Subgroups — C₁₁×#22551 #14599744

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3480	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1980	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1980	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1963	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1806	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#559	C₄	1	2	yes	complemented
13	C₁₁×#559	C₄	1	1	yes	characteristic, complemented
14	C₁₁×#557	C₄	1	1	yes	characteristic, complemented
15	C₁₁×#556	C₄	1	1	yes	characteristic, complemented
16	C₁₁×#556	C₄	1	2	yes	complemented
17	C₁₁×#553	—	2	2	no	—
18	C₁₁×#553	—	2	1	no	—
19	C₁₁×#550	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#548	—	2	1	no	—
21	C₁₁×#532	C₂²	1	1	yes	characteristic
22	C₁₁×#532	C₂²	1	2	yes	—
23	C₁₁×#529	—	2	1	no	—
24	C₁₁×#529	—	2	2	no	—
25	C₄×C₁₁×#41	—	2	1	no	—
26	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
27	C₄×C₁₁×#41	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#446	—	2	1	no	—
30	C₁₁×#446	—	2	2	no	—
31	C₈×Q₈×C₁₁	—	2	1	no	—
32	C₁₁×#423	C₂²	1	1	yes	characteristic
33	C₁₁×#423	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	2	yes	—
35	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×#104	C₂²	1	2	yes	—
38	C₂×C₁₁×#104	C₂²	1	2	yes	—
39	C₂×C₁₁×#104	C₂²	1	2	yes	—
40	C₂×C₁₁×#104	C₂²	1	2	yes	—
41	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
43	C₁₁×#391	—	2	1	no	—
44	C₁₁×#389	—	2	1	no	—
45	C₁₁×#387	—	2	2	no	—
46	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
48	C₁₁×#376	C₂²	1	2	yes	—
49	C₄³×C₁₁	C₂²	1	1	yes	characteristic
50	C₁₁×#339	C₂²	1	1	yes	characteristic
51	C₁₁×#339	C₂²	1	1	yes	characteristic
52	C₁₁×#339	C₂²	1	2	yes	—
53	C₂×C₁₁×#41	—	2	1	no	—
54	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
55	C₂×C₁₁×#41	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
57	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
60	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
62	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
63	C₁₁×#127	C₂×C₄	1	2	yes	—
64	C₁₁×#126	—	2	2	no	—
65	C₁₁×#126	—	2	2	no	—
66	C₁₁×#126	—	2	2	no	—
67	C₁₁×#125	—	2	2	no	—
68	C₁₁×#125	—	2	1	no	—
69	C₁₁×#124	—	2	1	no	—
70	C₁₁×#124	—	2	2	no	—
71	C₁₁×#124	C₂×C₄	1	2	yes	—
72	C₁₁×#124	C₂×C₄	1	2	yes	—
73	C₁₁×#124	C₂×C₄	1	2	yes	—
74	C₁₁×#123	—	2	2	no	—
75	C₁₁×#123	—	2	2	no	—
76	C₁₁×#123	—	2	2	no	—
77	C₁₁×C₂²⋊Q₈	—	2	1	no	—
78	C₁₁×C₂²⋊Q₈	—	2	2	no	—
79	C₁₁×#121	—	2	1	no	—
80	C₁₁×#121	—	2	2	no	—
81	C₁₁×#121	—	2	1	no	—
82	C₁₁×#121	—	2	2	no	—
83	C₁₁×#121	—	2	2	no	—
84	C₁₁×#121	—	2	1	no	—
85	C₄×Q₈×C₁₁	—	2	1	no	—
86	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
88	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
90	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₁	D₄	1	2	yes	—
96	C₄×D₄×C₁₁	—	2	1	no	—
97	C₄×D₄×C₁₁	—	2	2	no	—
98	C₄×D₄×C₁₁	—	2	1	no	—
99	C₄×D₄×C₁₁	—	2	2	no	—
100	C₄×D₄×C₁₁	—	2	2	no	—
101	C₄×D₄×C₁₁	—	2	1	no	—
102	C₄×D₄×C₁₁	—	2	1	no	—
103	C₄×D₄×C₁₁	—	2	2	no	—
104	C₄×D₄×C₁₁	—	2	2	no	—
105	C₄×D₄×C₁₁	—	2	1	no	—
