Subgroups — C₁₁×C₃⋊#10597010 #34088872

Order 19668.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×D₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#10597010	—	3	1	no	maximal, Hall
3	C₃×C₁₁×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₁₄₉	D₃	1	1	yes	characteristic
5	C₃⋊#10597010	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₄₉	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₄₉	C₂×C₁₁	1	1	yes	characteristic
8	#10597010	—	3	1	no	Hall
9	C₃×C₁₄₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
10	D₁₄₉	D₃×C₁₁	1	1	yes	characteristic
11	C₁₄₉	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Sylow
12	C₁₁×Dic₃	—	149	1	no	maximal, Hall
13	C₂×C₃×C₁₁	—	149	1	no	—
14	C₄×C₁₁	—	447	1	no	Hall
15	C₃×C₁₁	#10597010	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁	—	149	1	no	—
17	Dic₃	—	149	1	no	Hall
18	C₁₁	C₃⋊#10597010	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	149	1	no	—
20	C₄	—	447	1	no	Sylow
21	C₃	C₁₁×#10597010	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	149	1	no	—

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.