Subgroups — C₂²×C₄⋊Q₈ #3441

Order 128.

812 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	C₂×C₄⋊Q₈	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈	—	2	16	no	—
6	C₂²×Q₈	C₂²	1	24	yes	—
7	C₂³×C₄	C₂²	1	4	yes	—
8	C₂³×C₄	C₂²	1	1	yes	characteristic
9	C₂³×C₄	C₂²	1	2	yes	—
10	C₄⋊Q₈	C₂²	1	64	yes	direct product factor
11	C₂×C₄⋊C₄	C₂²	1	48	yes	—
12	C₂×C₄²	C₂²	1	12	yes	—
13	C₂⁴	C₂³	1	1	yes	characteristic
14	C₂×Q₈	—	2	96	no	—
15	C₂×Q₈	C₂³	1	32	yes	—
16	C₂²×C₄	—	2	16	no	—
17	C₂²×C₄	D₄	1	8	yes	—
18	C₂²×C₄	Q₈	1	16	yes	complemented
19	C₂²×C₄	C₂³	1	24	yes	—
20	C₂²×C₄	C₂³	1	6	yes	—
21	C₂²×C₄	C₂³	1	12	yes	—
22	C₄⋊C₄	C₂³	1	64	yes	—
23	C₄²	C₂³	1	16	yes	—
24	C₂³	C₂×D₄	1	4	yes	—
25	C₂³	C₂×Q₈	1	8	yes	—
26	C₂³	C₂⁴	1	3	yes	—
27	Q₈	—	2	64	no	—
28	C₂×C₄	—	2	48	no	—
29	C₂×C₄	C₂×D₄	1	24	yes	—
30	C₂×C₄	C₂×Q₈	1	48	yes	complemented
31	C₂×C₄	C₂⁴	1	16	yes	—
32	C₂×C₄	C₂⁴	1	4	yes	—
33	C₂×C₄	C₂⁴	1	8	yes	—
34	C₂²	C₄⋊Q₈	1	16	yes	direct product factor
35	C₂²	C₂²×D₄	1	6	yes	—
36	C₂²	C₂²×Q₈	1	12	yes	—
37	C₂²	C₂⁵	1	1	yes	characteristic
38	C₄	—	2	16	no	—
39	C₄	C₂²×D₄	1	8	yes	—
40	C₄	C₂²×Q₈	1	16	yes	complemented
41	C₂	C₂×C₄⋊Q₈	1	12	yes	direct product factor
42	C₂	C₂³×D₄	1	1	yes	characteristic
43	C₂	C₂³×Q₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂² ▷ 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.