Subgroups — C₁₁×#60142 #14637335

Order 2816.

2714 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3449	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2935	C₂	1	8	yes	maximal, complemented
5	C₁₁×#2933	C₂	1	8	yes	maximal, complemented
6	C₁₁×#2930	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2929	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₁₁×#568	—	2	8	no	—
15	C₂×C₁₁×#131	—	2	8	no	—
16	C₂×C₁₁×#131	C₂²	1	4	yes	—
17	C₂×C₁₁×#131	C₂²	1	4	yes	—
18	C₂×C₁₁×#131	C₂²	1	4	yes	complemented
19	C₂×C₁₁×#131	C₂²	1	4	yes	complemented
20	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	complemented
24	C₂²×C₁₁×M₁₆	C₂²	1	4	yes	complemented
25	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₁	C₂²	1	2	yes	complemented
27	C₁₁×#537	C₄	1	4	yes	—
28	C₁₁×#536	C₄	1	2	yes	—
29	C₁₁×#536	C₄	1	2	yes	—
30	C₁₁×#535	C₄	1	2	yes	—
31	C₁₁×#535	C₄	1	2	yes	—
32	C₁₁×#534	C₄	1	4	yes	—
33	C₁₁×#532	C₂²	1	4	yes	—
34	C₁₁×#525	C₂²	1	4	yes	—
35	C₁₁×#525	C₂²	1	4	yes	—
36	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
37	C₁₁×#436	C₂²	1	16	yes	complemented
38	C₁₁×#435	C₂²	1	16	yes	complemented
39	C₁₁×#435	C₂²	1	16	yes	complemented
40	C₈×D₄×C₁₁	C₂²	1	16	yes	complemented
41	C₁₁×#424	C₂²	1	2	yes	complemented
42	C₁₁×#424	C₂²	1	2	yes	complemented
43	C₁₁×#424	C₂²	1	4	yes	complemented
44	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	complemented
45	C₁₁×#408	C₂²	1	2	yes	—
46	C₁₁×#408	C₂²	1	2	yes	—
47	C₁₁×#408	C₂²	1	4	yes	—
48	C₁₁×#408	C₂²	1	4	yes	complemented
49	C₁₁×#408	C₂²	1	4	yes	complemented
50	C₁₁×#407	C₂²	1	4	yes	complemented
51	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
52	C₁₁×#405	C₂²	1	4	yes	complemented
53	C₁₁×#405	C₂²	1	4	yes	complemented
54	C₄×C₁₁×M₁₆	C₂²	1	4	yes	complemented
55	C₂×C₁₁×#41	—	2	4	no	—
56	C₂×C₁₁×#41	—	2	4	no	—
57	C₂×C₁₁×#41	—	2	4	no	—
58	C₂×C₁₁×#41	—	2	4	no	—
59	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
62	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
63	C₂×C₁₁×#41	C₂³	1	2	yes	—
64	C₂×C₁₁×#41	C₂³	1	2	yes	—
65	C₂×C₁₁×#41	C₂³	1	2	yes	—
66	C₂×C₁₁×#41	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
70	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×#131	—	2	16	no	—
77	C₁₁×#131	—	2	16	no	—
78	C₁₁×#131	—	2	16	no	—
79	C₁₁×#131	—	2	16	no	—
80	C₂×C₁₁×M₁₆	—	2	4	no	—
81	C₂×C₁₁×M₁₆	—	2	4	no	—
82	C₂×C₁₁×M₁₆	—	2	16	no	—
83	C₂×C₁₁×M₁₆	—	2	8	no	—
84	C₂×C₁₁×M₁₆	D₄	1	8	yes	complemented
85	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
86	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
87	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
88	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
89	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
90	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
91	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
92	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
93	C₂²×C₈×C₁₁	—	2	4	no	—
94	C₂²×C₈×C₁₁	—	2	8	no	—
95	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
97	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
102	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
103	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
104	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
105	C₁₁×#127	C₂×C₄	1	4	yes	—
106	C₁₁×#124	C₂×C₄	1	4	yes	—
107	C₁₁×#124	C₂×C₄	1	4	yes	—
108	C₁₁×#123	C₂×C₄	1	8	yes	—
109	C₁₁×#123	C₂×C₄	1	8	yes	—
110	C₁₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
111	C₁₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
112	C₁₁×#121	C₂×C₄	1	8	yes	—
113	C₁₁×#121	C₂×C₄	1	8	yes	—
114	C₁₁×#121	C₂×C₄	1	16	yes	—
115	C₁₁×#120	C₂×C₄	1	8	yes	—
116	C₁₁×#120	C₂×C₄	1	8	yes	—
117	C₄×D₄×C₁₁	C₂³	1	16	yes	—
118	C₁₁×#117	C₂×C₄	1	2	yes	—
119	C₁₁×#117	C₂×C₄	1	2	yes	—
120	C₁₁×#117	C₂³	1	2	yes	—
121	C₁₁×#117	C₂³	1	2	yes	—
122	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
123	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
124	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
125	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
126	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
127	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
129	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
130	C₁₁×#97	C₂³	1	8	yes	—
131	C₄×C₈×C₁₁	C₂³	1	8	yes	—
