Subgroups — C₂×C₄×C₄₁×C₇₁ #72200596

Order 23288.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₁×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₁×C₇₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₁×C₇₁	C₄	1	2	yes	direct product factor
4	C₂×C₄₁×C₇₁	C₂²	1	1	yes	characteristic
5	C₄₁×C₇₁	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄×C₇₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄×C₄₁	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₇₁	C₂×C₄₁	1	1	yes	characteristic
9	C₄×C₇₁	C₂×C₄₁	1	2	yes	direct product factor
10	C₂²×C₄₁	C₂×C₇₁	1	1	yes	characteristic
11	C₄×C₄₁	C₂×C₇₁	1	2	yes	direct product factor
12	C₂×C₇₁	C₄×C₄₁	1	2	yes	direct product factor
13	C₂×C₇₁	C₂²×C₄₁	1	1	yes	characteristic
14	C₂×C₄₁	C₄×C₇₁	1	2	yes	direct product factor
15	C₂×C₄₁	C₂²×C₇₁	1	1	yes	characteristic
16	C₇₁	C₂×C₄×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄₁	C₂×C₄×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄	C₄₁×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₄₁×C₇₁	1	1	yes	characteristic
20	C₄	C₂×C₄₁×C₇₁	1	2	yes	direct product factor
21	C₂	C₄×C₄₁×C₇₁	1	2	yes	direct product factor
22	C₂	C₂²×C₄₁×C₇₁	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.