Subgroups — C₁₁×#60723 #14637916

Order 2816.

1886 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3185	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3182	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3178	C₂	1	8	yes	maximal, complemented
6	C₁₁×#3170	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3167	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#3063	C₂	1	4	yes	maximal, complemented
13	C₁₁×#2947	C₂	1	4	yes	maximal, complemented
14	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₁×#137	C₂²	1	4	yes	—
16	C₂×C₁₁×#131	C₂²	1	2	yes	—
17	C₁₁×#557	—	2	1	no	—
18	C₁₁×#557	—	2	1	no	—
19	C₁₁×#556	—	2	1	no	—
20	C₁₁×#556	—	2	1	no	—
21	C₁₁×#556	—	2	1	no	—
22	C₁₁×#555	—	2	1	no	—
23	C₁₁×#554	—	2	1	no	—
24	C₁₁×#553	—	2	2	no	—
25	C₁₁×#552	—	2	2	no	—
26	C₁₁×#552	—	2	2	no	—
27	C₁₁×#548	—	2	2	no	—
28	C₁₁×#547	—	2	1	no	—
29	C₁₁×#542	C₂²	1	4	yes	—
30	C₁₁×#541	C₂²	1	4	yes	—
31	C₁₁×#537	C₂²	1	2	yes	—
32	C₁₁×#536	C₂²	1	2	yes	—
33	C₁₁×#533	C₂²	1	2	yes	—
34	C₁₁×#533	C₂²	1	2	yes	—
35	C₁₁×#533	C₂²	1	2	yes	—
36	C₁₁×#533	C₂²	1	1	yes	characteristic
37	C₁₁×#532	C₂²	1	1	yes	characteristic
38	C₁₁×#532	C₂²	1	2	yes	—
39	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₁×#520	C₂²	1	2	yes	—
42	C₁₁×#519	C₂²	1	2	yes	—
43	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
44	C₁₁×#501	C₂²	1	4	yes	—
45	C₁₁×#500	C₂²	1	2	yes	—
46	C₁₁×#498	C₂²	1	2	yes	—
47	C₁₁×#497	C₂²	1	4	yes	—
48	C₁₁×#494	C₂²	1	2	yes	—
49	C₁₁×#492	C₂²	1	2	yes	—
50	C₁₁×#488	C₂²	1	4	yes	—
51	C₁₁×#487	C₂²	1	2	yes	—
52	C₁₁×#487	C₂²	1	1	yes	characteristic
53	C₁₁×#487	C₂²	1	4	yes	—
54	C₁₁×#487	C₂²	1	2	yes	—
55	C₁₁×#487	C₂²	1	1	yes	characteristic
56	C₁₁×#486	C₂²	1	1	yes	characteristic
57	C₁₁×#486	C₂²	1	1	yes	characteristic
58	C₁₁×#470	C₂²	1	8	yes	—
59	C₁₁×#468	C₂²	1	8	yes	—
60	C₁₁×#467	C₂²	1	8	yes	—
61	C₁₁×#465	C₂²	1	8	yes	—
62	C₁₁×#441	C₂²	1	8	yes	—
63	C₁₁×#440	C₂²	1	8	yes	—
64	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	—
65	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	—
66	C₁₁×#428	C₂²	1	4	yes	—
67	C₁₁×#416	C₂²	1	4	yes	—
68	C₂×C₁₁×#103	C₂²	1	4	yes	—
69	C₁₁×#405	C₂²	1	4	yes	—
70	C₁₁×#405	C₂²	1	2	yes	—
71	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
72	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
73	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
74	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
75	C₂×C₁₁×#41	—	2	2	no	—
76	C₂×C₁₁×#41	C₂³	1	2	yes	—
77	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₁	—	2	1	no	—
79	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
80	C₁₁×#137	—	2	16	no	—
81	C₂×C₁₁×Q₁₆	C₂³	1	8	yes	—
82	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
83	C₁₁×#131	—	2	8	no	—
84	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
