Subgroups — C₁₁×#23020 #14600213

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3054	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	C₂×C₁₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1975	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×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1753	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	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₁₁×#525	C₂²	1	2	yes	—
17	C₁₁×#470	C₄	1	2	yes	complemented
18	C₁₁×#469	C₄	1	2	yes	complemented
19	C₁₁×#468	C₄	1	2	yes	complemented
20	C₁₁×#468	C₄	1	2	yes	complemented
21	C₁₁×#443	—	2	4	no	—
22	C₁₁×#436	—	2	2	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₁₁×#435	—	2	2	no	—
25	C₈×D₄×C₁₁	—	2	2	no	—
26	C₁₁×#430	—	2	4	no	—
27	C₂×C₁₁×#108	C₂²	1	2	yes	—
28	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
30	C₁₁×#427	C₂²	1	1	yes	characteristic
31	C₁₁×#424	C₂²	1	2	yes	—
32	C₂×C₁₁×#104	C₂²	1	2	yes	—
33	C₂×C₁₁×#104	C₂²	1	2	yes	—
34	C₁₁×#416	C₂²	1	2	yes	—
35	C₁₁×#408	C₂²	1	2	yes	—
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₁×#405	C₂²	1	2	yes	—
38	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₁×#339	C₂²	1	2	yes	—
42	C₁₁×#339	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	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#135	—	2	2	no	—
48	C₁₁×#135	—	2	2	no	—
49	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
52	C₁₁×#131	—	2	4	no	—
53	C₁₁×#131	—	4	2	no	—
54	C₂×C₁₁×M₁₆	—	2	2	no	—
55	C₂×C₁₁×M₁₆	—	2	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	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₁	—	2	2	no	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×#123	—	2	2	no	—
71	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
73	C₁₁×#121	C₂×C₄	1	2	yes	—
74	C₁₁×#121	C₂×C₄	1	2	yes	—
75	C₁₁×#120	—	2	2	no	—
76	C₄×D₄×C₁₁	—	2	2	no	—
77	C₄×D₄×C₁₁	—	2	2	no	—
78	C₁₁×#117	C₂³	1	2	yes	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₁₁×#108	—	2	4	no	—
83	C₁₁×#108	—	2	2	no	—
84	C₁₁×#108	D₄	1	4	yes	complemented
85	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
86	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#106	C₂×C₄	1	2	yes	—
88	C₁₁×C₄⋊C₈	—	2	2	no	—
89	C₁₁×C₄⋊C₈	—	2	2	no	—
90	C₁₁×#104	—	2	4	no	—
91	C₁₁×#104	—	4	2	no	—
92	C₁₁×#103	C₂×C₄	1	2	yes	—
93	C₁₁×#103	C₂×C₄	1	2	yes	—
94	C₁₁×#102	C₂×C₄	1	2	yes	—
95	C₁₁×#102	C₂×C₄	1	2	yes	—
96	C₁₁×C₂²⋊C₈	—	2	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
99	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
100	C₁₁×#97	—	2	2	no	—
101	C₁₁×#97	—	2	2	no	—
102	C₄×C₈×C₁₁	—	2	2	no	—
103	C₄×C₈×C₁₁	—	2	2	no	—
104	C₁₁×#95	—	2	1	no	—
105	#23020	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₁	#41	1	1	yes	characteristic
107	C₁₁×#41	—	2	2	no	—
108	C₁₁×#41	—	2	2	no	—
109	C₁₁×#41	—	2	2	no	—
110	C₁₁×#41	—	2	2	no	—
111	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	2	2	no	—
115	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	2	no	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
127	C₁₁×Q₁₆	—	2	2	no	—
128	C₁₁×SD₁₆	—	2	4	no	—
129	C₁₁×D₈	—	2	2	no	—
130	C₁₁×M₁₆	—	2	4	no	—
131	C₁₁×M₁₆	—	2	4	no	—
132	C₁₁×M₁₆	—	2	2	no	—
133	C₁₁×M₁₆	—	2	2	no	—
134	C₁₁×M₁₆	—	2	2	no	—
135	C₁₁×M₁₆	—	4	4	no	—
136	C₁₁×M₁₆	—	4	4	no	—
137	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	1	no	—
146	C₂×C₈×C₁₁	—	4	4	no	—
147	C₂×C₈×C₁₁	—	4	4	no	—
148	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₁	#41	1	2	yes	—
156	C₁₁×C₄⋊C₄	—	2	2	no	—
157	C₁₁×C₄⋊C₄	—	2	2	no	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
160	C₁₁×C₂²⋊C₄	—	2	2	no	—
161	C₁₁×C₂²⋊C₄	—	2	2	no	—
162	C₁₁×C₂²⋊C₄	—	2	2	no	—
163	C₁₁×C₂²⋊C₄	—	2	2	no	—
164	C₁₁×C₂²⋊C₄	—	2	2	no	—
165	C₁₁×C₂²⋊C₄	—	4	2	no	—
166	C₄²×C₁₁	—	2	2	no	—
167	C₄²×C₁₁	—	2	1	no	—
168	C₄²×C₁₁	—	2	1	no	—
169	C₄²×C₁₁	—	2	1	no	—
170	C₄²×C₁₁	—	2	1	no	—
171	#3054	C₂×C₁₁	1	1	yes	characteristic
