Subgroups — Dic₂₃⋊C₆₄ #19212101

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	1	yes	maximal, characteristic
2	C₃₂×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₂₃	C₄	1	1	yes	characteristic
6	C₂₃⋊C₆₄	—	2	1	no	—
7	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
8	C₂₃×C₆₄	—	2	1	no	—
9	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₂₃	C₈	1	1	yes	characteristic
11	C₂×C₂₃⋊C₁₆	C₈	1	1	yes	characteristic
12	C₂₃×C₃₂	D₄	1	1	yes	characteristic
13	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
14	C₂₃⋊C₃₂	—	2	1	no	—
15	C₂×C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₂₃	C₁₆	1	1	yes	characteristic
17	C₂×C₂₃⋊C₈	C₁₆	1	1	yes	characteristic
18	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₂₃	M₁₆	1	1	yes	characteristic
20	C₂₃⋊C₁₆	—	2	1	no	—
21	C₄⋊C₆₄	—	23	1	no	maximal, Sylow
22	C₂×C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
23	C₂×Dic₂₃	C₃₂	1	1	yes	characteristic
24	C₂×Dic₂₃	C₃₂	1	1	yes	characteristic
25	C₈×C₂₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₂₃	M₃₂	1	1	yes	characteristic
27	C₂₃⋊C₈	—	2	1	no	—
28	C₂×C₆₄	—	23	1	no	—
29	C₂×C₆₄	D₂₃	1	1	yes	characteristic
30	C₄×C₃₂	—	23	1	no	—
31	C₂²×C₂₃	C₂×C₃₂	1	1	yes	characteristic
32	C₄×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
33	C₄×C₂₃	M₆₄	1	1	yes	characteristic
34	Dic₂₃	—	2	1	no	—
35	Dic₂₃	C₆₄	1	2	yes	complemented
36	C₂×C₃₂	—	23	1	no	—
37	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
38	C₄×C₁₆	—	23	1	no	—
39	C₆₄	—	2	1	no	—
40	C₆₄	—	46	1	no	—
41	C₂×C₂₃	C₄⋊C₃₂	1	1	yes	characteristic
42	C₂×C₂₃	C₂×C₆₄	1	1	yes	characteristic
43	C₂×C₂₃	M₁₂₈	1	1	yes	characteristic
44	C₂×C₁₆	—	23	1	no	—
45	C₂×C₁₆	C₄×D₂₃	1	1	yes	characteristic
46	C₄×C₈	—	23	1	no	—
47	C₃₂	—	46	1	no	—
48	C₃₂	Dic₄₆	1	1	yes	characteristic
49	C₃₂	C₂²⋊D₂₃	1	1	yes	characteristic
50	C₂₃	C₄⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	23	1	no	—
52	C₂×C₈	C₈×D₂₃	1	1	yes	characteristic
53	C₄²	—	23	1	no	—
54	C₁₆	—	46	1	no	—
55	C₁₆	#67262	1	1	yes	characteristic
56	C₁₆	Dic₂₃⋊C₄	1	1	yes	characteristic
57	C₂×C₄	—	23	1	no	—
58	C₂×C₄	—	23	1	no	—
59	C₂×C₄	C₁₆×D₂₃	1	1	yes	characteristic
60	C₈	—	46	1	no	—
61	C₈	#10624980	1	1	yes	characteristic
62	C₈	Dic₂₃⋊C₈	1	1	yes	characteristic
63	C₂²	C₃₂×D₂₃	1	1	yes	characteristic
64	C₄	—	23	2	no	—
65	C₄	—	46	1	no	—
66	C₄	Dic₂₃⋊C₁₆	1	1	yes	characteristic
67	C₄	#13092250	1	1	yes	characteristic
68	C₂	Dic₂₃⋊C₃₂	1	1	yes	characteristic
69	C₂	D₂₃×C₆₄	1	1	yes	characteristic
70	C₂	#15671607	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
35. Dic₂₃	C₆₄	semidirect
50. C₂₃	C₄⋊C₆₄	semidirect

Subgroups — Dic23⋊C64 #19212101

Conjugacy classes of subgroups

Complements

Subgroups — Dic₂₃⋊C₆₄ #19212101