Subgroups — C₁₁×#19434 #14596627

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3205	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1702	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1688	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#137	—	2	1	no	—
11	C₂²×C₁₁×SD₁₆	—	2	1	no	—
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#493	C₂²	1	2	yes	—
16	C₁₁×#486	C₂²	1	2	yes	—
17	C₁₁×#464	—	2	2	no	—
18	C₁₁×#462	C₂²	1	2	yes	complemented
19	C₁₁×#460	—	2	2	no	—
20	C₁₁×#460	C₂²	1	4	yes	—
21	C₁₁×#460	C₂²	1	2	yes	complemented
22	C₁₁×#459	—	2	2	no	—
23	C₁₁×#447	—	2	2	no	—
24	C₁₁×#446	—	2	2	no	—
25	C₁₁×#446	C₂²	1	4	yes	complemented
26	C₁₁×#432	—	2	2	no	—
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#431	C₂²	1	1	yes	characteristic
29	C₁₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₁×#417	—	2	1	no	—
32	C₂×C₁₁×#102	—	2	1	no	—
33	C₁₁×#334	C₂²	1	4	yes	complemented
34	C₁₁×#332	C₂²	1	2	yes	complemented
35	C₁₁×#331	C₂²	1	4	yes	—
36	C₁₁×#331	C₂²	1	2	yes	complemented
37	C₂×C₁₁×#41	—	2	1	no	—
38	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₁	—	2	1	no	—
40	C₂²×D₄×C₁₁	—	2	1	no	—
41	C₂²×D₄×C₁₁	—	2	1	no	—
42	C₁₁×#137	—	4	4	no	—
43	C₂×C₁₁×Q₁₆	—	2	2	no	—
44	C₂×C₁₁×SD₁₆	—	2	4	no	—
45	C₂×C₁₁×SD₁₆	—	2	2	no	—
46	C₂×C₁₁×SD₁₆	—	4	4	no	—
47	C₂×C₁₁×D₈	—	2	4	no	—
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
51	C₁₁×#127	—	2	1	no	—
52	C₁₁×#127	—	2	1	no	—
53	C₁₁×#127	—	2	1	no	—
54	C₁₁×#127	C₂³	1	1	yes	characteristic
55	C₁₁×#127	C₂³	1	2	yes	—
56	C₁₁×#124	—	2	1	no	—
57	C₁₁×#121	—	2	1	no	—
58	C₁₁×#121	—	2	1	no	—
59	C₄×Q₈×C₁₁	—	2	1	no	—
60	C₄×Q₈×C₁₁	—	2	1	no	—
61	C₄×Q₈×C₁₁	D₄	1	2	yes	—
62	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	—	2	1	no	—
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	—	2	4	no	—
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	—	2	1	no	—
72	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
73	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₁×#103	—	2	2	no	—
77	C₁₁×#102	—	2	4	no	—
78	C₁₁×#102	—	2	4	no	—
79	C₁₁×#102	—	2	2	no	—
80	C₁₁×C₂²⋊C₈	—	2	1	no	—
81	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
82	C₁₁×#97	—	2	4	no	—
83	C₄×C₈×C₁₁	—	2	1	no	—
84	C₄×C₈×C₁₁	C₂³	1	2	yes	—
85	#19434	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	—	4	1	no	—
87	C₁₁×#41	—	4	2	no	—
88	C₁₁×#41	—	4	2	no	—
89	C₂×Q₈×C₁₁	—	2	1	no	—
90	C₂×Q₈×C₁₁	—	2	2	no	—
91	C₂×Q₈×C₁₁	—	2	2	no	—
92	C₂×Q₈×C₁₁	—	2	1	no	—
93	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₁₁	—	2	1	no	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	1	no	—
98	C₂×D₄×C₁₁	—	2	1	no	—
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	4	1	no	—
101	C₂×D₄×C₁₁	—	4	1	no	—
102	C₂×D₄×C₁₁	—	4	1	no	—
103	C₂×D₄×C₁₁	—	4	1	no	—
104	C₂×D₄×C₁₁	—	4	2	no	—
105	C₂×D₄×C₁₁	—	4	2	no	—
106	C₂×D₄×C₁₁	—	8	2	no	—
107	C₂×D₄×C₁₁	—	8	2	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	4	1	no	—
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
114	C₁₁×Q₁₆	—	4	4	no	—
115	C₁₁×SD₁₆	—	4	8	no	—
116	C₁₁×SD₁₆	—	4	4	no	—
117	C₁₁×D₈	—	8	4	no	—
118	C₁₁×M₁₆	—	4	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	4	2	no	—
123	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	2	1	no	—
126	C₁₁×C₄⋊C₄	—	2	2	no	—
