Subgroups — C₂³×SD₁₆ #3575

Order 128.

860 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×SD₁₆	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵	—	2	1	no	—
6	C₂²×Q₈	—	2	7	no	—
7	C₂²×Q₈	C₂²	1	14	yes	complemented
8	C₂²×D₄	—	2	7	no	—
9	C₂²×D₄	C₂²	1	14	yes	—
10	C₂³×C₄	—	2	1	no	—
11	C₂³×C₄	C₂²	1	1	yes	characteristic
12	C₂×SD₁₆	C₂²	1	112	yes	direct product factor
13	C₂²×C₈	C₂²	1	14	yes	complemented
14	C₂⁴	—	2	14	no	—
15	C₂⁴	—	4	8	no	—
16	C₂⁴	D₄	1	1	yes	characteristic
17	C₂×Q₈	—	2	42	no	—
18	C₂×Q₈	C₂³	1	28	yes	complemented
19	C₂×D₄	—	2	42	no	—
20	C₂×D₄	C₂³	1	28	yes	—
21	C₂²×C₄	—	2	14	no	—
22	C₂²×C₄	D₄	1	7	yes	—
23	C₂²×C₄	C₂³	1	7	yes	—
24	SD₁₆	C₂³	1	64	yes	direct product factor
25	C₂×C₈	C₂³	1	28	yes	complemented
26	C₂³	—	2	28	no	—
27	C₂³	—	4	56	no	—
28	C₂³	SD₁₆	1	8	yes	direct product factor
29	C₂³	C₂×D₄	1	7	yes	—
30	Q₈	—	2	28	no	—
31	Q₈	C₂⁴	1	8	yes	complemented
32	D₄	—	2	28	no	—
33	D₄	C₂⁴	1	8	yes	—
34	C₂×C₄	—	2	28	no	—
35	C₂×C₄	C₂×D₄	1	21	yes	—
36	C₂×C₄	C₂⁴	1	7	yes	—
37	C₈	C₂⁴	1	8	yes	complemented
38	C₂²	—	2	8	no	—
39	C₂²	—	4	56	no	—
40	C₂²	C₂×SD₁₆	1	28	yes	direct product factor
41	C₂²	C₂²×D₄	1	7	yes	—
42	C₄	—	2	8	no	—
43	C₄	C₂²×D₄	1	7	yes	—
44	C₄	C₂⁵	1	1	yes	characteristic
45	C₂	—	4	8	no	—
46	C₂	C₂²×SD₁₆	1	14	yes	direct product factor
47	C₂	C₂³×D₄	1	1	yes	characteristic

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