106	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
107	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
108	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
110	C₁₁×#117	—	2	2	no	—
111	C₁₁×#117	—	2	1	no	—
112	C₁₁×#117	—	2	2	no	—
113	C₁₁×#117	—	2	1	no	—
114	C₁₁×#117	C₂³	1	1	yes	characteristic
115	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
118	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₁	—	2	1	no	—
120	C₂×C₄²×C₁₁	—	2	2	no	—
121	C₂×C₄²×C₁₁	—	2	1	no	—
122	C₂×C₄²×C₁₁	—	2	1	no	—
123	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
128	C₁₁×C₄⋊C₈	—	2	1	no	—
129	C₁₁×C₄⋊C₈	—	2	2	no	—
130	C₁₁×C₄⋊C₈	—	2	2	no	—
131	C₁₁×C₄⋊C₈	—	2	1	no	—
132	C₁₁×#104	—	2	2	no	—
133	C₁₁×#104	—	2	4	no	—
134	C₁₁×#104	—	2	4	no	—
135	C₁₁×#104	—	2	2	no	—
136	C₁₁×#104	—	4	2	no	—
137	C₁₁×#104	—	4	2	no	—
138	C₁₁×#104	—	4	2	no	—
139	C₁₁×#97	—	2	2	no	—
140	C₁₁×#97	—	2	1	no	—
141	C₄×C₈×C₁₁	—	2	1	no	—
142	C₄×C₈×C₁₁	—	2	2	no	—
143	C₁₁×#95	—	2	2	no	—
144	C₁₁×#95	—	2	2	no	—
145	C₁₁×#95	—	2	1	no	—
146	C₁₁×#95	—	2	2	no	—
147	#22551	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₁₁×#41	—	2	1	no	—
149	C₁₁×#41	—	2	2	no	—
150	C₁₁×#41	—	2	2	no	—
151	C₁₁×#41	—	2	1	no	—
152	C₁₁×#41	—	2	2	no	—
153	C₁₁×#41	—	2	1	no	—
154	C₁₁×#41	—	2	1	no	—
155	C₁₁×#41	—	2	2	no	—
156	C₁₁×#41	—	4	4	no	—
157	C₂×Q₈×C₁₁	—	4	2	no	—
158	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₁	C₂²⋊C₄	1	2	yes	—
161	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
163	C₂×D₄×C₁₁	—	2	1	no	—
164	C₂×D₄×C₁₁	—	2	2	no	—
165	C₂×D₄×C₁₁	—	2	2	no	—
166	C₂×D₄×C₁₁	—	2	1	no	—
167	C₂×D₄×C₁₁	—	2	2	no	—
168	C₂×D₄×C₁₁	—	2	1	no	—
169	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
170	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₁₁	—	2	1	no	—
172	C₂²×C₄×C₁₁	—	2	1	no	—
173	C₂²×C₄×C₁₁	—	2	2	no	—
174	C₂²×C₄×C₁₁	—	2	1	no	—
175	C₂²×C₄×C₁₁	—	2	1	no	—
176	C₂²×C₄×C₁₁	—	2	2	no	—
177	C₂²×C₄×C₁₁	—	2	1	no	—
178	C₂²×C₄×C₁₁	—	2	2	no	—
179	C₂²×C₄×C₁₁	—	2	2	no	—
180	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
185	C₁₁×M₁₆	—	2	2	no	—
186	C₁₁×M₁₆	—	2	1	no	—
187	C₁₁×M₁₆	—	2	2	no	—
188	C₁₁×M₁₆	—	2	1	no	—
189	C₁₁×M₁₆	—	2	1	no	—
190	C₁₁×M₁₆	#41	1	2	yes	complemented
191	C₂×C₈×C₁₁	—	2	1	no	—
192	C₂×C₈×C₁₁	—	2	1	no	—
193	C₂×C₈×C₁₁	—	2	2	no	—
194	C₁₁×C₄⋊C₄	—	2	2	no	—
195	C₁₁×C₄⋊C₄	—	2	1	no	—
196	C₁₁×C₄⋊C₄	—	2	1	no	—
197	C₁₁×C₄⋊C₄	—	2	2	no	—
198	C₁₁×C₄⋊C₄	—	2	2	no	—
199	C₁₁×C₄⋊C₄	—	2	1	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	1	no	—
202	C₁₁×C₄⋊C₄	—	4	2	no	—
203	C₁₁×C₄⋊C₄	—	4	4	no	—
204	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
205	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
206	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
207	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
208	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
209	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
212	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
213	C₁₁×C₂²⋊C₄	—	2	1	no	—
214	C₁₁×C₂²⋊C₄	—	2	2	no	—
215	C₁₁×C₂²⋊C₄	—	2	2	no	—
