Subgroups — C₂×D₆₀₅₆ #37564398

Order 24224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₂₈	C₂	1	2	yes	maximal, complemented
2	D₆₀₅₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇₅₇	—	2	2	no	—
5	D₃₀₂₈	—	2	2	no	—
6	D₃₀₂₈	C₂²	1	4	yes	complemented
7	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
8	C₈×C₇₅₇	C₂²	1	2	yes	complemented
9	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
10	C₂×D₇₅₇	—	2	4	no	—
11	C₂×D₇₅₇	—	4	4	no	—
12	C₄×C₇₅₇	D₄	1	1	yes	characteristic
13	C₄×C₇₅₇	C₂³	1	1	yes	characteristic
14	C₂×C₇₅₇	D₈	1	2	yes	complemented
15	C₂×C₇₅₇	C₂×D₄	1	1	yes	characteristic
16	D₇₅₇	—	4	4	no	—
17	C₇₅₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₈	—	757	1	no	maximal, Sylow
19	C₂×D₄	—	757	2	no	—
20	D₈	—	757	4	no	—
21	C₂×C₈	D₇₅₇	1	1	yes	characteristic, complemented
22	C₂³	—	1514	2	no	—
23	D₄	—	1514	2	no	—
24	D₄	—	757	4	no	—
25	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
26	C₈	C₂×D₇₅₇	1	2	yes	complemented
27	C₂²	—	3028	4	no	—
28	C₂²	—	1514	4	no	—
29	C₂²	D₃₀₂₈	1	1	yes	characteristic
30	C₄	D₃₀₂₈	1	1	yes	characteristic
31	C₄	C₂²×D₇₅₇	1	1	yes	characteristic
32	C₂	—	3028	4	no	—
33	C₂	D₆₀₅₆	1	2	yes	direct product factor
34	C₂	C₂×D₃₀₂₈	1	1	yes	characteristic

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.