Subgroups — C₁₁×#23018 #14600211

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2933	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1871	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#525	C₂²	1	2	yes	—
17	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#465	C₄	1	2	yes	complemented
22	C₁₁×#465	C₄	1	2	yes	complemented
23	C₁₁×#443	—	2	4	no	—
24	C₁₁×#436	—	2	2	no	—
25	C₁₁×#435	—	2	2	no	—
26	C₁₁×#435	—	2	2	no	—
27	C₈×D₄×C₁₁	—	2	2	no	—
28	C₂×C₁₁×#108	—	2	4	no	—
29	C₂×C₁₁×#108	C₂²	1	2	yes	—
30	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
32	C₁₁×#427	C₂²	1	1	yes	characteristic
33	C₁₁×#424	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	2	yes	—
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₁₁×#416	C₂²	1	2	yes	—
37	C₁₁×#408	C₂²	1	2	yes	—
38	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₁×#405	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
42	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₁₁×#339	C₂²	1	2	yes	—
44	C₁₁×#339	C₂²	1	2	yes	—
45	C₁₁×#336	C₂²	1	1	yes	characteristic
46	C₁₁×#336	C₂²	1	1	yes	characteristic
47	C₂×C₁₁×#41	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×#135	—	2	2	no	—
50	C₁₁×#135	—	2	2	no	—
51	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
54	C₁₁×#131	—	2	4	no	—
55	C₁₁×#131	—	4	2	no	—
56	C₂×C₁₁×M₁₆	—	2	2	no	—
57	C₂×C₁₁×M₁₆	—	2	2	no	—
58	C₂×C₁₁×M₁₆	—	2	4	no	—
59	C₂×C₁₁×M₁₆	—	4	2	no	—
60	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₁	—	2	2	no	—
63	C₂²×C₈×C₁₁	—	2	2	no	—
64	C₂²×C₈×C₁₁	—	2	2	no	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#123	—	2	2	no	—
75	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
76	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
77	C₁₁×#121	C₂×C₄	1	2	yes	—
78	C₁₁×#121	C₂×C₄	1	2	yes	—
79	C₁₁×#120	—	2	2	no	—
80	C₄×D₄×C₁₁	—	2	2	no	—
81	C₄×D₄×C₁₁	—	2	2	no	—
82	C₁₁×#117	C₂³	1	2	yes	—
83	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×#108	—	2	4	no	—
87	C₁₁×#108	—	2	2	no	—
88	C₁₁×#108	D₄	1	4	yes	complemented
89	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#106	C₂×C₄	1	2	yes	—
92	C₁₁×C₄⋊C₈	—	2	2	no	—
93	C₁₁×C₄⋊C₈	—	2	2	no	—
94	C₁₁×#104	—	2	4	no	—
95	C₁₁×#104	—	4	2	no	—
96	C₁₁×#103	C₂×C₄	1	2	yes	—
97	C₁₁×#103	C₂×C₄	1	2	yes	—
98	C₁₁×#102	C₂×C₄	1	2	yes	—
99	C₁₁×#102	C₂×C₄	1	2	yes	—
100	C₁₁×C₂²⋊C₈	—	2	2	no	—
101	C₁₁×C₂²⋊C₈	—	2	2	no	—
102	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
103	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
104	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
105	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
106	C₁₁×#97	—	2	2	no	—
107	C₄×C₈×C₁₁	—	2	2	no	—
108	C₄×C₈×C₁₁	—	2	2	no	—
109	C₄×C₈×C₁₁	—	2	2	no	—
110	C₁₁×#95	—	2	1	no	—
111	#23018	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₁	#41	1	1	yes	characteristic
113	C₁₁×#41	—	2	2	no	—
114	C₁₁×#41	—	2	2	no	—
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₁₁	—	2	2	no	—
119	C₂×D₄×C₁₁	—	2	2	no	—
120	C₂×D₄×C₁₁	—	2	2	no	—
121	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	1	no	—
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	2	no	—
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
135	C₁₁×Q₁₆	—	2	2	no	—
136	C₁₁×SD₁₆	—	2	4	no	—
137	C₁₁×D₈	—	2	2	no	—
138	C₁₁×M₁₆	—	2	2	no	—
139	C₁₁×M₁₆	—	2	2	no	—
140	C₁₁×M₁₆	—	2	2	no	—
141	C₁₁×M₁₆	—	4	4	no	—
142	C₁₁×M₁₆	—	4	4	no	—
143	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	2	no	—
