Subgroups — #15673009

Order 2944.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092768	C₂	1	3	yes	maximal, complemented
2	#13092764	C₂	1	3	yes	maximal
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625045	C₂²	1	1	yes	characteristic
5	#10625040	C₂²	1	3	yes	—
6	C₄×C₈×C₂₃	C₂²	1	3	yes	—
7	#10625003	—	2	6	no	—
8	#10624998	—	2	6	no	—
9	C₂×D₉₂	—	2	3	no	—
10	C₂×Dic₄₆	—	2	3	no	—
11	C₂×C₈×C₂₃	D₄	1	6	yes	—
12	C₄²×C₂₃	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₂₃	—	2	3	no	—
14	C₄⋊Dic₂₃	—	2	3	no	—
15	C₂²×D₂₃	—	4	1	no	—
16	C₂×C₄×C₂₃	C₂×D₄	1	3	yes	—
17	C₂×Dic₂₃	—	4	3	no	—
18	D₉₂	—	4	6	no	—
19	Dic₄₆	—	4	6	no	—
20	C₈×C₂₃	—	2	6	no	—
21	#1711	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	#127	1	1	yes	characteristic
23	C₂×D₂₃	—	8	3	no	—
24	C₄×C₂₃	#135	1	6	yes	—
25	Dic₂₃	—	8	3	no	—
26	#487	—	23	3	no	—
27	#486	—	23	3	no	—
28	C₈²	D₂₃	1	1	yes	characteristic, complemented
29	C₂×C₂₃	#495	1	3	yes	—
30	D₂₃	—	16	1	no	—
31	C₄⋊Q₈	—	23	3	no	—
32	#127	—	23	1	no	—
33	#103	—	46	6	no	—
34	#102	—	46	6	no	—
35	C₄×C₈	C₂×D₂₃	1	3	yes	—
36	C₂₃	#1711	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	46	3	no	—
38	C₂×D₄	—	46	3	no	—
39	C₂×C₈	D₉₂	1	6	yes	—
40	C₄⋊C₄	—	46	3	no	—
41	C₄⋊C₄	—	46	3	no	—
42	C₄²	C₂²×D₂₃	1	1	yes	characteristic
43	C₂³	—	92	1	no	—
44	Q₈	—	92	6	no	—
45	D₄	—	92	6	no	—
46	C₂×C₄	—	92	3	no	—
47	C₂×C₄	C₂×D₉₂	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	184	3	no	—
50	C₂²	#10625045	1	1	yes	characteristic
51	C₄	—	184	3	no	—
52	C₄	#10625075	1	6	yes	—
53	C₂	—	368	1	no	—
54	C₂	#13092801	1	3	yes	—

	subgroup	G/H
center	C₂²	#10625045
commutator, cosocle	C₄²×C₂₃	C₂³
Frattini	C₄²	C₂²×D₂₃
Fitting	C₈²×C₂₃	C₂
socle	C₂²×C₂₃	#127
prime radical	#10625045	C₂²
hypercenter	C₈²	D₂₃
hypocenter	C₂₃	#1711
LCS	G ▷ C₄²×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #13092768	C₂	semidirect
3. C₈²×C₂₃	C₂	semidirect
28. C₈²	D₂₃	semidirect
36. C₂₃	#1711	semidirect

Maximal subgroups

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

subgroup	index
#13092768	2
#13092764	2
C₈²×C₂₃	2
#1711	23