Subgroups — C₂₃×#2252 #15669871

Order 2944.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₂₃	Q₈	semidirect
23. #2252	C₂₃	direct (N × H)
41. C₂₃	#2252	direct (N × H)
48. C₁₆	Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#500	2
C₂₃×#366	2
C₄×C₁₆×C₂₃	2
#2252	23

Subgroups — C23×#2252 #15669871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2252 #15669871