Subgroups — C₁₁×#24281 #14601474

Order 2816.

1564 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#472	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3003	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2045	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2018	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1978	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1783	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
12	C₂²×C₁₁×D₈	—	2	8	no	—
13	C₂²×C₁₁×D₈	—	2	2	no	—
14	C₂²×C₁₁×D₈	—	2	2	no	—
15	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
16	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#525	C₂²	1	1	yes	characteristic
20	C₁₁×#472	—	2	8	no	—
21	C₁₁×#450	—	2	4	no	—
22	C₁₁×#447	—	2	4	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
26	C₁₁×#424	C₂²	1	1	yes	characteristic, complemented
27	C₁₁×#418	C₂²	1	4	yes	complemented
28	C₂×C₁₁×#100	C₂²	1	4	yes	complemented
29	C₂×C₁₁×#100	C₂²	1	4	yes	complemented
30	C₁₁×#408	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#407	C₂²	1	1	yes	characteristic
32	C₁₁×#407	C₂²	1	2	yes	—
33	C₁₁×#405	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#341	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₁	—	2	2	no	—
36	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₁	—	2	8	no	—
38	C₂²×D₄×C₁₁	—	2	4	no	—
39	C₂²×D₄×C₁₁	—	2	4	no	—
40	C₂²×D₄×C₁₁	—	2	2	no	—
41	C₂²×D₄×C₁₁	—	4	4	no	—
42	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
45	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
46	C₂×C₁₁×SD₁₆	—	2	4	no	—
47	C₂×C₁₁×D₈	—	2	16	no	—
48	C₂×C₁₁×D₈	—	2	16	no	—
49	C₂×C₁₁×D₈	—	2	8	no	—
50	C₂×C₁₁×D₈	—	2	4	no	—
51	C₂×C₁₁×D₈	—	2	4	no	—
52	C₂×C₁₁×D₈	—	2	2	no	—
53	C₂×C₁₁×D₈	—	2	2	no	—
54	C₂×C₁₁×D₈	—	2	4	no	—
55	C₂×C₁₁×D₈	D₄	1	8	yes	complemented
56	C₁₁×#131	—	2	4	no	—
57	C₂×C₁₁×M₁₆	—	2	1	no	—
58	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
59	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	—	2	4	no	—
62	C₂²×C₈×C₁₁	—	2	1	no	—
63	C₂²×C₈×C₁₁	D₄	1	2	yes	—
64	C₂²×C₈×C₁₁	D₄	1	2	yes	—
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#123	—	2	1	no	—
68	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₁₁×#121	D₄	1	2	yes	—
70	C₁₁×#120	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	2	no	—
72	C₁₁×#117	C₂³	1	1	yes	characteristic
73	C₁₁×#108	—	2	4	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×#102	—	2	8	no	—
76	C₁₁×#100	—	2	8	no	—
77	C₁₁×#100	—	4	4	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	4	no	—
80	C₁₁×C₂²⋊C₈	—	2	2	no	—
81	C₁₁×#97	—	2	1	no	—
82	C₄×C₈×C₁₁	—	2	1	no	—
83	#24281	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	—	2	4	no	—
85	C₂⁴×C₁₁	—	4	8	no	—
86	C₂⁴×C₁₁	—	4	4	no	—
87	C₂⁴×C₁₁	—	8	8	no	—
88	C₂⁴×C₁₁	#41	1	1	yes	characteristic
89	C₁₁×#41	—	2	2	no	—
90	C₁₁×#41	—	2	2	no	—
91	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₁₁	—	2	16	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	2	1	no	—
