Subgroups — C₂²×C₄×C₇×C₉×C₂₉ #72206161

Order 29232.

324 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	C₂³×C₇×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×C₉×C₂₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×C₄×C₇×C₂₉	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₃×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₂×C₃×C₄×C₇×C₂₉	C₂×C₃	1	6	yes	—
6	C₂²×C₄×C₉×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₄×C₇×C₂₉	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂³×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic
9	C₂×C₄×C₉×C₂₉	C₂×C₇	1	6	yes	direct product factor
10	C₂²×C₇×C₉×C₂₉	C₄	1	4	yes	direct product factor
11	C₂²×C₇×C₉×C₂₉	C₂²	1	3	yes	—
12	C₄×C₇×C₉×C₂₉	C₂²	1	4	yes	direct product factor
13	C₂×C₇×C₉×C₂₉	C₂×C₄	1	6	yes	direct product factor
14	C₂×C₇×C₉×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃×C₇×C₂₉	C₃×C₄	1	4	yes	—
16	C₂²×C₃×C₇×C₂₉	C₂²×C₃	1	3	yes	—
17	C₃×C₄×C₇×C₂₉	C₂²×C₃	1	4	yes	—
18	C₇×C₉×C₂₉	C₂²×C₄	1	1	yes	characteristic, direct product factor, Hall
19	C₂³×C₇×C₂₉	C₂×C₉	1	1	yes	characteristic
20	C₂×C₄×C₇×C₂₉	C₂×C₉	1	6	yes	direct product factor
21	C₂²×C₃×C₄×C₂₉	C₃×C₇	1	1	yes	characteristic
22	C₂×C₃×C₇×C₂₉	C₂×C₃×C₄	1	6	yes	—
23	C₂×C₃×C₇×C₂₉	C₂³×C₃	1	1	yes	characteristic
24	C₂²×C₉×C₂₉	C₄×C₇	1	4	yes	direct product factor
25	C₂²×C₉×C₂₉	C₂²×C₇	1	3	yes	—
26	C₄×C₉×C₂₉	C₂²×C₇	1	4	yes	direct product factor
27	C₂²×C₄×C₇×C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₇×C₂₉	C₄×C₉	1	4	yes	direct product factor
29	C₂²×C₇×C₂₉	C₂²×C₉	1	3	yes	—
30	C₄×C₇×C₂₉	C₂²×C₉	1	4	yes	direct product factor
31	C₂³×C₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic
32	C₂×C₃×C₄×C₂₉	C₂×C₃×C₇	1	6	yes	—
33	C₃×C₇×C₂₉	C₂²×C₃×C₄	1	1	yes	characteristic
34	C₂×C₉×C₂₉	C₂×C₄×C₇	1	6	yes	direct product factor
35	C₂×C₉×C₂₉	C₂³×C₇	1	1	yes	characteristic
36	C₂³×C₇×C₉	C₂×C₂₉	1	1	yes	characteristic
37	C₂×C₄×C₇×C₉	C₂×C₂₉	1	6	yes	direct product factor
38	C₂²×C₄×C₂₉	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇×C₂₉	C₂×C₄×C₉	1	6	yes	direct product factor
40	C₂×C₇×C₂₉	C₂³×C₉	1	1	yes	characteristic
41	C₂²×C₃×C₂₉	C₃×C₄×C₇	1	4	yes	—
42	C₂²×C₃×C₂₉	C₂²×C₃×C₇	1	3	yes	—
43	C₃×C₄×C₂₉	C₂²×C₃×C₇	1	4	yes	—
44	C₂²×C₃×C₄×C₇	C₃×C₂₉	1	1	yes	characteristic
45	C₉×C₂₉	C₂²×C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
46	C₂²×C₇×C₉	C₄×C₂₉	1	4	yes	direct product factor
47	C₂²×C₇×C₉	C₂²×C₂₉	1	3	yes	—
