Subgroups — #15673153

Order 2944.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092375	C₂	1	3	yes	maximal
2	#13092174	C₂	1	3	yes	maximal
3	C₂₃×#338	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₃	C₂²	1	3	yes	—
5	#10625097	C₂²	1	3	yes	—
6	C₂²×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
7	#10624997	C₄	1	6	yes	complemented
8	C₈×Dic₂₃	C₄	1	6	yes	complemented
9	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
10	M₁₆×C₂₃	—	2	6	no	—
11	C₂×C₈×C₂₃	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₂₃	—	2	3	no	—
13	C₄⋊Dic₂₃	—	2	3	no	—
14	C₄×Dic₂₃	C₂×C₄	1	6	yes	—
15	C₂×C₂₃⋊C₈	C₂×C₄	1	3	yes	—
16	C₂×C₂₃⋊C₈	C₂×C₄	1	3	yes	—
17	C₂³×C₂₃	#41	1	1	yes	characteristic
18	C₂×C₄×C₂₃	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₂₃	#41	1	3	yes	—
20	C₂×Dic₂₃	—	2	6	no	—
21	C₈×C₂₃	—	2	6	no	—
22	C₂₃⋊C₈	C₄²	1	1	yes	characteristic
23	C₂₃⋊C₈	C₄²	1	3	yes	—
24	#1747	—	23	1	no	maximal, Sylow
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	#117	1	3	yes	—
27	C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
28	C₄×C₂₃	#117	1	3	yes	—
29	Dic₂₃	—	4	6	no	—
30	#405	—	23	3	no	—
31	#338	D₂₃	1	1	yes	characteristic
32	H(3,ℤ/4)	—	23	3	no	—
33	C₂×C₂₃	—	2	3	no	—
34	C₂×C₂₃	#376	1	1	yes	characteristic
35	C₂×M₁₆	C₂×D₂₃	1	3	yes	—
36	C₂²×C₈	—	23	1	no	—
37	#117	—	23	3	no	—
38	#97	—	23	6	no	—
39	C₄×C₈	—	23	6	no	—
40	C₂₃	#1747	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	23	3	no	—
44	C₂×C₈	—	23	3	no	—
45	C₂×C₈	C₄×D₂₃	1	6	yes	—
46	C₄⋊C₄	—	46	3	no	—
47	C₂²⋊C₄	—	46	3	no	—
48	C₄²	—	23	6	no	—
49	C₂³	#67292	1	1	yes	characteristic
50	C₂×C₄	—	46	6	no	—
51	C₂×C₄	C₂×C₄×D₂₃	1	3	yes	—
52	C₂×C₄	#67290	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	23	1	no	—
55	C₈	—	23	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#10625063	1	3	yes	—
58	C₄	—	92	6	no	—
59	C₄	C₄²×D₂₃	1	1	yes	characteristic
60	C₄	#10625048	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#13092262	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₂₃
commutator	C₄×C₂₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₃
Fitting	C₂₃×#338	C₂
socle	C₂×C₂₃	#376
prime radical	C₂³×C₂₃	#41
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#338	D₂₃
hypocenter	C₂₃	#1747
LCS	G ▷ C₄×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
7. #10624997	C₄	semidirect
8. C₈×Dic₂₃	C₄	semidirect
40. C₂₃	#1747	semidirect

Maximal subgroups

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

subgroup	index
#13092375	2
#13092174	2
C₂₃×#338	2
#1747	23