Subgroups — C₁₁×#19430 #14596623

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3109	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1701	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1697	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1695	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1691	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1554	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₁₁×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#500	C₂²	1	1	yes	characteristic, complemented
16	C₁₁×#498	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#486	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#486	C₂²	1	1	yes	characteristic, complemented
19	C₁₁×#483	—	2	1	no	—
20	C₁₁×#482	—	2	2	no	—
21	C₁₁×#481	—	2	1	no	—
22	C₁₁×#478	—	2	2	no	—
23	C₁₁×#476	C₂²	1	2	yes	—
24	C₁₁×#476	C₂²	1	2	yes	—
25	C₁₁×#461	C₂²	1	2	yes	—
26	C₁₁×#459	C₂²	1	2	yes	—
27	C₁₁×#450	—	2	1	no	—
28	C₁₁×#447	—	2	1	no	—
29	C₁₁×#442	—	2	2	no	—
30	C₄×C₁₁×SD₁₆	—	2	2	no	—
31	C₁₁×#436	—	2	2	no	—
32	C₁₁×#436	C₂²	1	2	yes	—
33	C₁₁×#436	C₂²	1	2	yes	—
34	C₁₁×#432	C₂²	1	1	yes	characteristic
35	C₁₁×#431	C₂²	1	1	yes	characteristic
36	C₁₁×#431	C₂²	1	1	yes	characteristic
37	C₁₁×#431	C₂²	1	1	yes	characteristic
38	C₁₁×#407	—	2	2	no	—
39	C₁₁×#335	C₂²	1	2	yes	complemented
40	C₁₁×#334	C₂²	1	2	yes	complemented
41	C₁₁×#333	C₂²	1	2	yes	complemented
42	C₁₁×#333	C₂²	1	2	yes	complemented
43	C₁₁×#332	C₂²	1	2	yes	complemented
44	C₁₁×#331	C₂²	1	2	yes	complemented
45	C₂×C₁₁×#41	—	2	1	no	—
46	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	—	2	1	no	—
48	C₂×C₁₁×SD₁₆	—	2	2	no	—
49	C₂×C₁₁×D₈	—	2	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	—	2	2	no	—
52	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
54	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
55	C₁₁×#127	C₂³	1	1	yes	characteristic
56	C₁₁×#125	—	2	1	no	—
57	C₁₁×#124	—	2	1	no	—
58	C₁₁×C₂²⋊Q₈	—	2	1	no	—
59	C₁₁×C₂²⋊Q₈	—	2	1	no	—
60	C₁₁×#121	—	2	1	no	—
61	C₁₁×#121	—	2	1	no	—
62	C₄×Q₈×C₁₁	—	2	1	no	—
63	C₄×Q₈×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	—	2	1	no	—
66	C₄×D₄×C₁₁	—	2	1	no	—
67	C₄×D₄×C₁₁	—	2	1	no	—
68	C₄×D₄×C₁₁	D₄	1	2	yes	—
69	C₄×D₄×C₁₁	C₂³	1	2	yes	—
70	C₁₁×#117	—	2	1	no	—
71	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#107	—	2	2	no	—
75	C₁₁×#106	—	2	2	no	—
76	C₁₁×#106	—	2	2	no	—
77	C₁₁×#106	—	2	2	no	—
78	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
79	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₁×#103	—	2	2	no	—
83	C₁₁×#102	—	2	2	no	—
84	C₁₁×#102	—	2	2	no	—
85	C₁₁×#102	—	2	2	no	—
86	C₁₁×#102	—	2	2	no	—
87	C₁₁×#102	—	2	2	no	—
88	C₁₁×C₂²⋊C₈	—	2	1	no	—
89	C₁₁×C₂²⋊C₈	—	2	1	no	—
90	C₁₁×C₂²⋊C₈	—	2	1	no	—
91	C₁₁×C₂²⋊C₈	—	2	2	no	—
92	C₁₁×C₂²⋊C₈	—	2	2	no	—
