Subgroups — C₂²×C₈₃₉⋊C₈ #41001559

Order 26848.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈₃₉⋊C₈	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₄×C₈₃₉	C₂	1	1	yes	maximal, characteristic
3	C₈₃₉⋊C₈	C₂²	1	4	yes	direct product factor
4	C₂³×C₈₃₉	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈₃₉	C₄	1	3	yes	—
6	C₂×C₄×C₈₃₉	C₂²	1	3	yes	—
7	C₂²×C₈₃₉	C₈	1	4	yes	complemented
8	C₂²×C₈₃₉	C₂×C₄	1	3	yes	—
9	C₄×C₈₃₉	C₂×C₄	1	3	yes	—
10	C₄×C₈₃₉	C₂³	1	1	yes	characteristic
11	C₂×C₈₃₉	C₂×C₈	1	6	yes	complemented
12	C₂×C₈₃₉	C₂²×C₄	1	1	yes	characteristic
13	C₈₃₉	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₈	—	839	1	no	maximal, Sylow
15	C₂²×C₄	D₈₃₉	1	1	yes	characteristic
16	C₂×C₈	—	839	6	no	—
17	C₂³	Dic₈₃₉	1	1	yes	characteristic
18	C₂×C₄	Dic₈₃₉	1	3	yes	—
19	C₂×C₄	C₂×D₈₃₉	1	3	yes	—
20	C₈	—	839	4	no	—
21	C₂²	C₈₃₉⋊C₈	1	4	yes	direct product factor
22	C₂²	C₂×Dic₈₃₉	1	3	yes	—
23	C₄	C₂×Dic₈₃₉	1	3	yes	—
24	C₄	C₂²×D₈₃₉	1	1	yes	characteristic
25	C₂	C₂×C₈₃₉⋊C₈	1	6	yes	direct product factor
26	C₂	C₂²×Dic₈₃₉	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.