Subgroups — C₁₁×#36601 #14613794

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2861	C₂	1	2	yes	maximal
2	C₁₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2596	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2580	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2573	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2512	C₂	1	2	yes	maximal
8	C₁₁×#2511	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2469	C₂	1	4	yes	maximal, complemented
10	C₁₁×#2373	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2357	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₁×#125	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
15	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×#126	C₂²	1	4	yes	—
17	C₂×C₁₁×#125	C₂²	1	2	yes	—
18	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#400	C₂²	1	4	yes	—
24	C₁₁×#400	C₂²	1	4	yes	—
25	C₁₁×#400	C₂²	1	2	yes	—
26	C₁₁×#399	C₂²	1	2	yes	—
27	C₁₁×#397	C₂²	1	4	yes	—
28	C₁₁×#396	C₂²	1	4	yes	—
29	C₁₁×#395	C₂²	1	2	yes	—
30	C₁₁×#393	C₂²	1	2	yes	—
31	C₁₁×#391	C₂²	1	1	yes	characteristic
32	C₁₁×#391	C₂²	1	2	yes	—
33	C₁₁×#391	C₂²	1	2	yes	—
34	C₁₁×#390	C₂²	1	1	yes	characteristic
35	C₁₁×#390	C₂²	1	2	yes	—
36	C₁₁×#390	C₂²	1	2	yes	—
37	C₁₁×#389	C₂²	1	4	yes	—
38	C₁₁×#389	C₂²	1	2	yes	—
39	C₁₁×#389	C₂²	1	2	yes	—
40	C₁₁×#389	C₂²	1	4	yes	—
41	C₁₁×#388	C₂²	1	4	yes	—
42	C₁₁×#388	C₂²	1	4	yes	—
43	C₁₁×#388	C₂²	1	4	yes	—
44	C₁₁×#388	C₂²	1	4	yes	—
45	C₁₁×#388	C₂²	1	4	yes	—
46	C₁₁×#388	C₂²	1	4	yes	—
47	C₁₁×#388	C₂²	1	4	yes	—
48	C₁₁×#387	C₂²	1	4	yes	—
49	C₁₁×#387	C₂²	1	4	yes	—
50	C₁₁×#387	C₂²	1	4	yes	—
51	C₁₁×#387	C₂²	1	4	yes	—
52	C₁₁×#387	C₂²	1	4	yes	—
53	C₁₁×#387	C₂²	1	4	yes	—
54	C₁₁×#385	C₂²	1	4	yes	—
55	C₁₁×#384	C₂²	1	2	yes	—
56	C₁₁×#383	C₂²	1	2	yes	—
57	C₁₁×#382	C₂²	1	1	yes	characteristic
58	C₁₁×#382	C₂²	1	1	yes	characteristic
59	C₁₁×#382	C₂²	1	1	yes	characteristic
60	C₁₁×#381	C₂²	1	2	yes	—
61	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₁₁×#376	C₂²	1	2	yes	—
73	C₄³×C₁₁	C₂²	1	1	yes	characteristic
74	C₄³×C₁₁	C₂²	1	2	yes	—
75	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
79	C₁₁×#126	—	2	16	no	—
80	C₁₁×#125	—	2	8	no	—
81	C₁₁×#124	—	2	4	no	—
82	C₄×Q₈×C₁₁	—	2	8	no	—
83	C₄×Q₈×C₁₁	—	2	4	no	—
84	C₄×Q₈×C₁₁	—	2	4	no	—
85	C₄×D₄×C₁₁	—	2	4	no	—
86	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
123	C₁₁×#95	C₂³	1	1	yes	characteristic
124	C₁₁×#95	C₂³	1	2	yes	—
125	C₁₁×#95	C₂³	1	4	yes	—
126	C₁₁×#95	C₂³	1	4	yes	—
127	C₁₁×#95	C₂³	1	2	yes	—
128	C₁₁×#95	C₂³	1	4	yes	—
129	C₁₁×#95	C₂³	1	1	yes	characteristic
130	C₁₁×#95	C₂³	1	2	yes	—
131	C₁₁×#95	C₂³	1	2	yes	—
132	C₁₁×#95	C₂³	1	4	yes	—
133	C₁₁×#95	C₂³	1	4	yes	—
134	C₁₁×#95	C₂³	1	4	yes	—
135	C₁₁×#95	C₂³	1	4	yes	—
136	C₁₁×#95	C₂³	1	2	yes	—
137	C₁₁×#95	C₂³	1	2	yes	—
138	C₁₁×#95	C₂³	1	4	yes	—
139	C₁₁×#95	C₂³	1	4	yes	—
140	C₁₁×#95	C₂³	1	4	yes	—
141	#36601	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
143	C₂×Q₈×C₁₁	—	2	4	no	—
144	C₂×Q₈×C₁₁	—	2	2	no	—
145	C₂×Q₈×C₁₁	—	2	2	no	—
146	C₂×Q₈×C₁₁	—	2	2	no	—
147	C₂×Q₈×C₁₁	—	2	2	no	—
148	C₂×D₄×C₁₁	—	2	2	no	—
149	C₂×D₄×C₁₁	—	2	2	no	—
150	C₂×D₄×C₁₁	—	2	2	no	—
