Subgroups — Q₁₆×#89137 #20296064

Order 6976.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#89137	C₂	1	2	yes	maximal
2	#16812768	C₂	1	1	yes	maximal, characteristic
3	#16812762	C₂	1	2	yes	maximal
4	C₈×#89137	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
6	D₁₀₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊#89137	—	2	2	no	—
8	C₄⋊#89137	C₂²	1	2	yes	—
9	C₄×#89137	—	2	2	no	—
10	C₄×#89137	C₂²	1	1	yes	characteristic
11	Q₈×D₁₀₉	C₂²	1	2	yes	—
12	Dic₄₃₆	C₄	1	1	yes	characteristic, complemented
13	#13182019	C₄	1	2	yes	complemented
14	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₀₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#89137	—	2	2	no	—
17	C₂×#89137	D₄	1	1	yes	characteristic
18	C₂×#89137	D₄	1	1	yes	characteristic
19	Q₈×C₁₀₉	C₂×C₄	1	2	yes	—
20	C₄×D₁₀₉	—	2	2	no	—
21	C₄×D₁₀₉	C₂³	1	1	yes	characteristic
22	Dic₂₁₈	—	2	2	no	—
23	Dic₂₁₈	C₂×C₄	1	2	yes	—
24	#11724786	—	2	1	no	—
25	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
26	#11724784	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₀₉	C₂×D₄	1	1	yes	characteristic
28	#89137	—	2	1	no	—
29	#89137	—	4	2	no	—
30	#89137	Q₁₆	1	2	yes	direct product factor
31	C₄×C₁₀₉	—	2	2	no	—
32	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₀₉	—	2	2	no	—
34	Dic₁₀₉	#41	1	1	yes	characteristic
35	C₂×C₁₀₉	C₄×D₄	1	1	yes	characteristic
36	D₁₀₉	C₂×Q₁₆	1	1	yes	characteristic
37	D₁₀₉	#135	1	1	yes	characteristic
38	C₁₀₉	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₄×Q₁₆	—	109	1	no	maximal, Sylow
40	C₂×Q₁₆	—	109	1	no	—
41	C₄×Q₈	—	109	2	no	—
42	#107	—	109	1	no	—
43	#103	—	109	2	no	—
44	C₄×C₈	—	109	1	no	—
45	C₂×Q₈	—	109	2	no	—
46	Q₁₆	—	109	2	no	—
47	Q₁₆	—	109	1	no	—
48	Q₁₆	#89137	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	109	1	no	—
50	C₂×C₈	—	109	1	no	—
51	C₄⋊C₄	—	109	2	no	—
52	C₄⋊C₄	—	218	2	no	—
53	C₄²	—	109	1	no	—
54	C₄²	—	218	2	no	—
55	Q₈	—	109	2	no	—
56	Q₈	—	218	2	no	—
57	Q₈	C₂×#89137	1	2	yes	—
58	C₂×C₄	—	109	1	no	—
59	C₂×C₄	—	109	1	no	—
60	C₂×C₄	—	109	1	no	—
61	C₂×C₄	—	218	2	no	—
62	C₂×C₄	—	218	2	no	—
63	C₈	—	109	1	no	—
64	C₈	—	218	1	no	—
65	C₈	C₂×#89137	1	1	yes	characteristic
66	C₂²	—	109	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	109	2	no	—
69	C₄	—	109	1	no	—
70	C₄	—	436	2	no	—
71	C₄	—	218	1	no	—
72	C₄	—	218	2	no	—
73	C₄	C₂²×#89137	1	1	yes	characteristic
74	C₂	—	109	1	no	—
75	C₂	—	109	1	no	—
76	C₂	D₄×#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#89137
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₄	C₂²×#89137
Fitting	Q₁₆×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₄×D₄
hypercenter	Q₁₆	#89137
hypocenter	C₁₀₉	C₄×Q₁₆
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₄₃₆	C₄	semidirect
13. #13182019	C₄	semidirect
15. Q₁₆×C₁₀₉	C₄	semidirect
30. #89137	Q₁₆	direct (N × H)
38. C₁₀₉	C₄×Q₁₆	semidirect
48. Q₁₆	#89137	direct (N × H)

Subgroups — Q16×#89137 #20296064

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×#89137 #20296064