48	C₄×C₇×C₉	C₂²×C₂₉	1	4	yes	direct product factor
49	C₂³×C₂₉	C₂×C₇×C₉	1	1	yes	characteristic
50	C₂×C₄×C₂₉	C₂×C₇×C₉	1	6	yes	direct product factor
51	C₇×C₂₉	C₂²×C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
52	C₂×C₃×C₂₉	C₂×C₃×C₄×C₇	1	6	yes	—
53	C₂×C₃×C₂₉	C₂³×C₃×C₇	1	1	yes	characteristic
54	C₂³×C₃×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic
55	C₂×C₃×C₄×C₇	C₂×C₃×C₂₉	1	6	yes	—
56	C₂²×C₄×C₉	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
57	C₂×C₇×C₉	C₂×C₄×C₂₉	1	6	yes	direct product factor
58	C₂×C₇×C₉	C₂³×C₂₉	1	1	yes	characteristic
59	C₂²×C₂₉	C₄×C₇×C₉	1	4	yes	direct product factor
60	C₂²×C₂₉	C₂²×C₇×C₉	1	3	yes	—
61	C₄×C₂₉	C₂²×C₇×C₉	1	4	yes	direct product factor
62	C₂²×C₄×C₇	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
63	C₃×C₂₉	C₂²×C₃×C₄×C₇	1	1	yes	characteristic
64	C₂²×C₃×C₇	C₃×C₄×C₂₉	1	4	yes	—
65	C₂²×C₃×C₇	C₂²×C₃×C₂₉	1	3	yes	—
66	C₃×C₄×C₇	C₂²×C₃×C₂₉	1	4	yes	—
67	C₂³×C₉	C₂×C₇×C₂₉	1	1	yes	characteristic
68	C₂×C₄×C₉	C₂×C₇×C₂₉	1	6	yes	direct product factor
69	C₇×C₉	C₂²×C₄×C₂₉	1	1	yes	characteristic, direct product factor, Hall
70	C₂×C₂₉	C₂×C₄×C₇×C₉	1	6	yes	direct product factor
71	C₂×C₂₉	C₂³×C₇×C₉	1	1	yes	characteristic
72	C₂³×C₇	C₂×C₉×C₂₉	1	1	yes	characteristic
73	C₂×C₄×C₇	C₂×C₉×C₂₉	1	6	yes	direct product factor
74	C₂²×C₃×C₄	C₃×C₇×C₂₉	1	1	yes	characteristic
75	C₂×C₃×C₇	C₂×C₃×C₄×C₂₉	1	6	yes	—
76	C₂×C₃×C₇	C₂³×C₃×C₂₉	1	1	yes	characteristic
77	C₂²×C₉	C₄×C₇×C₂₉	1	4	yes	direct product factor
78	C₂²×C₉	C₂²×C₇×C₂₉	1	3	yes	—
79	C₄×C₉	C₂²×C₇×C₂₉	1	4	yes	direct product factor
80	C₂₉	C₂²×C₄×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₇	C₄×C₉×C₂₉	1	4	yes	direct product factor
82	C₂²×C₇	C₂²×C₉×C₂₉	1	3	yes	—
83	C₄×C₇	C₂²×C₉×C₂₉	1	4	yes	direct product factor
84	C₂³×C₃	C₂×C₃×C₇×C₂₉	1	1	yes	characteristic
85	C₂×C₃×C₄	C₂×C₃×C₇×C₂₉	1	6	yes	—
86	C₃×C₇	C₂²×C₃×C₄×C₂₉	1	1	yes	characteristic
87	C₂×C₉	C₂×C₄×C₇×C₂₉	1	6	yes	direct product factor
88	C₂×C₉	C₂³×C₇×C₂₉	1	1	yes	characteristic
89	C₂²×C₄	C₇×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₇	C₂×C₄×C₉×C₂₉	1	6	yes	direct product factor
91	C₂×C₇	C₂³×C₉×C₂₉	1	1	yes	characteristic
92	C₂²×C₃	C₃×C₄×C₇×C₂₉	1	4	yes	—
93	C₂²×C₃	C₂²×C₃×C₇×C₂₉	1	3	yes	—
94	C₃×C₄	C₂²×C₃×C₇×C₂₉	1	4	yes	—
95	C₉	C₂²×C₄×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	C₂×C₇×C₉×C₂₉	1	1	yes	characteristic
97	C₂×C₄	C₂×C₇×C₉×C₂₉	1	6	yes	direct product factor
98	C₇	C₂²×C₄×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
