Subgroups — C₁₁×#60720 #14637913

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3181	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3178	C₂	1	8	yes	maximal, complemented
5	C₁₁×#3172	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3059	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3057	C₂	1	2	yes	maximal
12	C₁₁×#2950	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2949	C₂	1	2	yes	maximal, complemented
14	C₁₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	2	yes	—
18	C₁₁×#559	—	2	2	no	—
19	C₁₁×#557	—	2	2	no	—
20	C₁₁×#556	—	2	2	no	—
21	C₁₁×#556	—	2	2	no	—
22	C₁₁×#552	—	2	4	no	—
23	C₁₁×#551	—	2	4	no	—
24	C₁₁×#542	C₂²	1	4	yes	—
25	C₁₁×#541	C₂²	1	4	yes	complemented
26	C₁₁×#536	C₂²	1	2	yes	—
27	C₁₁×#536	C₂²	1	1	yes	characteristic
28	C₁₁×#535	C₂²	1	1	yes	characteristic
29	C₁₁×#533	C₂²	1	1	yes	characteristic
30	C₁₁×#533	C₂²	1	1	yes	characteristic
31	C₁₁×#533	C₂²	1	4	yes	complemented
32	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₁×#529	C₂²	1	4	yes	—
34	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
35	C₁₁×#519	C₂²	1	2	yes	—
36	C₁₁×#519	C₂²	1	1	yes	characteristic
37	C₁₁×#518	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
39	C₁₁×#501	C₂²	1	2	yes	complemented
40	C₁₁×#501	C₂²	1	4	yes	complemented
41	C₁₁×#501	C₂²	1	2	yes	complemented
42	C₁₁×#497	C₂²	1	2	yes	—
43	C₁₁×#497	C₂²	1	4	yes	—
44	C₁₁×#497	C₂²	1	2	yes	—
45	C₁₁×#491	C₂²	1	4	yes	complemented
46	C₁₁×#489	C₂²	1	4	yes	—
47	C₁₁×#488	C₂²	1	4	yes	—
48	C₁₁×#487	C₂²	1	4	yes	complemented
49	C₁₁×#470	C₂²	1	8	yes	complemented
50	C₁₁×#468	C₂²	1	8	yes	—
51	C₁₁×#467	C₂²	1	8	yes	complemented
52	C₁₁×#465	C₂²	1	8	yes	—
53	C₁₁×#441	C₂²	1	8	yes	complemented
54	C₁₁×#440	C₂²	1	8	yes	—
55	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
56	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	—
57	C₁₁×#427	C₂²	1	2	yes	—
58	C₁₁×#427	C₂²	1	2	yes	—
59	C₁₁×#419	C₂²	1	2	yes	—
60	C₁₁×#419	C₂²	1	2	yes	—
61	C₁₁×#419	C₂²	1	2	yes	—
62	C₁₁×#418	C₂²	1	2	yes	—
63	C₁₁×#405	C₂²	1	2	yes	—
64	C₁₁×#405	C₂²	1	4	yes	complemented
65	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₁×M₁₆	C₂²	1	2	yes	complemented
67	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
68	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
69	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×Q₁₆	—	2	8	no	—
74	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
75	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
76	C₂×C₁₁×SD₁₆	—	2	8	no	—
77	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
79	C₁₁×#131	—	2	8	no	—
80	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
81	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
82	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
83	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
84	C₁₁×C₄⋊Q₈	—	2	1	no	—
85	C₁₁×C₄⋊Q₈	—	2	2	no	—
86	C₁₁×C₄⋊Q₈	—	2	2	no	—
87	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₁×#127	—	2	1	no	—
92	C₁₁×#126	—	2	4	no	—
93	C₁₁×#126	—	2	8	no	—
94	C₁₁×#126	—	2	4	no	—
95	C₁₁×#125	—	2	8	no	—
