Subgroups — C₁₁×#60719 #14637912

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 614 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, complemented
2	C₁₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3180	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3179	C₂	1	8	yes	maximal, complemented
5	C₁₁×#3171	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3058	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3057	C₂	1	2	yes	maximal, complemented
12	C₁₁×#2949	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2948	C₂	1	2	yes	maximal, complemented
14	C₁₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	2	yes	—
18	C₁₁×#559	—	2	2	no	—
19	C₁₁×#559	—	2	2	no	—
20	C₁₁×#556	—	2	2	no	—
21	C₁₁×#551	—	2	4	no	—
22	C₁₁×#550	—	2	2	no	—
23	C₁₁×#546	—	2	4	no	—
24	C₁₁×#542	C₂²	1	4	yes	complemented
25	C₁₁×#540	C₂²	1	4	yes	complemented
26	C₁₁×#536	C₂²	1	1	yes	characteristic
27	C₁₁×#535	C₂²	1	2	yes	—
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×#532	C₂²	1	4	yes	complemented
32	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
33	C₁₁×#529	C₂²	1	4	yes	complemented
34	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
35	C₁₁×#519	C₂²	1	1	yes	characteristic
36	C₁₁×#518	C₂²	1	1	yes	characteristic
37	C₁₁×#518	C₂²	1	2	yes	—
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×#496	C₂²	1	2	yes	—
43	C₁₁×#496	C₂²	1	4	yes	—
44	C₁₁×#496	C₂²	1	2	yes	—
45	C₁₁×#490	C₂²	1	4	yes	complemented
46	C₁₁×#489	C₂²	1	4	yes	complemented
47	C₁₁×#488	C₂²	1	4	yes	complemented
48	C₁₁×#486	C₂²	1	4	yes	complemented
49	C₁₁×#469	C₂²	1	8	yes	complemented
50	C₁₁×#468	C₂²	1	8	yes	complemented
51	C₁₁×#466	C₂²	1	8	yes	complemented
52	C₁₁×#465	C₂²	1	8	yes	complemented
53	C₁₁×#442	C₂²	1	8	yes	complemented
54	C₁₁×#440	C₂²	1	8	yes	complemented
55	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
56	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
57	C₁₁×#427	C₂²	1	2	yes	—
58	C₁₁×#427	C₂²	1	2	yes	—
59	C₁₁×#419	C₂²	1	2	yes	—
60	C₁₁×#418	C₂²	1	2	yes	—
61	C₁₁×#418	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	—	2	4	no	—
70	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₁	—	2	2	no	—
73	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
75	C₂×C₁₁×SD₁₆	—	2	8	no	—
76	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₁×D₈	—	2	8	no	—
79	C₂×C₁₁×D₈	C₂³	1	4	yes	—
80	C₂×C₁₁×D₈	C₂³	1	4	yes	—
81	C₁₁×#131	—	2	8	no	—
82	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
83	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
85	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
86	C₁₁×C₄⋊Q₈	—	2	1	no	—
87	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₁×#127	—	2	2	no	—
90	C₁₁×#127	—	2	1	no	—
91	C₁₁×#127	—	2	2	no	—
