Subgroups — C₄⋊(C₂₃⋊C₆₄) #19212102

Order 5888.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃⋊C₆₄	C₂	1	2	yes	maximal
2	C₄×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂₃⋊C₆₄	—	2	2	no	—
4	C₂×C₂₃×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₂₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₂₃	C₈	1	1	yes	characteristic
10	C₂₃×C₃₂	—	2	1	no	—
11	C₂₃×C₃₂	D₄	1	1	yes	characteristic
12	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₂₃	C₁₆	1	1	yes	characteristic
16	C₁₆×C₂₃	—	2	1	no	—
17	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₂₃	M₁₆	1	1	yes	characteristic
19	C₄⋊C₆₄	—	23	1	no	maximal, Sylow
20	C₂×C₄×C₂₃	C₃₂	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₃₂	1	1	yes	characteristic
22	C₂×C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₂₃	—	2	1	no	—
24	C₈×C₂₃	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₂₃	M₃₂	1	1	yes	characteristic
26	C₂×C₆₄	—	23	2	no	—
27	C₄×C₃₂	D₂₃	1	1	yes	characteristic
28	C₂²×C₂₃	C₂×C₃₂	1	1	yes	characteristic
29	C₄×C₂₃	—	2	1	no	—
30	C₄×C₂₃	C₆₄	1	2	yes	complemented
31	C₄×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
32	C₄×C₂₃	M₆₄	1	1	yes	characteristic
33	C₂×C₃₂	Dic₂₃	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
35	C₄×C₁₆	Dic₂₃	1	1	yes	characteristic
36	C₆₄	—	46	2	no	—
37	C₂×C₂₃	C₄⋊C₃₂	1	1	yes	characteristic
38	C₂×C₂₃	C₂×C₆₄	1	1	yes	characteristic
39	C₂×C₂₃	M₁₂₈	1	1	yes	characteristic
40	C₂×C₁₆	C₂₃⋊C₈	1	1	yes	characteristic
41	C₂×C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
42	C₄×C₈	C₂₃⋊C₈	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	Dic₄₆	1	1	yes	characteristic
45	C₃₂	D₉₂	1	1	yes	characteristic
46	C₂₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₈	C₂₃⋊C₁₆	1	1	yes	characteristic
48	C₂×C₈	C₂×C₂₃⋊C₈	1	1	yes	characteristic
49	C₄²	C₂₃⋊C₁₆	1	1	yes	characteristic
50	C₁₆	—	2	1	no	—
51	C₁₆	#67267	1	1	yes	characteristic
52	C₁₆	C₄⋊Dic₂₃	1	1	yes	characteristic
53	C₂×C₄	C₂₃⋊C₃₂	1	1	yes	characteristic
54	C₂×C₄	C₂₃⋊C₃₂	1	1	yes	characteristic
55	C₂×C₄	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
58	C₈	#10624994	1	1	yes	characteristic
59	C₂²	C₂×C₂₃⋊C₃₂	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	C₂₃⋊C₆₄	1	2	yes	complemented
62	C₄	C₄⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic
63	C₄	#13092251	1	1	yes	characteristic
64	C₂	C₄⋊(C₂₃⋊C₃₂)	1	1	yes	characteristic
65	C₂	C₂×C₂₃⋊C₆₄	1	1	yes	characteristic
66	C₂	#15671608	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₆₄
Fitting	C₄×C₂₃×C₃₂	C₂
socle	C₂²×C₂₃	C₂×C₃₂
hypercenter	C₄×C₃₂	D₂₃
hypocenter	C₂₃	C₄⋊C₆₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
30. C₄×C₂₃	C₆₄	semidirect
46. C₂₃	C₄⋊C₆₄	semidirect
61. C₄	C₂₃⋊C₆₄	semidirect

Subgroups — C4⋊(C23⋊C64) #19212102

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊(C₂₃⋊C₆₄) #19212102