Subgroups — C₂³×Dic₆ #5951

Order 192.

850 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	C₂³×Dic₃	C₂	1	2	yes	maximal
3	C₂²×Dic₆	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Q₈	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₂²	1	14	yes	—
7	C₂²×Dic₃	C₂²	1	28	yes	—
8	C₂×Dic₆	C₂²	1	112	yes	direct product factor
9	C₂²×Q₈	—	3	28	no	—
10	C₂³×C₄	—	3	2	no	—
11	C₂³×C₄	D₃	1	1	yes	characteristic
12	C₂³×C₃	Q₈	1	8	yes	complemented
13	C₂³×C₃	C₂³	1	7	yes	—
14	C₂×C₃×C₄	C₂³	1	28	yes	—
15	C₂×Dic₃	C₂³	1	56	yes	—
16	Dic₆	C₂³	1	64	yes	direct product factor
17	C₂⁴	C₂×D₃	1	1	yes	characteristic
18	C₂×Q₈	—	3	112	no	—
19	C₂²×C₄	—	3	28	no	—
20	C₂²×C₄	C₂×D₃	1	14	yes	—
21	C₂²×C₃	C₂×Q₈	1	28	yes	complemented
22	C₂²×C₃	C₂⁴	1	7	yes	—
23	C₃×C₄	C₂⁴	1	8	yes	—
24	Dic₃	C₂⁴	1	16	yes	—
25	C₂³	Dic₆	1	8	yes	direct product factor
26	C₂³	C₂²×D₃	1	7	yes	—
27	Q₈	—	3	64	no	—
28	C₂×C₄	—	3	56	no	—
29	C₂×C₄	C₂²×D₃	1	28	yes	—
30	C₂×C₃	C₂²×Q₈	1	14	yes	complemented
31	C₂×C₃	C₂⁵	1	1	yes	characteristic
32	C₂²	C₂×Dic₆	1	28	yes	direct product factor
33	C₂²	C₂³×D₃	1	7	yes	—
34	C₄	—	3	16	no	—
35	C₄	C₂³×D₃	1	8	yes	—
36	C₃	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
37	C₂	C₂²×Dic₆	1	14	yes	direct product factor
38	C₂	C₂⁴×D₃	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.