92	C₁₁×#127	C₂³	1	2	yes	—
93	C₁₁×#127	C₂³	1	2	yes	—
94	C₁₁×#126	—	2	4	no	—
95	C₁₁×#126	—	2	4	no	—
96	C₁₁×#125	C₂³	1	2	yes	—
97	C₁₁×#125	C₂³	1	2	yes	—
98	C₁₁×#124	—	2	1	no	—
99	C₁₁×#124	—	2	2	no	—
100	C₁₁×#124	—	2	1	no	—
101	C₁₁×#124	—	2	4	no	—
102	C₁₁×#124	—	2	2	no	—
103	C₁₁×#124	—	2	4	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	8	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	C₂³	1	4	yes	—
114	C₁₁×#121	—	2	4	no	—
115	C₁₁×#121	—	2	8	no	—
116	C₁₁×#121	C₂³	1	4	yes	—
117	C₁₁×#121	C₂³	1	8	yes	—
118	C₁₁×#120	—	2	4	no	—
119	C₁₁×#120	—	2	2	no	—
120	C₄×Q₈×C₁₁	—	2	2	no	—
121	C₄×Q₈×C₁₁	—	2	2	no	—
122	C₄×Q₈×C₁₁	—	2	2	no	—
123	C₄×Q₈×C₁₁	D₄	1	2	yes	—
124	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
125	C₄×D₄×C₁₁	—	2	4	no	—
126	C₄×D₄×C₁₁	—	2	4	no	—
127	C₄×D₄×C₁₁	—	2	2	no	—
128	C₄×D₄×C₁₁	—	2	4	no	—
129	C₄×D₄×C₁₁	D₄	1	4	yes	—
130	C₄×D₄×C₁₁	D₄	1	2	yes	—
131	C₄×D₄×C₁₁	C₂³	1	4	yes	—
132	C₄×D₄×C₁₁	C₂³	1	8	yes	—
133	C₁₁×#117	—	2	2	no	—
134	C₁₁×#117	—	2	4	no	—
135	C₁₁×#117	C₂³	1	2	yes	—
136	C₁₁×#117	C₂³	1	1	yes	characteristic
137	C₁₁×#117	C₂³	1	1	yes	characteristic
138	C₁₁×#117	C₂³	1	1	yes	characteristic
139	C₁₁×#117	C₂³	1	2	yes	—
140	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
141	C₂×C₁₁×C₂²⋊C₄	—	2	4	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×#102	C₂³	1	8	yes	—
151	C₁₁×#102	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	#60719	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₁	—	2	1	no	—
162	C₂⁴×C₁₁	—	2	2	no	—
163	C₁₁×#41	—	2	4	no	—
164	C₁₁×#41	—	8	8	no	—
165	C₂×Q₈×C₁₁	—	2	1	no	—
166	C₂×Q₈×C₁₁	—	2	2	no	—
167	C₂×Q₈×C₁₁	—	2	2	no	—
168	C₂×Q₈×C₁₁	—	2	4	no	—
169	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
171	C₂×D₄×C₁₁	—	2	4	no	—
172	C₂×D₄×C₁₁	—	2	8	no	—
173	C₂×D₄×C₁₁	—	2	1	no	—
174	C₂×D₄×C₁₁	—	2	2	no	—
175	C₂×D₄×C₁₁	—	2	4	no	—
176	C₂×D₄×C₁₁	—	2	4	no	—
177	C₂×D₄×C₁₁	—	2	4	no	—
178	C₂×D₄×C₁₁	—	2	4	no	—
179	C₂×D₄×C₁₁	—	2	4	no	—
180	C₂×D₄×C₁₁	—	8	4	no	—
181	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
182	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
183	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
184	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₁	—	2	1	no	—
186	C₂²×C₄×C₁₁	—	2	4	no	—
187	C₂²×C₄×C₁₁	—	2	8	no	—
188	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
192	C₁₁×SD₁₆	—	2	8	no	—
193	C₁₁×SD₁₆	—	2	8	no	—
194	C₁₁×D₈	—	2	8	no	—
195	C₁₁×D₈	—	2	8	no	—
196	C₁₁×M₁₆	—	2	8	no	—
197	C₁₁×M₁₆	—	2	4	no	—
198	C₂×C₈×C₁₁	—	2	8	no	—
199	C₂×C₈×C₁₁	#41	1	8	yes	complemented
200	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
201	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
202	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
