Subgroups — C₂×C₄×C₇×C₂₂₃ #72190831

Order 12488.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₂₂₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×C₂₂₃	C₄	1	2	yes	direct product factor
4	C₂×C₇×C₂₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₂₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₂₂₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₂₂₃	C₂×C₇	1	1	yes	characteristic
8	C₄×C₂₂₃	C₂×C₇	1	2	yes	direct product factor
9	C₂×C₂₂₃	C₄×C₇	1	2	yes	direct product factor
10	C₂×C₂₂₃	C₂²×C₇	1	1	yes	characteristic
11	C₂₂₃	C₂×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₄×C₇	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₇	C₂×C₂₂₃	1	1	yes	characteristic
14	C₄×C₇	C₂×C₂₂₃	1	2	yes	direct product factor
15	C₂×C₇	C₄×C₂₂₃	1	2	yes	direct product factor
16	C₂×C₇	C₂²×C₂₂₃	1	1	yes	characteristic
17	C₂×C₄	C₇×C₂₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₇	C₂×C₄×C₂₂₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₇×C₂₂₃	1	1	yes	characteristic
20	C₄	C₂×C₇×C₂₂₃	1	2	yes	direct product factor
21	C₂	C₄×C₇×C₂₂₃	1	2	yes	direct product factor
22	C₂	C₂²×C₇×C₂₂₃	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.