Subgroups — Q₈×#11744753 #20299646

Order 7232.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11744753	C₂	1	3	yes	maximal
2	C₄×#11744753	C₂	1	3	yes	maximal
3	Q₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744753	C₂²	1	3	yes	—
5	C₂×#11744753	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₁₁₃	C₄	1	3	yes	—
7	C₄×Dic₁₁₃	C₂²	1	3	yes	—
8	C₂×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
9	Q₈×C₁₁₃	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₁₃	C₂×C₄	1	3	yes	—
11	C₂×Dic₁₁₃	C₂×C₄	1	3	yes	—
12	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
13	#11744753	—	2	3	no	—
14	#11744753	Q₈	1	2	yes	direct product factor
15	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₁₃	C₂×C₈	1	6	yes	—
17	Dic₁₁₃	—	2	3	no	—
18	Dic₁₁₃	C₂×Q₈	1	1	yes	characteristic
19	Dic₁₁₃	#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	—	113	1	no	—
26	C₄⋊C₈	—	113	3	no	—
27	C₄×C₈	—	113	3	no	—
28	C₂×Q₈	#90673	1	1	yes	characteristic
29	C₂×C₈	—	113	1	no	—
30	C₂×C₈	—	113	3	no	—
31	C₄⋊C₄	—	113	3	no	—
32	C₄²	—	113	3	no	—
33	Q₈	#11744753	1	4	yes	direct product factor
34	C₂×C₄	—	113	1	no	—
35	C₂×C₄	—	113	3	no	—
36	C₂×C₄	C₂×#90673	1	3	yes	—
37	C₈	—	113	2	no	—
38	C₈	—	226	3	no	—
39	C₂²	C₂²×#90673	1	1	yes	characteristic
40	C₄	—	113	1	no	—
41	C₄	—	113	1	no	—
42	C₄	—	226	3	no	—
43	C₄	C₂×#11744753	1	6	yes	—
44	C₂	Q₈×#90673	1	1	yes	characteristic
45	C₂	C₂²×#11744753	1	1	yes	characteristic
46	C₂	#16813710	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#90673
commutator	C₂×C₁₁₃	C₂²×C₈
Fitting	C₂×Q₈×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₂²×C₄
hypercenter	C₂×Q₈	#90673
hypocenter	C₁₁₃	C₈×Q₈
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₁₁₃	C₈	semidirect
14. #11744753	Q₈	direct (N × H)
23. C₁₁₃	C₈×Q₈	semidirect
33. Q₈	#11744753	direct (N × H)

Subgroups — Q8×#11744753 #20299646

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11744753 #20299646