96	C₁₁×#125	—	2	4	no	—
97	C₁₁×#125	C₂³	1	2	yes	—
98	C₁₁×#125	C₂³	1	2	yes	—
99	C₁₁×#124	—	2	1	no	—
100	C₁₁×#124	—	2	2	no	—
101	C₁₁×#124	—	2	1	no	—
102	C₁₁×#124	—	2	4	no	—
103	C₁₁×#124	—	2	2	no	—
104	C₁₁×#124	C₂³	1	2	yes	—
105	C₁₁×#124	C₂³	1	2	yes	—
106	C₁₁×#123	—	2	2	no	—
107	C₁₁×#123	—	2	4	no	—
108	C₁₁×#123	—	2	4	no	—
109	C₁₁×#123	—	2	4	no	—
110	C₁₁×C₂²⋊Q₈	—	2	2	no	—
111	C₁₁×C₂²⋊Q₈	—	2	2	no	—
112	C₁₁×C₂²⋊Q₈	—	2	4	no	—
113	C₁₁×C₂²⋊Q₈	—	2	4	no	—
114	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
116	C₁₁×#121	C₂³	1	4	yes	—
117	C₁₁×#120	—	2	2	no	—
118	C₄×Q₈×C₁₁	—	2	4	no	—
119	C₄×Q₈×C₁₁	—	2	2	no	—
120	C₄×Q₈×C₁₁	—	2	2	no	—
121	C₄×Q₈×C₁₁	—	2	2	no	—
122	C₄×Q₈×C₁₁	—	2	4	no	—
123	C₄×Q₈×C₁₁	D₄	1	2	yes	—
124	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
125	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
126	C₄×D₄×C₁₁	—	2	4	no	—
127	C₄×D₄×C₁₁	—	2	2	no	—
128	C₄×D₄×C₁₁	D₄	1	4	yes	—
129	C₄×D₄×C₁₁	D₄	1	2	yes	—
130	C₄×D₄×C₁₁	C₂³	1	4	yes	—
131	C₁₁×#117	—	2	4	no	—
132	C₁₁×#117	—	2	2	no	—
133	C₁₁×#117	—	2	4	no	—
134	C₁₁×#117	—	2	4	no	—
135	C₁₁×#117	C₂³	1	1	yes	characteristic
136	C₁₁×#117	C₂³	1	1	yes	characteristic
137	C₁₁×#117	C₂³	1	2	yes	—
138	C₁₁×#117	C₂³	1	1	yes	characteristic
139	C₁₁×#117	C₂³	1	2	yes	—
140	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
143	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
145	C₁₁×#107	C₂³	1	4	yes	—
146	C₁₁×#107	C₂³	1	4	yes	—
147	C₁₁×#106	C₂³	1	4	yes	—
148	C₁₁×#106	C₂³	1	4	yes	—
149	C₁₁×#103	C₂³	1	8	yes	—
150	C₁₁×#103	C₂³	1	8	yes	—
151	C₁₁×#103	C₂³	1	8	yes	—
152	C₁₁×#102	C₂³	1	8	yes	—
153	C₁₁×#97	C₂³	1	2	yes	—
154	C₁₁×#97	C₂³	1	1	yes	characteristic
155	C₁₁×#97	C₂³	1	1	yes	characteristic
156	C₁₁×#97	C₂³	1	2	yes	—
157	C₁₁×#97	C₂³	1	4	yes	—
158	C₄×C₈×C₁₁	C₂³	1	2	yes	—
159	C₄×C₈×C₁₁	C₂³	1	4	yes	—
160	#60720	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₁	—	2	1	no	—
162	C₁₁×#41	—	2	4	no	—
163	C₂×Q₈×C₁₁	—	2	2	no	—
164	C₂×Q₈×C₁₁	—	2	1	no	—
165	C₂×Q₈×C₁₁	—	2	2	no	—
166	C₂×Q₈×C₁₁	—	2	2	no	—
167	C₂×Q₈×C₁₁	—	2	4	no	—
168	C₂×Q₈×C₁₁	—	2	4	no	—
169	C₂×Q₈×C₁₁	—	2	4	no	—
170	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
172	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
173	C₂×D₄×C₁₁	—	2	4	no	—
174	C₂×D₄×C₁₁	—	2	1	no	—
175	C₂×D₄×C₁₁	—	2	4	no	—
176	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₁	—	2	1	no	—
180	C₂²×C₄×C₁₁	—	2	2	no	—
181	C₂²×C₄×C₁₁	—	2	4	no	—
182	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
186	C₁₁×Q₁₆	—	2	8	no	—
187	C₁₁×Q₁₆	—	2	8	no	—
188	C₁₁×SD₁₆	—	2	8	no	—
189	C₁₁×SD₁₆	—	2	8	no	—
190	C₁₁×M₁₆	—	2	8	no	—
191	C₁₁×M₁₆	—	2	4	no	—
192	C₂×C₈×C₁₁	—	2	8	no	—
193	C₂×C₈×C₁₁	#41	1	8	yes	—
194	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
195	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
196	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
197	C₁₁×C₄⋊C₄	—	2	4	no	—
198	C₁₁×C₄⋊C₄	—	2	4	no	—
199	C₁₁×C₄⋊C₄	—	2	2	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	4	no	—
202	C₁₁×C₄⋊C₄	—	2	8	no	—
203	C₁₁×C₄⋊C₄	—	2	4	no	—
