Subgroups — C₃×C₄⋊C₈ #848

Order 96.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	2	yes	maximal
2	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃×C₈	—	2	2	no	—
8	C₂×C₈	C₂×C₃	1	2	yes	—
9	C₄²	C₂×C₃	1	1	yes	characteristic
10	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄	—	2	1	no	—
12	C₃×C₄	C₈	1	2	yes	complemented
13	C₃×C₄	D₄	1	1	yes	characteristic
14	C₃×C₄	Q₈	1	1	yes	characteristic
15	C₂×C₄	C₃×C₄	1	1	yes	characteristic
16	C₂×C₄	C₃×C₄	1	1	yes	characteristic
17	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
18	C₈	—	2	2	no	—
19	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₃	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃	M₁₆	1	1	yes	characteristic
22	C₂²	C₂×C₃×C₄	1	1	yes	characteristic
23	C₄	—	2	1	no	—
24	C₄	C₃×C₈	1	2	yes	complemented
25	C₄	C₃×D₄	1	1	yes	characteristic
26	C₄	C₃×Q₈	1	1	yes	characteristic
27	C₃	C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
28	C₂	C₃×C₄⋊C₄	1	1	yes	characteristic
29	C₂	C₂×C₃×C₈	1	1	yes	characteristic
30	C₂	C₃×M₁₆	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.