Subgroups — D₂₃×#376 #15675722

Order 2944.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₂₃	C₂	1	3	yes	maximal
2	#13092263	C₂	1	3	yes	maximal, complemented
3	#13092262	C₂	1	4	yes	maximal, complemented
4	#95×D₂₃	C₂	1	4	yes	maximal
5	C₂₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₂₃	C₂²	1	6	yes	—
7	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₃	C₂²	1	3	yes	—
9	C₂×C₄×Dic₂₃	C₂²	1	6	yes	—
10	C₂×C₄×Dic₂₃	C₂²	1	3	yes	—
11	C₄²×D₂₃	C₄	1	24	yes	complemented
12	C₂₃×#95	C₂²	1	4	yes	—
13	C₂₃⋊#95	C₂²	1	12	yes	—
14	C₂³×D₂₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₂₃	C₂³	1	6	yes	—
16	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₃	C₂³	1	6	yes	—
18	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×D₂₃	—	2	24	no	—
20	C₂×C₄×D₂₃	C₂×C₄	1	24	yes	—
21	C₂×C₄×D₂₃	C₂×C₄	1	12	yes	—
22	C₄²×C₂₃	C₂×C₄	1	12	yes	complemented
23	C₄×Dic₂₃	C₂×C₄	1	12	yes	complemented
24	C₄×Dic₂₃	C₂×C₄	1	24	yes	complemented
25	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
26	C₂²×D₂₃	C₂²×C₄	1	6	yes	—
27	C₂²×D₂₃	#41	1	8	yes	—
28	C₂×C₄×C₂₃	—	2	12	no	—
29	C₂×C₄×C₂₃	C₂²×C₄	1	12	yes	—
30	C₂×C₄×C₂₃	C₂²×C₄	1	6	yes	—
31	C₂×Dic₂₃	—	2	12	no	—
32	C₂×Dic₂₃	C₂²×C₄	1	12	yes	—
33	C₂×Dic₂₃	C₂²×C₄	1	6	yes	—
34	C₄×D₂₃	—	2	48	no	—
35	C₄×D₂₃	C₄²	1	16	yes	—
36	C₂×#376	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	C₂³×C₄	1	3	yes	—
38	C₂²×C₂₃	C₂×#41	1	4	yes	—
39	C₂×D₂₃	C₂×C₄²	1	4	yes	—
40	C₂×D₂₃	#117	1	24	yes	—
41	C₄×C₂₃	—	2	12	no	—
42	C₄×C₂₃	C₂×C₄²	1	4	yes	—
43	Dic₂₃	—	2	12	no	—
44	Dic₂₃	C₂×C₄²	1	4	yes	—
45	C₂²×C₄²	—	23	3	no	—
46	#376	—	23	3	no	—
47	#376	—	23	4	no	—
48	#376	D₂₃	1	1	yes	characteristic, direct product factor
49	C₂×#95	—	23	4	no	—
50	C₂×C₂₃	C₂²×C₄²	1	1	yes	characteristic
51	C₂×C₂₃	C₂×#117	1	6	yes	—
52	D₂₃	#376	1	8	yes	direct product factor
53	C₂³×C₄	—	23	1	no	—
54	C₂³×C₄	—	23	6	no	—
55	C₂×C₄²	—	23	6	no	—
56	C₂×C₄²	—	23	3	no	—
57	C₂×C₄²	—	23	24	no	—
58	C₂×C₄²	C₂×D₂₃	1	3	yes	—
59	#95	—	23	12	no	—
60	#95	C₂×D₂₃	1	4	yes	—
61	C₂₃	C₂×#376	1	1	yes	characteristic, complemented, Sylow
62	C₂⁴	—	23	1	no	—
63	C₂²×C₄	—	23	1	no	—
64	C₂²×C₄	—	23	12	no	—
65	C₂²×C₄	—	23	6	no	—
66	C₂²×C₄	—	23	24	no	—
67	C₂²×C₄	—	46	24	no	—
68	C₂²×C₄	C₂²×D₂₃	1	6	yes	—
69	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
70	C₄²	—	23	24	no	—
71	C₄²	—	23	12	no	—
72	C₄²	C₄×D₂₃	1	12	yes	complemented
73	C₂³	—	23	6	no	—
74	C₂³	—	23	8	no	—
75	C₂³	C₂³×D₂₃	1	1	yes	characteristic
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	23	6	no	—
78	C₂×C₄	—	23	16	no	—
79	C₂×C₄	—	23	12	no	—
80	C₂×C₄	—	46	48	no	—
81	C₂×C₄	—	46	12	no	—
82	C₂×C₄	C₂×C₄×D₂₃	1	12	yes	—
83	C₂×C₄	C₂×C₄×D₂₃	1	6	yes	—
84	C₂²	—	23	24	no	—
85	C₂²	—	23	4	no	—
86	C₂²	C₂²×C₄×D₂₃	1	3	yes	—
87	C₂²	#41×D₂₃	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	—	23	4	no	—
90	C₄	—	46	12	no	—
91	C₄	C₄²×D₂₃	1	4	yes	—
92	C₂	—	23	8	no	—
93	C₂	C₂×C₄²×D₂₃	1	1	yes	characteristic
94	C₂	#117×D₂₃	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂²×C₄²
Frattini	C₂³	C₂³×D₂₃
Fitting	C₂₃×#376	C₂
socle, cosocle	C₂³×C₂₃	C₂⁴
prime radical	C₂³×D₂₃	C₂³
hypercenter	#376	D₂₃
hypocenter	C₂₃	C₂×#376
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
2. #13092263	C₂	semidirect
3. #13092262	C₂	semidirect
5. C₂₃×#376	C₂	semidirect
11. C₄²×D₂₃	C₄	semidirect
22. C₄²×C₂₃	C₂×C₄	semidirect
23. C₄×Dic₂₃	C₂×C₄	semidirect
24. C₄×Dic₂₃	C₂×C₄	semidirect
48. #376	D₂₃	direct (N × H)
52. D₂₃	#376	direct (N × H)
61. C₂₃	C₂×#376	semidirect
72. C₄²	C₄×D₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄²×D₂₃	2
#13092263	2
#13092262	2
#95×D₂₃	2
C₂₃×#376	2
C₂×#376	23

Subgroups — D23×#376 #15675722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#376 #15675722