Subgroups — C₄²×D₇₅₇ #37564335

Order 24224.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₇₅₇	C₂	1	3	yes	maximal
2	C₄×Dic₇₅₇	C₂	1	3	yes	maximal, complemented
3	C₄²×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇₅₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇₅₇	C₂²	1	3	yes	—
6	C₄×D₇₅₇	C₄	1	12	yes	direct product factor
7	C₂×C₄×C₇₅₇	C₂²	1	3	yes	—
8	C₂²×C₇₅₇	C₂³	1	1	yes	characteristic
9	C₂×D₇₅₇	C₂×C₄	1	6	yes	—
10	C₄×C₇₅₇	C₂×C₄	1	6	yes	complemented
11	Dic₇₅₇	C₂×C₄	1	6	yes	complemented
12	C₂×C₇₅₇	C₂²×C₄	1	3	yes	—
13	D₇₅₇	C₄²	1	4	yes	direct product factor
14	C₇₅₇	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄²	—	757	1	no	maximal, Sylow
16	C₂²×C₄	—	757	3	no	—
17	C₄²	—	757	3	no	—
18	C₄²	D₇₅₇	1	1	yes	characteristic, direct product factor
19	C₂³	—	757	1	no	—
20	C₂×C₄	—	757	3	no	—
21	C₂×C₄	—	757	12	no	—
22	C₂×C₄	C₂×D₇₅₇	1	3	yes	—
23	C₂²	—	757	6	no	—
24	C₂²	C₂²×D₇₅₇	1	1	yes	characteristic
25	C₄	—	757	6	no	—
26	C₄	C₄×D₇₅₇	1	6	yes	direct product factor
27	C₂	—	757	4	no	—
28	C₂	C₂×C₄×D₇₅₇	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.