Subgroups — C₁₁×#19422 #14596615

Order 2816.

768 conjugacy classes of subgroups.

The subgroup lattice has 436 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, complemented
2	C₁₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1701	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1687	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×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×C₁₁×D₈	—	2	1	no	—
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#493	C₂²	1	2	yes	complemented
16	C₁₁×#486	C₂²	1	2	yes	complemented
17	C₁₁×#463	—	2	2	no	—
18	C₁₁×#461	C₂²	1	2	yes	complemented
19	C₁₁×#459	—	2	2	no	—
20	C₁₁×#459	—	2	2	no	—
21	C₁₁×#459	C₂²	1	4	yes	—
22	C₁₁×#459	C₂²	1	2	yes	complemented
23	C₁₁×#447	—	2	2	no	—
24	C₁₁×#436	—	2	2	no	—
25	C₁₁×#436	C₂²	1	4	yes	complemented
26	C₁₁×#431	C₂²	1	1	yes	characteristic
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₁×#417	—	2	1	no	—
31	C₂×C₁₁×#102	—	2	1	no	—
32	C₁₁×#407	—	2	2	no	—
33	C₁₁×#334	C₂²	1	4	yes	complemented
34	C₁₁×#332	C₂²	1	2	yes	complemented
35	C₁₁×#331	C₂²	1	2	yes	complemented
36	C₁₁×#331	C₂²	1	4	yes	complemented
37	C₂×C₁₁×#41	—	2	1	no	—
38	C₂²×D₄×C₁₁	—	2	1	no	—
39	C₂²×D₄×C₁₁	—	2	1	no	—
40	C₂²×D₄×C₁₁	—	2	1	no	—
41	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁	—	2	1	no	—
43	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
44	C₂×C₁₁×SD₁₆	—	2	2	no	—
45	C₂×C₁₁×D₈	—	2	4	no	—
46	C₂×C₁₁×D₈	—	2	2	no	—
47	C₂×C₁₁×D₈	—	2	4	no	—
48	C₂×C₁₁×D₈	—	4	4	no	—
49	C₂×C₁₁×M₁₆	—	2	1	no	—
50	C₂×C₁₁×M₁₆	—	2	4	no	—
51	C₂²×C₈×C₁₁	—	2	1	no	—
52	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₁₁×#127	—	2	1	no	—
54	C₁₁×#127	—	2	1	no	—
55	C₁₁×#127	—	2	1	no	—
56	C₁₁×#127	C₂³	1	1	yes	characteristic
57	C₁₁×#127	C₂³	1	2	yes	—
58	C₁₁×#124	—	2	1	no	—
59	C₁₁×#121	—	2	1	no	—
60	C₁₁×#121	—	2	1	no	—
61	C₄×D₄×C₁₁	—	2	1	no	—
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	D₄	1	2	yes	—
66	C₄×D₄×C₁₁	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
82	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
83	C₄×C₈×C₁₁	—	2	1	no	—
84	C₄×C₈×C₁₁	C₂³	1	2	yes	—
85	#19422	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	—	2	1	no	—
87	C₂⁴×C₁₁	—	4	1	no	—
88	C₁₁×#41	—	4	2	no	—
89	C₁₁×#41	—	4	2	no	—
90	C₂×Q₈×C₁₁	—	2	1	no	—
91	C₂×D₄×C₁₁	—	2	1	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
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	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	4	1	no	—
113	C₂²×C₄×C₁₁	—	8	2	no	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
117	C₁₁×SD₁₆	—	4	4	no	—
118	C₁₁×D₈	—	4	8	no	—
119	C₁₁×D₈	—	4	4	no	—
120	C₁₁×D₈	—	8	4	no	—
121	C₁₁×M₁₆	—	4	2	no	—
122	C₁₁×M₁₆	—	8	4	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	4	2	no	—
127	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
128	C₁₁×C₄⋊C₄	—	2	1	no	—
129	C₁₁×C₄⋊C₄	—	2	1	no	—
130	C₁₁×C₄⋊C₄	—	2	1	no	—
131	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
132	C₁₁×C₂²⋊C₄	—	2	2	no	—
133	C₁₁×C₂²⋊C₄	—	2	2	no	—
134	C₁₁×C₂²⋊C₄	—	4	1	no	—
135	C₁₁×C₂²⋊C₄	—	4	1	no	—
136	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₁	#41	1	1	yes	characteristic
139	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
140	#3205	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#3036	C₂×C₁₁	1	1	yes	characteristic, complemented
