Subgroups — C₁₇×#10624479 #27136643

Order 12393.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×#733	C₃	1	2	yes	maximal
2	C₁₇×#6867	C₃	1	2	yes	maximal
3	C₃×C₁₇×3₋¹⁺²	—	3	2	no	—
4	C₃²×C₉×C₁₇	C₃²	1	1	yes	characteristic
5	C₁₇×#733	—	3	6	no	—
6	C₁₇×C₃²⋊C₉	—	3	2	no	—
7	#10624479	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₁₇×3₋¹⁺²	—	3	6	no	—
10	C₁₇×3₋¹⁺²	—	9	4	no	—
11	C₃×C₉×C₁₇	—	3	2	no	—
12	C₃×C₉×C₁₇	—	3	2	no	—
13	C₃×C₉×C₁₇	—	9	2	no	—
14	C₃×C₉×C₁₇	—	9	2	no	—
15	C₃×#733	C₃×C₁₇	1	2	yes	—
16	#6867	C₃×C₁₇	1	2	yes	—
17	C₃²×C₁₇	—	9	1	no	—
18	C₃²×C₁₇	AΣL(1,𝔽₂₇)	1	2	yes	—
19	C₃²×C₁₇	#732	1	2	yes	—
20	C₉×C₁₇	—	9	1	no	—
21	C₉×C₁₇	—	9	6	no	—
22	C₉×C₁₇	—	27	2	no	—
23	C₃×3₋¹⁺²	—	3	2	no	—
24	C₃²×C₉	C₃²×C₁₇	1	1	yes	characteristic
25	#733	—	3	6	no	—
26	C₃²⋊C₉	—	3	2	no	—
27	C₃×C₁₇	—	3	2	no	—
28	C₃×C₁₇	—	3	2	no	—
29	C₃×C₁₇	#6856	1	1	yes	characteristic
30	C₃³	C₁₇×H(3,𝔽₃)	1	1	yes	characteristic
31	3₋¹⁺²	—	3	6	no	—
32	3₋¹⁺²	—	9	4	no	—
33	C₃×C₉	—	3	2	no	—
34	C₃×C₉	—	3	2	no	—
35	C₃×C₉	—	9	2	no	—
36	C₃×C₉	—	9	2	no	—
37	C₁₇	#10624479	1	1	yes	characteristic, direct product factor, Sylow
38	C₃²	—	9	1	no	—
39	C₃²	C₁₇×AΣL(1,𝔽₂₇)	1	2	yes	—
40	C₃²	C₁₇×#732	1	2	yes	—
41	C₉	—	9	1	no	—
42	C₉	—	9	6	no	—
43	C₉	—	27	2	no	—
44	C₃	—	3	2	no	—
45	C₃	—	3	2	no	—
46	C₃	C₁₇×#6856	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₇	#6856
commutator, Frattini, cosocle	C₃²×C₉	C₃²×C₁₇
prime radical	C₃³×C₁₇	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₇ ◁ C₃³×C₁₇ ◁ C₃²×C₉×C₁₇ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. #10624479	C₁₇	direct (N × H)
37. C₁₇	#10624479	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.