Subgroups — #97×C₇₆₉ #37589757

Order 24608.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₇₆₉	C₂	1	2	yes	maximal
2	C₄²×C₇₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇₆₉	C₄	1	2	yes	—
4	C₂×C₄×C₇₆₉	C₂²	1	1	yes	characteristic
5	C₈×C₇₆₉	C₄	1	4	yes	complemented
6	C₂²×C₇₆₉	C₂×C₄	1	1	yes	characteristic
7	C₄×C₇₆₉	—	2	2	no	—
8	C₄×C₇₆₉	C₂×C₄	1	2	yes	—
9	C₂×C₇₆₉	C₄²	1	1	yes	characteristic
10	C₂×C₇₆₉	M₁₆	1	2	yes	—
11	C₇₆₉	#97	1	1	yes	characteristic, direct product factor, Sylow
12	#97	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₈	C₂×C₇₆₉	1	2	yes	—
14	C₄²	C₂×C₇₆₉	1	1	yes	characteristic
15	C₂×C₄	C₄×C₇₆₉	1	2	yes	—
16	C₂×C₄	C₂²×C₇₆₉	1	1	yes	characteristic
17	C₈	C₄×C₇₆₉	1	4	yes	complemented
18	C₂²	C₂×C₄×C₇₆₉	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₂×C₄×C₇₆₉	1	2	yes	—
21	C₂	C₄²×C₇₆₉	1	1	yes	characteristic
22	C₂	M₁₆×C₇₆₉	1	2	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.