95	C₂×D₄×C₁₁	—	2	4	no	—
96	C₂×D₄×C₁₁	—	2	4	no	—
97	C₂×D₄×C₁₁	—	2	4	no	—
98	C₂×D₄×C₁₁	—	2	4	no	—
99	C₂×D₄×C₁₁	—	2	4	no	—
100	C₂×D₄×C₁₁	—	4	16	no	—
101	C₂×D₄×C₁₁	—	4	8	no	—
102	C₂×D₄×C₁₁	—	4	8	no	—
103	C₂×D₄×C₁₁	—	4	4	no	—
104	C₂×D₄×C₁₁	C₂×D₄	1	8	yes	—
105	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
113	C₁₁×SD₁₆	—	4	8	no	—
114	C₁₁×D₈	—	2	16	no	—
115	C₁₁×D₈	—	2	8	no	—
116	C₁₁×D₈	—	2	8	no	—
117	C₁₁×D₈	—	4	8	no	—
118	C₁₁×M₁₆	—	2	2	no	—
119	C₁₁×M₁₆	—	2	4	no	—
120	C₁₁×M₁₆	—	2	2	no	—
121	C₁₁×M₁₆	—	2	4	no	—
122	C₁₁×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₁	—	2	4	no	—
124	C₂×C₈×C₁₁	—	2	4	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	4	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	4	2	no	—
130	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
134	C₁₁×C₄⋊C₄	—	2	2	no	—
135	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₁₁×C₂²⋊C₄	—	2	2	no	—
137	C₁₁×C₂²⋊C₄	—	2	1	no	—
138	C₁₁×C₂²⋊C₄	—	2	2	no	—
139	C₄²×C₁₁	—	2	1	no	—
140	C₂³×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
141	C₂×#472	C₂×C₁₁	1	2	yes	complemented
142	#3003	C₂×C₁₁	1	2	yes	complemented
143	#2929	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#2045	C₂×C₁₁	1	2	yes	complemented
145	#2018	C₂×C₁₁	1	2	yes	complemented
146	#1978	C₂×C₁₁	1	2	yes	complemented
147	#1810	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#1783	C₂×C₁₁	1	2	yes	complemented
149	C₂³×C₁₁	—	2	2	no	—
150	C₂³×C₁₁	—	2	4	no	—
151	C₂³×C₁₁	—	2	1	no	—
152	C₂³×C₁₁	—	2	8	no	—
153	C₂³×C₁₁	—	4	16	no	—
154	C₂³×C₁₁	—	4	4	no	—
155	C₂³×C₁₁	—	4	4	no	—
156	C₂³×C₁₁	—	8	8	no	—
157	C₂³×C₁₁	—	8	32	no	—
158	C₂³×C₁₁	—	8	8	no	—
159	C₂³×C₁₁	—	8	8	no	—
160	C₂³×C₁₁	#121	1	2	yes	—
161	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
162	Q₈×C₁₁	—	2	2	no	—
163	D₄×C₁₁	—	2	8	no	—
164	D₄×C₁₁	—	2	2	no	—
165	D₄×C₁₁	—	2	8	no	—
166	D₄×C₁₁	—	4	16	no	—
167	D₄×C₁₁	—	4	2	no	—
168	D₄×C₁₁	—	4	4	no	—
169	D₄×C₁₁	—	4	4	no	—
170	D₄×C₁₁	—	4	4	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	4	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	1	no	—
177	C₂×C₄×C₁₁	—	4	1	no	—
178	C₂×C₄×C₁₁	—	4	1	no	—
179	C₂×C₄×C₁₁	#121	1	2	yes	—
180	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₁₁	—	2	2	no	—
185	C₈×C₁₁	—	4	1	no	—
186	C₈×C₁₁	—	4	1	no	—
187	C₈×C₁₁	—	4	4	no	—
188	C₈×C₁₁	#120	1	2	yes	—
189	C₈×C₁₁	#120	1	2	yes	—
190	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
191	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	4	yes	complemented
192	C₂²×D₈	—	2	8	no	—
193	C₂²×D₈	—	2	2	no	—
194	C₂²×D₈	—	2	2	no	—
195	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
196	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
197	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic, complemented
198	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
199	#525	C₂²×C₁₁	1	1	yes	characteristic
200	#472	—	2	8	no	—
201	#450	—	2	4	no	—
202	#447	—	2	4	no	—
203	#435	—	2	2	no	—
