Subgroups — C₂₃×#1453 #15669072

Order 2944.

190 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	C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#322	C₂	1	2	yes	maximal, complemented
5	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₁₆×C₂₃	C₄	1	2	yes	—
7	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×C₄⋊C₈	C₄	1	4	yes	—
9	C₂₃×C₂²⋊C₈	C₄	1	4	yes	—
10	C₂₃×#97	C₄	1	2	yes	—
11	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₃	C₂²	1	2	yes	—
13	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
17	M₁₆×C₂₃	—	2	4	no	—
18	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
22	C₄²×C₂₃	C₂×C₄	1	2	yes	—
23	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₂₃	C₂³	1	1	yes	characteristic
25	C₂³×C₂₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₃	—	2	2	no	—
27	C₂×C₄×C₂₃	—	2	4	no	—
28	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₄²	1	2	yes	—
30	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
32	C₈×C₂₃	—	2	2	no	—
33	C₈×C₂₃	—	2	4	no	—
34	C₈×C₂₃	—	2	4	no	—
35	C₈×C₂₃	M₁₆	1	4	yes	—
36	#1453	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	2	2	no	—
39	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	C₂×M₁₆	1	2	yes	—
43	C₄×C₂₃	#131	1	4	yes	—
44	#431	C₂×C₂₃	1	2	yes	—
45	C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic
46	#322	C₂×C₂₃	1	1	yes	characteristic, complemented
47	#322	C₂×C₂₃	1	2	yes	complemented
48	C₈²	C₂×C₂₃	1	1	yes	characteristic, complemented
49	C₂×C₂₃	—	4	1	no	—
50	C₂×C₂₃	C₄×M₁₆	1	1	yes	characteristic
51	C₂×C₂₃	#405	1	2	yes	—
52	C₂×M₁₆	C₄×C₂₃	1	2	yes	—
53	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
54	C₄⋊C₈	C₄×C₂₃	1	4	yes	—
55	C₂²⋊C₈	C₄×C₂₃	1	4	yes	—
56	#97	C₄×C₂₃	1	2	yes	—
57	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
58	C₄×C₈	C₂²×C₂₃	1	2	yes	—
59	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
60	C₄×C₈	C₂²×C₂₃	1	2	yes	—
61	C₂₃	#1453	1	1	yes	characteristic, direct product factor, Sylow
62	C₂²×C₄	C₂×C₄×C₂₃	1	2	yes	—
63	C₂²×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
66	C₂×C₈	C₂×C₄×C₂₃	1	4	yes	—
67	C₂×C₈	C₂×C₄×C₂₃	1	4	yes	—
68	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
69	C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
70	C₄²	C₂×C₄×C₂₃	1	2	yes	—
71	C₄²	C₂³×C₂₃	1	1	yes	characteristic
72	C₂³	C₄²×C₂₃	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄²×C₂₃	1	1	yes	characteristic
76	C₂×C₄	C₄²×C₂₃	1	2	yes	—
77	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
79	C₈	—	2	2	no	—
80	C₈	—	2	4	no	—
81	C₈	—	2	4	no	—
82	C₈	M₁₆×C₂₃	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄²×C₂₃	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×M₁₆×C₂₃	1	2	yes	—
89	C₄	C₂₃×#131	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×M₁₆×C₂₃	1	1	yes	characteristic
92	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
4. C₂₃×#322	C₂	semidirect
5. C₈²×C₂₃	C₂	semidirect
36. #1453	C₂₃	direct (N × H)
46. #322	C₂×C₂₃	semidirect
47. #322	C₂×C₂₃	semidirect
48. C₈²	C₂×C₂₃	semidirect
61. C₂₃	#1453	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
C₄×M₁₆×C₂₃	2
C₂₃×#322	2
C₈²×C₂₃	2
#1453	23

Subgroups — C23×#1453 #15669072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1453 #15669072