151	C₂²×C₄×C₁₁	—	2	4	no	—
152	C₂²×C₄×C₁₁	—	4	4	no	—
153	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
167	C₁₁×C₄⋊C₄	—	2	2	no	—
168	C₁₁×C₄⋊C₄	—	2	4	no	—
169	C₁₁×C₄⋊C₄	—	2	4	no	—
170	C₁₁×C₄⋊C₄	—	2	4	no	—
171	C₁₁×C₄⋊C₄	—	2	2	no	—
172	C₁₁×C₄⋊C₄	—	2	2	no	—
173	C₁₁×C₄⋊C₄	—	2	4	no	—
174	C₁₁×C₄⋊C₄	—	2	8	no	—
175	C₁₁×C₄⋊C₄	—	2	8	no	—
176	C₁₁×C₄⋊C₄	—	2	4	no	—
177	C₁₁×C₄⋊C₄	—	2	4	no	—
178	C₁₁×C₄⋊C₄	—	2	8	no	—
179	C₁₁×C₄⋊C₄	—	2	8	no	—
180	C₁₁×C₄⋊C₄	—	4	4	no	—
181	C₁₁×C₄⋊C₄	—	4	4	no	—
182	C₁₁×C₄⋊C₄	#41	1	8	yes	—
183	C₁₁×C₂²⋊C₄	—	2	4	no	—
184	C₁₁×C₂²⋊C₄	—	2	8	no	—
185	C₁₁×C₂²⋊C₄	—	2	8	no	—
186	C₁₁×C₂²⋊C₄	—	2	8	no	—
187	C₁₁×C₂²⋊C₄	—	2	8	no	—
188	C₁₁×C₂²⋊C₄	—	4	4	no	—
189	C₁₁×C₂²⋊C₄	—	4	4	no	—
190	C₄²×C₁₁	—	2	4	no	—
191	C₄²×C₁₁	—	2	4	no	—
192	C₄²×C₁₁	—	2	4	no	—
193	C₄²×C₁₁	—	2	4	no	—
194	C₄²×C₁₁	—	2	4	no	—
195	C₄²×C₁₁	—	2	8	no	—
196	C₄²×C₁₁	—	2	2	no	—
197	C₄²×C₁₁	—	2	4	no	—
198	C₄²×C₁₁	—	4	2	no	—
199	C₄²×C₁₁	—	4	2	no	—
200	C₄²×C₁₁	—	4	2	no	—
201	C₄²×C₁₁	—	4	4	no	—
202	C₄²×C₁₁	#41	1	4	yes	—
203	C₄²×C₁₁	#41	1	4	yes	—
204	#2861	C₂×C₁₁	1	2	yes	—
205	#2859	C₂×C₁₁	1	1	yes	characteristic, complemented
206	#2596	C₂×C₁₁	1	4	yes	complemented
207	#2581	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#2580	C₂×C₁₁	1	1	yes	characteristic
209	#2573	C₂×C₁₁	1	4	yes	complemented
210	#2512	C₂×C₁₁	1	2	yes	—
211	#2511	C₂×C₁₁	1	2	yes	complemented
212	#2469	C₂×C₁₁	1	4	yes	complemented
213	#2373	C₂×C₁₁	1	4	yes	complemented
214	#2357	C₂×C₁₁	1	1	yes	characteristic
215	#2356	C₂×C₁₁	1	1	yes	characteristic, complemented
216	C₄×#125	C₂×C₁₁	1	2	yes	complemented
217	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
218	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
219	C₂³×C₁₁	—	2	4	no	—
220	C₂³×C₁₁	—	2	2	no	—
221	C₂³×C₁₁	—	2	2	no	—
222	C₂³×C₁₁	—	2	2	no	—
223	C₂³×C₁₁	—	2	4	no	—
224	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
225	Q₈×C₁₁	—	2	8	no	—
226	Q₈×C₁₁	—	4	4	no	—
227	D₄×C₁₁	—	4	4	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	2	no	—
230	C₂×C₄×C₁₁	—	2	2	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	2	no	—
234	C₂×C₄×C₁₁	—	2	2	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	4	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	2	4	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	2	4	no	—
248	C₂×C₄×C₁₁	—	2	4	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	4	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	8	4	no	—
258	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
259	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
261	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
262	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
263	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
266	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
267	C₂×#126	C₂²×C₁₁	1	4	yes	—
268	C₂×#125	C₂²×C₁₁	1	2	yes	—
269	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
271	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
274	#400	C₂²×C₁₁	1	4	yes	—
275	#400	C₂²×C₁₁	1	4	yes	—
276	#400	C₂²×C₁₁	1	2	yes	—
277	#399	C₂²×C₁₁	1	2	yes	—