216	C₁₁×C₂²⋊C₄	—	2	2	no	—
217	C₁₁×C₂²⋊C₄	—	2	2	no	—
218	C₁₁×C₂²⋊C₄	—	2	1	no	—
219	C₁₁×C₂²⋊C₄	—	2	1	no	—
220	C₁₁×C₂²⋊C₄	—	2	2	no	—
221	C₁₁×C₂²⋊C₄	—	2	2	no	—
222	C₁₁×C₂²⋊C₄	—	2	2	no	—
223	C₁₁×C₂²⋊C₄	—	2	2	no	—
224	C₄²×C₁₁	—	2	1	no	—
225	C₄²×C₁₁	—	2	2	no	—
226	C₄²×C₁₁	—	2	2	no	—
227	C₄²×C₁₁	—	2	1	no	—
228	C₄²×C₁₁	—	2	1	no	—
229	C₄²×C₁₁	—	2	1	no	—
230	C₄²×C₁₁	—	2	1	no	—
231	C₄²×C₁₁	—	2	2	no	—
232	C₄²×C₁₁	—	2	1	no	—
233	C₄²×C₁₁	—	2	2	no	—
234	C₄²×C₁₁	—	4	2	no	—
235	C₄²×C₁₁	—	4	2	no	—
236	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
238	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
239	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₁₁	C₂×D₄	1	2	yes	—
242	C₄²×C₁₁	C₂×D₄	1	2	yes	—
243	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
244	C₄²×C₁₁	#41	1	2	yes	complemented
245	#3480	C₂×C₁₁	1	1	yes	characteristic
246	Q₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
247	#2295	C₂×C₁₁	1	1	yes	characteristic, complemented
248	#1980	C₂×C₁₁	1	1	yes	characteristic, complemented
249	#1980	C₂×C₁₁	1	2	yes	complemented
250	#1963	C₂×C₁₁	1	2	yes	complemented
251	#1962	C₂×C₁₁	1	1	yes	characteristic, complemented
252	#1806	C₂×C₁₁	1	1	yes	characteristic, complemented
253	#1806	C₂×C₁₁	1	2	yes	complemented
254	#1759	C₂×C₁₁	1	2	yes	complemented
255	C₄×#104	C₂×C₁₁	1	1	yes	characteristic, complemented
256	C₂³×C₁₁	—	2	2	no	—
257	C₂³×C₁₁	—	2	1	no	—
258	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₁₁	—	2	2	no	—
260	Q₈×C₁₁	—	2	2	no	—
261	Q₈×C₁₁	—	2	1	no	—
262	Q₈×C₁₁	—	2	2	no	—
263	Q₈×C₁₁	—	2	1	no	—
264	Q₈×C₁₁	—	2	2	no	—
265	Q₈×C₁₁	—	4	2	no	—
266	D₄×C₁₁	—	2	1	no	—
267	D₄×C₁₁	—	2	2	no	—
268	D₄×C₁₁	—	2	1	no	—
269	D₄×C₁₁	—	2	2	no	—
270	D₄×C₁₁	—	4	4	no	—
271	D₄×C₁₁	—	4	1	no	—
272	D₄×C₁₁	—	4	2	no	—
273	D₄×C₁₁	—	4	1	no	—
274	D₄×C₁₁	—	4	2	no	—
275	D₄×C₁₁	—	4	2	no	—
276	D₄×C₁₁	—	8	1	no	—
277	D₄×C₁₁	—	8	2	no	—
278	C₂×C₄×C₁₁	—	2	2	no	—
279	C₂×C₄×C₁₁	—	2	2	no	—
280	C₂×C₄×C₁₁	—	2	1	no	—
281	C₂×C₄×C₁₁	—	2	1	no	—
282	C₂×C₄×C₁₁	—	2	2	no	—
283	C₂×C₄×C₁₁	—	2	1	no	—
284	C₂×C₄×C₁₁	—	2	2	no	—
285	C₂×C₄×C₁₁	—	4	1	no	—
286	C₂×C₄×C₁₁	—	4	2	no	—
287	C₂×C₄×C₁₁	—	4	2	no	—
288	C₂×C₄×C₁₁	—	4	4	no	—
289	C₂×C₄×C₁₁	—	4	1	no	—
290	C₂×C₄×C₁₁	—	4	1	no	—
291	C₂×C₄×C₁₁	—	4	1	no	—
292	C₂×C₄×C₁₁	—	4	1	no	—
293	C₂×C₄×C₁₁	—	4	1	no	—
294	C₂×C₄×C₁₁	—	4	2	no	—
295	C₂×C₄×C₁₁	—	4	1	no	—
296	C₂×C₄×C₁₁	—	4	2	no	—
297	C₂×C₄×C₁₁	—	4	2	no	—
298	C₂×C₄×C₁₁	—	4	2	no	—
299	C₂×C₄×C₁₁	—	4	2	no	—
300	C₂×C₄×C₁₁	—	4	2	no	—
301	C₂×C₄×C₁₁	—	8	1	no	—
302	C₂×C₄×C₁₁	—	8	2	no	—
303	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
312	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
317	C₈×C₁₁	—	2	2	no	—
318	C₈×C₁₁	—	4	1	no	—
319	C₈×C₁₁	—	4	2	no	—
320	#559	C₄×C₁₁	1	2	yes	complemented
321	#559	C₄×C₁₁	1	1	yes	characteristic, complemented
322	#557	C₄×C₁₁	1	1	yes	characteristic, complemented
323	#556	C₄×C₁₁	1	1	yes	characteristic, complemented
324	#556	C₄×C₁₁	1	2	yes	complemented
325	#553	—	2	2	no	—
326	#553	—	2	1	no	—
327	#550	C₄×C₁₁	1	1	yes	characteristic, complemented
328	#548	—	2	1	no	—
