Subgroups — C₄⋊#20259013 #37566993

Order 24352.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259013	C₂	1	2	yes	maximal
2	C₄×#15690200	C₂	1	1	yes	maximal, characteristic
3	#20259013	—	2	2	no	—
4	C₂×#15690200	C₄	1	1	yes	characteristic
5	C₂×#15690200	C₂²	1	1	yes	characteristic
6	C₄×D₇₆₁	C₄	1	1	yes	characteristic
7	C₂×D₇₆₁	C₂×C₄	1	1	yes	characteristic
8	#15690200	—	2	1	no	—
9	#15690200	D₄	1	1	yes	characteristic
10	#15690200	Q₈	1	1	yes	characteristic
11	C₄×C₇₆₁	C₈	1	1	yes	characteristic, complemented
12	Dic₇₆₁	C₈	1	1	yes	characteristic, complemented
13	C₂×C₇₆₁	C₂×C₈	1	1	yes	characteristic
14	D₇₆₁	C₄⋊C₄	1	1	yes	characteristic
15	D₇₆₁	M₁₆	1	1	yes	characteristic
16	C₇₆₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
17	C₄⋊C₈	—	761	1	no	maximal, Sylow
18	C₂×C₈	—	761	2	no	—
19	C₄²	—	761	1	no	—
20	C₂×C₄	—	761	1	no	—
21	C₂×C₄	—	761	1	no	—
22	C₂×C₄	—	761	1	no	—
23	C₈	—	1522	2	no	—
24	C₂²	—	761	1	no	—
25	C₄	—	1522	1	no	—
26	C₄	—	761	1	no	—
27	C₄	—	761	1	no	—
28	C₄	—	761	1	no	—
29	C₄	#20259013	1	1	yes	characteristic, complemented
30	C₂	—	761	1	no	—
31	C₂	—	761	1	no	—
32	C₂	C₂×#20259013	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.