Subgroups — Q₈×#15690484 #37589980

Order 24608.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15690484	C₂	1	3	yes	maximal
2	C₄×#15690484	C₂	1	3	yes	maximal
3	Q₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15690484	C₂²	1	3	yes	—
5	C₂×#15690484	C₂²	1	1	yes	characteristic
6	Dic₁₅₃₈	C₄	1	3	yes	complemented
7	C₄×D₇₆₉	C₂²	1	3	yes	—
8	Q₈×C₇₆₉	C₄	1	1	yes	characteristic, complemented
9	C₂×D₇₆₉	C₂³	1	1	yes	characteristic
10	#15690484	—	2	3	no	—
11	#15690484	Q₈	1	2	yes	direct product factor
12	C₄×C₇₆₉	C₂×C₄	1	3	yes	—
13	Dic₇₆₉	C₂×C₄	1	3	yes	—
14	C₂×C₇₆₉	C₂²×C₄	1	1	yes	characteristic
15	D₇₆₉	C₂×Q₈	1	1	yes	characteristic
16	D₇₆₉	#41	1	1	yes	characteristic
17	C₇₆₉	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	769	1	no	maximal, Sylow
19	C₂×Q₈	—	769	1	no	—
20	C₄⋊C₄	—	769	3	no	—
21	C₄²	—	769	3	no	—
22	Q₈	—	769	3	no	—
23	Q₈	#15690484	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	769	1	no	—
25	C₂×C₄	—	769	3	no	—
26	C₂×C₄	—	769	3	no	—
27	C₂²	—	769	1	no	—
28	C₄	—	769	2	no	—
29	C₄	—	769	3	no	—
30	C₄	—	1538	3	no	—
31	C₄	C₂×#15690484	1	3	yes	—
32	C₂	—	769	1	no	—
33	C₂	—	769	1	no	—
34	C₂	C₂²×#15690484	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.