Subgroups — Q₃₂×D₁₀₉ #20295452

Order 6976.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₀₉	C₂	1	2	yes	maximal
2	Dic₈₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812645	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₁₀₉	—	2	2	no	—
7	Dic₄₃₆	C₂²	1	2	yes	—
8	#13182019	—	2	2	no	—
9	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
10	#13182004	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₀₉	C₂²	1	2	yes	—
12	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
13	Q₈×C₁₀₉	—	2	2	no	—
14	C₄×D₁₀₉	—	4	2	no	—
15	C₄×D₁₀₉	D₄	1	1	yes	characteristic
16	Dic₂₁₈	—	2	2	no	—
17	Dic₂₁₈	—	4	2	no	—
18	C₈×C₁₀₉	C₂³	1	1	yes	characteristic
19	#11724784	D₄	1	1	yes	characteristic
20	C₂×D₁₀₉	D₈	1	1	yes	characteristic
21	C₄×C₁₀₉	—	4	2	no	—
22	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
23	Dic₁₀₉	—	4	2	no	—
24	Dic₁₀₉	D₈	1	1	yes	characteristic
25	C₂×C₁₀₉	C₂×D₈	1	1	yes	characteristic
26	D₁₀₉	Q₃₂	1	2	yes	direct product factor
27	C₁₀₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	109	1	no	maximal, Sylow
29	C₂×Q₁₆	—	109	2	no	—
30	Q₃₂	—	109	2	no	—
31	Q₃₂	—	109	1	no	—
32	Q₃₂	D₁₀₉	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	109	1	no	—
34	C₂×Q₈	—	218	2	no	—
35	Q₁₆	—	109	2	no	—
36	Q₁₆	—	218	2	no	—
37	Q₁₆	C₂×D₁₀₉	1	2	yes	—
38	C₂×C₈	—	109	1	no	—
39	C₁₆	—	109	1	no	—
40	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	436	2	no	—
43	Q₈	—	218	2	no	—
44	C₂×C₄	—	109	1	no	—
45	C₂×C₄	—	436	2	no	—
46	C₈	—	109	1	no	—
47	C₈	C₂²×D₁₀₉	1	1	yes	characteristic
48	C₂²	—	109	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	109	1	no	—
51	C₄	—	436	2	no	—
52	C₄	D₄×D₁₀₉	1	1	yes	characteristic
53	C₂	—	109	2	no	—
54	C₂	D₈×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₀₉
commutator	C₈×C₁₀₉	C₂³
Frattini	C₈	C₂²×D₁₀₉
Fitting	Q₃₂×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×D₈
hypercenter	Q₃₂	D₁₀₉
hypocenter	C₁₀₉	C₂×Q₃₂
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₈₇₂	C₂	semidirect
3. #16812645	C₂	semidirect
5. Q₃₂×C₁₀₉	C₂	semidirect
26. D₁₀₉	Q₃₂	direct (N × H)
27. C₁₀₉	C₂×Q₃₂	semidirect
32. Q₃₂	D₁₀₉	direct (N × H)

Subgroups — Q32×D109 #20295452

Conjugacy classes of subgroups

Complements

Subgroups — Q₃₂×D₁₀₉ #20295452