Subgroups — C₁₁×#19631 #14596824

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 476 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, complemented
3	C₁₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1722	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1721	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1709	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1706	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#137	—	2	2	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	—	2	2	no	—
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₁₁×#532	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
18	C₁₁×#500	C₂²	1	1	yes	characteristic, complemented
19	C₁₁×#500	C₂²	1	2	yes	complemented
20	C₁₁×#497	—	2	2	no	—
21	C₁₁×#496	—	2	2	no	—
22	C₁₁×#494	C₂²	1	2	yes	complemented
23	C₁₁×#493	C₂²	1	2	yes	—
24	C₁₁×#493	C₂²	1	2	yes	—
25	C₁₁×#493	C₂²	1	1	yes	characteristic, complemented
26	C₁₁×#492	C₂²	1	2	yes	—
27	C₁₁×#492	C₂²	1	2	yes	complemented
28	C₁₁×#486	—	2	2	no	—
29	C₁₁×#486	C₂²	1	2	yes	—
30	C₁₁×#486	C₂²	1	2	yes	—
31	C₁₁×#486	C₂²	1	2	yes	—
32	C₁₁×#486	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#486	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#486	C₂²	1	2	yes	complemented
35	C₁₁×#480	—	2	2	no	—
36	C₁₁×#474	—	2	2	no	—
37	C₁₁×#466	—	2	2	no	—
38	C₁₁×#459	—	2	2	no	—
39	C₁₁×#447	—	2	2	no	—
40	C₄×C₁₁×D₈	—	2	2	no	—
41	C₁₁×#431	C₂²	1	1	yes	characteristic
42	C₂×C₁₁×#102	—	2	2	no	—
43	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
45	C₁₁×#322	C₂²	1	2	yes	complemented
46	C₈²×C₁₁	C₂²	1	2	yes	complemented
47	C₂×C₁₁×#41	—	2	1	no	—
48	C₂×C₁₁×#41	—	2	1	no	—
49	C₂²×Q₈×C₁₁	—	2	1	no	—
50	C₂²×D₄×C₁₁	—	2	1	no	—
51	C₂²×D₄×C₁₁	—	2	1	no	—
52	C₂²×D₄×C₁₁	—	2	1	no	—
53	C₁₁×#137	—	4	8	no	—
54	C₁₁×AGL(1,ℤ/8)	—	4	8	no	—
55	C₂×C₁₁×Q₁₆	—	2	4	no	—
56	C₂×C₁₁×SD₁₆	—	2	4	no	—
57	C₂×C₁₁×SD₁₆	—	2	4	no	—
58	C₂×C₁₁×D₈	—	2	4	no	—
59	C₂×C₁₁×D₈	—	2	2	no	—
60	C₂×C₁₁×D₈	—	2	4	no	—
61	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
62	C₂²×C₈×C₁₁	D₄	1	2	yes	—
63	C₁₁×C₄⋊Q₈	—	2	1	no	—
64	C₁₁×C₄⋊Q₈	—	2	1	no	—
65	C₁₁×C₄⋊Q₈	—	2	1	no	—
66	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₁×#127	—	2	1	no	—
70	C₁₁×#127	—	2	1	no	—
71	C₁₁×#127	—	2	1	no	—
72	C₁₁×#127	C₂³	1	2	yes	—
73	C₁₁×#127	C₂³	1	1	yes	characteristic
74	C₁₁×#127	C₂³	1	1	yes	characteristic
75	C₁₁×#124	—	2	1	no	—
76	C₁₁×#124	—	2	1	no	—
77	C₁₁×#121	—	2	1	no	—
78	C₁₁×#121	—	2	1	no	—
79	C₁₁×#121	—	2	1	no	—
80	C₁₁×#121	—	2	1	no	—
81	C₄×D₄×C₁₁	—	2	1	no	—
82	C₄×D₄×C₁₁	—	2	1	no	—
83	C₄×D₄×C₁₁	—	2	1	no	—
84	C₄×D₄×C₁₁	—	2	1	no	—
85	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₁₁×#107	—	2	2	no	—
89	C₁₁×#107	—	2	4	no	—
90	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
91	C₁₁×#102	—	2	4	no	—
92	C₁₁×#102	—	2	4	no	—
93	C₁₁×#102	—	2	2	no	—
94	C₁₁×#102	—	2	2	no	—
95	C₁₁×#102	—	2	4	no	—
96	C₁₁×#102	—	2	4	no	—
97	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
98	C₁₁×#97	D₄	1	2	yes	—
99	C₄×C₈×C₁₁	D₄	1	2	yes	—
100	C₄×C₈×C₁₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₁	C₂³	1	2	yes	—
