Subgroups — C₂³×C₄×C₉²×C₁₁ #72205482

Order 28512.

5428 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	C₂⁴×C₉²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₉²×C₁₁	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃×C₄×C₉×C₁₁	C₃	1	4	yes	maximal
4	C₂³×C₉²×C₁₁	C₄	1	8	yes	direct product factor
5	C₂³×C₉²×C₁₁	C₂²	1	7	yes	—
6	C₂×C₄×C₉²×C₁₁	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₃×C₉×C₁₁	C₂×C₃	1	4	yes	—
8	C₂²×C₃×C₄×C₉×C₁₁	C₂×C₃	1	56	yes	—
9	C₂²×C₉²×C₁₁	C₂×C₄	1	28	yes	direct product factor
10	C₂²×C₉²×C₁₁	C₂³	1	7	yes	—
11	C₄×C₉²×C₁₁	C₂³	1	8	yes	direct product factor
12	C₂³×C₃²×C₄×C₁₁	C₃²	1	1	yes	characteristic
13	C₂³×C₄×C₉×C₁₁	C₉	1	12	yes	direct product factor
14	C₂³×C₄×C₉²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂³×C₃×C₉×C₁₁	C₃×C₄	1	32	yes	—
16	C₂³×C₃×C₉×C₁₁	C₂²×C₃	1	28	yes	—
17	C₂×C₃×C₄×C₉×C₁₁	C₂²×C₃	1	112	yes	—
18	C₂×C₉²×C₁₁	C₂²×C₄	1	14	yes	direct product factor
19	C₂×C₉²×C₁₁	C₂⁴	1	1	yes	characteristic
20	C₂⁴×C₃²×C₁₁	C₂×C₃²	1	1	yes	characteristic
21	C₂²×C₃²×C₄×C₁₁	C₂×C₃²	1	14	yes	—
22	C₂⁴×C₉×C₁₁	C₂×C₉	1	12	yes	—
23	C₂²×C₄×C₉×C₁₁	C₂×C₉	1	168	yes	direct product factor
24	C₂⁴×C₉²	C₂×C₁₁	1	1	yes	characteristic
25	C₂²×C₄×C₉²	C₂×C₁₁	1	14	yes	direct product factor
26	C₂²×C₃×C₉×C₁₁	C₂×C₃×C₄	1	112	yes	—
27	C₂²×C₃×C₉×C₁₁	C₂³×C₃	1	28	yes	—
28	C₃×C₄×C₉×C₁₁	C₂³×C₃	1	32	yes	—
29	C₂³×C₃×C₄×C₁₁	C₃×C₉	1	4	yes	—
30	C₉²×C₁₁	C₂³×C₄	1	1	yes	characteristic, direct product factor, Hall
31	C₂³×C₃×C₄×C₉	C₃×C₁₁	1	4	yes	—
32	C₂³×C₃²×C₁₁	C₃²×C₄	1	8	yes	—
33	C₂³×C₃²×C₁₁	C₂²×C₃²	1	7	yes	—
34	C₂×C₃²×C₄×C₁₁	C₂²×C₃²	1	28	yes	—
35	C₂³×C₉×C₁₁	C₄×C₉	1	96	yes	direct product factor
36	C₂³×C₉×C₁₁	C₂²×C₉	1	84	yes	—
37	C₂×C₄×C₉×C₁₁	C₂²×C₉	1	336	yes	direct product factor
38	C₂³×C₉²	C₄×C₁₁	1	8	yes	direct product factor
39	C₂³×C₉²	C₂²×C₁₁	1	7	yes	—
40	C₂×C₄×C₉²	C₂²×C₁₁	1	28	yes	direct product factor
41	C₂×C₃×C₉×C₁₁	C₂²×C₃×C₄	1	56	yes	—
42	C₂×C₃×C₉×C₁₁	C₂⁴×C₃	1	4	yes	—
43	C₂⁴×C₃×C₁₁	C₂×C₃×C₉	1	4	yes	—
44	C₂²×C₃×C₄×C₁₁	C₂×C₃×C₉	1	56	yes	—
45	C₂⁴×C₃×C₉	C₂×C₃×C₁₁	1	4	yes	—
46	C₂²×C₃×C₄×C₉	C₂×C₃×C₁₁	1	56	yes	—
