Subgroups — Q₃₂×D₄₇ #15689549

Order 3008.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₄₇	C₂	1	2	yes	maximal
2	Dic₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093970	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₄₇	—	2	2	no	—
7	Q₁₆×C₄₇	C₂²	1	2	yes	—
8	#10625337	—	2	2	no	—
9	Dic₁₈₈	C₂²	1	2	yes	—
10	C₈×D₄₇	C₂²	1	1	yes	characteristic
11	C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	Q₈×C₄₇	—	2	2	no	—
14	C₄×D₄₇	—	4	2	no	—
15	C₄×D₄₇	D₄	1	1	yes	characteristic
16	Dic₉₄	—	2	2	no	—
17	Dic₉₄	—	4	2	no	—
18	C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄₇⋊C₈	D₄	1	1	yes	characteristic
20	C₂×D₄₇	D₈	1	1	yes	characteristic
21	C₄×C₄₇	—	4	2	no	—
22	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
23	Dic₄₇	—	4	2	no	—
24	Dic₄₇	D₈	1	1	yes	characteristic
25	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
26	D₄₇	Q₃₂	1	2	yes	direct product factor
27	C₂×Q₃₂	—	47	1	no	maximal, Sylow
28	C₄₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₁₆	—	47	2	no	—
30	Q₃₂	—	47	2	no	—
31	Q₃₂	—	47	1	no	—
32	Q₃₂	D₄₇	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	47	1	no	—
34	C₂×Q₈	—	94	2	no	—
35	Q₁₆	—	47	2	no	—
36	Q₁₆	—	94	2	no	—
37	Q₁₆	C₂×D₄₇	1	2	yes	—
38	C₂×C₈	—	47	1	no	—
39	C₁₆	—	47	1	no	—
40	C₁₆	C₂×D₄₇	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	94	2	no	—
43	Q₈	—	188	2	no	—
44	C₂×C₄	—	47	1	no	—
45	C₂×C₄	—	188	2	no	—
46	C₈	—	47	1	no	—
47	C₈	C₂²×D₄₇	1	1	yes	characteristic
48	C₂²	—	47	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	47	1	no	—
51	C₄	—	188	2	no	—
52	C₄	D₄×D₄₇	1	1	yes	characteristic
53	C₂	—	47	2	no	—
54	C₂	D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₇
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	Q₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₈
prime radical	C₂×D₄₇	D₈
hypercenter	Q₃₂	D₄₇
hypocenter	C₄₇	C₂×Q₃₂
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₃₇₆	C₂	semidirect
3. #13093970	C₂	semidirect
5. Q₃₂×C₄₇	C₂	semidirect
26. D₄₇	Q₃₂	direct (N × H)
28. C₄₇	C₂×Q₃₂	semidirect
32. Q₃₂	D₄₇	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×D₄₇	2
Dic₃₇₆	2
#13093970	2
C₁₆×D₄₇	2
Q₃₂×C₄₇	2
C₂×Q₃₂	47

Subgroups — Q32×D47 #15689549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₄₇ #15689549