203	C₁₁×C₄⋊C₄	—	2	2	no	—
204	C₁₁×C₄⋊C₄	—	2	4	no	—
205	C₁₁×C₄⋊C₄	—	2	4	no	—
206	C₁₁×C₄⋊C₄	—	2	2	no	—
207	C₁₁×C₄⋊C₄	—	2	2	no	—
208	C₁₁×C₄⋊C₄	—	2	4	no	—
209	C₁₁×C₄⋊C₄	—	2	2	no	—
210	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
211	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
212	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
213	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
214	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
215	C₁₁×C₂²⋊C₄	—	2	2	no	—
216	C₁₁×C₂²⋊C₄	—	2	1	no	—
217	C₁₁×C₂²⋊C₄	—	2	1	no	—
218	C₁₁×C₂²⋊C₄	—	2	4	no	—
219	C₁₁×C₂²⋊C₄	—	2	4	no	—
220	C₁₁×C₂²⋊C₄	—	2	8	no	—
221	C₁₁×C₂²⋊C₄	—	2	4	no	—
222	C₁₁×C₂²⋊C₄	—	2	4	no	—
223	C₁₁×C₂²⋊C₄	—	2	4	no	—
224	C₁₁×C₂²⋊C₄	—	2	8	no	—
225	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
226	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
227	C₄²×C₁₁	—	2	4	no	—
228	C₄²×C₁₁	—	2	2	no	—
229	C₄²×C₁₁	—	2	1	no	—
230	C₄²×C₁₁	—	2	1	no	—
231	C₄²×C₁₁	C₂×D₄	1	4	yes	—
232	C₄²×C₁₁	C₂×D₄	1	2	yes	—
233	C₄²×C₁₁	C₂⁴	1	2	yes	—
234	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
235	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
236	#3510	C₂×C₁₁	1	1	yes	characteristic, complemented
237	#3508	C₂×C₁₁	1	1	yes	characteristic, complemented
238	#3180	C₂×C₁₁	1	4	yes	complemented
239	#3179	C₂×C₁₁	1	8	yes	complemented
240	#3171	C₂×C₁₁	1	4	yes	complemented
241	#3162	C₂×C₁₁	1	1	yes	characteristic, complemented
242	C₂×#496	C₂×C₁₁	1	1	yes	characteristic, complemented
243	#3140	C₂×C₁₁	1	1	yes	characteristic, complemented
244	#3138	C₂×C₁₁	1	1	yes	characteristic, complemented
245	#3058	C₂×C₁₁	1	2	yes	complemented
246	#3057	C₂×C₁₁	1	2	yes	complemented
247	#2949	C₂×C₁₁	1	2	yes	complemented
248	#2948	C₂×C₁₁	1	2	yes	complemented
249	#2875	C₂×C₁₁	1	1	yes	characteristic, complemented
250	C₂³×C₁₁	—	2	2	no	—
251	C₂³×C₁₁	—	2	4	no	—
252	C₂³×C₁₁	—	4	2	no	—
253	C₂³×C₁₁	—	4	4	no	—
254	C₂³×C₁₁	—	8	4	no	—
255	C₂³×C₁₁	—	8	2	no	—
256	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
257	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
258	Q₈×C₁₁	—	2	2	no	—
259	Q₈×C₁₁	—	2	4	no	—
260	Q₈×C₁₁	—	4	4	no	—
261	Q₈×C₁₁	—	4	2	no	—
262	Q₈×C₁₁	—	8	2	no	—
263	D₄×C₁₁	—	2	4	no	—
264	D₄×C₁₁	—	2	2	no	—
265	D₄×C₁₁	—	2	4	no	—
266	D₄×C₁₁	—	2	4	no	—
267	D₄×C₁₁	—	2	4	no	—
268	D₄×C₁₁	—	4	8	no	—
269	D₄×C₁₁	—	4	2	no	—
270	D₄×C₁₁	—	4	4	no	—
271	D₄×C₁₁	—	8	4	no	—
272	D₄×C₁₁	—	8	4	no	—
273	D₄×C₁₁	—	8	8	no	—
274	C₂×C₄×C₁₁	—	2	4	no	—
275	C₂×C₄×C₁₁	—	2	2	no	—
276	C₂×C₄×C₁₁	—	2	2	no	—
277	C₂×C₄×C₁₁	—	2	2	no	—
278	C₂×C₄×C₁₁	—	2	4	no	—
279	C₂×C₄×C₁₁	—	4	2	no	—
280	C₂×C₄×C₁₁	—	4	4	no	—
281	C₂×C₄×C₁₁	—	4	2	no	—
282	C₂×C₄×C₁₁	—	8	4	no	—
283	C₂×C₄×C₁₁	—	8	8	no	—