47	C₂²×C₃²×C₁₁	C₂×C₃²×C₄	1	28	yes	—
48	C₂²×C₃²×C₁₁	C₂³×C₃²	1	7	yes	—
49	C₃²×C₄×C₁₁	C₂³×C₃²	1	8	yes	—
50	C₂²×C₉×C₁₁	C₂×C₄×C₉	1	336	yes	direct product factor
51	C₂²×C₉×C₁₁	C₂³×C₉	1	84	yes	—
52	C₄×C₉×C₁₁	C₂³×C₉	1	96	yes	direct product factor
53	C₂³×C₄×C₁₁	C₉²	1	1	yes	characteristic, direct product factor, Hall
54	C₂²×C₉²	C₂×C₄×C₁₁	1	28	yes	direct product factor
55	C₂²×C₉²	C₂³×C₁₁	1	7	yes	—
56	C₄×C₉²	C₂³×C₁₁	1	8	yes	direct product factor
57	C₃×C₉×C₁₁	C₂³×C₃×C₄	1	4	yes	—
58	C₂³×C₃²×C₄	C₃²×C₁₁	1	1	yes	characteristic
59	C₂³×C₄×C₉	C₉×C₁₁	1	12	yes	direct product factor
60	C₂³×C₃×C₁₁	C₃×C₄×C₉	1	32	yes	—
61	C₂³×C₃×C₁₁	C₂²×C₃×C₉	1	28	yes	—
62	C₂×C₃×C₄×C₁₁	C₂²×C₃×C₉	1	112	yes	—
63	C₂³×C₃×C₉	C₃×C₄×C₁₁	1	32	yes	—
64	C₂³×C₃×C₉	C₂²×C₃×C₁₁	1	28	yes	—
65	C₂×C₃×C₄×C₉	C₂²×C₃×C₁₁	1	112	yes	—
66	C₂×C₃²×C₁₁	C₂²×C₃²×C₄	1	14	yes	—
67	C₂×C₃²×C₁₁	C₂⁴×C₃²	1	1	yes	characteristic
68	C₂×C₉×C₁₁	C₂²×C₄×C₉	1	168	yes	direct product factor
69	C₂×C₉×C₁₁	C₂⁴×C₉	1	12	yes	—
70	C₂⁴×C₁₁	C₂×C₉²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂×C₉²	1	14	yes	direct product factor
72	C₂×C₉²	C₂²×C₄×C₁₁	1	14	yes	direct product factor
73	C₂×C₉²	C₂⁴×C₁₁	1	1	yes	characteristic
74	C₂⁴×C₃²	C₂×C₃²×C₁₁	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂×C₃²×C₁₁	1	14	yes	—
76	C₂⁴×C₉	C₂×C₉×C₁₁	1	12	yes	—
77	C₂²×C₄×C₉	C₂×C₉×C₁₁	1	168	yes	direct product factor
78	C₂²×C₃×C₁₁	C₂×C₃×C₄×C₉	1	112	yes	—
79	C₂²×C₃×C₁₁	C₂³×C₃×C₉	1	28	yes	—
80	C₃×C₄×C₁₁	C₂³×C₃×C₉	1	32	yes	—
81	C₂²×C₃×C₉	C₂×C₃×C₄×C₁₁	1	112	yes	—
82	C₂²×C₃×C₉	C₂³×C₃×C₁₁	1	28	yes	—
83	C₃×C₄×C₉	C₂³×C₃×C₁₁	1	32	yes	—
84	C₃²×C₁₁	C₂³×C₃²×C₄	1	1	yes	characteristic
85	C₉×C₁₁	C₂³×C₄×C₉	1	12	yes	direct product factor
86	C₂³×C₃×C₄	C₃×C₉×C₁₁	1	4	yes	—
87	C₂³×C₁₁	C₄×C₉²	1	8	yes	direct product factor
88	C₂³×C₁₁	C₂²×C₉²	1	7	yes	—
89	C₂×C₄×C₁₁	C₂²×C₉²	1	28	yes	direct product factor
90	C₉²	C₂³×C₄×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
91	C₂³×C₃²	C₃²×C₄×C₁₁	1	8	yes	—
92	C₂³×C₃²	C₂²×C₃²×C₁₁	1	7	yes	—
93	C₂×C₃²×C₄	C₂²×C₃²×C₁₁	1	28	yes	—
94	C₂³×C₉	C₄×C₉×C₁₁	1	96	yes	direct product factor
