Subgroups — C₄²×C₇×C₉₇ #72189409

Order 10864.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₉₇	C₂	1	3	yes	maximal
2	C₂²×C₇×C₉₇	C₂²	1	1	yes	characteristic
3	C₄×C₇×C₉₇	C₄	1	6	yes	direct product factor
4	C₄²×C₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₉₇	C₂×C₄	1	3	yes	—
6	C₂×C₄×C₉₇	C₂×C₇	1	3	yes	—
7	C₇×C₉₇	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₉₇	C₂²×C₇	1	1	yes	characteristic
9	C₄×C₉₇	C₄×C₇	1	6	yes	direct product factor
10	C₂×C₉₇	C₂×C₄×C₇	1	3	yes	—
11	C₄²×C₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₉₇	C₄²×C₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₄×C₇	C₂×C₉₇	1	3	yes	—
14	C₂²×C₇	C₂²×C₉₇	1	1	yes	characteristic
15	C₄×C₇	C₄×C₉₇	1	6	yes	direct product factor
16	C₄²	C₇×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₇	C₂×C₄×C₉₇	1	3	yes	—
18	C₂×C₄	C₂×C₇×C₉₇	1	3	yes	—
19	C₇	C₄²×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₂²×C₇×C₉₇	1	1	yes	characteristic
21	C₄	C₄×C₇×C₉₇	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₇×C₉₇	1	3	yes	—

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.