Subgroups — #46828278

Order 34476.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#11759818	C₂	1	1	yes	maximal, characteristic
2	#26040114	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#92789	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11725132⋊C₃	—	13	1	no	maximal
7	Dic₂₂₁⋊C₃	—	13	1	no	maximal
8	#14523149	—	17	1	no	maximal, Hall
9	C₂×C₁₇×C₁₃⋊C₃	—	13	1	no	—
10	C₁₇×D₁₃⋊C₃	—	13	1	no	—
11	#11759818	D₁₇	1	1	yes	characteristic
12	#11725132	—	13	1	no	—
13	Dic₂₂₁	—	13	1	no	—
14	#10621730	—	17	1	no	Hall
15	C₁₇×C₁₃⋊C₃	—	13	1	no	—
16	C₁₇×C₁₃⋊C₃	—	13	1	no	—
17	#92789	Dic₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃×C₁₇	—	13	1	no	—
19	C₁₇×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic
20	C₁₃×D₁₃	C₃×D₁₇	1	1	yes	characteristic
21	C₁₃×C₁₇	—	12	1	no	—
22	C₁₃×C₁₇	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃×C₁₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
24	C₃×Dic₁₇	—	169	1	no	Hall
25	C₁₃²	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₁₃)	—	221	1	no	—
27	Dic₁₃⋊C₃	—	221	1	no	—
28	C₂×C₃×C₁₇	—	169	1	no	—
29	C₂×C₁₃⋊C₃	—	13	1	no	—
30	D₁₃⋊C₃	—	13	1	no	—
31	Dic₁₇	—	169	1	no	Hall
32	#261	—	221	1	no	—
33	Dic₁₃	—	221	1	no	—
34	C₃×C₁₇	—	169	1	no	Hall
35	C₁₃⋊C₃	—	13	1	no	—
36	C₁₃⋊C₃	—	13	1	no	—
37	C₂×C₁₇	—	13	1	no	—
38	C₂×C₁₃	—	13	1	no	—
39	D₁₃	C₁₇⋊(D₁₃⋊C₃)	1	1	yes	characteristic
40	C₁₇	#14523149	1	1	yes	characteristic, complemented, Sylow
41	C₁₃	—	12	1	no	—
42	C₁₃	Dic₂₂₁⋊C₃	1	1	yes	characteristic, complemented
43	C₁₃	#11725132⋊C₃	1	1	yes	characteristic, complemented
44	C₃×C₄	—	2873	1	no	Hall
45	C₂×C₃	—	169	1	no	—
46	C₄	—	2873	1	no	Sylow
47	C₃	—	169	1	no	Sylow
48	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₇	C₃×C₄
prime radical	C₁₇×#11759818	C₂
cosocle	C₁₃×C₁₇×D₁₃	C₂×C₃
LCS	G ▷ C₁₃²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #26040114	C₃	semidirect
3. C₁₇×#92789	C₄	semidirect
5. C₁₃²×C₁₇	C₃×C₄	semidirect
17. #92789	Dic₁₇	semidirect
22. C₁₃×C₁₇	Dic₁₃⋊C₃	semidirect
23. C₁₃×C₁₇	AGL(1,𝔽₁₃)	semidirect
25. C₁₃²	C₃×Dic₁₇	semidirect
40. C₁₇	#14523149	semidirect
42. C₁₃	Dic₂₂₁⋊C₃	semidirect
43. C₁₃	#11725132⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#11759818	2
#26040114	3
#11725132⋊C₃	13
Dic₂₂₁⋊C₃	13
#14523149	17