147	C₂×C₈×C₁₁	—	2	2	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	2	no	—
151	C₂×C₈×C₁₁	—	2	2	no	—
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	—	4	4	no	—
157	C₂×C₈×C₁₁	—	4	4	no	—
158	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₁	#41	1	2	yes	—
168	C₁₁×C₄⋊C₄	—	2	2	no	—
169	C₁₁×C₄⋊C₄	—	2	2	no	—
170	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
171	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
172	C₁₁×C₂²⋊C₄	—	2	4	no	—
173	C₁₁×C₂²⋊C₄	—	2	2	no	—
174	C₁₁×C₂²⋊C₄	—	2	2	no	—
175	C₁₁×C₂²⋊C₄	—	2	2	no	—
176	C₁₁×C₂²⋊C₄	—	2	2	no	—
177	C₁₁×C₂²⋊C₄	—	2	2	no	—
178	C₄²×C₁₁	—	2	2	no	—
179	C₄²×C₁₁	—	2	1	no	—
180	C₄²×C₁₁	—	2	1	no	—
181	C₄²×C₁₁	—	2	1	no	—
182	C₄²×C₁₁	—	2	1	no	—
183	#3050	C₂×C₁₁	1	1	yes	characteristic
184	C₂×#443	C₂×C₁₁	1	1	yes	characteristic, complemented
185	#2933	C₂×C₁₁	1	2	yes	complemented
186	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
187	#1974	C₂×C₁₁	1	1	yes	characteristic, complemented
188	#1945	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1929	C₂×C₁₁	1	2	yes	complemented
190	#1871	C₂×C₁₁	1	2	yes	complemented
191	#1866	C₂×C₁₁	1	2	yes	complemented
192	#1772	C₂×C₁₁	1	1	yes	characteristic, complemented
193	C₈×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
194	C₂³×C₁₁	—	2	1	no	—
195	C₂³×C₁₁	—	2	1	no	—
196	C₂³×C₁₁	—	2	2	no	—
197	C₂³×C₁₁	—	2	2	no	—
198	C₂³×C₁₁	—	4	1	no	—
199	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
201	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
202	Q₈×C₁₁	—	2	2	no	—
203	Q₈×C₁₁	—	2	2	no	—
204	D₄×C₁₁	—	2	2	no	—
205	D₄×C₁₁	—	2	2	no	—
206	D₄×C₁₁	—	4	2	no	—
207	D₄×C₁₁	—	4	2	no	—
208	D₄×C₁₁	—	4	4	no	—
209	D₄×C₁₁	—	8	2	no	—
210	C₂×C₄×C₁₁	—	2	1	no	—
211	C₂×C₄×C₁₁	—	2	1	no	—
212	C₂×C₄×C₁₁	—	2	1	no	—
213	C₂×C₄×C₁₁	—	2	1	no	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	1	no	—
216	C₂×C₄×C₁₁	—	2	1	no	—
217	C₂×C₄×C₁₁	—	2	1	no	—
218	C₂×C₄×C₁₁	—	2	1	no	—
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	2	2	no	—
221	C₂×C₄×C₁₁	—	2	2	no	—
222	C₂×C₄×C₁₁	—	2	2	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	4	1	no	—
226	C₂×C₄×C₁₁	—	4	1	no	—
227	C₂×C₄×C₁₁	—	4	1	no	—
228	C₂×C₄×C₁₁	—	4	1	no	—
229	C₂×C₄×C₁₁	—	4	2	no	—
230	C₂×C₄×C₁₁	—	4	2	no	—
231	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₁₁	—	2	1	no	—
240	C₈×C₁₁	—	2	1	no	—
241	C₈×C₁₁	—	2	1	no	—
242	C₈×C₁₁	—	2	1	no	—
243	C₈×C₁₁	—	2	4	no	—
244	C₈×C₁₁	—	2	1	no	—
245	C₈×C₁₁	—	2	1	no	—
246	C₈×C₁₁	—	4	2	no	—
247	C₈×C₁₁	C₄×D₄	1	2	yes	—
248	C₈×C₁₁	C₄×D₄	1	2	yes	—
249	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#131	C₂²×C₁₁	1	2	yes	—
251	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
252	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
253	#525	C₂²×C₁₁	1	2	yes	—
254	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
255	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
256	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
257	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
258	#465	C₄×C₁₁	1	2	yes	complemented
259	#465	C₄×C₁₁	1	2	yes	complemented
260	#443	—	2	4	no	—
261	#436	—	2	2	no	—
262	#435	—	2	2	no	—
263	#435	—	2	2	no	—
264	C₈×D₄	—	2	2	no	—
265	C₂×#108	—	2	4	no	—
266	C₂×#108	C₂²×C₁₁	1	2	yes	—
267	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
269	#427	C₂²×C₁₁	1	1	yes	characteristic
270	#424	C₂²×C₁₁	1	2	yes	—
271	C₂×#104	C₂²×C₁₁	1	2	yes	—
272	C₂×#104	C₂²×C₁₁	1	2	yes	—
