Subgroups — C₂₃×#1418 #15669037

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#508	C₂	1	1	yes	maximal, characteristic
2	C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#135	—	2	1	no	—
5	C₂₃×Q₃₂	C₄	1	1	yes	characteristic, complemented
6	C₂₃×SD₃₂	—	2	1	no	—
7	C₂₃×D₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#107	—	2	1	no	—
10	C₂₃×C₃₂	—	2	1	no	—
11	#41×C₂₃	—	4	1	no	—
12	Q₁₆×C₂₃	—	2	1	no	—
13	SD₁₆×C₂₃	—	4	1	no	—
14	D₈×C₂₃	—	2	1	no	—
15	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₂₃	—	4	1	no	—
17	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₃	D₄	1	1	yes	characteristic
19	Q₈×C₂₃	—	4	1	no	—
20	D₄×C₂₃	—	4	1	no	—
21	D₄×C₂₃	—	8	1	no	—
22	C₂×C₄×C₂₃	—	8	1	no	—
23	C₂×C₄×C₂₃	—	8	1	no	—
24	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
25	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
27	#1418	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₂₃	—	8	1	no	—
29	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
30	C₄×C₂₃	—	8	1	no	—
31	C₄×C₂₃	—	16	1	no	—
32	C₄×C₂₃	#102	1	1	yes	characteristic
33	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
34	#508	C₂×C₂₃	1	1	yes	characteristic
35	M₆₄	C₂×C₂₃	1	1	yes	characteristic, complemented
36	#367	C₂×C₂₃	1	1	yes	characteristic, complemented
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	—	16	1	no	—
39	C₂×C₂₃	#357	1	1	yes	characteristic
40	#135	—	2	1	no	—
41	Q₃₂	C₄×C₂₃	1	1	yes	characteristic, complemented
42	SD₃₂	—	2	1	no	—
43	D₁₆	C₄×C₂₃	1	1	yes	characteristic, complemented
44	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
45	#107	—	2	1	no	—
46	C₃₂	—	2	1	no	—
47	C₂₃	#1418	1	1	yes	characteristic, direct product factor, Sylow
48	#41	—	4	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	4	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
55	C₁₆	D₄×C₂₃	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	8	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	8	1	no	—
61	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
63	C₈	SD₁₆×C₂₃	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
66	C₄	—	8	1	no	—
67	C₄	—	16	1	no	—
68	C₄	C₂₃×#102	1	1	yes	characteristic
69	C₄	C₂₃×SD₃₂	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	16	1	no	—
72	C₂	C₂₃×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	#357
commutator	C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
prime radical	C₂₃×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×M₆₄	C₂	semidirect
3. C₂₃×#367	C₂	semidirect
5. C₂₃×Q₃₂	C₄	semidirect
7. C₂₃×D₁₆	C₄	semidirect
27. #1418	C₂₃	direct (N × H)
35. M₆₄	C₂×C₂₃	semidirect
36. #367	C₂×C₂₃	semidirect
41. Q₃₂	C₄×C₂₃	semidirect
43. D₁₆	C₄×C₂₃	semidirect
47. C₂₃	#1418	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×#508	2
C₂₃×M₆₄	2
C₂₃×#367	2
#1418	23

Subgroups — C23×#1418 #15669037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1418 #15669037