Subgroups — C₂×C₃³×C₇×C₁₆ #72185222

Order 6048.

784 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₇×C₁₆	C₃	1	13	yes	maximal, direct product factor
4	C₂×C₃³×C₄×C₇	C₄	1	1	yes	characteristic
5	C₃³×C₇×C₈	C₄	1	1	yes	characteristic
6	C₃³×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₇×C₈	C₂×C₃	1	13	yes	—
8	C₃²×C₇×C₁₆	C₂×C₃	1	26	yes	direct product factor
9	C₂×C₃³×C₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃³×C₇	C₈	1	1	yes	characteristic
11	C₃³×C₄×C₇	C₈	1	1	yes	characteristic
12	C₃³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₇×C₁₆	C₃²	1	13	yes	direct product factor
14	C₂×C₃²×C₄×C₇	C₃×C₄	1	13	yes	—
15	C₃²×C₇×C₈	C₃×C₄	1	13	yes	—
16	C₃²×C₇×C₈	C₂²×C₃	1	13	yes	—
17	C₂×C₃³×C₈	C₂×C₇	1	1	yes	characteristic
18	C₃³×C₁₆	C₂×C₇	1	2	yes	direct product factor
19	C₂×C₃³×C₇	C₁₆	1	2	yes	direct product factor
20	C₂×C₃³×C₇	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃×C₇×C₈	C₂×C₃²	1	13	yes	—
22	C₃×C₇×C₁₆	C₂×C₃²	1	26	yes	direct product factor
23	C₂×C₃²×C₁₆	C₃×C₇	1	13	yes	direct product factor
24	C₂²×C₃²×C₇	C₃×C₈	1	13	yes	—
25	C₃²×C₄×C₇	C₃×C₈	1	13	yes	—
26	C₃²×C₄×C₇	C₂×C₃×C₄	1	13	yes	—
27	C₂×C₇×C₁₆	C₃³	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃³×C₄	C₄×C₇	1	1	yes	characteristic
29	C₃³×C₈	C₄×C₇	1	1	yes	characteristic
30	C₃³×C₈	C₂²×C₇	1	1	yes	characteristic
31	C₃³×C₇	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃×C₄×C₇	C₃²×C₄	1	13	yes	—
33	C₃×C₇×C₈	C₃²×C₄	1	13	yes	—
34	C₃×C₇×C₈	C₂²×C₃²	1	13	yes	—
35	C₂×C₃²×C₈	C₂×C₃×C₇	1	13	yes	—
36	C₃²×C₁₆	C₂×C₃×C₇	1	26	yes	direct product factor
37	C₂×C₃²×C₇	C₃×C₁₆	1	26	yes	direct product factor
38	C₂×C₃²×C₇	C₂×C₃×C₈	1	13	yes	—
39	C₂×C₇×C₈	C₂×C₃³	1	1	yes	characteristic
40	C₇×C₁₆	C₂×C₃³	1	2	yes	direct product factor
41	C₂²×C₃³	C₇×C₈	1	1	yes	characteristic
42	C₃³×C₄	C₇×C₈	1	1	yes	characteristic
43	C₃³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
44	C₂×C₃×C₁₆	C₃²×C₇	1	13	yes	direct product factor
45	C₂²×C₃×C₇	C₃²×C₈	1	13	yes	—
46	C₃×C₄×C₇	C₃²×C₈	1	13	yes	—
47	C₃×C₄×C₇	C₂×C₃²×C₄	1	13	yes	—
48	C₂×C₃²×C₄	C₃×C₄×C₇	1	13	yes	—
49	C₃²×C₈	C₃×C₄×C₇	1	13	yes	—
50	C₃²×C₈	C₂²×C₃×C₇	1	13	yes	—
51	C₃²×C₇	C₂×C₃×C₁₆	1	13	yes	direct product factor
52	C₂×C₄×C₇	C₃³×C₄	1	1	yes	characteristic
53	C₇×C₈	C₃³×C₄	1	1	yes	characteristic
54	C₇×C₈	C₂²×C₃³	1	1	yes	characteristic
55	C₂×C₃³	C₇×C₁₆	1	2	yes	direct product factor
56	C₂×C₃³	C₂×C₇×C₈	1	1	yes	characteristic
57	C₂×C₃×C₈	C₂×C₃²×C₇	1	13	yes	—
58	C₃×C₁₆	C₂×C₃²×C₇	1	26	yes	direct product factor
59	C₂×C₃×C₇	C₃²×C₁₆	1	26	yes	direct product factor
60	C₂×C₃×C₇	C₂×C₃²×C₈	1	13	yes	—
61	C₂²×C₃²	C₃×C₇×C₈	1	13	yes	—
62	C₃²×C₄	C₃×C₇×C₈	1	13	yes	—
63	C₃²×C₄	C₂×C₃×C₄×C₇	1	13	yes	—
