Subgroups — C₁₁×#23019 #14600212

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 534 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×#444	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×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1946	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×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1752	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×#444	—	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×C₁₁×#97	C₂²	1	1	yes	characteristic
41	C₂×C₁₁×#97	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	2	yes	—
103	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
104	C₁₁×#97	—	2	2	no	—
105	C₁₁×#97	—	2	2	no	—
106	C₁₁×#97	—	2	2	no	—
107	C₄×C₈×C₁₁	—	2	2	no	—
108	C₁₁×#95	—	2	1	no	—
109	#23019	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₁	#41	1	1	yes	characteristic
111	C₁₁×#41	—	2	2	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₁₁×#41	—	2	2	no	—
114	C₁₁×#41	—	2	2	no	—
115	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₁	—	2	2	no	—
117	C₂×D₄×C₁₁	—	2	2	no	—
118	C₂×D₄×C₁₁	—	2	2	no	—
119	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	2	no	—
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₁₁×Q₁₆	—	2	2	no	—
134	C₁₁×SD₁₆	—	2	4	no	—
135	C₁₁×D₈	—	2	2	no	—
136	C₁₁×M₁₆	—	2	2	no	—
137	C₁₁×M₁₆	—	2	2	no	—
138	C₁₁×M₁₆	—	2	2	no	—
139	C₁₁×M₁₆	—	4	4	no	—
140	C₁₁×M₁₆	—	4	4	no	—
141	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	1	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	2	no	—
149	C₂×C₈×C₁₁	—	2	2	no	—
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	—	2	1	no	—
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	4	4	no	—
155	C₂×C₈×C₁₁	—	4	4	no	—
156	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₁	#41	1	2	yes	—
164	C₁₁×C₄⋊C₄	—	2	2	no	—
165	C₁₁×C₄⋊C₄	—	2	2	no	—
166	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
167	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₁₁×C₂²⋊C₄	—	2	2	no	—
169	C₁₁×C₂²⋊C₄	—	2	2	no	—
170	C₁₁×C₂²⋊C₄	—	2	2	no	—
171	C₁₁×C₂²⋊C₄	—	2	2	no	—
172	C₁₁×C₂²⋊C₄	—	2	2	no	—
173	C₁₁×C₂²⋊C₄	—	4	2	no	—
174	C₄²×C₁₁	—	2	2	no	—
175	C₄²×C₁₁	—	2	1	no	—
176	C₄²×C₁₁	—	2	1	no	—
177	C₄²×C₁₁	—	2	1	no	—
178	C₄²×C₁₁	—	2	1	no	—
179	#3050	C₂×C₁₁	1	1	yes	characteristic
180	C₂×#444	C₂×C₁₁	1	1	yes	characteristic, complemented
181	#2933	C₂×C₁₁	1	2	yes	complemented
182	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
183	#1975	C₂×C₁₁	1	1	yes	characteristic, complemented
184	#1946	C₂×C₁₁	1	1	yes	characteristic, complemented
185	#1929	C₂×C₁₁	1	2	yes	complemented
186	#1871	C₂×C₁₁	1	2	yes	complemented
187	#1866	C₂×C₁₁	1	2	yes	complemented
188	#1773	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1752	C₂×C₁₁	1	1	yes	characteristic, complemented
190	C₂³×C₁₁	—	2	1	no	—
191	C₂³×C₁₁	—	2	1	no	—
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	2	2	no	—
194	C₂³×C₁₁	—	4	1	no	—
195	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
196	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
197	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
198	Q₈×C₁₁	—	2	2	no	—
199	Q₈×C₁₁	—	2	2	no	—
200	D₄×C₁₁	—	2	2	no	—
201	D₄×C₁₁	—	2	2	no	—
202	D₄×C₁₁	—	4	2	no	—
203	D₄×C₁₁	—	4	2	no	—
204	D₄×C₁₁	—	4	4	no	—
205	D₄×C₁₁	—	8	2	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	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	2	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	4	2	no	—
220	C₂×C₄×C₁₁	—	4	2	no	—
221	C₂×C₄×C₁₁	—	4	1	no	—
222	C₂×C₄×C₁₁	—	4	1	no	—
223	C₂×C₄×C₁₁	—	4	1	no	—
224	C₂×C₄×C₁₁	—	4	1	no	—
225	C₂×C₄×C₁₁	—	4	1	no	—
226	C₂×C₄×C₁₁	—	4	1	no	—
227	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
