Subgroups — C₁₁×#24810 #14602003

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3069	C₂	1	2	yes	maximal
2	C₂×C₁₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2955	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#2916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2070	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2049	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1953	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1902	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1813	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#575	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#137	C₂²	1	2	yes	—
14	C₂×C₁₁×#137	C₂²	1	2	yes	—
15	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
16	C₁₁×#568	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
19	C₁₁×#473	—	2	4	no	—
20	C₁₁×#473	—	2	2	no	—
21	C₁₁×#473	—	2	2	no	—
22	C₁₁×#473	—	2	2	no	—
23	C₁₁×#473	—	2	2	no	—
24	C₁₁×#471	—	2	4	no	—
25	C₁₁×#444	—	2	2	no	—
26	C₁₁×#443	—	2	2	no	—
27	C₁₁×#430	—	2	2	no	—
28	C₁₁×#430	C₂²	1	2	yes	—
29	C₁₁×#430	C₂²	1	1	yes	characteristic
30	C₁₁×#430	C₂²	1	2	yes	—
31	C₂×C₁₁×#108	—	2	2	no	—
32	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
35	C₁₁×#421	C₂²	1	1	yes	characteristic
36	C₁₁×#421	C₂²	1	1	yes	characteristic
37	C₁₁×#419	C₂²	1	2	yes	—
38	C₁₁×#413	C₂²	1	2	yes	—
39	C₂×C₁₁×#101	C₂²	1	2	yes	—
40	C₂×C₁₁×#101	C₂²	1	2	yes	—
41	C₂×C₁₁×#101	C₂²	1	2	yes	—
42	C₁₁×#405	C₂²	1	1	yes	characteristic
43	C₁₁×#344	C₂²	1	2	yes	—
44	C₁₁×#338	C₂²	1	2	yes	—
45	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
46	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
48	C₁₁×#137	—	2	1	no	—
49	C₁₁×#137	—	2	4	no	—
50	C₁₁×#137	—	2	4	no	—
51	C₁₁×#137	—	2	4	no	—
52	C₁₁×#137	—	4	2	no	—
53	C₁₁×#137	D₄	1	2	yes	—
54	C₁₁×AGL(1,ℤ/8)	—	2	1	no	—
55	C₁₁×AGL(1,ℤ/8)	D₄	1	2	yes	—
56	C₁₁×#135	—	2	2	no	—
57	C₂×C₁₁×Q₁₆	—	2	2	no	—
58	C₂×C₁₁×Q₁₆	—	2	2	no	—
59	C₂×C₁₁×Q₁₆	—	2	1	no	—
60	C₂×C₁₁×Q₁₆	—	2	1	no	—
61	C₂×C₁₁×Q₁₆	—	2	1	no	—
62	C₂×C₁₁×Q₁₆	—	2	1	no	—
63	C₂×C₁₁×Q₁₆	—	2	1	no	—
64	C₂×C₁₁×Q₁₆	—	2	1	no	—
65	C₂×C₁₁×SD₁₆	—	2	2	no	—
66	C₂×C₁₁×SD₁₆	—	2	2	no	—
67	C₁₁×#131	—	2	1	no	—
68	C₁₁×#131	—	2	1	no	—
69	C₁₁×#131	—	2	4	no	—
70	C₁₁×#131	—	2	1	no	—
71	C₁₁×#131	—	2	1	no	—
72	C₁₁×#131	—	2	1	no	—
73	C₁₁×#131	—	2	1	no	—
74	C₁₁×#131	—	4	2	no	—
75	C₁₁×#131	D₄	1	2	yes	—
76	C₁₁×#131	D₄	1	2	yes	—
77	C₂×C₁₁×M₁₆	—	2	1	no	—
78	C₂×C₁₁×M₁₆	—	2	1	no	—
79	C₂×C₁₁×M₁₆	—	2	4	no	—
80	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
82	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
83	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
84	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₁	—	2	1	no	—
