Subgroups — C₁₁×#23181 #14600374

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3150	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2935	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1980	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1974	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#135	C₂²	1	2	yes	—
15	C₂×C₁₁×#131	C₂²	1	2	yes	—
16	C₂×C₁₁×#131	C₂²	1	2	yes	—
17	C₁₁×#532	C₂²	1	2	yes	—
18	C₁₁×#497	C₄	1	2	yes	complemented
19	C₁₁×#497	C₄	1	2	yes	complemented
20	C₁₁×#496	C₄	1	2	yes	complemented
21	C₁₁×#496	C₄	1	2	yes	complemented
22	C₁₁×#444	—	2	4	no	—
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	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₂×C₁₁×#104	C₂²	1	2	yes	—
33	C₂×C₁₁×#104	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	2	yes	—
35	C₁₁×#408	C₂²	1	2	yes	—
36	C₁₁×#408	C₂²	1	2	yes	—
37	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
38	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₁×#341	C₂²	1	2	yes	—
43	C₁₁×#336	C₂²	1	1	yes	characteristic
44	C₁₁×#336	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×#41	C₂³	1	2	yes	—
46	C₂×C₁₁×#41	C₂³	1	2	yes	—
47	C₁₁×#135	—	2	2	no	—
48	C₁₁×#135	—	2	2	no	—
49	C₁₁×#135	—	2	2	no	—
50	C₁₁×#135	—	2	2	no	—
51	C₁₁×#135	—	4	2	no	—
52	C₁₁×#135	—	4	2	no	—
53	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
63	C₁₁×#131	—	2	4	no	—
64	C₁₁×#131	—	2	4	no	—
65	C₁₁×#131	—	4	2	no	—
66	C₁₁×#131	—	4	2	no	—
67	C₂×C₁₁×M₁₆	—	2	2	no	—
68	C₂×C₁₁×M₁₆	—	2	2	no	—
69	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₁	—	2	2	no	—
72	C₂²×C₈×C₁₁	—	2	2	no	—
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
78	C₁₁×#127	C₂×C₄	1	2	yes	—
79	C₁₁×#124	C₂×C₄	1	2	yes	—
80	C₁₁×#124	C₂×C₄	1	2	yes	—
81	C₁₁×#121	—	2	2	no	—
82	C₁₁×#121	—	2	2	no	—
83	C₄×D₄×C₁₁	—	2	2	no	—
84	C₄×D₄×C₁₁	—	2	2	no	—
85	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
89	C₁₁×#108	—	2	2	no	—
90	C₁₁×#108	D₄	1	4	yes	complemented
91	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
92	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
93	C₁₁×#104	—	2	4	no	—
94	C₁₁×#104	—	2	4	no	—
95	C₁₁×#104	—	4	2	no	—
96	C₁₁×#104	—	4	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×C₂²⋊C₈	—	2	2	no	—
99	C₁₁×C₂²⋊C₈	—	2	2	no	—
100	C₁₁×C₂²⋊C₈	—	2	2	no	—
101	C₁₁×#97	—	2	2	no	—
102	C₁₁×#97	—	2	2	no	—
103	C₁₁×#97	C₂×C₄	1	2	yes	—
104	C₁₁×#97	C₂×C₄	1	2	yes	—
105	C₄×C₈×C₁₁	—	2	2	no	—
106	C₄×C₈×C₁₁	—	2	2	no	—
107	C₁₁×#95	—	2	1	no	—
108	#23181	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₁×#41	—	2	2	no	—
110	C₁₁×#41	—	2	2	no	—
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	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂×D₄×C₁₁	—	2	2	no	—
120	C₂×D₄×C₁₁	—	2	2	no	—
121	C₂×D₄×C₁₁	—	2	2	no	—
122	C₂×D₄×C₁₁	—	2	2	no	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	2	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
132	C₁₁×Q₁₆	—	2	2	no	—
133	C₁₁×Q₁₆	—	2	2	no	—
134	C₁₁×Q₁₆	—	4	2	no	—
