1	1	yes	characteristic, complemented, Hall
20	D₄₁	—	13	1	no	—
21	C₃×D₁₃	—	41	1	no	—
22	#261	—	369	1	no	Hall
23	C₄₁	C₉⋊#261	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₃	C₃⋊#4223	1	1	yes	characteristic
25	Dic₉	—	533	1	no	Hall
26	D₁₃	—	41	1	no	—
27	C₂×C₉	—	533	1	no	—
28	C₁₃	C₉⋊#4223	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	1599	1	no	—
30	C₉	#14523821	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	533	1	no	—
32	C₄	—	4797	1	no	Sylow
33	C₃	C₃⋊#14523821	1	1	yes	characteristic
34	C₂	—	533	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₃×C₄₁	C₄
Frattini	C₃	C₃⋊#14523821
socle	C₃×C₁₃×C₄₁	Dic₃
prime radical	C₃×D₅₃₃	D₃
cosocle	C₉×D₅₃₃	C₂
LCS	G ▷ C₉×C₁₃×C₄₁
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.