132	#60142	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
135	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₁₁×#41	—	2	8	no	—
137	C₁₁×#41	—	2	8	no	—
138	C₁₁×#41	—	2	8	no	—
139	C₁₁×#41	—	2	8	no	—
140	C₁₁×#41	—	2	4	no	—
141	C₁₁×#41	—	2	4	no	—
142	C₁₁×#41	—	2	4	no	—
143	C₁₁×#41	—	2	4	no	—
144	C₁₁×#41	—	2	4	no	—
145	C₁₁×#41	—	2	4	no	—
146	C₁₁×#41	—	2	4	no	—
147	C₁₁×#41	—	2	4	no	—
148	C₂×Q₈×C₁₁	—	2	4	no	—
149	C₂×Q₈×C₁₁	—	2	4	no	—
150	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
153	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₁	—	2	8	no	—
155	C₂×D₄×C₁₁	—	2	8	no	—
156	C₂×D₄×C₁₁	—	2	4	no	—
157	C₂×D₄×C₁₁	—	2	4	no	—
158	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
159	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
160	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
161	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
163	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
166	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
167	C₂²×C₄×C₁₁	—	2	4	no	—
168	C₂²×C₄×C₁₁	—	2	4	no	—
169	C₂²×C₄×C₁₁	—	2	4	no	—
170	C₂²×C₄×C₁₁	—	2	4	no	—
171	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₁	#41	1	4	yes	—
181	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
186	C₁₁×M₁₆	—	2	16	no	—
187	C₁₁×M₁₆	—	2	16	no	—
188	C₁₁×M₁₆	—	2	4	no	—
189	C₁₁×M₁₆	—	2	4	no	—
190	C₁₁×M₁₆	—	2	4	no	—
191	C₁₁×M₁₆	—	2	4	no	—
192	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
193	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
194	C₂×C₈×C₁₁	—	2	16	no	—
195	C₂×C₈×C₁₁	—	2	16	no	—
196	C₂×C₈×C₁₁	—	2	2	no	—
197	C₂×C₈×C₁₁	—	2	2	no	—
198	C₂×C₈×C₁₁	—	2	4	no	—
199	C₂×C₈×C₁₁	—	2	4	no	—
200	C₂×C₈×C₁₁	—	2	4	no	—
201	C₂×C₈×C₁₁	—	2	4	no	—
202	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
203	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
204	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
205	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
206	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
207	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
208	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
209	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
210	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
211	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
212	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
213	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
214	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
215	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
216	C₄²×C₁₁	C₂⁴	1	4	yes	—
217	C₂×#568	C₂×C₁₁	1	1	yes	characteristic, complemented
218	C₂²×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#3449	C₂×C₁₁	1	1	yes	characteristic
220	#2935	C₂×C₁₁	1	8	yes	complemented
221	#2933	C₂×C₁₁	1	8	yes	complemented
222	#2930	C₂×C₁₁	1	4	yes	complemented
223	#2929	C₂×C₁₁	1	4	yes	complemented
224	C₂×#424	C₂×C₁₁	1	1	yes	characteristic, complemented
225	#2879	C₂×C₁₁	1	1	yes	characteristic, complemented
226	C₂×#408	C₂×C₁₁	1	1	yes	characteristic, complemented
227	#2873	C₂×C₁₁	1	1	yes	characteristic, complemented
228	C₂³×C₁₁	—	2	4	no	—
229	C₂³×C₁₁	—	2	4	no	—
230	C₂³×C₁₁	—	4	2	no	—
231	C₂³×C₁₁	—	4	4	no	—
232	C₂³×C₁₁	—	4	4	no	—
233	C₂³×C₁₁	C₄×D₄	1	4	yes	—
234	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
235	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
236	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
237	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
238	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
239	Q₈×C₁₁	—	2	4	no	—
240	Q₈×C₁₁	—	2	4	no	—
241	Q₈×C₁₁	—	2	4	no	—
242	Q₈×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	8	no	—
244	D₄×C₁₁	—	2	8	no	—
245	D₄×C₁₁	—	2	8	no	—
246	D₄×C₁₁	—	2	8	no	—
247	D₄×C₁₁	—	2	4	no	—
248	D₄×C₁₁	—	2	4	no	—
249	D₄×C₁₁	—	2	4	no	—
250	D₄×C₁₁	—	2	4	no	—
251	D₄×C₁₁	—	4	16	no	—
252	C₂×C₄×C₁₁	—	2	4	no	—
253	C₂×C₄×C₁₁	—	2	4	no	—
254	C₂×C₄×C₁₁	—	2	8	no	—
255	C₂×C₄×C₁₁	—	2	8	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	2	4	no	—
258	C₂×C₄×C₁₁	—	2	4	no	—
259	C₂×C₄×C₁₁	—	2	4	no	—
260	C₂×C₄×C₁₁	—	4	4	no	—
261	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
262	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
263	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
