Subgroups — #37566963

Order 24352.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131657	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#15690200	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₇₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15690200	—	2	1	no	—
5	#20259011	—	2	1	no	—
6	Dic₁₅₂₂	—	2	1	no	—
7	Dic₁₅₂₂	C₄	1	1	yes	characteristic, complemented
8	C₄×D₇₆₁	—	2	1	no	—
9	C₄×D₇₆₁	C₂²	1	1	yes	characteristic
10	Q₈×C₇₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₇₆₁	D₄	1	1	yes	characteristic
12	#15690200	—	4	1	no	—
13	C₄×C₇₆₁	—	2	1	no	—
14	C₄×C₇₆₁	C₂×C₄	1	1	yes	characteristic
15	Dic₇₆₁	—	2	1	no	—
16	Dic₇₆₁	D₄	1	1	yes	characteristic
17	C₂×C₇₆₁	C₂²⋊C₄	1	1	yes	characteristic
18	D₇₆₁	SD₁₆	1	1	yes	characteristic
19	D₇₆₁	Q₁₆	1	1	yes	characteristic
20	C₇₆₁	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	761	1	no	maximal, Sylow
22	C₂×Q₈	—	761	1	no	—
23	C₂×C₈	—	761	1	no	—
24	C₄⋊C₄	—	761	1	no	—
25	Q₈	—	1522	1	no	—
26	Q₈	—	761	1	no	—
27	Q₈	#15690200	1	1	yes	characteristic, complemented
28	C₂×C₄	—	1522	1	no	—
29	C₂×C₄	—	1522	1	no	—
30	C₂×C₄	—	761	1	no	—
31	C₈	—	1522	1	no	—
32	C₂²	—	761	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	3044	1	no	—
35	C₄	—	1522	1	no	—
36	C₄	—	761	1	no	—
37	C₄	C₂×#15690200	1	1	yes	characteristic
38	C₂	—	761	1	no	—
39	C₂	—	761	1	no	—
40	C₂	C₂²⋊#15690200	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.