Subgroups — C₄×C₂₃×#401 #19161492

Order 5888.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#401	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1443	C₂	1	7	yes	maximal
3	C₄×C₂₃×#95	C₂	1	7	yes	maximal
4	C₂²×C₄²×C₂₃	C₂²	1	7	yes	—
5	C₂₃×#401	C₄	1	8	yes	direct product factor
6	C₂×C₂₃×#95	C₂²	1	21	yes	—
7	C₂×C₂₃×#95	C₂²	1	7	yes	—
8	C₂³×C₄×C₂₃	C₂³	1	7	yes	—
9	C₂³×C₄×C₂₃	C₂³	1	7	yes	—
10	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
11	C₂×C₄²×C₂₃	—	2	42	no	—
12	C₂₃×#95	—	2	42	no	—
13	C₂₃×#95	C₂×C₄	1	28	yes	—
14	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄×C₂₃	—	2	21	no	—
16	C₂²×C₄×C₂₃	—	2	21	no	—
17	C₂²×C₄×C₂₃	—	2	21	no	—
18	C₂²×C₄×C₂₃	—	2	21	no	—
19	C₂²×C₄×C₂₃	C₂²×C₄	1	14	yes	—
20	C₂²×C₄×C₂₃	#41	1	14	yes	—
21	C₂²×C₄×C₂₃	#41	1	14	yes	—
22	C₄²×C₂₃	—	4	28	no	—
23	C₄×#401	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
25	C₂³×C₂₃	C₂×#41	1	7	yes	—
26	C₂³×C₂₃	C₂×#41	1	7	yes	—
27	C₂×C₄×C₂₃	—	2	42	no	—
28	C₂×C₄×C₂₃	—	2	42	no	—
29	C₂×C₄×C₂₃	—	4	7	no	—
30	C₂×C₄×C₂₃	—	4	7	no	—
31	C₂×C₄×C₂₃	—	4	21	no	—
32	C₂×C₄×C₂₃	—	4	21	no	—
33	C₂×C₄×C₂₃	#126	1	28	yes	—
34	C₂×#401	C₂×C₂₃	1	1	yes	characteristic
35	#1443	C₂×C₂₃	1	7	yes	—
36	C₄×#95	C₂×C₂₃	1	7	yes	—
37	C₂²×C₂₃	C₄×#41	1	7	yes	—
38	C₂²×C₂₃	C₂×#126	1	7	yes	—
39	C₂²×C₂₃	#529	1	21	yes	—
40	C₄×C₂₃	—	4	14	no	—
41	C₄×C₂₃	—	4	14	no	—
42	C₄×C₂₃	#401	1	8	yes	direct product factor
43	C₂²×C₄²	C₂²×C₂₃	1	7	yes	—
44	#401	C₄×C₂₃	1	8	yes	direct product factor
45	C₂×#95	C₂²×C₂₃	1	21	yes	—
46	C₂×#95	C₂²×C₂₃	1	7	yes	—
47	C₂×C₂₃	C₄×#126	1	7	yes	—
48	C₂×C₂₃	C₂×#401	1	1	yes	characteristic
49	C₂×C₂₃	#2401	1	7	yes	—
50	C₂³×C₄	C₂³×C₂₃	1	7	yes	—
51	C₂³×C₄	C₂³×C₂₃	1	7	yes	—
52	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
53	C₂×C₄²	—	2	42	no	—
54	#95	—	2	42	no	—
55	#95	C₂×C₄×C₂₃	1	28	yes	—
56	C₂₃	C₄×#401	1	1	yes	characteristic, direct product factor, Sylow
57	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
58	C₂²×C₄	—	2	21	no	—
59	C₂²×C₄	—	2	21	no	—
60	C₂²×C₄	—	2	21	no	—
61	C₂²×C₄	—	2	21	no	—
62	C₂²×C₄	C₂²×C₄×C₂₃	1	14	yes	—
63	C₂²×C₄	#41×C₂₃	1	14	yes	—
64	C₂²×C₄	#41×C₂₃	1	14	yes	—
65	C₄²	—	4	28	no	—
66	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
67	C₂³	C₂×#41×C₂₃	1	7	yes	—
68	C₂³	C₂×#41×C₂₃	1	7	yes	—
69	C₂×C₄	—	2	42	no	—
70	C₂×C₄	—	2	42	no	—
71	C₂×C₄	—	4	7	no	—
72	C₂×C₄	—	4	7	no	—
73	C₂×C₄	—	4	21	no	—
74	C₂×C₄	—	4	21	no	—
75	C₂×C₄	C₂₃×#126	1	28	yes	—
76	C₂²	C₄×#41×C₂₃	1	7	yes	—
77	C₂²	C₂×C₂₃×#126	1	7	yes	—
78	C₂²	C₂₃×#529	1	21	yes	—
79	C₄	—	4	14	no	—
80	C₄	—	4	14	no	—
81	C₄	C₂₃×#401	1	8	yes	direct product factor
82	C₂	C₄×C₂₃×#126	1	7	yes	—
83	C₂	C₂×C₂₃×#401	1	1	yes	characteristic
84	C₂	C₂₃×#2401	1	7	yes	—

	subgroup	G/H
center	C₂³×C₄×C₂₃	C₂³
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂⁴×C₂₃
socle, prime radical	C₂⁴×C₂₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂₃×#401	C₄	direct (N × H)
23. C₄×#401	C₂₃	direct (N × H)
42. C₄×C₂₃	#401	direct (N × H)
44. #401	C₄×C₂₃	direct (N × H)
56. C₂₃	C₄×#401	direct (N × H)
81. C₄	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
C₂₃×#1443	2
C₄×C₂₃×#95	2
C₄×#401	23

Subgroups — C4×C23×#401 #19161492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#401 #19161492