Subgroups — C₁₉²×C₂²⋊C₉ #27188751

Order 12996.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₉²	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₉²	—	4	1	no	maximal, Hall
3	C₂×C₃×C₁₉²	—	3	1	no	—
4	C₂²×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉²	A₄	1	1	yes	characteristic
6	C₂×C₁₉²	—	3	1	no	—
7	C₁₉×C₂²⋊C₉	C₁₉	1	20	yes	maximal, direct product factor
8	C₁₉²	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₃×C₁₉	C₃×C₁₉	1	20	yes	—
10	C₉×C₁₉	—	4	20	no	—
11	C₂×C₃×C₁₉	—	3	20	no	—
12	C₂²×C₁₉	C₉×C₁₉	1	20	yes	complemented
13	C₃×C₁₉	A₄×C₁₉	1	20	yes	—
14	C₂×C₁₉	—	3	20	no	—
15	C₂²⋊C₉	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
16	C₁₉	C₁₉×C₂²⋊C₉	1	20	yes	direct product factor
17	C₂²×C₃	C₃×C₁₉²	1	1	yes	characteristic
18	C₉	—	4	1	no	Sylow
19	C₂×C₃	—	3	1	no	—
20	C₂²	C₉×C₁₉²	1	1	yes	characteristic, complemented, Sylow
21	C₃	A₄×C₁₉²	1	1	yes	characteristic
22	C₂	—	3	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.