235	C₈×C₁₁	—	2	1	no	—
236	C₈×C₁₁	—	2	1	no	—
237	C₈×C₁₁	—	2	2	no	—
238	C₈×C₁₁	—	2	4	no	—
239	C₈×C₁₁	—	2	2	no	—
240	C₈×C₁₁	—	4	2	no	—
241	C₈×C₁₁	C₄×D₄	1	2	yes	—
242	C₈×C₁₁	C₄×D₄	1	2	yes	—
243	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×#131	C₂²×C₁₁	1	2	yes	—
245	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
246	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
247	#525	C₂²×C₁₁	1	2	yes	—
248	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
249	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
250	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
251	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
252	#465	C₄×C₁₁	1	2	yes	complemented
253	#465	C₄×C₁₁	1	2	yes	complemented
254	#444	—	2	4	no	—
255	#436	—	2	2	no	—
256	#435	—	2	2	no	—
257	#435	—	2	2	no	—
258	C₈×D₄	—	2	2	no	—
259	C₂×#108	—	2	4	no	—
260	C₂×#108	C₂²×C₁₁	1	2	yes	—
261	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
263	#427	C₂²×C₁₁	1	1	yes	characteristic
264	#424	C₂²×C₁₁	1	2	yes	—
265	C₂×#104	C₂²×C₁₁	1	2	yes	—
266	C₂×#104	C₂²×C₁₁	1	2	yes	—
267	#416	C₂²×C₁₁	1	2	yes	—
268	#408	C₂²×C₁₁	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
270	#405	C₂²×C₁₁	1	2	yes	—
271	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
272	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
274	#339	C₂²×C₁₁	1	2	yes	—
275	#339	C₂²×C₁₁	1	2	yes	—
276	#336	C₂²×C₁₁	1	1	yes	characteristic
277	#336	C₂²×C₁₁	1	1	yes	characteristic
278	C₂²×C₁₁	—	2	1	no	—
279	C₂²×C₁₁	—	2	1	no	—
280	C₂²×C₁₁	—	2	1	no	—
281	C₂²×C₁₁	—	2	1	no	—
282	C₂²×C₁₁	—	2	1	no	—
283	C₂²×C₁₁	—	2	1	no	—
284	C₂²×C₁₁	—	2	1	no	—
285	C₂²×C₁₁	—	4	2	no	—
286	C₂²×C₁₁	—	4	2	no	—
287	C₂²×C₁₁	—	4	2	no	—
288	C₂²×C₁₁	—	4	2	no	—
289	C₂²×C₁₁	—	4	2	no	—
290	C₂²×C₁₁	#444	1	2	yes	complemented
291	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₁₁	#548	1	1	yes	characteristic
293	C₂²×C₁₁	#553	1	1	yes	characteristic
294	C₄×C₁₁	—	2	1	no	—
295	C₄×C₁₁	—	2	1	no	—
296	C₄×C₁₁	—	4	2	no	—
297	C₄×C₁₁	—	4	2	no	—
298	C₄×C₁₁	—	4	2	no	—
299	C₄×C₁₁	—	8	1	no	—
300	C₄×C₁₁	—	8	1	no	—
301	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₁₁	#520	1	1	yes	characteristic
303	C₄×C₁₁	D₄²	1	1	yes	characteristic
304	C₄×C₁₁	#547	1	1	yes	characteristic
305	C₂×#41	C₂³×C₁₁	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
307	#135	—	2	2	no	—
308	#135	—	2	2	no	—
309	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
310	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
311	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
312	#131	—	2	4	no	—
313	#131	—	4	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	4	no	—
317	C₂×M₁₆	—	4	2	no	—
318	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
319	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
325	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
332	#123	—	2	2	no	—
333	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
334	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
335	#121	C₂×C₄×C₁₁	1	2	yes	—
336	#121	C₂×C₄×C₁₁	1	2	yes	—
337	#120	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	#117	C₂³×C₁₁	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
344	#108	—	2	4	no	—
345	#108	—	2	2	no	—
346	#108	D₄×C₁₁	1	4	yes	complemented
347	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
348	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
349	#106	C₂×C₄×C₁₁	1	2	yes	—
350	C₄⋊C₈	—	2	2	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#104	—	2	4	no	—
353	#104	—	4	2	no	—
354	#103	C₂×C₄×C₁₁	1	2	yes	—
355	#103	C₂×C₄×C₁₁	1	2	yes	—
356	#102	C₂×C₄×C₁₁	1	2	yes	—
357	#102	C₂×C₄×C₁₁	1	2	yes	—
358	C₂²⋊C₈	—	2	2	no	—
359	C₂²⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
