Subgroups — Q₈×C₅₉⋊C₁₆ #21426000

Order 7552.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅₉⋊C₁₆)	C₂	1	3	yes	maximal
2	C₄×C₅₉⋊C₁₆	C₂	1	3	yes	maximal
3	C₈×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₁₆	C₂²	1	3	yes	—
5	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₅₉	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₅₉	C₄	1	3	yes	—
8	C₄×C₈×C₅₉	C₂²	1	3	yes	—
9	C₂×Q₈×C₅₉	C₈	1	1	yes	characteristic
10	C₂×C₈×C₅₉	C₂×C₄	1	3	yes	—
11	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
12	C₄⋊C₄×C₅₉	C₈	1	3	yes	—
13	C₄²×C₅₉	C₂×C₄	1	3	yes	—
14	C₅₉⋊C₁₆	—	2	3	no	—
15	C₅₉⋊C₁₆	Q₈	1	2	yes	direct product factor
16	Q₈×C₅₉	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₅₉	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₅₉	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
20	C₈×C₅₉	—	2	3	no	—
21	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
22	C₈×C₅₉	#41	1	1	yes	characteristic
23	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₅₉	—	2	3	no	—
25	C₄×C₅₉	C₂×C₁₆	1	6	yes	—
26	C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₅₉	#131	1	1	yes	characteristic
28	Q₈×C₁₆	—	59	1	no	maximal, Sylow
29	C₂×C₅₉	C₈×Q₈	1	1	yes	characteristic
30	C₂×C₅₉	C₂²×C₁₆	1	1	yes	characteristic
31	C₂×C₅₉	#504	1	1	yes	characteristic
32	C₈×Q₈	D₅₉	1	1	yes	characteristic
33	C₄⋊C₁₆	—	59	3	no	—
34	C₄×C₁₆	—	59	3	no	—
35	C₅₉	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₄×Q₈	Dic₅₉	1	1	yes	characteristic
37	C₂×C₁₆	—	59	1	no	—
38	C₂×C₁₆	—	59	3	no	—
39	C₄⋊C₈	Dic₅₉	1	3	yes	—
40	C₄×C₈	C₂×D₅₉	1	3	yes	—
41	C₂×Q₈	C₅₉⋊C₈	1	1	yes	characteristic
42	C₂×C₈	C₂×Dic₅₉	1	3	yes	—
43	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
44	C₄⋊C₄	C₅₉⋊C₈	1	3	yes	—
45	C₄²	C₂×Dic₅₉	1	3	yes	—
46	C₁₆	—	59	2	no	—
47	C₁₆	—	118	3	no	—
48	Q₈	C₅₉⋊C₁₆	1	4	yes	direct product factor
49	C₂×C₄	C₂×C₅₉⋊C₈	1	3	yes	—
50	C₂×C₄	C₂×C₅₉⋊C₈	1	3	yes	—
51	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₅₉	1	1	yes	characteristic
54	C₈	#11745689	1	1	yes	characteristic
55	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×C₅₉⋊C₁₆	1	6	yes	—
58	C₄	Q₈×Dic₅₉	1	1	yes	characteristic
59	C₄	#14273734	1	1	yes	characteristic
60	C₂	Q₈×C₅₉⋊C₈	1	1	yes	characteristic
61	C₂	C₂²×C₅₉⋊C₁₆	1	1	yes	characteristic
62	C₂	#16837819	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₉
commutator	C₂×C₅₉	C₂²×C₁₆
Fitting	C₈×Q₈×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×C₈
hypercenter	C₈×Q₈	D₅₉
hypocenter	C₅₉	Q₈×C₁₆
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
15. C₅₉⋊C₁₆	Q₈	direct (N × H)
16. Q₈×C₅₉	C₁₆	semidirect
35. C₅₉	Q₈×C₁₆	semidirect
48. Q₈	C₅₉⋊C₁₆	direct (N × H)

Subgroups — Q8×C59⋊C16 #21426000

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×C₅₉⋊C₁₆ #21426000