284	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
290	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
291	C₈×C₁₁	—	2	4	no	—
292	C₈×C₁₁	C₂×#41	1	4	yes	—
293	C₈×C₁₁	C₂×#41	1	4	yes	—
294	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
295	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
296	C₂×#131	C₂²×C₁₁	1	2	yes	—
297	#559	—	2	2	no	—
298	#559	—	2	2	no	—
299	#556	—	2	2	no	—
300	#551	—	2	4	no	—
301	#550	—	2	2	no	—
302	#546	—	2	4	no	—
303	#542	C₂²×C₁₁	1	4	yes	complemented
304	#540	C₂²×C₁₁	1	4	yes	complemented
305	#536	C₂²×C₁₁	1	1	yes	characteristic
306	#535	C₂²×C₁₁	1	2	yes	—
307	#535	C₂²×C₁₁	1	1	yes	characteristic
308	#533	C₂²×C₁₁	1	1	yes	characteristic
309	#533	C₂²×C₁₁	1	1	yes	characteristic
310	#532	C₂²×C₁₁	1	4	yes	complemented
311	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
312	#529	C₂²×C₁₁	1	4	yes	complemented
313	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
314	#519	C₂²×C₁₁	1	1	yes	characteristic
315	#518	C₂²×C₁₁	1	1	yes	characteristic
316	#518	C₂²×C₁₁	1	2	yes	—
317	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
318	#501	C₂²×C₁₁	1	2	yes	complemented
319	#501	C₂²×C₁₁	1	4	yes	complemented
320	#501	C₂²×C₁₁	1	2	yes	complemented
321	#496	C₂²×C₁₁	1	2	yes	—
322	#496	C₂²×C₁₁	1	4	yes	—
323	#496	C₂²×C₁₁	1	2	yes	—
324	#490	C₂²×C₁₁	1	4	yes	complemented
325	#489	C₂²×C₁₁	1	4	yes	complemented
326	#488	C₂²×C₁₁	1	4	yes	complemented
327	#486	C₂²×C₁₁	1	4	yes	complemented
328	#469	C₂²×C₁₁	1	8	yes	complemented
329	#468	C₂²×C₁₁	1	8	yes	complemented
330	#466	C₂²×C₁₁	1	8	yes	complemented
331	#465	C₂²×C₁₁	1	8	yes	complemented
332	#442	C₂²×C₁₁	1	8	yes	complemented
333	#440	C₂²×C₁₁	1	8	yes	complemented
334	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
335	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
336	#427	C₂²×C₁₁	1	2	yes	—
337	#427	C₂²×C₁₁	1	2	yes	—
338	#419	C₂²×C₁₁	1	2	yes	—
339	#418	C₂²×C₁₁	1	2	yes	—
340	#418	C₂²×C₁₁	1	2	yes	—
341	#418	C₂²×C₁₁	1	2	yes	—
342	#405	C₂²×C₁₁	1	2	yes	—
343	#405	C₂²×C₁₁	1	4	yes	complemented
344	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
345	C₄×M₁₆	C₂²×C₁₁	1	2	yes	complemented
346	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
347	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
348	C₂²×C₁₁	—	2	2	no	—
349	C₂²×C₁₁	—	2	4	no	—
350	C₂²×C₁₁	—	2	2	no	—
351	C₂²×C₁₁	—	4	8	no	—
352	C₂²×C₁₁	—	4	4	no	—
353	C₂²×C₁₁	—	4	2	no	—
354	C₂²×C₁₁	—	4	4	no	—
355	C₂²×C₁₁	—	16	4	no	—
356	C₂²×C₁₁	—	16	2	no	—
357	C₂²×C₁₁	#532	1	2	yes	—
358	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
359	C₄×C₁₁	—	2	2	no	—
360	C₄×C₁₁	—	2	4	no	—
361	C₄×C₁₁	—	2	2	no	—
362	C₄×C₁₁	—	2	2	no	—
363	C₄×C₁₁	—	4	4	no	—
364	C₄×C₁₁	—	4	2	no	—
365	C₄×C₁₁	—	4	2	no	—
366	C₄×C₁₁	—	4	2	no	—
