Subgroups — C₁₁×#19623 #14596816

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1715	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1714	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1708	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×AGL(1,ℤ/8)	—	2	2	no	—
13	C₁₁×#533	C₂²	1	1	yes	characteristic
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
17	C₁₁×#501	—	2	2	no	—
18	C₁₁×#500	C₂²	1	2	yes	complemented
19	C₁₁×#498	C₂²	1	2	yes	complemented
20	C₁₁×#498	C₂²	1	1	yes	characteristic, complemented
21	C₁₁×#496	—	2	2	no	—
22	C₁₁×#493	C₂²	1	2	yes	—
23	C₁₁×#492	C₂²	1	2	yes	—
24	C₁₁×#492	C₂²	1	2	yes	—
25	C₁₁×#492	C₂²	1	1	yes	characteristic, complemented
26	C₁₁×#492	C₂²	1	2	yes	complemented
27	C₁₁×#487	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×#487	C₂²	1	2	yes	complemented
29	C₁₁×#486	—	2	2	no	—
30	C₁₁×#486	C₂²	1	2	yes	—
31	C₁₁×#486	C₂²	1	2	yes	—
32	C₁₁×#486	C₂²	1	2	yes	—
33	C₁₁×#486	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#465	—	2	2	no	—
35	C₁₁×#461	—	2	2	no	—
36	C₁₁×#460	—	2	2	no	—
37	C₁₁×#450	—	2	2	no	—
38	C₁₁×#448	—	2	2	no	—
39	C₄×C₁₁×SD₁₆	—	2	2	no	—
40	C₁₁×#431	C₂²	1	1	yes	characteristic
41	C₁₁×#428	—	2	2	no	—
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	C₂²×Q₈×C₁₁	—	2	1	no	—
49	C₂²×D₄×C₁₁	—	2	1	no	—
50	C₂²×D₄×C₁₁	—	2	1	no	—
51	C₂²×D₄×C₁₁	—	2	1	no	—
52	C₁₁×AGL(1,ℤ/8)	—	4	8	no	—
53	C₂×C₁₁×SD₁₆	—	2	4	no	—
54	C₂×C₁₁×SD₁₆	—	2	2	no	—
55	C₂×C₁₁×SD₁₆	—	2	4	no	—
56	C₂×C₁₁×SD₁₆	—	2	4	no	—
57	C₂×C₁₁×D₈	—	2	4	no	—
58	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
59	C₂²×C₈×C₁₁	D₄	1	2	yes	—
60	C₁₁×C₄⋊Q₈	—	2	1	no	—
61	C₁₁×C₄⋊Q₈	—	2	1	no	—
62	C₁₁×C₄⋊Q₈	—	2	1	no	—
63	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₁₁×#127	—	2	1	no	—
68	C₁₁×#127	—	2	1	no	—
69	C₁₁×#127	—	2	1	no	—
70	C₁₁×#127	C₂³	1	2	yes	—
71	C₁₁×#127	C₂³	1	1	yes	characteristic
72	C₁₁×#125	—	2	1	no	—
73	C₁₁×#124	—	2	1	no	—
74	C₁₁×C₂²⋊Q₈	—	2	1	no	—
75	C₁₁×C₂²⋊Q₈	—	2	1	no	—
76	C₁₁×#121	—	2	1	no	—
77	C₁₁×#121	—	2	1	no	—
78	C₄×Q₈×C₁₁	—	2	1	no	—
79	C₄×Q₈×C₁₁	—	2	1	no	—
80	C₄×D₄×C₁₁	—	2	1	no	—
81	C₄×D₄×C₁₁	—	2	1	no	—
82	C₁₁×#117	—	2	1	no	—
83	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×#107	—	2	4	no	—
87	C₁₁×#106	—	2	4	no	—
88	C₁₁×#106	—	2	2	no	—
89	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
90	C₁₁×#103	—	2	2	no	—
91	C₁₁×#103	—	2	4	no	—
92	C₁₁×#102	—	2	4	no	—
93	C₁₁×#102	—	2	4	no	—
94	C₁₁×#102	—	2	2	no	—
95	C₁₁×#102	—	2	4	no	—
96	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
97	C₁₁×#97	D₄	1	2	yes	—
98	C₄×C₈×C₁₁	D₄	1	2	yes	—
99	C₄×C₈×C₁₁	C₂³	1	2	yes	—
100	C₄×C₈×C₁₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
103	#19623	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₁	—	4	1	no	—
105	C₁₁×#41	—	4	4	no	—
106	C₂×Q₈×C₁₁	—	2	1	no	—
107	C₂×Q₈×C₁₁	—	2	2	no	—
108	C₂×Q₈×C₁₁	—	2	1	no	—
109	C₂×Q₈×C₁₁	—	2	1	no	—
110	C₂×Q₈×C₁₁	—	4	1	no	—
111	C₂×Q₈×C₁₁	—	8	2	no	—
