Subgroups — #26040084⋊C₃ #46828136

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₁₆₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#26040084	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₆₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₁₆₉	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11725132⋊C₃	—	13	1	no	maximal
7	#10621721⋊C₃	—	17	1	no	maximal, Hall
8	C₁₇×D₁₃⋊C₃	—	13	1	no	—
9	D₁₆₉⋊C₃	D₁₇	1	1	yes	characteristic
10	#11725132	—	13	1	no	—
11	#10621721	—	17	1	no	Hall
12	C₁₇×C₁₃⋊C₃	—	13	1	no	—
13	C₁₆₉⋊C₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₁₇×D₁₃	—	13	1	no	—
15	D₁₆₉	C₃×D₁₇	1	1	yes	characteristic
16	C₁₃×C₁₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic
17	C₃×Dic₁₇	—	169	1	no	Hall
18	C₁₆₉	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
19	AGL(1,𝔽₁₃)	—	221	1	no	—
20	C₂×C₃×C₁₇	—	169	1	no	—
21	D₁₃⋊C₃	—	13	1	no	—
22	Dic₁₇	—	169	1	no	Hall
23	#261	—	221	1	no	—
24	C₃×C₁₇	—	169	1	no	Hall
25	C₁₃⋊C₃	—	13	1	no	—
26	C₂×C₁₇	—	169	1	no	—
27	D₁₃	—	13	1	no	—
28	C₁₇	#10621721⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	#11725132⋊C₃	1	1	yes	characteristic
30	C₃×C₄	—	2873	1	no	Hall
31	C₂×C₃	—	169	1	no	—
32	C₄	—	2873	1	no	Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₁₇×C₁₆₉	C₃×C₄
Frattini	C₁₃	#11725132⋊C₃
socle	C₁₃×C₁₇	AGL(1,𝔽₁₃)
prime radical	C₁₇×D₁₆₉⋊C₃	C₂
cosocle	C₁₇×D₁₆₉	C₂×C₃
LCS	G ▷ C₁₇×C₁₆₉
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.