367	C₄×C₁₁	#532	1	2	yes	—
368	C₄×C₁₁	C₂²×#41	1	2	yes	—
369	C₂×#41	—	2	4	no	—
370	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
372	C₂²×D₄	—	2	2	no	—
373	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
375	C₂×SD₁₆	—	2	8	no	—
376	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
377	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
378	C₂×D₈	—	2	8	no	—
379	C₂×D₈	C₂³×C₁₁	1	4	yes	—
380	C₂×D₈	C₂³×C₁₁	1	4	yes	—
381	#131	—	2	8	no	—
382	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
383	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
384	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
385	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
388	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
389	#127	—	2	2	no	—
390	#127	—	2	1	no	—
391	#127	—	2	2	no	—
392	#127	C₂³×C₁₁	1	2	yes	—
393	#127	C₂³×C₁₁	1	2	yes	—
394	#126	—	2	4	no	—
395	#126	—	2	4	no	—
396	#125	C₂³×C₁₁	1	2	yes	—
397	#125	C₂³×C₁₁	1	2	yes	—
398	#124	—	2	1	no	—
399	#124	—	2	2	no	—
400	#124	—	2	1	no	—
401	#124	—	2	4	no	—
402	#124	—	2	2	no	—
403	#124	—	2	4	no	—
404	#124	C₂³×C₁₁	1	2	yes	—
405	#124	C₂³×C₁₁	1	2	yes	—
406	#123	—	2	2	no	—
407	#123	—	2	4	no	—
408	#123	—	2	8	no	—
409	#123	—	2	4	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
414	#121	—	2	4	no	—
415	#121	—	2	8	no	—
416	#121	C₂³×C₁₁	1	4	yes	—
417	#121	C₂³×C₁₁	1	8	yes	—
418	#120	—	2	4	no	—
419	#120	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	D₄×C₁₁	1	2	yes	—
424	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	D₄×C₁₁	1	4	yes	—
430	C₄×D₄	D₄×C₁₁	1	2	yes	—
431	C₄×D₄	C₂³×C₁₁	1	4	yes	—
432	C₄×D₄	C₂³×C₁₁	1	8	yes	—
433	#117	—	2	2	no	—
434	#117	—	2	4	no	—
435	#117	C₂³×C₁₁	1	2	yes	—
436	#117	C₂³×C₁₁	1	1	yes	characteristic
437	#117	C₂³×C₁₁	1	1	yes	characteristic
438	#117	C₂³×C₁₁	1	1	yes	characteristic
439	#117	C₂³×C₁₁	1	2	yes	—
440	C₂×C₂²⋊C₄	—	2	2	no	—
441	C₂×C₂²⋊C₄	—	2	4	no	—
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
445	#107	C₂³×C₁₁	1	4	yes	—
446	#107	C₂³×C₁₁	1	4	yes	—
447	#106	C₂³×C₁₁	1	4	yes	—
448	#106	C₂³×C₁₁	1	4	yes	—
449	#103	C₂³×C₁₁	1	8	yes	—
450	#102	C₂³×C₁₁	1	8	yes	—
451	#102	C₂³×C₁₁	1	8	yes	—
452	#102	C₂³×C₁₁	1	8	yes	—
453	#97	C₂³×C₁₁	1	1	yes	characteristic
454	#97	C₂³×C₁₁	1	1	yes	characteristic
455	#97	C₂³×C₁₁	1	2	yes	—
456	#97	C₂³×C₁₁	1	2	yes	—
457	#97	C₂³×C₁₁	1	4	yes	—
458	C₄×C₈	C₂³×C₁₁	1	2	yes	—
459	C₄×C₈	C₂³×C₁₁	1	4	yes	—
460	C₂×C₁₁	—	2	2	no	—
461	C₂×C₁₁	—	4	2	no	—
462	C₂×C₁₁	—	8	4	no	—
463	C₂×C₁₁	—	8	2	no	—
464	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
465	C₂×C₁₁	#3585	1	2	yes	—
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	2	no	—
468	#41	—	2	4	no	—
469	#41	—	8	8	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	4	no	—
