Subgroups — #37556599

Order 23648.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₇₃₉	C₂	1	1	yes	maximal, characteristic
2	C₇₃₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×C₇₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₇₃₉	C₄	1	1	yes	characteristic
5	C₇₃₉⋊C₈	C₄	1	1	yes	characteristic
6	C₈×C₇₃₉	C₂²	1	1	yes	characteristic
7	C₂×D₇₃₉	C₈	1	1	yes	characteristic
8	C₄×C₇₃₉	C₂×C₄	1	1	yes	characteristic
9	Dic₇₃₉	C₈	1	1	yes	characteristic
10	C₂×C₇₃₉	C₂×C₈	1	1	yes	characteristic
11	D₇₃₉	—	2	1	no	—
12	C₇₃₉	M₃₂	1	1	yes	characteristic, complemented, Sylow
13	M₃₂	—	739	1	no	maximal, Sylow
14	C₂×C₈	—	739	1	no	—
15	C₁₆	—	739	1	no	—
16	C₁₆	D₇₃₉	1	1	yes	characteristic, complemented
17	C₂×C₄	—	739	1	no	—
18	C₈	—	739	1	no	—
19	C₈	C₂×D₇₃₉	1	1	yes	characteristic
20	C₂²	—	739	1	no	—
21	C₄	—	739	1	no	—
22	C₄	C₄×D₇₃₉	1	1	yes	characteristic
23	C₂	—	1478	1	no	—
24	C₂	C₈×D₇₃₉	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.