Subgroups — C₂×C₉²×C₁₄₉ #72201428

Order 24138.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₁₄₉	C₃	1	4	yes	maximal
2	C₉²×C₁₄₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₉×C₁₄₉	C₂×C₃	1	4	yes	—
4	C₂×C₃²×C₁₄₉	C₃²	1	1	yes	characteristic
5	C₂×C₉×C₁₄₉	C₉	1	12	yes	direct product factor
6	C₃²×C₁₄₉	C₂×C₃²	1	1	yes	characteristic
7	C₉×C₁₄₉	C₂×C₉	1	12	yes	direct product factor
8	C₂×C₃×C₁₄₉	C₃×C₉	1	4	yes	—
9	C₃×C₁₄₉	C₂×C₃×C₉	1	4	yes	—
10	C₂×C₁₄₉	C₉²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉²	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₄₉	C₂×C₉²	1	1	yes	characteristic, direct product factor, Sylow
13	C₉²	C₂×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₉	C₃×C₁₄₉	1	4	yes	—
15	C₃×C₉	C₂×C₃×C₁₄₉	1	4	yes	—
16	C₂×C₃²	C₃²×C₁₄₉	1	1	yes	characteristic
17	C₂×C₉	C₉×C₁₄₉	1	12	yes	direct product factor
18	C₃²	C₂×C₃²×C₁₄₉	1	1	yes	characteristic
19	C₉	C₂×C₉×C₁₄₉	1	12	yes	direct product factor
20	C₂×C₃	C₃×C₉×C₁₄₉	1	4	yes	—
21	C₃	C₂×C₃×C₉×C₁₄₉	1	4	yes	—
22	C₂	C₉²×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow

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.