112	C₂×D₄×C₁₁	—	2	2	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	—	4	4	no	—
119	C₂×D₄×C₁₁	—	4	1	no	—
120	C₂×D₄×C₁₁	—	4	1	no	—
121	C₂×D₄×C₁₁	—	4	1	no	—
122	C₂×D₄×C₁₁	—	4	1	no	—
123	C₂×D₄×C₁₁	—	4	4	no	—
124	C₂×D₄×C₁₁	—	8	2	no	—
125	C₂²×C₄×C₁₁	—	4	1	no	—
126	C₂²×C₄×C₁₁	—	4	1	no	—
127	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₁₁×SD₁₆	—	4	4	no	—
131	C₁₁×SD₁₆	—	4	8	no	—
132	C₁₁×SD₁₆	—	8	4	no	—
133	C₁₁×SD₁₆	—	8	4	no	—
134	C₁₁×D₈	—	4	8	no	—
135	C₁₁×M₁₆	SD₁₆	1	8	yes	complemented
136	C₂×C₈×C₁₁	—	4	2	no	—
137	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
140	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
141	C₁₁×C₄⋊C₄	—	2	2	no	—
142	C₁₁×C₄⋊C₄	—	2	1	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	4	1	no	—
150	C₁₁×C₄⋊C₄	—	4	1	no	—
151	C₁₁×C₄⋊C₄	—	4	1	no	—
152	C₁₁×C₄⋊C₄	—	4	1	no	—
153	C₁₁×C₂²⋊C₄	—	4	1	no	—
154	C₁₁×C₂²⋊C₄	—	4	1	no	—
155	C₁₁×C₂²⋊C₄	—	4	1	no	—
156	C₄²×C₁₁	—	4	1	no	—
157	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
161	#3208	C₂×C₁₁	1	1	yes	characteristic, complemented
162	#3206	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#3167	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#3165	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#3151	C₂×C₁₁	1	1	yes	characteristic
166	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
167	#1715	C₂×C₁₁	1	2	yes	complemented
168	#1714	C₂×C₁₁	1	2	yes	complemented
169	#1708	C₂×C₁₁	1	2	yes	complemented
170	#1706	C₂×C₁₁	1	2	yes	complemented
171	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₂³×C₁₁	—	4	1	no	—
173	C₂³×C₁₁	—	4	2	no	—
174	C₂³×C₁₁	—	8	2	no	—
175	C₂³×C₁₁	—	8	2	no	—
176	C₂³×C₁₁	—	8	2	no	—
177	C₂³×C₁₁	#127	1	1	yes	characteristic
178	Q₈×C₁₁	—	4	2	no	—
179	Q₈×C₁₁	—	4	2	no	—
180	Q₈×C₁₁	—	4	2	no	—
181	Q₈×C₁₁	—	4	4	no	—
182	Q₈×C₁₁	—	8	2	no	—
183	D₄×C₁₁	—	4	2	no	—
184	D₄×C₁₁	—	4	4	no	—
185	D₄×C₁₁	—	4	2	no	—
186	D₄×C₁₁	—	4	4	no	—
187	D₄×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	4	4	no	—
189	D₄×C₁₁	—	8	2	no	—
190	D₄×C₁₁	—	8	2	no	—
191	D₄×C₁₁	—	8	2	no	—
192	D₄×C₁₁	—	8	2	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	4	1	no	—
197	C₂×C₄×C₁₁	—	4	1	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	8	2	no	—
200	C₂×C₄×C₁₁	—	8	2	no	—
201	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
202	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
203	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
205	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₁₁	—	2	2	no	—
209	C₈×C₁₁	—	2	2	no	—
210	C₈×C₁₁	—	2	4	no	—
211	C₈×C₁₁	C₂×SD₁₆	1	8	yes	—
212	C₂×AGL(1,ℤ/8)	—	2	2	no	—
213	#533	C₂²×C₁₁	1	1	yes	characteristic
214	#532	C₂²×C₁₁	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
217	#501	—	2	2	no	—
218	#500	C₂²×C₁₁	1	2	yes	complemented
219	#498	C₂²×C₁₁	1	2	yes	complemented
220	#498	C₂²×C₁₁	1	1	yes	characteristic, complemented
221	#496	—	2	2	no	—
222	#493	C₂²×C₁₁	1	2	yes	—
223	#492	C₂²×C₁₁	1	2	yes	—
224	#492	C₂²×C₁₁	1	2	yes	—
