Subgroups — C₂×D₆₈₇₂ #42117851

Order 27488.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₄₃₆	C₂	1	2	yes	maximal, complemented
2	D₆₈₇₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₈₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₈₅₉	—	2	2	no	—
5	D₃₄₃₆	—	2	2	no	—
6	D₃₄₃₆	C₂²	1	4	yes	complemented
7	C₂×C₄×C₈₅₉	C₂²	1	1	yes	characteristic
8	C₈×C₈₅₉	C₂²	1	2	yes	complemented
9	C₂²×C₈₅₉	D₄	1	1	yes	characteristic
10	C₂×D₈₅₉	—	2	4	no	—
11	C₂×D₈₅₉	—	4	4	no	—
12	C₄×C₈₅₉	D₄	1	1	yes	characteristic
13	C₄×C₈₅₉	C₂³	1	1	yes	characteristic
14	C₂×C₈₅₉	D₈	1	2	yes	complemented
15	C₂×C₈₅₉	C₂×D₄	1	1	yes	characteristic
16	D₈₅₉	—	4	4	no	—
17	C₈₅₉	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₈	—	859	1	no	maximal, Sylow
19	C₂×D₄	—	859	2	no	—
20	D₈	—	859	4	no	—
21	C₂×C₈	D₈₅₉	1	1	yes	characteristic, complemented
22	C₂³	—	1718	2	no	—
23	D₄	—	859	4	no	—
24	D₄	—	1718	2	no	—
25	C₂×C₄	C₂×D₈₅₉	1	1	yes	characteristic
26	C₈	C₂×D₈₅₉	1	2	yes	complemented
27	C₂²	—	3436	4	no	—
28	C₂²	—	1718	4	no	—
29	C₂²	D₃₄₃₆	1	1	yes	characteristic
30	C₄	D₃₄₃₆	1	1	yes	characteristic
31	C₄	C₂²×D₈₅₉	1	1	yes	characteristic
32	C₂	—	3436	4	no	—
33	C₂	D₆₈₇₂	1	2	yes	direct product factor
34	C₂	C₂×D₃₄₃₆	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.