102	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
104	#19631	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₁	—	4	1	no	—
106	C₁₁×#41	—	4	4	no	—
107	C₁₁×#41	—	4	4	no	—
108	C₂×Q₈×C₁₁	—	2	1	no	—
109	C₂×Q₈×C₁₁	—	2	1	no	—
110	C₂×Q₈×C₁₁	—	2	2	no	—
111	C₂×Q₈×C₁₁	—	4	1	no	—
112	C₂×Q₈×C₁₁	—	4	4	no	—
113	C₂×D₄×C₁₁	—	2	1	no	—
114	C₂×D₄×C₁₁	—	2	2	no	—
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	—	2	1	no	—
117	C₂×D₄×C₁₁	—	2	2	no	—
118	C₂×D₄×C₁₁	—	2	1	no	—
119	C₂×D₄×C₁₁	—	2	1	no	—
120	C₂×D₄×C₁₁	—	2	1	no	—
121	C₂×D₄×C₁₁	—	2	2	no	—
122	C₂×D₄×C₁₁	—	4	4	no	—
123	C₂×D₄×C₁₁	—	4	1	no	—
124	C₂×D₄×C₁₁	—	4	1	no	—
125	C₂×D₄×C₁₁	—	4	1	no	—
126	C₂×D₄×C₁₁	—	4	1	no	—
127	C₂×D₄×C₁₁	—	4	1	no	—
128	C₂×D₄×C₁₁	—	4	4	no	—
129	C₂×D₄×C₁₁	—	8	2	no	—
130	C₂²×C₄×C₁₁	—	4	1	no	—
131	C₂²×C₄×C₁₁	—	4	1	no	—
132	C₂²×C₄×C₁₁	—	4	1	no	—
133	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₁₁×Q₁₆	—	4	8	no	—
137	C₁₁×SD₁₆	—	4	8	no	—
138	C₁₁×SD₁₆	—	4	8	no	—
139	C₁₁×D₈	—	4	4	no	—
140	C₁₁×D₈	—	4	8	no	—
141	C₁₁×D₈	—	8	4	no	—
142	C₁₁×M₁₆	D₈	1	8	yes	complemented
143	C₂×C₈×C₁₁	—	4	2	no	—
144	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
148	C₁₁×C₄⋊C₄	—	2	2	no	—
149	C₁₁×C₄⋊C₄	—	2	1	no	—
150	C₁₁×C₄⋊C₄	—	2	2	no	—
151	C₁₁×C₄⋊C₄	—	2	1	no	—
152	C₁₁×C₄⋊C₄	—	2	1	no	—
153	C₁₁×C₄⋊C₄	—	2	1	no	—
154	C₁₁×C₄⋊C₄	—	4	1	no	—
155	C₁₁×C₄⋊C₄	—	4	1	no	—
156	C₁₁×C₂²⋊C₄	—	4	1	no	—
157	C₁₁×C₂²⋊C₄	—	4	1	no	—
158	C₁₁×C₂²⋊C₄	—	4	1	no	—
159	C₁₁×C₂²⋊C₄	—	4	1	no	—
160	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
164	#3226	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#3205	C₂×C₁₁	1	1	yes	characteristic, complemented
166	#3169	C₂×C₁₁	1	1	yes	characteristic, complemented
167	#3152	C₂×C₁₁	1	1	yes	characteristic, complemented
168	#3151	C₂×C₁₁	1	1	yes	characteristic, complemented
169	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1722	C₂×C₁₁	1	2	yes	complemented
171	#1721	C₂×C₁₁	1	2	yes	complemented
172	#1709	C₂×C₁₁	1	2	yes	complemented
173	#1706	C₂×C₁₁	1	2	yes	complemented
174	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₂³×C₁₁	—	4	1	no	—
176	C₂³×C₁₁	—	4	1	no	—
177	C₂³×C₁₁	—	4	2	no	—
178	C₂³×C₁₁	—	8	2	no	—
179	C₂³×C₁₁	—	8	2	no	—
180	C₂³×C₁₁	—	8	2	no	—
181	C₂³×C₁₁	#127	1	1	yes	characteristic
182	Q₈×C₁₁	—	4	2	no	—
183	Q₈×C₁₁	—	4	4	no	—
184	Q₈×C₁₁	—	4	2	no	—
185	Q₈×C₁₁	—	8	2	no	—
186	D₄×C₁₁	—	4	2	no	—
187	D₄×C₁₁	—	4	4	no	—
188	D₄×C₁₁	—	4	2	no	—
189	D₄×C₁₁	—	4	2	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	4	4	no	—
192	D₄×C₁₁	—	4	2	no	—
193	D₄×C₁₁	—	4	4	no	—
194	D₄×C₁₁	—	4	2	no	—
195	D₄×C₁₁	—	8	2	no	—
196	D₄×C₁₁	—	8	2	no	—
197	D₄×C₁₁	—	8	2	no	—
198	D₄×C₁₁	—	8	2	no	—
199	D₄×C₁₁	—	8	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	4	1	no	—
203	C₂×C₄×C₁₁	—	4	1	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	8	2	no	—
206	C₂×C₄×C₁₁	—	8	2	no	—
207	C₂×C₄×C₁₁	—	8	2	no	—
208	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
209	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
210	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
212	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₁₁	—	2	2	no	—
