Subgroups — C₃×C₄×C₈²×C₂₉ #72199708

Order 22272.

1500 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₈×C₂₉	C₂	1	3	yes	maximal
2	C₂×C₃×C₈²×C₂₉	C₂	1	4	yes	maximal
3	C₃×C₄³×C₂₉	C₂²	1	1	yes	characteristic
4	C₂×C₃×C₄×C₈×C₂₉	C₄	1	12	yes	—
5	C₂×C₃×C₄×C₈×C₂₉	C₂²	1	6	yes	—
6	C₃×C₈²×C₂₉	C₄	1	16	yes	direct product factor
7	C₂²×C₃×C₈×C₂₉	C₂×C₄	1	12	yes	—
8	C₂×C₃×C₄²×C₂₉	C₂×C₄	1	6	yes	—
9	C₂×C₃×C₄²×C₂₉	C₂³	1	1	yes	characteristic
10	C₃×C₄×C₈×C₂₉	C₈	1	48	yes	direct product factor
11	C₃×C₄×C₈×C₂₉	C₂×C₄	1	24	yes	—
12	C₄×C₈²×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄²×C₈×C₂₉	C₂×C₃	1	3	yes	—
14	C₂×C₈²×C₂₉	C₂×C₃	1	4	yes	—
15	C₂×C₄×C₈×C₂₉	C₃×C₄	1	12	yes	—
16	C₂×C₄×C₈×C₂₉	C₂²×C₃	1	6	yes	—
17	C₄³×C₂₉	C₂²×C₃	1	1	yes	characteristic
18	C₈²×C₂₉	C₃×C₄	1	16	yes	direct product factor
19	C₂²×C₃×C₄×C₂₉	C₄²	1	4	yes	—
20	C₂²×C₃×C₄×C₂₉	C₂²×C₄	1	3	yes	—
21	C₂×C₃×C₈×C₂₉	C₄²	1	24	yes	—
22	C₂×C₃×C₈×C₂₉	C₂×C₈	1	48	yes	—
23	C₃×C₄²×C₂₉	C₂×C₈	1	24	yes	—
24	C₃×C₄²×C₂₉	C₂²×C₄	1	4	yes	—
25	C₂²×C₈×C₂₉	C₂×C₃×C₄	1	12	yes	—
26	C₂×C₄²×C₂₉	C₂×C₃×C₄	1	6	yes	—
27	C₂×C₄²×C₂₉	C₂³×C₃	1	1	yes	characteristic
28	C₄×C₈×C₂₉	C₃×C₈	1	48	yes	direct product factor
29	C₄×C₈×C₂₉	C₂×C₃×C₄	1	24	yes	—
30	C₃×C₄×C₈²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂³×C₃×C₂₉	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₃×C₄×C₂₉	C₄×C₈	1	24	yes	—
33	C₂×C₃×C₄×C₂₉	C₂×C₄²	1	6	yes	—
34	C₂×C₃×C₄×C₂₉	C₂²×C₈	1	12	yes	—
35	C₃×C₈×C₂₉	C₄×C₈	1	48	yes	direct product factor
36	C₂²×C₄×C₂₉	C₃×C₄²	1	4	yes	—
37	C₂²×C₄×C₂₉	C₂²×C₃×C₄	1	3	yes	—
38	C₂×C₈×C₂₉	C₃×C₄²	1	24	yes	—
39	C₂×C₈×C₂₉	C₂×C₃×C₈	1	48	yes	—
40	C₄²×C₂₉	C₂×C₃×C₈	1	24	yes	—
41	C₄²×C₂₉	C₂²×C₃×C₄	1	4	yes	—
42	C₃×C₄²×C₈	C₂×C₂₉	1	3	yes	—
43	C₂×C₃×C₈²	C₂×C₂₉	1	4	yes	—
44	C₂²×C₃×C₂₉	C₄³	1	1	yes	characteristic
45	C₂²×C₃×C₂₉	C₂×C₄×C₈	1	6	yes	—
46	C₃×C₄×C₂₉	C₈²	1	16	yes	direct product factor
47	C₃×C₄×C₂₉	C₂×C₄×C₈	1	12	yes	—
