Subgroups — C₁₁×#13181892 #34061699

Order 19074.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₇×D₁₇	—	3	1	no	maximal, Hall
3	C₁₁×C₁₇²	D₃	1	1	yes	characteristic, complemented, Hall
4	#13181892	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₇²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₁₇	—	3	1	no	Hall
7	C₂×C₁₁×C₁₇	—	51	1	no	—
8	C₁₁×D₁₇	—	3	1	no	—
9	C₁₇²	D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
10	C₁₁×C₁₇	—	3	1	no	—
11	C₁₁×C₁₇	—	3	1	no	—
12	C₁₁×C₁₇	—	6	2	no	—
13	D₃×C₁₁	—	289	1	no	maximal, Hall
14	C₂×C₁₇	—	51	1	no	—
15	D₁₇	—	3	1	no	—
16	C₃×C₁₁	—	289	1	no	Hall
17	C₂×C₁₁	—	51	1	no	Hall
18	C₁₇	—	3	1	no	—
19	C₁₇	—	3	1	no	—
20	C₁₇	—	6	2	no	—
21	C₁₁	#13181892	1	1	yes	characteristic, direct product factor, Sylow
22	D₃	—	289	1	no	Hall
23	C₃	—	289	1	no	Sylow
24	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	#13181892
commutator, cosocle, hypocenter	C₁₇²⋊C₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇²	D₃
LCS	G ▷ C₁₇²⋊C₃
UCS	C₁ ◁ C₁₁

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.