216	C₈×C₁₁	—	2	2	no	—
217	C₈×C₁₁	—	2	4	no	—
218	C₈×C₁₁	C₂×D₈	1	8	yes	—
219	C₂×#137	—	2	2	no	—
220	C₂×AGL(1,ℤ/8)	—	2	2	no	—
221	#532	C₂²×C₁₁	1	1	yes	characteristic
222	#532	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
225	#500	C₂²×C₁₁	1	1	yes	characteristic, complemented
226	#500	C₂²×C₁₁	1	2	yes	complemented
227	#497	—	2	2	no	—
228	#496	—	2	2	no	—
229	#494	C₂²×C₁₁	1	2	yes	complemented
230	#493	C₂²×C₁₁	1	2	yes	—
231	#493	C₂²×C₁₁	1	2	yes	—
232	#493	C₂²×C₁₁	1	1	yes	characteristic, complemented
233	#492	C₂²×C₁₁	1	2	yes	—
234	#492	C₂²×C₁₁	1	2	yes	complemented
235	#486	—	2	2	no	—
236	#486	C₂²×C₁₁	1	2	yes	—
237	#486	C₂²×C₁₁	1	2	yes	—
238	#486	C₂²×C₁₁	1	2	yes	—
239	#486	C₂²×C₁₁	1	1	yes	characteristic, complemented
240	#486	C₂²×C₁₁	1	1	yes	characteristic, complemented
241	#486	C₂²×C₁₁	1	2	yes	complemented
242	#480	—	2	2	no	—
243	#474	—	2	2	no	—
244	#466	—	2	2	no	—
245	#459	—	2	2	no	—
246	#447	—	2	2	no	—
247	C₄×D₈	—	2	2	no	—
248	#431	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×#102	—	2	2	no	—
250	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
252	#322	C₂²×C₁₁	1	2	yes	complemented
253	C₈²	C₂²×C₁₁	1	2	yes	complemented
254	C₂²×C₁₁	—	2	1	no	—
255	C₂²×C₁₁	—	2	1	no	—
256	C₂²×C₁₁	—	8	1	no	—
257	C₂²×C₁₁	—	8	1	no	—
258	C₂²×C₁₁	—	8	2	no	—
259	C₂²×C₁₁	—	8	2	no	—
260	C₂²×C₁₁	—	8	1	no	—
261	C₂²×C₁₁	—	8	1	no	—
262	C₂²×C₁₁	—	8	2	no	—
263	C₂²×C₁₁	—	8	1	no	—
264	C₂²×C₁₁	—	8	1	no	—
265	C₂²×C₁₁	—	16	4	no	—
266	C₂²×C₁₁	#493	1	2	yes	—
267	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	2	1	no	—
270	C₄×C₁₁	—	8	1	no	—
271	C₄×C₁₁	—	8	1	no	—
272	C₄×C₁₁	—	8	2	no	—
273	C₄×C₁₁	#493	1	2	yes	—
274	C₄×C₁₁	C₂²×D₈	1	2	yes	—
275	C₄×C₁₁	#575	1	2	yes	—
276	C₄×C₁₁	#577	1	2	yes	—
277	C₂×#41	—	2	1	no	—
278	C₂×#41	—	2	1	no	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	#137	—	4	8	no	—
284	AGL(1,ℤ/8)	—	4	8	no	—
285	C₂×Q₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×D₈	—	2	4	no	—
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	4	no	—
291	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
292	C₂²×C₈	D₄×C₁₁	1	2	yes	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
297	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
299	#127	—	2	1	no	—
300	#127	—	2	1	no	—
301	#127	—	2	1	no	—
302	#127	C₂³×C₁₁	1	2	yes	—
303	#127	C₂³×C₁₁	1	1	yes	characteristic
304	#127	C₂³×C₁₁	1	1	yes	characteristic
305	#124	—	2	1	no	—
306	#124	—	2	1	no	—
307	#121	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#107	—	2	4	no	—
320	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
321	#102	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	4	no	—
326	#102	—	2	4	no	—
327	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
328	#97	D₄×C₁₁	1	2	yes	—
329	C₄×C₈	D₄×C₁₁	1	2	yes	—
330	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₁₁	1	2	yes	—
332	C₄×C₈	C₂³×C₁₁	1	2	yes	—
333	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
334	C₂×C₁₁	—	2	2	no	—
335	C₂×C₁₁	—	16	1	no	—
336	C₂×C₁₁	—	16	1	no	—
337	C₂×C₁₁	—	16	2	no	—
338	C₂×C₁₁	C₂×#493	1	1	yes	characteristic
339	C₂×C₁₁	#3153	1	1	yes	characteristic
