Subgroups — C₂×C₃×C₇×C₁₁×C₆₄ #72206439

Order 29568.

160 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₁₁×C₆₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×C₁₁×C₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₁₁×C₁₆	C₄	1	1	yes	characteristic
5	C₃×C₇×C₁₁×C₃₂	C₄	1	1	yes	characteristic
6	C₃×C₇×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₇×C₁₁×C₃₂	C₂×C₃	1	1	yes	characteristic
8	C₇×C₁₁×C₆₄	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃×C₁₁×C₆₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₈×C₁₁	C₈	1	1	yes	characteristic
11	C₃×C₇×C₁₁×C₁₆	C₈	1	1	yes	characteristic
12	C₃×C₇×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₇×C₆₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₇×C₁₁×C₁₆	C₃×C₄	1	1	yes	characteristic
15	C₇×C₁₁×C₃₂	C₃×C₄	1	1	yes	characteristic
16	C₇×C₁₁×C₃₂	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃×C₁₁×C₃₂	C₂×C₇	1	1	yes	characteristic
18	C₃×C₁₁×C₆₄	C₂×C₇	1	2	yes	direct product factor
19	C₂×C₃×C₄×C₇×C₁₁	C₁₆	1	1	yes	characteristic
20	C₃×C₇×C₈×C₁₁	C₁₆	1	1	yes	characteristic
21	C₃×C₇×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
22	C₂×C₁₁×C₆₄	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₇×C₃₂	C₂×C₁₁	1	1	yes	characteristic
24	C₃×C₇×C₆₄	C₂×C₁₁	1	2	yes	direct product factor
25	C₂×C₇×C₈×C₁₁	C₃×C₈	1	1	yes	characteristic
26	C₇×C₁₁×C₁₆	C₃×C₈	1	1	yes	characteristic
27	C₇×C₁₁×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
28	C₂×C₃×C₁₁×C₁₆	C₄×C₇	1	1	yes	characteristic
29	C₃×C₁₁×C₃₂	C₄×C₇	1	1	yes	characteristic
30	C₃×C₁₁×C₃₂	C₂²×C₇	1	1	yes	characteristic
31	C₂²×C₃×C₇×C₁₁	C₃₂	1	1	yes	characteristic
32	C₃×C₄×C₇×C₁₁	C₃₂	1	1	yes	characteristic
33	C₃×C₄×C₇×C₁₁	C₂×C₁₆	1	1	yes	characteristic
34	C₂×C₇×C₆₄	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₁×C₃₂	C₂×C₃×C₇	1	1	yes	characteristic
36	C₁₁×C₆₄	C₂×C₃×C₇	1	2	yes	direct product factor
37	C₂×C₃×C₇×C₁₆	C₄×C₁₁	1	1	yes	characteristic
38	C₃×C₇×C₃₂	C₄×C₁₁	1	1	yes	characteristic
39	C₃×C₇×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
40	C₂×C₄×C₇×C₁₁	C₃×C₁₆	1	1	yes	characteristic
41	C₇×C₈×C₁₁	C₃×C₁₆	1	1	yes	characteristic
42	C₇×C₈×C₁₁	C₂×C₃×C₈	1	1	yes	characteristic
