Subgroups — C₂×C₄²×C₇₅₇ #37564262

Order 24224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇₅₇	C₂	1	3	yes	maximal
2	C₄²×C₇₅₇	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₇₅₇	C₂²	1	1	yes	characteristic
4	C₂×C₄×C₇₅₇	C₄	1	12	yes	direct product factor
5	C₂×C₄×C₇₅₇	C₂²	1	6	yes	—
6	C₂²×C₇₅₇	C₂×C₄	1	6	yes	—
7	C₂²×C₇₅₇	C₂³	1	1	yes	characteristic
8	C₄×C₇₅₇	C₂×C₄	1	12	yes	direct product factor
9	C₂×C₇₅₇	C₄²	1	4	yes	direct product factor
10	C₂×C₇₅₇	C₂²×C₄	1	3	yes	—
11	C₇₅₇	C₂×C₄²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₄²	C₇₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₄	C₂×C₇₅₇	1	3	yes	—
14	C₄²	C₂×C₇₅₇	1	4	yes	direct product factor
15	C₂³	C₂²×C₇₅₇	1	1	yes	characteristic
16	C₂×C₄	C₄×C₇₅₇	1	12	yes	direct product factor
17	C₂×C₄	C₂²×C₇₅₇	1	6	yes	—
18	C₂²	C₂×C₄×C₇₅₇	1	6	yes	—
19	C₂²	C₂³×C₇₅₇	1	1	yes	characteristic
20	C₄	C₂×C₄×C₇₅₇	1	12	yes	direct product factor
21	C₂	C₄²×C₇₅₇	1	4	yes	direct product factor
22	C₂	C₂²×C₄×C₇₅₇	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.