135	C₁₁×SD₁₆	—	2	4	no	—
136	C₁₁×SD₁₆	—	2	4	no	—
137	C₁₁×SD₁₆	—	4	2	no	—
138	C₁₁×SD₁₆	—	4	2	no	—
139	C₁₁×D₈	—	2	2	no	—
140	C₁₁×D₈	—	2	2	no	—
141	C₁₁×D₈	—	4	2	no	—
142	C₁₁×M₁₆	—	2	2	no	—
143	C₁₁×M₁₆	—	2	2	no	—
144	C₁₁×M₁₆	—	2	2	no	—
145	C₁₁×M₁₆	—	4	4	no	—
146	C₁₁×M₁₆	—	4	4	no	—
147	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
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	2	yes	—
159	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₁	#41	1	2	yes	—
166	C₁₁×C₄⋊C₄	—	2	2	no	—
167	C₁₁×C₄⋊C₄	—	2	2	no	—
168	C₁₁×C₄⋊C₄	—	4	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	C₄²×C₁₁	—	2	1	no	—
174	C₄²×C₁₁	—	2	1	no	—
175	C₄²×C₁₁	—	2	1	no	—
176	C₄²×C₁₁	—	2	1	no	—
177	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
178	C₄²×C₁₁	C₂×D₄	1	2	yes	—
179	#3150	C₂×C₁₁	1	1	yes	characteristic
180	C₂×#444	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₂×#443	C₂×C₁₁	1	1	yes	characteristic, complemented
182	#2935	C₂×C₁₁	1	2	yes	complemented
183	#1980	C₂×C₁₁	1	2	yes	complemented
184	#1975	C₂×C₁₁	1	1	yes	characteristic, complemented
185	#1974	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#1876	C₂×C₁₁	1	2	yes	complemented
187	#1876	C₂×C₁₁	1	2	yes	complemented
188	#1778	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1771	C₂×C₁₁	1	1	yes	characteristic, complemented
190	C₂³×C₁₁	—	2	2	no	—
191	C₂³×C₁₁	—	2	2	no	—
192	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
193	Q₈×C₁₁	—	2	2	no	—
194	Q₈×C₁₁	—	2	2	no	—
195	Q₈×C₁₁	—	2	2	no	—
196	Q₈×C₁₁	—	2	2	no	—
197	D₄×C₁₁	—	2	2	no	—
198	D₄×C₁₁	—	2	2	no	—
199	D₄×C₁₁	—	2	2	no	—
200	D₄×C₁₁	—	2	2	no	—
201	D₄×C₁₁	—	4	4	no	—
202	D₄×C₁₁	—	4	2	no	—
203	D₄×C₁₁	—	4	2	no	—
204	D₄×C₁₁	—	4	2	no	—
205	D₄×C₁₁	—	4	2	no	—
206	D₄×C₁₁	—	8	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	4	1	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	—	4	1	no	—
213	C₂×C₄×C₁₁	—	4	1	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	2	no	—
216	C₂×C₄×C₁₁	—	4	2	no	—
217	C₂×C₄×C₁₁	—	4	2	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	1	no	—
220	C₂×C₄×C₁₁	—	4	1	no	—
221	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
229	C₈×C₁₁	—	2	2	no	—
230	C₈×C₁₁	—	2	1	no	—
231	C₈×C₁₁	—	2	2	no	—
232	C₈×C₁₁	—	2	1	no	—
233	C₈×C₁₁	—	2	4	no	—
234	C₈×C₁₁	—	4	2	no	—
235	C₈×C₁₁	C₄×D₄	1	2	yes	—
236	C₈×C₁₁	C₄×D₄	1	2	yes	—
237	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×#135	C₂²×C₁₁	1	2	yes	—
240	C₂×#131	C₂²×C₁₁	1	2	yes	—
241	C₂×#131	C₂²×C₁₁	1	2	yes	—
242	#532	C₂²×C₁₁	1	2	yes	—
243	#497	C₄×C₁₁	1	2	yes	complemented
244	#497	C₄×C₁₁	1	2	yes	complemented
245	#496	C₄×C₁₁	1	2	yes	complemented
246	#496	C₄×C₁₁	1	2	yes	complemented
247	#444	—	2	4	no	—
248	#443	—	2	4	no	—
249	#436	—	2	2	no	—
250	#435	—	2	2	no	—
251	#435	—	2	2	no	—
252	C₈×D₄	—	2	2	no	—
253	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
254	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×#104	C₂²×C₁₁	1	2	yes	—
257	C₂×#104	C₂²×C₁₁	1	2	yes	—