85	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
87	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
88	C₁₁×C₄⋊Q₈	—	2	2	no	—
89	C₁₁×C₄⋊Q₈	—	2	1	no	—
90	C₁₁×C₄⋊Q₈	—	2	1	no	—
91	C₁₁×C₄⋊Q₈	—	2	1	no	—
92	C₁₁×C₄⋊Q₈	—	2	1	no	—
93	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₁₁×#127	C₂³	1	1	yes	characteristic
101	C₁₁×#126	—	2	4	no	—
102	C₁₁×#126	—	2	4	no	—
103	C₁₁×#126	—	2	4	no	—
104	C₁₁×#125	—	2	4	no	—
105	C₁₁×#125	—	2	4	no	—
106	C₁₁×#125	—	2	2	no	—
107	C₁₁×#125	—	2	2	no	—
108	C₁₁×#125	—	2	2	no	—
109	C₁₁×#125	C₂³	1	2	yes	—
110	C₁₁×#124	—	2	2	no	—
111	C₁₁×#124	—	2	4	no	—
112	C₁₁×#124	—	2	2	no	—
113	C₁₁×#124	C₂³	1	2	yes	—
114	C₁₁×#123	—	2	4	no	—
115	C₁₁×#123	—	2	4	no	—
116	C₁₁×C₂²⋊Q₈	—	2	2	no	—
117	C₁₁×C₂²⋊Q₈	—	2	2	no	—
118	C₁₁×C₂²⋊Q₈	—	2	1	no	—
119	C₁₁×C₂²⋊Q₈	—	2	1	no	—
120	C₁₁×C₂²⋊Q₈	—	2	2	no	—
121	C₁₁×C₂²⋊Q₈	—	2	2	no	—
122	C₁₁×C₂²⋊Q₈	—	2	4	no	—
123	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₁×#121	—	2	2	no	—
127	C₁₁×#121	—	2	4	no	—
128	C₁₁×#121	—	2	1	no	—
129	C₁₁×#121	—	2	1	no	—
130	C₁₁×#121	—	2	2	no	—
131	C₁₁×#121	C₂³	1	4	yes	—
132	C₄×Q₈×C₁₁	—	2	2	no	—
133	C₄×Q₈×C₁₁	—	2	2	no	—
134	C₄×Q₈×C₁₁	—	2	2	no	—
135	C₄×Q₈×C₁₁	—	2	2	no	—
136	C₄×Q₈×C₁₁	—	2	2	no	—
137	C₄×Q₈×C₁₁	—	2	1	no	—
138	C₄×Q₈×C₁₁	—	2	1	no	—
139	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
141	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
143	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
144	C₄×D₄×C₁₁	—	2	4	no	—
145	C₄×D₄×C₁₁	—	2	1	no	—
146	C₄×D₄×C₁₁	—	2	2	no	—
147	C₄×D₄×C₁₁	—	2	1	no	—
148	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
149	C₄×D₄×C₁₁	D₄	1	2	yes	—
150	C₄×D₄×C₁₁	D₄	1	2	yes	—
151	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
152	C₄×D₄×C₁₁	C₂³	1	4	yes	—
153	C₁₁×#117	—	2	2	no	—
154	C₁₁×#117	—	2	2	no	—
155	C₁₁×#117	—	2	2	no	—
156	C₁₁×#117	—	2	2	no	—
157	C₁₁×#117	—	2	4	no	—
158	C₁₁×#117	C₂³	1	2	yes	—
159	C₁₁×#117	C₂³	1	1	yes	characteristic
160	C₁₁×#117	C₂³	1	2	yes	—
161	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
162	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
165	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
168	C₁₁×#107	C₂³	1	8	yes	—
169	C₁₁×#106	C₂³	1	8	yes	—
170	C₁₁×#103	C₂³	1	8	yes	—
171	C₁₁×#103	C₂³	1	8	yes	—
172	C₁₁×#103	C₂³	1	4	yes	—
173	C₁₁×#103	C₂³	1	4	yes	—
174	C₁₁×#102	C₂³	1	4	yes	—
175	C₁₁×#102	C₂³	1	4	yes	—
176	C₁₁×#97	C₂³	1	2	yes	—
177	C₁₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₁₁	C₂³	1	2	yes	—
179	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₁	C₂³	1	4	yes	—
182	C₄×C₈×C₁₁	C₂³	1	2	yes	—
183	#60723	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₁×#41	—	2	4	no	—
185	C₁₁×#41	—	2	8	no	—
186	C₁₁×#41	—	8	4	no	—
187	C₂×Q₈×C₁₁	—	2	1	no	—
188	C₂×Q₈×C₁₁	—	2	1	no	—
189	C₂×Q₈×C₁₁	—	2	2	no	—
