Subgroups — ΓL(1,𝔽₈)×#401 #13054932

Order 1344.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×#95	C₂	1	7	yes	maximal
2	C₇×#401	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	7	yes	—
4	C₇×#95	C₂×C₃	1	7	yes	—
5	C₃×#401	—	7	1	no	maximal, Hall
6	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
7	C₂×C₄×ΓL(1,𝔽₈)	—	2	21	no	—
8	C₂²×C₄×C₇	C₂²×C₃	1	7	yes	—
9	C₃×#95	—	7	7	no	—
10	C₂²×ΓL(1,𝔽₈)	#41	1	7	yes	—
11	C₄×ΓL(1,𝔽₈)	—	4	7	no	—
12	#401	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
14	C₂×C₄×C₇	—	2	21	no	—
15	C₂²×C₃×C₄	—	7	7	no	—
16	C₂×ΓL(1,𝔽₈)	#126	1	7	yes	—
17	#95	C₂×ΓL(1,𝔽₈)	1	7	yes	—
18	C₂²×C₇	C₃×#41	1	7	yes	—
19	C₄×C₇	—	4	7	no	—
20	C₂³×C₃	—	7	1	no	—
21	C₂×C₃×C₄	—	14	21	no	—
22	ΓL(1,𝔽₈)	#401	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₄	C₂²×ΓL(1,𝔽₈)	1	7	yes	—
24	C₂×C₇	C₃×#126	1	7	yes	—
25	C₂²×C₃	—	7	7	no	—
26	C₃×C₄	—	28	7	no	—
27	C₂³	C₂³×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₂×C₄	—	2	21	no	—
29	C₇	C₃×#401	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	7	7	no	—
31	C₂²	#41×ΓL(1,𝔽₈)	1	7	yes	—
32	C₄	—	4	7	no	—
33	C₃	—	7	1	no	Sylow
34	C₂	ΓL(1,𝔽₈)×#126	1	7	yes	—

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.