48	C₄×C₈²	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂³×C₂₉	C₂×C₃×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₂₉	C₃×C₄×C₈	1	24	yes	—
51	C₂×C₄×C₂₉	C₂×C₃×C₄²	1	6	yes	—
52	C₂×C₄×C₂₉	C₂²×C₃×C₈	1	12	yes	—
53	C₈×C₂₉	C₃×C₄×C₈	1	48	yes	direct product factor
54	C₂×C₃×C₄×C₈	C₄×C₂₉	1	12	yes	—
55	C₂×C₃×C₄×C₈	C₂²×C₂₉	1	6	yes	—
56	C₃×C₄³	C₂²×C₂₉	1	1	yes	characteristic
57	C₃×C₈²	C₄×C₂₉	1	16	yes	direct product factor
58	C₂×C₃×C₂₉	C₂×C₈²	1	4	yes	—
59	C₂×C₃×C₂₉	C₄²×C₈	1	3	yes	—
60	C₄²×C₈	C₂×C₃×C₂₉	1	3	yes	—
61	C₂×C₈²	C₂×C₃×C₂₉	1	4	yes	—
62	C₂²×C₂₉	C₃×C₄³	1	1	yes	characteristic
63	C₂²×C₂₉	C₂×C₃×C₄×C₈	1	6	yes	—
64	C₄×C₂₉	C₃×C₈²	1	16	yes	direct product factor
65	C₄×C₂₉	C₂×C₃×C₄×C₈	1	12	yes	—
66	C₂²×C₃×C₈	C₂×C₄×C₂₉	1	12	yes	—
67	C₂×C₃×C₄²	C₂×C₄×C₂₉	1	6	yes	—
68	C₂×C₃×C₄²	C₂³×C₂₉	1	1	yes	characteristic
69	C₃×C₄×C₈	C₈×C₂₉	1	48	yes	direct product factor
70	C₃×C₄×C₈	C₂×C₄×C₂₉	1	24	yes	—
71	C₃×C₂₉	C₄×C₈²	1	1	yes	characteristic, direct product factor, Hall
72	C₂×C₄×C₈	C₃×C₄×C₂₉	1	12	yes	—
73	C₂×C₄×C₈	C₂²×C₃×C₂₉	1	6	yes	—
74	C₄³	C₂²×C₃×C₂₉	1	1	yes	characteristic
75	C₈²	C₃×C₄×C₂₉	1	16	yes	direct product factor
76	C₂×C₂₉	C₂×C₃×C₈²	1	4	yes	—
77	C₂×C₂₉	C₃×C₄²×C₈	1	3	yes	—
78	C₂²×C₃×C₄	C₄²×C₂₉	1	4	yes	—
79	C₂²×C₃×C₄	C₂²×C₄×C₂₉	1	3	yes	—
80	C₂×C₃×C₈	C₄²×C₂₉	1	24	yes	—
81	C₂×C₃×C₈	C₂×C₈×C₂₉	1	48	yes	—
82	C₃×C₄²	C₂×C₈×C₂₉	1	24	yes	—
83	C₃×C₄²	C₂²×C₄×C₂₉	1	4	yes	—
84	C₂²×C₈	C₂×C₃×C₄×C₂₉	1	12	yes	—
85	C₂×C₄²	C₂×C₃×C₄×C₂₉	1	6	yes	—
86	C₂×C₄²	C₂³×C₃×C₂₉	1	1	yes	characteristic
87	C₄×C₈	C₃×C₈×C₂₉	1	48	yes	direct product factor
88	C₄×C₈	C₂×C₃×C₄×C₂₉	1	24	yes	—
89	C₂₉	C₃×C₄×C₈²	1	1	yes	characteristic, direct product factor, Sylow
90	C₂³×C₃	C₂×C₄²×C₂₉	1	1	yes	characteristic
91	C₂×C₃×C₄	C₄×C₈×C₂₉	1	24	yes	—
92	C₂×C₃×C₄	C₂×C₄²×C₂₉	1	6	yes	—
93	C₂×C₃×C₄	C₂²×C₈×C₂₉	1	12	yes	—
94	C₃×C₈	C₄×C₈×C₂₉	1	48	yes	direct product factor
95	C₂²×C₄	C₃×C₄²×C₂₉	1	4	yes	—
96	C₂²×C₄	C₂²×C₃×C₄×C₂₉	1	3	yes	—
97	C₂×C₈	C₃×C₄²×C₂₉	1	24	yes	—
