Subgroups — C₁₇×#10624538 #27136702

Order 12393.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#6880	C₃	1	2	yes	maximal, complemented
2	C₁₇×#6879	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₇×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#733	—	3	2	no	—
5	C₁₇×#732	—	3	1	no	—
6	C₃×C₁₇×C₂₇	—	3	1	no	—
7	C₉²×C₁₇	C₃²	1	1	yes	characteristic
8	#10624538	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₁₇×3₋¹⁺²	—	9	2	no	—
10	C₁₇×H(3,𝔽₃)	—	9	1	no	—
11	C₃×C₉×C₁₇	—	3	1	no	—
12	C₃×C₉×C₁₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₁₇×C₂₇	—	3	3	no	—
14	#6880	C₃×C₁₇	1	2	yes	complemented
15	#6879	C₃×C₁₇	1	1	yes	characteristic
16	C₉×C₂₇	C₃×C₁₇	1	1	yes	characteristic, complemented
17	C₃²×C₁₇	—	27	1	no	—
18	C₃²×C₁₇	#732	1	1	yes	characteristic
19	C₉×C₁₇	—	3	3	no	—
20	C₉×C₁₇	—	3	1	no	—
21	C₉×C₁₇	—	27	2	no	—
22	#733	—	3	2	no	—
23	#732	—	3	1	no	—
24	C₃×C₂₇	—	3	1	no	—
25	C₉²	C₃²×C₁₇	1	1	yes	characteristic
26	C₃×C₁₇	—	3	1	no	—
27	C₃×C₁₇	—	81	1	no	—
28	C₃×C₁₇	#6879	1	1	yes	characteristic
29	3₋¹⁺²	—	9	2	no	—
30	H(3,𝔽₃)	—	9	1	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	C₁₇×H(3,𝔽₃)	1	1	yes	characteristic
33	C₂₇	—	3	3	no	—
34	C₁₇	#10624538	1	1	yes	characteristic, direct product factor, Sylow
35	C₃²	—	27	1	no	—
36	C₃²	C₁₇×#732	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	3	1	no	—
39	C₉	—	27	2	no	—
40	C₃	—	3	1	no	—
41	C₃	—	81	1	no	—
42	C₃	C₁₇×#6879	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₇	#6879
commutator, Frattini, cosocle	C₉²	C₃²×C₁₇
prime radical	C₁₇×#6879	C₃
LCS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₇ ◁ C₃²×C₁₇ ◁ C₃×C₉×C₁₇ ◁ C₉²×C₁₇ ◁ G

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.