190	C₂×Q₈×C₁₁	—	2	2	no	—
191	C₂×Q₈×C₁₁	—	2	2	no	—
192	C₂×Q₈×C₁₁	—	2	8	no	—
193	C₂×Q₈×C₁₁	—	8	2	no	—
194	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
197	C₂×D₄×C₁₁	—	2	2	no	—
198	C₂×D₄×C₁₁	—	2	4	no	—
199	C₂×D₄×C₁₁	—	2	1	no	—
200	C₂×D₄×C₁₁	—	2	1	no	—
201	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₁	—	2	2	no	—
205	C₂²×C₄×C₁₁	—	2	2	no	—
206	C₂²×C₄×C₁₁	—	2	2	no	—
207	C₂²×C₄×C₁₁	—	2	4	no	—
208	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
214	C₁₁×Q₁₆	—	2	16	no	—
215	C₁₁×SD₁₆	—	2	16	no	—
216	C₁₁×M₁₆	—	2	8	no	—
217	C₁₁×M₁₆	#41	1	8	yes	complemented
218	C₂×C₈×C₁₁	—	2	8	no	—
219	C₂×C₈×C₁₁	—	2	4	no	—
220	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
221	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
222	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
223	C₁₁×C₄⋊C₄	—	2	2	no	—
224	C₁₁×C₄⋊C₄	—	2	2	no	—
225	C₁₁×C₄⋊C₄	—	2	2	no	—
226	C₁₁×C₄⋊C₄	—	2	2	no	—
227	C₁₁×C₄⋊C₄	—	2	4	no	—
228	C₁₁×C₄⋊C₄	—	2	2	no	—
229	C₁₁×C₄⋊C₄	—	2	2	no	—
230	C₁₁×C₄⋊C₄	—	2	2	no	—
231	C₁₁×C₄⋊C₄	—	2	1	no	—
232	C₁₁×C₄⋊C₄	—	2	1	no	—
233	C₁₁×C₄⋊C₄	—	2	1	no	—
234	C₁₁×C₄⋊C₄	—	2	4	no	—
235	C₁₁×C₄⋊C₄	—	2	4	no	—
236	C₁₁×C₄⋊C₄	—	2	1	no	—
237	C₁₁×C₄⋊C₄	—	2	4	no	—
238	C₁₁×C₄⋊C₄	—	2	2	no	—
239	C₁₁×C₄⋊C₄	—	2	2	no	—
240	C₁₁×C₄⋊C₄	—	2	4	no	—
241	C₁₁×C₄⋊C₄	—	2	4	no	—
242	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
243	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
245	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
246	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
247	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
248	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
249	C₁₁×C₂²⋊C₄	—	2	2	no	—
250	C₁₁×C₂²⋊C₄	—	2	4	no	—
251	C₁₁×C₂²⋊C₄	—	2	4	no	—
252	C₁₁×C₂²⋊C₄	—	2	4	no	—
253	C₁₁×C₂²⋊C₄	—	2	4	no	—
254	C₁₁×C₂²⋊C₄	—	2	4	no	—
255	C₁₁×C₂²⋊C₄	—	2	2	no	—
256	C₁₁×C₂²⋊C₄	—	2	2	no	—
257	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
260	C₄²×C₁₁	—	2	4	no	—
261	C₄²×C₁₁	—	2	4	no	—
262	C₄²×C₁₁	—	2	4	no	—
263	C₄²×C₁₁	—	2	2	no	—
264	C₄²×C₁₁	C₂×D₄	1	2	yes	—
265	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₁	C₂×D₄	1	2	yes	—
268	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
269	C₄²×C₁₁	C₂⁴	1	2	yes	—
270	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
271	#3511	C₂×C₁₁	1	1	yes	characteristic
272	#3509	C₂×C₁₁	1	1	yes	characteristic, complemented
273	#3185	C₂×C₁₁	1	2	yes	complemented
274	#3182	C₂×C₁₁	1	2	yes	complemented
275	#3178	C₂×C₁₁	1	8	yes	complemented
276	#3170	C₂×C₁₁	1	2	yes	complemented
277	#3167	C₂×C₁₁	1	2	yes	complemented
278	#3165	C₂×C₁₁	1	1	yes	characteristic, complemented
279	#3152	C₂×C₁₁	1	1	yes	characteristic, complemented
280	#3131	C₂×C₁₁	1	1	yes	characteristic, complemented
281	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