264	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
265	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
266	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
276	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
277	C₈×C₁₁	—	2	2	no	—
278	C₈×C₁₁	—	2	4	no	—
279	C₈×C₁₁	—	2	2	no	—
280	C₈×C₁₁	—	2	4	no	—
281	C₈×C₁₁	C₂²×D₄	1	8	yes	—
282	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
283	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
284	#568	—	2	8	no	—
285	C₂×#131	—	2	8	no	—
286	C₂×#131	C₂²×C₁₁	1	4	yes	—
287	C₂×#131	C₂²×C₁₁	1	4	yes	—
288	C₂×#131	C₂²×C₁₁	1	4	yes	complemented
289	C₂×#131	C₂²×C₁₁	1	4	yes	complemented
290	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
293	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	complemented
294	C₂²×M₁₆	C₂²×C₁₁	1	4	yes	complemented
295	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₁₁	1	2	yes	complemented
297	#537	C₄×C₁₁	1	4	yes	—
298	#536	C₄×C₁₁	1	2	yes	—
299	#536	C₄×C₁₁	1	2	yes	—
300	#535	C₄×C₁₁	1	2	yes	—
301	#535	C₄×C₁₁	1	2	yes	—
302	#534	C₄×C₁₁	1	4	yes	—
303	#532	C₂²×C₁₁	1	4	yes	—
304	#525	C₂²×C₁₁	1	4	yes	—
305	#525	C₂²×C₁₁	1	4	yes	—
306	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
307	#436	C₂²×C₁₁	1	16	yes	complemented
308	#435	C₂²×C₁₁	1	16	yes	complemented
309	#435	C₂²×C₁₁	1	16	yes	complemented
310	C₈×D₄	C₂²×C₁₁	1	16	yes	complemented
311	#424	C₂²×C₁₁	1	2	yes	complemented
312	#424	C₂²×C₁₁	1	2	yes	complemented
313	#424	C₂²×C₁₁	1	4	yes	complemented
314	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
315	#408	C₂²×C₁₁	1	2	yes	—
316	#408	C₂²×C₁₁	1	2	yes	—
317	#408	C₂²×C₁₁	1	4	yes	—
318	#408	C₂²×C₁₁	1	4	yes	complemented
319	#408	C₂²×C₁₁	1	4	yes	complemented
320	#407	C₂²×C₁₁	1	4	yes	complemented
321	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
322	#405	C₂²×C₁₁	1	4	yes	complemented
323	#405	C₂²×C₁₁	1	4	yes	complemented
324	C₄×M₁₆	C₂²×C₁₁	1	4	yes	complemented
325	C₂²×C₁₁	—	2	2	no	—
326	C₂²×C₁₁	—	2	2	no	—
327	C₂²×C₁₁	—	2	2	no	—
328	C₂²×C₁₁	—	2	4	no	—
329	C₂²×C₁₁	—	2	4	no	—
330	C₂²×C₁₁	—	2	8	no	—
331	C₂²×C₁₁	—	2	8	no	—
332	C₂²×C₁₁	—	4	4	no	—
333	C₂²×C₁₁	—	4	8	no	—
334	C₂²×C₁₁	—	8	4	no	—
335	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
336	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
337	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
338	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
339	C₄×C₁₁	—	2	4	no	—
340	C₄×C₁₁	—	2	4	no	—
341	C₄×C₁₁	—	2	8	no	—
342	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
343	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
344	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
345	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
347	C₂×#41	—	2	4	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	2	4	no	—
351	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
352	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
353	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
354	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
355	C₂×#41	C₂³×C₁₁	1	2	yes	—
356	C₂×#41	C₂³×C₁₁	1	2	yes	—
357	C₂×#41	C₂³×C₁₁	1	2	yes	—
358	C₂×#41	C₂³×C₁₁	1	2	yes	—
359	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
360	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
361	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
362	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
363	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
364	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
368	#131	—	2	16	no	—
369	#131	—	2	16	no	—
370	#131	—	2	16	no	—
371	#131	—	2	16	no	—
372	C₂×M₁₆	—	2	4	no	—
373	C₂×M₁₆	—	2	4	no	—
374	C₂×M₁₆	—	2	16	no	—
375	C₂×M₁₆	—	2	8	no	—
376	C₂×M₁₆	D₄×C₁₁	1	8	yes	complemented
377	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
378	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
379	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
380	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
381	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
382	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
383	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
384	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
385	C₂²×C₈	—	2	4	no	—
386	C₂²×C₈	—	2	8	no	—
387	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
