Subgroups — Q₈×#3926 #12019931

Order 1280.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3926	C₂	1	3	yes	maximal
3	C₄×#3926	C₂	1	3	yes	maximal
4	C₅×C₈×Q₈	C₄	1	1	yes	characteristic
5	C₅×C₄⋊C₁₆	C₄	1	3	yes	—
6	C₄×C₅×C₁₆	C₂²	1	3	yes	—
7	C₂×#3926	C₂²	1	3	yes	—
8	C₂×#3926	C₂²	1	1	yes	characteristic
9	Q₈×C₃₂	—	5	1	no	maximal, Sylow
10	C₄×C₅×Q₈	C₈	1	1	yes	characteristic
11	C₂×C₅×C₁₆	C₂×C₄	1	3	yes	—
12	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
13	C₅×C₄⋊C₈	C₈	1	3	yes	—
14	C₄×C₅×C₈	C₂×C₄	1	3	yes	—
15	#3926	—	2	3	no	—
16	#3926	Q₈	1	2	yes	direct product factor
17	Q₈×C₁₆	D₅	1	1	yes	characteristic
18	C₄⋊C₃₂	—	5	3	no	—
19	C₄×C₃₂	—	5	3	no	—
20	C₂×C₅×Q₈	C₁₆	1	1	yes	characteristic
21	C₂×C₅×C₈	C₂×C₈	1	3	yes	—
22	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
23	C₅×C₄⋊C₄	C₁₆	1	3	yes	—
24	C₄²×C₅	C₂×C₈	1	3	yes	—
25	C₅×C₁₆	—	2	3	no	—
26	C₅×C₁₆	C₂×Q₈	1	1	yes	characteristic
27	C₅×C₁₆	#41	1	1	yes	characteristic
28	C₈×Q₈	Dic₅	1	1	yes	characteristic
29	C₂×C₃₂	—	5	1	no	—
30	C₂×C₃₂	—	5	3	no	—
31	C₄⋊C₁₆	Dic₅	1	3	yes	—
32	C₄×C₁₆	C₂×D₅	1	3	yes	—
33	C₅×Q₈	C₃₂	1	4	yes	complemented
34	C₂×C₄×C₅	C₂×C₁₆	1	3	yes	—
35	C₂×C₄×C₅	C₂×C₁₆	1	3	yes	—
36	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
37	C₅×C₈	—	2	3	no	—
38	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
39	C₅×C₈	#131	1	1	yes	characteristic
40	C₄×Q₈	#168	1	1	yes	characteristic
41	C₂×C₁₆	C₂×Dic₅	1	3	yes	—
42	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
43	C₄⋊C₈	#168	1	3	yes	—
44	C₄×C₈	C₂×Dic₅	1	3	yes	—
45	C₃₂	—	5	2	no	—
46	C₃₂	—	10	3	no	—
47	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
48	C₄×C₅	—	2	3	no	—
49	C₄×C₅	C₂×C₃₂	1	6	yes	—
50	C₄×C₅	C₈×Q₈	1	1	yes	characteristic
51	C₄×C₅	#504	1	1	yes	characteristic
52	C₂×Q₈	#672	1	1	yes	characteristic
53	C₂×C₈	C₂×#168	1	3	yes	—
54	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
55	C₄⋊C₄	#672	1	3	yes	—
56	C₄²	C₂×#168	1	3	yes	—
57	C₁₆	—	2	3	no	—
58	C₁₆	Q₈×D₅	1	1	yes	characteristic
59	C₁₆	#713	1	1	yes	characteristic
60	C₂×C₅	Q₈×C₁₆	1	1	yes	characteristic
61	C₂×C₅	C₂²×C₃₂	1	1	yes	characteristic
62	C₂×C₅	#2258	1	1	yes	characteristic
63	Q₈	#3926	1	4	yes	direct product factor
64	C₂×C₄	C₂×#672	1	3	yes	—
65	C₂×C₄	C₂×#672	1	3	yes	—
66	C₂×C₄	C₂²×#168	1	1	yes	characteristic
67	C₈	—	2	3	no	—
68	C₈	Q₈×Dic₅	1	1	yes	characteristic
69	C₈	#4094	1	1	yes	characteristic
70	C₅	Q₈×C₃₂	1	1	yes	characteristic, complemented, Sylow
71	C₂²	C₂²×#672	1	1	yes	characteristic
72	C₄	—	2	3	no	—
73	C₄	C₂×#3926	1	6	yes	—
74	C₄	Q₈×#168	1	1	yes	characteristic
75	C₄	#65429	1	1	yes	characteristic
76	C₂	Q₈×#672	1	1	yes	characteristic
77	C₂	C₂²×#3926	1	1	yes	characteristic
78	C₂	#10602244	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃₂
Fitting	C₅×Q₈×C₁₆	C₂
socle, prime radical	C₂²×C₅	C₂²×C₁₆
cosocle	C₂×C₅×C₁₆	C₂³
hypercenter	Q₈×C₁₆	D₅
hypocenter	C₅	Q₈×C₃₂
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₆ ◁ Q₈×C₁₆

Complements

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

N	H ≅ G/N	type
16. #3926	Q₈	direct (N × H)
33. C₅×Q₈	C₃₂	semidirect
63. Q₈	#3926	direct (N × H)
70. C₅	Q₈×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₅×Q₈×C₁₆	2
C₄⋊#3926	2
C₄×#3926	2
Q₈×C₃₂	5

Subgroups — Q8×#3926 #12019931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#3926 #12019931