Subgroups — C₁₁×#19170 #14596363

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1688	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1686	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1668	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	—	2	1	no	—
14	C₂²×C₁₁×SD₁₆	—	2	1	no	—
15	C₁₁×#532	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#496	—	2	2	no	—
19	C₁₁×#493	C₂²	1	2	yes	—
20	C₁₁×#492	C₂²	1	2	yes	—
21	C₁₁×#481	—	2	1	no	—
22	C₁₁×#475	C₂²	1	1	yes	characteristic, complemented
23	C₁₁×#475	C₂²	1	1	yes	characteristic, complemented
24	C₁₁×#460	—	2	1	no	—
25	C₁₁×#460	—	2	1	no	—
26	C₁₁×#460	C₂²	1	2	yes	—
27	C₁₁×#460	C₂²	1	2	yes	—
28	C₁₁×#460	C₂²	1	1	yes	characteristic, complemented
29	C₁₁×#460	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#448	—	2	1	no	—
31	C₁₁×#446	—	2	2	no	—
32	C₁₁×#446	C₂²	1	2	yes	complemented
33	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
34	C₄×C₁₁×SD₁₆	—	2	1	no	—
35	C₄×C₁₁×SD₁₆	—	2	1	no	—
36	C₁₁×#431	C₂²	1	1	yes	characteristic
37	C₁₁×#423	—	2	1	no	—
38	C₁₁×#423	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×#102	—	2	1	no	—
41	C₄×C₁₁×M₁₆	—	2	1	no	—
42	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₁×#335	C₂²	1	2	yes	complemented
44	C₁₁×#334	C₂²	1	2	yes	complemented
45	C₁₁×#332	C₂²	1	2	yes	complemented
46	C₁₁×#331	C₂²	1	2	yes	—
47	C₁₁×#331	C₂²	1	2	yes	—
48	C₁₁×#331	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	—	2	1	no	—
50	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₁	—	2	1	no	—
52	C₂²×D₄×C₁₁	—	2	1	no	—
53	C₂²×D₄×C₁₁	—	2	1	no	—
54	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
55	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
56	C₂×C₁₁×SD₁₆	—	2	2	no	—
57	C₂×C₁₁×SD₁₆	—	2	2	no	—
58	C₂×C₁₁×SD₁₆	—	2	1	no	—
59	C₂×C₁₁×SD₁₆	—	2	1	no	—
60	C₂×C₁₁×SD₁₆	—	2	2	no	—
61	C₂×C₁₁×SD₁₆	—	2	2	no	—
62	C₂×C₁₁×SD₁₆	—	4	4	no	—
63	C₂×C₁₁×D₈	—	2	2	no	—
64	C₂×C₁₁×D₈	—	2	2	no	—
65	C₂×C₁₁×M₁₆	—	2	1	no	—
66	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
67	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	—	2	1	no	—
69	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₁×#127	—	2	1	no	—
71	C₁₁×#127	—	2	1	no	—
72	C₁₁×#127	—	2	1	no	—
73	C₁₁×#127	C₂³	1	2	yes	—
74	C₁₁×#127	C₂³	1	1	yes	characteristic
75	C₁₁×#124	—	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×Q₈×C₁₁	D₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₁₁	—	2	1	no	—
85	C₄×D₄×C₁₁	—	2	1	no	—
86	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₁	—	2	1	no	—
89	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
90	C₁₁×#106	—	2	1	no	—
91	C₁₁×#106	—	2	1	no	—
92	C₁₁×C₄⋊C₈	—	2	2	no	—
93	C₁₁×C₄⋊C₈	—	2	2	no	—
94	C₁₁×C₄⋊C₈	—	2	1	no	—
95	C₁₁×C₄⋊C₈	—	2	1	no	—
96	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
97	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₁×#103	—	2	1	no	—
