Subgroups — #19212107

Order 5888.

66 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	#15671597	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1423	C₂	1	1	yes	maximal, characteristic
4	#13092243	—	2	1	no	—
5	C₂₃⋊C₆₄	C₄	1	2	yes	complemented
6	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₂₃×#366	—	2	1	no	—
8	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
9	C₂₃×#107	—	4	1	no	—
10	#10625000	—	4	1	no	—
11	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
14	C₄⋊C₄×C₂₃	—	8	1	no	—
15	C₄⋊Dic₂₃	—	8	1	no	—
16	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
18	#7546	—	23	1	no	maximal, Sylow
19	C₂×C₄×C₂₃	—	16	1	no	—
20	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
21	C₂×Dic₂₃	—	16	1	no	—
22	C₈×C₂₃	#107	1	1	yes	characteristic
23	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
24	C₂×C₆₄	—	23	1	no	—
25	#1423	—	23	1	no	—
26	#1423	D₂₃	1	1	yes	characteristic
27	C₂²×C₂₃	D₃₂	1	1	yes	characteristic
28	C₄×C₂₃	—	32	1	no	—
29	C₄×C₂₃	#366	1	1	yes	characteristic
30	C₄×C₂₃	Q₆₄	1	1	yes	characteristic
31	Dic₂₃	—	32	1	no	—
32	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
33	#366	—	2	1	no	—
34	#366	—	46	1	no	—
35	C₆₄	—	23	2	no	—
36	C₂×C₂₃	#1423	1	1	yes	characteristic
37	C₂×C₂₃	SD₁₂₈	1	1	yes	characteristic
38	C₂×C₂₃	SD₁₂₈	1	1	yes	characteristic
39	C₂×C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
40	#107	—	4	1	no	—
41	#107	—	92	1	no	—
42	C₃₂	Dic₄₆	1	1	yes	characteristic
43	C₃₂	C₄×D₂₃	1	1	yes	characteristic
44	C₂₃	#7546	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₈	#67272	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	184	1	no	—
48	C₁₆	Dic₂₃⋊C₄	1	1	yes	characteristic
49	C₁₆	#67275	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	368	1	no	—
52	C₂×C₄	#10625008	1	1	yes	characteristic
53	C₈	#10624989	1	1	yes	characteristic
54	C₈	#10625011	1	1	yes	characteristic
55	C₂²	#13092252	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	736	1	no	—
58	C₄	#13092242	1	1	yes	characteristic
59	C₄	#13092257	1	1	yes	characteristic
60	C₂	#15671596	1	1	yes	characteristic
61	C₂	#15671611	1	1	yes	characteristic
62	C₂	#15671612	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13092252
commutator	C₂₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂₃×#1423	C₂
socle	C₂²×C₂₃	D₃₂
hypercenter	#1423	D₂₃
hypocenter	C₂₃	#7546
LCS	G ▷ C₂₃×C₃₂ ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. C₂₃⋊C₆₄	C₄	semidirect
44. C₂₃	#7546	semidirect