Subgroups — #15675672

Order 2944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092822	C₂	1	2	yes	maximal
2	#13092243	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	#10625040	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	#10625000	—	2	2	no	—
8	#10625000	C₂²	1	4	yes	—
9	C₂×Dic₄₆	—	4	2	no	—
10	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
12	C₄²×C₂₃	D₄	1	1	yes	characteristic
13	C₄⋊Dic₂₃	—	2	4	no	—
14	C₄⋊Dic₂₃	—	4	2	no	—
15	C₁₆×C₂₃	Q₈	1	4	yes	complemented
16	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
17	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₂₃	—	4	4	no	—
20	Dic₄₆	—	8	4	no	—
21	C₈×C₂₃	Q₁₆	1	2	yes	—
22	C₈×C₂₃	C₂×Q₈	1	2	yes	—
23	#2252	—	23	1	no	maximal, Sylow
24	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
25	C₄×C₂₃	D₁₆	1	2	yes	—
26	C₄×C₂₃	Q₃₂	1	2	yes	—
27	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
28	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
29	Dic₂₃	—	8	4	no	—
30	#500	—	23	2	no	—
31	#366	—	23	4	no	—
32	C₄×C₁₆	D₂₃	1	1	yes	characteristic
33	C₂×C₂₃	#500	1	1	yes	characteristic
34	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
35	C₂×C₂₃	C₂×Q₃₂	1	1	yes	characteristic
36	C₄⋊Q₈	—	46	2	no	—
37	C₂×C₁₆	C₂×D₂₃	1	2	yes	—
38	#107	—	23	4	no	—
39	#107	—	46	2	no	—
40	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
41	C₂₃	#2252	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	92	2	no	—
43	C₂×C₈	D₉₂	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
45	C₄⋊C₄	—	46	4	no	—
46	C₄⋊C₄	—	92	2	no	—
47	C₄²	D₉₂	1	1	yes	characteristic
48	C₁₆	Dic₄₆	1	4	yes	complemented
49	Q₈	—	184	4	no	—
50	C₂×C₄	—	92	4	no	—
51	C₂×C₄	D₁₈₄	1	1	yes	characteristic
52	C₂×C₄	D₁₈₄	1	1	yes	characteristic
53	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
54	C₈	Dic₉₂	1	2	yes	—
55	C₈	C₂×Dic₄₆	1	2	yes	—
56	C₂²	C₂×D₁₈₄	1	1	yes	characteristic
57	C₄	—	184	4	no	—
58	C₄	D₃₆₈	1	2	yes	—
59	C₄	Dic₁₈₄	1	2	yes	—
60	C₄	#10625040	1	1	yes	characteristic
61	C₄	C₂×Dic₉₂	1	1	yes	characteristic
62	C₂	#13092822	1	1	yes	characteristic
63	C₂	C₂×D₃₆₈	1	1	yes	characteristic
64	C₂	C₂×Dic₁₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₈₄
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₄×C₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	C₄×C₁₆	D₂₃
hypocenter	C₂₃	#2252
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₂₃	Q₈	semidirect
41. C₂₃	#2252	semidirect
48. C₁₆	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
#13092822	2
#13092243	2
C₄×C₁₆×C₂₃	2
#2252	23