Subgroups — C₁₁×#22205 #14599398

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 492 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	C₁₁×#2929	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1897	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#131	C₂²	1	2	yes	—
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#525	C₂²	1	2	yes	—
15	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
16	C₁₁×#470	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#470	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#469	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#469	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#468	C₄	1	2	yes	complemented
21	C₁₁×#468	C₄	1	2	yes	complemented
22	C₁₁×#435	—	2	2	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₈×D₄×C₁₁	—	2	2	no	—
26	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
28	C₁₁×#427	C₂²	1	1	yes	characteristic
29	C₁₁×#424	C₂²	1	2	yes	—
30	C₂×C₁₁×#104	C₂²	1	2	yes	—
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₁₁×#416	C₂²	1	2	yes	—
33	C₁₁×#408	C₂²	1	2	yes	—
34	C₁₁×#407	C₂²	1	2	yes	—
35	C₁₁×#405	C₂²	1	2	yes	—
36	C₁₁×#341	C₂²	1	2	yes	—
37	C₁₁×#339	C₂²	1	2	yes	—
38	C₁₁×#339	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₂×C₁₁×#41	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×#135	—	4	1	no	—
44	C₁₁×#135	—	4	1	no	—
45	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
48	C₁₁×#131	—	4	2	no	—
49	C₁₁×#131	—	4	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	—	4	1	no	—
52	C₂×C₁₁×M₁₆	—	4	1	no	—
53	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	—	2	2	no	—
60	C₂²×C₈×C₁₁	—	4	1	no	—
61	C₂²×C₈×C₁₁	—	4	1	no	—
62	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	D₄	1	2	yes	—
64	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
68	C₁₁×#123	—	2	2	no	—
69	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
70	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₁×#121	C₂×C₄	1	2	yes	—
72	C₁₁×#121	C₂×C₄	1	2	yes	—
73	C₁₁×#120	—	2	2	no	—
74	C₄×D₄×C₁₁	—	2	2	no	—
75	C₄×D₄×C₁₁	—	2	2	no	—
76	C₁₁×#117	—	4	1	no	—
77	C₁₁×#117	—	4	1	no	—
78	C₁₁×#117	C₂³	1	2	yes	—
79	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
82	C₁₁×#108	—	4	1	no	—
83	C₁₁×#108	—	4	1	no	—
84	C₁₁×#107	C₂×C₄	1	2	yes	—
85	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
86	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
87	C₁₁×C₄⋊C₈	—	2	2	no	—
88	C₁₁×C₄⋊C₈	—	2	2	no	—
89	C₁₁×#104	—	4	2	no	—
90	C₁₁×#104	—	4	2	no	—
91	C₁₁×#103	C₂×C₄	1	2	yes	—
92	C₁₁×#103	C₂×C₄	1	2	yes	—
93	C₁₁×#102	C₂×C₄	1	2	yes	—
94	C₁₁×#102	C₂×C₄	1	2	yes	—
95	C₁₁×C₂²⋊C₈	—	2	2	no	—
96	C₁₁×C₂²⋊C₈	—	2	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×C₂²⋊C₈	—	2	2	no	—
99	C₁₁×#97	—	2	2	no	—
100	C₄×C₈×C₁₁	—	2	2	no	—
101	#22205	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₁	#41	1	1	yes	characteristic
103	C₁₁×#41	—	2	2	no	—
104	C₁₁×#41	—	2	2	no	—
105	C₁₁×#41	—	2	2	no	—
106	C₁₁×#41	—	2	2	no	—
107	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
124	C₁₁×Q₁₆	—	4	1	no	—
125	C₁₁×SD₁₆	—	4	2	no	—
126	C₁₁×D₈	—	4	1	no	—
127	C₁₁×M₁₆	—	2	2	no	—
128	C₁₁×M₁₆	—	2	2	no	—
129	C₁₁×M₁₆	—	2	2	no	—
130	C₁₁×M₁₆	—	2	2	no	—
131	C₁₁×M₁₆	—	4	1	no	—
132	C₁₁×M₁₆	—	4	1	no	—
133	C₁₁×M₁₆	—	4	1	no	—
134	C₁₁×M₁₆	—	4	1	no	—
135	C₁₁×M₁₆	—	4	4	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
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	—	4	1	no	—
145	C₂×C₈×C₁₁	—	4	2	no	—
146	C₂×C₈×C₁₁	—	4	1	no	—
147	C₂×C₈×C₁₁	—	4	4	no	—
148	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
154	C₁₁×C₄⋊C₄	—	2	2	no	—
155	C₁₁×C₄⋊C₄	—	2	2	no	—
156	C₁₁×C₄⋊C₄	—	4	2	no	—
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₁₁×C₂²⋊C₄	—	2	2	no	—