278	#397	C₂²×C₁₁	1	4	yes	—
279	#396	C₂²×C₁₁	1	4	yes	—
280	#395	C₂²×C₁₁	1	2	yes	—
281	#393	C₂²×C₁₁	1	2	yes	—
282	#391	C₂²×C₁₁	1	2	yes	—
283	#391	C₂²×C₁₁	1	2	yes	—
284	#391	C₂²×C₁₁	1	1	yes	characteristic
285	#390	C₂²×C₁₁	1	2	yes	—
286	#390	C₂²×C₁₁	1	2	yes	—
287	#390	C₂²×C₁₁	1	1	yes	characteristic
288	#389	C₂²×C₁₁	1	2	yes	—
289	#389	C₂²×C₁₁	1	2	yes	—
290	#389	C₂²×C₁₁	1	4	yes	—
291	#389	C₂²×C₁₁	1	4	yes	—
292	#388	C₂²×C₁₁	1	4	yes	—
293	#388	C₂²×C₁₁	1	4	yes	—
294	#388	C₂²×C₁₁	1	4	yes	—
295	#388	C₂²×C₁₁	1	4	yes	—
296	#388	C₂²×C₁₁	1	4	yes	—
297	#388	C₂²×C₁₁	1	4	yes	—
298	#388	C₂²×C₁₁	1	4	yes	—
299	#387	C₂²×C₁₁	1	4	yes	—
300	#387	C₂²×C₁₁	1	4	yes	—
301	#387	C₂²×C₁₁	1	4	yes	—
302	#387	C₂²×C₁₁	1	4	yes	—
303	#387	C₂²×C₁₁	1	4	yes	—
304	#387	C₂²×C₁₁	1	4	yes	—
305	#385	C₂²×C₁₁	1	4	yes	—
306	#384	C₂²×C₁₁	1	2	yes	—
307	#383	C₂²×C₁₁	1	2	yes	—
308	#382	C₂²×C₁₁	1	1	yes	characteristic
309	#382	C₂²×C₁₁	1	1	yes	characteristic
310	#382	C₂²×C₁₁	1	1	yes	characteristic
311	#381	C₂²×C₁₁	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
313	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
316	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
318	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
320	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
323	#376	C₂²×C₁₁	1	2	yes	—
324	C₄³	C₂²×C₁₁	1	2	yes	—
325	C₄³	C₂²×C₁₁	1	1	yes	characteristic
326	C₂²×C₁₁	—	4	2	no	—
327	C₂²×C₁₁	—	4	2	no	—
328	C₂²×C₁₁	—	4	4	no	—
329	C₂²×C₁₁	—	4	2	no	—
330	C₂²×C₁₁	—	4	4	no	—
331	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
332	C₂²×C₁₁	C₂²×#41	1	2	yes	—
333	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
334	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂²×C₁₁	#585	1	2	yes	—
336	C₄×C₁₁	—	2	4	no	—
337	C₄×C₁₁	—	2	2	no	—
338	C₄×C₁₁	—	2	4	no	—
339	C₄×C₁₁	—	2	2	no	—
340	C₄×C₁₁	—	2	4	no	—
341	C₄×C₁₁	—	2	4	no	—
342	C₄×C₁₁	—	4	2	no	—
343	C₄×C₁₁	—	4	2	no	—
344	C₄×C₁₁	—	4	4	no	—
345	C₄×C₁₁	—	4	4	no	—
346	C₄×C₁₁	—	4	2	no	—
347	C₄×C₁₁	—	4	2	no	—
348	C₄×C₁₁	—	4	2	no	—
349	C₄×C₁₁	#556	1	4	yes	—
350	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
351	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
354	#126	—	2	16	no	—
355	#125	—	2	8	no	—
356	#124	—	2	4	no	—
357	C₄×Q₈	—	2	8	no	—
358	C₄×Q₈	—	2	4	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×D₄	—	2	4	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
384	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
386	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
387	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
389	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
390	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
393	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
396	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
398	#95	C₂³×C₁₁	1	1	yes	characteristic
399	#95	C₂³×C₁₁	1	2	yes	—
400	#95	C₂³×C₁₁	1	4	yes	—
401	#95	C₂³×C₁₁	1	4	yes	—
402	#95	C₂³×C₁₁	1	2	yes	—
403	#95	C₂³×C₁₁	1	4	yes	—
404	#95	C₂³×C₁₁	1	1	yes	characteristic
405	#95	C₂³×C₁₁	1	2	yes	—
406	#95	C₂³×C₁₁	1	2	yes	—
407	#95	C₂³×C₁₁	1	4	yes	—
408	#95	C₂³×C₁₁	1	4	yes	—
