Subgroups — D₂₃×#383 #15675785

Order 2944.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic
2	#13092285	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092284	C₂	1	6	yes	maximal, complemented
4	#95×D₂₃	C₂	1	6	yes	maximal
5	C₂₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
7	C₂²×C₄×D₂₃	C₂²	1	3	yes	—
8	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₂₃	C₂²	1	3	yes	—
10	C₄²×D₂₃	C₄	1	8	yes	complemented
11	C₂₃×#95	C₂²	1	6	yes	—
12	C₂₃⋊#95	C₂²	1	12	yes	—
13	C₂₃⋊#95	C₂²	1	6	yes	—
14	C₂³×D₂₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
16	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
17	C₂²×Dic₂₃	C₂³	1	4	yes	—
18	C₂²×Dic₂₃	C₂³	1	3	yes	—
19	C₂×C₄×D₂₃	—	2	12	no	—
20	C₂×C₄×D₂₃	—	2	24	no	—
21	C₂×C₄×D₂₃	C₂×C₄	1	12	yes	—
22	C₄²×C₂₃	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₂₃	C₂×C₄	1	12	yes	complemented
24	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
25	C₂²×D₂₃	C₂²×C₄	1	2	yes	—
26	C₂²×D₂₃	#41	1	12	yes	—
27	C₂×C₄×C₂₃	—	2	6	no	—
28	C₂×C₄×C₂₃	—	2	12	no	—
29	C₂×C₄×C₂₃	C₂²×C₄	1	6	yes	—
30	C₂×Dic₂₃	—	2	6	no	—
31	C₂×Dic₂₃	—	2	12	no	—
32	C₂×Dic₂₃	C₂²×C₄	1	6	yes	—
33	C₄×D₂₃	—	2	24	no	—
34	C₄×D₂₃	—	4	16	no	—
35	C₂×#383	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
37	C₂²×C₂₃	C₂×#41	1	6	yes	—
38	C₂×D₂₃	#117	1	12	yes	—
39	C₂×D₂₃	#126	1	16	yes	—
40	C₄×C₂₃	—	2	6	no	—
41	C₄×C₂₃	—	4	4	no	—
42	Dic₂₃	—	2	6	no	—
43	Dic₂₃	—	4	4	no	—
44	C₂²×C₄²	—	23	1	no	—
45	#383	—	23	1	no	—
46	#383	—	23	6	no	—
47	#383	D₂₃	1	1	yes	characteristic, direct product factor
48	C₂×#95	—	23	6	no	—
49	C₂×C₂₃	C₂×#117	1	3	yes	—
50	C₂×C₂₃	C₂×#126	1	4	yes	—
51	D₂₃	#383	1	8	yes	direct product factor
52	C₂³×C₄	—	23	3	no	—
53	C₂³×C₄	—	23	4	no	—
54	C₂×C₄²	—	23	3	no	—
55	C₂×C₄²	—	23	8	no	—
56	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
57	#95	—	23	12	no	—
58	#95	—	23	6	no	—
59	#95	C₂×D₂₃	1	6	yes	—
60	C₂₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	—	23	1	no	—
62	C₂²×C₄	—	23	3	no	—
63	C₂²×C₄	—	23	12	no	—
64	C₂²×C₄	—	23	4	no	—
65	C₂²×C₄	—	46	12	no	—
66	C₂²×C₄	—	46	24	no	—
67	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
68	C₂²×C₄	C₂²×D₂₃	1	3	yes	—
69	C₄²	—	23	12	no	—
70	C₄²	C₄×D₂₃	1	4	yes	complemented
71	C₂³	—	23	2	no	—
72	C₂³	—	23	12	no	—
73	C₂³	C₂³×D₂₃	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	23	6	no	—
77	C₂×C₄	—	46	24	no	—
78	C₂×C₄	—	46	6	no	—
79	C₂×C₄	—	46	12	no	—
80	C₂×C₄	—	92	16	no	—
81	C₂×C₄	C₂×C₄×D₂₃	1	6	yes	—
82	C₂²	—	23	12	no	—
83	C₂²	—	23	16	no	—
84	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
85	C₂²	#41×D₂₃	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	46	6	no	—
89	C₄	—	92	4	no	—
90	C₂	—	23	8	no	—
91	C₂	#117×D₂₃	1	3	yes	—
92	C₂	#126×D₂₃	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₃
commutator	C₂²×C₂₃	C₂³×C₄
Fitting	C₂₃×#383	C₂
socle, cosocle	C₂³×C₂₃	C₂⁴
prime radical	C₂³×D₂₃	C₂³
hypercenter	#383	D₂₃
hypocenter	C₂₃	C₂×#383
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #13092285	C₂	semidirect
3. #13092284	C₂	semidirect
5. C₂₃×#383	C₂	semidirect
10. C₄²×D₂₃	C₄	semidirect
22. C₄²×C₂₃	C₂×C₄	semidirect
23. C₄×Dic₂₃	C₂×C₄	semidirect
47. #383	D₂₃	direct (N × H)
51. D₂₃	#383	direct (N × H)
60. C₂₃	C₂×#383	semidirect
70. 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
#13092285	2
#13092284	2
#95×D₂₃	2
C₂₃×#383	2
C₂×#383	23

Subgroups — D23×#383 #15675785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#383 #15675785