172	C₂×#443	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#2933	C₂×C₁₁	1	2	yes	complemented
174	C₂×#430	C₂×C₁₁	1	1	yes	characteristic, complemented
175	#1975	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#1945	C₂×C₁₁	1	1	yes	characteristic, complemented
177	#1929	C₂×C₁₁	1	2	yes	complemented
178	#1871	C₂×C₁₁	1	2	yes	complemented
179	#1866	C₂×C₁₁	1	2	yes	complemented
180	#1773	C₂×C₁₁	1	1	yes	characteristic, complemented
181	#1753	C₂×C₁₁	1	1	yes	characteristic, complemented
182	C₂³×C₁₁	—	2	1	no	—
183	C₂³×C₁₁	—	2	1	no	—
184	C₂³×C₁₁	—	2	2	no	—
185	C₂³×C₁₁	—	4	1	no	—
186	C₂³×C₁₁	—	4	1	no	—
187	C₂³×C₁₁	C₄×D₄	1	2	yes	—
188	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
189	Q₈×C₁₁	—	2	2	no	—
190	Q₈×C₁₁	—	2	2	no	—
191	D₄×C₁₁	—	2	2	no	—
192	D₄×C₁₁	—	2	2	no	—
193	D₄×C₁₁	—	4	4	no	—
194	D₄×C₁₁	—	4	2	no	—
195	D₄×C₁₁	—	4	2	no	—
196	D₄×C₁₁	—	8	2	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	4	1	no	—
208	C₂×C₄×C₁₁	—	4	1	no	—
209	C₂×C₄×C₁₁	—	4	2	no	—
210	C₂×C₄×C₁₁	—	4	2	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	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	1	no	—
223	C₈×C₁₁	—	2	1	no	—
224	C₈×C₁₁	—	2	4	no	—
225	C₈×C₁₁	—	2	2	no	—
226	C₈×C₁₁	—	4	2	no	—
227	C₈×C₁₁	C₄×D₄	1	2	yes	—
228	C₈×C₁₁	C₄×D₄	1	2	yes	—
229	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
230	C₂×#131	C₂²×C₁₁	1	2	yes	—
231	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
232	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
233	#525	C₂²×C₁₁	1	2	yes	—
234	#470	C₄×C₁₁	1	2	yes	complemented
235	#469	C₄×C₁₁	1	2	yes	complemented
236	#468	C₄×C₁₁	1	2	yes	complemented
237	#468	C₄×C₁₁	1	2	yes	complemented
238	#443	—	2	4	no	—
239	#436	—	2	2	no	—
240	#435	—	2	2	no	—
241	#435	—	2	2	no	—
242	C₈×D₄	—	2	2	no	—
243	#430	—	2	4	no	—
244	C₂×#108	C₂²×C₁₁	1	2	yes	—
245	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
246	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
247	#427	C₂²×C₁₁	1	1	yes	characteristic
248	#424	C₂²×C₁₁	1	2	yes	—
249	C₂×#104	C₂²×C₁₁	1	2	yes	—
250	C₂×#104	C₂²×C₁₁	1	2	yes	—
251	#416	C₂²×C₁₁	1	2	yes	—
252	#408	C₂²×C₁₁	1	2	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
254	#405	C₂²×C₁₁	1	2	yes	—
255	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
258	#339	C₂²×C₁₁	1	2	yes	—
259	#339	C₂²×C₁₁	1	2	yes	—
260	#336	C₂²×C₁₁	1	1	yes	characteristic
261	#336	C₂²×C₁₁	1	1	yes	characteristic
262	C₂²×C₁₁	—	2	1	no	—
263	C₂²×C₁₁	—	2	1	no	—
264	C₂²×C₁₁	—	2	2	no	—
265	C₂²×C₁₁	—	2	2	no	—
266	C₂²×C₁₁	—	2	2	no	—
267	C₂²×C₁₁	—	4	2	no	—
268	C₂²×C₁₁	—	4	2	no	—
269	C₂²×C₁₁	—	4	2	no	—
270	C₂²×C₁₁	—	8	1	no	—
271	C₂²×C₁₁	—	8	1	no	—
272	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₁₁	#548	1	1	yes	characteristic
274	C₂²×C₁₁	#553	1	1	yes	characteristic
275	C₄×C₁₁	—	2	2	no	—
276	C₄×C₁₁	—	4	2	no	—
277	C₄×C₁₁	—	4	2	no	—
278	C₄×C₁₁	—	4	2	no	—
279	C₄×C₁₁	—	4	2	no	—
280	C₄×C₁₁	—	8	1	no	—
281	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₁	#520	1	1	yes	characteristic
283	C₄×C₁₁	D₄²	1	1	yes	characteristic
284	C₄×C₁₁	#547	1	1	yes	characteristic
285	C₂×#41	C₂³×C₁₁	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
287	#135	—	2	2	no	—
288	#135	—	2	2	no	—
289	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
290	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
291	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
292	#131	—	2	4	no	—
293	#131	—	4	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	4	2	no	—
300	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
301	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
302	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
303	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
304	C₂²×C₈	—	2	2	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
310	#123	—	2	2	no	—
311	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
