Subgroups — C₂²×D₁₆ #3408

Order 128.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄	—	2	2	no	—
5	C₂×D₈	—	2	6	no	—
6	C₂×D₈	C₂²	1	12	yes	complemented
7	C₂²×C₈	C₂²	1	1	yes	characteristic
8	D₁₆	C₂²	1	16	yes	direct product factor
9	C₂×C₁₆	C₂²	1	6	yes	complemented
10	C₂⁴	—	4	2	no	—
11	C₂×D₄	—	2	12	no	—
12	C₂×D₄	—	4	6	no	—
13	C₂²×C₄	D₄	1	1	yes	characteristic
14	D₈	—	2	12	no	—
15	D₈	C₂³	1	8	yes	complemented
16	C₂×C₈	D₄	1	3	yes	—
17	C₂×C₈	C₂³	1	3	yes	—
18	C₁₆	C₂³	1	4	yes	complemented
19	C₂³	—	4	12	no	—
20	C₂³	—	8	8	no	—
21	C₂³	D₈	1	1	yes	characteristic
22	D₄	—	2	8	no	—
23	D₄	—	4	12	no	—
24	C₂×C₄	D₈	1	3	yes	—
25	C₂×C₄	C₂×D₄	1	3	yes	—
26	C₈	C₂×D₄	1	3	yes	—
27	C₈	C₂⁴	1	1	yes	characteristic
28	C₂²	—	4	8	no	—
29	C₂²	—	8	24	no	—
30	C₂²	D₁₆	1	4	yes	direct product factor
31	C₂²	C₂×D₈	1	3	yes	—
32	C₄	C₂×D₈	1	3	yes	—
33	C₄	C₂²×D₄	1	1	yes	characteristic
34	C₂	—	8	8	no	—
35	C₂	C₂×D₁₆	1	6	yes	direct product factor
36	C₂	C₂²×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	D₈
commutator, Frattini, cosocle	C₈	C₂⁴
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₈ ▷ 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.