361	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
362	#97	—	2	2	no	—
363	#97	—	2	2	no	—
364	#97	—	2	2	no	—
365	C₄×C₈	—	2	2	no	—
366	#95	—	2	1	no	—
367	C₂×C₁₁	—	2	1	no	—
368	C₂×C₁₁	—	2	1	no	—
369	C₂×C₁₁	—	2	2	no	—
370	C₂×C₁₁	—	4	1	no	—
371	C₂×C₁₁	—	8	2	no	—
372	C₂×C₁₁	#2361	1	1	yes	characteristic
373	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
374	C₂×C₁₁	#2957	1	1	yes	characteristic
375	C₂⁴	C₁₁×#41	1	1	yes	characteristic
376	#41	—	2	2	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
396	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
398	Q₁₆	—	2	2	no	—
399	SD₁₆	—	2	4	no	—
400	D₈	—	2	2	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	4	4	no	—
405	M₁₆	—	4	4	no	—
406	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	4	no	—
420	C₂×C₈	—	4	4	no	—
421	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
422	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
423	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
424	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
426	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
427	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
428	C₂×C₈	C₁₁×#41	1	2	yes	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
432	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₁₁	#23019	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
451	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
452	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	4	no	—
460	D₄	—	8	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
483	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
484	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
488	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	4	no	—
494	C₈	—	2	2	no	—
495	C₈	—	4	2	no	—
496	C₈	C₄×D₄×C₁₁	1	2	yes	—
497	C₈	C₄×D₄×C₁₁	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	C₁₁×#444	1	2	yes	complemented
511	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
512	C₂²	C₁₁×#548	1	1	yes	characteristic
513	C₂²	C₁₁×#553	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
522	C₄	C₁₁×#520	1	1	yes	characteristic
523	C₄	D₄²×C₁₁	1	1	yes	characteristic
524	C₄	C₁₁×#547	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	2	no	—
528	C₂	—	4	1	no	—
529	C₂	—	8	2	no	—
530	C₂	C₁₁×#2361	1	1	yes	characteristic
531	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
532	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×#444	C₂	semidirect
3. C₁₁×#2933	C₂	semidirect
4. C₂²×C₁₁×#108	C₂	semidirect
5. C₁₁×#1975	C₂	semidirect
6. C₁₁×#1946	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1871	C₂	semidirect
9. C₁₁×#1866	C₂	semidirect
10. C₁₁×#1773	C₂	semidirect
11. C₁₁×#1752	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
109. #23019	C₁₁	direct (N × H)
180. C₂×#444	C₂×C₁₁	semidirect
181. #2933	C₂×C₁₁	semidirect
182. C₂²×#108	C₂×C₁₁	semidirect
183. #1975	C₂×C₁₁	semidirect
184. #1946	C₂×C₁₁	semidirect
185. #1929	C₂×C₁₁	semidirect
186. #1871	C₂×C₁₁	semidirect
187. #1866	C₂×C₁₁	semidirect
188. #1773	C₂×C₁₁	semidirect
189. #1752	C₂×C₁₁	semidirect
248. #467	C₄×C₁₁	semidirect
249. #467	C₄×C₁₁	semidirect
250. #466	C₄×C₁₁	semidirect
251. #466	C₄×C₁₁	semidirect
252. #465	C₄×C₁₁	semidirect
253. #465	C₄×C₁₁	semidirect
290. C₂²×C₁₁	#444	semidirect
346. #108	D₄×C₁₁	semidirect
444. C₁₁	#23019	direct (N × H)
510. C₂²	C₁₁×#444	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×#444	2
C₁₁×#2933	2
C₂²×C₁₁×#108	2
C₁₁×#1975	2
C₁₁×#1946	2
C₁₁×#1929	2
C₁₁×#1871	2
C₁₁×#1866	2
C₁₁×#1773	2
C₁₁×#1752	2
#23019	11

Subgroups — C11×#23019 #14600212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23019 #14600212