Subgroups — C₁₁×#19186 #14596379

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3205	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1685	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1665	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×SD₁₆	—	2	1	no	—
11	C₂²×C₁₁×SD₁₆	—	2	1	no	—
12	C₂×C₁₁×#131	—	2	1	no	—
13	C₁₁×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
16	C₁₁×#500	—	2	1	no	—
17	C₁₁×#493	—	2	1	no	—
18	C₁₁×#492	—	2	1	no	—
19	C₁₁×#492	—	2	1	no	—
20	C₁₁×#492	C₂²	1	2	yes	—
21	C₁₁×#492	C₂²	1	2	yes	—
22	C₁₁×#486	—	2	1	no	—
23	C₁₁×#486	—	2	1	no	—
24	C₁₁×#480	—	2	2	no	—
25	C₁₁×#474	C₂²	1	4	yes	complemented
26	C₁₁×#459	C₂²	1	4	yes	—
27	C₁₁×#447	—	2	2	no	—
28	C₁₁×#436	—	2	1	no	—
29	C₁₁×#436	C₂²	1	2	yes	complemented
30	C₈×D₄×C₁₁	—	2	1	no	—
31	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
32	C₁₁×#431	C₂²	1	1	yes	characteristic
33	C₁₁×#431	C₂²	1	1	yes	characteristic
34	C₁₁×#423	C₂²	1	1	yes	characteristic
35	C₁₁×#408	—	2	1	no	—
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	2	yes	complemented
38	C₁₁×#334	C₂²	1	2	yes	complemented
39	C₁₁×#332	C₂²	1	4	yes	complemented
40	C₁₁×#331	C₂²	1	4	yes	—
41	C₂×C₁₁×#41	—	2	1	no	—
42	C₂²×Q₈×C₁₁	—	2	1	no	—
43	C₂²×D₄×C₁₁	—	2	1	no	—
44	C₂²×D₄×C₁₁	—	2	1	no	—
45	C₂²×D₄×C₁₁	—	2	1	no	—
46	C₂×C₁₁×SD₁₆	—	2	2	no	—
47	C₂×C₁₁×SD₁₆	—	2	2	no	—
48	C₂×C₁₁×SD₁₆	—	2	2	no	—
49	C₂×C₁₁×SD₁₆	—	2	2	no	—
50	C₂×C₁₁×SD₁₆	—	4	4	no	—
51	C₂×C₁₁×SD₁₆	—	4	4	no	—
52	C₂×C₁₁×D₈	—	2	4	no	—
53	C₁₁×#131	—	4	4	no	—
54	C₂×C₁₁×M₁₆	—	2	1	no	—
55	C₂×C₁₁×M₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₁	—	2	2	no	—
57	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
59	C₁₁×C₄⋊Q₈	—	2	1	no	—
60	C₁₁×C₄⋊Q₈	—	2	1	no	—
61	C₁₁×C₄⋊Q₈	—	2	1	no	—
62	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₁×#127	—	2	1	no	—
65	C₁₁×#127	—	2	1	no	—
66	C₁₁×#127	—	2	1	no	—
67	C₁₁×#127	D₄	1	1	yes	characteristic
68	C₁₁×#127	C₂³	1	2	yes	—
69	C₁₁×#124	—	2	1	no	—
70	C₁₁×#121	—	2	1	no	—
71	C₁₁×#121	D₄	1	2	yes	—
72	C₄×D₄×C₁₁	—	2	1	no	—
73	C₄×D₄×C₁₁	C₂³	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#107	—	2	4	no	—
78	C₁₁×C₄⋊C₈	—	2	1	no	—
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×#102	—	2	4	no	—
83	C₁₁×#102	—	2	4	no	—
84	C₁₁×C₂²⋊C₈	—	2	1	no	—
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×C₂²⋊C₈	—	2	2	no	—
87	C₁₁×C₂²⋊C₈	—	2	2	no	—
88	C₄×C₈×C₁₁	—	2	1	no	—
89	C₄×C₈×C₁₁	—	2	1	no	—
90	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
94	#19186	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₁	—	4	1	no	—
96	C₁₁×#41	—	4	2	no	—
97	C₁₁×#41	—	4	2	no	—
98	C₂×Q₈×C₁₁	—	2	1	no	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	4	1	no	—
101	C₂×Q₈×C₁₁	—	4	2	no	—
102	C₂×Q₈×C₁₁	—	4	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	1	no	—
105	C₂×D₄×C₁₁	—	2	1	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	4	1	no	—
110	C₂×D₄×C₁₁	—	4	1	no	—
111	C₂×D₄×C₁₁	—	4	1	no	—
112	C₂×D₄×C₁₁	—	4	2	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	8	2	no	—
115	C₂×D₄×C₁₁	—	8	2	no	—
116	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	4	1	no	—
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
122	C₁₁×SD₁₆	—	4	4	no	—
123	C₁₁×SD₁₆	—	4	4	no	—
124	C₁₁×SD₁₆	—	4	4	no	—
125	C₁₁×SD₁₆	—	4	4	no	—
126	C₁₁×D₈	—	8	4	no	—
127	C₁₁×M₁₆	—	4	4	no	—
128	C₁₁×M₁₆	—	4	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	—	2	2	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	4	4	no	—
134	C₂×C₈×C₁₁	D₈	1	4	yes	complemented
135	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₁₁×C₄⋊C₄	—	2	2	no	—
142	C₁₁×C₄⋊C₄	—	4	1	no	—