390	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
391	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
392	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
393	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
394	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
395	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
396	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
397	#127	C₂×C₄×C₁₁	1	4	yes	—
398	#124	C₂×C₄×C₁₁	1	4	yes	—
399	#124	C₂×C₄×C₁₁	1	4	yes	—
400	#123	C₂×C₄×C₁₁	1	8	yes	—
401	#123	C₂×C₄×C₁₁	1	8	yes	—
402	C₂²⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
403	C₂²⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
404	#121	C₂×C₄×C₁₁	1	8	yes	—
405	#121	C₂×C₄×C₁₁	1	8	yes	—
406	#121	C₂×C₄×C₁₁	1	16	yes	—
407	#120	C₂×C₄×C₁₁	1	8	yes	—
408	#120	C₂×C₄×C₁₁	1	8	yes	—
409	C₄×D₄	C₂³×C₁₁	1	16	yes	—
410	#117	C₂×C₄×C₁₁	1	2	yes	—
411	#117	C₂×C₄×C₁₁	1	2	yes	—
412	#117	C₂³×C₁₁	1	2	yes	—
413	#117	C₂³×C₁₁	1	2	yes	—
414	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
416	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
417	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
418	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
419	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
420	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
421	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
422	#97	C₂³×C₁₁	1	8	yes	—
423	C₄×C₈	C₂³×C₁₁	1	8	yes	—
424	C₂×C₁₁	—	2	2	no	—
425	C₂×C₁₁	—	2	2	no	—
426	C₂×C₁₁	—	2	2	no	—
427	C₂×C₁₁	—	4	4	no	—
428	C₂×C₁₁	—	4	4	no	—
429	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
430	C₂×C₁₁	#3573	1	2	yes	—
431	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
432	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
433	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
434	#41	—	2	8	no	—
435	#41	—	2	8	no	—
436	#41	—	2	8	no	—
437	#41	—	2	8	no	—
438	#41	—	2	4	no	—
439	#41	—	2	4	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	4	no	—
444	#41	—	2	4	no	—
445	#41	—	2	4	no	—
446	C₂×Q₈	—	2	4	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
449	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
450	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
457	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
458	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
459	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
460	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
461	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
463	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
464	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
470	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
471	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
472	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
478	C₂²×C₄	C₁₁×#41	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
484	M₁₆	—	2	4	no	—
485	M₁₆	—	2	4	no	—
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	4	no	—
488	M₁₆	—	2	16	no	—
489	M₁₆	—	2	16	no	—
490	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
491	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	4	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	16	no	—
499	C₂×C₈	—	2	16	no	—
500	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
501	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
502	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
503	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
504	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
505	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
506	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
508	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
509	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
510	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
511	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
512	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
513	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
514	C₄²	C₂⁴×C₁₁	1	4	yes	—
515	C₁₁	#60142	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	C₄×D₄×C₁₁	1	4	yes	—
522	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
523	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
524	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
