Subgroups — Q₃₂×D₃₄₉ #36374570

Order 22336.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₃₄₉	C₂	1	2	yes	maximal
2	Dic₂₇₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#26013585	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₃₄₉	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₃₄₉	—	2	2	no	—
7	Dic₁₃₉₆	C₂²	1	2	yes	—
8	#19150223	—	2	2	no	—
9	C₈×D₃₄₉	C₂²	1	1	yes	characteristic
10	#19150208	C₂²	1	1	yes	characteristic
11	Q₁₆×C₃₄₉	C₂²	1	2	yes	—
12	C₁₆×C₃₄₉	C₂²	1	1	yes	characteristic
13	Dic₆₉₈	—	2	2	no	—
14	Dic₆₉₈	—	4	2	no	—
15	C₄×D₃₄₉	—	4	2	no	—
16	C₄×D₃₄₉	D₄	1	1	yes	characteristic
17	#14584095	D₄	1	1	yes	characteristic
18	Q₈×C₃₄₉	—	2	2	no	—
19	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
20	C₂×D₃₄₉	D₈	1	1	yes	characteristic
21	C₄×C₃₄₉	—	4	2	no	—
22	C₄×C₃₄₉	C₂×D₄	1	1	yes	characteristic
23	Dic₃₄₉	—	4	2	no	—
24	Dic₃₄₉	D₈	1	1	yes	characteristic
25	C₂×C₃₄₉	C₂×D₈	1	1	yes	characteristic
26	D₃₄₉	Q₃₂	1	2	yes	direct product factor
27	C₃₄₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	349	1	no	maximal, Sylow
29	C₂×Q₁₆	—	349	2	no	—
30	Q₃₂	—	349	2	no	—
31	Q₃₂	—	349	1	no	—
32	Q₃₂	D₃₄₉	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	349	1	no	—
34	C₂×Q₈	—	698	2	no	—
35	Q₁₆	—	349	2	no	—
36	Q₁₆	—	698	2	no	—
37	Q₁₆	C₂×D₃₄₉	1	2	yes	—
38	C₂×C₈	—	349	1	no	—
39	C₁₆	—	349	1	no	—
40	C₁₆	C₂×D₃₄₉	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	1396	2	no	—
43	Q₈	—	698	2	no	—
44	C₂×C₄	—	349	1	no	—
45	C₂×C₄	—	1396	2	no	—
46	C₈	—	349	1	no	—
47	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
48	C₂²	—	349	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	349	1	no	—
51	C₄	—	1396	2	no	—
52	C₄	D₄×D₃₄₉	1	1	yes	characteristic
53	C₂	—	349	2	no	—
54	C₂	D₈×D₃₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₄₉
commutator, cosocle	C₈×C₃₄₉	C₂³
Frattini	C₈	C₂²×D₃₄₉
Fitting	Q₃₂×C₃₄₉	C₂
socle	C₂×C₃₄₉	C₂×D₈
prime radical	C₂×D₃₄₉	D₈
hypercenter	Q₃₂	D₃₄₉
hypocenter	C₃₄₉	C₂×Q₃₂
LCS	G ▷ C₈×C₃₄₉ ▷ C₄×C₃₄₉ ▷ C₂×C₃₄₉ ▷ C₃₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₂₇₉₂	C₂	semidirect
3. #26013585	C₂	semidirect
5. Q₃₂×C₃₄₉	C₂	semidirect
26. D₃₄₉	Q₃₂	direct (N × H)
27. C₃₄₉	C₂×Q₃₂	semidirect
32. Q₃₂	D₃₄₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₁₆×D₃₄₉	2
Dic₂₇₉₂	2
#26013585	2
C₁₆×D₃₄₉	2
Q₃₂×C₃₄₉	2
C₂×Q₃₂	349

Subgroups — Q32×D349 #36374570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₃₄₉ #36374570