127	C₁₁×C₄⋊C₄	—	2	1	no	—
128	C₁₁×C₄⋊C₄	—	2	1	no	—
129	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
130	C₁₁×C₂²⋊C₄	—	4	1	no	—
131	C₁₁×C₂²⋊C₄	—	4	1	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	—	2	2	no	—
134	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₁	#41	1	1	yes	characteristic
137	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
138	#3205	C₂×C₁₁	1	1	yes	characteristic
139	#3037	C₂×C₁₁	1	1	yes	characteristic, complemented
140	C₂×#460	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#2983	C₂×C₁₁	1	1	yes	characteristic, complemented
142	#1702	C₂×C₁₁	1	4	yes	complemented
143	#1688	C₂×C₁₁	1	4	yes	complemented
144	#1570	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#1545	C₂×C₁₁	1	1	yes	characteristic, complemented
146	#1540	C₂×C₁₁	1	1	yes	characteristic, complemented
147	C₂³×C₁₁	—	4	1	no	—
148	C₂³×C₁₁	—	4	2	no	—
149	C₂³×C₁₁	—	8	2	no	—
150	C₂³×C₁₁	—	8	2	no	—
151	C₂³×C₁₁	—	8	2	no	—
152	C₂³×C₁₁	#121	1	1	yes	characteristic
153	Q₈×C₁₁	—	2	2	no	—
154	Q₈×C₁₁	—	2	2	no	—
155	Q₈×C₁₁	—	4	2	no	—
156	Q₈×C₁₁	—	4	1	no	—
157	Q₈×C₁₁	—	4	1	no	—
158	D₄×C₁₁	—	4	2	no	—
159	D₄×C₁₁	—	4	1	no	—
160	D₄×C₁₁	—	4	2	no	—
161	D₄×C₁₁	—	4	1	no	—
162	D₄×C₁₁	—	4	2	no	—
163	D₄×C₁₁	—	4	4	no	—
164	D₄×C₁₁	—	8	1	no	—
165	D₄×C₁₁	—	8	2	no	—
166	D₄×C₁₁	—	8	2	no	—
167	D₄×C₁₁	—	8	2	no	—
168	D₄×C₁₁	—	8	2	no	—
169	D₄×C₁₁	—	8	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	4	1	no	—
174	C₂×C₄×C₁₁	—	4	2	no	—
175	C₂×C₄×C₁₁	—	4	1	no	—
176	C₂×C₄×C₁₁	—	8	1	no	—
177	C₂×C₄×C₁₁	—	8	2	no	—
178	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
186	C₈×C₁₁	—	2	4	no	—
187	C₈×C₁₁	—	4	2	no	—
188	C₈×C₁₁	—	4	2	no	—
189	C₈×C₁₁	—	4	2	no	—
190	C₂×#137	—	2	1	no	—
191	C₂²×SD₁₆	—	2	1	no	—
192	#532	C₂²×C₁₁	1	1	yes	characteristic
193	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
195	#493	C₂²×C₁₁	1	2	yes	—
196	#486	C₂²×C₁₁	1	2	yes	—
197	#464	—	2	2	no	—
198	#462	C₂²×C₁₁	1	2	yes	complemented
199	#460	—	2	2	no	—
200	#460	C₂²×C₁₁	1	4	yes	—
201	#460	C₂²×C₁₁	1	2	yes	complemented
202	#459	—	2	2	no	—
203	#447	—	2	2	no	—
204	#446	—	2	2	no	—
205	#446	C₂²×C₁₁	1	4	yes	complemented
206	#432	—	2	2	no	—
207	#431	C₂²×C₁₁	1	1	yes	characteristic
208	#431	C₂²×C₁₁	1	1	yes	characteristic
209	#423	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
211	#417	—	2	1	no	—
212	C₂×#102	—	2	1	no	—
213	#334	C₂²×C₁₁	1	4	yes	complemented
214	#332	C₂²×C₁₁	1	2	yes	complemented
215	#331	C₂²×C₁₁	1	4	yes	—
216	#331	C₂²×C₁₁	1	2	yes	complemented
217	C₂²×C₁₁	—	2	1	no	—
218	C₂²×C₁₁	—	2	1	no	—
219	C₂²×C₁₁	—	8	2	no	—
220	C₂²×C₁₁	—	8	1	no	—
221	C₂²×C₁₁	—	8	1	no	—
222	C₂²×C₁₁	—	8	2	no	—
223	C₂²×C₁₁	—	8	2	no	—
224	C₂²×C₁₁	—	8	1	no	—
225	C₂²×C₁₁	—	16	4	no	—
226	C₂²×C₁₁	#469	1	2	yes	—
227	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
228	C₄×C₁₁	—	2	1	no	—
229	C₄×C₁₁	—	2	1	no	—
230	C₄×C₁₁	—	2	1	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	—	4	2	no	—
233	C₄×C₁₁	—	8	1	no	—
234	C₄×C₁₁	#469	1	2	yes	—
235	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₄×C₁₁	#577	1	2	yes	—
238	C₂×#41	—	2	1	no	—
239	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	#137	—	4	4	no	—
244	C₂×Q₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	4	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	4	4	no	—