95	C₂³×C₉	C₂²×C₉×C₁₁	1	84	yes	—
96	C₂×C₄×C₉	C₂²×C₉×C₁₁	1	336	yes	direct product factor
97	C₂×C₃×C₁₁	C₂²×C₃×C₄×C₉	1	56	yes	—
98	C₂×C₃×C₁₁	C₂⁴×C₃×C₉	1	4	yes	—
99	C₂×C₃×C₉	C₂²×C₃×C₄×C₁₁	1	56	yes	—
100	C₂×C₃×C₉	C₂⁴×C₃×C₁₁	1	4	yes	—
101	C₂⁴×C₃	C₂×C₃×C₉×C₁₁	1	4	yes	—
102	C₂²×C₃×C₄	C₂×C₃×C₉×C₁₁	1	56	yes	—
103	C₂²×C₁₁	C₂×C₄×C₉²	1	28	yes	direct product factor
104	C₂²×C₁₁	C₂³×C₉²	1	7	yes	—
105	C₄×C₁₁	C₂³×C₉²	1	8	yes	direct product factor
106	C₂²×C₃²	C₂×C₃²×C₄×C₁₁	1	28	yes	—
107	C₂²×C₃²	C₂³×C₃²×C₁₁	1	7	yes	—
108	C₃²×C₄	C₂³×C₃²×C₁₁	1	8	yes	—
109	C₂²×C₉	C₂×C₄×C₉×C₁₁	1	336	yes	direct product factor
110	C₂²×C₉	C₂³×C₉×C₁₁	1	84	yes	—
111	C₄×C₉	C₂³×C₉×C₁₁	1	96	yes	direct product factor
112	C₃×C₁₁	C₂³×C₃×C₄×C₉	1	4	yes	—
113	C₂³×C₄	C₉²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
114	C₃×C₉	C₂³×C₃×C₄×C₁₁	1	4	yes	—
115	C₂³×C₃	C₃×C₄×C₉×C₁₁	1	32	yes	—
116	C₂³×C₃	C₂²×C₃×C₉×C₁₁	1	28	yes	—
117	C₂×C₃×C₄	C₂²×C₃×C₉×C₁₁	1	112	yes	—
118	C₂×C₁₁	C₂²×C₄×C₉²	1	14	yes	direct product factor
119	C₂×C₁₁	C₂⁴×C₉²	1	1	yes	characteristic
120	C₂×C₃²	C₂²×C₃²×C₄×C₁₁	1	14	yes	—
121	C₂×C₃²	C₂⁴×C₃²×C₁₁	1	1	yes	characteristic
122	C₂×C₉	C₂²×C₄×C₉×C₁₁	1	168	yes	direct product factor
123	C₂×C₉	C₂⁴×C₉×C₁₁	1	12	yes	—
124	C₂⁴	C₂×C₉²×C₁₁	1	1	yes	characteristic
125	C₂²×C₄	C₂×C₉²×C₁₁	1	14	yes	direct product factor
126	C₂²×C₃	C₂×C₃×C₄×C₉×C₁₁	1	112	yes	—
127	C₂²×C₃	C₂³×C₃×C₉×C₁₁	1	28	yes	—
128	C₃×C₄	C₂³×C₃×C₉×C₁₁	1	32	yes	—
129	C₁₁	C₂³×C₄×C₉²	1	1	yes	characteristic, direct product factor, Sylow
130	C₃²	C₂³×C₃²×C₄×C₁₁	1	1	yes	characteristic
131	C₉	C₂³×C₄×C₉×C₁₁	1	12	yes	direct product factor
132	C₂³	C₄×C₉²×C₁₁	1	8	yes	direct product factor
133	C₂³	C₂²×C₉²×C₁₁	1	7	yes	—
134	C₂×C₄	C₂²×C₉²×C₁₁	1	28	yes	direct product factor
135	C₂×C₃	C₂²×C₃×C₄×C₉×C₁₁	1	56	yes	—
136	C₂×C₃	C₂⁴×C₃×C₉×C₁₁	1	4	yes	—
137	C₂²	C₂×C₄×C₉²×C₁₁	1	28	yes	direct product factor
138	C₂²	C₂³×C₉²×C₁₁	1	7	yes	—
139	C₄	C₂³×C₉²×C₁₁	1	8	yes	direct product factor
140	C₃	C₂³×C₃×C₄×C₉×C₁₁	1	4	yes	—
141	C₂	C₂²×C₄×C₉²×C₁₁	1	14	yes	direct product factor