101	C₁₁×#103	—	2	1	no	—
102	C₁₁×#102	—	2	2	no	—
103	C₁₁×#102	—	2	2	no	—
104	C₁₁×#102	—	2	1	no	—
105	C₁₁×#102	—	2	1	no	—
106	C₁₁×C₂²⋊C₈	—	2	1	no	—
107	C₁₁×#97	—	2	2	no	—
108	C₁₁×#97	D₄	1	2	yes	—
109	C₄×C₈×C₁₁	—	2	2	no	—
110	C₄×C₈×C₁₁	—	2	1	no	—
111	C₄×C₈×C₁₁	C₂³	1	2	yes	—
112	#19170	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₁	—	4	1	no	—
114	C₁₁×#41	—	4	2	no	—
115	C₁₁×#41	—	4	2	no	—
116	C₂×Q₈×C₁₁	—	2	1	no	—
117	C₂×Q₈×C₁₁	—	2	2	no	—
118	C₂×Q₈×C₁₁	—	2	1	no	—
119	C₂×Q₈×C₁₁	—	4	1	no	—
120	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	—	2	2	no	—
124	C₂×D₄×C₁₁	—	2	1	no	—
125	C₂×D₄×C₁₁	—	2	2	no	—
126	C₂×D₄×C₁₁	—	2	1	no	—
127	C₂×D₄×C₁₁	—	2	2	no	—
128	C₂×D₄×C₁₁	—	4	2	no	—
129	C₂×D₄×C₁₁	—	4	2	no	—
130	C₂×D₄×C₁₁	—	4	1	no	—
131	C₂×D₄×C₁₁	—	4	1	no	—
132	C₂×D₄×C₁₁	—	4	1	no	—
133	C₂×D₄×C₁₁	—	4	1	no	—
134	C₂×D₄×C₁₁	—	4	2	no	—
135	C₂×D₄×C₁₁	—	4	2	no	—
136	C₂×D₄×C₁₁	—	8	2	no	—
137	C₂²×C₄×C₁₁	—	2	1	no	—
138	C₂²×C₄×C₁₁	—	2	1	no	—
139	C₂²×C₄×C₁₁	—	4	1	no	—
140	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
143	C₁₁×SD₁₆	—	4	2	no	—
144	C₁₁×SD₁₆	—	4	4	no	—
145	C₁₁×SD₁₆	—	4	4	no	—
146	C₁₁×SD₁₆	—	4	4	no	—
147	C₁₁×SD₁₆	—	4	2	no	—
148	C₁₁×SD₁₆	—	4	4	no	—
149	C₁₁×D₈	—	4	4	no	—
150	C₁₁×D₈	—	4	4	no	—
151	C₁₁×M₁₆	—	2	2	no	—
152	C₁₁×M₁₆	—	4	2	no	—
153	C₁₁×M₁₆	SD₁₆	1	4	yes	complemented
154	C₂×C₈×C₁₁	—	2	2	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	—	2	1	no	—
157	C₂×C₈×C₁₁	—	2	2	no	—
158	C₂×C₈×C₁₁	—	4	2	no	—
159	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
161	C₁₁×C₄⋊C₄	—	2	1	no	—
162	C₁₁×C₄⋊C₄	—	2	1	no	—
163	C₁₁×C₄⋊C₄	—	2	1	no	—
164	C₁₁×C₄⋊C₄	—	2	1	no	—
165	C₁₁×C₄⋊C₄	—	2	1	no	—
166	C₁₁×C₄⋊C₄	—	2	1	no	—
167	C₁₁×C₄⋊C₄	—	2	1	no	—
168	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₁₁×C₂²⋊C₄	—	4	1	no	—
171	C₁₁×C₂²⋊C₄	—	4	1	no	—
172	C₄²×C₁₁	—	2	1	no	—
173	C₄²×C₁₁	—	2	1	no	—
174	C₄²×C₁₁	—	2	1	no	—
175	C₄²×C₁₁	—	2	1	no	—
176	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₁	#41	1	1	yes	characteristic
179	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
180	#3151	C₂×C₁₁	1	1	yes	characteristic
181	#3103	C₂×C₁₁	1	1	yes	characteristic, complemented
182	C₂×#460	C₂×C₁₁	1	1	yes	characteristic, complemented
183	Q₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
184	#1688	C₂×C₁₁	1	2	yes	complemented
185	#1686	C₂×C₁₁	1	2	yes	complemented
186	#1668	C₂×C₁₁	1	2	yes	complemented
187	#1666	C₂×C₁₁	1	2	yes	complemented
188	#1565	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1547	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#1545	C₂×C₁₁	1	1	yes	characteristic, complemented
191	C₂³×C₁₁	—	4	1	no	—
192	C₂³×C₁₁	—	4	2	no	—
193	C₂³×C₁₁	—	8	2	no	—
194	C₂³×C₁₁	—	8	2	no	—
195	C₂³×C₁₁	—	8	2	no	—
196	C₂³×C₁₁	#121	1	1	yes	characteristic
197	Q₈×C₁₁	—	2	1	no	—
198	Q₈×C₁₁	—	2	1	no	—
199	Q₈×C₁₁	—	2	1	no	—