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	—	4	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	—	2	2	no	—
167	C₄²×C₁₁	—	2	2	no	—
168	#3054	C₂×C₁₁	1	1	yes	characteristic
169	#2929	C₂×C₁₁	1	2	yes	complemented
170	#1929	C₂×C₁₁	1	2	yes	complemented
171	#1922	C₂×C₁₁	1	2	yes	complemented
172	#1897	C₂×C₁₁	1	2	yes	complemented
173	#1876	C₂×C₁₁	1	2	yes	complemented
174	#1866	C₂×C₁₁	1	2	yes	complemented
175	#1811	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#1729	C₂×C₁₁	1	1	yes	characteristic, complemented
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	2	no	—
180	C₂³×C₁₁	—	4	2	no	—
181	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
184	Q₈×C₁₁	—	2	2	no	—
185	Q₈×C₁₁	—	2	2	no	—
186	D₄×C₁₁	—	2	2	no	—
187	D₄×C₁₁	—	2	2	no	—
188	D₄×C₁₁	—	4	4	no	—
189	D₄×C₁₁	—	4	4	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	4	2	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	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	—	4	2	no	—
206	C₂×C₄×C₁₁	—	4	2	no	—
207	C₂×C₄×C₁₁	—	4	4	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
217	C₈×C₁₁	—	2	1	no	—
218	C₈×C₁₁	—	2	1	no	—
219	C₈×C₁₁	—	2	1	no	—
220	C₈×C₁₁	—	2	1	no	—
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	2	no	—
223	C₈×C₁₁	—	4	2	no	—
224	C₈×C₁₁	—	4	2	no	—
225	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×#131	C₂²×C₁₁	1	2	yes	—
227	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
229	#525	C₂²×C₁₁	1	2	yes	—
230	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
231	#470	C₄×C₁₁	1	1	yes	characteristic, complemented
232	#470	C₄×C₁₁	1	1	yes	characteristic, complemented
233	#469	C₄×C₁₁	1	1	yes	characteristic, complemented
234	#469	C₄×C₁₁	1	1	yes	characteristic, complemented
235	#468	C₄×C₁₁	1	2	yes	complemented
236	#468	C₄×C₁₁	1	2	yes	complemented
237	#435	—	2	2	no	—
238	#435	—	2	2	no	—
239	C₈×D₄	—	2	2	no	—
240	C₈×D₄	—	2	2	no	—
241	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
243	#427	C₂²×C₁₁	1	1	yes	characteristic
244	#424	C₂²×C₁₁	1	2	yes	—
245	C₂×#104	C₂²×C₁₁	1	2	yes	—
246	C₂×#104	C₂²×C₁₁	1	2	yes	—
247	#416	C₂²×C₁₁	1	2	yes	—
248	#408	C₂²×C₁₁	1	2	yes	—
249	#407	C₂²×C₁₁	1	2	yes	—
250	#405	C₂²×C₁₁	1	2	yes	—
251	#341	C₂²×C₁₁	1	2	yes	—
252	#339	C₂²×C₁₁	1	2	yes	—
253	#339	C₂²×C₁₁	1	2	yes	—
254	#336	C₂²×C₁₁	1	2	yes	—
255	#336	C₂²×C₁₁	1	2	yes	—
256	C₂²×C₁₁	—	2	2	no	—
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	2	no	—
260	C₂²×C₁₁	—	2	2	no	—
261	C₂²×C₁₁	—	4	2	no	—
262	C₂²×C₁₁	—	4	2	no	—
263	C₂²×C₁₁	—	4	2	no	—
264	C₂²×C₁₁	—	4	2	no	—
265	C₂²×C₁₁	—	4	2	no	—
266	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₁₁	#538	1	1	yes	characteristic
268	C₂²×C₁₁	#539	1	1	yes	characteristic
269	C₄×C₁₁	—	2	1	no	—
270	C₄×C₁₁	—	2	1	no	—
271	C₄×C₁₁	—	4	2	no	—
272	C₄×C₁₁	—	4	2	no	—
273	C₄×C₁₁	—	4	2	no	—
274	C₄×C₁₁	—	8	2	no	—
275	C₄×C₁₁	#518	1	1	yes	characteristic
276	C₄×C₁₁	#520	1	1	yes	characteristic
277	C₄×C₁₁	#534	1	1	yes	characteristic
278	C₄×C₁₁	#537	1	1	yes	characteristic
279	C₂×#41	C₂³×C₁₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
281	#135	—	4	1	no	—
282	#135	—	4	1	no	—
283	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
284	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
285	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
286	#131	—	4	2	no	—
287	#131	—	4	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	4	1	no	—
290	C₂×M₁₆	—	4	1	no	—
291	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
292	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
293	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
294	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
296	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	4	1	no	—
299	C₂²×C₈	—	4	1	no	—
