Subgroups — C₂₃×#7464 #19155090

Order 5888.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1397	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1373	C₂	1	2	yes	maximal
3	C₂×C₂₃×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₂₃×C₃₂	C₄	1	1	yes	characteristic
5	C₂₃×#364	—	2	2	no	—
6	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃×M₃₂	—	4	2	no	—
8	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₂₃×C₃₂	—	2	1	no	—
12	C₂₃×C₃₂	C₈	1	2	yes	—
13	C₂×C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
15	C₄²×C₂₃	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₂₃	—	2	1	no	—
17	C₁₆×C₂₃	—	8	2	no	—
18	C₁₆×C₂₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₂₃	M₁₆	1	1	yes	characteristic
20	#7464	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	#107	1	1	yes	characteristic
23	C₈×C₂₃	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₂₃	#108	1	1	yes	characteristic
25	C₈×C₂₃	SD₃₂	1	2	yes	—
26	#1397	C₂×C₂₃	1	1	yes	characteristic
27	#1373	C₂×C₂₃	1	2	yes	—
28	C₂²×C₂₃	#368	1	1	yes	characteristic
29	C₄×C₂₃	—	4	1	no	—
30	C₄×C₂₃	#335	1	1	yes	characteristic
31	C₄×C₂₃	#367	1	1	yes	characteristic
32	C₂×C₃₂	C₄×C₂₃	1	1	yes	characteristic
33	C₂×C₃₂	C₄×C₂₃	1	1	yes	characteristic
34	#364	—	2	2	no	—
35	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	#1372	1	1	yes	characteristic
38	M₃₂	—	4	2	no	—
39	C₂×C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
40	C₂×C₁₆	Q₈×C₂₃	1	1	yes	characteristic
41	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
42	C₃₂	—	2	1	no	—
43	C₃₂	C₈×C₂₃	1	2	yes	—
44	C₂₃	#7464	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₈	C₄⋊C₄×C₂₃	1	1	yes	characteristic
46	C₂×C₈	D₈×C₂₃	1	1	yes	characteristic
47	C₄²	Q₁₆×C₂₃	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	8	2	no	—
50	C₁₆	C₂×C₈×C₂₃	1	1	yes	characteristic
51	C₁₆	M₁₆×C₂₃	1	1	yes	characteristic
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	C₂₃×#107	1	1	yes	characteristic
54	C₈	C₂₃×C₄⋊C₈	1	1	yes	characteristic
55	C₈	C₂₃×#108	1	1	yes	characteristic
56	C₈	C₂₃×SD₃₂	1	2	yes	—
57	C₂²	C₂₃×#368	1	1	yes	characteristic
58	C₄	—	4	1	no	—
59	C₄	C₂₃×#335	1	1	yes	characteristic
60	C₄	C₂₃×#367	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	C₂₃×#1372	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#367
commutator	C₁₆	C₂×C₈×C₂₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₃
socle	C₂×C₂₃	#1372
prime radical	C₂²×C₂₃	#368
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₄×C₈×C₂₃ ◁ C₄×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
20. #7464	C₂₃	direct (N × H)
44. C₂₃	#7464	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×#1397	2
C₂₃×#1373	2
#7464	23

Subgroups — C23×#7464 #19155090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7464 #19155090