Subgroups — #1141⋊C₃ #66549

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#1141	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
6	C₂×AGL(1,𝔽₇)	—	2	1	no	—
7	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
8	C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
10	C₇⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₈	—	7	1	no	maximal, Hall
12	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
13	C₂×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
14	AGL(1,𝔽₇)	—	4	1	no	—
15	C₂²×C₇	—	2	1	no	—
16	C₂×D₇	—	2	1	no	—
17	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
18	C₃×D₄	—	7	1	no	—
19	C₃×D₄	—	7	1	no	—
20	C₃×C₈	—	7	1	no	—
21	ΓL(1,𝔽₈)	D₈	1	1	yes	characteristic, complemented, Hall
22	D₈	—	7	1	no	Sylow
23	C₂×C₇	—	4	1	no	—
24	C₂×C₇	C₃×D₄	1	1	yes	characteristic
25	D₇	—	4	1	no	—
26	C₂²×C₃	—	14	1	no	—
27	C₂²×C₃	—	14	1	no	—
28	C₃×C₄	—	7	1	no	—
29	D₄	—	7	1	no	—
30	D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
31	C₈	—	7	1	no	—
32	C₇	C₃×D₈	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	7	1	no	—
34	C₂×C₃	—	28	1	no	—
35	C₂×C₃	—	28	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	14	1	no	—
38	C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
39	C₃	—	7	1	no	Sylow
40	C₂	—	4	1	no	—
41	C₂	—	28	1	no	—
42	C₂	(C₂²⋊D₇)⋊C₃	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.