282	#3063	C₂×C₁₁	1	4	yes	complemented
283	#2947	C₂×C₁₁	1	4	yes	complemented
284	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
285	C₂³×C₁₁	—	2	2	no	—
286	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₁₁	—	2	2	no	—
289	Q₈×C₁₁	—	2	8	no	—
290	Q₈×C₁₁	—	2	4	no	—
291	Q₈×C₁₁	—	4	4	no	—
292	Q₈×C₁₁	—	4	2	no	—
293	Q₈×C₁₁	—	4	4	no	—
294	Q₈×C₁₁	—	4	2	no	—
295	Q₈×C₁₁	—	8	2	no	—
296	D₄×C₁₁	—	2	4	no	—
297	D₄×C₁₁	—	2	2	no	—
298	D₄×C₁₁	—	2	4	no	—
299	D₄×C₁₁	—	4	4	no	—
300	D₄×C₁₁	—	4	2	no	—
301	D₄×C₁₁	—	4	2	no	—
302	D₄×C₁₁	—	8	4	no	—
303	C₂×C₄×C₁₁	—	2	2	no	—
304	C₂×C₄×C₁₁	—	2	4	no	—
305	C₂×C₄×C₁₁	—	2	2	no	—
306	C₂×C₄×C₁₁	—	2	4	no	—
307	C₂×C₄×C₁₁	—	2	4	no	—
308	C₂×C₄×C₁₁	—	2	2	no	—
309	C₂×C₄×C₁₁	—	2	2	no	—
310	C₂×C₄×C₁₁	—	2	2	no	—
311	C₂×C₄×C₁₁	—	2	4	no	—
312	C₂×C₄×C₁₁	—	2	4	no	—
313	C₂×C₄×C₁₁	—	4	4	no	—
314	C₂×C₄×C₁₁	—	4	4	no	—
315	C₂×C₄×C₁₁	—	8	4	no	—
316	C₂×C₄×C₁₁	—	8	2	no	—
317	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
326	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
327	C₈×C₁₁	—	2	2	no	—
328	C₈×C₁₁	—	2	2	no	—
329	C₈×C₁₁	C₂×#41	1	8	yes	—
330	C₂×#137	C₂²×C₁₁	1	4	yes	—
331	C₂×#131	C₂²×C₁₁	1	2	yes	—
332	#557	—	2	1	no	—
333	#557	—	2	1	no	—
334	#556	—	2	1	no	—
335	#556	—	2	1	no	—
336	#556	—	2	1	no	—
337	#555	—	2	1	no	—
338	#554	—	2	1	no	—
339	#553	—	2	2	no	—
340	#552	—	2	2	no	—
341	#552	—	2	2	no	—
342	#548	—	2	2	no	—
343	#547	—	2	1	no	—
344	#542	C₂²×C₁₁	1	4	yes	—
345	#541	C₂²×C₁₁	1	4	yes	—
346	#537	C₂²×C₁₁	1	2	yes	—
347	#536	C₂²×C₁₁	1	2	yes	—
348	#533	C₂²×C₁₁	1	2	yes	—
349	#533	C₂²×C₁₁	1	2	yes	—
350	#533	C₂²×C₁₁	1	2	yes	—
351	#533	C₂²×C₁₁	1	1	yes	characteristic
352	#532	C₂²×C₁₁	1	1	yes	characteristic
353	#532	C₂²×C₁₁	1	2	yes	—
354	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
355	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
356	#520	C₂²×C₁₁	1	2	yes	—
357	#519	C₂²×C₁₁	1	2	yes	—
358	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
359	#501	C₂²×C₁₁	1	4	yes	—
360	#500	C₂²×C₁₁	1	2	yes	—
361	#498	C₂²×C₁₁	1	2	yes	—
362	#497	C₂²×C₁₁	1	4	yes	—
363	#494	C₂²×C₁₁	1	2	yes	—
364	#492	C₂²×C₁₁	1	2	yes	—
365	#488	C₂²×C₁₁	1	4	yes	—
366	#487	C₂²×C₁₁	1	2	yes	—
367	#487	C₂²×C₁₁	1	4	yes	—
368	#487	C₂²×C₁₁	1	2	yes	—
369	#487	C₂²×C₁₁	1	1	yes	characteristic
370	#487	C₂²×C₁₁	1	1	yes	characteristic
371	#486	C₂²×C₁₁	1	1	yes	characteristic
372	#486	C₂²×C₁₁	1	1	yes	characteristic
373	#470	C₂²×C₁₁	1	8	yes	—
374	#468	C₂²×C₁₁	1	8	yes	—
375	#467	C₂²×C₁₁	1	8	yes	—
376	#465	C₂²×C₁₁	1	8	yes	—
377	#441	C₂²×C₁₁	1	8	yes	—
378	#440	C₂²×C₁₁	1	8	yes	—
379	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	—
380	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	—
381	#428	C₂²×C₁₁	1	4	yes	—
382	#416	C₂²×C₁₁	1	4	yes	—
383	C₂×#103	C₂²×C₁₁	1	4	yes	—
384	#405	C₂²×C₁₁	1	4	yes	—
