Subgroups — C₂×C₃×C₁₆×C₁₂₁ #72190049

Order 11616.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆×C₁₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₆×C₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₂₁	C₄	1	1	yes	characteristic
5	C₃×C₈×C₁₂₁	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₂₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₂₁	C₂×C₃	1	1	yes	characteristic
8	C₁₆×C₁₂₁	C₂×C₃	1	2	yes	direct product factor
9	C₂²×C₃×C₁₂₁	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₂₁	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₂₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₁₁×C₁₆	C₁₁	1	1	yes	maximal, characteristic
13	C₂×C₄×C₁₂₁	C₃×C₄	1	1	yes	characteristic
14	C₈×C₁₂₁	C₃×C₄	1	1	yes	characteristic
15	C₈×C₁₂₁	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₃×C₁₂₁	C₁₆	1	2	yes	direct product factor
17	C₂×C₃×C₁₂₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₃×C₈×C₁₁	C₂×C₁₁	1	1	yes	characteristic
19	C₃×C₁₁×C₁₆	C₂×C₁₁	1	2	yes	—
20	C₂²×C₁₂₁	C₃×C₈	1	1	yes	characteristic
21	C₄×C₁₂₁	C₃×C₈	1	1	yes	characteristic
22	C₄×C₁₂₁	C₂×C₃×C₄	1	1	yes	characteristic
23	C₃×C₁₂₁	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₁₁×C₁₆	C₃×C₁₁	1	1	yes	characteristic
25	C₂×C₃×C₄×C₁₁	C₄×C₁₁	1	1	yes	characteristic
26	C₃×C₈×C₁₁	C₄×C₁₁	1	1	yes	characteristic
27	C₃×C₈×C₁₁	C₂²×C₁₁	1	1	yes	characteristic
28	C₂×C₁₂₁	C₃×C₁₆	1	2	yes	direct product factor
29	C₂×C₁₂₁	C₂×C₃×C₈	1	1	yes	characteristic
30	C₂×C₈×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic
31	C₁₁×C₁₆	C₂×C₃×C₁₁	1	2	yes	—
32	C₂²×C₃×C₁₁	C₈×C₁₁	1	1	yes	characteristic
33	C₃×C₄×C₁₁	C₈×C₁₁	1	1	yes	characteristic
34	C₃×C₄×C₁₁	C₂×C₄×C₁₁	1	1	yes	characteristic
35	C₁₂₁	C₂×C₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×C₁₆	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₄×C₁₁	C₃×C₄×C₁₁	1	1	yes	characteristic
38	C₈×C₁₁	C₃×C₄×C₁₁	1	1	yes	characteristic
39	C₈×C₁₁	C₂²×C₃×C₁₁	1	1	yes	characteristic
40	C₂×C₃×C₁₁	C₁₁×C₁₆	1	2	yes	—
41	C₂×C₃×C₁₁	C₂×C₈×C₁₁	1	1	yes	characteristic
42	C₂×C₃×C₈	C₂×C₁₂₁	1	1	yes	characteristic
43	C₃×C₁₆	C₂×C₁₂₁	1	2	yes	direct product factor
44	C₂²×C₁₁	C₃×C₈×C₁₁	1	1	yes	characteristic
45	C₄×C₁₁	C₃×C₈×C₁₁	1	1	yes	characteristic
46	C₄×C₁₁	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic
47	C₃×C₁₁	C₂×C₁₁×C₁₆	1	1	yes	characteristic
48	C₂×C₁₆	C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×C₄	C₄×C₁₂₁	1	1	yes	characteristic
50	C₃×C₈	C₄×C₁₂₁	1	1	yes	characteristic
51	C₃×C₈	C₂²×C₁₂₁	1	1	yes	characteristic
52	C₂×C₁₁	C₃×C₁₁×C₁₆	1	2	yes	—
53	C₂×C₁₁	C₂×C₃×C₈×C₁₁	1	1	yes	characteristic
54	C₂×C₈	C₂×C₃×C₁₂₁	1	1	yes	characteristic
55	C₁₆	C₂×C₃×C₁₂₁	1	2	yes	direct product factor
56	C₂²×C₃	C₈×C₁₂₁	1	1	yes	characteristic
57	C₃×C₄	C₈×C₁₂₁	1	1	yes	characteristic
58	C₃×C₄	C₂×C₄×C₁₂₁	1	1	yes	characteristic
59	C₁₁	C₂×C₃×C₁₁×C₁₆	1	1	yes	characteristic
60	C₂×C₄	C₃×C₄×C₁₂₁	1	1	yes	characteristic
61	C₈	C₃×C₄×C₁₂₁	1	1	yes	characteristic
62	C₈	C₂²×C₃×C₁₂₁	1	1	yes	characteristic
63	C₂×C₃	C₁₆×C₁₂₁	1	2	yes	direct product factor
64	C₂×C₃	C₂×C₈×C₁₂₁	1	1	yes	characteristic
65	C₂²	C₃×C₈×C₁₂₁	1	1	yes	characteristic
66	C₄	C₃×C₈×C₁₂₁	1	1	yes	characteristic
67	C₄	C₂×C₃×C₄×C₁₂₁	1	1	yes	characteristic
68	C₃	C₂×C₁₆×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×C₁₆×C₁₂₁	1	2	yes	direct product factor
70	C₂	C₂×C₃×C₈×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₁₁	C₂²×C₃×C₁₁
socle, prime radical	C₂²×C₃×C₁₁	C₈×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₆×C₁₂₁	C₂	direct (N × H)
3. C₂×C₁₆×C₁₂₁	C₃	direct (N × H)
8. C₁₆×C₁₂₁	C₂×C₃	direct (N × H)
16. C₂×C₃×C₁₂₁	C₁₆	direct (N × H)
23. C₃×C₁₂₁	C₂×C₁₆	direct (N × H)
28. C₂×C₁₂₁	C₃×C₁₆	direct (N × H)
35. C₁₂₁	C₂×C₃×C₁₆	direct (N × H)
36. C₂×C₃×C₁₆	C₁₂₁	direct (N × H)
43. C₃×C₁₆	C₂×C₁₂₁	direct (N × H)
48. C₂×C₁₆	C₃×C₁₂₁	direct (N × H)
55. C₁₆	C₂×C₃×C₁₂₁	direct (N × H)
63. C₂×C₃	C₁₆×C₁₂₁	direct (N × H)
68. C₃	C₂×C₁₆×C₁₂₁	direct (N × H)
69. C₂	C₃×C₁₆×C₁₂₁	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×C₃×C₈×C₁₂₁	2
C₃×C₁₆×C₁₂₁	2
C₂×C₁₆×C₁₂₁	3
C₂×C₃×C₁₁×C₁₆	11

Subgroups — C2×C3×C16×C121 #72190049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₆×C₁₂₁ #72190049