Subgroups — C₂³×C₃⋊C₈ #5780

Order 192.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊C₈	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₈	—	3	1	no	maximal, Sylow
4	C₂⁴×C₃	C₄	1	1	yes	characteristic
5	C₂²×C₃×C₄	C₄	1	7	yes	—
6	C₂²×C₃×C₄	C₂²	1	7	yes	—
7	C₂×C₃⋊C₈	C₂²	1	28	yes	direct product factor
8	C₂³×C₄	D₃	1	1	yes	characteristic
9	C₂²×C₈	—	3	14	no	—
10	C₂³×C₃	C₈	1	8	yes	complemented
11	C₂³×C₃	C₂×C₄	1	7	yes	—
12	C₂×C₃×C₄	C₂×C₄	1	21	yes	—
13	C₂×C₃×C₄	C₂³	1	7	yes	—
14	C₃⋊C₈	C₂³	1	8	yes	direct product factor
15	C₂⁴	Dic₃	1	1	yes	characteristic
16	C₂²×C₄	Dic₃	1	7	yes	—
17	C₂²×C₄	C₂×D₃	1	7	yes	—
18	C₂×C₈	—	3	28	no	—
19	C₂²×C₃	C₂×C₈	1	28	yes	complemented
20	C₂²×C₃	C₂²×C₄	1	7	yes	—
21	C₃×C₄	C₂²×C₄	1	7	yes	—
22	C₃×C₄	C₂⁴	1	1	yes	characteristic
23	C₂³	C₃⋊C₈	1	8	yes	direct product factor
24	C₂³	C₂×Dic₃	1	7	yes	—
25	C₂×C₄	C₂×Dic₃	1	21	yes	—
26	C₂×C₄	C₂²×D₃	1	7	yes	—
27	C₈	—	3	8	no	—
28	C₂×C₃	C₂²×C₈	1	14	yes	complemented
29	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
30	C₂²	C₂×C₃⋊C₈	1	28	yes	direct product factor
31	C₂²	C₂²×Dic₃	1	7	yes	—
32	C₄	C₂²×Dic₃	1	7	yes	—
33	C₄	C₂³×D₃	1	1	yes	characteristic
34	C₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
35	C₂	C₂²×C₃⋊C₈	1	14	yes	direct product factor
36	C₂	C₂³×Dic₃	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.