142	C₂×#459	C₂×C₁₁	1	1	yes	characteristic, complemented
143	#2975	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#1701	C₂×C₁₁	1	4	yes	complemented
145	#1687	C₂×C₁₁	1	4	yes	complemented
146	#1570	C₂×C₁₁	1	1	yes	characteristic, complemented
147	#1545	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#1540	C₂×C₁₁	1	1	yes	characteristic, complemented
149	C₂³×C₁₁	—	2	2	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	1	no	—
152	C₂³×C₁₁	—	4	2	no	—
153	C₂³×C₁₁	—	8	1	no	—
154	C₂³×C₁₁	—	8	1	no	—
155	C₂³×C₁₁	—	8	2	no	—
156	C₂³×C₁₁	—	8	2	no	—
157	C₂³×C₁₁	—	8	2	no	—
158	C₂³×C₁₁	#121	1	1	yes	characteristic
159	Q₈×C₁₁	—	4	1	no	—
160	Q₈×C₁₁	—	4	1	no	—
161	D₄×C₁₁	—	2	2	no	—
162	D₄×C₁₁	—	2	2	no	—
163	D₄×C₁₁	—	4	2	no	—
164	D₄×C₁₁	—	4	1	no	—
165	D₄×C₁₁	—	4	2	no	—
166	D₄×C₁₁	—	4	1	no	—
167	D₄×C₁₁	—	4	2	no	—
168	D₄×C₁₁	—	4	4	no	—
169	D₄×C₁₁	—	4	2	no	—
170	D₄×C₁₁	—	8	1	no	—
171	D₄×C₁₁	—	8	2	no	—
172	D₄×C₁₁	—	8	2	no	—
173	D₄×C₁₁	—	8	2	no	—
174	D₄×C₁₁	—	8	2	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	—	4	1	no	—
179	C₂×C₄×C₁₁	—	4	4	no	—
180	C₂×C₄×C₁₁	—	4	1	no	—
181	C₂×C₄×C₁₁	—	8	2	no	—
182	C₂×C₄×C₁₁	—	8	1	no	—
183	C₂×C₄×C₁₁	—	8	2	no	—
184	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₁	—	2	4	no	—
193	C₈×C₁₁	—	4	2	no	—
194	C₈×C₁₁	—	4	2	no	—
195	C₈×C₁₁	—	4	2	no	—
196	C₂×AGL(1,ℤ/8)	—	2	1	no	—
197	C₂²×D₈	—	2	1	no	—
198	#532	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
201	#493	C₂²×C₁₁	1	2	yes	complemented
202	#486	C₂²×C₁₁	1	2	yes	complemented
203	#463	—	2	2	no	—
204	#461	C₂²×C₁₁	1	2	yes	complemented
205	#459	—	2	2	no	—
206	#459	—	2	2	no	—
207	#459	C₂²×C₁₁	1	4	yes	—
208	#459	C₂²×C₁₁	1	2	yes	complemented
209	#447	—	2	2	no	—
210	#436	—	2	2	no	—
211	#436	C₂²×C₁₁	1	4	yes	complemented
212	#431	C₂²×C₁₁	1	1	yes	characteristic
213	#431	C₂²×C₁₁	1	1	yes	characteristic
214	#423	C₂²×C₁₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
216	#417	—	2	1	no	—
217	C₂×#102	—	2	1	no	—
218	#407	—	2	2	no	—
219	#334	C₂²×C₁₁	1	4	yes	complemented
220	#332	C₂²×C₁₁	1	2	yes	complemented
221	#331	C₂²×C₁₁	1	2	yes	complemented
222	#331	C₂²×C₁₁	1	4	yes	complemented
223	C₂²×C₁₁	—	2	1	no	—
224	C₂²×C₁₁	—	2	1	no	—
225	C₂²×C₁₁	—	4	2	no	—
226	C₂²×C₁₁	—	4	2	no	—
227	C₂²×C₁₁	—	4	2	no	—
228	C₂²×C₁₁	—	8	4	no	—
229	C₂²×C₁₁	—	8	2	no	—
230	C₂²×C₁₁	—	8	1	no	—
231	C₂²×C₁₁	—	8	1	no	—
232	C₂²×C₁₁	—	8	2	no	—
233	C₂²×C₁₁	—	8	2	no	—
234	C₂²×C₁₁	—	8	1	no	—
235	C₂²×C₁₁	—	16	4	no	—
236	C₂²×C₁₁	#469	1	2	yes	—
237	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
238	C₄×C₁₁	—	2	1	no	—
239	C₄×C₁₁	—	2	1	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	4	2	no	—
242	C₄×C₁₁	—	8	1	no	—
243	C₄×C₁₁	#469	1	2	yes	—
244	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₄×C₁₁	#576	1	2	yes	—
247	C₂×#41	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	AGL(1,ℤ/8)	—	4	4	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×D₈	—	4	4	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	C₂³×C₁₁	1	2	yes	—
267	#127	C₂³×C₁₁	1	1	yes	characteristic
268	#124	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	D₄×C₁₁	1	2	yes	—
276	C₄×D₄	C₂³×C₁₁	1	2	yes	—
277	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
283	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
284	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