204	C₁₁×C₄⋊C₄	—	2	2	no	—
205	C₁₁×C₄⋊C₄	—	2	2	no	—
206	C₁₁×C₄⋊C₄	—	2	4	no	—
207	C₁₁×C₄⋊C₄	—	2	8	no	—
208	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
209	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
210	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
212	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
213	C₁₁×C₂²⋊C₄	—	2	1	no	—
214	C₁₁×C₂²⋊C₄	—	2	1	no	—
215	C₁₁×C₂²⋊C₄	—	2	2	no	—
216	C₁₁×C₂²⋊C₄	—	2	8	no	—
217	C₁₁×C₂²⋊C₄	—	2	4	no	—
218	C₁₁×C₂²⋊C₄	—	2	4	no	—
219	C₁₁×C₂²⋊C₄	—	2	4	no	—
220	C₁₁×C₂²⋊C₄	—	2	4	no	—
221	C₁₁×C₂²⋊C₄	—	2	4	no	—
222	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
224	C₄²×C₁₁	—	2	4	no	—
225	C₄²×C₁₁	—	2	8	no	—
226	C₄²×C₁₁	—	2	1	no	—
227	C₄²×C₁₁	—	2	1	no	—
228	C₄²×C₁₁	—	2	2	no	—
229	C₄²×C₁₁	C₂×D₄	1	4	yes	—
230	C₄²×C₁₁	C₂×D₄	1	2	yes	—
231	C₄²×C₁₁	C₂⁴	1	2	yes	—
232	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
233	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
234	#3510	C₂×C₁₁	1	1	yes	characteristic
235	#3509	C₂×C₁₁	1	1	yes	characteristic, complemented
236	#3181	C₂×C₁₁	1	4	yes	complemented
237	#3178	C₂×C₁₁	1	8	yes	complemented
238	#3172	C₂×C₁₁	1	4	yes	complemented
239	#3162	C₂×C₁₁	1	1	yes	characteristic, complemented
240	C₂×#497	C₂×C₁₁	1	1	yes	characteristic, complemented
241	#3140	C₂×C₁₁	1	1	yes	characteristic, complemented
242	#3139	C₂×C₁₁	1	1	yes	characteristic, complemented
243	#3059	C₂×C₁₁	1	2	yes	complemented
244	#3057	C₂×C₁₁	1	2	yes	—
245	#2950	C₂×C₁₁	1	2	yes	complemented
246	#2949	C₂×C₁₁	1	2	yes	complemented
247	#2875	C₂×C₁₁	1	1	yes	characteristic, complemented
248	C₂³×C₁₁	—	2	2	no	—
249	C₂³×C₁₁	—	4	2	no	—
250	C₂³×C₁₁	—	8	2	no	—
251	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₁₁	—	2	2	no	—
254	Q₈×C₁₁	—	2	4	no	—
255	Q₈×C₁₁	—	2	4	no	—
256	Q₈×C₁₁	—	2	4	no	—
257	Q₈×C₁₁	—	4	4	no	—
258	Q₈×C₁₁	—	4	2	no	—
259	Q₈×C₁₁	—	4	4	no	—
260	Q₈×C₁₁	—	8	2	no	—
261	D₄×C₁₁	—	2	4	no	—
262	D₄×C₁₁	—	2	2	no	—
263	D₄×C₁₁	—	2	4	no	—
264	D₄×C₁₁	—	4	2	no	—
265	D₄×C₁₁	—	8	4	no	—
266	C₂×C₄×C₁₁	—	2	4	no	—
267	C₂×C₄×C₁₁	—	2	4	no	—
268	C₂×C₄×C₁₁	—	2	2	no	—
269	C₂×C₄×C₁₁	—	2	2	no	—
270	C₂×C₄×C₁₁	—	2	4	no	—
271	C₂×C₄×C₁₁	—	2	2	no	—
272	C₂×C₄×C₁₁	—	4	4	no	—
273	C₂×C₄×C₁₁	—	4	2	no	—
274	C₂×C₄×C₁₁	—	4	2	no	—
275	C₂×C₄×C₁₁	—	4	4	no	—
276	C₂×C₄×C₁₁	—	8	4	no	—
277	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
283	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
284	C₈×C₁₁	—	2	4	no	—
285	C₈×C₁₁	C₂×#41	1	4	yes	—
286	C₈×C₁₁	C₂×#41	1	4	yes	—
287	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
288	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
289	C₂×#131	C₂²×C₁₁	1	2	yes	—
290	#559	—	2	2	no	—
291	#557	—	2	2	no	—
292	#556	—	2	2	no	—
293	#556	—	2	2	no	—
294	#552	—	2	4	no	—
295	#551	—	2	4	no	—
296	#542	C₂²×C₁₁	1	4	yes	—
297	#541	C₂²×C₁₁	1	4	yes	complemented
298	#536	C₂²×C₁₁	1	2	yes	—
299	#536	C₂²×C₁₁	1	1	yes	characteristic
300	#535	C₂²×C₁₁	1	1	yes	characteristic
301	#533	C₂²×C₁₁	1	1	yes	characteristic
302	#533	C₂²×C₁₁	1	1	yes	characteristic
303	#533	C₂²×C₁₁	1	4	yes	complemented
