Subgroups — C₄²×C₅×C₈×C₁₁ #72186113

Order 7040.

816 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₈×C₁₁	C₂	1	6	yes	maximal
3	C₂²×C₅×C₈×C₁₁	C₂²	1	4	yes	—
4	C₂×C₄²×C₅×C₁₁	C₄	1	4	yes	—
5	C₂×C₄²×C₅×C₁₁	C₂²	1	3	yes	—
6	C₄×C₅×C₈×C₁₁	C₄	1	24	yes	direct product factor
7	C₄²×C₈×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₄×C₅×C₁₁	C₂×C₄	1	6	yes	—
9	C₂²×C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
10	C₂×C₅×C₈×C₁₁	C₂×C₄	1	24	yes	—
11	C₄²×C₅×C₁₁	C₈	1	16	yes	direct product factor
12	C₄²×C₅×C₁₁	C₂×C₄	1	12	yes	—
13	C₂×C₄×C₈×C₁₁	C₂×C₅	1	6	yes	—
14	C₄³×C₁₁	C₂×C₅	1	1	yes	characteristic
15	C₄²×C₅×C₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂³×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅×C₁₁	C₄²	1	12	yes	—
18	C₂×C₄×C₅×C₁₁	C₂×C₈	1	24	yes	—
19	C₂×C₄×C₅×C₁₁	C₂²×C₄	1	6	yes	—
20	C₅×C₈×C₁₁	C₄²	1	16	yes	direct product factor
21	C₂²×C₈×C₁₁	C₂²×C₅	1	4	yes	—
22	C₂×C₄²×C₁₁	C₄×C₅	1	4	yes	—
23	C₂×C₄²×C₁₁	C₂²×C₅	1	3	yes	—
24	C₄×C₈×C₁₁	C₄×C₅	1	24	yes	direct product factor
25	C₂×C₄×C₅×C₈	C₂×C₁₁	1	6	yes	—
26	C₄³×C₅	C₂×C₁₁	1	1	yes	characteristic
27	C₂²×C₅×C₁₁	C₂×C₄²	1	3	yes	—
28	C₂²×C₅×C₁₁	C₂²×C₈	1	4	yes	—
29	C₄×C₅×C₁₁	C₄×C₈	1	24	yes	direct product factor
30	C₄×C₅×C₁₁	C₂×C₄²	1	4	yes	—
31	C₂²×C₄×C₁₁	C₂×C₄×C₅	1	6	yes	—
32	C₂²×C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₂×C₄×C₅	1	24	yes	—
34	C₄²×C₁₁	C₅×C₈	1	16	yes	direct product factor
35	C₄²×C₁₁	C₂×C₄×C₅	1	12	yes	—
36	C₂²×C₅×C₈	C₂²×C₁₁	1	4	yes	—
37	C₂×C₄²×C₅	C₄×C₁₁	1	4	yes	—
38	C₂×C₄²×C₅	C₂²×C₁₁	1	3	yes	—
39	C₄×C₅×C₈	C₄×C₁₁	1	24	yes	direct product factor
40	C₄²×C₈	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅×C₁₁	C₄³	1	1	yes	characteristic
42	C₂×C₅×C₁₁	C₂×C₄×C₈	1	6	yes	—
43	C₂³×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₄²×C₅	1	12	yes	—
45	C₂×C₄×C₁₁	C₂×C₅×C₈	1	24	yes	—
46	C₂×C₄×C₁₁	C₂²×C₄×C₅	1	6	yes	—
47	C₈×C₁₁	C₄²×C₅	1	16	yes	direct product factor
48	C₂²×C₄×C₅	C₂×C₄×C₁₁	1	6	yes	—
49	C₂²×C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
50	C₂×C₅×C₈	C₂×C₄×C₁₁	1	24	yes	—
51	C₄²×C₅	C₈×C₁₁	1	16	yes	direct product factor
52	C₄²×C₅	C₂×C₄×C₁₁	1	12	yes	—
53	C₂×C₄×C₈	C₂×C₅×C₁₁	1	6	yes	—
54	C₄³	C₂×C₅×C₁₁	1	1	yes	characteristic
55	C₅×C₁₁	C₄²×C₈	1	1	yes	characteristic, direct product factor, Hall
56	C₂²×C₁₁	C₂×C₄²×C₅	1	3	yes	—
57	C₂²×C₁₁	C₂²×C₅×C₈	1	4	yes	—
58	C₄×C₁₁	C₄×C₅×C₈	1	24	yes	direct product factor
59	C₄×C₁₁	C₂×C₄²×C₅	1	4	yes	—