87	C₂²×C₈×C₁₁	—	2	1	no	—
88	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
89	C₁₁×#117	C₂³	1	1	yes	characteristic
90	C₁₁×#108	—	2	4	no	—
91	C₁₁×#108	—	2	2	no	—
92	C₁₁×#108	—	2	4	no	—
93	C₁₁×#108	—	2	1	no	—
94	C₁₁×#108	—	2	1	no	—
95	C₁₁×#108	—	2	1	no	—
96	C₁₁×#108	—	2	1	no	—
97	C₁₁×#108	D₄	1	2	yes	—
98	C₁₁×#108	D₄	1	2	yes	—
99	C₁₁×#104	—	2	2	no	—
100	C₁₁×#104	—	2	2	no	—
101	C₁₁×#103	—	4	2	no	—
102	C₁₁×#101	—	2	2	no	—
103	C₁₁×#101	—	2	4	no	—
104	C₁₁×#101	—	2	4	no	—
105	C₁₁×#101	—	2	4	no	—
106	C₁₁×#100	—	2	2	no	—
107	C₁₁×#97	—	2	1	no	—
108	C₄×C₈×C₁₁	—	2	1	no	—
109	#24810	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₁×#41	—	2	1	no	—
111	C₁₁×#41	—	2	1	no	—
112	C₁₁×#41	—	2	1	no	—
113	C₁₁×#41	—	2	1	no	—
114	C₁₁×#41	—	2	1	no	—
115	C₁₁×#41	—	2	1	no	—
116	C₁₁×#41	C₂×D₄	1	2	yes	—
117	C₁₁×#41	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₁	—	2	2	no	—
119	C₂×Q₈×C₁₁	—	2	2	no	—
120	C₂×Q₈×C₁₁	—	2	2	no	—
121	C₂×Q₈×C₁₁	—	2	2	no	—
122	C₂×Q₈×C₁₁	—	2	2	no	—
123	C₂×Q₈×C₁₁	—	2	2	no	—
124	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₁	#41	1	1	yes	characteristic
126	C₂×D₄×C₁₁	—	2	1	no	—
127	C₂×D₄×C₁₁	—	2	1	no	—
128	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₁	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	2	no	—
133	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₁₁×Q₁₆	—	2	2	no	—
135	C₁₁×Q₁₆	—	4	4	no	—
136	C₁₁×Q₁₆	—	4	1	no	—
137	C₁₁×Q₁₆	—	4	1	no	—
138	C₁₁×Q₁₆	—	4	1	no	—
139	C₁₁×Q₁₆	—	4	1	no	—
140	C₁₁×Q₁₆	—	4	4	no	—
141	C₁₁×SD₁₆	—	2	2	no	—
142	C₁₁×SD₁₆	—	2	2	no	—
143	C₁₁×SD₁₆	—	4	4	no	—
144	C₁₁×SD₁₆	—	4	4	no	—
145	C₁₁×D₈	—	2	2	no	—
146	C₁₁×M₁₆	—	2	2	no	—
147	C₁₁×M₁₆	—	2	2	no	—
148	C₁₁×M₁₆	—	2	2	no	—
149	C₁₁×M₁₆	—	2	2	no	—
150	C₁₁×M₁₆	—	2	1	no	—
151	C₁₁×M₁₆	—	2	2	no	—
152	C₁₁×M₁₆	—	2	1	no	—
153	C₁₁×M₁₆	—	2	2	no	—
154	C₁₁×M₁₆	—	2	1	no	—
155	C₁₁×M₁₆	—	2	1	no	—
156	C₁₁×M₁₆	—	2	2	no	—
157	C₁₁×M₁₆	—	4	4	no	—
158	C₁₁×M₁₆	—	4	1	no	—
159	C₁₁×M₁₆	—	4	1	no	—
160	C₁₁×M₁₆	C₂×D₄	1	2	yes	—
161	C₁₁×M₁₆	C₂×D₄	1	2	yes	—
162	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₁₁	—	2	2	no	—
164	C₂×C₈×C₁₁	—	2	2	no	—
165	C₂×C₈×C₁₁	—	2	1	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	2	no	—
168	C₂×C₈×C₁₁	—	2	1	no	—
169	C₂×C₈×C₁₁	—	2	2	no	—
170	C₂×C₈×C₁₁	—	2	2	no	—
171	C₂×C₈×C₁₁	—	4	4	no	—
172	C₂×C₈×C₁₁	—	4	1	no	—
173	C₂×C₈×C₁₁	—	4	1	no	—
174	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
179	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
180	C₁₁×C₄⋊C₄	—	2	1	no	—
181	C₁₁×C₂²⋊C₄	—	2	1	no	—
182	C₄²×C₁₁	—	2	1	no	—
183	#3069	C₂×C₁₁	1	2	yes	—