248	C₂×D₈	—	2	4	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	C₂³×C₁₁	1	2	yes	—
256	#127	C₂³×C₁₁	1	1	yes	characteristic
257	#124	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	D₄×C₁₁	1	2	yes	—
263	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
274	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
275	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
277	#103	—	2	2	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	2	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
283	#97	—	2	4	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	C₂³×C₁₁	1	2	yes	—
286	C₂×C₁₁	—	2	2	no	—
287	C₂×C₁₁	—	16	1	no	—
288	C₂×C₁₁	—	16	2	no	—
289	C₂×C₁₁	#3043	1	1	yes	characteristic
290	C₂×C₁₁	C₂×#469	1	1	yes	characteristic
291	C₂×C₁₁	#3068	1	1	yes	characteristic
292	C₂⁴	—	4	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
319	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
320	Q₁₆	—	4	4	no	—
321	SD₁₆	—	4	8	no	—
322	SD₁₆	—	4	4	no	—
323	D₈	—	8	4	no	—
324	M₁₆	—	4	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
342	C₄²	C₁₁×#41	1	1	yes	characteristic
343	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
344	C₁₁	#19434	1	1	yes	characteristic, direct product factor, Sylow
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₁₁×#121	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
377	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
378	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
379	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
380	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	16	4	no	—
397	C₂²	C₁₁×#469	1	2	yes	—
398	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	1	no	—
405	C₄	C₁₁×#469	1	2	yes	—
406	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₄	C₁₁×#577	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	16	2	no	—
411	C₂	—	16	1	no	—
412	C₂	C₁₁×#3043	1	1	yes	characteristic
413	C₂	C₂×C₁₁×#469	1	1	yes	characteristic
414	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×#3205	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
2. C₁₁×#3037	C₂	semidirect
3. C₂×C₁₁×#460	C₂	semidirect
4. C₁₁×#2983	C₂	semidirect
5. C₁₁×#1702	C₂	semidirect
6. C₁₁×#1688	C₂	semidirect
7. C₁₁×#1570	C₂	semidirect
8. C₁₁×#1545	C₂	semidirect
9. C₁₁×#1540	C₂	semidirect
18. C₁₁×#462	C₂²	semidirect
21. C₁₁×#460	C₂²	semidirect
25. C₁₁×#446	C₂²	semidirect
33. C₁₁×#334	C₂²	semidirect
34. C₁₁×#332	C₂²	semidirect
36. C₁₁×#331	C₂²	semidirect
85. #19434	C₁₁	direct (N × H)
139. #3037	C₂×C₁₁	semidirect
140. C₂×#460	C₂×C₁₁	semidirect
141. #2983	C₂×C₁₁	semidirect
142. #1702	C₂×C₁₁	semidirect
143. #1688	C₂×C₁₁	semidirect
144. #1570	C₂×C₁₁	semidirect
145. #1545	C₂×C₁₁	semidirect
146. #1540	C₂×C₁₁	semidirect
198. #462	C₂²×C₁₁	semidirect
201. #460	C₂²×C₁₁	semidirect
205. #446	C₂²×C₁₁	semidirect
213. #334	C₂²×C₁₁	semidirect
214. #332	C₂²×C₁₁	semidirect
216. #331	C₂²×C₁₁	semidirect
344. C₁₁	#19434	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×#3205	2
C₁₁×#3037	2
C₂×C₁₁×#460	2
C₁₁×#2983	2
C₁₁×#1702	2
C₁₁×#1688	2
C₁₁×#1570	2
C₁₁×#1545	2
C₁₁×#1540	2
#19434	11

Subgroups — C11×#19434 #14596627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19434 #14596627