Subgroups — C₂²×C₃×C₈ #969

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂³×C₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄	C₄	1	3	yes	—
6	C₂×C₃×C₄	C₂²	1	3	yes	—
7	C₃×C₈	C₂²	1	4	yes	direct product factor
8	C₂²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₂×C₈	C₂×C₃	1	6	yes	direct product factor
10	C₂²×C₃	C₈	1	4	yes	direct product factor
11	C₂²×C₃	C₂×C₄	1	3	yes	—
12	C₃×C₄	C₂×C₄	1	3	yes	—
13	C₃×C₄	C₂³	1	1	yes	characteristic
14	C₂³	C₃×C₄	1	1	yes	characteristic
15	C₂×C₄	C₃×C₄	1	3	yes	—
16	C₂×C₄	C₂²×C₃	1	3	yes	—
17	C₈	C₂²×C₃	1	4	yes	direct product factor
18	C₂×C₃	C₂×C₈	1	6	yes	direct product factor
19	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
20	C₂²	C₃×C₈	1	4	yes	direct product factor
21	C₂²	C₂×C₃×C₄	1	3	yes	—
22	C₄	C₂×C₃×C₄	1	3	yes	—
23	C₄	C₂³×C₃	1	1	yes	characteristic
24	C₃	C₂²×C₈	1	1	yes	characteristic, direct product factor, Sylow
25	C₂	C₂×C₃×C₈	1	6	yes	direct product factor
26	C₂	C₂²×C₃×C₄	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.