Subgroups — C₂×C₄×Q₈ #516

Order 64.

149 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₄	C₂	1	3	yes	maximal
4	C₂×C₄²	C₂	1	3	yes	maximal
5	C₂×Q₈	C₄	1	8	yes	direct product factor
6	C₂×Q₈	C₂²	1	4	yes	—
7	C₂²×C₄	C₂²	1	3	yes	—
8	C₂²×C₄	C₂²	1	3	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₄⋊C₄	C₂²	1	12	yes	—
11	C₄²	C₂²	1	12	yes	—
12	C₂³	C₂³	1	1	yes	characteristic
13	Q₈	C₂×C₄	1	16	yes	direct product factor
14	C₂×C₄	—	2	6	no	—
15	C₂×C₄	C₂×C₄	1	12	yes	—
16	C₂×C₄	Q₈	1	4	yes	direct product factor
17	C₂×C₄	C₂³	1	6	yes	—
18	C₂×C₄	C₂³	1	6	yes	—
19	C₂×C₄	C₂³	1	2	yes	—
20	C₂²	C₂²×C₄	1	2	yes	—
21	C₂²	C₂×Q₈	1	2	yes	—
22	C₂²	#41	1	2	yes	—
23	C₂²	C₂⁴	1	1	yes	characteristic
24	C₄	—	2	6	no	—
25	C₄	C₂²×C₄	1	12	yes	—
26	C₄	C₂×Q₈	1	4	yes	direct product factor
27	C₂	C₄×Q₈	1	4	yes	direct product factor
28	C₂	C₂³×C₄	1	1	yes	characteristic
29	C₂	C₂²×Q₈	1	1	yes	characteristic
30	C₂	C₂×#41	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.