Subgroups — #37589962

Order 24608.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134389	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#15690484	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₇₆₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15690484	—	2	1	no	—
5	#20259677	—	2	1	no	—
6	Dic₁₅₃₈	—	2	1	no	—
7	Dic₁₅₃₈	C₄	1	1	yes	characteristic, complemented
8	C₄×D₇₆₉	—	2	1	no	—
9	C₄×D₇₆₉	C₂²	1	1	yes	characteristic
10	Q₈×C₇₆₉	C₄	1	1	yes	characteristic, complemented
11	C₂×D₇₆₉	D₄	1	1	yes	characteristic
12	#15690484	—	4	1	no	—
13	C₄×C₇₆₉	—	2	1	no	—
14	C₄×C₇₆₉	C₂×C₄	1	1	yes	characteristic
15	Dic₇₆₉	—	2	1	no	—
16	Dic₇₆₉	D₄	1	1	yes	characteristic
17	C₂×C₇₆₉	C₂²⋊C₄	1	1	yes	characteristic
18	D₇₆₉	SD₁₆	1	1	yes	characteristic
19	D₇₆₉	Q₁₆	1	1	yes	characteristic
20	C₇₆₉	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	769	1	no	maximal, Sylow
22	C₂×Q₈	—	769	1	no	—
23	C₂×C₈	—	769	1	no	—
24	C₄⋊C₄	—	769	1	no	—
25	Q₈	—	769	1	no	—
26	Q₈	—	1538	1	no	—
27	Q₈	#15690484	1	1	yes	characteristic, complemented
28	C₂×C₄	—	769	1	no	—
29	C₂×C₄	—	1538	1	no	—
30	C₂×C₄	—	1538	1	no	—
31	C₈	—	1538	1	no	—
32	C₂²	—	769	1	no	—
33	C₄	—	769	1	no	—
34	C₄	—	2	1	no	—
35	C₄	—	1538	1	no	—
36	C₄	—	3076	1	no	—
37	C₄	C₂×#15690484	1	1	yes	characteristic
38	C₂	—	769	1	no	—
39	C₂	—	769	1	no	—
40	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.