340	C₂×C₁₁	#3154	1	1	yes	characteristic
341	C₂⁴	—	4	1	no	—
342	#41	—	4	4	no	—
343	#41	—	4	4	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
372	Q₁₆	—	4	8	no	—
373	SD₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	D₈	—	4	4	no	—
376	D₈	—	4	8	no	—
377	D₈	—	8	4	no	—
378	M₁₆	C₁₁×D₈	1	8	yes	complemented
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
383	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
399	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
400	C₁₁	#19631	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	C₁₁×#127	1	1	yes	characteristic
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	8	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
435	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
436	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
438	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	4	no	—
444	C₈	C₂×C₁₁×D₈	1	8	yes	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	16	4	no	—
457	C₂²	C₁₁×#493	1	2	yes	—
458	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	2	no	—
464	C₄	C₁₁×#493	1	2	yes	—
465	C₄	C₂²×C₁₁×D₈	1	2	yes	—
466	C₄	C₁₁×#575	1	2	yes	—
467	C₄	C₁₁×#577	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	16	2	no	—
470	C₂	—	16	1	no	—
471	C₂	—	16	1	no	—
472	C₂	C₂×C₁₁×#493	1	1	yes	characteristic
473	C₂	C₁₁×#3153	1	1	yes	characteristic
474	C₂	C₁₁×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
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×#3226	C₂	semidirect
2. C₁₁×#3205	C₂	semidirect
3. C₁₁×#3169	C₂	semidirect
4. C₁₁×#3152	C₂	semidirect
5. C₁₁×#3151	C₂	semidirect
6. C₂×C₁₁×#486	C₂	semidirect
7. C₁₁×#1722	C₂	semidirect
8. C₁₁×#1721	C₂	semidirect
9. C₁₁×#1709	C₂	semidirect
10. C₁₁×#1706	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
18. C₁₁×#500	C₂²	semidirect
19. C₁₁×#500	C₂²	semidirect
22. C₁₁×#494	C₂²	semidirect
25. C₁₁×#493	C₂²	semidirect
27. C₁₁×#492	C₂²	semidirect
32. C₁₁×#486	C₂²	semidirect
33. C₁₁×#486	C₂²	semidirect
34. C₁₁×#486	C₂²	semidirect
45. C₁₁×#322	C₂²	semidirect
46. C₈²×C₁₁	C₂²	semidirect
104. #19631	C₁₁	direct (N × H)
142. C₁₁×M₁₆	D₈	semidirect
164. #3226	C₂×C₁₁	semidirect
165. #3205	C₂×C₁₁	semidirect
166. #3169	C₂×C₁₁	semidirect
167. #3152	C₂×C₁₁	semidirect
168. #3151	C₂×C₁₁	semidirect
169. C₂×#486	C₂×C₁₁	semidirect
170. #1722	C₂×C₁₁	semidirect
171. #1721	C₂×C₁₁	semidirect
172. #1709	C₂×C₁₁	semidirect
173. #1706	C₂×C₁₁	semidirect
174. C₈×M₁₆	C₂×C₁₁	semidirect
225. #500	C₂²×C₁₁	semidirect
226. #500	C₂²×C₁₁	semidirect
229. #494	C₂²×C₁₁	semidirect
232. #493	C₂²×C₁₁	semidirect
234. #492	C₂²×C₁₁	semidirect
239. #486	C₂²×C₁₁	semidirect
240. #486	C₂²×C₁₁	semidirect
241. #486	C₂²×C₁₁	semidirect
252. #322	C₂²×C₁₁	semidirect
253. C₈²	C₂²×C₁₁	semidirect
378. M₁₆	C₁₁×D₈	semidirect
400. C₁₁	#19631	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
C₁₁×#3169	2
C₁₁×#3152	2
C₁₁×#3151	2
C₂×C₁₁×#486	2
C₁₁×#1722	2
C₁₁×#1721	2
C₁₁×#1709	2
C₁₁×#1706	2
C₈×C₁₁×M₁₆	2
#19631	11

Subgroups — C11×#19631 #14596824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19631 #14596824