258	C₂×#104	C₂²×C₁₁	1	2	yes	—
259	C₂×#104	C₂²×C₁₁	1	2	yes	—
260	#408	C₂²×C₁₁	1	2	yes	—
261	#408	C₂²×C₁₁	1	2	yes	—
262	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
263	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
267	#341	C₂²×C₁₁	1	2	yes	—
268	#336	C₂²×C₁₁	1	1	yes	characteristic
269	#336	C₂²×C₁₁	1	1	yes	characteristic
270	C₂²×C₁₁	—	2	1	no	—
271	C₂²×C₁₁	—	2	1	no	—
272	C₂²×C₁₁	—	4	2	no	—
273	C₂²×C₁₁	—	4	2	no	—
274	C₂²×C₁₁	—	4	2	no	—
275	C₂²×C₁₁	—	4	2	no	—
276	C₂²×C₁₁	—	4	2	no	—
277	C₂²×C₁₁	—	4	2	no	—
278	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₁₁	#550	1	1	yes	characteristic
280	C₂²×C₁₁	#559	1	1	yes	characteristic
281	C₄×C₁₁	—	2	2	no	—
282	C₄×C₁₁	—	2	2	no	—
283	C₄×C₁₁	—	4	2	no	—
284	C₄×C₁₁	—	4	2	no	—
285	C₄×C₁₁	—	4	2	no	—
286	C₄×C₁₁	—	8	1	no	—
287	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
288	C₄×C₁₁	#518	1	1	yes	characteristic
289	C₄×C₁₁	D₄²	1	1	yes	characteristic
290	C₄×C₁₁	#550	1	1	yes	characteristic
291	C₂×#41	C₂³×C₁₁	1	2	yes	—
292	C₂×#41	C₂³×C₁₁	1	2	yes	—
293	#135	—	2	2	no	—
294	#135	—	2	2	no	—
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	#135	—	4	2	no	—
298	#135	—	4	2	no	—
299	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
302	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
303	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
304	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
305	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
306	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
308	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
309	#131	—	2	4	no	—
310	#131	—	2	4	no	—
311	#131	—	4	2	no	—
312	#131	—	4	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
316	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
323	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
324	#127	C₂×C₄×C₁₁	1	2	yes	—
325	#124	C₂×C₄×C₁₁	1	2	yes	—
326	#124	C₂×C₄×C₁₁	1	2	yes	—
327	#121	—	2	2	no	—
328	#121	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
335	#108	—	2	2	no	—
336	#108	D₄×C₁₁	1	4	yes	complemented
337	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
338	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
339	#104	—	2	4	no	—
340	#104	—	2	4	no	—
341	#104	—	4	2	no	—
342	#104	—	4	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	#97	—	2	2	no	—
348	#97	—	2	2	no	—
349	#97	C₂×C₄×C₁₁	1	2	yes	—
350	#97	C₂×C₄×C₁₁	1	2	yes	—
351	C₄×C₈	—	2	2	no	—
352	C₄×C₈	—	2	2	no	—
353	#95	—	2	1	no	—
354	C₂×C₁₁	—	2	1	no	—
355	C₂×C₁₁	—	2	1	no	—
356	C₂×C₁₁	—	8	2	no	—
357	C₂×C₁₁	—	8	2	no	—
358	C₂×C₁₁	#2366	1	1	yes	characteristic
359	C₂×C₁₁	#2955	1	1	yes	characteristic
360	C₂×C₁₁	#2956	1	1	yes	characteristic
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
370	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
382	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
384	Q₁₆	—	2	2	no	—
385	Q₁₆	—	2	2	no	—
386	Q₁₆	—	4	2	no	—
387	SD₁₆	—	2	4	no	—
