Subgroups — Q₈⋊#11724784 #20294757

Order 6976.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724784	C₂	1	1	yes	maximal, characteristic
2	C₄×#11724784	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724784	—	2	1	no	—
5	C₂×#11724784	—	2	1	no	—
6	C₂×Q₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₉	—	2	1	no	—
8	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
9	C₄²×C₁₀₉	—	2	1	no	—
10	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
11	Q₈×C₁₀₉	—	2	1	no	—
12	Q₈×C₁₀₉	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₀₉	—	2	1	no	—
14	C₂×C₄×C₁₀₉	—	2	1	no	—
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
18	#11724784	—	2	2	no	—
19	#11724784	—	4	1	no	—
20	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₉	—	2	2	no	—
22	C₄×C₁₀₉	—	2	1	no	—
23	C₄×C₁₀₉	—	4	1	no	—
24	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
26	C₄×C₁₀₉	SD₁₆	1	1	yes	characteristic
27	C₄×C₁₀₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₀₉	#103	1	1	yes	characteristic
30	C₂×C₁₀₉	#104	1	1	yes	characteristic
31	C₁₀₉	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	109	1	no	maximal, Sylow
33	C₄×Q₈	D₁₀₉	1	1	yes	characteristic
34	C₄⋊C₈	—	109	1	no	—
35	C₄×C₈	—	109	1	no	—
36	C₂×Q₈	Dic₁₀₉	1	1	yes	characteristic
37	C₂×C₈	—	218	1	no	—
38	C₂×C₈	—	218	1	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	Dic₁₀₉	1	1	yes	characteristic
41	C₄²	—	2	1	no	—
42	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
43	Q₈	—	2	1	no	—
44	Q₈	#11724784	1	2	yes	complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
50	C₈	—	436	1	no	—
51	C₈	—	218	2	no	—
52	C₂²	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	2	1	no	—
55	C₄	—	4	1	no	—
56	C₄	C₂×#11724784	1	1	yes	characteristic
57	C₄	#13182013	1	1	yes	characteristic
58	C₄	#13182016	1	1	yes	characteristic
59	C₄	#13182019	1	1	yes	characteristic
60	C₂	C₂²⋊#11724784	1	1	yes	characteristic
61	C₂	#16812623	1	1	yes	characteristic
62	C₂	#16812626	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₀₉
commutator	C₄×C₁₀₉	C₂×C₈
Frattini	C₄²	C₂×D₁₀₉
Fitting	C₄×Q₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	C₄×Q₈	D₁₀₉
hypocenter	C₁₀₉	Q₈⋊C₈
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
12. Q₈×C₁₀₉	C₈	semidirect
31. C₁₀₉	Q₈⋊C₈	semidirect
44. Q₈	#11724784	semidirect

Subgroups — Q8⋊#11724784 #20294757

Conjugacy classes of subgroups

Complements

Subgroups — Q₈⋊#11724784 #20294757