285	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
286	#103	—	2	2	no	—
287	#102	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	4	no	—
292	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	C₂³×C₁₁	1	2	yes	—
295	C₂×C₁₁	—	2	2	no	—
296	C₂×C₁₁	—	8	2	no	—
297	C₂×C₁₁	—	16	1	no	—
298	C₂×C₁₁	—	16	2	no	—
299	C₂×C₁₁	#3041	1	1	yes	characteristic
300	C₂×C₁₁	C₂×#469	1	1	yes	characteristic
301	C₂×C₁₁	#3068	1	1	yes	characteristic
302	C₂⁴	—	2	1	no	—
303	C₂⁴	—	4	1	no	—
304	#41	—	4	2	no	—
305	#41	—	4	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂×D₄	—	8	2	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	8	no	—
335	D₈	—	4	4	no	—
336	D₈	—	8	4	no	—
337	M₁₆	—	4	2	no	—
338	M₁₆	—	8	4	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₄²	C₁₁×#41	1	1	yes	characteristic
355	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
356	C₁₁	#19422	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³	—	2	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	—	8	2	no	—
364	C₂³	—	8	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	C₁₁×#121	1	1	yes	characteristic
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	2	no	—
383	D₄	—	8	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
393	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
394	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
395	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
396	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	16	4	no	—
417	C₂²	C₁₁×#469	1	2	yes	—
418	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	1	no	—
424	C₄	C₁₁×#469	1	2	yes	—
425	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₄	C₁₁×#576	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	8	2	no	—
430	C₂	—	16	2	no	—
431	C₂	—	16	1	no	—
432	C₂	C₁₁×#3041	1	1	yes	characteristic
433	C₂	C₂×C₁₁×#469	1	1	yes	characteristic
434	C₂	C₁₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
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×#3205	C₂	semidirect
2. C₁₁×#3036	C₂	semidirect
3. C₂×C₁₁×#459	C₂	semidirect
4. C₁₁×#2975	C₂	semidirect
5. C₁₁×#1701	C₂	semidirect
6. C₁₁×#1687	C₂	semidirect
7. C₁₁×#1570	C₂	semidirect
8. C₁₁×#1545	C₂	semidirect
9. C₁₁×#1540	C₂	semidirect
15. C₁₁×#493	C₂²	semidirect
16. C₁₁×#486	C₂²	semidirect
18. C₁₁×#461	C₂²	semidirect
22. C₁₁×#459	C₂²	semidirect
25. C₁₁×#436	C₂²	semidirect
33. C₁₁×#334	C₂²	semidirect
34. C₁₁×#332	C₂²	semidirect
35. C₁₁×#331	C₂²	semidirect
36. C₁₁×#331	C₂²	semidirect
85. #19422	C₁₁	direct (N × H)
140. #3205	C₂×C₁₁	semidirect
141. #3036	C₂×C₁₁	semidirect
142. C₂×#459	C₂×C₁₁	semidirect
143. #2975	C₂×C₁₁	semidirect
144. #1701	C₂×C₁₁	semidirect
145. #1687	C₂×C₁₁	semidirect
146. #1570	C₂×C₁₁	semidirect
147. #1545	C₂×C₁₁	semidirect
148. #1540	C₂×C₁₁	semidirect
201. #493	C₂²×C₁₁	semidirect
202. #486	C₂²×C₁₁	semidirect
204. #461	C₂²×C₁₁	semidirect
208. #459	C₂²×C₁₁	semidirect
211. #436	C₂²×C₁₁	semidirect
219. #334	C₂²×C₁₁	semidirect
220. #332	C₂²×C₁₁	semidirect
221. #331	C₂²×C₁₁	semidirect
222. #331	C₂²×C₁₁	semidirect
356. C₁₁	#19422	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×#3036	2
C₂×C₁₁×#459	2
C₁₁×#2975	2
C₁₁×#1701	2
C₁₁×#1687	2
C₁₁×#1570	2
C₁₁×#1545	2
C₁₁×#1540	2
#19422	11

Subgroups — C11×#19422 #14596615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19422 #14596615