329	#532	C₂²×C₁₁	1	1	yes	characteristic
330	#532	C₂²×C₁₁	1	2	yes	—
331	#529	—	2	1	no	—
332	#529	—	2	2	no	—
333	C₄×#41	—	2	1	no	—
334	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
335	C₄×#41	C₂²×C₁₁	1	2	yes	—
336	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
337	#446	—	2	1	no	—
338	#446	—	2	2	no	—
339	C₈×Q₈	—	2	1	no	—
340	#423	C₂²×C₁₁	1	1	yes	characteristic
341	#423	C₂²×C₁₁	1	2	yes	—
342	C₂×#104	C₂²×C₁₁	1	2	yes	—
343	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
344	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
345	C₂×#104	C₂²×C₁₁	1	2	yes	—
346	C₂×#104	C₂²×C₁₁	1	2	yes	—
347	C₂×#104	C₂²×C₁₁	1	2	yes	—
348	C₂×#104	C₂²×C₁₁	1	2	yes	—
349	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
350	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
351	#391	—	2	1	no	—
352	#389	—	2	1	no	—
353	#387	—	2	2	no	—
354	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
356	#376	C₂²×C₁₁	1	2	yes	—
357	C₄³	C₂²×C₁₁	1	1	yes	characteristic
358	#339	C₂²×C₁₁	1	1	yes	characteristic
359	#339	C₂²×C₁₁	1	2	yes	—
360	#339	C₂²×C₁₁	1	1	yes	characteristic
361	C₂²×C₁₁	—	2	1	no	—
362	C₂²×C₁₁	—	2	1	no	—
363	C₂²×C₁₁	—	4	2	no	—
364	C₂²×C₁₁	—	4	1	no	—
365	C₂²×C₁₁	—	4	2	no	—
366	C₂²×C₁₁	—	4	1	no	—
367	C₂²×C₁₁	—	4	2	no	—
368	C₂²×C₁₁	—	4	1	no	—
369	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×C₁₁	#548	1	1	yes	characteristic
371	C₂²×C₁₁	#550	1	1	yes	characteristic
372	C₄×C₁₁	—	2	1	no	—
373	C₄×C₁₁	—	2	2	no	—
374	C₄×C₁₁	—	2	2	no	—
375	C₄×C₁₁	—	2	1	no	—
376	C₄×C₁₁	—	2	2	no	—
377	C₄×C₁₁	—	2	1	no	—
378	C₄×C₁₁	—	2	2	no	—
379	C₄×C₁₁	—	4	2	no	—
380	C₄×C₁₁	—	4	2	no	—
381	C₄×C₁₁	—	4	2	no	—
382	C₄×C₁₁	—	4	1	no	—
383	C₄×C₁₁	—	4	1	no	—
384	C₄×C₁₁	—	4	1	no	—
385	C₄×C₁₁	—	8	2	no	—
386	C₄×C₁₁	#421	1	2	yes	—
387	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
388	C₄×C₁₁	#520	1	1	yes	characteristic
389	C₄×C₁₁	#548	1	1	yes	characteristic
390	C₄×C₁₁	#550	1	1	yes	characteristic
391	C₂×#41	—	2	1	no	—
392	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
393	C₂×#41	C₂³×C₁₁	1	2	yes	—
394	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
395	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
396	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
397	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
398	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
399	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
400	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
401	#127	C₂×C₄×C₁₁	1	2	yes	—
402	#126	—	2	2	no	—
403	#126	—	2	2	no	—
404	#126	—	2	2	no	—
405	#125	—	2	2	no	—
406	#125	—	2	1	no	—
407	#124	—	2	1	no	—
408	#124	—	2	2	no	—
409	#124	C₂×C₄×C₁₁	1	2	yes	—
410	#124	C₂×C₄×C₁₁	1	2	yes	—
411	#124	C₂×C₄×C₁₁	1	2	yes	—
412	#123	—	2	2	no	—
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	C₂²⋊Q₈	—	2	1	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	2	no	—
419	#121	—	2	1	no	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
425	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
426	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