200	Q₈×C₁₁	—	4	2	no	—
201	Q₈×C₁₁	—	4	1	no	—
202	Q₈×C₁₁	—	4	1	no	—
203	Q₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	complemented
204	D₄×C₁₁	—	4	1	no	—
205	D₄×C₁₁	—	4	2	no	—
206	D₄×C₁₁	—	4	1	no	—
207	D₄×C₁₁	—	4	2	no	—
208	D₄×C₁₁	—	4	2	no	—
209	D₄×C₁₁	—	4	1	no	—
210	D₄×C₁₁	—	4	1	no	—
211	D₄×C₁₁	—	4	2	no	—
212	D₄×C₁₁	—	8	1	no	—
213	D₄×C₁₁	—	8	2	no	—
214	D₄×C₁₁	—	8	2	no	—
215	D₄×C₁₁	—	8	2	no	—
216	D₄×C₁₁	—	8	2	no	—
217	D₄×C₁₁	—	8	2	no	—
218	C₂×C₄×C₁₁	—	2	1	no	—
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	2	1	no	—
221	C₂×C₄×C₁₁	—	2	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	4	1	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	—	4	1	no	—
227	C₂×C₄×C₁₁	—	8	1	no	—
228	C₂×C₄×C₁₁	—	8	2	no	—
229	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
233	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₁	—	2	2	no	—
238	C₈×C₁₁	—	4	2	no	—
239	C₈×C₁₁	—	4	2	no	—
240	C₈×C₁₁	—	4	1	no	—
241	C₈×C₁₁	—	4	1	no	—
242	C₈×C₁₁	C₂×SD₁₆	1	4	yes	complemented
243	C₂×AGL(1,ℤ/8)	—	2	1	no	—
244	C₂×AGL(1,ℤ/8)	—	2	1	no	—
245	C₂²×SD₁₆	—	2	1	no	—
246	#532	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
249	#496	—	2	2	no	—
250	#493	C₂²×C₁₁	1	2	yes	—
251	#492	C₂²×C₁₁	1	2	yes	—
252	#481	—	2	1	no	—
253	#475	C₂²×C₁₁	1	1	yes	characteristic, complemented
254	#475	C₂²×C₁₁	1	1	yes	characteristic, complemented
255	#460	—	2	1	no	—
256	#460	—	2	1	no	—
257	#460	C₂²×C₁₁	1	2	yes	—
258	#460	C₂²×C₁₁	1	2	yes	—
259	#460	C₂²×C₁₁	1	1	yes	characteristic, complemented
260	#460	C₂²×C₁₁	1	1	yes	characteristic, complemented
261	#448	—	2	1	no	—
262	#446	—	2	2	no	—
263	#446	C₂²×C₁₁	1	2	yes	complemented
264	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
265	C₄×SD₁₆	—	2	1	no	—
266	C₄×SD₁₆	—	2	1	no	—
267	#431	C₂²×C₁₁	1	1	yes	characteristic
268	#423	—	2	1	no	—
269	#423	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
271	C₂×#102	—	2	1	no	—
272	C₄×M₁₆	—	2	1	no	—
273	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
274	#335	C₂²×C₁₁	1	2	yes	complemented
275	#334	C₂²×C₁₁	1	2	yes	complemented
276	#332	C₂²×C₁₁	1	2	yes	complemented
277	#331	C₂²×C₁₁	1	2	yes	—
278	#331	C₂²×C₁₁	1	2	yes	—
279	#331	C₂²×C₁₁	1	2	yes	complemented
280	C₂²×C₁₁	—	2	1	no	—
281	C₂²×C₁₁	—	2	1	no	—
282	C₂²×C₁₁	—	8	1	no	—
283	C₂²×C₁₁	—	8	2	no	—
284	C₂²×C₁₁	—	8	2	no	—
285	C₂²×C₁₁	—	8	1	no	—
286	C₂²×C₁₁	—	8	2	no	—
287	C₂²×C₁₁	—	8	1	no	—
288	C₂²×C₁₁	—	16	4	no	—
289	C₂²×C₁₁	#460	1	2	yes	—
290	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
291	C₄×C₁₁	—	2	1	no	—
292	C₄×C₁₁	—	2	2	no	—
293	C₄×C₁₁	—	2	1	no	—
294	C₄×C₁₁	—	2	1	no	—
295	C₄×C₁₁	—	4	1	no	—
296	C₄×C₁₁	—	4	1	no	—
297	C₄×C₁₁	—	4	1	no	—
298	C₄×C₁₁	—	8	1	no	—
299	C₄×C₁₁	#460	1	2	yes	—
300	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
301	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₄×C₁₁	#575	1	1	yes	characteristic
