Subgroups — #15671458

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092238	C₂	1	1	yes	maximal, characteristic
2	#13092238	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#499	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#125	C₄	1	2	yes	—
5	C₂₃×#107	—	2	1	no	—
6	C₂₃×#106	—	2	1	no	—
7	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	#10624994	—	2	1	no	—
9	#10624994	—	2	1	no	—
10	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₂₃	—	2	2	no	—
13	C₄⋊C₄×C₂₃	—	4	2	no	—
14	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂₃⋊C₁₆	—	4	1	no	—
16	C₂₃⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	—	4	2	no	—
19	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
23	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
24	#1366	—	23	1	no	maximal, Sylow
25	C₂²×C₂₃	#100	1	1	yes	characteristic
26	C₄×C₂₃	—	4	1	no	—
27	C₄×C₂₃	—	8	2	no	—
28	C₄×C₂₃	#103	1	1	yes	characteristic
29	C₄×C₂₃	#103	1	1	yes	characteristic
30	#499	D₂₃	1	1	yes	characteristic
31	#364	—	23	1	no	—
32	#364	—	23	1	no	—
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	#333	1	1	yes	characteristic
35	#125	Dic₂₃	1	2	yes	—
36	M₃₂	—	46	1	no	—
37	M₃₂	—	46	1	no	—
38	#107	—	2	1	no	—
39	#106	—	2	1	no	—
40	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
41	C₂₃	#1366	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
44	C₄⋊C₄	—	2	2	no	—
45	C₄⋊C₄	—	4	2	no	—
46	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
47	C₁₆	—	92	1	no	—
48	C₁₆	—	92	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
52	C₈	#67274	1	1	yes	characteristic
53	C₈	#67274	1	1	yes	characteristic
54	C₈	#67275	1	1	yes	characteristic
55	C₈	#67275	1	1	yes	characteristic
56	C₂²	#10625015	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	2	no	—
59	C₄	#10625017	1	1	yes	characteristic
60	C₄	#10625017	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#13092166	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092166
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#499	C₂
socle	C₂×C₂₃	#333
prime radical	C₂²×C₂₃	#100
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#499	D₂₃
hypocenter	C₂₃	#1366
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
41. C₂₃	#1366	semidirect

Maximal subgroups

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

subgroup	index
#13092238	2
C₂₃×#499	2
#1366	23