Subgroups — Q₈×D₈ #3378

Order 128.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Q₈	C₂	1	2	yes	maximal, complemented
2	#500	C₂	1	3	yes	maximal, complemented
3	#474	C₂	1	6	yes	maximal, complemented
4	C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₈	C₂	1	3	yes	maximal
6	C₂²×Q₈	—	2	2	no	—
7	C₂×D₈	C₂²	1	1	yes	characteristic
8	C₄⋊Q₈	C₂²	1	6	yes	—
9	C₂²⋊Q₈	—	2	6	no	—
10	C₄×Q₈	C₂²	1	1	yes	characteristic
11	C₄×D₄	C₂²	1	6	yes	—
12	#107	C₂²	1	3	yes	—
13	#107	C₂²	1	6	yes	—
14	C₄⋊C₈	C₂²	1	3	yes	—
15	#102	C₂²	1	6	yes	—
16	C₄×C₈	C₂²	1	3	yes	—
17	C₂×Q₈	—	2	6	no	—
18	C₂×Q₈	—	4	8	no	—
19	C₂×Q₈	D₄	1	1	yes	characteristic
20	C₂×D₄	C₂³	1	2	yes	—
21	C₂²×C₄	—	2	6	no	—
22	D₈	Q₈	1	4	yes	direct product factor
23	C₂×C₈	C₂³	1	3	yes	—
24	C₂×C₈	C₂³	1	1	yes	characteristic
25	C₄⋊C₄	—	2	6	no	—
26	C₄⋊C₄	D₄	1	3	yes	—
27	C₄⋊C₄	C₂³	1	6	yes	—
28	C₂²⋊C₄	—	2	6	no	—
29	C₄²	C₂³	1	3	yes	—
30	C₂³	—	2	2	no	—
31	Q₈	—	4	12	no	—
32	Q₈	D₈	1	4	yes	direct product factor
33	D₄	—	2	2	no	—
34	D₄	C₂×Q₈	1	4	yes	complemented
35	C₂×C₄	—	2	6	no	—
36	C₂×C₄	—	4	12	no	—
37	C₂×C₄	C₂×D₄	1	3	yes	—
38	C₂×C₄	C₂×D₄	1	3	yes	—
39	C₂×C₄	C₂⁴	1	1	yes	characteristic
40	C₈	—	2	3	no	—
41	C₈	C₂×Q₈	1	2	yes	complemented
42	C₂²	—	2	4	no	—
43	C₂²	—	4	2	no	—
44	C₂²	—	4	2	no	—
45	C₂²	C₂²×D₄	1	1	yes	characteristic
46	C₄	—	2	3	no	—
47	C₄	—	4	6	no	—
48	C₄	C₂×D₈	1	6	yes	—
49	C₄	C₂²×Q₈	1	1	yes	characteristic
50	C₄	2₋¹⁺⁴	1	1	yes	characteristic
51	C₂	—	4	4	no	—
52	C₂	D₄×Q₈	1	1	yes	characteristic
53	C₂	C₂²×D₈	1	1	yes	characteristic
54	C₂	#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₄×Q₈	C₂	semidirect
2. #500	C₂	semidirect
3. #474	C₂	semidirect
4. C₈×Q₈	C₂	semidirect
22. D₈	Q₈	direct (N × H)
32. Q₈	D₈	direct (N × H)
34. D₄	C₂×Q₈	semidirect
41. C₈	C₂×Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×Q₈	2
#500	2
#474	2
C₈×Q₈	2
C₄×D₈	2

Subgroups — Q8×D8 #3378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×D₈ #3378