304	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
305	#529	C₂²×C₁₁	1	4	yes	—
306	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
307	#519	C₂²×C₁₁	1	2	yes	—
308	#519	C₂²×C₁₁	1	1	yes	characteristic
309	#518	C₂²×C₁₁	1	1	yes	characteristic
310	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
311	#501	C₂²×C₁₁	1	2	yes	complemented
312	#501	C₂²×C₁₁	1	4	yes	complemented
313	#501	C₂²×C₁₁	1	2	yes	complemented
314	#497	C₂²×C₁₁	1	2	yes	—
315	#497	C₂²×C₁₁	1	4	yes	—
316	#497	C₂²×C₁₁	1	2	yes	—
317	#491	C₂²×C₁₁	1	4	yes	complemented
318	#489	C₂²×C₁₁	1	4	yes	—
319	#488	C₂²×C₁₁	1	4	yes	—
320	#487	C₂²×C₁₁	1	4	yes	complemented
321	#470	C₂²×C₁₁	1	8	yes	complemented
322	#468	C₂²×C₁₁	1	8	yes	—
323	#467	C₂²×C₁₁	1	8	yes	complemented
324	#465	C₂²×C₁₁	1	8	yes	—
325	#441	C₂²×C₁₁	1	8	yes	complemented
326	#440	C₂²×C₁₁	1	8	yes	—
327	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
328	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	—
329	#427	C₂²×C₁₁	1	2	yes	—
330	#427	C₂²×C₁₁	1	2	yes	—
331	#419	C₂²×C₁₁	1	2	yes	—
332	#419	C₂²×C₁₁	1	2	yes	—
333	#419	C₂²×C₁₁	1	2	yes	—
334	#418	C₂²×C₁₁	1	2	yes	—
335	#405	C₂²×C₁₁	1	2	yes	—
336	#405	C₂²×C₁₁	1	4	yes	complemented
337	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
338	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
339	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
340	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
341	C₂²×C₁₁	—	2	2	no	—
342	C₂²×C₁₁	—	2	4	no	—
343	C₂²×C₁₁	—	2	2	no	—
344	C₂²×C₁₁	—	4	4	no	—
345	C₂²×C₁₁	—	4	2	no	—
346	C₂²×C₁₁	—	16	2	no	—
347	C₂²×C₁₁	#532	1	2	yes	—
348	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₁₁	—	2	2	no	—
350	C₄×C₁₁	—	2	4	no	—
351	C₄×C₁₁	—	2	2	no	—
352	C₄×C₁₁	—	2	2	no	—
353	C₄×C₁₁	—	4	2	no	—
354	C₄×C₁₁	—	4	2	no	—
355	C₄×C₁₁	—	4	4	no	—
356	C₄×C₁₁	—	4	2	no	—
357	C₄×C₁₁	—	4	4	no	—
358	C₄×C₁₁	#532	1	2	yes	—
359	C₄×C₁₁	C₂²×#41	1	2	yes	—
360	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
364	C₂×Q₁₆	—	2	8	no	—
365	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
366	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
367	C₂×SD₁₆	—	2	8	no	—
368	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
369	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
370	#131	—	2	8	no	—
371	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
372	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
373	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
374	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
375	C₄⋊Q₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	2	no	—
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
379	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
380	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
381	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
382	#127	—	2	1	no	—
383	#126	—	2	4	no	—
384	#126	—	2	8	no	—
385	#126	—	2	4	no	—
386	#125	—	2	8	no	—
387	#125	—	2	4	no	—
388	#125	C₂³×C₁₁	1	2	yes	—
389	#125	C₂³×C₁₁	1	2	yes	—
390	#124	—	2	1	no	—
391	#124	—	2	2	no	—