143	C₁₁×C₄⋊C₄	—	4	1	no	—
144	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₁₁×C₂²⋊C₄	—	2	2	no	—
146	C₁₁×C₂²⋊C₄	—	2	2	no	—
147	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₁	#41	1	1	yes	characteristic
150	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
151	#3226	C₂×C₁₁	1	1	yes	characteristic, complemented
152	#3205	C₂×C₁₁	1	1	yes	characteristic
153	C₂×#492	C₂×C₁₁	1	1	yes	characteristic, complemented
154	#2931	C₂×C₁₁	1	1	yes	characteristic, complemented
155	#1685	C₂×C₁₁	1	4	yes	complemented
156	#1665	C₂×C₁₁	1	4	yes	complemented
157	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#1546	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1545	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	—	2	2	no	—
161	C₂³×C₁₁	—	4	2	no	—
162	C₂³×C₁₁	—	8	2	no	—
163	C₂³×C₁₁	—	8	2	no	—
164	C₂³×C₁₁	—	8	2	no	—
165	C₂³×C₁₁	#121	1	1	yes	characteristic
166	Q₈×C₁₁	—	4	2	no	—
167	Q₈×C₁₁	—	4	2	no	—
168	Q₈×C₁₁	—	4	2	no	—
169	Q₈×C₁₁	—	8	2	no	—
170	D₄×C₁₁	—	2	4	no	—
171	D₄×C₁₁	—	4	4	no	—
172	D₄×C₁₁	—	4	2	no	—
173	D₄×C₁₁	—	4	2	no	—
174	D₄×C₁₁	—	4	4	no	—
175	D₄×C₁₁	—	4	2	no	—
176	D₄×C₁₁	—	4	2	no	—
177	D₄×C₁₁	—	8	2	no	—
178	D₄×C₁₁	—	8	2	no	—
179	D₄×C₁₁	—	8	2	no	—
180	D₄×C₁₁	—	8	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	4	2	no	—
185	C₂×C₄×C₁₁	—	4	2	no	—
186	C₂×C₄×C₁₁	—	4	2	no	—
187	C₂×C₄×C₁₁	—	8	2	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	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
196	C₈×C₁₁	—	2	1	no	—
197	C₈×C₁₁	—	2	1	no	—
198	C₈×C₁₁	—	4	2	no	—
199	C₈×C₁₁	—	4	2	no	—
200	C₈×C₁₁	—	4	2	no	—
201	C₈×C₁₁	C₂×D₈	1	2	yes	—
202	C₈×C₁₁	C₂×D₈	1	2	yes	—
203	C₂²×SD₁₆	—	2	1	no	—
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂×#131	—	2	1	no	—
206	#532	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
208	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
209	#500	—	2	1	no	—
210	#493	—	2	1	no	—
211	#492	—	2	1	no	—
212	#492	—	2	1	no	—
213	#492	C₂²×C₁₁	1	2	yes	—
214	#492	C₂²×C₁₁	1	2	yes	—
215	#486	—	2	1	no	—
216	#486	—	2	1	no	—
217	#480	—	2	2	no	—
218	#474	C₂²×C₁₁	1	4	yes	complemented
219	#459	C₂²×C₁₁	1	4	yes	—
220	#447	—	2	2	no	—
221	#436	—	2	1	no	—
222	#436	C₂²×C₁₁	1	2	yes	complemented
223	C₈×D₄	—	2	1	no	—
224	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
225	#431	C₂²×C₁₁	1	1	yes	characteristic
226	#431	C₂²×C₁₁	1	1	yes	characteristic
227	#423	C₂²×C₁₁	1	1	yes	characteristic
228	#408	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
230	#335	C₂²×C₁₁	1	2	yes	complemented
231	#334	C₂²×C₁₁	1	2	yes	complemented
232	#332	C₂²×C₁₁	1	4	yes	complemented
233	#331	C₂²×C₁₁	1	4	yes	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	—	4	2	no	—
237	C₂²×C₁₁	—	4	2	no	—
238	C₂²×C₁₁	—	4	2	no	—
239	C₂²×C₁₁	—	8	2	no	—
240	C₂²×C₁₁	—	8	2	no	—
241	C₂²×C₁₁	—	8	2	no	—
242	C₂²×C₁₁	—	16	4	no	—
243	C₂²×C₁₁	#459	1	2	yes	—
244	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	2	1	no	—
247	C₄×C₁₁	—	4	2	no	—
248	C₄×C₁₁	—	8	2	no	—
249	C₄×C₁₁	#459	1	2	yes	—
250	C₄×C₁₁	#471	1	2	yes	—
251	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×C₁₁	#577	1	2	yes	—
254	C₂×#41	—	2	1	no	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	4	4	no	—
264	C₂×SD₁₆	—	4	4	no	—
265	C₂×D₈	—	2	4	no	—
266	#131	—	4	4	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
271	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	D₄×C₁₁	1	1	yes	characteristic
281	#127	C₂³×C₁₁	1	2	yes	—
282	#124	—	2	1	no	—
283	#121	—	2	1	no	—
284	#121	D₄×C₁₁	1	2	yes	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂³×C₁₁	1	2	yes	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
