Subgroups — C₂⁴×C₇×C₈×C₁₁ #72188564

Order 9856.

3952 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₇×C₈×C₁₁	C₂	1	30	yes	maximal, direct product factor
3	C₂⁵×C₇×C₁₁	C₄	1	1	yes	characteristic
4	C₂³×C₄×C₇×C₁₁	C₄	1	15	yes	—
5	C₂³×C₄×C₇×C₁₁	C₂²	1	15	yes	—
6	C₂²×C₇×C₈×C₁₁	C₂²	1	140	yes	direct product factor
7	C₂⁴×C₈×C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₇×C₁₁	C₈	1	16	yes	direct product factor
9	C₂⁴×C₇×C₁₁	C₂×C₄	1	15	yes	—
10	C₂²×C₄×C₇×C₁₁	C₂×C₄	1	105	yes	—
11	C₂²×C₄×C₇×C₁₁	C₂³	1	35	yes	—
12	C₂×C₇×C₈×C₁₁	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₇×C₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁴×C₄×C₁₁	C₂×C₇	1	1	yes	characteristic
15	C₂³×C₈×C₁₁	C₂×C₇	1	30	yes	direct product factor
16	C₂³×C₇×C₁₁	C₂×C₈	1	120	yes	direct product factor
17	C₂³×C₇×C₁₁	C₂²×C₄	1	35	yes	—
18	C₂×C₄×C₇×C₁₁	C₂²×C₄	1	105	yes	—
19	C₂×C₄×C₇×C₁₁	C₂⁴	1	15	yes	—
20	C₇×C₈×C₁₁	C₂⁴	1	16	yes	direct product factor
21	C₂⁴×C₄×C₇	C₂×C₁₁	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂×C₁₁	1	30	yes	direct product factor
23	C₂⁵×C₁₁	C₄×C₇	1	1	yes	characteristic
24	C₂³×C₄×C₁₁	C₄×C₇	1	15	yes	—
25	C₂³×C₄×C₁₁	C₂²×C₇	1	15	yes	—
26	C₂²×C₈×C₁₁	C₂²×C₇	1	140	yes	direct product factor
27	C₂²×C₇×C₁₁	C₂²×C₈	1	140	yes	direct product factor
28	C₂²×C₇×C₁₁	C₂³×C₄	1	15	yes	—
29	C₄×C₇×C₁₁	C₂³×C₄	1	15	yes	—
30	C₄×C₇×C₁₁	C₂⁵	1	1	yes	characteristic
31	C₂⁵×C₇	C₄×C₁₁	1	1	yes	characteristic
32	C₂³×C₄×C₇	C₄×C₁₁	1	15	yes	—
33	C₂³×C₄×C₇	C₂²×C₁₁	1	15	yes	—
34	C₂²×C₇×C₈	C₂²×C₁₁	1	140	yes	direct product factor
35	C₂⁴×C₁₁	C₇×C₈	1	16	yes	direct product factor
36	C₂⁴×C₁₁	C₂×C₄×C₇	1	15	yes	—
37	C₂²×C₄×C₁₁	C₂×C₄×C₇	1	105	yes	—
38	C₂²×C₄×C₁₁	C₂³×C₇	1	35	yes	—
39	C₂×C₈×C₁₁	C₂³×C₇	1	120	yes	direct product factor
40	C₂×C₇×C₁₁	C₂³×C₈	1	30	yes	direct product factor
41	C₂×C₇×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
42	C₂⁴×C₈	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂⁴×C₇	C₈×C₁₁	1	16	yes	direct product factor
44	C₂⁴×C₇	C₂×C₄×C₁₁	1	15	yes	—
45	C₂²×C₄×C₇	C₂×C₄×C₁₁	1	105	yes	—
46	C₂²×C₄×C₇	C₂³×C₁₁	1	35	yes	—
47	C₂×C₇×C₈	C₂³×C₁₁	1	120	yes	direct product factor
48	C₂³×C₁₁	C₂×C₇×C₈	1	120	yes	direct product factor
49	C₂³×C₁₁	C₂²×C₄×C₇	1	35	yes	—
50	C₂×C₄×C₁₁	C₂²×C₄×C₇	1	105	yes	—
51	C₂×C₄×C₁₁	C₂⁴×C₇	1	15	yes	—
52	C₈×C₁₁	C₂⁴×C₇	1	16	yes	direct product factor
53	C₇×C₁₁	C₂⁴×C₈	1	1	yes	characteristic, direct product factor, Hall
54	C₂⁴×C₄	C₂×C₇×C₁₁	1	1	yes	characteristic
55	C₂³×C₈	C₂×C₇×C₁₁	1	30	yes	direct product factor
56	C₂³×C₇	C₂×C₈×C₁₁	1	120	yes	direct product factor
57	C₂³×C₇	C₂²×C₄×C₁₁	1	35	yes	—
58	C₂×C₄×C₇	C₂²×C₄×C₁₁	1	105	yes	—
59	C₂×C₄×C₇	C₂⁴×C₁₁	1	15	yes	—
60	C₇×C₈	C₂⁴×C₁₁	1	16	yes	direct product factor
61	C₂²×C₁₁	C₂²×C₇×C₈	1	140	yes	direct product factor
62	C₂²×C₁₁	C₂³×C₄×C₇	1	15	yes	—
63	C₄×C₁₁	C₂³×C₄×C₇	1	15	yes	—
64	C₄×C₁₁	C₂⁵×C₇	1	1	yes	characteristic
65	C₂⁵	C₄×C₇×C₁₁	1	1	yes	characteristic
66	C₂³×C₄	C₄×C₇×C₁₁	1	15	yes	—