300	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
301	C₂²×C₈	D₄×C₁₁	1	2	yes	—
302	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
306	#123	—	2	2	no	—
307	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
308	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
309	#121	C₂×C₄×C₁₁	1	2	yes	—
310	#121	C₂×C₄×C₁₁	1	2	yes	—
311	#120	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	#117	—	4	1	no	—
315	#117	—	4	1	no	—
316	#117	C₂³×C₁₁	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
320	#108	—	4	1	no	—
321	#108	—	4	1	no	—
322	#107	C₂×C₄×C₁₁	1	2	yes	—
323	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
324	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	2	2	no	—
327	#104	—	4	2	no	—
328	#104	—	4	2	no	—
329	#103	C₂×C₄×C₁₁	1	2	yes	—
330	#103	C₂×C₄×C₁₁	1	2	yes	—
331	#102	C₂×C₄×C₁₁	1	2	yes	—
332	#102	C₂×C₄×C₁₁	1	2	yes	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	#97	—	2	2	no	—
338	C₄×C₈	—	2	2	no	—
339	C₂×C₁₁	—	2	1	no	—
340	C₂×C₁₁	—	2	1	no	—
341	C₂×C₁₁	—	4	1	no	—
342	C₂×C₁₁	—	4	1	no	—
343	C₂×C₁₁	—	8	2	no	—
344	C₂×C₁₁	#2325	1	1	yes	characteristic
345	C₂×C₁₁	#2955	1	2	yes	—
346	C₂⁴	C₁₁×#41	1	1	yes	characteristic
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
368	Q₁₆	—	4	1	no	—
369	SD₁₆	—	4	2	no	—
370	D₈	—	4	1	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	4	1	no	—
377	M₁₆	—	4	1	no	—
378	M₁₆	—	4	1	no	—
379	M₁₆	—	4	4	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	4	1	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
393	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
394	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
402	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₁₁	#22205	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
418	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
419	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
446	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
447	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
449	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
472	C₂²	C₁₁×#538	1	1	yes	characteristic
473	C₂²	C₁₁×#539	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	2	no	—
480	C₄	C₁₁×#518	1	1	yes	characteristic
481	C₄	C₁₁×#520	1	1	yes	characteristic
482	C₄	C₁₁×#534	1	1	yes	characteristic
483	C₄	C₁₁×#537	1	1	yes	characteristic
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	4	1	no	—
487	C₂	—	4	1	no	—
488	C₂	—	8	2	no	—
489	C₂	C₁₁×#2325	1	1	yes	characteristic
490	C₂	C₁₁×#2955	1	2	yes	—

	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 ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2929	C₂	semidirect
3. C₁₁×#1929	C₂	semidirect
4. C₁₁×#1922	C₂	semidirect
5. C₁₁×#1897	C₂	semidirect
6. C₁₁×#1876	C₂	semidirect
7. C₁₁×#1866	C₂	semidirect
8. C₁₁×#1811	C₂	semidirect
9. C₁₁×#1729	C₂	semidirect
16. C₁₁×#470	C₄	semidirect
17. C₁₁×#470	C₄	semidirect
18. C₁₁×#469	C₄	semidirect
19. C₁₁×#469	C₄	semidirect
20. C₁₁×#468	C₄	semidirect
21. C₁₁×#468	C₄	semidirect
101. #22205	C₁₁	direct (N × H)
169. #2929	C₂×C₁₁	semidirect
170. #1929	C₂×C₁₁	semidirect
171. #1922	C₂×C₁₁	semidirect
172. #1897	C₂×C₁₁	semidirect
173. #1876	C₂×C₁₁	semidirect
174. #1866	C₂×C₁₁	semidirect
175. #1811	C₂×C₁₁	semidirect
176. #1729	C₂×C₁₁	semidirect
231. #470	C₄×C₁₁	semidirect
232. #470	C₄×C₁₁	semidirect
233. #469	C₄×C₁₁	semidirect
234. #469	C₄×C₁₁	semidirect
235. #468	C₄×C₁₁	semidirect
236. #468	C₄×C₁₁	semidirect
412. C₁₁	#22205	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
C₁₁×#2929	2
C₁₁×#1929	2
C₁₁×#1922	2
C₁₁×#1897	2
C₁₁×#1876	2
C₁₁×#1866	2
C₁₁×#1811	2
C₁₁×#1729	2
#22205	11

Subgroups — C11×#22205 #14599398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22205 #14599398