Subgroups — D₄₇×Q₁₂₈ #26137326

Order 12032.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×D₄₇	C₂	1	2	yes	maximal
2	Dic₁₅₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241605	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₃₂×D₄₇	—	2	2	no	—
7	Dic₇₅₂	C₂²	1	2	yes	—
8	#15688963	—	2	2	no	—
9	C₃₂×D₄₇	C₂²	1	1	yes	characteristic
10	C₄₇⋊C₆₄	C₂²	1	1	yes	characteristic
11	C₄₇×Q₆₄	C₂²	1	2	yes	—
12	C₄₇×C₆₄	C₂²	1	1	yes	characteristic
13	Q₁₆×D₄₇	—	4	2	no	—
14	Dic₃₇₆	—	2	2	no	—
15	#13093970	—	4	2	no	—
16	C₁₆×D₄₇	D₄	1	1	yes	characteristic
17	C₄₇⋊C₃₂	D₄	1	1	yes	characteristic
18	Q₃₂×C₄₇	—	2	2	no	—
19	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
20	Q₈×D₄₇	—	8	2	no	—
21	Q₁₆×C₄₇	—	4	2	no	—
22	#10625337	—	8	2	no	—
23	Dic₁₈₈	—	4	2	no	—
24	C₈×D₄₇	D₈	1	1	yes	characteristic
25	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
26	C₄₇⋊C₁₆	D₈	1	1	yes	characteristic
27	Q₈×C₄₇	—	8	2	no	—
28	C₄×D₄₇	—	16	2	no	—
29	C₄×D₄₇	D₁₆	1	1	yes	characteristic
30	Dic₉₄	—	8	2	no	—
31	Dic₉₄	—	16	2	no	—
32	C₈×C₄₇	C₂×D₈	1	1	yes	characteristic
33	C₄₇⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂×Q₁₂₈	—	47	1	no	maximal, Sylow
35	C₂×D₄₇	D₃₂	1	1	yes	characteristic
36	C₄×C₄₇	—	16	2	no	—
37	C₄×C₄₇	C₂×D₁₆	1	1	yes	characteristic
38	Dic₄₇	—	16	2	no	—
39	Dic₄₇	D₃₂	1	1	yes	characteristic
40	C₂×Q₆₄	—	47	2	no	—
41	Q₁₂₈	—	47	2	no	—
42	Q₁₂₈	—	47	1	no	—
43	Q₁₂₈	D₄₇	1	1	yes	characteristic, direct product factor
44	C₂×C₆₄	—	47	1	no	—
45	C₂×C₄₇	C₂×D₃₂	1	1	yes	characteristic
46	D₄₇	Q₁₂₈	1	2	yes	direct product factor
47	C₂×Q₃₂	—	94	2	no	—
48	Q₆₄	—	47	2	no	—
49	Q₆₄	—	94	2	no	—
50	Q₆₄	C₂×D₄₇	1	2	yes	—
51	C₂×C₃₂	—	47	1	no	—
52	C₆₄	—	47	1	no	—
53	C₆₄	C₂×D₄₇	1	1	yes	characteristic
54	C₄₇	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	188	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	94	2	no	—
58	Q₃₂	—	188	2	no	—
59	C₂×C₁₆	—	47	1	no	—
60	C₃₂	—	47	1	no	—
61	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
62	C₂×Q₈	—	376	2	no	—
63	Q₁₆	—	4	2	no	—
64	Q₁₆	—	376	2	no	—
65	Q₁₆	—	188	2	no	—
66	C₂×C₈	—	47	1	no	—
67	C₁₆	—	47	1	no	—
68	C₁₆	D₄×D₄₇	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	376	2	no	—
71	Q₈	—	752	2	no	—
72	C₂×C₄	—	47	1	no	—
73	C₂×C₄	—	752	2	no	—
74	C₈	—	47	1	no	—
75	C₈	D₈×D₄₇	1	1	yes	characteristic
76	C₂²	—	47	1	no	—
77	C₄	—	16	2	no	—
78	C₄	—	47	1	no	—
79	C₄	—	752	2	no	—
80	C₄	D₁₆×D₄₇	1	1	yes	characteristic
81	C₂	—	47	2	no	—
82	C₂	D₃₂×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₄₇
commutator, cosocle	C₃₂×C₄₇	C₂³
Frattini	C₃₂	C₂²×D₄₇
Fitting	C₄₇×Q₁₂₈	C₂
socle	C₂×C₄₇	C₂×D₃₂
prime radical	C₂×D₄₇	D₃₂
hypercenter	Q₁₂₈	D₄₇
hypocenter	C₄₇	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₄₇ ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
2. Dic₁₅₀₄	C₂	semidirect
3. #20241605	C₂	semidirect
5. C₄₇×Q₁₂₈	C₂	semidirect
43. Q₁₂₈	D₄₇	direct (N × H)
46. D₄₇	Q₁₂₈	direct (N × H)
54. C₄₇	C₂×Q₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
Q₆₄×D₄₇	2
Dic₁₅₀₄	2
#20241605	2
C₆₄×D₄₇	2
C₄₇×Q₁₂₈	2
C₂×Q₁₂₈	47

Subgroups — D47×Q128 #26137326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×Q₁₂₈ #26137326