Subgroups — C₃×C₄×C₁₆ #4592

Order 192.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄²	C₄	1	1	yes	characteristic
7	C₃×C₁₆	C₄	1	4	yes	direct product factor
8	C₂×C₁₆	C₂×C₃	1	2	yes	—
9	C₄×C₈	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₄	C₈	1	2	yes	—
11	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	C₈	1	2	yes	—
13	C₃×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₈	C₃×C₄	1	1	yes	characteristic
15	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
16	C₄²	C₃×C₄	1	1	yes	characteristic
17	C₁₆	C₃×C₄	1	4	yes	direct product factor
18	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
19	C₃×C₄	C₁₆	1	4	yes	direct product factor
20	C₃×C₄	C₄²	1	1	yes	characteristic
21	C₃×C₄	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄	C₃×C₈	1	2	yes	—
23	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
24	C₈	C₃×C₈	1	2	yes	—
25	C₈	C₂×C₃×C₄	1	2	yes	—
26	C₂×C₃	C₄×C₈	1	1	yes	characteristic
27	C₂×C₃	C₂×C₁₆	1	2	yes	—
28	C₂²	C₂×C₃×C₈	1	1	yes	characteristic
29	C₄	C₃×C₁₆	1	4	yes	direct product factor
30	C₄	C₃×C₄²	1	1	yes	characteristic
31	C₄	C₂×C₃×C₈	1	1	yes	characteristic
32	C₃	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×C₄×C₈	1	1	yes	characteristic
34	C₂	C₂×C₃×C₁₆	1	2	yes	—

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.