Subgroups — C₂²×SD₃₂ #3409

Order 128.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₈	C₂	1	1	yes	maximal, characteristic
3	C₂×SD₃₂	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈	—	2	1	no	—
6	C₂²×D₄	—	2	1	no	—
7	C₂×Q₁₆	—	2	3	no	—
8	C₂×Q₁₆	C₂²	1	6	yes	complemented
9	C₂×D₈	—	2	3	no	—
10	C₂×D₈	C₂²	1	6	yes	—
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	SD₃₂	C₂²	1	16	yes	direct product factor
13	C₂×C₁₆	C₂²	1	6	yes	complemented
14	C₂⁴	—	4	1	no	—
15	C₂×Q₈	—	2	6	no	—
16	C₂×Q₈	—	4	3	no	—
17	C₂×D₄	—	2	6	no	—
18	C₂×D₄	—	4	3	no	—
19	C₂²×C₄	—	4	1	no	—
20	C₂²×C₄	D₄	1	1	yes	characteristic
21	Q₁₆	—	2	6	no	—
22	Q₁₆	C₂³	1	4	yes	complemented
23	D₈	—	2	6	no	—
24	D₈	C₂³	1	4	yes	—
25	C₂×C₈	D₄	1	3	yes	—
26	C₂×C₈	C₂³	1	3	yes	—
27	C₁₆	C₂³	1	4	yes	complemented
28	C₂³	—	4	6	no	—
29	C₂³	—	8	4	no	—
30	C₂³	D₈	1	1	yes	characteristic
31	Q₈	—	2	4	no	—
32	Q₈	—	4	6	no	—
33	D₄	—	2	4	no	—
34	D₄	—	4	6	no	—
35	C₂×C₄	—	4	6	no	—
36	C₂×C₄	D₈	1	3	yes	—
37	C₂×C₄	C₂×D₄	1	3	yes	—
38	C₈	C₂×D₄	1	3	yes	—
39	C₈	C₂⁴	1	1	yes	characteristic
40	C₂²	—	4	4	no	—
41	C₂²	—	8	12	no	—
42	C₂²	SD₃₂	1	4	yes	direct product factor
43	C₂²	C₂×D₈	1	3	yes	—
44	C₄	—	4	4	no	—
45	C₄	C₂×D₈	1	3	yes	—
46	C₄	C₂²×D₄	1	1	yes	characteristic
47	C₂	—	8	4	no	—
48	C₂	C₂×SD₃₂	1	6	yes	direct product factor
49	C₂	C₂²×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	D₈
commutator, Frattini, cosocle	C₈	C₂⁴
prime radical	C₂²×D₈	C₂
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.