Subgroups — C₂²×C₁₁×#365 #14610595

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×#106	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#365	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₁₁×M₁₆	—	2	1	no	—
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
8	C₂×C₁₁×M₃₂	C₄	1	6	yes	complemented
9	C₂×C₁₁×M₃₂	C₂²	1	6	yes	—
10	C₂²×C₁₁×C₁₆	C₄	1	2	yes	complemented
11	C₂×C₁₁×#108	—	2	3	no	—
12	C₂×C₁₁×#108	C₂²	1	6	yes	—
13	C₂×C₁₁×#106	—	2	3	no	—
14	C₂×C₁₁×#106	C₂²	1	6	yes	—
15	C₁₁×#365	C₂²	1	16	yes	direct product factor
16	C₂³×C₄×C₁₁	—	4	1	no	—
17	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₁₁×M₁₆	—	2	6	no	—
19	C₂×C₁₁×M₁₆	—	4	3	no	—
20	C₂²×C₈×C₁₁	—	4	1	no	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
23	C₂²×C₈×C₁₁	D₄	1	3	yes	—
24	C₂²×C₈×C₁₁	Q₈	1	3	yes	—
25	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
27	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
28	C₂×C₁₁×C₄⋊C₄	—	4	3	no	—
29	C₁₁×M₃₂	C₂×C₄	1	12	yes	complemented
30	C₁₁×M₃₂	C₂³	1	4	yes	—
31	C₂×C₁₁×C₁₆	C₂×C₄	1	12	yes	complemented
32	C₁₁×#108	—	2	6	no	—
33	C₁₁×#108	C₂³	1	4	yes	—
34	C₁₁×#106	—	2	6	no	—
35	C₁₁×#106	C₂³	1	4	yes	—
36	C₂²×#365	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁴×C₁₁	SD₁₆	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	—	4	6	no	—
39	C₂²×C₄×C₁₁	—	8	4	no	—
40	C₂²×C₄×C₁₁	C₄⋊C₄	1	3	yes	—
41	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	SD₁₆	1	3	yes	—
43	C₂²×C₄×C₁₁	SD₁₆	1	3	yes	—
44	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
46	C₁₁×M₁₆	—	2	4	no	—
47	C₁₁×M₁₆	—	4	6	no	—
48	C₂×C₈×C₁₁	—	4	6	no	—
49	C₂×C₈×C₁₁	C₄⋊C₄	1	3	yes	—
50	C₂×C₈×C₁₁	C₄⋊C₄	1	6	yes	—
51	C₂×C₈×C₁₁	C₄⋊C₄	1	3	yes	—
52	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
54	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
55	C₂×C₈×C₁₁	C₂×Q₈	1	3	yes	—
56	C₂×C₈×C₁₁	C₂×Q₈	1	3	yes	—
57	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	6	no	—
60	C₁₁×C₁₆	C₂²×C₄	1	8	yes	complemented
61	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic
62	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic
63	C₂²×#106	C₂×C₁₁	1	1	yes	characteristic
64	C₂×#365	C₂×C₁₁	1	12	yes	direct product factor
65	C₂³×C₁₁	—	2	4	no	—
66	C₂³×C₁₁	#106	1	3	yes	—
67	C₂³×C₁₁	#106	1	1	yes	characteristic
68	C₂³×C₁₁	C₂×SD₁₆	1	3	yes	—
69	C₂×C₄×C₁₁	—	4	4	no	—
70	C₂×C₄×C₁₁	—	8	12	no	—
71	C₂×C₄×C₁₁	#106	1	6	yes	—
72	C₂×C₄×C₁₁	#106	1	3	yes	—
73	C₂×C₄×C₁₁	#106	1	3	yes	—
74	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
75	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
76	C₂×C₄×C₁₁	C₂×SD₁₆	1	3	yes	—
77	C₂×C₄×C₁₁	C₂×SD₁₆	1	3	yes	—
78	C₂×C₄×C₁₁	C₂×SD₁₆	1	3	yes	—
79	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
80	C₈×C₁₁	—	4	4	no	—
81	C₈×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
82	C₈×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
83	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
84	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
85	C₂²×M₁₆	—	2	1	no	—
86	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
87	C₂²×C₄⋊C₄	—	2	1	no	—
88	C₂×M₃₂	C₄×C₁₁	1	6	yes	complemented
89	C₂×M₃₂	C₂²×C₁₁	1	6	yes	—
90	C₂²×C₁₆	C₄×C₁₁	1	2	yes	complemented
91	C₂×#108	—	2	3	no	—
92	C₂×#108	C₂²×C₁₁	1	6	yes	—
93	C₂×#106	—	2	3	no	—
94	C₂×#106	C₂²×C₁₁	1	6	yes	—
95	#365	C₂²×C₁₁	1	16	yes	direct product factor
96	C₂²×C₁₁	—	2	6	no	—
97	C₂²×C₁₁	—	2	6	no	—
98	C₂²×C₁₁	#365	1	4	yes	direct product factor
99	C₂²×C₁₁	C₂×#106	1	3	yes	—
100	C₂²×C₁₁	C₂×#106	1	3	yes	—
101	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
102	C₄×C₁₁	—	8	4	no	—
103	C₄×C₁₁	C₂×#106	1	3	yes	—
104	C₄×C₁₁	C₂×#106	1	3	yes	—
105	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
106	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
107	C₂³×C₄	—	4	1	no	—
108	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
109	C₂×M₁₆	—	2	6	no	—
110	C₂×M₁₆	—	4	3	no	—
111	C₂²×C₈	—	4	1	no	—
