Subgroups — C₂⁴×Q₁₆ #63079

Order 256.

5583 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈	C₂	1	2	yes	maximal
2	C₂³×Q₁₆	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈	—	2	30	no	—
5	C₂³×Q₈	C₂²	1	60	yes	—
6	C₂⁴×C₄	—	2	2	no	—
7	C₂⁴×C₄	C₂²	1	1	yes	characteristic
8	C₂²×Q₁₆	C₂²	1	560	yes	direct product factor
9	C₂³×C₈	C₂²	1	30	yes	—
10	C₂⁵	D₄	1	1	yes	characteristic
11	C₂²×Q₈	—	2	420	no	—
12	C₂²×Q₈	C₂³	1	280	yes	—
13	C₂³×C₄	—	2	60	no	—
14	C₂³×C₄	D₄	1	15	yes	—
15	C₂³×C₄	C₂³	1	15	yes	—
16	C₂×Q₁₆	C₂³	1	960	yes	direct product factor
17	C₂²×C₈	C₂³	1	140	yes	—
18	C₂⁴	Q₁₆	1	16	yes	direct product factor
19	C₂⁴	C₂×D₄	1	15	yes	—
20	C₂×Q₈	—	2	840	no	—
21	C₂×Q₈	C₂⁴	1	240	yes	—
22	C₂²×C₄	—	2	280	no	—
23	C₂²×C₄	C₂×D₄	1	105	yes	—
24	C₂²×C₄	C₂⁴	1	35	yes	—
25	Q₁₆	C₂⁴	1	256	yes	direct product factor
26	C₂×C₈	C₂⁴	1	120	yes	—
27	C₂³	C₂×Q₁₆	1	120	yes	direct product factor
28	C₂³	C₂²×D₄	1	35	yes	—
29	Q₈	—	2	240	no	—
30	Q₈	C₂⁵	1	32	yes	—
31	C₂×C₄	—	2	240	no	—
32	C₂×C₄	C₂²×D₄	1	105	yes	—
33	C₂×C₄	C₂⁵	1	15	yes	—
34	C₈	C₂⁵	1	16	yes	—
35	C₂²	C₂²×Q₁₆	1	140	yes	direct product factor
36	C₂²	C₂³×D₄	1	15	yes	—
37	C₄	—	2	32	no	—
38	C₄	C₂³×D₄	1	15	yes	—
39	C₄	C₂⁶	1	1	yes	characteristic
40	C₂	C₂³×Q₁₆	1	30	yes	direct product factor
41	C₂	C₂⁴×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁵	D₄
commutator, Frattini, cosocle	C₄	C₂⁶
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

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.