312	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
313	#121	C₂×C₄×C₁₁	1	2	yes	—
314	#121	C₂×C₄×C₁₁	1	2	yes	—
315	#120	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	#117	C₂³×C₁₁	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
322	#108	—	2	4	no	—
323	#108	—	2	2	no	—
324	#108	D₄×C₁₁	1	4	yes	complemented
325	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
326	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
327	#106	C₂×C₄×C₁₁	1	2	yes	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	#104	—	2	4	no	—
331	#104	—	4	2	no	—
332	#103	C₂×C₄×C₁₁	1	2	yes	—
333	#103	C₂×C₄×C₁₁	1	2	yes	—
334	#102	C₂×C₄×C₁₁	1	2	yes	—
335	#102	C₂×C₄×C₁₁	1	2	yes	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
339	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
340	#97	—	2	2	no	—
341	#97	—	2	2	no	—
342	C₄×C₈	—	2	2	no	—
343	C₄×C₈	—	2	2	no	—
344	#95	—	2	1	no	—
345	C₂×C₁₁	—	2	1	no	—
346	C₂×C₁₁	—	2	1	no	—
347	C₂×C₁₁	—	4	2	no	—
348	C₂×C₁₁	—	8	2	no	—
349	C₂×C₁₁	#2361	1	1	yes	characteristic
350	C₂×C₁₁	#2955	1	1	yes	characteristic
351	C₂×C₁₁	#2956	1	1	yes	characteristic
352	C₂⁴	C₁₁×#41	1	1	yes	characteristic
353	#41	—	2	2	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
371	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
373	Q₁₆	—	2	2	no	—
374	SD₁₆	—	2	4	no	—
375	D₈	—	2	2	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	4	4	no	—
382	M₁₆	—	4	4	no	—
383	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	—	4	4	no	—
394	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
395	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
399	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
401	C₂×C₈	C₁₁×#41	1	2	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
405	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₁₁	#23020	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₄×D₄×C₁₁	1	2	yes	—
424	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
455	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	2	1	no	—
460	C₈	—	2	4	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	C₄×D₄×C₁₁	1	2	yes	—
464	C₈	C₄×D₄×C₁₁	1	2	yes	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
476	C₂²	C₁₁×#548	1	1	yes	characteristic
477	C₂²	C₁₁×#553	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
485	C₄	C₁₁×#520	1	1	yes	characteristic
486	C₄	D₄²×C₁₁	1	1	yes	characteristic
487	C₄	C₁₁×#547	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	1	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	2	no	—
492	C₂	C₁₁×#2361	1	1	yes	characteristic
493	C₂	C₁₁×#2955	1	1	yes	characteristic
494	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×#3054	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. C₂×C₁₁×#430	C₂	semidirect
5. C₁₁×#1975	C₂	semidirect
6. C₁₁×#1945	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1871	C₂	semidirect
9. C₁₁×#1866	C₂	semidirect
10. C₁₁×#1773	C₂	semidirect
11. C₁₁×#1753	C₂	semidirect
17. C₁₁×#470	C₄	semidirect
18. C₁₁×#469	C₄	semidirect
19. C₁₁×#468	C₄	semidirect
20. C₁₁×#468	C₄	semidirect
84. C₁₁×#108	D₄	semidirect
105. #23020	C₁₁	direct (N × H)
172. C₂×#443	C₂×C₁₁	semidirect
173. #2933	C₂×C₁₁	semidirect
174. C₂×#430	C₂×C₁₁	semidirect
175. #1975	C₂×C₁₁	semidirect
176. #1945	C₂×C₁₁	semidirect
177. #1929	C₂×C₁₁	semidirect
178. #1871	C₂×C₁₁	semidirect
179. #1866	C₂×C₁₁	semidirect
180. #1773	C₂×C₁₁	semidirect
181. #1753	C₂×C₁₁	semidirect
234. #470	C₄×C₁₁	semidirect
235. #469	C₄×C₁₁	semidirect
236. #468	C₄×C₁₁	semidirect
237. #468	C₄×C₁₁	semidirect
324. #108	D₄×C₁₁	semidirect
417. C₁₁	#23020	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×#3054	2
C₂×C₁₁×#443	2
C₁₁×#2933	2
C₂×C₁₁×#430	2
C₁₁×#1975	2
C₁₁×#1945	2
C₁₁×#1929	2
C₁₁×#1871	2
C₁₁×#1866	2
C₁₁×#1773	2
C₁₁×#1753	2
#23020	11

Subgroups — C11×#23020 #14600213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23020 #14600213