112	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
113	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
114	C₂²×C₈	D₄×C₁₁	1	3	yes	—
115	C₂²×C₈	Q₈×C₁₁	1	3	yes	—
116	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
117	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
118	C₂×C₄⋊C₄	—	2	6	no	—
119	C₂×C₄⋊C₄	—	4	3	no	—
120	M₃₂	C₂×C₄×C₁₁	1	12	yes	complemented
121	M₃₂	C₂³×C₁₁	1	4	yes	—
122	C₂×C₁₆	C₂×C₄×C₁₁	1	12	yes	complemented
123	#108	—	2	6	no	—
124	#108	C₂³×C₁₁	1	4	yes	—
125	#106	—	2	6	no	—
126	#106	C₂³×C₁₁	1	4	yes	—
127	C₂×C₁₁	—	2	1	no	—
128	C₂×C₁₁	—	2	3	no	—
129	C₂×C₁₁	C₂×#365	1	6	yes	direct product factor
130	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
131	C₂⁴	C₁₁×SD₁₆	1	1	yes	characteristic
132	C₂²×C₄	—	4	6	no	—
133	C₂²×C₄	—	8	4	no	—
134	C₂²×C₄	C₁₁×C₄⋊C₄	1	3	yes	—
135	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
136	C₂²×C₄	C₁₁×SD₁₆	1	3	yes	—
137	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
138	C₂²×C₄	C₁₁×SD₁₆	1	3	yes	—
139	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
140	M₁₆	—	2	4	no	—
141	M₁₆	—	4	6	no	—
142	C₂×C₈	—	4	6	no	—
143	C₂×C₈	C₁₁×C₄⋊C₄	1	3	yes	—
144	C₂×C₈	C₁₁×C₄⋊C₄	1	6	yes	—
145	C₂×C₈	C₁₁×C₄⋊C₄	1	3	yes	—
146	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
147	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
148	C₂×C₈	C₂×D₄×C₁₁	1	3	yes	—
149	C₂×C₈	C₂×Q₈×C₁₁	1	3	yes	—
150	C₂×C₈	C₂×Q₈×C₁₁	1	3	yes	—
151	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	6	no	—
154	C₁₆	C₂²×C₄×C₁₁	1	8	yes	complemented
155	C₁₁	C₂²×#365	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	—	2	4	no	—
157	C₂³	C₁₁×#106	1	3	yes	—
158	C₂³	C₁₁×#106	1	1	yes	characteristic
159	C₂³	C₂×C₁₁×SD₁₆	1	3	yes	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	8	12	no	—
162	C₂×C₄	C₁₁×#106	1	6	yes	—
163	C₂×C₄	C₁₁×#106	1	3	yes	—
164	C₂×C₄	C₁₁×#106	1	3	yes	—
165	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
166	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
167	C₂×C₄	C₂×C₁₁×SD₁₆	1	3	yes	—
168	C₂×C₄	C₂×C₁₁×SD₁₆	1	3	yes	—
169	C₂×C₄	C₂×C₁₁×SD₁₆	1	3	yes	—
170	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
171	C₈	—	4	4	no	—
172	C₈	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
173	C₈	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
174	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
175	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
176	C₂²	—	2	6	no	—
177	C₂²	—	2	6	no	—
178	C₂²	C₁₁×#365	1	4	yes	direct product factor
179	C₂²	C₂×C₁₁×#106	1	3	yes	—
180	C₂²	C₂×C₁₁×#106	1	3	yes	—
181	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
182	C₄	—	8	4	no	—
183	C₄	C₂×C₁₁×#106	1	3	yes	—
184	C₄	C₂×C₁₁×#106	1	3	yes	—
185	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
186	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
187	C₂	—	2	1	no	—
188	C₂	—	2	3	no	—
189	C₂	C₂×C₁₁×#365	1	6	yes	direct product factor
190	C₂	C₂²×C₁₁×#106	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#106
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₁×#365	C₂	direct (N × H)
8. C₂×C₁₁×M₃₂	C₄	semidirect
10. C₂²×C₁₁×C₁₆	C₄	semidirect
15. C₁₁×#365	C₂²	direct (N × H)
29. C₁₁×M₃₂	C₂×C₄	semidirect
31. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
36. C₂²×#365	C₁₁	direct (N × H)
60. C₁₁×C₁₆	C₂²×C₄	semidirect
64. C₂×#365	C₂×C₁₁	direct (N × H)
88. C₂×M₃₂	C₄×C₁₁	semidirect
90. C₂²×C₁₆	C₄×C₁₁	semidirect
95. #365	C₂²×C₁₁	direct (N × H)
98. C₂²×C₁₁	#365	direct (N × H)
120. M₃₂	C₂×C₄×C₁₁	semidirect
122. C₂×C₁₆	C₂×C₄×C₁₁	semidirect
129. C₂×C₁₁	C₂×#365	direct (N × H)
154. C₁₆	C₂²×C₄×C₁₁	semidirect
155. C₁₁	C₂²×#365	direct (N × H)
178. C₂²	C₁₁×#365	direct (N × H)
189. C₂	C₂×C₁₁×#365	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×M₃₂	2
C₂²×C₁₁×#108	2
C₂²×C₁₁×#106	2
C₂×C₁₁×#365	2
C₂²×#365	11

Subgroups — C22×C11×#365 #14610595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#365 #14610595