Subgroups — C₂×C₄×C₃₇×C₈₃ #72201807

Order 24568.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₇×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃₇×C₈₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₇×C₈₃	C₄	1	2	yes	direct product factor
4	C₂×C₃₇×C₈₃	C₂²	1	1	yes	characteristic
5	C₃₇×C₈₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄×C₈₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₈₃	C₂×C₃₇	1	1	yes	characteristic
8	C₄×C₈₃	C₂×C₃₇	1	2	yes	direct product factor
9	C₂×C₄×C₃₇	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₈₃	C₄×C₃₇	1	2	yes	direct product factor
11	C₂×C₈₃	C₂²×C₃₇	1	1	yes	characteristic
12	C₂²×C₃₇	C₂×C₈₃	1	1	yes	characteristic
13	C₄×C₃₇	C₂×C₈₃	1	2	yes	direct product factor
14	C₈₃	C₂×C₄×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃₇	C₄×C₈₃	1	2	yes	direct product factor
16	C₂×C₃₇	C₂²×C₈₃	1	1	yes	characteristic
17	C₃₇	C₂×C₄×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄	C₃₇×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₃₇×C₈₃	1	1	yes	characteristic
20	C₄	C₂×C₃₇×C₈₃	1	2	yes	direct product factor
21	C₂	C₄×C₃₇×C₈₃	1	2	yes	direct product factor
22	C₂	C₂²×C₃₇×C₈₃	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.