184	C₂×#473	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂×#473	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#2955	C₂×C₁₁	1	1	yes	characteristic
187	#2916	C₂×C₁₁	1	1	yes	characteristic, complemented
188	#2070	C₂×C₁₁	1	2	yes	complemented
189	#2049	C₂×C₁₁	1	2	yes	complemented
190	#1979	C₂×C₁₁	1	1	yes	characteristic, complemented
191	#1953	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#1902	C₂×C₁₁	1	2	yes	complemented
193	#1813	C₂×C₁₁	1	1	yes	characteristic, complemented
194	C₂³×C₁₁	—	2	1	no	—
195	C₂³×C₁₁	—	2	1	no	—
196	C₂³×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
197	Q₈×C₁₁	—	2	1	no	—
198	Q₈×C₁₁	—	2	1	no	—
199	Q₈×C₁₁	—	2	1	no	—
200	Q₈×C₁₁	—	4	2	no	—
201	Q₈×C₁₁	—	4	2	no	—
202	Q₈×C₁₁	—	4	2	no	—
203	Q₈×C₁₁	—	4	2	no	—
204	Q₈×C₁₁	#121	1	2	yes	—
205	D₄×C₁₁	—	2	2	no	—
206	D₄×C₁₁	—	2	2	no	—
207	D₄×C₁₁	—	2	1	no	—
208	D₄×C₁₁	—	2	1	no	—
209	D₄×C₁₁	—	2	1	no	—
210	D₄×C₁₁	—	4	1	no	—
211	D₄×C₁₁	—	4	1	no	—
212	D₄×C₁₁	#121	1	2	yes	—
213	C₂×C₄×C₁₁	—	2	1	no	—
214	C₂×C₄×C₁₁	—	2	2	no	—
215	C₂×C₄×C₁₁	—	2	2	no	—
216	C₂×C₄×C₁₁	—	2	1	no	—
217	C₂×C₄×C₁₁	—	4	1	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	1	no	—
220	C₂×C₄×C₁₁	—	4	2	no	—
221	C₂×C₄×C₁₁	—	4	2	no	—
222	C₂×C₄×C₁₁	—	4	2	no	—
223	C₂×C₄×C₁₁	C₂²×D₄	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	C₂×#41	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	2	no	—
231	C₈×C₁₁	—	2	4	no	—
232	C₈×C₁₁	—	4	1	no	—
233	C₈×C₁₁	—	4	2	no	—
234	C₈×C₁₁	—	4	2	no	—
235	C₈×C₁₁	#121	1	1	yes	characteristic
236	C₈×C₁₁	#121	1	1	yes	characteristic
237	C₈×C₁₁	#121	1	1	yes	characteristic
238	C₈×C₁₁	#121	1	1	yes	characteristic
239	#575	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×#137	C₂²×C₁₁	1	2	yes	—
241	C₂×#137	C₂²×C₁₁	1	2	yes	—
242	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
243	#568	C₂²×C₁₁	1	2	yes	—
244	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
246	#473	—	2	4	no	—
247	#473	—	2	2	no	—
248	#473	—	2	2	no	—
249	#473	—	2	2	no	—
250	#473	—	2	2	no	—
251	#471	—	2	4	no	—
252	#444	—	2	2	no	—
253	#443	—	2	2	no	—
254	#430	—	2	2	no	—
255	#430	C₂²×C₁₁	1	2	yes	—
256	#430	C₂²×C₁₁	1	1	yes	characteristic
257	#430	C₂²×C₁₁	1	2	yes	—
258	C₂×#108	—	2	2	no	—
259	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
260	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
261	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
262	#421	C₂²×C₁₁	1	1	yes	characteristic
263	#421	C₂²×C₁₁	1	1	yes	characteristic
264	#419	C₂²×C₁₁	1	2	yes	—
265	#413	C₂²×C₁₁	1	2	yes	—
266	C₂×#101	C₂²×C₁₁	1	2	yes	—
267	C₂×#101	C₂²×C₁₁	1	2	yes	—
268	C₂×#101	C₂²×C₁₁	1	2	yes	—
269	#405	C₂²×C₁₁	1	1	yes	characteristic
270	#344	C₂²×C₁₁	1	2	yes	—
271	#338	C₂²×C₁₁	1	2	yes	—
