Subgroups — C₂²×C₂²⋊C₄ #512

Order 64.

337 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊C₄	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴	—	2	8	no	—
5	C₂⁴	C₄	1	8	yes	complemented
6	C₂⁴	C₂²	1	6	yes	—
7	C₂⁴	C₂²	1	1	yes	characteristic
8	C₂²×C₄	—	2	8	no	—
9	C₂²×C₄	C₂²	1	12	yes	complemented
10	C₂²⋊C₄	C₂²	1	16	yes	direct product factor
11	C₂³	—	2	32	no	—
12	C₂³	—	2	24	no	—
13	C₂³	C₂×C₄	1	4	yes	—
14	C₂³	C₂×C₄	1	24	yes	complemented
15	C₂³	D₄	1	8	yes	—
16	C₂³	C₂³	1	4	yes	—
17	C₂³	C₂³	1	3	yes	—
18	C₂×C₄	—	2	24	no	—
19	C₂×C₄	C₂³	1	8	yes	complemented
20	C₂²	—	2	48	no	—
21	C₂²	—	2	8	no	—
22	C₂²	C₂²⋊C₄	1	16	yes	direct product factor
23	C₂²	C₂²×C₄	1	6	yes	—
24	C₂²	C₂²×C₄	1	8	yes	complemented
25	C₂²	C₂×D₄	1	12	yes	—
26	C₂²	C₂⁴	1	1	yes	characteristic
27	C₄	—	2	8	no	—
28	C₂	—	2	8	no	—
29	C₂	C₂×C₂²⋊C₄	1	12	yes	direct product factor
30	C₂	C₂³×C₄	1	1	yes	characteristic
31	C₂	C₂²×D₄	1	2	yes	—

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.