304	C₂×#41	—	2	1	no	—
305	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	1	no	—
309	AGL(1,ℤ/8)	—	4	4	no	—
310	AGL(1,ℤ/8)	—	4	4	no	—
311	C₂×SD₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	1	no	—
314	C₂×SD₁₆	—	2	1	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	4	4	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
322	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
323	C₂²×C₈	—	2	1	no	—
324	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
325	#127	—	2	1	no	—
326	#127	—	2	1	no	—
327	#127	—	2	1	no	—
328	#127	C₂³×C₁₁	1	2	yes	—
329	#127	C₂³×C₁₁	1	1	yes	characteristic
330	#124	—	2	1	no	—
331	#121	—	2	1	no	—
332	#121	—	2	1	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
336	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
337	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
338	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
345	#106	—	2	1	no	—
346	#106	—	2	1	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
352	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
353	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
354	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
355	#103	—	2	1	no	—
356	#103	—	2	1	no	—
357	#102	—	2	2	no	—
358	#102	—	2	2	no	—
359	#102	—	2	1	no	—
360	#102	—	2	1	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	#97	—	2	2	no	—
363	#97	D₄×C₁₁	1	2	yes	—
364	C₄×C₈	—	2	2	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	C₂³×C₁₁	1	2	yes	—
367	C₂×C₁₁	—	2	2	no	—
368	C₂×C₁₁	—	16	1	no	—
369	C₂×C₁₁	—	16	2	no	—
370	C₂×C₁₁	C₂×#460	1	1	yes	characteristic
371	C₂×C₁₁	#3055	1	1	yes	characteristic
372	C₂×C₁₁	#3068	1	1	yes	characteristic
373	C₂⁴	—	4	1	no	—
374	#41	—	4	2	no	—
375	#41	—	4	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
381	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	1	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
403	SD₁₆	—	4	4	no	—
404	SD₁₆	—	4	4	no	—
405	SD₁₆	—	4	2	no	—
406	SD₁₆	—	4	4	no	—
407	SD₁₆	—	4	2	no	—
408	SD₁₆	—	4	4	no	—
409	D₈	—	4	4	no	—
410	D₈	—	4	4	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	C₁₁×SD₁₆	1	4	yes	complemented
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
429	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
430	C₂²⋊C₄	—	4	1	no	—
431	C₂²⋊C₄	—	4	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
438	C₄²	C₁₁×#41	1	1	yes	characteristic
439	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
440	C₁₁	#19170	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³	—	4	1	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	8	2	no	—
444	C₂³	—	8	2	no	—
445	C₂³	—	8	2	no	—
446	C₂³	C₁₁×#121	1	1	yes	characteristic
447	Q₈	—	2	1	no	—
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	1	no	—
452	Q₈	—	4	1	no	—
453	Q₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	complemented