474	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
475	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	8	4	no	—
486	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
487	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
488	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
489	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	8	no	—
493	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
494	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
497	SD₁₆	—	2	8	no	—
498	SD₁₆	—	2	8	no	—
499	D₈	—	2	8	no	—
500	D₈	—	2	8	no	—
501	M₁₆	—	2	4	no	—
502	M₁₆	—	2	8	no	—
503	C₂×C₈	—	2	8	no	—
504	C₂×C₈	C₁₁×#41	1	8	yes	complemented
505	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
506	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
507	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
516	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
517	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
518	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
519	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	8	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
531	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	C₂×D₄×C₁₁	1	4	yes	—
537	C₄²	C₂×D₄×C₁₁	1	2	yes	—
538	C₄²	C₂⁴×C₁₁	1	2	yes	—
539	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
540	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
541	C₁₁	#60719	1	1	yes	characteristic, direct product factor, Sylow
542	C₂³	—	2	2	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	8	4	no	—
547	C₂³	—	8	2	no	—
548	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
549	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
550	Q₈	—	2	2	no	—
551	Q₈	—	2	4	no	—
552	Q₈	—	4	4	no	—
553	Q₈	—	4	2	no	—
554	Q₈	—	8	2	no	—
555	D₄	—	2	4	no	—
556	D₄	—	2	2	no	—
557	D₄	—	2	4	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	4	no	—
560	D₄	—	4	8	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	4	no	—
563	D₄	—	8	4	no	—
564	D₄	—	8	4	no	—
565	D₄	—	8	8	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	8	4	no	—
575	C₂×C₄	—	8	8	no	—
576	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
577	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
581	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
582	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	C₂×C₁₁×#41	1	4	yes	—
585	C₈	C₂×C₁₁×#41	1	4	yes	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	8	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	16	4	no	—
594	C₂²	—	16	2	no	—
595	C₂²	C₁₁×#532	1	2	yes	—
596	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	C₁₁×#532	1	2	yes	—
606	C₄	C₂²×C₁₁×#41	1	2	yes	—
607	C₂	—	2	2	no	—
