Subgroups — Q₈×C₈₃⋊C₁₆ #24909367

Order 10624.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₈₃⋊C₁₆)	C₂	1	3	yes	maximal
2	C₄×C₈₃⋊C₁₆	C₂	1	3	yes	maximal
3	C₈×Q₈×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	C₂²	1	3	yes	—
5	C₂×C₈₃⋊C₁₆	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₈₃	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₈₃	C₄	1	3	yes	—
8	C₄×C₈×C₈₃	C₂²	1	3	yes	—
9	C₈₃⋊C₁₆	—	2	3	no	—
10	C₈₃⋊C₁₆	Q₈	1	2	yes	direct product factor
11	C₂×Q₈×C₈₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₈₃	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
14	C₄⋊C₄×C₈₃	C₈	1	3	yes	—
15	C₄²×C₈₃	C₂×C₄	1	3	yes	—
16	Q₈×C₈₃	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₈₃	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₈₃	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
20	C₈×C₈₃	—	2	3	no	—
21	C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
22	C₈×C₈₃	#41	1	1	yes	characteristic
23	C₂²×C₈₃	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₈₃	—	2	3	no	—
25	C₄×C₈₃	C₂×C₁₆	1	6	yes	—
26	C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₈₃	#131	1	1	yes	characteristic
28	C₂×C₈₃	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₈₃	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₈₃	#504	1	1	yes	characteristic
31	Q₈×C₁₆	—	83	1	no	maximal, Sylow
32	C₈₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₈×Q₈	D₈₃	1	1	yes	characteristic
34	C₄⋊C₁₆	—	83	3	no	—
35	C₄×C₁₆	—	83	3	no	—
36	C₄×Q₈	Dic₈₃	1	1	yes	characteristic
37	C₂×C₁₆	—	83	1	no	—
38	C₂×C₁₆	—	83	3	no	—
39	C₄⋊C₈	Dic₈₃	1	3	yes	—
40	C₄×C₈	C₂×D₈₃	1	3	yes	—
41	C₂×Q₈	C₈₃⋊C₈	1	1	yes	characteristic
42	C₂×C₈	C₂×Dic₈₃	1	3	yes	—
43	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
44	C₄⋊C₄	C₈₃⋊C₈	1	3	yes	—
45	C₄²	C₂×Dic₈₃	1	3	yes	—
46	C₁₆	—	83	2	no	—
47	C₁₆	—	166	3	no	—
48	Q₈	C₈₃⋊C₁₆	1	4	yes	direct product factor
49	C₂×C₄	C₂×C₈₃⋊C₈	1	3	yes	—
50	C₂×C₄	C₂×C₈₃⋊C₈	1	3	yes	—
51	C₂×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₈₃	1	1	yes	characteristic
54	C₈	#13050591	1	1	yes	characteristic
55	C₂²	C₂²×C₈₃⋊C₈	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×C₈₃⋊C₁₆	1	6	yes	—
58	C₄	Q₈×Dic₈₃	1	1	yes	characteristic
59	C₄	#14581799	1	1	yes	characteristic
60	C₂	Q₈×C₈₃⋊C₈	1	1	yes	characteristic
61	C₂	C₂²×C₈₃⋊C₁₆	1	1	yes	characteristic
62	C₂	#19128118	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₈₃
commutator	C₂×C₈₃	C₂²×C₁₆
Fitting	C₈×Q₈×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	C₂²×C₈
cosocle	C₂×C₈×C₈₃	C₂³
hypercenter	C₈×Q₈	D₈₃
hypocenter	C₈₃	Q₈×C₁₆
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
10. C₈₃⋊C₁₆	Q₈	direct (N × H)
16. Q₈×C₈₃	C₁₆	semidirect
32. C₈₃	Q₈×C₁₆	semidirect
48. Q₈	C₈₃⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊(C₈₃⋊C₁₆)	2
C₄×C₈₃⋊C₁₆	2
C₈×Q₈×C₈₃	2
Q₈×C₁₆	83

Subgroups — Q8×C83⋊C16 #24909367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₈₃⋊C₁₆ #24909367