272	C₂²×C₁₁	—	2	2	no	—
273	C₂²×C₁₁	—	4	1	no	—
274	C₂²×C₁₁	—	4	1	no	—
275	C₂²×C₁₁	—	8	1	no	—
276	C₂²×C₁₁	—	8	1	no	—
277	C₂²×C₁₁	#537	1	1	yes	characteristic
278	C₂²×C₁₁	#547	1	1	yes	characteristic
279	C₂²×C₁₁	#548	1	1	yes	characteristic
280	C₄×C₁₁	—	2	2	no	—
281	C₄×C₁₁	—	4	1	no	—
282	C₄×C₁₁	—	8	1	no	—
283	C₄×C₁₁	—	8	2	no	—
284	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
285	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
286	C₄×C₁₁	D₄²	1	1	yes	characteristic
287	C₄×C₁₁	#553	1	1	yes	characteristic
288	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
289	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
291	#137	—	2	1	no	—
292	#137	—	2	4	no	—
293	#137	—	2	4	no	—
294	#137	—	2	4	no	—
295	#137	—	4	2	no	—
296	#137	D₄×C₁₁	1	2	yes	—
297	AGL(1,ℤ/8)	—	2	1	no	—
298	AGL(1,ℤ/8)	D₄×C₁₁	1	2	yes	—
299	#135	—	2	2	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×Q₁₆	—	2	2	no	—
302	C₂×Q₁₆	—	2	1	no	—
303	C₂×Q₁₆	—	2	1	no	—
304	C₂×Q₁₆	—	2	1	no	—
305	C₂×Q₁₆	—	2	1	no	—
306	C₂×Q₁₆	—	2	1	no	—
307	C₂×Q₁₆	—	2	1	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	#131	—	2	1	no	—
311	#131	—	2	1	no	—
312	#131	—	2	4	no	—
313	#131	—	2	1	no	—
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	2	1	no	—
317	#131	—	4	2	no	—
318	#131	D₄×C₁₁	1	2	yes	—
319	#131	D₄×C₁₁	1	2	yes	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	4	no	—
323	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
324	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
325	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
327	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
328	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
332	#117	C₂³×C₁₁	1	1	yes	characteristic
333	#108	—	2	4	no	—
334	#108	—	2	2	no	—
335	#108	—	2	4	no	—
336	#108	—	2	1	no	—
337	#108	—	2	1	no	—
338	#108	—	2	1	no	—
339	#108	—	2	1	no	—
340	#108	D₄×C₁₁	1	2	yes	—
341	#108	D₄×C₁₁	1	2	yes	—
342	#104	—	2	2	no	—
343	#104	—	2	2	no	—
344	#103	—	4	2	no	—
345	#101	—	2	2	no	—
346	#101	—	2	4	no	—
347	#101	—	2	4	no	—
348	#101	—	2	4	no	—
349	#100	—	2	2	no	—
350	#97	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₂×C₁₁	—	2	1	no	—
353	C₂×C₁₁	—	2	1	no	—
354	C₂×C₁₁	—	2	1	no	—
355	C₂×C₁₁	—	4	2	no	—
356	C₂×C₁₁	—	8	1	no	—
357	C₂×C₁₁	#2416	1	1	yes	characteristic
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	—	2	1	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	C₂×D₄×C₁₁	1	2	yes	—
365	#41	C₂×D₄×C₁₁	1	2	yes	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
373	C₂×Q₈	C₁₁×#41	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂×D₄	C₁₁×#41	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
382	Q₁₆	—	2	2	no	—
