Subgroups — Q₈×#6090 #13116740

Order 1664.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6090	C₂	1	3	yes	maximal
3	C₄×#6090	C₂	1	3	yes	maximal
4	C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
5	C₁₃×C₄⋊C₈	C₄	1	3	yes	—
6	C₄×C₈×C₁₃	C₂²	1	3	yes	—
7	C₂×#6090	C₂²	1	3	yes	—
8	C₂×#6090	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
10	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
11	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₈	1	3	yes	—
13	C₄²×C₁₃	C₂×C₄	1	3	yes	—
14	#6090	—	2	3	no	—
15	#6090	Q₈	1	2	yes	direct product factor
16	Q₈×C₁₆	—	13	1	no	maximal, Sylow
17	Q₈×C₁₃	C₁₆	1	4	yes	complemented
18	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
20	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₈×C₁₃	—	2	3	no	—
22	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
23	C₈×C₁₃	#41	1	1	yes	characteristic
24	C₈×Q₈	D₁₃	1	1	yes	characteristic
25	C₄⋊C₁₆	—	13	3	no	—
26	C₄×C₁₆	—	13	3	no	—
27	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
28	C₄×C₁₃	—	2	3	no	—
29	C₄×C₁₃	C₂×C₁₆	1	6	yes	—
30	C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
31	C₄×C₁₃	#131	1	1	yes	characteristic
32	C₄×Q₈	Dic₁₃	1	1	yes	characteristic
33	C₂×C₁₆	—	13	1	no	—
34	C₂×C₁₆	—	13	3	no	—
35	C₄⋊C₈	Dic₁₃	1	3	yes	—
36	C₄×C₈	C₂×D₁₃	1	3	yes	—
37	C₂×C₁₃	C₈×Q₈	1	1	yes	characteristic
38	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
39	C₂×C₁₃	#504	1	1	yes	characteristic
40	C₂×Q₈	#1055	1	1	yes	characteristic
41	C₂×C₈	C₂×Dic₁₃	1	3	yes	—
42	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
43	C₄⋊C₄	#1055	1	3	yes	—
44	C₄²	C₂×Dic₁₃	1	3	yes	—
45	C₁₆	—	13	2	no	—
46	C₁₆	—	26	3	no	—
47	C₁₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
48	Q₈	#6090	1	4	yes	direct product factor
49	C₂×C₄	C₂×#1055	1	3	yes	—
50	C₂×C₄	C₂×#1055	1	3	yes	—
51	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₁₃	1	1	yes	characteristic
54	C₈	#6131	1	1	yes	characteristic
55	C₂²	C₂²×#1055	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#6090	1	6	yes	—
58	C₄	Q₈×Dic₁₃	1	1	yes	characteristic
59	C₄	#88202	1	1	yes	characteristic
60	C₂	Q₈×#1055	1	1	yes	characteristic
61	C₂	C₂²×#6090	1	1	yes	characteristic
62	C₂	#11718801	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂²×C₁₆
Fitting	C₈×Q₈×C₁₃	C₂
socle, prime radical	C₂²×C₁₃	C₂²×C₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₈×Q₈	D₁₃
hypocenter	C₁₃	Q₈×C₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
15. #6090	Q₈	direct (N × H)
17. Q₈×C₁₃	C₁₆	semidirect
47. C₁₃	Q₈×C₁₆	semidirect
48. Q₈	#6090	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×Q₈×C₁₃	2
C₄⋊#6090	2
C₄×#6090	2
Q₈×C₁₆	13

Subgroups — Q8×#6090 #13116740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#6090 #13116740