93	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
94	C₁₁×#97	—	2	1	no	—
95	C₄×C₈×C₁₁	—	2	1	no	—
96	C₄×C₈×C₁₁	—	2	1	no	—
97	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	#19430	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₁	—	2	1	no	—
101	C₁₁×#41	—	8	2	no	—
102	C₂×Q₈×C₁₁	—	2	1	no	—
103	C₂×Q₈×C₁₁	—	2	1	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×D₄×C₁₁	—	2	1	no	—
106	C₂×D₄×C₁₁	—	2	1	no	—
107	C₂×D₄×C₁₁	—	2	1	no	—
108	C₂×D₄×C₁₁	—	2	1	no	—
109	C₂×D₄×C₁₁	—	4	2	no	—
110	C₂×D₄×C₁₁	—	4	1	no	—
111	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	2	no	—
115	C₂²×C₄×C₁₁	—	4	1	no	—
116	C₂²×C₄×C₁₁	—	8	2	no	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
120	C₁₁×SD₁₆	—	4	4	no	—
121	C₁₁×D₈	—	4	4	no	—
122	C₁₁×M₁₆	—	8	2	no	—
123	C₁₁×M₁₆	—	8	2	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
129	C₁₁×C₄⋊C₄	—	2	1	no	—
130	C₁₁×C₄⋊C₄	—	2	1	no	—
131	C₁₁×C₄⋊C₄	—	2	1	no	—
132	C₁₁×C₄⋊C₄	—	2	1	no	—
133	C₁₁×C₄⋊C₄	—	2	1	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	1	no	—
136	C₁₁×C₄⋊C₄	—	4	1	no	—
137	C₁₁×C₄⋊C₄	—	4	1	no	—
138	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₁×C₂²⋊C₄	—	2	2	no	—
140	C₁₁×C₂²⋊C₄	—	2	2	no	—
141	C₁₁×C₂²⋊C₄	—	4	1	no	—
142	C₁₁×C₂²⋊C₄	—	4	1	no	—
143	C₁₁×C₂²⋊C₄	—	4	1	no	—
144	C₄²×C₁₁	—	4	1	no	—
145	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₁	#41	1	1	yes	characteristic
148	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
149	#3228	C₂×C₁₁	1	1	yes	characteristic, complemented
150	#3109	C₂×C₁₁	1	1	yes	characteristic
151	#3101	C₂×C₁₁	1	1	yes	characteristic, complemented
152	#2975	C₂×C₁₁	1	1	yes	characteristic, complemented
153	#1701	C₂×C₁₁	1	2	yes	complemented
154	#1697	C₂×C₁₁	1	2	yes	complemented
155	#1695	C₂×C₁₁	1	2	yes	complemented
156	#1691	C₂×C₁₁	1	2	yes	complemented
157	#1572	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#1554	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1543	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	—	2	2	no	—
161	C₂³×C₁₁	—	4	2	no	—
162	C₂³×C₁₁	—	4	1	no	—
163	C₂³×C₁₁	—	8	1	no	—
164	C₂³×C₁₁	—	8	1	no	—
165	C₂³×C₁₁	#121	1	1	yes	characteristic
166	Q₈×C₁₁	—	4	2	no	—
167	Q₈×C₁₁	—	8	1	no	—
168	Q₈×C₁₁	—	8	1	no	—
169	D₄×C₁₁	—	2	2	no	—
170	D₄×C₁₁	—	2	2	no	—
171	D₄×C₁₁	—	4	2	no	—
172	D₄×C₁₁	—	4	2	no	—
173	D₄×C₁₁	—	4	2	no	—
174	D₄×C₁₁	—	8	1	no	—
175	D₄×C₁₁	—	8	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	4	1	no	—
180	C₂×C₄×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	—	4	2	no	—
182	C₂×C₄×C₁₁	—	4	1	no	—
183	C₂×C₄×C₁₁	—	4	1	no	—
184	C₂×C₄×C₁₁	—	4	1	no	—
185	C₂×C₄×C₁₁	—	8	2	no	—
186	C₂×C₄×C₁₁	—	8	2	no	—
187	C₂×C₄×C₁₁	—	8	1	no	—
188	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
194	C₈×C₁₁	—	2	2	no	—
195	C₈×C₁₁	—	2	2	no	—