525	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
526	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
527	Q₈	—	2	4	no	—
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	D₄	—	2	8	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	8	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	4	16	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
550	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
551	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
552	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
553	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
554	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
555	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
556	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
561	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
562	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
563	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
564	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	4	no	—
568	C₈	—	2	4	no	—
569	C₈	C₂²×D₄×C₁₁	1	8	yes	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	8	4	no	—
580	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
581	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
582	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
583	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
584	C₄	—	2	4	no	—
585	C₄	—	2	4	no	—
586	C₄	—	2	8	no	—
587	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
588	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
589	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
590	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
591	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	4	no	—
596	C₂	—	4	4	no	—
597	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
598	C₂	C₁₁×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁴×C₄
prime radical	C₁₁×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#568	C₂	semidirect
2. C₂²×C₁₁×#131	C₂	semidirect
4. C₁₁×#2935	C₂	semidirect
5. C₁₁×#2933	C₂	semidirect
6. C₁₁×#2930	C₂	semidirect
7. C₁₁×#2929	C₂	semidirect
8. C₂×C₁₁×#424	C₂	semidirect
9. C₁₁×#2879	C₂	semidirect
10. C₂×C₁₁×#408	C₂	semidirect
11. C₁₁×#2873	C₂	semidirect
18. C₂×C₁₁×#131	C₂²	semidirect
19. C₂×C₁₁×#131	C₂²	semidirect
23. C₂²×C₁₁×M₁₆	C₂²	semidirect
24. C₂²×C₁₁×M₁₆	C₂²	semidirect
26. C₂³×C₈×C₁₁	C₂²	semidirect
37. C₁₁×#436	C₂²	semidirect
38. C₁₁×#435	C₂²	semidirect
39. C₁₁×#435	C₂²	semidirect
40. C₈×D₄×C₁₁	C₂²	semidirect
41. C₁₁×#424	C₂²	semidirect
42. C₁₁×#424	C₂²	semidirect
43. C₁₁×#424	C₂²	semidirect
44. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
48. C₁₁×#408	C₂²	semidirect
49. C₁₁×#408	C₂²	semidirect
50. C₁₁×#407	C₂²	semidirect
51. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
52. C₁₁×#405	C₂²	semidirect
53. C₁₁×#405	C₂²	semidirect
54. C₄×C₁₁×M₁₆	C₂²	semidirect
84. C₂×C₁₁×M₁₆	D₄	semidirect
132. #60142	C₁₁	direct (N × H)
217. C₂×#568	C₂×C₁₁	semidirect
218. C₂²×#131	C₂×C₁₁	semidirect
220. #2935	C₂×C₁₁	semidirect
221. #2933	C₂×C₁₁	semidirect
222. #2930	C₂×C₁₁	semidirect
223. #2929	C₂×C₁₁	semidirect
224. C₂×#424	C₂×C₁₁	semidirect
225. #2879	C₂×C₁₁	semidirect
226. C₂×#408	C₂×C₁₁	semidirect
227. #2873	C₂×C₁₁	semidirect
288. C₂×#131	C₂²×C₁₁	semidirect
289. C₂×#131	C₂²×C₁₁	semidirect
293. C₂²×M₁₆	C₂²×C₁₁	semidirect
294. C₂²×M₁₆	C₂²×C₁₁	semidirect
296. C₂³×C₈	C₂²×C₁₁	semidirect
307. #436	C₂²×C₁₁	semidirect
308. #435	C₂²×C₁₁	semidirect
309. #435	C₂²×C₁₁	semidirect
310. C₈×D₄	C₂²×C₁₁	semidirect
311. #424	C₂²×C₁₁	semidirect
312. #424	C₂²×C₁₁	semidirect
313. #424	C₂²×C₁₁	semidirect
314. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
318. #408	C₂²×C₁₁	semidirect
319. #408	C₂²×C₁₁	semidirect
320. #407	C₂²×C₁₁	semidirect
321. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
322. #405	C₂²×C₁₁	semidirect
323. #405	C₂²×C₁₁	semidirect
324. C₄×M₁₆	C₂²×C₁₁	semidirect
376. C₂×M₁₆	D₄×C₁₁	semidirect
515. C₁₁	#60142	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×C₁₁×#568	2
C₂²×C₁₁×#131	2
C₁₁×#3449	2
C₁₁×#2935	2
C₁₁×#2933	2
C₁₁×#2930	2
C₁₁×#2929	2
C₂×C₁₁×#424	2
C₁₁×#2879	2
C₂×C₁₁×#408	2
C₁₁×#2873	2
#60142	11

Subgroups — C11×#60142 #14637335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60142 #14637335