Subgroups — C₉×GL(3,𝔽₂) #13094540

Order 1512.

55 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×GL(3,𝔽₂)	C₃	1	1	yes	maximal, characteristic
2	C₉×S₄	—	7	2	no	maximal, Hall
3	C₉×ΓL(1,𝔽₈)	—	8	1	no	maximal, Hall
4	GL(3,𝔽₂)	C₉	1	1	yes	characteristic, direct product factor
5	C₉×A₄	—	7	2	no	—
6	C₃×S₄	—	7	2	no	—
7	D₄×C₉	—	21	1	no	—
8	C₃×ΓL(1,𝔽₈)	—	8	1	no	—
9	C₇×C₉	—	8	1	no	—
10	C₇⋊C₉	—	8	2	no	—
11	D₃×C₉	—	28	1	no	—
12	C₃×A₄	—	7	2	no	—
13	C₂²×C₉	—	7	2	no	—
14	C₂²⋊C₉	—	14	2	no	—
15	C₄×C₉	—	21	1	no	—
16	C₃×C₉	—	28	1	no	Sylow
17	S₄	—	7	2	no	—
18	C₃×D₄	—	21	1	no	—
19	C₃×C₇	—	8	1	no	—
20	ΓL(1,𝔽₈)	—	8	1	no	—
21	ΓL(1,𝔽₈)	—	8	2	no	—
22	C₃×D₃	—	28	1	no	—
23	C₂×C₉	—	21	1	no	—
24	C₂²×C₃	—	7	2	no	—
25	A₄	—	7	2	no	—
26	A₄	—	14	2	no	—
27	C₃×C₄	—	21	1	no	—
28	C₃²	—	28	1	no	—
29	C₉	—	56	1	no	—
30	C₉	GL(3,𝔽₂)	1	1	yes	maximal normal, characteristic, direct product factor
31	D₄	—	21	1	no	Sylow
32	C₇	—	8	1	no	Sylow
33	C₂×C₃	—	21	1	no	—
34	D₃	—	28	1	no	—
35	C₂²	—	7	2	no	—
36	C₄	—	21	1	no	—
37	C₃	—	28	1	no	—
38	C₃	—	56	1	no	—
39	C₃	C₃×GL(3,𝔽₂)	1	1	yes	characteristic
40	C₂	—	21	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. GL(3,𝔽₂)	C₉	direct (N × H)
30. C₉	GL(3,𝔽₂)	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.