Subgroups — Dic₁₀₇⋊C₁₆ #20292445

Order 6848.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₀₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₇	C₄	1	1	yes	characteristic
6	C₁₀₇⋊C₁₆	—	2	1	no	—
7	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₀₇	—	2	1	no	—
9	C₂×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₇	C₈	1	1	yes	characteristic
11	C₂×Dic₁₀₇	C₈	1	1	yes	characteristic
12	C₈×C₁₀₇	D₄	1	1	yes	characteristic
13	C₈×C₁₀₇	Q₈	1	1	yes	characteristic
14	C₁₀₇⋊C₈	—	2	1	no	—
15	C₂²×C₁₀₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₀₇	M₁₆	1	1	yes	characteristic
18	Dic₁₀₇	—	2	1	no	—
19	Dic₁₀₇	C₁₆	1	2	yes	complemented
20	C₂×C₁₀₇	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₀₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₀₇	M₃₂	1	1	yes	characteristic
23	C₁₀₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	107	1	no	maximal, Sylow
25	C₂×C₁₆	—	107	1	no	—
26	C₂×C₁₆	D₁₀₇	1	1	yes	characteristic
27	C₄×C₈	—	107	1	no	—
28	C₂×C₈	—	107	1	no	—
29	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
30	C₄²	—	107	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	214	1	no	—
33	C₂×C₄	—	107	1	no	—
34	C₂×C₄	—	107	1	no	—
35	C₂×C₄	C₄×D₁₀₇	1	1	yes	characteristic
36	C₈	—	214	1	no	—
37	C₈	Dic₂₁₄	1	1	yes	characteristic
38	C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
39	C₂²	C₈×D₁₀₇	1	1	yes	characteristic
40	C₄	—	107	2	no	—
41	C₄	—	214	1	no	—
42	C₄	Dic₁₀₇⋊C₄	1	1	yes	characteristic
43	C₄	#13133801	1	1	yes	characteristic
44	C₂	Dic₁₀₇⋊C₈	1	1	yes	characteristic
45	C₂	C₁₆×D₁₀₇	1	1	yes	characteristic
46	C₂	#16812048	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₇
commutator	C₂×C₁₀₇	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×C₈
hypercenter	C₂×C₁₆	D₁₀₇
hypocenter	C₁₀₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₀₇	C₁₆	semidirect
23. C₁₀₇	C₄⋊C₁₆	semidirect

Subgroups — Dic107⋊C16 #20292445

Conjugacy classes of subgroups

Complements

Subgroups — Dic₁₀₇⋊C₁₆ #20292445