60	C₂³×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
61	C₂×C₄×C₅	C₄²×C₁₁	1	12	yes	—
62	C₂×C₄×C₅	C₂×C₈×C₁₁	1	24	yes	—
63	C₂×C₄×C₅	C₂²×C₄×C₁₁	1	6	yes	—
64	C₅×C₈	C₄²×C₁₁	1	16	yes	direct product factor
65	C₂²×C₈	C₂²×C₅×C₁₁	1	4	yes	—
66	C₂×C₄²	C₄×C₅×C₁₁	1	4	yes	—
67	C₂×C₄²	C₂²×C₅×C₁₁	1	3	yes	—
68	C₄×C₈	C₄×C₅×C₁₁	1	24	yes	direct product factor
69	C₂×C₁₁	C₄³×C₅	1	1	yes	characteristic
70	C₂×C₁₁	C₂×C₄×C₅×C₈	1	6	yes	—
71	C₂²×C₅	C₂×C₄²×C₁₁	1	3	yes	—
72	C₂²×C₅	C₂²×C₈×C₁₁	1	4	yes	—
73	C₄×C₅	C₄×C₈×C₁₁	1	24	yes	direct product factor
74	C₄×C₅	C₂×C₄²×C₁₁	1	4	yes	—
75	C₂²×C₄	C₂×C₄×C₅×C₁₁	1	6	yes	—
76	C₂²×C₄	C₂³×C₅×C₁₁	1	1	yes	characteristic
77	C₂×C₈	C₂×C₄×C₅×C₁₁	1	24	yes	—
78	C₄²	C₅×C₈×C₁₁	1	16	yes	direct product factor
79	C₄²	C₂×C₄×C₅×C₁₁	1	12	yes	—
80	C₁₁	C₄²×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×C₅	C₄³×C₁₁	1	1	yes	characteristic
82	C₂×C₅	C₂×C₄×C₈×C₁₁	1	6	yes	—
83	C₂³	C₂²×C₄×C₅×C₁₁	1	1	yes	characteristic
84	C₂×C₄	C₄²×C₅×C₁₁	1	12	yes	—
85	C₂×C₄	C₂×C₅×C₈×C₁₁	1	24	yes	—
86	C₂×C₄	C₂²×C₄×C₅×C₁₁	1	6	yes	—
87	C₈	C₄²×C₅×C₁₁	1	16	yes	direct product factor
88	C₅	C₄²×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₂×C₄²×C₅×C₁₁	1	3	yes	—
90	C₂²	C₂²×C₅×C₈×C₁₁	1	4	yes	—
91	C₄	C₄×C₅×C₈×C₁₁	1	24	yes	direct product factor
92	C₄	C₂×C₄²×C₅×C₁₁	1	4	yes	—
93	C₂	C₂×C₄×C₅×C₈×C₁₁	1	6	yes	—
94	C₂	C₄³×C₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂³×C₅×C₁₁
socle, prime radical	C₂³×C₅×C₁₁	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄×C₅×C₈×C₁₁	C₄	direct (N × H)
7. C₄²×C₈×C₁₁	C₅	direct (N × H)
11. C₄²×C₅×C₁₁	C₈	direct (N × H)
15. C₄²×C₅×C₈	C₁₁	direct (N × H)
20. C₅×C₈×C₁₁	C₄²	direct (N × H)
24. C₄×C₈×C₁₁	C₄×C₅	direct (N × H)
29. C₄×C₅×C₁₁	C₄×C₈	direct (N × H)
34. C₄²×C₁₁	C₅×C₈	direct (N × H)
39. C₄×C₅×C₈	C₄×C₁₁	direct (N × H)
40. C₄²×C₈	C₅×C₁₁	direct (N × H)
47. C₈×C₁₁	C₄²×C₅	direct (N × H)
51. C₄²×C₅	C₈×C₁₁	direct (N × H)
55. C₅×C₁₁	C₄²×C₈	direct (N × H)
58. C₄×C₁₁	C₄×C₅×C₈	direct (N × H)
64. C₅×C₈	C₄²×C₁₁	direct (N × H)
68. C₄×C₈	C₄×C₅×C₁₁	direct (N × H)
73. C₄×C₅	C₄×C₈×C₁₁	direct (N × H)
78. C₄²	C₅×C₈×C₁₁	direct (N × H)
80. C₁₁	C₄²×C₅×C₈	direct (N × H)
87. C₈	C₄²×C₅×C₁₁	direct (N × H)
88. C₅	C₄²×C₈×C₁₁	direct (N × H)
91. C₄	C₄×C₅×C₈×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄³×C₅×C₁₁	2
C₂×C₄×C₅×C₈×C₁₁	2
C₄²×C₈×C₁₁	5
C₄²×C₅×C₈	11

Subgroups — C42×C5×C8×C11 #72186113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅×C₈×C₁₁ #72186113