Subgroups — C₃×C₄×Q₈ #959

Order 96.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄	C₂	1	3	yes	maximal
3	C₃×C₄²	C₂	1	3	yes	maximal
4	C₄×Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₈	C₄	1	4	yes	direct product factor
6	C₂×C₃×C₄	C₂²	1	3	yes	—
7	C₂×C₃×C₄	C₂²	1	3	yes	—
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₄⋊C₄	C₂×C₃	1	3	yes	—
11	C₄²	C₂×C₃	1	3	yes	—
12	C₂²×C₃	C₂³	1	1	yes	characteristic
13	C₃×C₄	—	2	3	no	—
14	C₃×C₄	C₂×C₄	1	6	yes	—
15	C₃×C₄	Q₈	1	2	yes	direct product factor
16	Q₈	C₃×C₄	1	4	yes	direct product factor
17	C₂×C₄	C₂²×C₃	1	3	yes	—
18	C₂×C₄	C₂²×C₃	1	3	yes	—
19	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₃	#41	1	1	yes	characteristic
23	C₂²	C₂³×C₃	1	1	yes	characteristic
24	C₄	—	2	3	no	—
25	C₄	C₂×C₃×C₄	1	6	yes	—
26	C₄	C₃×Q₈	1	2	yes	direct product factor
27	C₃	C₄×Q₈	1	1	yes	characteristic, direct product factor, Sylow
28	C₂	C₂²×C₃×C₄	1	1	yes	characteristic
29	C₂	C₂×C₃×Q₈	1	1	yes	characteristic
30	C₂	C₃×#41	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.