204	C₈×D₄	—	2	2	no	—
205	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
206	#424	C₂²×C₁₁	1	1	yes	characteristic, complemented
207	#418	C₂²×C₁₁	1	4	yes	complemented
208	C₂×#100	C₂²×C₁₁	1	4	yes	complemented
209	C₂×#100	C₂²×C₁₁	1	4	yes	complemented
210	#408	C₂²×C₁₁	1	1	yes	characteristic, complemented
211	#407	C₂²×C₁₁	1	2	yes	—
212	#407	C₂²×C₁₁	1	1	yes	characteristic
213	#405	C₂²×C₁₁	1	1	yes	characteristic, complemented
214	#341	C₂²×C₁₁	1	2	yes	complemented
215	C₂²×C₁₁	—	2	8	no	—
216	C₂²×C₁₁	—	2	2	no	—
217	C₂²×C₁₁	—	2	2	no	—
218	C₂²×C₁₁	—	2	2	no	—
219	C₂²×C₁₁	—	4	1	no	—
220	C₂²×C₁₁	—	4	8	no	—
221	C₂²×C₁₁	—	4	2	no	—
222	C₂²×C₁₁	—	8	8	no	—
223	C₂²×C₁₁	—	8	8	no	—
224	C₂²×C₁₁	—	8	32	no	—
225	C₂²×C₁₁	—	8	8	no	—
226	C₂²×C₁₁	#472	1	4	yes	complemented
227	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
228	C₂²×C₁₁	#546	1	2	yes	—
229	C₄×C₁₁	—	2	2	no	—
230	C₄×C₁₁	—	4	1	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
233	C₄×C₁₁	#535	1	1	yes	characteristic
234	C₄×C₁₁	D₄²	1	2	yes	—
235	C₂⁵	—	2	2	no	—
236	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
237	C₂²×D₄	—	2	8	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	4	4	no	—
242	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
243	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
244	AGL(1,ℤ/8)	—	2	8	no	—
245	AGL(1,ℤ/8)	—	4	4	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×D₈	—	2	16	no	—
248	C₂×D₈	—	2	16	no	—
249	C₂×D₈	—	2	8	no	—
250	C₂×D₈	—	2	4	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	D₄×C₁₁	1	8	yes	complemented
256	#131	—	2	4	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
260	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	D₄×C₁₁	1	2	yes	—
264	C₂²×C₈	D₄×C₁₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
267	#123	—	2	1	no	—
268	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
269	#121	D₄×C₁₁	1	2	yes	—
270	#120	—	2	1	no	—
271	C₄×D₄	—	2	2	no	—
272	#117	C₂³×C₁₁	1	1	yes	characteristic
273	#108	—	2	4	no	—
274	C₄⋊C₈	—	2	2	no	—
275	#102	—	2	8	no	—
276	#100	—	2	8	no	—
277	#100	—	4	4	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#97	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₂×C₁₁	—	2	2	no	—
284	C₂×C₁₁	—	2	4	no	—
285	C₂×C₁₁	—	8	1	no	—
286	C₂×C₁₁	—	8	8	no	—
287	C₂×C₁₁	#2408	1	1	yes	characteristic
288	C₂×C₁₁	C₂×#472	1	2	yes	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	4	8	no	—
291	C₂⁴	—	4	4	no	—
292	C₂⁴	—	8	8	no	—
293	C₂⁴	C₁₁×#41	1	1	yes	characteristic
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
297	C₂×D₄	—	2	16	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	4	16	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	C₂×D₄×C₁₁	1	8	yes	—
310	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
316	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
318	SD₁₆	—	4	8	no	—
319	D₈	—	2	16	no	—
320	D₈	—	2	8	no	—
321	D₈	—	2	8	no	—