225	#492	C₂²×C₁₁	1	1	yes	characteristic, complemented
226	#492	C₂²×C₁₁	1	2	yes	complemented
227	#487	C₂²×C₁₁	1	1	yes	characteristic, complemented
228	#487	C₂²×C₁₁	1	2	yes	complemented
229	#486	—	2	2	no	—
230	#486	C₂²×C₁₁	1	2	yes	—
231	#486	C₂²×C₁₁	1	2	yes	—
232	#486	C₂²×C₁₁	1	2	yes	—
233	#486	C₂²×C₁₁	1	1	yes	characteristic, complemented
234	#465	—	2	2	no	—
235	#461	—	2	2	no	—
236	#460	—	2	2	no	—
237	#450	—	2	2	no	—
238	#448	—	2	2	no	—
239	C₄×SD₁₆	—	2	2	no	—
240	#431	C₂²×C₁₁	1	1	yes	characteristic
241	#428	—	2	2	no	—
242	C₂×#102	—	2	2	no	—
243	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
245	#322	C₂²×C₁₁	1	2	yes	complemented
246	C₈²	C₂²×C₁₁	1	2	yes	complemented
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	—	2	1	no	—
249	C₂²×C₁₁	—	8	1	no	—
250	C₂²×C₁₁	—	8	2	no	—
251	C₂²×C₁₁	—	8	2	no	—
252	C₂²×C₁₁	—	8	1	no	—
253	C₂²×C₁₁	—	8	2	no	—
254	C₂²×C₁₁	—	8	1	no	—
255	C₂²×C₁₁	—	16	4	no	—
256	C₂²×C₁₁	#492	1	2	yes	—
257	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
258	C₄×C₁₁	—	2	1	no	—
259	C₄×C₁₁	—	2	1	no	—
260	C₄×C₁₁	—	8	1	no	—
261	C₄×C₁₁	—	8	1	no	—
262	C₄×C₁₁	—	8	2	no	—
263	C₄×C₁₁	—	8	1	no	—
264	C₄×C₁₁	#492	1	2	yes	—
265	C₄×C₁₁	C₂²×SD₁₆	1	2	yes	—
266	C₄×C₁₁	#575	1	2	yes	—
267	C₄×C₁₁	#576	1	2	yes	—
268	C₂×#41	—	2	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	AGL(1,ℤ/8)	—	4	8	no	—
274	C₂×SD₁₆	—	2	4	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×D₈	—	2	4	no	—
279	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
280	C₂²×C₈	D₄×C₁₁	1	2	yes	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
285	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
287	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
288	#127	—	2	1	no	—
289	#127	—	2	1	no	—
290	#127	—	2	1	no	—
291	#127	C₂³×C₁₁	1	2	yes	—
292	#127	C₂³×C₁₁	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	#124	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	#117	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
307	#107	—	2	4	no	—
308	#106	—	2	4	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
311	#103	—	2	2	no	—
312	#103	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	2	no	—
316	#102	—	2	4	no	—
317	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
318	#97	D₄×C₁₁	1	2	yes	—
319	C₄×C₈	D₄×C₁₁	1	2	yes	—
320	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₁₁	1	2	yes	—
322	C₄×C₈	C₂³×C₁₁	1	2	yes	—
323	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
324	C₂×C₁₁	—	2	2	no	—
325	C₂×C₁₁	—	16	1	no	—
326	C₂×C₁₁	—	16	2	no	—
327	C₂×C₁₁	C₂×#492	1	1	yes	characteristic
328	C₂×C₁₁	#3153	1	1	yes	characteristic
329	C₂×C₁₁	#3155	1	1	yes	characteristic
330	C₂⁴	—	4	1	no	—
331	#41	—	4	4	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	4	1	no	—
337	C₂×Q₈	—	8	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
356	SD₁₆	—	4	4	no	—
357	SD₁₆	—	4	8	no	—
358	SD₁₆	—	8	4	no	—
359	SD₁₆	—	8	4	no	—
360	D₈	—	4	8	no	—
361	M₁₆	C₁₁×SD₁₆	1	8	yes	complemented
