Subgroups — Q₃₂×D₁₂₇ #22550302

Order 8128.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₂₇	C₂	1	2	yes	maximal
2	Dic₁₀₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#16861155	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₂₇	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₁₂₇	—	2	2	no	—
7	Dic₅₀₈	C₂²	1	2	yes	—
8	#14523238	—	2	2	no	—
9	C₈×D₁₂₇	C₂²	1	1	yes	characteristic
10	C₁₂₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₂₇	C₂²	1	2	yes	—
12	C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
13	Dic₂₅₄	—	2	2	no	—
14	Dic₂₅₄	—	4	2	no	—
15	C₄×D₁₂₇	—	4	2	no	—
16	C₄×D₁₂₇	D₄	1	1	yes	characteristic
17	C₁₂₇⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₁₂₇	—	2	2	no	—
19	C₈×C₁₂₇	C₂³	1	1	yes	characteristic
20	C₂×D₁₂₇	D₈	1	1	yes	characteristic
21	C₄×C₁₂₇	—	4	2	no	—
22	C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
23	Dic₁₂₇	—	4	2	no	—
24	Dic₁₂₇	D₈	1	1	yes	characteristic
25	C₂×C₁₂₇	C₂×D₈	1	1	yes	characteristic
26	D₁₂₇	Q₃₂	1	2	yes	direct product factor
27	C₁₂₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	127	1	no	maximal, Sylow
29	C₂×Q₁₆	—	127	2	no	—
30	Q₃₂	—	127	2	no	—
31	Q₃₂	—	127	1	no	—
32	Q₃₂	D₁₂₇	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	127	1	no	—
34	C₂×Q₈	—	254	2	no	—
35	Q₁₆	—	127	2	no	—
36	Q₁₆	—	254	2	no	—
37	Q₁₆	C₂×D₁₂₇	1	2	yes	—
38	C₂×C₈	—	127	1	no	—
39	C₁₆	—	127	1	no	—
40	C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	508	2	no	—
43	Q₈	—	254	2	no	—
44	C₂×C₄	—	127	1	no	—
45	C₂×C₄	—	508	2	no	—
46	C₈	—	127	1	no	—
47	C₈	C₂²×D₁₂₇	1	1	yes	characteristic
48	C₂²	—	127	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	127	1	no	—
51	C₄	—	508	2	no	—
52	C₄	D₄×D₁₂₇	1	1	yes	characteristic
53	C₂	—	127	2	no	—
54	C₂	D₈×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₂₇
commutator	C₈×C₁₂₇	C₂³
Frattini	C₈	C₂²×D₁₂₇
Fitting	Q₃₂×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂×D₈
hypercenter	Q₃₂	D₁₂₇
hypocenter	C₁₂₇	C₂×Q₃₂
LCS	G ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₀₁₆	C₂	semidirect
3. #16861155	C₂	semidirect
5. Q₃₂×C₁₂₇	C₂	semidirect
26. D₁₂₇	Q₃₂	direct (N × H)
27. C₁₂₇	C₂×Q₃₂	semidirect
32. Q₃₂	D₁₂₇	direct (N × H)

Subgroups — Q32×D127 #22550302

Conjugacy classes of subgroups

Complements

Subgroups — Q₃₂×D₁₂₇ #22550302