Subgroups — Dic₄₇⋊C₆₄ #26104173

Order 12032.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₄₇	C₄	1	1	yes	characteristic
6	C₄₇⋊C₆₄	—	2	1	no	—
7	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
8	C₄₇×C₆₄	—	2	1	no	—
9	C₂×C₄₇⋊C₁₆	C₈	1	1	yes	characteristic
10	C₈×Dic₄₇	C₈	1	1	yes	characteristic
11	C₄₇⋊C₃₂	—	2	1	no	—
12	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₄₇	D₄	1	1	yes	characteristic
14	C₃₂×C₄₇	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₄₇	C₁₆	1	1	yes	characteristic
17	C₂×C₄₇⋊C₈	C₁₆	1	1	yes	characteristic
18	C₁₆×C₄₇	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₄₇	M₁₆	1	1	yes	characteristic
20	C₄₇⋊C₁₆	—	2	1	no	—
21	C₂×C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₄₇	C₃₂	1	1	yes	characteristic
23	C₂×Dic₄₇	C₃₂	1	1	yes	characteristic
24	C₈×C₄₇	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₄₇	M₃₂	1	1	yes	characteristic
26	C₄₇⋊C₈	—	2	1	no	—
27	C₄⋊C₆₄	—	47	1	no	maximal, Sylow
28	C₂²×C₄₇	C₂×C₃₂	1	1	yes	characteristic
29	C₄×C₄₇	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₄₇	M₆₄	1	1	yes	characteristic
31	Dic₄₇	—	2	1	no	—
32	Dic₄₇	C₆₄	1	2	yes	complemented
33	C₂×C₆₄	—	47	1	no	—
34	C₂×C₆₄	D₄₇	1	1	yes	characteristic
35	C₄×C₃₂	—	47	1	no	—
36	C₂×C₄₇	C₄⋊C₃₂	1	1	yes	characteristic
37	C₂×C₄₇	C₂×C₆₄	1	1	yes	characteristic
38	C₂×C₄₇	M₁₂₈	1	1	yes	characteristic
39	C₂×C₃₂	—	47	1	no	—
40	C₂×C₃₂	C₂×D₄₇	1	1	yes	characteristic
41	C₄×C₁₆	—	47	1	no	—
42	C₆₄	—	2	1	no	—
43	C₆₄	—	94	1	no	—
44	C₄₇	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₆	—	47	1	no	—
46	C₂×C₁₆	C₄×D₄₇	1	1	yes	characteristic
47	C₄×C₈	—	47	1	no	—
48	C₃₂	—	94	1	no	—
49	C₃₂	Dic₉₄	1	1	yes	characteristic
50	C₃₂	C₂²⋊D₄₇	1	1	yes	characteristic
51	C₂×C₈	—	47	1	no	—
52	C₂×C₈	C₈×D₄₇	1	1	yes	characteristic
53	C₄²	—	47	1	no	—
54	C₁₆	—	94	1	no	—
55	C₁₆	#10625324	1	1	yes	characteristic
56	C₁₆	Dic₄₇⋊C₄	1	1	yes	characteristic
57	C₂×C₄	—	47	1	no	—
58	C₂×C₄	—	47	1	no	—
59	C₂×C₄	C₁₆×D₄₇	1	1	yes	characteristic
60	C₈	—	94	1	no	—
61	C₈	Dic₄₇⋊C₈	1	1	yes	characteristic
62	C₈	#13093963	1	1	yes	characteristic
63	C₂²	C₃₂×D₄₇	1	1	yes	characteristic
64	C₄	—	47	2	no	—
65	C₄	—	94	1	no	—
66	C₄	Dic₄₇⋊C₁₆	1	1	yes	characteristic
67	C₄	#15688956	1	1	yes	characteristic
68	C₂	Dic₄₇⋊C₃₂	1	1	yes	characteristic
69	C₂	C₆₄×D₄₇	1	1	yes	characteristic
70	C₂	#20241598	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₆₄
Fitting	C₂×C₄₇×C₆₄	C₂
socle, prime radical	C₂²×C₄₇	C₂×C₃₂
cosocle	C₂×C₃₂×C₄₇	C₂²
hypercenter	C₂×C₆₄	D₄₇
hypocenter	C₄₇	C₄⋊C₆₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
32. Dic₄₇	C₆₄	semidirect
44. C₄₇	C₄⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₆₄	2
C₃₂×Dic₄₇	2
C₂×C₄₇×C₆₄	2
C₄⋊C₆₄	47

Subgroups — Dic47⋊C64 #26104173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₇⋊C₆₄ #26104173