Subgroups — Q₁₆×Dic₁₀₇ #20292722

Order 6848.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₀₇	C₂	1	2	yes	maximal
2	#16812043	C₂	1	1	yes	maximal, characteristic
3	#16812033	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₀₇	—	2	2	no	—
8	C₄⋊Dic₁₀₇	C₂²	1	2	yes	—
9	C₄×Dic₁₀₇	—	2	2	no	—
10	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₀₇	C₂²	1	2	yes	—
12	Q₁₆×C₁₀₇	C₄	1	4	yes	complemented
13	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	Q₈×C₁₀₇	—	2	2	no	—
15	Q₈×C₁₀₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₁₀₇	—	2	2	no	—
17	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₇	—	2	2	no	—
19	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
20	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
21	C₈×C₁₀₇	C₂×C₄	1	2	yes	—
22	C₁₀₇⋊C₈	—	2	1	no	—
23	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₀₇	—	2	4	no	—
25	C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₀₇	#41	1	1	yes	characteristic
27	Dic₁₀₇	—	2	1	no	—
28	Dic₁₀₇	—	4	2	no	—
29	Dic₁₀₇	Q₁₆	1	2	yes	direct product factor
30	C₂×C₁₀₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₀₇	#135	1	1	yes	characteristic
33	C₁₀₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	107	1	no	maximal, Sylow
35	C₂×Q₁₆	D₁₀₇	1	1	yes	characteristic
36	C₄×Q₈	—	107	2	no	—
37	#107	—	107	1	no	—
38	#103	—	107	2	no	—
39	C₄×C₈	—	107	1	no	—
40	C₂×Q₈	C₂×D₁₀₇	1	2	yes	—
41	Q₁₆	Dic₁₀₇	1	4	yes	direct product factor
42	C₂×C₈	—	107	1	no	—
43	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
44	C₄⋊C₄	—	107	2	no	—
45	C₄⋊C₄	—	214	2	no	—
46	C₄²	—	107	1	no	—
47	C₄²	—	214	2	no	—
48	Q₈	—	2	2	no	—
49	Q₈	C₂×Dic₁₀₇	1	4	yes	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	107	1	no	—
52	C₂×C₄	—	107	1	no	—
53	C₂×C₄	—	214	2	no	—
54	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
55	C₈	—	214	1	no	—
56	C₈	C₂×Dic₁₀₇	1	2	yes	—
57	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
58	C₄	—	2	4	no	—
59	C₄	—	107	2	no	—
60	C₄	—	428	2	no	—
61	C₄	—	214	1	no	—
62	C₄	C₂²×Dic₁₀₇	1	1	yes	characteristic
63	C₄	#13133817	1	1	yes	characteristic
64	C₂	D₄×Dic₁₀₇	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₀₇	1	1	yes	characteristic
66	C₂	#16812132	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₄×C₁₀₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	C₂×Q₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₀₇
hypocenter	C₁₀₇	C₄×Q₁₆
LCS	G ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₁₀₇	C₄	semidirect
29. Dic₁₀₇	Q₁₆	direct (N × H)
33. C₁₀₇	C₄×Q₁₆	semidirect
41. Q₁₆	Dic₁₀₇	direct (N × H)

Subgroups — Q16×Dic107 #20292722

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×Dic₁₀₇ #20292722