67	C₂³×C₄	C₂²×C₇×C₁₁	1	15	yes	—
68	C₂²×C₈	C₂²×C₇×C₁₁	1	140	yes	direct product factor
69	C₂²×C₇	C₂²×C₈×C₁₁	1	140	yes	direct product factor
70	C₂²×C₇	C₂³×C₄×C₁₁	1	15	yes	—
71	C₄×C₇	C₂³×C₄×C₁₁	1	15	yes	—
72	C₄×C₇	C₂⁵×C₁₁	1	1	yes	characteristic
73	C₂×C₁₁	C₂³×C₇×C₈	1	30	yes	direct product factor
74	C₂×C₁₁	C₂⁴×C₄×C₇	1	1	yes	characteristic
75	C₂⁴	C₇×C₈×C₁₁	1	16	yes	direct product factor
76	C₂⁴	C₂×C₄×C₇×C₁₁	1	15	yes	—
77	C₂²×C₄	C₂×C₄×C₇×C₁₁	1	105	yes	—
78	C₂²×C₄	C₂³×C₇×C₁₁	1	35	yes	—
79	C₂×C₈	C₂³×C₇×C₁₁	1	120	yes	direct product factor
80	C₂×C₇	C₂³×C₈×C₁₁	1	30	yes	direct product factor
81	C₂×C₇	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
82	C₁₁	C₂⁴×C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³	C₂×C₇×C₈×C₁₁	1	120	yes	direct product factor
84	C₂³	C₂²×C₄×C₇×C₁₁	1	35	yes	—
85	C₂×C₄	C₂²×C₄×C₇×C₁₁	1	105	yes	—
86	C₂×C₄	C₂⁴×C₇×C₁₁	1	15	yes	—
87	C₈	C₂⁴×C₇×C₁₁	1	16	yes	direct product factor
88	C₇	C₂⁴×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₂²×C₇×C₈×C₁₁	1	140	yes	direct product factor
90	C₂²	C₂³×C₄×C₇×C₁₁	1	15	yes	—
91	C₄	C₂³×C₄×C₇×C₁₁	1	15	yes	—
92	C₄	C₂⁵×C₇×C₁₁	1	1	yes	characteristic
93	C₂	C₂³×C₇×C₈×C₁₁	1	30	yes	direct product factor
94	C₂	C₂⁴×C₄×C₇×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁵×C₇×C₁₁
socle, prime radical	C₂⁵×C₇×C₁₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₇×C₈×C₁₁	C₂	direct (N × H)
6. C₂²×C₇×C₈×C₁₁	C₂²	direct (N × H)
7. C₂⁴×C₈×C₁₁	C₇	direct (N × H)
8. C₂⁴×C₇×C₁₁	C₈	direct (N × H)
12. C₂×C₇×C₈×C₁₁	C₂³	direct (N × H)
13. C₂⁴×C₇×C₈	C₁₁	direct (N × H)
15. C₂³×C₈×C₁₁	C₂×C₇	direct (N × H)
16. C₂³×C₇×C₁₁	C₂×C₈	direct (N × H)
20. C₇×C₈×C₁₁	C₂⁴	direct (N × H)
22. C₂³×C₇×C₈	C₂×C₁₁	direct (N × H)
26. C₂²×C₈×C₁₁	C₂²×C₇	direct (N × H)
27. C₂²×C₇×C₁₁	C₂²×C₈	direct (N × H)
34. C₂²×C₇×C₈	C₂²×C₁₁	direct (N × H)
35. C₂⁴×C₁₁	C₇×C₈	direct (N × H)
39. C₂×C₈×C₁₁	C₂³×C₇	direct (N × H)
40. C₂×C₇×C₁₁	C₂³×C₈	direct (N × H)
42. C₂⁴×C₈	C₇×C₁₁	direct (N × H)
43. C₂⁴×C₇	C₈×C₁₁	direct (N × H)
47. C₂×C₇×C₈	C₂³×C₁₁	direct (N × H)
48. C₂³×C₁₁	C₂×C₇×C₈	direct (N × H)
52. C₈×C₁₁	C₂⁴×C₇	direct (N × H)
53. C₇×C₁₁	C₂⁴×C₈	direct (N × H)
55. C₂³×C₈	C₂×C₇×C₁₁	direct (N × H)
56. C₂³×C₇	C₂×C₈×C₁₁	direct (N × H)
60. C₇×C₈	C₂⁴×C₁₁	direct (N × H)
61. C₂²×C₁₁	C₂²×C₇×C₈	direct (N × H)
68. C₂²×C₈	C₂²×C₇×C₁₁	direct (N × H)
69. C₂²×C₇	C₂²×C₈×C₁₁	direct (N × H)
73. C₂×C₁₁	C₂³×C₇×C₈	direct (N × H)
75. C₂⁴	C₇×C₈×C₁₁	direct (N × H)
79. C₂×C₈	C₂³×C₇×C₁₁	direct (N × H)
80. C₂×C₇	C₂³×C₈×C₁₁	direct (N × H)
82. C₁₁	C₂⁴×C₇×C₈	direct (N × H)
83. C₂³	C₂×C₇×C₈×C₁₁	direct (N × H)
87. C₈	C₂⁴×C₇×C₁₁	direct (N × H)
88. C₇	C₂⁴×C₈×C₁₁	direct (N × H)
89. C₂²	C₂²×C₇×C₈×C₁₁	direct (N × H)
93. C₂	C₂³×C₇×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
C₂⁴×C₄×C₇×C₁₁	2
C₂³×C₇×C₈×C₁₁	2
C₂⁴×C₈×C₁₁	7
C₂⁴×C₇×C₈	11

Subgroups — C24×C7×C8×C11 #72188564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₇×C₈×C₁₁ #72188564