Subgroups — Q₈×#11724784 #20295152

Order 6976.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724784	C₂	1	3	yes	maximal
2	C₄×#11724784	C₂	1	3	yes	maximal
3	C₄×Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724784	C₂²	1	3	yes	—
5	C₂×#11724784	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₉	C₄	1	3	yes	—
8	C₄²×C₁₀₉	C₂²	1	3	yes	—
9	Q₈×C₁₀₉	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
13	#11724784	—	2	3	no	—
14	#11724784	Q₈	1	2	yes	direct product factor
15	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₀₉	—	2	3	no	—
17	C₄×C₁₀₉	C₂×C₈	1	6	yes	—
18	C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₁₀₉	#41	1	1	yes	characteristic
20	C₂×C₁₀₉	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₀₉	#131	1	1	yes	characteristic
23	C₁₀₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	109	1	no	maximal, Sylow
25	C₄×Q₈	D₁₀₉	1	1	yes	characteristic
26	C₄⋊C₈	—	109	3	no	—
27	C₄×C₈	—	109	3	no	—
28	C₂×Q₈	Dic₁₀₉	1	1	yes	characteristic
29	C₂×C₈	—	109	1	no	—
30	C₂×C₈	—	109	3	no	—
31	C₄⋊C₄	Dic₁₀₉	1	3	yes	—
32	C₄²	C₂×D₁₀₉	1	3	yes	—
33	Q₈	#11724784	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₁₀₉	1	3	yes	—
35	C₂×C₄	C₂×Dic₁₀₉	1	3	yes	—
36	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
37	C₈	—	109	2	no	—
38	C₈	—	218	3	no	—
39	C₂²	C₂²×Dic₁₀₉	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#11724784	1	6	yes	—
42	C₄	Q₈×D₁₀₉	1	1	yes	characteristic
43	C₄	#13182030	1	1	yes	characteristic
44	C₂	Q₈×Dic₁₀₉	1	1	yes	characteristic
45	C₂	C₂²×#11724784	1	1	yes	characteristic
46	C₂	#16812706	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₉
commutator	C₂×C₁₀₉	C₂²×C₈
Fitting	C₄×Q₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×C₄
hypercenter	C₄×Q₈	D₁₀₉
hypocenter	C₁₀₉	C₈×Q₈
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₁₀₉	C₈	semidirect
14. #11724784	Q₈	direct (N × H)
23. C₁₀₉	C₈×Q₈	semidirect
33. Q₈	#11724784	direct (N × H)

Subgroups — Q8×#11724784 #20295152

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11724784 #20295152