Subgroups — C₂²×Q₈×C₉ #63721

Order 288.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	12	yes	maximal, direct product factor
2	C₂²×C₄×C₉	C₂	1	3	yes	maximal
3	C₂²×C₃×Q₈	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₉	C₂²	1	1	yes	characteristic
5	Q₈×C₉	C₂²	1	16	yes	direct product factor
6	C₂×C₄×C₉	C₂²	1	18	yes	—
7	C₂×C₃×Q₈	C₂×C₃	1	12	yes	—
8	C₂²×C₃×C₄	C₂×C₃	1	3	yes	—
9	C₂²×C₉	Q₈	1	4	yes	direct product factor
10	C₂²×C₉	C₂³	1	3	yes	—
11	C₄×C₉	C₂³	1	12	yes	—
12	C₂²×Q₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂³×C₃	C₂²×C₃	1	1	yes	characteristic
14	C₃×Q₈	C₂²×C₃	1	16	yes	—
15	C₂×C₃×C₄	C₂²×C₃	1	18	yes	—
16	C₂×C₉	C₂×Q₈	1	6	yes	direct product factor
17	C₂×C₉	C₂⁴	1	1	yes	characteristic
18	C₂×Q₈	C₂×C₉	1	12	yes	direct product factor
19	C₂²×C₄	C₂×C₉	1	3	yes	—
20	C₂²×C₃	C₃×Q₈	1	4	yes	—
21	C₂²×C₃	C₂³×C₃	1	3	yes	—
22	C₃×C₄	C₂³×C₃	1	12	yes	—
23	C₉	C₂²×Q₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³	C₂²×C₉	1	1	yes	characteristic
25	Q₈	C₂²×C₉	1	16	yes	direct product factor
26	C₂×C₄	C₂²×C₉	1	18	yes	—
27	C₂×C₃	C₂×C₃×Q₈	1	6	yes	—
28	C₂×C₃	C₂⁴×C₃	1	1	yes	characteristic
29	C₂²	Q₈×C₉	1	4	yes	direct product factor
30	C₂²	C₂³×C₉	1	3	yes	—
31	C₄	C₂³×C₉	1	12	yes	—
32	C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
33	C₂	C₂×Q₈×C₉	1	6	yes	direct product factor
34	C₂	C₂⁴×C₉	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.