385	#405	C₂²×C₁₁	1	2	yes	—
386	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
387	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
388	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
389	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
390	C₂²×C₁₁	—	2	1	no	—
391	C₂²×C₁₁	—	2	1	no	—
392	C₂²×C₁₁	—	2	2	no	—
393	C₂²×C₁₁	—	2	2	no	—
394	C₂²×C₁₁	—	2	2	no	—
395	C₂²×C₁₁	—	4	2	no	—
396	C₂²×C₁₁	—	4	2	no	—
397	C₂²×C₁₁	—	4	2	no	—
398	C₂²×C₁₁	#532	1	2	yes	—
399	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₁₁	—	2	2	no	—
401	C₄×C₁₁	—	2	2	no	—
402	C₄×C₁₁	—	2	1	no	—
403	C₄×C₁₁	—	2	2	no	—
404	C₄×C₁₁	—	2	1	no	—
405	C₄×C₁₁	—	4	2	no	—
406	C₄×C₁₁	—	4	4	no	—
407	C₄×C₁₁	—	4	4	no	—
408	C₄×C₁₁	—	4	2	no	—
409	C₄×C₁₁	—	4	2	no	—
410	C₄×C₁₁	#532	1	2	yes	—
411	C₄×C₁₁	#577	1	2	yes	—
412	C₄×C₁₁	#578	1	2	yes	—
413	C₄×C₁₁	C₂²×#41	1	2	yes	—
414	C₂×#41	—	2	2	no	—
415	C₂×#41	C₂³×C₁₁	1	2	yes	—
416	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
417	C₂²×Q₈	—	2	1	no	—
418	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
419	#137	—	2	16	no	—
420	C₂×Q₁₆	C₂³×C₁₁	1	8	yes	—
421	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
422	#131	—	2	8	no	—
423	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
424	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
425	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
426	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
427	C₄⋊Q₈	—	2	2	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
433	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
434	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
435	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
436	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
437	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
438	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
439	#127	C₂³×C₁₁	1	1	yes	characteristic
440	#126	—	2	4	no	—
441	#126	—	2	4	no	—
442	#126	—	2	4	no	—
443	#125	—	2	4	no	—
444	#125	—	2	4	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#125	—	2	2	no	—
448	#125	C₂³×C₁₁	1	2	yes	—
449	#124	—	2	2	no	—
450	#124	—	2	4	no	—
451	#124	—	2	2	no	—
452	#124	C₂³×C₁₁	1	2	yes	—
453	#123	—	2	4	no	—
454	#123	—	2	4	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	4	no	—
462	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
463	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
464	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
465	#121	—	2	2	no	—
466	#121	—	2	4	no	—
467	#121	—	2	1	no	—
468	#121	—	2	1	no	—
469	#121	—	2	2	no	—
470	#121	C₂³×C₁₁	1	4	yes	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	—	2	1	no	—
478	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
479	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
