Subgroups — C₃²×C₄×C₁₆×C₂₉ #72194682

Order 16704.

348 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₁₆×C₂₉	C₂	1	2	yes	maximal
3	C₃×C₄×C₁₆×C₂₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₄²×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₃²×C₈×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₃²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₃²×C₁₆×C₂₉	C₄	1	4	yes	direct product factor
8	C₃×C₄×C₈×C₂₉	C₂×C₃	1	4	yes	—
9	C₂×C₃×C₁₆×C₂₉	C₂×C₃	1	8	yes	—
10	C₂×C₃²×C₄×C₂₉	C₈	1	2	yes	—
11	C₂×C₃²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₈×C₂₉	C₈	1	2	yes	—
13	C₃²×C₈×C₂₉	C₂×C₄	1	2	yes	—
14	C₄×C₁₆×C₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₈×C₂₉	C₃×C₄	1	4	yes	—
16	C₂×C₃×C₈×C₂₉	C₂²×C₃	1	4	yes	—
17	C₃×C₄²×C₂₉	C₃×C₄	1	4	yes	—
18	C₃×C₁₆×C₂₉	C₃×C₄	1	16	yes	direct product factor
19	C₂²×C₃²×C₂₉	C₂×C₈	1	1	yes	characteristic
20	C₃²×C₄×C₂₉	C₁₆	1	4	yes	direct product factor
21	C₃²×C₄×C₂₉	C₄²	1	1	yes	characteristic
22	C₃²×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₁₆×C₂₉	C₂×C₃²	1	2	yes	—
24	C₄×C₈×C₂₉	C₂×C₃²	1	1	yes	characteristic
25	C₂×C₃×C₄×C₂₉	C₃×C₈	1	8	yes	—
26	C₂×C₃×C₄×C₂₉	C₂×C₃×C₄	1	4	yes	—
27	C₃×C₈×C₂₉	C₃×C₈	1	8	yes	—
28	C₃×C₈×C₂₉	C₂×C₃×C₄	1	8	yes	—
29	C₃²×C₄×C₁₆	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₃²×C₂₉	C₄×C₈	1	1	yes	characteristic
31	C₂×C₃²×C₂₉	C₂×C₁₆	1	2	yes	—
32	C₂×C₈×C₂₉	C₃²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₂₉	C₂²×C₃²	1	1	yes	characteristic
34	C₄²×C₂₉	C₃²×C₄	1	1	yes	characteristic
35	C₁₆×C₂₉	C₃²×C₄	1	4	yes	direct product factor
36	C₂²×C₃×C₂₉	C₂×C₃×C₈	1	4	yes	—
37	C₃×C₄×C₂₉	C₃×C₁₆	1	16	yes	direct product factor
38	C₃×C₄×C₂₉	C₃×C₄²	1	4	yes	—
39	C₃×C₄×C₂₉	C₂×C₃×C₈	1	4	yes	—
40	C₂×C₃²×C₁₆	C₂×C₂₉	1	2	yes	—
41	C₃²×C₄×C₈	C₂×C₂₉	1	1	yes	characteristic
42	C₃²×C₂₉	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₄×C₂₉	C₃²×C₈	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×C₃²×C₄	1	1	yes	characteristic
45	C₈×C₂₉	C₃²×C₈	1	2	yes	—
46	C₈×C₂₉	C₂×C₃²×C₄	1	2	yes	—
47	C₃×C₄×C₁₆	C₃×C₂₉	1	4	yes	direct product factor
48	C₂×C₃×C₂₉	C₃×C₄×C₈	1	4	yes	—
49	C₂×C₃×C₂₉	C₂×C₃×C₁₆	1	8	yes	—
50	C₂×C₃²×C₈	C₄×C₂₉	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂²×C₂₉	1	1	yes	characteristic
52	C₃²×C₄²	C₄×C₂₉	1	1	yes	characteristic
53	C₃²×C₁₆	C₄×C₂₉	1	4	yes	direct product factor
54	C₂²×C₂₉	C₂×C₃²×C₈	1	1	yes	characteristic
55	C₄×C₂₉	C₃²×C₁₆	1	4	yes	direct product factor
56	C₄×C₂₉	C₃²×C₄²	1	1	yes	characteristic
57	C₄×C₂₉	C₂×C₃²×C₈	1	1	yes	characteristic
58	C₂×C₃×C₁₆	C₂×C₃×C₂₉	1	8	yes	—
59	C₃×C₄×C₈	C₂×C₃×C₂₉	1	4	yes	—
60	C₃×C₂₉	C₃×C₄×C₁₆	1	4	yes	direct product factor
61	C₂×C₃²×C₄	C₈×C₂₉	1	2	yes	—
62	C₂×C₃²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
63	C₃²×C₈	C₈×C₂₉	1	2	yes	—
64	C₃²×C₈	C₂×C₄×C₂₉	1	2	yes	—