322	D₈	—	4	8	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₁₁	#24281	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	4	16	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	4	no	—
353	C₂³	—	8	8	no	—
354	C₂³	—	8	32	no	—
355	C₂³	—	8	8	no	—
356	C₂³	—	8	8	no	—
357	C₂³	C₁₁×#121	1	2	yes	—
358	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	8	no	—
363	D₄	—	4	16	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	C₁₁×#121	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
379	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
380	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
381	C₈	—	2	2	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	4	no	—
385	C₈	C₁₁×#120	1	2	yes	—
386	C₈	C₁₁×#120	1	2	yes	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	8	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	8	8	no	—
395	C₂²	—	8	8	no	—
396	C₂²	—	8	32	no	—
397	C₂²	—	8	8	no	—
398	C₂²	C₁₁×#472	1	4	yes	complemented
399	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
400	C₂²	C₁₁×#546	1	2	yes	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
405	C₄	C₁₁×#535	1	1	yes	characteristic
406	C₄	D₄²×C₁₁	1	2	yes	—
407	C₂	—	2	2	no	—
408	C₂	—	2	4	no	—
409	C₂	—	8	1	no	—
410	C₂	—	8	8	no	—
411	C₂	C₁₁×#2408	1	1	yes	characteristic
412	C₂	C₂×C₁₁×#472	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×D₈	C₂	semidirect
2. C₂×C₁₁×#472	C₂	semidirect
3. C₁₁×#3003	C₂	semidirect
4. C₁₁×#2929	C₂	semidirect
5. C₁₁×#2045	C₂	semidirect
6. C₁₁×#2018	C₂	semidirect
7. C₁₁×#1978	C₂	semidirect
8. C₁₁×#1810	C₂	semidirect
9. C₁₁×#1783	C₂	semidirect
11. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₁×#131	C₂²	semidirect
25. C₂×C₁₁×#108	C₂²	semidirect
26. C₁₁×#424	C₂²	semidirect
27. C₁₁×#418	C₂²	semidirect
28. C₂×C₁₁×#100	C₂²	semidirect
29. C₂×C₁₁×#100	C₂²	semidirect
30. C₁₁×#408	C₂²	semidirect
33. C₁₁×#405	C₂²	semidirect
34. C₁₁×#341	C₂²	semidirect
55. C₂×C₁₁×D₈	D₄	semidirect
83. #24281	C₁₁	direct (N × H)
140. C₂³×D₈	C₂×C₁₁	semidirect
141. C₂×#472	C₂×C₁₁	semidirect
142. #3003	C₂×C₁₁	semidirect
143. #2929	C₂×C₁₁	semidirect
144. #2045	C₂×C₁₁	semidirect
145. #2018	C₂×C₁₁	semidirect
146. #1978	C₂×C₁₁	semidirect
147. #1810	C₂×C₁₁	semidirect
148. #1783	C₂×C₁₁	semidirect
191. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
197. C₂×#131	C₂²×C₁₁	semidirect
205. C₂×#108	C₂²×C₁₁	semidirect
206. #424	C₂²×C₁₁	semidirect
207. #418	C₂²×C₁₁	semidirect
208. C₂×#100	C₂²×C₁₁	semidirect
209. C₂×#100	C₂²×C₁₁	semidirect
210. #408	C₂²×C₁₁	semidirect
213. #405	C₂²×C₁₁	semidirect
214. #341	C₂²×C₁₁	semidirect
226. C₂²×C₁₁	#472	semidirect
255. C₂×D₈	D₄×C₁₁	semidirect
345. C₁₁	#24281	direct (N × H)
398. C₂²	C₁₁×#472	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₁×D₈	2
C₂×C₁₁×#472	2
C₁₁×#3003	2
C₁₁×#2929	2
C₁₁×#2045	2
C₁₁×#2018	2
C₁₁×#1978	2
C₁₁×#1810	2
C₁₁×#1783	2
#24281	11

Subgroups — C11×#24281 #14601474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24281 #14601474