Subgroups — A₄×AGL(1,𝔽₈) #10621676

Order 672.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×AGL(1,𝔽₈)	—	4	1	no	maximal
3	C₂×AGL(1,𝔽₈)	—	3	1	no	—
4	C₂³×A₄	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×A₄	—	8	1	no	maximal
6	AGL(1,𝔽₈)	A₄	1	1	yes	characteristic, direct product factor
7	C₂²×A₄	—	7	1	no	—
8	C₂⁵	C₃×C₇	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₇	—	8	1	no	—
10	C₂³×C₃	—	4	1	no	—
11	C₂×A₄	—	7	1	no	—
12	C₃×C₇	—	32	1	no	Hall
13	C₂⁴	—	3	1	no	—
14	C₂⁴	—	7	1	no	—
15	C₂⁴	—	21	1	no	—
16	C₂×C₇	—	24	1	no	—
17	C₂²×C₃	—	28	1	no	—
18	A₄	AGL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
19	C₂³	—	7	1	no	—
20	C₂³	—	21	1	no	—
21	C₂³	—	21	1	no	—
22	C₂³	—	21	3	no	—
23	C₂³	—	21	2	no	—
24	C₂³	C₇×A₄	1	1	yes	characteristic, complemented
25	C₇	—	8	1	no	Sylow
26	C₂×C₃	—	28	1	no	—
27	C₂²	—	7	1	no	—
28	C₂²	—	21	1	no	—
29	C₂²	—	21	1	no	—
30	C₂²	—	21	3	no	—
31	C₂²	—	21	2	no	—
32	C₂²	C₃×AGL(1,𝔽₈)	1	1	yes	characteristic, complemented
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	7	1	no	—
36	C₂	—	21	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁵	C₃×C₇
LCS	G ▷ C₂⁵
UCS	C₁

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.