Subgroups — C₂³×Q₁₆ #3576

Order 128.

732 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈	C₂	1	2	yes	maximal
2	C₂²×Q₁₆	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈	—	2	14	no	—
5	C₂²×Q₈	C₂²	1	28	yes	—
6	C₂³×C₄	—	2	2	no	—
7	C₂³×C₄	C₂²	1	1	yes	characteristic
8	C₂×Q₁₆	C₂²	1	112	yes	direct product factor
9	C₂²×C₈	C₂²	1	14	yes	—
10	C₂⁴	D₄	1	1	yes	characteristic
11	C₂×Q₈	—	2	84	no	—
12	C₂×Q₈	C₂³	1	56	yes	—
13	C₂²×C₄	—	2	28	no	—
14	C₂²×C₄	D₄	1	7	yes	—
15	C₂²×C₄	C₂³	1	7	yes	—
16	Q₁₆	C₂³	1	64	yes	direct product factor
17	C₂×C₈	C₂³	1	28	yes	—
18	C₂³	Q₁₆	1	8	yes	direct product factor
19	C₂³	C₂×D₄	1	7	yes	—
20	Q₈	—	2	56	no	—
21	Q₈	C₂⁴	1	16	yes	—
22	C₂×C₄	—	2	56	no	—
23	C₂×C₄	C₂×D₄	1	21	yes	—
24	C₂×C₄	C₂⁴	1	7	yes	—
25	C₈	C₂⁴	1	8	yes	—
26	C₂²	C₂×Q₁₆	1	28	yes	direct product factor
27	C₂²	C₂²×D₄	1	7	yes	—
28	C₄	—	2	16	no	—
29	C₄	C₂²×D₄	1	7	yes	—
30	C₄	C₂⁵	1	1	yes	characteristic
31	C₂	C₂²×Q₁₆	1	14	yes	direct product factor
32	C₂	C₂³×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴	D₄
commutator, Frattini, cosocle	C₄	C₂⁵
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×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.