392	#124	—	2	1	no	—
393	#124	—	2	4	no	—
394	#124	—	2	2	no	—
395	#124	C₂³×C₁₁	1	2	yes	—
396	#124	C₂³×C₁₁	1	2	yes	—
397	#123	—	2	2	no	—
398	#123	—	2	4	no	—
399	#123	—	2	4	no	—
400	#123	—	2	4	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	4	no	—
404	C₂²⋊Q₈	—	2	4	no	—
405	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
406	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
407	#121	C₂³×C₁₁	1	4	yes	—
408	#120	—	2	2	no	—
409	C₄×Q₈	—	2	4	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	4	no	—
414	C₄×Q₈	D₄×C₁₁	1	2	yes	—
415	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
416	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
417	C₄×D₄	—	2	4	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	D₄×C₁₁	1	4	yes	—
420	C₄×D₄	D₄×C₁₁	1	2	yes	—
421	C₄×D₄	C₂³×C₁₁	1	4	yes	—
422	#117	—	2	4	no	—
423	#117	—	2	2	no	—
424	#117	—	2	4	no	—
425	#117	—	2	4	no	—
426	#117	C₂³×C₁₁	1	1	yes	characteristic
427	#117	C₂³×C₁₁	1	1	yes	characteristic
428	#117	C₂³×C₁₁	1	2	yes	—
429	#117	C₂³×C₁₁	1	1	yes	characteristic
430	#117	C₂³×C₁₁	1	2	yes	—
431	C₂×C₄⋊C₄	—	2	2	no	—
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
436	#107	C₂³×C₁₁	1	4	yes	—
437	#107	C₂³×C₁₁	1	4	yes	—
438	#106	C₂³×C₁₁	1	4	yes	—
439	#106	C₂³×C₁₁	1	4	yes	—
440	#103	C₂³×C₁₁	1	8	yes	—
441	#103	C₂³×C₁₁	1	8	yes	—
442	#103	C₂³×C₁₁	1	8	yes	—
443	#102	C₂³×C₁₁	1	8	yes	—
444	#97	C₂³×C₁₁	1	1	yes	characteristic
445	#97	C₂³×C₁₁	1	1	yes	characteristic
446	#97	C₂³×C₁₁	1	2	yes	—
447	#97	C₂³×C₁₁	1	2	yes	—
448	#97	C₂³×C₁₁	1	4	yes	—
449	C₄×C₈	C₂³×C₁₁	1	2	yes	—
450	C₄×C₈	C₂³×C₁₁	1	4	yes	—
451	C₂×C₁₁	—	2	2	no	—
452	C₂×C₁₁	—	4	2	no	—
453	C₂×C₁₁	—	8	2	no	—
454	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
455	C₂×C₁₁	#3586	1	2	yes	—
456	C₂⁴	—	2	1	no	—
457	#41	—	2	4	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	4	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	4	no	—
465	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
466	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
467	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
472	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
473	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
478	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
481	Q₁₆	—	2	8	no	—
482	Q₁₆	—	2	8	no	—
483	SD₁₆	—	2	8	no	—
484	SD₁₆	—	2	8	no	—
485	M₁₆	—	2	4	no	—
486	M₁₆	—	2	8	no	—
487	C₂×C₈	—	2	8	no	—
488	C₂×C₈	C₁₁×#41	1	8	yes	—
489	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
490	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
491	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	8	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
504	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
507	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
518	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	8	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	C₂×D₄×C₁₁	1	4	yes	—
525	C₄²	C₂×D₄×C₁₁	1	2	yes	—
526	C₄²	C₂⁴×C₁₁	1	2	yes	—
527	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
