Subgroups — C₄²×D₈₃₉ #41001505

Order 26848.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈₃₉	C₂	1	3	yes	maximal
2	C₄×Dic₈₃₉	C₂	1	3	yes	maximal, complemented
3	C₄²×C₈₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₈₃₉	C₂²	1	1	yes	characteristic
5	C₂×Dic₈₃₉	C₂²	1	3	yes	—
6	C₄×D₈₃₉	C₄	1	12	yes	direct product factor
7	C₂×C₄×C₈₃₉	C₂²	1	3	yes	—
8	C₂²×C₈₃₉	C₂³	1	1	yes	characteristic
9	C₂×D₈₃₉	C₂×C₄	1	6	yes	—
10	C₄×C₈₃₉	C₂×C₄	1	6	yes	complemented
11	Dic₈₃₉	C₂×C₄	1	6	yes	complemented
12	C₂×C₈₃₉	C₂²×C₄	1	3	yes	—
13	D₈₃₉	C₄²	1	4	yes	direct product factor
14	C₈₃₉	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄²	—	839	1	no	maximal, Sylow
16	C₂²×C₄	—	839	3	no	—
17	C₄²	—	839	3	no	—
18	C₄²	D₈₃₉	1	1	yes	characteristic, direct product factor
19	C₂³	—	839	1	no	—
20	C₂×C₄	—	839	3	no	—
21	C₂×C₄	—	839	12	no	—
22	C₂×C₄	C₂×D₈₃₉	1	3	yes	—
23	C₂²	—	839	6	no	—
24	C₂²	C₂²×D₈₃₉	1	1	yes	characteristic
25	C₄	—	839	6	no	—
26	C₄	C₄×D₈₃₉	1	6	yes	direct product factor
27	C₂	—	839	4	no	—
28	C₂	C₂×C₄×D₈₃₉	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.