427	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
428	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
429	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
430	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
431	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
432	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
433	C₄×Q₈	D₄×C₁₁	1	2	yes	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
445	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
446	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
447	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
448	#117	—	2	2	no	—
449	#117	—	2	1	no	—
450	#117	—	2	2	no	—
451	#117	—	2	1	no	—
452	#117	C₂³×C₁₁	1	1	yes	characteristic
453	C₂×C₄⋊C₄	—	2	2	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
456	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	2	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	2	no	—
468	C₄⋊C₈	—	2	2	no	—
469	C₄⋊C₈	—	2	1	no	—
470	#104	—	2	2	no	—
471	#104	—	2	4	no	—
472	#104	—	2	4	no	—
473	#104	—	2	2	no	—
474	#104	—	4	2	no	—
475	#104	—	4	2	no	—
476	#104	—	4	2	no	—
477	#97	—	2	2	no	—
478	#97	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	C₄×C₈	—	2	2	no	—
481	#95	—	2	2	no	—
482	#95	—	2	2	no	—
483	#95	—	2	1	no	—
484	#95	—	2	2	no	—
485	C₂×C₁₁	—	2	1	no	—
486	C₂×C₁₁	—	2	1	no	—
487	C₂×C₁₁	—	8	2	no	—
488	C₂×C₁₁	—	8	1	no	—
489	C₂×C₁₁	#2341	1	1	yes	characteristic
490	C₂×C₁₁	C₂×#421	1	1	yes	characteristic
491	C₂×C₁₁	#2901	1	1	yes	characteristic
492	#41	—	2	1	no	—
493	#41	—	2	2	no	—
494	#41	—	2	2	no	—
495	#41	—	2	1	no	—
496	#41	—	2	2	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	2	no	—
500	#41	—	4	4	no	—
501	C₂×Q₈	—	4	2	no	—
502	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
504	C₂×Q₈	C₁₁×C₂²⋊C₄	1	2	yes	—
505	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
506	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
514	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	C₁₁×#41	1	2	yes	complemented
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
549	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
550	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
551	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
552	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
553	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
554	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	4	2	no	—
579	C₄²	—	4	2	no	—
580	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
581	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
582	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
583	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
584	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
585	C₄²	C₂×D₄×C₁₁	1	2	yes	—
586	C₄²	C₂×D₄×C₁₁	1	2	yes	—
587	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
588	C₄²	C₁₁×#41	1	2	yes	complemented
589	C₁₁	#22551	1	1	yes	characteristic, direct product factor, Sylow
590	C₂³	—	2	2	no	—
591	C₂³	—	2	1	no	—