383	Q₁₆	—	4	4	no	—
384	Q₁₆	—	4	4	no	—
385	Q₁₆	—	4	1	no	—
386	Q₁₆	—	4	1	no	—
387	Q₁₆	—	4	1	no	—
388	Q₁₆	—	4	1	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	D₈	—	2	2	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	4	4	no	—
406	M₁₆	—	4	1	no	—
407	M₁₆	—	4	1	no	—
408	M₁₆	C₂×D₄×C₁₁	1	2	yes	—
409	M₁₆	C₂×D₄×C₁₁	1	2	yes	—
410	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	4	4	no	—
420	C₂×C₈	—	4	1	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
423	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
426	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
427	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
428	C₄⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₁₁	#24810	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	C₁₁×#121	1	2	yes	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	C₁₁×#121	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
464	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
466	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	4	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	C₁₁×#121	1	1	yes	characteristic
474	C₈	C₁₁×#121	1	1	yes	characteristic
475	C₈	C₁₁×#121	1	1	yes	characteristic
476	C₈	C₁₁×#121	1	1	yes	characteristic
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	C₁₁×#537	1	1	yes	characteristic
483	C₂²	C₁₁×#547	1	1	yes	characteristic
484	C₂²	C₁₁×#548	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
490	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
491	C₄	D₄²×C₁₁	1	1	yes	characteristic
492	C₄	C₁₁×#553	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	C₁₁×#2416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#2416
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#575	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#473	C₂	semidirect
3. C₂×C₁₁×#473	C₂	semidirect
5. C₁₁×#2916	C₂	semidirect
6. C₁₁×#2070	C₂	semidirect
7. C₁₁×#2049	C₂	semidirect
8. C₁₁×#1979	C₂	semidirect
9. C₁₁×#1953	C₂	semidirect
10. C₁₁×#1902	C₂	semidirect
11. C₁₁×#1813	C₂	semidirect
109. #24810	C₁₁	direct (N × H)
184. C₂×#473	C₂×C₁₁	semidirect
185. C₂×#473	C₂×C₁₁	semidirect
187. #2916	C₂×C₁₁	semidirect
188. #2070	C₂×C₁₁	semidirect
189. #2049	C₂×C₁₁	semidirect
190. #1979	C₂×C₁₁	semidirect
191. #1953	C₂×C₁₁	semidirect
192. #1902	C₂×C₁₁	semidirect
193. #1813	C₂×C₁₁	semidirect
431. C₁₁	#24810	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×#3069	2
C₂×C₁₁×#473	2
C₁₁×#2955	2
C₁₁×#2916	2
C₁₁×#2070	2
C₁₁×#2049	2
C₁₁×#1979	2
C₁₁×#1953	2
C₁₁×#1902	2
C₁₁×#1813	2
#24810	11

Subgroups — C11×#24810 #14602003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24810 #14602003