Subgroups — #41001496

Order 26848.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₈₃₉	C₂	1	1	yes	maximal, characteristic
2	C₈₃₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×C₈₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₈₃₉	C₄	1	1	yes	characteristic
5	C₈₃₉⋊C₈	C₄	1	1	yes	characteristic
6	C₈×C₈₃₉	C₂²	1	1	yes	characteristic
7	C₂×D₈₃₉	C₈	1	1	yes	characteristic
8	C₄×C₈₃₉	C₂×C₄	1	1	yes	characteristic
9	Dic₈₃₉	C₈	1	1	yes	characteristic
10	C₂×C₈₃₉	C₂×C₈	1	1	yes	characteristic
11	D₈₃₉	—	2	1	no	—
12	C₈₃₉	M₃₂	1	1	yes	characteristic, complemented, Sylow
13	M₃₂	—	839	1	no	maximal, Sylow
14	C₂×C₈	—	839	1	no	—
15	C₁₆	—	839	1	no	—
16	C₁₆	D₈₃₉	1	1	yes	characteristic, complemented
17	C₂×C₄	—	839	1	no	—
18	C₈	—	839	1	no	—
19	C₈	C₂×D₈₃₉	1	1	yes	characteristic
20	C₂²	—	839	1	no	—
21	C₄	—	839	1	no	—
22	C₄	C₄×D₈₃₉	1	1	yes	characteristic
23	C₂	—	1678	1	no	—
24	C₂	C₈×D₈₃₉	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.