Subgroups — Q₃₂×D₁₃₉ #22581379

Order 8896.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₃₉	C₂	1	2	yes	maximal
2	Dic₁₁₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984788	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₁₃₉	—	2	2	no	—
7	Dic₅₅₆	C₂²	1	2	yes	—
8	#14555775	—	2	2	no	—
9	C₈×D₁₃₉	C₂²	1	1	yes	characteristic
10	C₁₃₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₃₉	C₂²	1	2	yes	—
12	C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
13	Dic₂₇₈	—	2	2	no	—
14	Dic₂₇₈	—	4	2	no	—
15	C₄×D₁₃₉	—	4	2	no	—
16	C₄×D₁₃₉	D₄	1	1	yes	characteristic
17	C₁₃₉⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₁₃₉	—	2	2	no	—
19	C₈×C₁₃₉	C₂³	1	1	yes	characteristic
20	C₂×D₁₃₉	D₈	1	1	yes	characteristic
21	C₄×C₁₃₉	—	4	2	no	—
22	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
23	Dic₁₃₉	—	4	2	no	—
24	Dic₁₃₉	D₈	1	1	yes	characteristic
25	C₂×C₁₃₉	C₂×D₈	1	1	yes	characteristic
26	D₁₃₉	Q₃₂	1	2	yes	direct product factor
27	C₁₃₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	139	1	no	maximal, Sylow
29	C₂×Q₁₆	—	139	2	no	—
30	Q₃₂	—	139	2	no	—
31	Q₃₂	—	139	1	no	—
32	Q₃₂	D₁₃₉	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	139	1	no	—
34	C₂×Q₈	—	278	2	no	—
35	Q₁₆	—	278	2	no	—
36	Q₁₆	—	139	2	no	—
37	Q₁₆	C₂×D₁₃₉	1	2	yes	—
38	C₂×C₈	—	139	1	no	—
39	C₁₆	—	139	1	no	—
40	C₁₆	C₂×D₁₃₉	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	278	2	no	—
43	Q₈	—	556	2	no	—
44	C₂×C₄	—	556	2	no	—
45	C₂×C₄	—	139	1	no	—
46	C₈	—	139	1	no	—
47	C₈	C₂²×D₁₃₉	1	1	yes	characteristic
48	C₂²	—	139	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	556	2	no	—
51	C₄	—	139	1	no	—
52	C₄	D₄×D₁₃₉	1	1	yes	characteristic
53	C₂	—	139	2	no	—
54	C₂	D₈×D₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₃₉
commutator	C₈×C₁₃₉	C₂³
Frattini	C₈	C₂²×D₁₃₉
Fitting	Q₃₂×C₁₃₉	C₂
socle	C₂×C₁₃₉	C₂×D₈
hypercenter	Q₃₂	D₁₃₉
hypocenter	C₁₃₉	C₂×Q₃₂
LCS	G ▷ C₈×C₁₃₉ ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₁₁₂	C₂	semidirect
3. #17984788	C₂	semidirect
5. Q₃₂×C₁₃₉	C₂	semidirect
26. D₁₃₉	Q₃₂	direct (N × H)
27. C₁₃₉	C₂×Q₃₂	semidirect
32. Q₃₂	D₁₃₉	direct (N × H)

Subgroups — Q32×D139 #22581379

Conjugacy classes of subgroups

Complements

Subgroups — Q₃₂×D₁₃₉ #22581379