Subgroups — #15671457

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092819	C₂	1	1	yes	maximal, characteristic
2	#13092238	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#364	C₂	1	1	yes	maximal, characteristic
4	#10625041	C₄	1	2	yes	—
5	C₂₃×M₃₂	—	2	1	no	—
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	#10625000	—	2	1	no	—
8	#10624999	—	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	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₂₃	—	2	2	no	—
14	Dic₂₃⋊C₄	—	4	2	no	—
15	C₁₆×C₂₃	—	4	1	no	—
16	C₂₃⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₂₃	—	4	2	no	—
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	#103	1	1	yes	characteristic
28	C₄×C₂₃	#103	1	1	yes	characteristic
29	Dic₂₃	—	8	2	no	—
30	#499	—	23	1	no	—
31	#364	—	23	1	no	—
32	#364	D₂₃	1	1	yes	characteristic
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	#333	1	1	yes	characteristic
35	#125	—	23	2	no	—
36	M₃₂	—	2	1	no	—
37	M₃₂	—	46	1	no	—
38	#107	—	46	1	no	—
39	#106	—	46	1	no	—
40	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
41	C₂₃	#1366	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	D₉₂	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
44	C₄⋊C₄	—	46	2	no	—
45	C₄⋊C₄	—	92	2	no	—
46	C₄²	C₄×D₂₃	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	92	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	92	2	no	—
51	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
52	C₈	#67263	1	1	yes	characteristic
53	C₈	Dic₉₂	1	1	yes	characteristic
54	C₈	#67273	1	1	yes	characteristic
55	C₈	#67275	1	1	yes	characteristic
56	C₂²	#10625005	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	184	2	no	—
59	C₄	#10624992	1	1	yes	characteristic
60	C₄	#10624998	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#13092165	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092165
commutator	C₄²×C₂₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#364	C₂
socle	C₂×C₂₃	#333
prime radical	C₂²×C₂₃	#100
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#364	D₂₃
hypocenter	C₂₃	#1366
LCS	G ▷ C₄²×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

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
#13092819	2
#13092238	2
C₂₃×#364	2
#1366	23