98	C₂×C₈	C₂×C₃×C₈×C₂₉	1	48	yes	—
99	C₄²	C₂×C₃×C₈×C₂₉	1	24	yes	—
100	C₄²	C₂²×C₃×C₄×C₂₉	1	4	yes	—
101	C₂²×C₃	C₄³×C₂₉	1	1	yes	characteristic
102	C₂²×C₃	C₂×C₄×C₈×C₂₉	1	6	yes	—
103	C₃×C₄	C₈²×C₂₉	1	16	yes	direct product factor
104	C₃×C₄	C₂×C₄×C₈×C₂₉	1	12	yes	—
105	C₂³	C₂×C₃×C₄²×C₂₉	1	1	yes	characteristic
106	C₂×C₄	C₃×C₄×C₈×C₂₉	1	24	yes	—
107	C₂×C₄	C₂×C₃×C₄²×C₂₉	1	6	yes	—
108	C₂×C₄	C₂²×C₃×C₈×C₂₉	1	12	yes	—
109	C₈	C₃×C₄×C₈×C₂₉	1	48	yes	direct product factor
110	C₂×C₃	C₂×C₈²×C₂₉	1	4	yes	—
111	C₂×C₃	C₄²×C₈×C₂₉	1	3	yes	—
112	C₂²	C₂×C₃×C₄×C₈×C₂₉	1	6	yes	—
113	C₂²	C₃×C₄³×C₂₉	1	1	yes	characteristic
114	C₄	C₃×C₈²×C₂₉	1	16	yes	direct product factor
115	C₄	C₂×C₃×C₄×C₈×C₂₉	1	12	yes	—
116	C₃	C₄×C₈²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
117	C₂	C₂×C₃×C₈²×C₂₉	1	4	yes	—
118	C₂	C₃×C₄²×C₈×C₂₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂³×C₃×C₂₉
socle, prime radical	C₂³×C₃×C₂₉	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₃×C₈²×C₂₉	C₄	direct (N × H)
10. C₃×C₄×C₈×C₂₉	C₈	direct (N × H)
12. C₄×C₈²×C₂₉	C₃	direct (N × H)
18. C₈²×C₂₉	C₃×C₄	direct (N × H)
28. C₄×C₈×C₂₉	C₃×C₈	direct (N × H)
30. C₃×C₄×C₈²	C₂₉	direct (N × H)
35. C₃×C₈×C₂₉	C₄×C₈	direct (N × H)
46. C₃×C₄×C₂₉	C₈²	direct (N × H)
48. C₄×C₈²	C₃×C₂₉	direct (N × H)
53. C₈×C₂₉	C₃×C₄×C₈	direct (N × H)
57. C₃×C₈²	C₄×C₂₉	direct (N × H)
64. C₄×C₂₉	C₃×C₈²	direct (N × H)
69. C₃×C₄×C₈	C₈×C₂₉	direct (N × H)
71. C₃×C₂₉	C₄×C₈²	direct (N × H)
75. C₈²	C₃×C₄×C₂₉	direct (N × H)
87. C₄×C₈	C₃×C₈×C₂₉	direct (N × H)
89. C₂₉	C₃×C₄×C₈²	direct (N × H)
94. C₃×C₈	C₄×C₈×C₂₉	direct (N × H)
103. C₃×C₄	C₈²×C₂₉	direct (N × H)
109. C₈	C₃×C₄×C₈×C₂₉	direct (N × H)
114. C₄	C₃×C₈²×C₂₉	direct (N × H)
116. C₃	C₄×C₈²×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
C₃×C₄²×C₈×C₂₉	2
C₂×C₃×C₈²×C₂₉	2
C₄×C₈²×C₂₉	3
C₃×C₄×C₈²	29

Subgroups — C3×C4×C82×C29 #72199708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₈²×C₂₉ #72199708