142	C₂	C₂⁴×C₉²×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃²	C₂⁴×C₃²×C₁₁
socle, prime radical	C₂⁴×C₃²×C₁₁	C₂×C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₉²×C₁₁	C₂	direct (N × H)
4. C₂³×C₉²×C₁₁	C₄	direct (N × H)
6. C₂×C₄×C₉²×C₁₁	C₂²	direct (N × H)
9. C₂²×C₉²×C₁₁	C₂×C₄	direct (N × H)
11. C₄×C₉²×C₁₁	C₂³	direct (N × H)
13. C₂³×C₄×C₉×C₁₁	C₉	direct (N × H)
14. C₂³×C₄×C₉²	C₁₁	direct (N × H)
18. C₂×C₉²×C₁₁	C₂²×C₄	direct (N × H)
23. C₂²×C₄×C₉×C₁₁	C₂×C₉	direct (N × H)
25. C₂²×C₄×C₉²	C₂×C₁₁	direct (N × H)
30. C₉²×C₁₁	C₂³×C₄	direct (N × H)
35. C₂³×C₉×C₁₁	C₄×C₉	direct (N × H)
37. C₂×C₄×C₉×C₁₁	C₂²×C₉	direct (N × H)
38. C₂³×C₉²	C₄×C₁₁	direct (N × H)
40. C₂×C₄×C₉²	C₂²×C₁₁	direct (N × H)
50. C₂²×C₉×C₁₁	C₂×C₄×C₉	direct (N × H)
52. C₄×C₉×C₁₁	C₂³×C₉	direct (N × H)
53. C₂³×C₄×C₁₁	C₉²	direct (N × H)
54. C₂²×C₉²	C₂×C₄×C₁₁	direct (N × H)
56. C₄×C₉²	C₂³×C₁₁	direct (N × H)
59. C₂³×C₄×C₉	C₉×C₁₁	direct (N × H)
68. C₂×C₉×C₁₁	C₂²×C₄×C₉	direct (N × H)
71. C₂²×C₄×C₁₁	C₂×C₉²	direct (N × H)
72. C₂×C₉²	C₂²×C₄×C₁₁	direct (N × H)
77. C₂²×C₄×C₉	C₂×C₉×C₁₁	direct (N × H)
85. C₉×C₁₁	C₂³×C₄×C₉	direct (N × H)
87. C₂³×C₁₁	C₄×C₉²	direct (N × H)
89. C₂×C₄×C₁₁	C₂²×C₉²	direct (N × H)
90. C₉²	C₂³×C₄×C₁₁	direct (N × H)
94. C₂³×C₉	C₄×C₉×C₁₁	direct (N × H)
96. C₂×C₄×C₉	C₂²×C₉×C₁₁	direct (N × H)
103. C₂²×C₁₁	C₂×C₄×C₉²	direct (N × H)
105. C₄×C₁₁	C₂³×C₉²	direct (N × H)
109. C₂²×C₉	C₂×C₄×C₉×C₁₁	direct (N × H)
111. C₄×C₉	C₂³×C₉×C₁₁	direct (N × H)
113. C₂³×C₄	C₉²×C₁₁	direct (N × H)
118. C₂×C₁₁	C₂²×C₄×C₉²	direct (N × H)
122. C₂×C₉	C₂²×C₄×C₉×C₁₁	direct (N × H)
125. C₂²×C₄	C₂×C₉²×C₁₁	direct (N × H)
129. C₁₁	C₂³×C₄×C₉²	direct (N × H)
131. C₉	C₂³×C₄×C₉×C₁₁	direct (N × H)
132. C₂³	C₄×C₉²×C₁₁	direct (N × H)
134. C₂×C₄	C₂²×C₉²×C₁₁	direct (N × H)
137. C₂²	C₂×C₄×C₉²×C₁₁	direct (N × H)
139. C₄	C₂³×C₉²×C₁₁	direct (N × H)
141. C₂	C₂²×C₄×C₉²×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₉²×C₁₁	2
C₂²×C₄×C₉²×C₁₁	2
C₂³×C₃×C₄×C₉×C₁₁	3
C₂³×C₄×C₉²	11

Subgroups — C23×C4×C92×C11 #72205482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₉²×C₁₁ #72205482