528	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
529	C₁₁	#60720	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	8	2	no	—
533	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
534	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	Q₈	—	2	4	no	—
537	Q₈	—	2	4	no	—
538	Q₈	—	2	4	no	—
539	Q₈	—	4	4	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	4	no	—
542	Q₈	—	8	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
560	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
563	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
565	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
566	C₈	—	2	4	no	—
567	C₈	C₂×C₁₁×#41	1	4	yes	—
568	C₈	C₂×C₁₁×#41	1	4	yes	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	16	2	no	—
575	C₂²	C₁₁×#532	1	2	yes	—
576	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	4	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	4	no	—
586	C₄	C₁₁×#532	1	2	yes	—
587	C₄	C₂²×C₁₁×#41	1	2	yes	—
588	C₂	—	2	2	no	—
589	C₂	—	4	2	no	—
590	C₂	—	8	2	no	—
591	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
592	C₂	C₁₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁×#3509	C₂	semidirect
3. C₁₁×#3181	C₂	semidirect
4. C₁₁×#3178	C₂	semidirect
5. C₁₁×#3172	C₂	semidirect
6. C₁₁×#3162	C₂	semidirect
7. C₂×C₁₁×#497	C₂	semidirect
8. C₁₁×#3140	C₂	semidirect
9. C₁₁×#3139	C₂	semidirect
10. C₁₁×#3059	C₂	semidirect
12. C₁₁×#2950	C₂	semidirect
13. C₁₁×#2949	C₂	semidirect
14. C₁₁×#2875	C₂	semidirect
25. C₁₁×#541	C₂²	semidirect
31. C₁₁×#533	C₂²	semidirect
39. C₁₁×#501	C₂²	semidirect
40. C₁₁×#501	C₂²	semidirect
41. C₁₁×#501	C₂²	semidirect
45. C₁₁×#491	C₂²	semidirect
48. C₁₁×#487	C₂²	semidirect
49. C₁₁×#470	C₂²	semidirect
51. C₁₁×#467	C₂²	semidirect
53. C₁₁×#441	C₂²	semidirect
55. C₄×C₁₁×Q₁₆	C₂²	semidirect
64. C₁₁×#405	C₂²	semidirect
66. C₄×C₁₁×M₁₆	C₂²	semidirect
68. C₂×C₁₁×#97	C₂²	semidirect
160. #60720	C₁₁	direct (N × H)
235. #3509	C₂×C₁₁	semidirect
236. #3181	C₂×C₁₁	semidirect
237. #3178	C₂×C₁₁	semidirect
238. #3172	C₂×C₁₁	semidirect
239. #3162	C₂×C₁₁	semidirect
240. C₂×#497	C₂×C₁₁	semidirect
241. #3140	C₂×C₁₁	semidirect
242. #3139	C₂×C₁₁	semidirect
243. #3059	C₂×C₁₁	semidirect
245. #2950	C₂×C₁₁	semidirect
246. #2949	C₂×C₁₁	semidirect
247. #2875	C₂×C₁₁	semidirect
297. #541	C₂²×C₁₁	semidirect
303. #533	C₂²×C₁₁	semidirect
311. #501	C₂²×C₁₁	semidirect
312. #501	C₂²×C₁₁	semidirect
313. #501	C₂²×C₁₁	semidirect
317. #491	C₂²×C₁₁	semidirect
320. #487	C₂²×C₁₁	semidirect
321. #470	C₂²×C₁₁	semidirect
323. #467	C₂²×C₁₁	semidirect
325. #441	C₂²×C₁₁	semidirect
327. C₄×Q₁₆	C₂²×C₁₁	semidirect
336. #405	C₂²×C₁₁	semidirect
338. C₄×M₁₆	C₂²×C₁₁	semidirect
340. C₂×#97	C₂²×C₁₁	semidirect
529. C₁₁	#60720	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×#3510	2
C₁₁×#3509	2
C₁₁×#3181	2
C₁₁×#3178	2
C₁₁×#3172	2
C₁₁×#3162	2
C₂×C₁₁×#497	2
C₁₁×#3140	2
C₁₁×#3139	2
C₁₁×#3059	2
C₁₁×#3057	2
C₁₁×#2950	2
C₁₁×#2949	2
C₁₁×#2875	2
#60720	11

Subgroups — C11×#60720 #14637913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60720 #14637913