196	C₈×C₁₁	—	4	2	no	—
197	C₈×C₁₁	—	4	2	no	—
198	C₈×C₁₁	—	4	2	no	—
199	#533	C₂²×C₁₁	1	1	yes	characteristic
200	#532	C₂²×C₁₁	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
202	#500	C₂²×C₁₁	1	1	yes	characteristic, complemented
203	#498	C₂²×C₁₁	1	1	yes	characteristic, complemented
204	#486	C₂²×C₁₁	1	1	yes	characteristic, complemented
205	#486	C₂²×C₁₁	1	1	yes	characteristic, complemented
206	#483	—	2	1	no	—
207	#482	—	2	2	no	—
208	#481	—	2	1	no	—
209	#478	—	2	2	no	—
210	#476	C₂²×C₁₁	1	2	yes	—
211	#476	C₂²×C₁₁	1	2	yes	—
212	#461	C₂²×C₁₁	1	2	yes	—
213	#459	C₂²×C₁₁	1	2	yes	—
214	#450	—	2	1	no	—
215	#447	—	2	1	no	—
216	#442	—	2	2	no	—
217	C₄×SD₁₆	—	2	2	no	—
218	#436	—	2	2	no	—
219	#436	C₂²×C₁₁	1	2	yes	—
220	#436	C₂²×C₁₁	1	2	yes	—
221	#432	C₂²×C₁₁	1	1	yes	characteristic
222	#431	C₂²×C₁₁	1	1	yes	characteristic
223	#431	C₂²×C₁₁	1	1	yes	characteristic
224	#431	C₂²×C₁₁	1	1	yes	characteristic
225	#407	—	2	2	no	—
226	#335	C₂²×C₁₁	1	2	yes	complemented
227	#334	C₂²×C₁₁	1	2	yes	complemented
228	#333	C₂²×C₁₁	1	2	yes	complemented
229	#333	C₂²×C₁₁	1	2	yes	complemented
230	#332	C₂²×C₁₁	1	2	yes	complemented
231	#331	C₂²×C₁₁	1	2	yes	complemented
232	C₂²×C₁₁	—	2	1	no	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	4	2	no	—
236	C₂²×C₁₁	—	4	2	no	—
237	C₂²×C₁₁	—	4	2	no	—
238	C₂²×C₁₁	—	8	4	no	—
239	C₂²×C₁₁	—	8	1	no	—
240	C₂²×C₁₁	—	8	1	no	—
241	C₂²×C₁₁	—	8	1	no	—
242	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
243	C₄×C₁₁	—	2	1	no	—
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	2	1	no	—
247	C₄×C₁₁	—	4	2	no	—
248	C₄×C₁₁	—	8	1	no	—
249	C₄×C₁₁	—	8	1	no	—
250	C₄×C₁₁	—	8	1	no	—
251	C₄×C₁₁	#575	1	2	yes	—
252	C₄×C₁₁	#577	1	2	yes	—
253	C₂×#41	—	2	1	no	—
254	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
261	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
262	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
263	#127	C₂³×C₁₁	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	#124	—	2	1	no	—
266	C₂²⋊Q₈	—	2	1	no	—
267	C₂²⋊Q₈	—	2	1	no	—
268	#121	—	2	1	no	—
269	#121	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	D₄×C₁₁	1	2	yes	—
277	C₄×D₄	C₂³×C₁₁	1	2	yes	—
278	#117	—	2	1	no	—
279	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
282	#107	—	2	2	no	—
283	#106	—	2	2	no	—
284	#106	—	2	2	no	—
285	#106	—	2	2	no	—
286	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
287	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
288	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
289	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
290	#103	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	—	2	2	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
302	#97	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×C₁₁	—	4	1	no	—