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	8	1	no	—
463	D₄	—	8	2	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	2	no	—
466	D₄	—	8	2	no	—
467	D₄	—	8	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
480	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
481	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
483	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	4	2	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	1	no	—
492	C₈	C₂×C₁₁×SD₁₆	1	4	yes	complemented
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	16	4	no	—
502	C₂²	C₁₁×#460	1	2	yes	—
503	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	8	1	no	—
512	C₄	C₁₁×#460	1	2	yes	—
513	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
514	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₄	C₁₁×#575	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	16	2	no	—
519	C₂	—	16	1	no	—
520	C₂	C₂×C₁₁×#460	1	1	yes	characteristic
521	C₂	C₁₁×#3055	1	1	yes	characteristic
522	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×#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
2. C₁₁×#3103	C₂	semidirect
3. C₂×C₁₁×#460	C₂	semidirect
4. Q₈×C₁₁×M₁₆	C₂	semidirect
5. C₁₁×#1688	C₂	semidirect
6. C₁₁×#1686	C₂	semidirect
7. C₁₁×#1668	C₂	semidirect
8. C₁₁×#1666	C₂	semidirect
9. C₁₁×#1565	C₂	semidirect
10. C₁₁×#1547	C₂	semidirect
11. C₁₁×#1545	C₂	semidirect
22. C₁₁×#475	C₂²	semidirect
23. C₁₁×#475	C₂²	semidirect
28. C₁₁×#460	C₂²	semidirect
29. C₁₁×#460	C₂²	semidirect
32. C₁₁×#446	C₂²	semidirect
33. C₈×Q₈×C₁₁	C₂²	semidirect
43. C₁₁×#335	C₂²	semidirect
44. C₁₁×#334	C₂²	semidirect
45. C₁₁×#332	C₂²	semidirect
48. C₁₁×#331	C₂²	semidirect
112. #19170	C₁₁	direct (N × H)
153. C₁₁×M₁₆	SD₁₆	semidirect
181. #3103	C₂×C₁₁	semidirect
182. C₂×#460	C₂×C₁₁	semidirect
183. Q₈×M₁₆	C₂×C₁₁	semidirect
184. #1688	C₂×C₁₁	semidirect
185. #1686	C₂×C₁₁	semidirect
186. #1668	C₂×C₁₁	semidirect
187. #1666	C₂×C₁₁	semidirect
188. #1565	C₂×C₁₁	semidirect
189. #1547	C₂×C₁₁	semidirect
190. #1545	C₂×C₁₁	semidirect
203. Q₈×C₁₁	AGL(1,ℤ/8)	semidirect
242. C₈×C₁₁	C₂×SD₁₆	semidirect
253. #475	C₂²×C₁₁	semidirect
254. #475	C₂²×C₁₁	semidirect
259. #460	C₂²×C₁₁	semidirect
260. #460	C₂²×C₁₁	semidirect
263. #446	C₂²×C₁₁	semidirect
264. C₈×Q₈	C₂²×C₁₁	semidirect
274. #335	C₂²×C₁₁	semidirect
275. #334	C₂²×C₁₁	semidirect
276. #332	C₂²×C₁₁	semidirect
279. #331	C₂²×C₁₁	semidirect
413. M₁₆	C₁₁×SD₁₆	semidirect
440. C₁₁	#19170	direct (N × H)
453. Q₈	C₁₁×AGL(1,ℤ/8)	semidirect
492. C₈	C₂×C₁₁×SD₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3151	2
C₁₁×#3103	2
C₂×C₁₁×#460	2
Q₈×C₁₁×M₁₆	2
C₁₁×#1688	2
C₁₁×#1686	2
C₁₁×#1668	2
C₁₁×#1666	2
C₁₁×#1565	2
C₁₁×#1547	2
C₁₁×#1545	2
#19170	11

Subgroups — C11×#19170 #14596363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19170 #14596363