Subgroups — Dic₁₂₇⋊C₁₆ #22549694

Order 8128.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₂₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₂₇	C₄	1	1	yes	characteristic
6	C₁₂₇⋊C₁₆	—	2	1	no	—
7	C₂×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₂₇	—	2	1	no	—
9	C₂×Dic₁₂₇	C₈	1	1	yes	characteristic
10	C₂×Dic₁₂₇	C₈	1	1	yes	characteristic
11	C₁₂₇⋊C₈	—	2	1	no	—
12	C₂×C₄×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₂₇	D₄	1	1	yes	characteristic
14	C₈×C₁₂₇	Q₈	1	1	yes	characteristic
15	C₂²×C₁₂₇	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₂₇	M₁₆	1	1	yes	characteristic
18	Dic₁₂₇	—	2	1	no	—
19	Dic₁₂₇	C₁₆	1	2	yes	complemented
20	C₂×C₁₂₇	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₂₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₂₇	M₃₂	1	1	yes	characteristic
23	C₁₂₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	127	1	no	maximal, Sylow
25	C₂×C₁₆	—	127	1	no	—
26	C₂×C₁₆	D₁₂₇	1	1	yes	characteristic
27	C₄×C₈	—	127	1	no	—
28	C₂×C₈	—	127	1	no	—
29	C₂×C₈	C₂×D₁₂₇	1	1	yes	characteristic
30	C₄²	—	127	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	254	1	no	—
33	C₂×C₄	—	127	1	no	—
34	C₂×C₄	—	127	1	no	—
35	C₂×C₄	C₄×D₁₂₇	1	1	yes	characteristic
36	C₈	—	254	1	no	—
37	C₈	C₂²⋊D₁₂₇	1	1	yes	characteristic
38	C₈	Dic₂₅₄	1	1	yes	characteristic
39	C₂²	C₈×D₁₂₇	1	1	yes	characteristic
40	C₄	—	127	2	no	—
41	C₄	—	254	1	no	—
42	C₄	Dic₁₂₇⋊C₄	1	1	yes	characteristic
43	C₄	#14523231	1	1	yes	characteristic
44	C₂	Dic₁₂₇⋊C₈	1	1	yes	characteristic
45	C₂	C₁₆×D₁₂₇	1	1	yes	characteristic
46	C₂	#16861148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₂₇
commutator	C₂×C₁₂₇	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂×C₈
hypercenter	C₂×C₁₆	D₁₂₇
hypocenter	C₁₂₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₂₇	C₁₆	semidirect
23. C₁₂₇	C₄⋊C₁₆	semidirect

Subgroups — Dic127⋊C16 #22549694

Conjugacy classes of subgroups

Complements

Subgroups — Dic₁₂₇⋊C₁₆ #22549694