308	C₂×C₁₁	—	8	2	no	—
309	C₂×C₁₁	—	16	1	no	—
310	C₂×C₁₁	#3042	1	1	yes	characteristic
311	C₂×C₁₁	#3054	1	1	yes	characteristic
312	C₂×C₁₁	#3068	1	1	yes	characteristic
313	C₂⁴	—	2	1	no	—
314	#41	—	8	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
332	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
333	SD₁₆	—	4	4	no	—
334	D₈	—	4	4	no	—
335	M₁₆	—	8	2	no	—
336	M₁₆	—	8	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
341	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
360	C₄²	C₁₁×#41	1	1	yes	characteristic
361	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
362	C₁₁	#19430	1	1	yes	characteristic, direct product factor, Sylow
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	8	1	no	—
367	C₂³	—	8	1	no	—
368	C₂³	C₁₁×#121	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
392	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
393	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	C₁₁×#575	1	2	yes	—
422	C₄	C₁₁×#577	1	2	yes	—
423	C₂	—	4	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₁₁×#3042	1	1	yes	characteristic
427	C₂	C₁₁×#3054	1	1	yes	characteristic
428	C₂	C₁₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3109	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3228	C₂	semidirect
3. C₁₁×#3101	C₂	semidirect
4. C₁₁×#2975	C₂	semidirect
5. C₁₁×#1701	C₂	semidirect
6. C₁₁×#1697	C₂	semidirect
7. C₁₁×#1695	C₂	semidirect
8. C₁₁×#1691	C₂	semidirect
9. C₁₁×#1572	C₂	semidirect
10. C₁₁×#1554	C₂	semidirect
11. C₁₁×#1543	C₂	semidirect
15. C₁₁×#500	C₂²	semidirect
16. C₁₁×#498	C₂²	semidirect
17. C₁₁×#486	C₂²	semidirect
18. C₁₁×#486	C₂²	semidirect
39. C₁₁×#335	C₂²	semidirect
40. C₁₁×#334	C₂²	semidirect
41. C₁₁×#333	C₂²	semidirect
42. C₁₁×#333	C₂²	semidirect
43. C₁₁×#332	C₂²	semidirect
44. C₁₁×#331	C₂²	semidirect
99. #19430	C₁₁	direct (N × H)
149. #3228	C₂×C₁₁	semidirect
151. #3101	C₂×C₁₁	semidirect
152. #2975	C₂×C₁₁	semidirect
153. #1701	C₂×C₁₁	semidirect
154. #1697	C₂×C₁₁	semidirect
155. #1695	C₂×C₁₁	semidirect
156. #1691	C₂×C₁₁	semidirect
157. #1572	C₂×C₁₁	semidirect
158. #1554	C₂×C₁₁	semidirect
159. #1543	C₂×C₁₁	semidirect
202. #500	C₂²×C₁₁	semidirect
203. #498	C₂²×C₁₁	semidirect
204. #486	C₂²×C₁₁	semidirect
205. #486	C₂²×C₁₁	semidirect
226. #335	C₂²×C₁₁	semidirect
227. #334	C₂²×C₁₁	semidirect
228. #333	C₂²×C₁₁	semidirect
229. #333	C₂²×C₁₁	semidirect
230. #332	C₂²×C₁₁	semidirect
231. #331	C₂²×C₁₁	semidirect
362. C₁₁	#19430	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×#3228	2
C₁₁×#3109	2
C₁₁×#3101	2
C₁₁×#2975	2
C₁₁×#1701	2
C₁₁×#1697	2
C₁₁×#1695	2
C₁₁×#1691	2
C₁₁×#1572	2
C₁₁×#1554	2
C₁₁×#1543	2
#19430	11

Subgroups — C11×#19430 #14596623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19430 #14596623