64	C₂×C₁₆	C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²×C₇	C₃³×C₈	1	1	yes	characteristic
66	C₄×C₇	C₃³×C₈	1	1	yes	characteristic
67	C₄×C₇	C₂×C₃³×C₄	1	1	yes	characteristic
68	C₃³	C₂×C₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×C₃×C₄	C₃²×C₄×C₇	1	13	yes	—
70	C₃×C₈	C₃²×C₄×C₇	1	13	yes	—
71	C₃×C₈	C₂²×C₃²×C₇	1	13	yes	—
72	C₃×C₇	C₂×C₃²×C₁₆	1	13	yes	direct product factor
73	C₂×C₃²	C₃×C₇×C₁₆	1	26	yes	direct product factor
74	C₂×C₃²	C₂×C₃×C₇×C₈	1	13	yes	—
75	C₂×C₈	C₂×C₃³×C₇	1	1	yes	characteristic
76	C₁₆	C₂×C₃³×C₇	1	2	yes	direct product factor
77	C₂×C₇	C₃³×C₁₆	1	2	yes	direct product factor
78	C₂×C₇	C₂×C₃³×C₈	1	1	yes	characteristic
79	C₂²×C₃	C₃²×C₇×C₈	1	13	yes	—
80	C₃×C₄	C₃²×C₇×C₈	1	13	yes	—
81	C₃×C₄	C₂×C₃²×C₄×C₇	1	13	yes	—
82	C₃²	C₂×C₃×C₇×C₁₆	1	13	yes	direct product factor
83	C₂×C₄	C₃³×C₄×C₇	1	1	yes	characteristic
84	C₈	C₃³×C₄×C₇	1	1	yes	characteristic
85	C₈	C₂²×C₃³×C₇	1	1	yes	characteristic
86	C₇	C₂×C₃³×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₃	C₃²×C₇×C₁₆	1	26	yes	direct product factor
88	C₂×C₃	C₂×C₃²×C₇×C₈	1	13	yes	—
89	C₂²	C₃³×C₇×C₈	1	1	yes	characteristic
90	C₄	C₃³×C₇×C₈	1	1	yes	characteristic
91	C₄	C₂×C₃³×C₄×C₇	1	1	yes	characteristic
92	C₃	C₂×C₃²×C₇×C₁₆	1	13	yes	direct product factor
93	C₂	C₃³×C₇×C₁₆	1	2	yes	direct product factor
94	C₂	C₂×C₃³×C₇×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃³×C₇
socle, prime radical	C₂²×C₃³×C₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₇×C₁₆	C₂	direct (N × H)
3. C₂×C₃²×C₇×C₁₆	C₃	direct (N × H)
8. C₃²×C₇×C₁₆	C₂×C₃	direct (N × H)
9. C₂×C₃³×C₁₆	C₇	direct (N × H)
13. C₂×C₃×C₇×C₁₆	C₃²	direct (N × H)
18. C₃³×C₁₆	C₂×C₇	direct (N × H)
19. C₂×C₃³×C₇	C₁₆	direct (N × H)
22. C₃×C₇×C₁₆	C₂×C₃²	direct (N × H)
23. C₂×C₃²×C₁₆	C₃×C₇	direct (N × H)
27. C₂×C₇×C₁₆	C₃³	direct (N × H)
31. C₃³×C₇	C₂×C₁₆	direct (N × H)
36. C₃²×C₁₆	C₂×C₃×C₇	direct (N × H)
37. C₂×C₃²×C₇	C₃×C₁₆	direct (N × H)
40. C₇×C₁₆	C₂×C₃³	direct (N × H)
44. C₂×C₃×C₁₆	C₃²×C₇	direct (N × H)
51. C₃²×C₇	C₂×C₃×C₁₆	direct (N × H)
55. C₂×C₃³	C₇×C₁₆	direct (N × H)
58. C₃×C₁₆	C₂×C₃²×C₇	direct (N × H)
59. C₂×C₃×C₇	C₃²×C₁₆	direct (N × H)
64. C₂×C₁₆	C₃³×C₇	direct (N × H)
68. C₃³	C₂×C₇×C₁₆	direct (N × H)
72. C₃×C₇	C₂×C₃²×C₁₆	direct (N × H)
73. C₂×C₃²	C₃×C₇×C₁₆	direct (N × H)
76. C₁₆	C₂×C₃³×C₇	direct (N × H)
77. C₂×C₇	C₃³×C₁₆	direct (N × H)
82. C₃²	C₂×C₃×C₇×C₁₆	direct (N × H)
86. C₇	C₂×C₃³×C₁₆	direct (N × H)
87. C₂×C₃	C₃²×C₇×C₁₆	direct (N × H)
92. C₃	C₂×C₃²×C₇×C₁₆	direct (N × H)
93. C₂	C₃³×C₇×C₁₆	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×C₃³×C₇×C₈	2
C₃³×C₇×C₁₆	2
C₂×C₃²×C₇×C₁₆	3
C₂×C₃³×C₁₆	7

Subgroups — C2×C33×C7×C16 #72185222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₇×C₁₆ #72185222