Subgroups — C₂₃×#2645 #15670264

Order 2944.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#401	C₂	1	2	yes	maximal
2	C₂₃×#400	C₂	1	6	yes	maximal
3	C₂₃×#391	C₂	1	3	yes	maximal
4	C₂₃×#389	C₂	1	3	yes	maximal
5	C₂₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
8	C₂×C₄⋊C₄×C₂₃	C₂²	1	6	yes	—
9	C₂×C₄²×C₂₃	C₂²	1	3	yes	—
10	C₂₃×#95	C₂²	1	3	yes	—
11	C₂₃×#95	C₂²	1	1	yes	characteristic
12	C₂₃×#95	C₂²	1	6	yes	—
13	C₂₃×#95	C₂²	1	6	yes	—
14	C₂₃×#95	C₂²	1	6	yes	—
15	C₂×Q₈×C₂₃	—	2	6	no	—
16	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
18	C₂²×C₄×C₂₃	C₂³	1	6	yes	—
19	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₂₃	—	2	6	no	—
22	C₄⋊C₄×C₂₃	—	4	6	no	—
23	C₄²×C₂₃	—	2	6	no	—
24	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
25	Q₈×C₂₃	—	4	4	no	—
26	C₂×C₄×C₂₃	—	2	3	no	—
27	C₂×C₄×C₂₃	—	2	3	no	—
28	C₂×C₄×C₂₃	—	2	6	no	—
29	C₂×C₄×C₂₃	—	2	6	no	—
30	C₂×C₄×C₂₃	—	2	3	no	—
31	C₂×C₄×C₂₃	—	2	6	no	—
32	C₂×C₄×C₂₃	—	2	6	no	—
33	C₂×C₄×C₂₃	—	2	3	no	—
34	C₂×C₄×C₂₃	—	2	6	no	—
35	C₂×C₄×C₂₃	#41	1	6	yes	—
36	#2645	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₂₃	C₂×#41	1	3	yes	—
38	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
39	C₂²×C₂₃	2₋¹⁺⁴	1	3	yes	—
40	C₄×C₂₃	—	4	2	no	—
41	C₄×C₂₃	—	4	3	no	—
42	C₄×C₂₃	—	4	3	no	—
43	C₄×C₂₃	—	4	6	no	—
44	C₄×C₂₃	#126	1	4	yes	—
45	#401	C₂×C₂₃	1	2	yes	—
46	#400	C₂×C₂₃	1	6	yes	—
47	#391	C₂×C₂₃	1	3	yes	—
48	#389	C₂×C₂₃	1	3	yes	—
49	#376	C₂×C₂₃	1	1	yes	characteristic
50	C₂×C₂₃	C₂×#126	1	1	yes	characteristic
51	C₂×C₂₃	#541	1	3	yes	—
52	C₂×C₂₃	#542	1	3	yes	—
53	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic
54	C₂×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
55	C₂×C₄⋊C₄	C₂²×C₂₃	1	6	yes	—
56	C₂×C₄²	C₂²×C₂₃	1	3	yes	—
57	#95	C₂²×C₂₃	1	3	yes	—
58	#95	C₂²×C₂₃	1	1	yes	characteristic
59	#95	C₂²×C₂₃	1	6	yes	—
60	#95	C₂²×C₂₃	1	6	yes	—
61	#95	C₂²×C₂₃	1	6	yes	—
62	C₂₃	#2645	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×Q₈	—	2	6	no	—
64	C₂²×C₄	C₂³×C₂₃	1	3	yes	—
65	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
66	C₂²×C₄	C₂³×C₂₃	1	3	yes	—
67	C₂²×C₄	C₂³×C₂₃	1	6	yes	—
68	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
69	C₄⋊C₄	—	2	6	no	—
70	C₄⋊C₄	—	4	6	no	—
71	C₄²	—	2	6	no	—
72	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	6	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	6	no	—
80	C₂×C₄	—	2	6	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	2	6	no	—
83	C₂×C₄	#41×C₂₃	1	6	yes	—
84	C₂²	C₂×#41×C₂₃	1	3	yes	—
85	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
86	C₂²	C₂₃×2₋¹⁺⁴	1	3	yes	—
87	C₄	—	4	2	no	—
88	C₄	—	4	3	no	—
89	C₄	—	4	3	no	—
90	C₄	—	4	6	no	—
91	C₄	C₂₃×#126	1	4	yes	—
92	C₂	C₂×C₂₃×#126	1	1	yes	characteristic
93	C₂	C₂₃×#541	1	3	yes	—
94	C₂	C₂₃×#542	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
36. #2645	C₂₃	direct (N × H)
62. C₂₃	#2645	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×#401	2
C₂₃×#400	2
C₂₃×#391	2
C₂₃×#389	2
C₂₃×#376	2
#2645	23

Subgroups — C23×#2645 #15670264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2645 #15670264