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
366	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
384	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
385	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
386	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
387	C₁₁	#19623	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	8	2	no	—
391	C₂³	—	8	2	no	—
392	C₂³	—	8	2	no	—
393	C₂³	C₁₁×#127	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	4	no	—
398	Q₈	—	8	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	4	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	2	no	—
408	D₄	—	8	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
418	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
419	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	2	no	—
426	C₈	—	2	4	no	—
427	C₈	C₂×C₁₁×SD₁₆	1	8	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	16	4	no	—
437	C₂²	C₁₁×#492	1	2	yes	—
438	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₁₁×#492	1	2	yes	—
446	C₄	C₂²×C₁₁×SD₁₆	1	2	yes	—
447	C₄	C₁₁×#575	1	2	yes	—
448	C₄	C₁₁×#576	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	16	2	no	—
451	C₂	—	16	1	no	—
452	C₂	C₂×C₁₁×#492	1	1	yes	characteristic
453	C₂	C₁₁×#3153	1	1	yes	characteristic
454	C₂	C₁₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3151	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×#3208	C₂	semidirect
2. C₁₁×#3206	C₂	semidirect
3. C₁₁×#3167	C₂	semidirect
4. C₁₁×#3165	C₂	semidirect
6. C₂×C₁₁×#486	C₂	semidirect
7. C₁₁×#1715	C₂	semidirect
8. C₁₁×#1714	C₂	semidirect
9. C₁₁×#1708	C₂	semidirect
10. C₁₁×#1706	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
18. C₁₁×#500	C₂²	semidirect
19. C₁₁×#498	C₂²	semidirect
20. C₁₁×#498	C₂²	semidirect
25. C₁₁×#492	C₂²	semidirect
26. C₁₁×#492	C₂²	semidirect
27. C₁₁×#487	C₂²	semidirect
28. C₁₁×#487	C₂²	semidirect
33. C₁₁×#486	C₂²	semidirect
45. C₁₁×#322	C₂²	semidirect
46. C₈²×C₁₁	C₂²	semidirect
103. #19623	C₁₁	direct (N × H)
135. C₁₁×M₁₆	SD₁₆	semidirect
161. #3208	C₂×C₁₁	semidirect
162. #3206	C₂×C₁₁	semidirect
163. #3167	C₂×C₁₁	semidirect
164. #3165	C₂×C₁₁	semidirect
166. C₂×#486	C₂×C₁₁	semidirect
167. #1715	C₂×C₁₁	semidirect
168. #1714	C₂×C₁₁	semidirect
169. #1708	C₂×C₁₁	semidirect
170. #1706	C₂×C₁₁	semidirect
171. C₈×M₁₆	C₂×C₁₁	semidirect
218. #500	C₂²×C₁₁	semidirect
219. #498	C₂²×C₁₁	semidirect
220. #498	C₂²×C₁₁	semidirect
225. #492	C₂²×C₁₁	semidirect
226. #492	C₂²×C₁₁	semidirect
227. #487	C₂²×C₁₁	semidirect
228. #487	C₂²×C₁₁	semidirect
233. #486	C₂²×C₁₁	semidirect
245. #322	C₂²×C₁₁	semidirect
246. C₈²	C₂²×C₁₁	semidirect
361. M₁₆	C₁₁×SD₁₆	semidirect
387. C₁₁	#19623	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×#3208	2
C₁₁×#3206	2
C₁₁×#3167	2
C₁₁×#3165	2
C₁₁×#3151	2
C₂×C₁₁×#486	2
C₁₁×#1715	2
C₁₁×#1714	2
C₁₁×#1708	2
C₁₁×#1706	2
C₈×C₁₁×M₁₆	2
#19623	11

Subgroups — C11×#19623 #14596816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19623 #14596816