Subgroups — Q₃₂×D₁₃₇ #22577829

Order 8768.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₃₇	C₂	1	2	yes	maximal
2	Dic₁₀₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984034	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₁₃₇	—	2	2	no	—
7	Dic₅₄₈	C₂²	1	2	yes	—
8	#14555500	—	2	2	no	—
9	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
10	#14555485	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₃₇	C₂²	1	2	yes	—
12	C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	Dic₂₇₄	—	2	2	no	—
14	Dic₂₇₄	—	4	2	no	—
15	C₄×D₁₃₇	—	4	2	no	—
16	C₄×D₁₃₇	D₄	1	1	yes	characteristic
17	#11764040	D₄	1	1	yes	characteristic
18	Q₈×C₁₃₇	—	2	2	no	—
19	C₈×C₁₃₇	C₂³	1	1	yes	characteristic
20	C₂×D₁₃₇	D₈	1	1	yes	characteristic
21	C₄×C₁₃₇	—	4	2	no	—
22	C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
23	Dic₁₃₇	—	4	2	no	—
24	Dic₁₃₇	D₈	1	1	yes	characteristic
25	C₂×C₁₃₇	C₂×D₈	1	1	yes	characteristic
26	D₁₃₇	Q₃₂	1	2	yes	direct product factor
27	C₁₃₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	137	1	no	maximal, Sylow
29	C₂×Q₁₆	—	137	2	no	—
30	Q₃₂	—	137	2	no	—
31	Q₃₂	—	137	1	no	—
32	Q₃₂	D₁₃₇	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	137	1	no	—
34	C₂×Q₈	—	274	2	no	—
35	Q₁₆	—	274	2	no	—
36	Q₁₆	—	137	2	no	—
37	Q₁₆	C₂×D₁₃₇	1	2	yes	—
38	C₂×C₈	—	137	1	no	—
39	C₁₆	—	137	1	no	—
40	C₁₆	C₂×D₁₃₇	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	274	2	no	—
43	Q₈	—	548	2	no	—
44	C₂×C₄	—	548	2	no	—
45	C₂×C₄	—	137	1	no	—
46	C₈	—	137	1	no	—
47	C₈	C₂²×D₁₃₇	1	1	yes	characteristic
48	C₂²	—	137	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	548	2	no	—
51	C₄	—	137	1	no	—
52	C₄	D₄×D₁₃₇	1	1	yes	characteristic
53	C₂	—	137	2	no	—
54	C₂	D₈×D₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₃₇
commutator	C₈×C₁₃₇	C₂³
Frattini	C₈	C₂²×D₁₃₇
Fitting	Q₃₂×C₁₃₇	C₂
socle	C₂×C₁₃₇	C₂×D₈
hypercenter	Q₃₂	D₁₃₇
hypocenter	C₁₃₇	C₂×Q₃₂
LCS	G ▷ C₈×C₁₃₇ ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₀₉₆	C₂	semidirect
3. #17984034	C₂	semidirect
5. Q₃₂×C₁₃₇	C₂	semidirect
26. D₁₃₇	Q₃₂	direct (N × H)
27. C₁₃₇	C₂×Q₃₂	semidirect
32. Q₃₂	D₁₃₇	direct (N × H)

Subgroups — Q32×D137 #22577829

Conjugacy classes of subgroups

Complements

Subgroups — Q₃₂×D₁₃₇ #22577829