Subgroups — C₂₃×#7332 #19154958

Order 5888.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#1397	C₂	1	2	yes	maximal
2	C₂₃×#1311	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×C₃₂	C₄	1	4	yes	—
4	C₄×C₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₈²×C₂₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₂₃	C₈	1	2	yes	—
8	C₂×C₁₆×C₂₃	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₂₃	C₈	1	2	yes	—
10	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂₃×C₃₂	—	2	4	no	—
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₂₃	C₁₆	1	4	yes	—
17	C₁₆×C₂₃	M₁₆	1	4	yes	—
18	#7332	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₄×C₂₃	C₄×C₈	1	1	yes	characteristic
20	C₂×C₄×C₂₃	M₃₂	1	2	yes	—
21	C₈×C₂₃	—	4	2	no	—
22	C₈×C₂₃	#97	1	2	yes	—
23	C₈×C₂₃	C₂×C₁₆	1	2	yes	—
24	#1397	C₂×C₂₃	1	2	yes	—
25	#1311	C₂×C₂₃	1	1	yes	characteristic
26	C₂²×C₂₃	#346	1	1	yes	characteristic
27	C₄×C₂₃	—	2	2	no	—
28	C₄×C₂₃	#322	1	1	yes	characteristic
29	C₄×C₂₃	C₄×C₁₆	1	1	yes	characteristic
30	C₂×C₃₂	C₄×C₂₃	1	4	yes	—
31	C₄×C₁₆	C₄×C₂₃	1	1	yes	characteristic
32	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
33	C₈²	C₄×C₂₃	1	1	yes	characteristic
34	C₂×C₂₃	#1312	1	1	yes	characteristic
35	C₂×C₂₃	#1398	1	2	yes	—
36	C₂×C₁₆	C₈×C₂₃	1	2	yes	—
37	C₂×C₁₆	C₂×C₄×C₂₃	1	2	yes	—
38	C₄×C₈	C₈×C₂₃	1	2	yes	—
39	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
40	C₃₂	—	2	4	no	—
41	C₂₃	#7332	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	C₄²×C₂₃	1	1	yes	characteristic
44	C₂×C₈	C₂×C₈×C₂₃	1	1	yes	characteristic
45	C₄²	C₂×C₈×C₂₃	1	1	yes	characteristic
46	C₁₆	C₁₆×C₂₃	1	4	yes	—
47	C₁₆	M₁₆×C₂₃	1	4	yes	—
48	C₂×C₄	C₄×C₈×C₂₃	1	1	yes	characteristic
49	C₂×C₄	C₂₃×M₃₂	1	2	yes	—
50	C₈	—	4	2	no	—
51	C₈	C₂₃×#97	1	2	yes	—
52	C₈	C₂×C₁₆×C₂₃	1	2	yes	—
53	C₂²	C₂₃×#346	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₂₃×#322	1	1	yes	characteristic
56	C₄	C₄×C₁₆×C₂₃	1	1	yes	characteristic
57	C₂	C₂₃×#1312	1	1	yes	characteristic
58	C₂	C₂₃×#1398	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₂₃	C₄²
commutator	C₄	C₄×C₁₆×C₂₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	#346
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
18. #7332	C₂₃	direct (N × H)
41. C₂₃	#7332	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×#1311	2
#7332	23

Subgroups — C23×#7332 #19154958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7332 #19154958