608	C₂	—	4	2	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
612	C₂	C₁₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
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
1. C₁₁×#3510	C₂	semidirect
2. C₁₁×#3508	C₂	semidirect
3. C₁₁×#3180	C₂	semidirect
4. C₁₁×#3179	C₂	semidirect
5. C₁₁×#3171	C₂	semidirect
6. C₁₁×#3162	C₂	semidirect
7. C₂×C₁₁×#496	C₂	semidirect
8. C₁₁×#3140	C₂	semidirect
9. C₁₁×#3138	C₂	semidirect
10. C₁₁×#3058	C₂	semidirect
11. C₁₁×#3057	C₂	semidirect
12. C₁₁×#2949	C₂	semidirect
13. C₁₁×#2948	C₂	semidirect
14. C₁₁×#2875	C₂	semidirect
24. C₁₁×#542	C₂²	semidirect
25. C₁₁×#540	C₂²	semidirect
31. C₁₁×#532	C₂²	semidirect
33. C₁₁×#529	C₂²	semidirect
39. C₁₁×#501	C₂²	semidirect
40. C₁₁×#501	C₂²	semidirect
41. C₁₁×#501	C₂²	semidirect
45. C₁₁×#490	C₂²	semidirect
46. C₁₁×#489	C₂²	semidirect
47. C₁₁×#488	C₂²	semidirect
48. C₁₁×#486	C₂²	semidirect
49. C₁₁×#469	C₂²	semidirect
50. C₁₁×#468	C₂²	semidirect
51. C₁₁×#466	C₂²	semidirect
52. C₁₁×#465	C₂²	semidirect
53. C₁₁×#442	C₂²	semidirect
54. C₁₁×#440	C₂²	semidirect
55. C₄×C₁₁×SD₁₆	C₂²	semidirect
56. C₄×C₁₁×D₈	C₂²	semidirect
64. C₁₁×#405	C₂²	semidirect
66. C₄×C₁₁×M₁₆	C₂²	semidirect
68. C₂×C₁₁×#97	C₂²	semidirect
160. #60719	C₁₁	direct (N × H)
199. C₂×C₈×C₁₁	#41	semidirect
236. #3510	C₂×C₁₁	semidirect
237. #3508	C₂×C₁₁	semidirect
238. #3180	C₂×C₁₁	semidirect
239. #3179	C₂×C₁₁	semidirect
240. #3171	C₂×C₁₁	semidirect
241. #3162	C₂×C₁₁	semidirect
242. C₂×#496	C₂×C₁₁	semidirect
243. #3140	C₂×C₁₁	semidirect
244. #3138	C₂×C₁₁	semidirect
245. #3058	C₂×C₁₁	semidirect
246. #3057	C₂×C₁₁	semidirect
247. #2949	C₂×C₁₁	semidirect
248. #2948	C₂×C₁₁	semidirect
249. #2875	C₂×C₁₁	semidirect
303. #542	C₂²×C₁₁	semidirect
304. #540	C₂²×C₁₁	semidirect
310. #532	C₂²×C₁₁	semidirect
312. #529	C₂²×C₁₁	semidirect
318. #501	C₂²×C₁₁	semidirect
319. #501	C₂²×C₁₁	semidirect
320. #501	C₂²×C₁₁	semidirect
324. #490	C₂²×C₁₁	semidirect
325. #489	C₂²×C₁₁	semidirect
326. #488	C₂²×C₁₁	semidirect
327. #486	C₂²×C₁₁	semidirect
328. #469	C₂²×C₁₁	semidirect
329. #468	C₂²×C₁₁	semidirect
330. #466	C₂²×C₁₁	semidirect
331. #465	C₂²×C₁₁	semidirect
332. #442	C₂²×C₁₁	semidirect
333. #440	C₂²×C₁₁	semidirect
334. C₄×SD₁₆	C₂²×C₁₁	semidirect
335. C₄×D₈	C₂²×C₁₁	semidirect
343. #405	C₂²×C₁₁	semidirect
345. C₄×M₁₆	C₂²×C₁₁	semidirect
347. C₂×#97	C₂²×C₁₁	semidirect
504. C₂×C₈	C₁₁×#41	semidirect
541. C₁₁	#60719	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×#3508	2
C₁₁×#3180	2
C₁₁×#3179	2
C₁₁×#3171	2
C₁₁×#3162	2
C₂×C₁₁×#496	2
C₁₁×#3140	2
C₁₁×#3138	2
C₁₁×#3058	2
C₁₁×#3057	2
C₁₁×#2949	2
C₁₁×#2948	2
C₁₁×#2875	2
#60719	11

Subgroups — C11×#60719 #14637912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60719 #14637912