43	C₂×C₃×C₈×C₁₁	C₇×C₈	1	1	yes	characteristic
44	C₃×C₁₁×C₁₆	C₇×C₈	1	1	yes	characteristic
45	C₃×C₁₁×C₁₆	C₂×C₄×C₇	1	1	yes	characteristic
46	C₂×C₃×C₇×C₁₁	C₆₄	1	2	yes	direct product factor
47	C₂×C₃×C₇×C₁₁	C₂×C₃₂	1	1	yes	characteristic
48	C₂×C₇×C₃₂	C₂×C₃×C₁₁	1	1	yes	characteristic
49	C₇×C₆₄	C₂×C₃×C₁₁	1	2	yes	direct product factor
50	C₂×C₃×C₆₄	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₁₁×C₁₆	C₃×C₄×C₇	1	1	yes	characteristic
52	C₁₁×C₃₂	C₃×C₄×C₇	1	1	yes	characteristic
53	C₁₁×C₃₂	C₂²×C₃×C₇	1	1	yes	characteristic
54	C₂×C₃×C₇×C₈	C₈×C₁₁	1	1	yes	characteristic
55	C₃×C₇×C₁₆	C₈×C₁₁	1	1	yes	characteristic
56	C₃×C₇×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
57	C₂²×C₇×C₁₁	C₃×C₃₂	1	1	yes	characteristic
58	C₄×C₇×C₁₁	C₃×C₃₂	1	1	yes	characteristic
59	C₄×C₇×C₁₁	C₂×C₃×C₁₆	1	1	yes	characteristic
60	C₂×C₃×C₄×C₁₁	C₇×C₁₆	1	1	yes	characteristic
61	C₃×C₈×C₁₁	C₇×C₁₆	1	1	yes	characteristic
62	C₃×C₈×C₁₁	C₂×C₇×C₈	1	1	yes	characteristic
63	C₃×C₇×C₁₁	C₂×C₆₄	1	1	yes	characteristic, direct product factor, Hall
64	C₂×C₇×C₁₆	C₃×C₄×C₁₁	1	1	yes	characteristic
65	C₇×C₃₂	C₃×C₄×C₁₁	1	1	yes	characteristic
66	C₇×C₃₂	C₂²×C₃×C₁₁	1	1	yes	characteristic
67	C₂×C₃×C₃₂	C₂×C₇×C₁₁	1	1	yes	characteristic
68	C₃×C₆₄	C₂×C₇×C₁₁	1	2	yes	direct product factor
69	C₂×C₈×C₁₁	C₃×C₇×C₈	1	1	yes	characteristic
70	C₁₁×C₁₆	C₃×C₇×C₈	1	1	yes	characteristic
71	C₁₁×C₁₆	C₂×C₃×C₄×C₇	1	1	yes	characteristic
72	C₂×C₃×C₄×C₇	C₁₁×C₁₆	1	1	yes	characteristic
73	C₃×C₇×C₈	C₁₁×C₁₆	1	1	yes	characteristic
74	C₃×C₇×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
75	C₂×C₇×C₁₁	C₃×C₆₄	1	2	yes	direct product factor
76	C₂×C₇×C₁₁	C₂×C₃×C₃₂	1	1	yes	characteristic
77	C₂²×C₃×C₁₁	C₇×C₃₂	1	1	yes	characteristic
78	C₃×C₄×C₁₁	C₇×C₃₂	1	1	yes	characteristic
79	C₃×C₄×C₁₁	C₂×C₇×C₁₆	1	1	yes	characteristic
80	C₂×C₆₄	C₃×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×C₇×C₈	C₃×C₈×C₁₁	1	1	yes	characteristic
82	C₇×C₁₆	C₃×C₈×C₁₁	1	1	yes	characteristic
83	C₇×C₁₆	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic
84	C₂×C₃×C₁₆	C₄×C₇×C₁₁	1	1	yes	characteristic
85	C₃×C₃₂	C₄×C₇×C₁₁	1	1	yes	characteristic
