Subgroups — #15673015

Order 2944.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092822	C₂	1	4	yes	maximal
2	#13092797	C₂	1	2	yes	maximal
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₂	—	2	4	no	—
5	#10625040	C₂²	1	4	yes	—
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₃	C₂²	1	2	yes	—
8	#10625000	—	2	8	no	—
9	C₂×Dic₄₆	—	2	4	no	—
10	C₂×C₈×C₂₃	D₄	1	2	yes	—
11	C₂×C₈×C₂₃	D₄	1	4	yes	—
12	C₄²×C₂₃	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₂₃	—	2	8	no	—
14	Dic₉₂	—	4	8	no	—
15	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
17	C₂×Dic₂₃	—	4	4	no	—
18	Dic₄₆	—	4	8	no	—
19	C₈×C₂₃	D₈	1	4	yes	—
20	C₈×C₂₃	Q₁₆	1	8	yes	complemented
21	#1713	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	#127	1	1	yes	characteristic
23	C₄×C₂₃	C₂×D₈	1	2	yes	—
24	C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
25	Dic₂₃	—	8	4	no	—
26	#500	—	23	4	no	—
27	#494	—	23	2	no	—
28	C₈²	D₂₃	1	1	yes	characteristic
29	C₂×C₂₃	#493	1	1	yes	characteristic
30	C₂×C₂₃	#494	1	2	yes	—
31	C₂×Q₁₆	—	46	4	no	—
32	C₄⋊Q₈	—	23	4	no	—
33	#107	—	46	8	no	—
34	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
35	C₄×C₈	C₂×D₂₃	1	2	yes	—
36	C₂₃	#1713	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	46	4	no	—
38	Q₁₆	—	92	8	no	—
39	C₂×C₈	D₉₂	1	2	yes	—
40	C₂×C₈	D₉₂	1	4	yes	—
41	C₄⋊C₄	—	46	8	no	—
42	C₄²	C₂²×D₂₃	1	1	yes	characteristic
43	Q₈	—	92	8	no	—
44	C₂×C₄	—	92	4	no	—
45	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₉₂	1	2	yes	—
47	C₈	D₁₈₄	1	4	yes	—
48	C₈	Dic₉₂	1	8	yes	complemented
49	C₂²	#10625045	1	1	yes	characteristic
50	C₄	—	184	4	no	—
51	C₄	C₂×D₁₈₄	1	2	yes	—
52	C₄	C₂×Dic₉₂	1	4	yes	—
53	C₂	#13092794	1	1	yes	characteristic
54	C₂	#13092797	1	2	yes	—

	subgroup	G/H
center	C₂²	#10625045
commutator, cosocle	C₄²×C₂₃	C₂³
Frattini	C₄²	C₂²×D₂₃
Fitting	C₈²×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	#127
hypercenter	C₈²	D₂₃
hypocenter	C₂₃	#1713
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
20. C₈×C₂₃	Q₁₆	semidirect
36. C₂₃	#1713	semidirect
48. C₈	Dic₉₂	semidirect

Maximal subgroups

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

subgroup	index
#13092822	2
#13092797	2
C₈²×C₂₃	2
#1713	23