Subgroups — Q₈×#11744751 #20298724

Order 7232.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11744751	C₂	1	3	yes	maximal
2	C₄×#11744751	C₂	1	3	yes	maximal
3	C₄×Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744751	C₂²	1	3	yes	—
5	C₂×#11744751	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₁₁₃	C₄	1	3	yes	—
8	C₄²×C₁₁₃	C₂²	1	3	yes	—
9	Q₈×C₁₁₃	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₁₃	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₁₁₃	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
13	#11744751	—	2	3	no	—
14	#11744751	Q₈	1	2	yes	direct product factor
15	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₁₃	—	2	3	no	—
17	C₄×C₁₁₃	C₂×C₈	1	6	yes	—
18	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₁₁₃	#41	1	1	yes	characteristic
20	C₂×C₁₁₃	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₁₃	#131	1	1	yes	characteristic
23	C₁₁₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	113	1	no	maximal, Sylow
25	C₄×Q₈	D₁₁₃	1	1	yes	characteristic
26	C₄⋊C₈	—	113	3	no	—
27	C₄×C₈	—	113	3	no	—
28	C₂×Q₈	Dic₁₁₃	1	1	yes	characteristic
29	C₂×C₈	—	113	1	no	—
30	C₂×C₈	—	113	3	no	—
31	C₄⋊C₄	Dic₁₁₃	1	3	yes	—
32	C₄²	C₂×D₁₁₃	1	3	yes	—
33	Q₈	#11744751	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₁₁₃	1	3	yes	—
35	C₂×C₄	C₂×Dic₁₁₃	1	3	yes	—
36	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
37	C₈	—	113	2	no	—
38	C₈	—	226	3	no	—
39	C₂²	C₂²×Dic₁₁₃	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#11744751	1	6	yes	—
42	C₄	Q₈×D₁₁₃	1	1	yes	characteristic
43	C₄	#14268648	1	1	yes	characteristic
44	C₂	Q₈×Dic₁₁₃	1	1	yes	characteristic
45	C₂	C₂²×#11744751	1	1	yes	characteristic
46	C₂	#16813629	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₁₃
commutator	C₂×C₁₁₃	C₂²×C₈
Fitting	C₄×Q₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂²×C₄
hypercenter	C₄×Q₈	D₁₁₃
hypocenter	C₁₁₃	C₈×Q₈
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₁₁₃	C₈	semidirect
14. #11744751	Q₈	direct (N × H)
23. C₁₁₃	C₈×Q₈	semidirect
33. Q₈	#11744751	direct (N × H)

Subgroups — Q8×#11744751 #20298724

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11744751 #20298724