86	C₃×C₃₂	C₂²×C₇×C₁₁	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₃×C₇×C₁₆	1	1	yes	characteristic
88	C₈×C₁₁	C₃×C₇×C₁₆	1	1	yes	characteristic
89	C₈×C₁₁	C₂×C₃×C₇×C₈	1	1	yes	characteristic
90	C₂²×C₃×C₇	C₁₁×C₃₂	1	1	yes	characteristic
91	C₃×C₄×C₇	C₁₁×C₃₂	1	1	yes	characteristic
92	C₃×C₄×C₇	C₂×C₁₁×C₁₆	1	1	yes	characteristic
93	C₇×C₁₁	C₂×C₃×C₆₄	1	1	yes	characteristic, direct product factor, Hall
94	C₂×C₃×C₁₁	C₇×C₆₄	1	2	yes	direct product factor
95	C₂×C₃×C₁₁	C₂×C₇×C₃₂	1	1	yes	characteristic
96	C₂×C₃₂	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic
97	C₆₄	C₂×C₃×C₇×C₁₁	1	2	yes	direct product factor
98	C₂×C₄×C₇	C₃×C₁₁×C₁₆	1	1	yes	characteristic
99	C₇×C₈	C₃×C₁₁×C₁₆	1	1	yes	characteristic
100	C₇×C₈	C₂×C₃×C₈×C₁₁	1	1	yes	characteristic
101	C₂×C₃×C₈	C₇×C₈×C₁₁	1	1	yes	characteristic
102	C₃×C₁₆	C₇×C₈×C₁₁	1	1	yes	characteristic
103	C₃×C₁₆	C₂×C₄×C₇×C₁₁	1	1	yes	characteristic
104	C₂²×C₁₁	C₃×C₇×C₃₂	1	1	yes	characteristic
105	C₄×C₁₁	C₃×C₇×C₃₂	1	1	yes	characteristic
106	C₄×C₁₁	C₂×C₃×C₇×C₁₆	1	1	yes	characteristic
107	C₂×C₃×C₇	C₁₁×C₆₄	1	2	yes	direct product factor
108	C₂×C₃×C₇	C₂×C₁₁×C₃₂	1	1	yes	characteristic
109	C₃×C₁₁	C₂×C₇×C₆₄	1	1	yes	characteristic, direct product factor, Hall
110	C₂×C₁₆	C₃×C₄×C₇×C₁₁	1	1	yes	characteristic
111	C₃₂	C₃×C₄×C₇×C₁₁	1	1	yes	characteristic
112	C₃₂	C₂²×C₃×C₇×C₁₁	1	1	yes	characteristic
113	C₂²×C₇	C₃×C₁₁×C₃₂	1	1	yes	characteristic
114	C₄×C₇	C₃×C₁₁×C₃₂	1	1	yes	characteristic
115	C₄×C₇	C₂×C₃×C₁₁×C₁₆	1	1	yes	characteristic
116	C₂×C₃×C₄	C₇×C₁₁×C₁₆	1	1	yes	characteristic
117	C₃×C₈	C₇×C₁₁×C₁₆	1	1	yes	characteristic
118	C₃×C₈	C₂×C₇×C₈×C₁₁	1	1	yes	characteristic
119	C₂×C₁₁	C₃×C₇×C₆₄	1	2	yes	direct product factor
120	C₂×C₁₁	C₂×C₃×C₇×C₃₂	1	1	yes	characteristic
121	C₃×C₇	C₂×C₁₁×C₆₄	1	1	yes	characteristic, direct product factor, Hall
122	C₂×C₈	C₃×C₇×C₈×C₁₁	1	1	yes	characteristic
123	C₁₆	C₃×C₇×C₈×C₁₁	1	1	yes	characteristic
124	C₁₆	C₂×C₃×C₄×C₇×C₁₁	1	1	yes	characteristic
125	C₂×C₇	C₃×C₁₁×C₆₄	1	2	yes	direct product factor
126	C₂×C₇	C₂×C₃×C₁₁×C₃₂	1	1	yes	characteristic
127	C₂²×C₃	C₇×C₁₁×C₃₂	1	1	yes	characteristic
128	C₃×C₄	C₇×C₁₁×C₃₂	1	1	yes	characteristic
129	C₃×C₄	C₂×C₇×C₁₁×C₁₆	1	1	yes	characteristic
