Subgroups — #15673551

Order 2944.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₂₃⋊C₈)	C₂	1	6	yes	maximal
2	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₃	C₂²	1	3	yes	—
4	C₂²×C₂₃⋊C₈	C₂²	1	4	yes	—
5	C₂₃×#95	C₄	1	4	yes	—
6	C₄⋊(C₂₃⋊C₈)	—	2	12	no	—
7	C₂²×C₄×C₂₃	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
9	C₄²×C₂₃	D₄	1	6	yes	—
10	C₄²×C₂₃	Q₈	1	6	yes	—
11	C₂×C₂₃⋊C₈	—	2	12	no	—
12	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	12	no	—
14	C₂×C₄×C₂₃	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₂₃	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₂₃	C₂×Q₈	1	3	yes	—
17	C₂₃⋊C₈	—	4	4	no	—
18	#1843	—	23	1	no	maximal, Sylow
19	C₂²×C₂₃	C₂×C₄⋊C₄	1	3	yes	—
20	C₂²×C₂₃	#131	1	4	yes	—
21	C₄×C₂₃	—	2	12	no	—
22	C₄×C₂₃	#127	1	1	yes	characteristic
23	C₄×C₂₃	C₄⋊Q₈	1	3	yes	—
24	C₂×C₄⋊C₈	—	23	6	no	—
25	#376	D₂₃	1	1	yes	characteristic
26	C₂×C₂₃	#384	1	1	yes	characteristic
27	C₂×C₂₃	#424	1	6	yes	—
28	C₂²×C₈	—	23	4	no	—
29	C₂×C₄²	C₂×D₂₃	1	3	yes	—
30	C₄⋊C₈	—	46	12	no	—
31	#95	Dic₂₃	1	4	yes	—
32	C₂₃	#1843	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	C₂×Dic₂₃	1	6	yes	—
34	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
35	C₂×C₈	—	46	12	no	—
36	C₄²	Dic₄₆	1	6	yes	—
37	C₄²	D₉₂	1	6	yes	—
38	C₂³	C₂²×Dic₂₃	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₂₃	1	12	yes	—
41	C₂×C₄	C₂×Dic₄₆	1	3	yes	—
42	C₂×C₄	C₂×D₉₂	1	3	yes	—
43	C₈	—	92	4	no	—
44	C₂²	C₂×C₄⋊Dic₂₃	1	3	yes	—
45	C₂²	#10625119	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#10625040	1	3	yes	—
48	C₄	#10625045	1	1	yes	characteristic
49	C₂	#13092287	1	1	yes	characteristic
50	C₂	#13092444	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₃
commutator, socle, prime radical	C₂³×C₂₃	C₂²×C₄
Fitting	C₂₃×#376	C₂
cosocle	C₂²×C₄×C₂₃	C₂³
hypercenter	#376	D₂₃
hypocenter	C₂₃	#1843
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
32. C₂₃	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₂₃⋊C₈)	2
C₂₃×#376	2
#1843	23