Subgroups — C₂₃×#1452 #15669071

Order 2944.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#431	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#322	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₂₃	C₄	1	2	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×C₄⋊C₈	C₄	1	4	yes	—
7	C₂₃×C₂²⋊C₈	C₄	1	4	yes	—
8	C₄×C₈×C₂₃	C₄	1	2	yes	—
9	C₄×C₈×C₂₃	C₂²	1	2	yes	—
10	C₄×C₈×C₂₃	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	—	2	4	no	—
14	C₂×C₈×C₂₃	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
16	C₄²×C₂₃	C₂×C₄	1	2	yes	—
17	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₂₃	C₂³	1	1	yes	characteristic
19	C₂³×C₂₃	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	4	no	—
21	C₂×C₄×C₂₃	C₄²	1	2	yes	—
22	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₃	M₁₆	1	4	yes	—
24	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
26	C₈×C₂₃	—	2	4	no	—
27	C₈×C₂₃	—	2	8	no	—
28	#1452	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₂₃	—	2	2	no	—
30	C₂²×C₂₃	#97	1	2	yes	—
31	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	#97	1	2	yes	—
34	C₄×C₂₃	C₂×M₁₆	1	2	yes	—
35	C₄×C₂₃	#131	1	4	yes	—
36	#431	C₂×C₂₃	1	2	yes	—
37	C₂×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
38	#322	C₂×C₂₃	1	4	yes	complemented
39	C₂×C₂₃	—	2	2	no	—
40	C₂×C₂₃	C₂×#97	1	1	yes	characteristic
41	C₂×C₂₃	#405	1	2	yes	—
42	C₂²×C₈	C₄×C₂₃	1	2	yes	—
43	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
44	C₄⋊C₈	C₄×C₂₃	1	4	yes	—
45	C₂²⋊C₈	C₄×C₂₃	1	4	yes	—
46	C₄×C₈	C₄×C₂₃	1	2	yes	—
47	C₄×C₈	C₂²×C₂₃	1	2	yes	—
48	C₄×C₈	C₂²×C₂₃	1	4	yes	—
49	C₂₃	#1452	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×C₄	C₂×C₄×C₂₃	1	2	yes	—
51	C₂²×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	C₂×C₄×C₂₃	1	4	yes	—
54	C₂×C₈	C₂×C₄×C₂₃	1	8	yes	—
55	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
56	C₄²	C₂×C₄×C₂₃	1	2	yes	—
57	C₄²	C₂³×C₂₃	1	1	yes	characteristic
58	C₂³	C₄²×C₂₃	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄²×C₂₃	1	2	yes	—
61	C₂×C₄	C₄²×C₂₃	1	1	yes	characteristic
62	C₂×C₄	M₁₆×C₂₃	1	4	yes	—
63	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
64	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
65	C₈	—	2	4	no	—
66	C₈	—	2	8	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂₃×#97	1	2	yes	—
69	C₂²	C₂×C₄²×C₂₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	C₂₃×#97	1	2	yes	—
72	C₄	C₂×M₁₆×C₂₃	1	2	yes	—
73	C₄	C₂₃×#131	1	4	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂×C₂₃×#97	1	1	yes	characteristic
76	C₂	C₂₃×#405	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂₃×#322	C₂	semidirect
28. #1452	C₂₃	direct (N × H)
38. #322	C₂×C₂₃	semidirect
49. C₂₃	#1452	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×#431	2
C₂×C₄×C₈×C₂₃	2
C₂₃×#322	2
#1452	23

Subgroups — C23×#1452 #15669071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1452 #15669071