Subgroups — C₂²×C₂₃×C₃₄₃ #72208317

Order 31556.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₃₄₃	C₂	1	3	yes	maximal, direct product factor
2	C₂₃×C₃₄₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₂₃×C₄₉	C₇	1	1	yes	maximal, characteristic
4	C₂×C₂₃×C₄₉	C₂×C₇	1	3	yes	—
5	C₂²×C₃₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂₃×C₄₉	C₂²×C₇	1	1	yes	characteristic
7	C₂×C₃₄₃	C₂×C₂₃	1	3	yes	direct product factor
8	C₂²×C₇×C₂₃	C₄₉	1	1	yes	characteristic
9	C₃₄₃	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₇×C₂₃	C₂×C₄₉	1	3	yes	—
11	C₂²×C₄₉	C₇×C₂₃	1	1	yes	characteristic
12	C₇×C₂₃	C₂²×C₄₉	1	1	yes	characteristic
13	C₂×C₄₉	C₂×C₇×C₂₃	1	3	yes	—
14	C₂²×C₂₃	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄₉	C₂²×C₇×C₂₃	1	1	yes	characteristic
16	C₂×C₂₃	C₂×C₃₄₃	1	3	yes	direct product factor
17	C₂²×C₇	C₂₃×C₄₉	1	1	yes	characteristic
18	C₂₃	C₂²×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂×C₂₃×C₄₉	1	3	yes	—
20	C₇	C₂²×C₂₃×C₄₉	1	1	yes	characteristic
21	C₂²	C₂₃×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₂₃×C₃₄₃	1	3	yes	direct product factor

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.