592	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	1	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	4	2	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	1	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	8	1	no	—
611	D₄	—	8	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	8	1	no	—
636	C₂×C₄	—	8	2	no	—
637	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
638	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
639	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
640	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
641	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
642	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
643	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
644	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
647	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
648	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
649	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
650	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
651	C₈	—	2	2	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
663	C₂²	C₁₁×#548	1	1	yes	characteristic
664	C₂²	C₁₁×#550	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	8	2	no	—
679	C₄	C₁₁×#421	1	2	yes	—
680	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
681	C₄	C₁₁×#520	1	1	yes	characteristic
682	C₄	C₁₁×#548	1	1	yes	characteristic
683	C₄	C₁₁×#550	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	1	no	—
688	C₂	C₁₁×#2341	1	1	yes	characteristic
689	C₂	C₂×C₁₁×#421	1	1	yes	characteristic
690	C₂	C₁₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
prime radical	C₁₁×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₁×M₁₆	C₂	semidirect
3. C₁₁×#2295	C₂	semidirect
4. C₁₁×#1980	C₂	semidirect
5. C₁₁×#1980	C₂	semidirect
6. C₁₁×#1963	C₂	semidirect
7. C₁₁×#1962	C₂	semidirect
8. C₁₁×#1806	C₂	semidirect
9. C₁₁×#1806	C₂	semidirect
10. C₁₁×#1759	C₂	semidirect
11. C₄×C₁₁×#104	C₂	semidirect
12. C₁₁×#559	C₄	semidirect
13. C₁₁×#559	C₄	semidirect
14. C₁₁×#557	C₄	semidirect
15. C₁₁×#556	C₄	semidirect
16. C₁₁×#556	C₄	semidirect
19. C₁₁×#550	C₄	semidirect
147. #22551	C₁₁	direct (N × H)
190. C₁₁×M₁₆	#41	semidirect
244. C₄²×C₁₁	#41	semidirect
246. Q₈×M₁₆	C₂×C₁₁	semidirect
247. #2295	C₂×C₁₁	semidirect
248. #1980	C₂×C₁₁	semidirect
249. #1980	C₂×C₁₁	semidirect
250. #1963	C₂×C₁₁	semidirect
251. #1962	C₂×C₁₁	semidirect
252. #1806	C₂×C₁₁	semidirect
253. #1806	C₂×C₁₁	semidirect
254. #1759	C₂×C₁₁	semidirect
255. C₄×#104	C₂×C₁₁	semidirect
320. #559	C₄×C₁₁	semidirect
321. #559	C₄×C₁₁	semidirect
322. #557	C₄×C₁₁	semidirect
323. #556	C₄×C₁₁	semidirect
324. #556	C₄×C₁₁	semidirect
327. #550	C₄×C₁₁	semidirect
534. M₁₆	C₁₁×#41	semidirect
588. C₄²	C₁₁×#41	semidirect
589. C₁₁	#22551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3480	2
Q₈×C₁₁×M₁₆	2
C₁₁×#2295	2
C₁₁×#1980	2
C₁₁×#1963	2
C₁₁×#1962	2
C₁₁×#1806	2
C₁₁×#1759	2
C₄×C₁₁×#104	2
#22551	11

Subgroups — C11×#22551 #14599744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22551 #14599744