130	C₁₁	C₂×C₃×C₇×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₄	C₃×C₇×C₁₁×C₁₆	1	1	yes	characteristic
132	C₈	C₃×C₇×C₁₁×C₁₆	1	1	yes	characteristic
133	C₈	C₂×C₃×C₇×C₈×C₁₁	1	1	yes	characteristic
134	C₇	C₂×C₃×C₁₁×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
135	C₂×C₃	C₇×C₁₁×C₆₄	1	2	yes	direct product factor
136	C₂×C₃	C₂×C₇×C₁₁×C₃₂	1	1	yes	characteristic
137	C₂²	C₃×C₇×C₁₁×C₃₂	1	1	yes	characteristic
138	C₄	C₃×C₇×C₁₁×C₃₂	1	1	yes	characteristic
139	C₄	C₂×C₃×C₇×C₁₁×C₁₆	1	1	yes	characteristic
140	C₃	C₂×C₇×C₁₁×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
141	C₂	C₃×C₇×C₁₁×C₆₄	1	2	yes	direct product factor
142	C₂	C₂×C₃×C₇×C₁₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂²×C₃×C₇×C₁₁
socle, prime radical	C₂²×C₃×C₇×C₁₁	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₁₁×C₆₄	C₂	direct (N × H)
3. C₂×C₇×C₁₁×C₆₄	C₃	direct (N × H)
8. C₇×C₁₁×C₆₄	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₁×C₆₄	C₇	direct (N × H)
13. C₂×C₃×C₇×C₆₄	C₁₁	direct (N × H)
18. C₃×C₁₁×C₆₄	C₂×C₇	direct (N × H)
22. C₂×C₁₁×C₆₄	C₃×C₇	direct (N × H)
24. C₃×C₇×C₆₄	C₂×C₁₁	direct (N × H)
34. C₂×C₇×C₆₄	C₃×C₁₁	direct (N × H)
36. C₁₁×C₆₄	C₂×C₃×C₇	direct (N × H)
46. C₂×C₃×C₇×C₁₁	C₆₄	direct (N × H)
49. C₇×C₆₄	C₂×C₃×C₁₁	direct (N × H)
50. C₂×C₃×C₆₄	C₇×C₁₁	direct (N × H)
63. C₃×C₇×C₁₁	C₂×C₆₄	direct (N × H)
68. C₃×C₆₄	C₂×C₇×C₁₁	direct (N × H)
75. C₂×C₇×C₁₁	C₃×C₆₄	direct (N × H)
80. C₂×C₆₄	C₃×C₇×C₁₁	direct (N × H)
93. C₇×C₁₁	C₂×C₃×C₆₄	direct (N × H)
94. C₂×C₃×C₁₁	C₇×C₆₄	direct (N × H)
97. C₆₄	C₂×C₃×C₇×C₁₁	direct (N × H)
107. C₂×C₃×C₇	C₁₁×C₆₄	direct (N × H)
109. C₃×C₁₁	C₂×C₇×C₆₄	direct (N × H)
119. C₂×C₁₁	C₃×C₇×C₆₄	direct (N × H)
121. C₃×C₇	C₂×C₁₁×C₆₄	direct (N × H)
125. C₂×C₇	C₃×C₁₁×C₆₄	direct (N × H)
130. C₁₁	C₂×C₃×C₇×C₆₄	direct (N × H)
134. C₇	C₂×C₃×C₁₁×C₆₄	direct (N × H)
135. C₂×C₃	C₇×C₁₁×C₆₄	direct (N × H)
140. C₃	C₂×C₇×C₁₁×C₆₄	direct (N × H)
141. C₂	C₃×C₇×C₁₁×C₆₄	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×C₇×C₁₁×C₃₂	2
C₃×C₇×C₁₁×C₆₄	2
C₂×C₇×C₁₁×C₆₄	3
C₂×C₃×C₁₁×C₆₄	7
C₂×C₃×C₇×C₆₄	11

Subgroups — C2×C3×C7×C11×C64 #72206439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₁×C₆₄ #72206439