290	#107	—	2	4	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
293	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
294	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
295	#102	—	2	4	no	—
296	#102	—	2	4	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	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
304	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
305	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×C₁₁	—	2	2	no	—
308	C₂×C₁₁	—	8	2	no	—
309	C₂×C₁₁	—	16	2	no	—
310	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
311	C₂×C₁₁	#3057	1	1	yes	characteristic
312	C₂×C₁₁	C₂×#471	1	1	yes	characteristic
313	C₂⁴	—	4	1	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	8	2	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
339	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
340	SD₁₆	—	4	4	no	—
341	SD₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	8	4	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	4	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	4	no	—
352	C₂×C₈	C₁₁×D₈	1	4	yes	complemented
353	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
367	C₄²	C₁₁×#41	1	1	yes	characteristic
368	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
369	C₁₁	#19186	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	C₁₁×#121	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	8	2	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
399	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
400	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
401	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
402	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
405	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₈	C₂×C₁₁×D₈	1	2	yes	—
412	C₈	C₂×C₁₁×D₈	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₁₁×#459	1	2	yes	—
423	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	C₁₁×#459	1	2	yes	—
429	C₄	C₁₁×#471	1	2	yes	—
430	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
431	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₄	C₁₁×#577	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	8	2	no	—
435	C₂	—	16	2	no	—
436	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
437	C₂	C₁₁×#3057	1	1	yes	characteristic
438	C₂	C₂×C₁₁×#471	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
1. C₁₁×#3226	C₂	semidirect
3. C₂×C₁₁×#492	C₂	semidirect
4. C₁₁×#2931	C₂	semidirect
5. C₁₁×#1685	C₂	semidirect
6. C₁₁×#1665	C₂	semidirect
7. C₁₁×#1564	C₂	semidirect
8. C₁₁×#1546	C₂	semidirect
9. C₁₁×#1545	C₂	semidirect
25. C₁₁×#474	C₂²	semidirect
29. C₁₁×#436	C₂²	semidirect
31. C₈×D₄×C₁₁	C₂²	semidirect
37. C₁₁×#335	C₂²	semidirect
38. C₁₁×#334	C₂²	semidirect
39. C₁₁×#332	C₂²	semidirect
94. #19186	C₁₁	direct (N × H)
134. C₂×C₈×C₁₁	D₈	semidirect
151. #3226	C₂×C₁₁	semidirect
153. C₂×#492	C₂×C₁₁	semidirect
154. #2931	C₂×C₁₁	semidirect
155. #1685	C₂×C₁₁	semidirect
156. #1665	C₂×C₁₁	semidirect
157. #1564	C₂×C₁₁	semidirect
158. #1546	C₂×C₁₁	semidirect
159. #1545	C₂×C₁₁	semidirect
218. #474	C₂²×C₁₁	semidirect
222. #436	C₂²×C₁₁	semidirect
224. C₈×D₄	C₂²×C₁₁	semidirect
230. #335	C₂²×C₁₁	semidirect
231. #334	C₂²×C₁₁	semidirect
232. #332	C₂²×C₁₁	semidirect
352. C₂×C₈	C₁₁×D₈	semidirect
369. C₁₁	#19186	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×#3226	2
C₁₁×#3205	2
C₂×C₁₁×#492	2
C₁₁×#2931	2
C₁₁×#1685	2
C₁₁×#1665	2
C₁₁×#1564	2
C₁₁×#1546	2
C₁₁×#1545	2
#19186	11

Subgroups — C11×#19186 #14596379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19186 #14596379