480	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
481	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
482	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
488	C₄×D₄	D₄×C₁₁	1	2	yes	—
489	C₄×D₄	D₄×C₁₁	1	2	yes	—
490	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₁₁	1	4	yes	—
492	#117	—	2	2	no	—
493	#117	—	2	2	no	—
494	#117	—	2	2	no	—
495	#117	—	2	2	no	—
496	#117	—	2	4	no	—
497	#117	C₂³×C₁₁	1	2	yes	—
498	#117	C₂³×C₁₁	1	1	yes	characteristic
499	#117	C₂³×C₁₁	1	2	yes	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
505	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
507	#107	C₂³×C₁₁	1	8	yes	—
508	#106	C₂³×C₁₁	1	8	yes	—
509	#103	C₂³×C₁₁	1	8	yes	—
510	#103	C₂³×C₁₁	1	8	yes	—
511	#103	C₂³×C₁₁	1	4	yes	—
512	#103	C₂³×C₁₁	1	4	yes	—
513	#102	C₂³×C₁₁	1	4	yes	—
514	#102	C₂³×C₁₁	1	4	yes	—
515	#97	C₂³×C₁₁	1	4	yes	—
516	#97	C₂³×C₁₁	1	2	yes	—
517	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
518	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
519	C₄×C₈	C₂³×C₁₁	1	2	yes	—
520	C₄×C₈	C₂³×C₁₁	1	4	yes	—
521	C₄×C₈	C₂³×C₁₁	1	2	yes	—
522	C₂×C₁₁	—	2	2	no	—
523	C₂×C₁₁	—	4	2	no	—
524	C₂×C₁₁	—	8	2	no	—
525	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
526	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
527	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
528	#41	—	2	4	no	—
529	#41	—	2	8	no	—
530	#41	—	8	4	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	8	no	—
537	C₂×Q₈	—	8	2	no	—
538	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
539	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
540	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
546	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
547	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
555	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
558	Q₁₆	—	2	16	no	—
559	SD₁₆	—	2	16	no	—
560	M₁₆	—	2	8	no	—
561	M₁₆	C₁₁×#41	1	8	yes	complemented
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	—	2	8	no	—
564	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
565	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
566	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
587	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
588	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
589	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
590	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
591	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
592	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
602	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
603	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	2	no	—
608	C₄²	C₂×D₄×C₁₁	1	2	yes	—
609	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
610	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