273	#416	C₂²×C₁₁	1	2	yes	—
274	#408	C₂²×C₁₁	1	2	yes	—
275	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
276	#405	C₂²×C₁₁	1	2	yes	—
277	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
280	#339	C₂²×C₁₁	1	2	yes	—
281	#339	C₂²×C₁₁	1	2	yes	—
282	#336	C₂²×C₁₁	1	1	yes	characteristic
283	#336	C₂²×C₁₁	1	1	yes	characteristic
284	C₂²×C₁₁	—	2	1	no	—
285	C₂²×C₁₁	—	2	1	no	—
286	C₂²×C₁₁	—	2	1	no	—
287	C₂²×C₁₁	—	2	1	no	—
288	C₂²×C₁₁	—	2	1	no	—
289	C₂²×C₁₁	—	2	1	no	—
290	C₂²×C₁₁	—	2	1	no	—
291	C₂²×C₁₁	—	4	2	no	—
292	C₂²×C₁₁	—	4	2	no	—
293	C₂²×C₁₁	—	4	2	no	—
294	C₂²×C₁₁	—	4	2	no	—
295	C₂²×C₁₁	—	4	2	no	—
296	C₂²×C₁₁	#443	1	2	yes	complemented
297	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂²×C₁₁	#548	1	1	yes	characteristic
299	C₂²×C₁₁	#553	1	1	yes	characteristic
300	C₄×C₁₁	—	2	1	no	—
301	C₄×C₁₁	—	2	1	no	—
302	C₄×C₁₁	—	4	2	no	—
303	C₄×C₁₁	—	4	2	no	—
304	C₄×C₁₁	—	4	2	no	—
305	C₄×C₁₁	—	4	2	no	—
306	C₄×C₁₁	—	4	2	no	—
307	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₁₁	#520	1	1	yes	characteristic
309	C₄×C₁₁	D₄²	1	1	yes	characteristic
310	C₄×C₁₁	#547	1	1	yes	characteristic
311	C₂×#41	C₂³×C₁₁	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
313	#135	—	2	2	no	—
314	#135	—	2	2	no	—
315	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
316	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
317	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
318	#131	—	2	4	no	—
319	#131	—	4	2	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	—	4	2	no	—
324	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
325	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
331	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
332	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
333	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
338	#123	—	2	2	no	—
339	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
340	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
341	#121	C₂×C₄×C₁₁	1	2	yes	—
342	#121	C₂×C₄×C₁₁	1	2	yes	—
343	#120	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	#117	C₂³×C₁₁	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
350	#108	—	2	4	no	—
351	#108	—	2	2	no	—
352	#108	D₄×C₁₁	1	4	yes	complemented
353	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
354	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
355	#106	C₂×C₄×C₁₁	1	2	yes	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	#104	—	2	4	no	—
359	#104	—	4	2	no	—
360	#103	C₂×C₄×C₁₁	1	2	yes	—
361	#103	C₂×C₄×C₁₁	1	2	yes	—
362	#102	C₂×C₄×C₁₁	1	2	yes	—
363	#102	C₂×C₄×C₁₁	1	2	yes	—
364	C₂²⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
367	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
368	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
369	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
370	#97	—	2	2	no	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	2	2	no	—
374	#95	—	2	1	no	—
375	C₂×C₁₁	—	2	1	no	—
376	C₂×C₁₁	—	2	1	no	—
377	C₂×C₁₁	—	2	2	no	—
378	C₂×C₁₁	—	4	1	no	—
379	C₂×C₁₁	—	8	2	no	—
380	C₂×C₁₁	#2361	1	1	yes	characteristic
381	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
382	C₂×C₁₁	#2957	1	1	yes	characteristic
383	C₂⁴	C₁₁×#41	1	1	yes	characteristic
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
404	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
406	Q₁₆	—	2	2	no	—
407	SD₁₆	—	2	4	no	—
