Subgroups — D₁₆×D₁₀₇ #20293046

Order 6848.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₁₀₇	C₂	1	2	yes	maximal, complemented
2	D₁₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812050	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₁₀₇	—	2	2	no	—
7	D₈₅₆	C₂²	1	2	yes	complemented
8	#13133803	—	2	2	no	—
9	C₈×D₁₀₇	C₂²	1	1	yes	characteristic
10	C₁₀₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₁₀₇	C₂²	1	2	yes	complemented
12	C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₁₀₇	—	4	2	no	—
14	D₄×C₁₀₇	—	2	2	no	—
15	C₂²⋊D₁₀₇	—	4	2	no	—
16	D₄₂₈	—	2	2	no	—
17	C₄×D₁₀₇	D₄	1	1	yes	characteristic
18	C₈×C₁₀₇	C₂³	1	1	yes	characteristic
19	C₁₀₇⋊C₈	D₄	1	1	yes	characteristic
20	C₂²×C₁₀₇	—	4	2	no	—
21	C₂×D₁₀₇	—	4	2	no	—
22	C₂×D₁₀₇	—	8	4	no	—
23	C₂×D₁₀₇	D₈	1	1	yes	characteristic
24	C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
25	Dic₁₀₇	D₈	1	1	yes	characteristic
26	C₂×C₁₀₇	—	8	2	no	—
27	C₂×C₁₀₇	C₂×D₈	1	1	yes	characteristic
28	D₁₀₇	—	8	2	no	—
29	D₁₀₇	D₁₆	1	2	yes	direct product factor
30	C₁₀₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	107	1	no	maximal, Sylow
32	C₂×D₈	—	107	2	no	—
33	D₁₆	—	107	2	no	—
34	D₁₆	—	107	1	no	—
35	D₁₆	D₁₀₇	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	107	1	no	—
37	C₂×D₄	—	214	2	no	—
38	D₈	—	107	2	no	—
39	D₈	—	214	2	no	—
40	D₈	C₂×D₁₀₇	1	2	yes	complemented
41	C₂×C₈	—	107	1	no	—
42	C₁₆	—	107	1	no	—
43	C₁₆	C₂×D₁₀₇	1	1	yes	characteristic, complemented
44	C₂³	—	428	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	428	2	no	—
47	D₄	—	214	2	no	—
48	C₂×C₄	—	107	1	no	—
49	C₈	—	107	1	no	—
50	C₈	C₂²×D₁₀₇	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	856	4	no	—
53	C₂²	—	107	1	no	—
54	C₂²	—	428	2	no	—
55	C₄	—	107	1	no	—
56	C₄	D₄×D₁₀₇	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	856	2	no	—
59	C₂	—	107	2	no	—
60	C₂	D₈×D₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₀₇
commutator	C₈×C₁₀₇	C₂³
Frattini	C₈	C₂²×D₁₀₇
Fitting	D₁₆×C₁₀₇	C₂
socle	C₂×C₁₀₇	C₂×D₈
hypercenter	D₁₆	D₁₀₇
hypocenter	C₁₀₇	C₂×D₁₆
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₁₀₇	C₂	semidirect
2. D₁₇₁₂	C₂	semidirect
3. #16812050	C₂	semidirect
4. C₁₆×D₁₀₇	C₂	semidirect
5. D₁₆×C₁₀₇	C₂	semidirect
7. D₈₅₆	C₂²	semidirect
10. C₁₀₇⋊C₁₆	C₂²	semidirect
11. D₈×C₁₀₇	C₂²	semidirect
12. C₁₆×C₁₀₇	C₂²	semidirect
29. D₁₀₇	D₁₆	direct (N × H)
30. C₁₀₇	C₂×D₁₆	semidirect
35. D₁₆	D₁₀₇	direct (N × H)
40. D₈	C₂×D₁₀₇	semidirect
43. C₁₆	C₂×D₁₀₇	semidirect

Subgroups — D16×D107 #20293046

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×D₁₀₇ #20293046