Subgroups — C₂₃×#2245 #15669864

Order 2944.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#499	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#494	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#358	C₂	1	4	yes	maximal
4	C₂₃×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₂₃	—	2	1	no	—
6	C₂×Q₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂₃×C₄⋊Q₈	—	2	1	no	—
8	C₂₃×#125	—	2	1	no	—
9	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
10	C₂₃×#107	C₂²	1	2	yes	—
11	C₂₃×#106	—	2	1	no	—
12	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₂₃	—	2	2	no	—
14	Q₁₆×C₂₃	—	2	4	no	—
15	Q₁₆×C₂₃	—	4	2	no	—
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₂₃	—	2	2	no	—
19	C₄⋊C₄×C₂₃	—	4	2	no	—
20	C₄⋊C₄×C₂₃	—	4	2	no	—
21	C₄²×C₂₃	D₄	1	1	yes	characteristic
22	C₁₆×C₂₃	—	2	2	no	—
23	Q₈×C₂₃	—	4	2	no	—
24	Q₈×C₂₃	—	4	2	no	—
25	C₂×C₄×C₂₃	—	4	2	no	—
26	C₂×C₄×C₂₃	—	4	2	no	—
27	C₂×C₄×C₂₃	D₈	1	2	yes	—
28	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₃	SD₁₆	1	2	yes	—
30	C₈×C₂₃	#41	1	2	yes	—
31	#2245	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	—	8	2	no	—
35	C₄×C₂₃	—	8	2	no	—
36	C₄×C₂₃	#124	1	1	yes	characteristic
37	C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
38	#499	C₂×C₂₃	1	1	yes	characteristic
39	#494	C₂×C₂₃	1	1	yes	characteristic
40	#358	C₂×C₂₃	1	4	yes	—
41	#346	C₂×C₂₃	1	1	yes	characteristic
42	C₂×C₂₃	#486	1	1	yes	characteristic
43	C₂×C₂₃	#510	1	2	yes	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	C₂²×C₂₃	1	2	yes	—
46	C₄⋊Q₈	—	2	1	no	—
47	#125	—	2	1	no	—
48	C₂×C₁₆	C₂²×C₂₃	1	2	yes	—
49	#107	C₂²×C₂₃	1	2	yes	—
50	#106	—	2	1	no	—
51	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
52	C₂₃	#2245	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×Q₈	—	2	2	no	—
54	Q₁₆	—	2	4	no	—
55	Q₁₆	—	4	2	no	—
56	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
57	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	4	2	no	—
61	C₄²	D₄×C₂₃	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	D₈×C₂₃	1	2	yes	—
68	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
69	C₈	SD₁₆×C₂₃	1	2	yes	—
70	C₈	#41×C₂₃	1	2	yes	—
71	C₂²	C₂×D₈×C₂₃	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	8	2	no	—
75	C₄	C₂₃×#124	1	1	yes	characteristic
76	C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
77	C₂	C₂₃×#486	1	1	yes	characteristic
78	C₂	C₂₃×#510	1	2	yes	—

	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
31. #2245	C₂₃	direct (N × H)
52. C₂₃	#2245	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#499	2
C₂₃×#494	2
C₂₃×#358	2
C₂₃×#346	2
#2245	23

Subgroups — C23×#2245 #15669864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2245 #15669864