Subgroups — #13092822

Order 1472.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₄×C₈×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	#500
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
14. C₈×C₂₃	Q₈	semidirect
27. C₂₃	#500	semidirect
38. C₈	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
#10625040	2
C₄×C₈×C₂₃	2
#10625000	2
#500	23