388	SD₁₆	—	2	4	no	—
389	SD₁₆	—	4	2	no	—
390	SD₁₆	—	4	2	no	—
391	D₈	—	2	2	no	—
392	D₈	—	2	2	no	—
393	D₈	—	4	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	4	4	no	—
398	M₁₆	—	4	4	no	—
399	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	4	4	no	—
409	C₂×C₈	—	4	4	no	—
410	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
411	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
412	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
413	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
414	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
415	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
417	C₂×C₈	C₁₁×#41	1	2	yes	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
430	C₄²	C₂×D₄×C₁₁	1	2	yes	—
431	C₁₁	#23181	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
464	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
465	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
468	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
469	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	1	no	—
475	C₈	—	2	4	no	—
476	C₈	—	4	2	no	—
477	C₈	C₄×D₄×C₁₁	1	2	yes	—
478	C₈	C₄×D₄×C₁₁	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
488	C₂²	C₁₁×#550	1	1	yes	characteristic
489	C₂²	C₁₁×#559	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
497	C₄	C₁₁×#518	1	1	yes	characteristic
498	C₄	D₄²×C₁₁	1	1	yes	characteristic
499	C₄	C₁₁×#550	1	1	yes	characteristic
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	8	2	no	—
503	C₂	—	8	2	no	—
504	C₂	C₁₁×#2366	1	1	yes	characteristic
505	C₂	C₁₁×#2955	1	1	yes	characteristic
506	C₂	C₁₁×#2956	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×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊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. C₂×C₁₁×#443	C₂	semidirect
4. C₁₁×#2935	C₂	semidirect
5. C₁₁×#1980	C₂	semidirect
6. C₁₁×#1975	C₂	semidirect
7. C₁₁×#1974	C₂	semidirect
8. C₁₁×#1876	C₂	semidirect
9. C₁₁×#1876	C₂	semidirect
10. C₁₁×#1778	C₂	semidirect
11. C₁₁×#1771	C₂	semidirect
18. C₁₁×#497	C₄	semidirect
19. C₁₁×#497	C₄	semidirect
20. C₁₁×#496	C₄	semidirect
21. C₁₁×#496	C₄	semidirect
90. C₁₁×#108	D₄	semidirect
108. #23181	C₁₁	direct (N × H)
180. C₂×#444	C₂×C₁₁	semidirect
181. C₂×#443	C₂×C₁₁	semidirect
182. #2935	C₂×C₁₁	semidirect
183. #1980	C₂×C₁₁	semidirect
184. #1975	C₂×C₁₁	semidirect
185. #1974	C₂×C₁₁	semidirect
186. #1876	C₂×C₁₁	semidirect
187. #1876	C₂×C₁₁	semidirect
188. #1778	C₂×C₁₁	semidirect
189. #1771	C₂×C₁₁	semidirect
243. #497	C₄×C₁₁	semidirect
244. #497	C₄×C₁₁	semidirect
245. #496	C₄×C₁₁	semidirect
246. #496	C₄×C₁₁	semidirect
336. #108	D₄×C₁₁	semidirect
431. C₁₁	#23181	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×#3150	2
C₂×C₁₁×#444	2
C₂×C₁₁×#443	2
C₁₁×#2935	2
C₁₁×#1980	2
C₁₁×#1975	2
C₁₁×#1974	2
C₁₁×#1876	2
C₁₁×#1778	2
C₁₁×#1771	2
#23181	11

Subgroups — C11×#23181 #14600374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23181 #14600374