409	#95	C₂³×C₁₁	1	4	yes	—
410	#95	C₂³×C₁₁	1	4	yes	—
411	#95	C₂³×C₁₁	1	2	yes	—
412	#95	C₂³×C₁₁	1	2	yes	—
413	#95	C₂³×C₁₁	1	4	yes	—
414	#95	C₂³×C₁₁	1	4	yes	—
415	#95	C₂³×C₁₁	1	4	yes	—
416	C₂×C₁₁	—	8	2	no	—
417	C₂×C₁₁	#3444	1	1	yes	characteristic
418	C₂×C₁₁	C₂×#556	1	1	yes	characteristic
419	C₂×C₁₁	#3480	1	2	yes	—
420	C₂×C₁₁	#3510	1	1	yes	characteristic
421	C₂×C₁₁	#3515	1	2	yes	—
422	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₄⋊C₄	—	4	4	no	—
462	C₄⋊C₄	C₁₁×#41	1	8	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	2	8	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	4	no	—
478	C₄²	—	4	2	no	—
479	C₄²	—	4	2	no	—
480	C₄²	—	4	2	no	—
481	C₄²	—	4	4	no	—
482	C₄²	C₁₁×#41	1	4	yes	—
483	C₄²	C₁₁×#41	1	4	yes	—
484	C₁₁	#36601	1	1	yes	characteristic, direct product factor, Sylow
485	C₂³	—	2	4	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
491	Q₈	—	2	8	no	—
492	Q₈	—	4	4	no	—
493	D₄	—	4	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
525	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
526	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
527	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
528	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
529	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
530	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
531	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
532	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	4	no	—
538	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
539	C₂²	C₂²×C₁₁×#41	1	2	yes	—
540	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
541	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂²	C₁₁×#585	1	2	yes	—
543	C₄	—	2	4	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	4	no	—
548	C₄	—	2	4	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	C₁₁×#556	1	4	yes	—
557	C₂	—	8	2	no	—
558	C₂	C₁₁×#3444	1	1	yes	characteristic
559	C₂	C₂×C₁₁×#556	1	1	yes	characteristic
560	C₂	C₁₁×#3480	1	2	yes	—
561	C₂	C₁₁×#3510	1	1	yes	characteristic
562	C₂	C₁₁×#3515	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2859	C₂	semidirect
3. C₁₁×#2596	C₂	semidirect
4. C₁₁×#2581	C₂	semidirect
6. C₁₁×#2573	C₂	semidirect
8. C₁₁×#2511	C₂	semidirect
9. C₁₁×#2469	C₂	semidirect
10. C₁₁×#2373	C₂	semidirect
12. C₁₁×#2356	C₂	semidirect
13. C₄×C₁₁×#125	C₂	semidirect
15. C₄²×Q₈×C₁₁	C₂	semidirect
141. #36601	C₁₁	direct (N × H)
205. #2859	C₂×C₁₁	semidirect
206. #2596	C₂×C₁₁	semidirect
207. #2581	C₂×C₁₁	semidirect
209. #2573	C₂×C₁₁	semidirect
211. #2511	C₂×C₁₁	semidirect
212. #2469	C₂×C₁₁	semidirect
213. #2373	C₂×C₁₁	semidirect
215. #2356	C₂×C₁₁	semidirect
216. C₄×#125	C₂×C₁₁	semidirect
218. C₄²×Q₈	C₂×C₁₁	semidirect
484. C₁₁	#36601	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×#2861	2
C₁₁×#2859	2
C₁₁×#2596	2
C₁₁×#2581	2
C₁₁×#2580	2
C₁₁×#2573	2
C₁₁×#2512	2
C₁₁×#2511	2
C₁₁×#2469	2
C₁₁×#2373	2
C₁₁×#2357	2
C₁₁×#2356	2
C₄×C₁₁×#125	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36601	11

Subgroups — C11×#36601 #14613794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36601 #14613794