408	D₈	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	4	4	no	—
413	M₁₆	—	4	4	no	—
414	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	4	4	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
430	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
431	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
432	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
433	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
434	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
435	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
436	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
437	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
438	C₂×C₈	C₁₁×#41	1	2	yes	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
442	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₁₁	#23018	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
461	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
462	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	4	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
493	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
497	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
498	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	4	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	4	2	no	—
508	C₈	C₄×D₄×C₁₁	1	2	yes	—
509	C₈	C₄×D₄×C₁₁	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	C₁₁×#443	1	2	yes	complemented
523	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
524	C₂²	C₁₁×#548	1	1	yes	characteristic
525	C₂²	C₁₁×#553	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
534	C₄	C₁₁×#520	1	1	yes	characteristic
535	C₄	D₄²×C₁₁	1	1	yes	characteristic
536	C₄	C₁₁×#547	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	8	2	no	—
542	C₂	C₁₁×#2361	1	1	yes	characteristic
543	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
544	C₂	C₁₁×#2957	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	C₂×C₄×D₄
prime radical	C₁₁×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#443	C₂	semidirect
3. C₁₁×#2933	C₂	semidirect
4. C₂²×C₁₁×#108	C₂	semidirect
5. C₁₁×#1974	C₂	semidirect
6. C₁₁×#1945	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1871	C₂	semidirect
9. C₁₁×#1866	C₂	semidirect
10. C₁₁×#1772	C₂	semidirect
11. C₈×C₁₁×C₂²⋊C₄	C₂	semidirect
17. C₁₁×#467	C₄	semidirect
18. C₁₁×#467	C₄	semidirect
19. C₁₁×#466	C₄	semidirect
20. C₁₁×#466	C₄	semidirect
21. C₁₁×#465	C₄	semidirect
22. C₁₁×#465	C₄	semidirect
88. C₁₁×#108	D₄	semidirect
111. #23018	C₁₁	direct (N × H)
184. C₂×#443	C₂×C₁₁	semidirect
185. #2933	C₂×C₁₁	semidirect
186. C₂²×#108	C₂×C₁₁	semidirect
187. #1974	C₂×C₁₁	semidirect
188. #1945	C₂×C₁₁	semidirect
189. #1929	C₂×C₁₁	semidirect
190. #1871	C₂×C₁₁	semidirect
191. #1866	C₂×C₁₁	semidirect
192. #1772	C₂×C₁₁	semidirect
193. C₈×C₂²⋊C₄	C₂×C₁₁	semidirect
254. #467	C₄×C₁₁	semidirect
255. #467	C₄×C₁₁	semidirect
256. #466	C₄×C₁₁	semidirect
257. #466	C₄×C₁₁	semidirect
258. #465	C₄×C₁₁	semidirect
259. #465	C₄×C₁₁	semidirect
296. C₂²×C₁₁	#443	semidirect
352. #108	D₄×C₁₁	semidirect
454. C₁₁	#23018	direct (N × H)
522. C₂²	C₁₁×#443	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3050	2
C₂×C₁₁×#443	2
C₁₁×#2933	2
C₂²×C₁₁×#108	2
C₁₁×#1974	2
C₁₁×#1945	2
C₁₁×#1929	2
C₁₁×#1871	2
C₁₁×#1866	2
C₁₁×#1772	2
C₈×C₁₁×C₂²⋊C₄	2
#23018	11

Subgroups — C11×#23018 #14600211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23018 #14600211