611	C₄²	C₂×D₄×C₁₁	1	2	yes	—
612	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
613	C₄²	C₂⁴×C₁₁	1	2	yes	—
614	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
615	C₁₁	#60723	1	1	yes	characteristic, direct product factor, Sylow
616	C₂³	—	2	2	no	—
617	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
618	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
619	Q₈	—	2	2	no	—
620	Q₈	—	2	8	no	—
621	Q₈	—	2	4	no	—
622	Q₈	—	4	4	no	—
623	Q₈	—	4	2	no	—
624	Q₈	—	4	4	no	—
625	Q₈	—	4	2	no	—
626	Q₈	—	8	2	no	—
627	D₄	—	2	4	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	4	no	—
630	D₄	—	4	4	no	—
631	D₄	—	4	2	no	—
632	D₄	—	4	2	no	—
633	D₄	—	8	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	—	8	2	no	—
648	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
655	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
656	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
657	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
658	C₈	—	2	2	no	—
659	C₈	—	2	2	no	—
660	C₈	C₂×C₁₁×#41	1	8	yes	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	C₁₁×#532	1	2	yes	—
670	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	4	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	C₁₁×#532	1	2	yes	—
682	C₄	C₁₁×#577	1	2	yes	—
683	C₄	C₁₁×#578	1	2	yes	—
684	C₄	C₂²×C₁₁×#41	1	2	yes	—
685	C₂	—	2	2	no	—
686	C₂	—	4	2	no	—
687	C₂	—	8	2	no	—
688	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
689	C₂	C₂×C₁₁×#577	1	1	yes	characteristic
690	C₂	C₂×C₁₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3511	C₂
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×#3185	C₂	semidirect
4. C₁₁×#3182	C₂	semidirect
5. C₁₁×#3178	C₂	semidirect
6. C₁₁×#3170	C₂	semidirect
7. C₁₁×#3167	C₂	semidirect
8. C₁₁×#3165	C₂	semidirect
9. C₁₁×#3152	C₂	semidirect
10. C₁₁×#3131	C₂	semidirect
11. C₂×C₁₁×#487	C₂	semidirect
12. C₁₁×#3063	C₂	semidirect
13. C₁₁×#2947	C₂	semidirect
14. C₄×C₁₁×#131	C₂	semidirect
183. #60723	C₁₁	direct (N × H)
217. C₁₁×M₁₆	#41	semidirect
272. #3509	C₂×C₁₁	semidirect
273. #3185	C₂×C₁₁	semidirect
274. #3182	C₂×C₁₁	semidirect
275. #3178	C₂×C₁₁	semidirect
276. #3170	C₂×C₁₁	semidirect
277. #3167	C₂×C₁₁	semidirect
278. #3165	C₂×C₁₁	semidirect
279. #3152	C₂×C₁₁	semidirect
280. #3131	C₂×C₁₁	semidirect
281. C₂×#487	C₂×C₁₁	semidirect
282. #3063	C₂×C₁₁	semidirect
283. #2947	C₂×C₁₁	semidirect
284. C₄×#131	C₂×C₁₁	semidirect
561. M₁₆	C₁₁×#41	semidirect
615. C₁₁	#60723	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×#3511	2
C₁₁×#3509	2
C₁₁×#3185	2
C₁₁×#3182	2
C₁₁×#3178	2
C₁₁×#3170	2
C₁₁×#3167	2
C₁₁×#3165	2
C₁₁×#3152	2
C₁₁×#3131	2
C₂×C₁₁×#487	2
C₁₁×#3063	2
C₁₁×#2947	2
C₄×C₁₁×#131	2
#60723	11

Subgroups — C11×#60723 #14637916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60723 #14637916