Subgroups — C₃×C₄₁×C₂₄₃ #44470968

Order 29889.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₈₁	C₃	1	1	yes	maximal, characteristic
2	C₄₁×C₂₄₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂₇×C₄₁	C₉	1	1	yes	characteristic
4	C₄₁×C₈₁	C₉	1	2	yes	—
5	C₄₁×C₈₁	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₄₁	C₂₇	1	1	yes	characteristic
7	C₂₇×C₄₁	C₂₇	1	2	yes	—
8	C₂₇×C₄₁	C₃×C₉	1	1	yes	characteristic
9	C₃×C₂₄₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃²×C₄₁	C₈₁	1	1	yes	characteristic
11	C₉×C₄₁	C₈₁	1	2	yes	—
12	C₉×C₄₁	C₃×C₂₇	1	1	yes	characteristic
13	C₃×C₈₁	C₃×C₄₁	1	1	yes	characteristic
14	C₂₄₃	C₃×C₄₁	1	3	yes	direct product factor
15	C₃×C₄₁	C₂₄₃	1	3	yes	direct product factor
16	C₃×C₄₁	C₃×C₈₁	1	1	yes	characteristic
17	C₃×C₂₇	C₉×C₄₁	1	1	yes	characteristic
18	C₈₁	C₉×C₄₁	1	2	yes	—
19	C₈₁	C₃²×C₄₁	1	1	yes	characteristic
20	C₄₁	C₃×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₉	C₂₇×C₄₁	1	1	yes	characteristic
22	C₂₇	C₂₇×C₄₁	1	2	yes	—
23	C₂₇	C₃×C₉×C₄₁	1	1	yes	characteristic
24	C₃²	C₄₁×C₈₁	1	1	yes	characteristic
25	C₉	C₄₁×C₈₁	1	2	yes	—
26	C₉	C₃×C₂₇×C₄₁	1	1	yes	characteristic
27	C₃	C₄₁×C₂₄₃	1	3	yes	direct product factor
28	C₃	C₃×C₄₁×C₈₁	1	1	yes	characteristic

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.