99	C₂×C₃	C₂×C₃×C₄×C₇×C₂₉	1	6	yes	—
100	C₂×C₃	C₂³×C₃×C₇×C₂₉	1	1	yes	characteristic
101	C₂²	C₄×C₇×C₉×C₂₉	1	4	yes	direct product factor
102	C₂²	C₂²×C₇×C₉×C₂₉	1	3	yes	—
103	C₄	C₂²×C₇×C₉×C₂₉	1	4	yes	direct product factor
104	C₃	C₂²×C₃×C₄×C₇×C₂₉	1	1	yes	characteristic
105	C₂	C₂×C₄×C₇×C₉×C₂₉	1	6	yes	direct product factor
106	C₂	C₂³×C₇×C₉×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂³×C₃×C₇×C₂₉
socle, prime radical	C₂³×C₃×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×C₉×C₂₉	C₂	direct (N × H)
6. C₂²×C₄×C₉×C₂₉	C₇	direct (N × H)
7. C₂²×C₄×C₇×C₂₉	C₉	direct (N × H)
9. C₂×C₄×C₉×C₂₉	C₂×C₇	direct (N × H)
10. C₂²×C₇×C₉×C₂₉	C₄	direct (N × H)
12. C₄×C₇×C₉×C₂₉	C₂²	direct (N × H)
13. C₂×C₇×C₉×C₂₉	C₂×C₄	direct (N × H)
18. C₇×C₉×C₂₉	C₂²×C₄	direct (N × H)
20. C₂×C₄×C₇×C₂₉	C₂×C₉	direct (N × H)
24. C₂²×C₉×C₂₉	C₄×C₇	direct (N × H)
26. C₄×C₉×C₂₉	C₂²×C₇	direct (N × H)
27. C₂²×C₄×C₇×C₉	C₂₉	direct (N × H)
28. C₂²×C₇×C₂₉	C₄×C₉	direct (N × H)
30. C₄×C₇×C₂₉	C₂²×C₉	direct (N × H)
34. C₂×C₉×C₂₉	C₂×C₄×C₇	direct (N × H)
37. C₂×C₄×C₇×C₉	C₂×C₂₉	direct (N × H)
38. C₂²×C₄×C₂₉	C₇×C₉	direct (N × H)
39. C₂×C₇×C₂₉	C₂×C₄×C₉	direct (N × H)
45. C₉×C₂₉	C₂²×C₄×C₇	direct (N × H)
46. C₂²×C₇×C₉	C₄×C₂₉	direct (N × H)
48. C₄×C₇×C₉	C₂²×C₂₉	direct (N × H)
50. C₂×C₄×C₂₉	C₂×C₇×C₉	direct (N × H)
51. C₇×C₂₉	C₂²×C₄×C₉	direct (N × H)
56. C₂²×C₄×C₉	C₇×C₂₉	direct (N × H)
57. C₂×C₇×C₉	C₂×C₄×C₂₉	direct (N × H)
59. C₂²×C₂₉	C₄×C₇×C₉	direct (N × H)
61. C₄×C₂₉	C₂²×C₇×C₉	direct (N × H)
62. C₂²×C₄×C₇	C₉×C₂₉	direct (N × H)
68. C₂×C₄×C₉	C₂×C₇×C₂₉	direct (N × H)
69. C₇×C₉	C₂²×C₄×C₂₉	direct (N × H)
70. C₂×C₂₉	C₂×C₄×C₇×C₉	direct (N × H)
73. C₂×C₄×C₇	C₂×C₉×C₂₉	direct (N × H)
77. C₂²×C₉	C₄×C₇×C₂₉	direct (N × H)
79. C₄×C₉	C₂²×C₇×C₂₉	direct (N × H)
80. C₂₉	C₂²×C₄×C₇×C₉	direct (N × H)
81. C₂²×C₇	C₄×C₉×C₂₉	direct (N × H)
83. C₄×C₇	C₂²×C₉×C₂₉	direct (N × H)
87. C₂×C₉	C₂×C₄×C₇×C₂₉	direct (N × H)
89. C₂²×C₄	C₇×C₉×C₂₉	direct (N × H)
90. C₂×C₇	C₂×C₄×C₉×C₂₉	direct (N × H)
95. C₉	C₂²×C₄×C₇×C₂₉	direct (N × H)
97. C₂×C₄	C₂×C₇×C₉×C₂₉	direct (N × H)
98. C₇	C₂²×C₄×C₉×C₂₉	direct (N × H)
101. C₂²	C₄×C₇×C₉×C₂₉	direct (N × H)
103. C₄	C₂²×C₇×C₉×C₂₉	direct (N × H)
105. C₂	C₂×C₄×C₇×C₉×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
C₂³×C₇×C₉×C₂₉	2
C₂×C₄×C₇×C₉×C₂₉	2
C₂²×C₃×C₄×C₇×C₂₉	3
C₂²×C₄×C₉×C₂₉	7
C₂²×C₄×C₇×C₉	29

Subgroups — C22×C4×C7×C9×C29 #72206161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₇×C₉×C₂₉ #72206161