Subgroups — D₅₆⋊C₃ #66541

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
2	C₈×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅₆	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×AGL(1,𝔽₇)	—	2	2	no	—
5	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
6	D₂₈	C₂×C₃	1	2	yes	complemented
7	C₇×C₈	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₈	—	7	1	no	maximal, Hall
9	C₂×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
10	AGL(1,𝔽₇)	—	4	2	no	—
11	C₂×D₇	—	2	2	no	—
12	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₃×D₄	—	7	2	no	—
14	C₃×C₈	—	7	1	no	—
15	ΓL(1,𝔽₈)	D₈	1	1	yes	characteristic, complemented, Hall
16	D₈	—	7	1	no	Sylow
17	C₂×C₇	C₃×D₄	1	1	yes	characteristic
18	D₇	—	4	2	no	—
19	C₂²×C₃	—	14	2	no	—
20	C₃×C₄	—	7	1	no	—
21	D₄	—	7	2	no	—
22	C₈	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
23	C₇	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	7	1	no	—
25	C₂×C₃	—	28	2	no	—
26	C₂²	—	14	2	no	—
27	C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₃	—	7	1	no	Sylow
29	C₂	—	28	2	no	—
30	C₂	C₄⋊AGL(1,𝔽₇)	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.