65	C₄×C₁₆	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₂₉	C₃²×C₄×C₈	1	1	yes	characteristic
67	C₂×C₂₉	C₂×C₃²×C₁₆	1	2	yes	—
68	C₂×C₃×C₈	C₃×C₄×C₂₉	1	4	yes	—
69	C₂×C₃×C₈	C₂²×C₃×C₂₉	1	4	yes	—
70	C₃×C₄²	C₃×C₄×C₂₉	1	4	yes	—
71	C₃×C₁₆	C₃×C₄×C₂₉	1	16	yes	direct product factor
72	C₂²×C₃²	C₂×C₈×C₂₉	1	1	yes	characteristic
73	C₃²×C₄	C₁₆×C₂₉	1	4	yes	direct product factor
74	C₃²×C₄	C₄²×C₂₉	1	1	yes	characteristic
75	C₃²×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
76	C₂×C₁₆	C₂×C₃²×C₂₉	1	2	yes	—
77	C₄×C₈	C₂×C₃²×C₂₉	1	1	yes	characteristic
78	C₂₉	C₃²×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₃×C₄	C₃×C₈×C₂₉	1	8	yes	—
80	C₂×C₃×C₄	C₂×C₃×C₄×C₂₉	1	4	yes	—
81	C₃×C₈	C₃×C₈×C₂₉	1	8	yes	—
82	C₃×C₈	C₂×C₃×C₄×C₂₉	1	8	yes	—
83	C₂×C₃²	C₄×C₈×C₂₉	1	1	yes	characteristic
84	C₂×C₃²	C₂×C₁₆×C₂₉	1	2	yes	—
85	C₂×C₈	C₃²×C₄×C₂₉	1	1	yes	characteristic
86	C₂×C₈	C₂²×C₃²×C₂₉	1	1	yes	characteristic
87	C₄²	C₃²×C₄×C₂₉	1	1	yes	characteristic
88	C₁₆	C₃²×C₄×C₂₉	1	4	yes	direct product factor
89	C₂²×C₃	C₂×C₃×C₈×C₂₉	1	4	yes	—
90	C₃×C₄	C₃×C₁₆×C₂₉	1	16	yes	direct product factor
91	C₃×C₄	C₃×C₄²×C₂₉	1	4	yes	—
92	C₃×C₄	C₂×C₃×C₈×C₂₉	1	4	yes	—
93	C₃²	C₄×C₁₆×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×C₄	C₃²×C₈×C₂₉	1	2	yes	—
95	C₂×C₄	C₂×C₃²×C₄×C₂₉	1	1	yes	characteristic
96	C₈	C₃²×C₈×C₂₉	1	2	yes	—
97	C₈	C₂×C₃²×C₄×C₂₉	1	2	yes	—
98	C₂×C₃	C₂×C₃×C₁₆×C₂₉	1	8	yes	—
99	C₂×C₃	C₃×C₄×C₈×C₂₉	1	4	yes	—
100	C₂²	C₂×C₃²×C₈×C₂₉	1	1	yes	characteristic
101	C₄	C₃²×C₁₆×C₂₉	1	4	yes	direct product factor
102	C₄	C₂×C₃²×C₈×C₂₉	1	1	yes	characteristic
103	C₄	C₃²×C₄²×C₂₉	1	1	yes	characteristic
104	C₃	C₃×C₄×C₁₆×C₂₉	1	4	yes	direct product factor
105	C₂	C₂×C₃²×C₁₆×C₂₉	1	2	yes	—
106	C₂	C₃²×C₄×C₈×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₃²×C₂₉
socle, prime radical	C₂²×C₃²×C₂₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₁₆×C₂₉	C₃	direct (N × H)
7. C₃²×C₁₆×C₂₉	C₄	direct (N × H)
14. C₄×C₁₆×C₂₉	C₃²	direct (N × H)
18. C₃×C₁₆×C₂₉	C₃×C₄	direct (N × H)
20. C₃²×C₄×C₂₉	C₁₆	direct (N × H)
29. C₃²×C₄×C₁₆	C₂₉	direct (N × H)
35. C₁₆×C₂₉	C₃²×C₄	direct (N × H)
37. C₃×C₄×C₂₉	C₃×C₁₆	direct (N × H)
42. C₃²×C₂₉	C₄×C₁₆	direct (N × H)
47. C₃×C₄×C₁₆	C₃×C₂₉	direct (N × H)
53. C₃²×C₁₆	C₄×C₂₉	direct (N × H)
55. C₄×C₂₉	C₃²×C₁₆	direct (N × H)
60. C₃×C₂₉	C₃×C₄×C₁₆	direct (N × H)
65. C₄×C₁₆	C₃²×C₂₉	direct (N × H)
71. C₃×C₁₆	C₃×C₄×C₂₉	direct (N × H)
73. C₃²×C₄	C₁₆×C₂₉	direct (N × H)
78. C₂₉	C₃²×C₄×C₁₆	direct (N × H)
88. C₁₆	C₃²×C₄×C₂₉	direct (N × H)
90. C₃×C₄	C₃×C₁₆×C₂₉	direct (N × H)
93. C₃²	C₄×C₁₆×C₂₉	direct (N × H)
101. C₄	C₃²×C₁₆×C₂₉	direct (N × H)
104. C₃	C₃×C₄×C₁₆×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₄×C₈×C₂₉	2
C₂×C₃²×C₁₆×C₂₉	2
C₃×C₄×C₁₆×C₂₉	3
C₃²×C₄×C₁₆	29

Subgroups — C32×C4×C16×C29 #72194682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₁₆×C₂₉ #72194682