Subgroups — C₄×C₈×C₇₅₇ #37564244

Order 24224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₇₅₇	C₂	1	2	yes	maximal
2	C₄²×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇₅₇	C₄	1	2	yes	—
4	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
5	C₈×C₇₅₇	C₄	1	4	yes	direct product factor
6	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
7	C₄×C₇₅₇	C₈	1	4	yes	direct product factor
8	C₄×C₇₅₇	C₂×C₄	1	2	yes	—
9	C₂×C₇₅₇	C₄²	1	1	yes	characteristic
10	C₂×C₇₅₇	C₂×C₈	1	2	yes	—
11	C₇₅₇	C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₈	C₇₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₈	C₂×C₇₅₇	1	2	yes	—
14	C₄²	C₂×C₇₅₇	1	1	yes	characteristic
15	C₂×C₄	C₄×C₇₅₇	1	2	yes	—
16	C₂×C₄	C₂²×C₇₅₇	1	1	yes	characteristic
17	C₈	C₄×C₇₅₇	1	4	yes	direct product factor
18	C₂²	C₂×C₄×C₇₅₇	1	1	yes	characteristic
19	C₄	C₈×C₇₅₇	1	4	yes	direct product factor
20	C₄	C₂×C₄×C₇₅₇	1	2	yes	—
21	C₂	C₄²×C₇₅₇	1	1	yes	characteristic
22	C₂	C₂×C₈×C₇₅₇	1	2	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.