Subgroups — Q₈×SL(2,𝔽₃) #5448

Order 192.

77 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×SL(2,𝔽₃)	C₂	1	3	yes	maximal
2	Q₈²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂×C₃×Q₈	—	4	1	no	maximal
4	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
5	C₄⋊Q₈	—	3	3	no	—
6	C₄×Q₈	—	3	1	no	—
7	C₄×Q₈	C₂×C₃	1	3	yes	—
8	C₃×Q₈	—	4	4	no	—
9	C₂×C₃×C₄	—	4	3	no	—
10	SL(2,𝔽₃)	Q₈	1	1	yes	characteristic, direct product factor
11	C₂×Q₈	—	3	2	no	—
12	C₂×Q₈	A₄	1	1	yes	characteristic
13	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
14	C₄⋊C₄	—	3	3	no	—
15	C₄⋊C₄	—	3	3	no	—
16	C₄²	—	3	3	no	—
17	C₂²×C₃	—	4	1	no	—
18	C₃×C₄	—	4	6	no	—
19	Q₈	—	3	1	no	—
20	Q₈	—	12	2	no	—
21	Q₈	SL(2,𝔽₃)	1	4	yes	direct product factor
22	Q₈	C₃×Q₈	1	1	yes	characteristic, complemented
23	C₂×C₄	—	3	1	no	—
24	C₂×C₄	—	3	3	no	—
25	C₂×C₄	C₂×A₄	1	3	yes	—
26	C₂×C₃	—	4	1	no	—
27	C₂×C₃	—	4	1	no	—
28	C₂×C₃	—	4	1	no	—
29	C₂²	C₂²×A₄	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₄	—	3	1	no	—
32	C₄	—	6	3	no	—
33	C₄	C₂×SL(2,𝔽₃)	1	6	yes	—
34	C₃	—	4	1	no	Sylow
35	C₂	C₂²×SL(2,𝔽₃)	1	1	yes	characteristic
36	C₂	Q₈×A₄	1	1	yes	characteristic
37	C₂	#994	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.