Subgroups — C₂²×C₂₃×#401 #19182174

Order 5888.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#401	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₂₃×#95	C₂	1	7	yes	maximal
3	C₂⁴×C₄×C₂₃	C₂²	1	7	yes	—
4	C₂₃×#401	C₂²	1	64	yes	direct product factor
5	C₂×C₂₃×#95	C₂²	1	84	yes	—
6	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
7	C₂³×C₄×C₂₃	—	2	84	no	—
8	C₂³×C₄×C₂₃	C₂³	1	42	yes	—
9	C₂₃×#95	C₂³	1	112	yes	—
10	C₂⁴×C₂₃	#41	1	28	yes	—
11	C₂⁴×C₂₃	C₂⁴	1	3	yes	—
12	C₂²×C₄×C₂₃	—	2	252	no	—
13	C₂²×C₄×C₂₃	—	4	112	no	—
14	C₂²×C₄×C₂₃	C₂⁴	1	28	yes	—
15	C₂²×#401	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₂₃	#126	1	112	yes	—
17	C₂³×C₂₃	C₂×#41	1	42	yes	—
18	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
19	C₂×C₄×C₂₃	—	2	84	no	—
20	C₂×C₄×C₂₃	—	4	168	no	—
21	C₂×#401	C₂×C₂₃	1	24	yes	direct product factor
22	C₂²×#95	C₂×C₂₃	1	7	yes	—
23	C₂²×C₂₃	#401	1	64	yes	direct product factor
24	C₂²×C₂₃	C₂×#126	1	84	yes	—
25	C₂²×C₂₃	C₂²×#41	1	7	yes	—
26	C₄×C₂₃	—	4	28	no	—
27	C₂⁴×C₄	C₂²×C₂₃	1	7	yes	—
28	#401	C₂²×C₂₃	1	64	yes	direct product factor
29	C₂×#95	C₂²×C₂₃	1	84	yes	—
30	C₂×C₂₃	C₂×#401	1	24	yes	direct product factor
31	C₂×C₂₃	C₂²×#126	1	7	yes	—
32	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
33	C₂³×C₄	—	2	84	no	—
34	C₂³×C₄	C₂³×C₂₃	1	42	yes	—
35	#95	C₂³×C₂₃	1	112	yes	—
36	C₂₃	C₂²×#401	1	1	yes	characteristic, direct product factor, Sylow
37	C₂⁴	#41×C₂₃	1	28	yes	—
38	C₂⁴	C₂⁴×C₂₃	1	3	yes	—
39	C₂²×C₄	—	2	252	no	—
40	C₂²×C₄	—	4	112	no	—
41	C₂²×C₄	C₂⁴×C₂₃	1	28	yes	—
42	C₂³	C₂₃×#126	1	112	yes	—
43	C₂³	C₂×#41×C₂₃	1	42	yes	—
44	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
45	C₂×C₄	—	2	84	no	—
46	C₂×C₄	—	4	168	no	—
47	C₂²	C₂₃×#401	1	64	yes	direct product factor
48	C₂²	C₂×C₂₃×#126	1	84	yes	—
49	C₂²	C₂²×#41×C₂₃	1	7	yes	—
50	C₄	—	4	28	no	—
51	C₂	C₂×C₂₃×#401	1	24	yes	direct product factor
52	C₂	C₂²×C₂₃×#126	1	7	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₂₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#401	C₂	direct (N × H)
4. C₂₃×#401	C₂²	direct (N × H)
15. C₂²×#401	C₂₃	direct (N × H)
21. C₂×#401	C₂×C₂₃	direct (N × H)
23. C₂²×C₂₃	#401	direct (N × H)
28. #401	C₂²×C₂₃	direct (N × H)
30. C₂×C₂₃	C₂×#401	direct (N × H)
36. C₂₃	C₂²×#401	direct (N × H)
47. C₂²	C₂₃×#401	direct (N × H)
51. C₂	C₂×C₂₃×#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#401	2
C₂²×C₂₃×#95	2
C₂²×#401	23

Subgroups — C22×C23×#401 #19182174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#401 #19182174