Subgroups — C₁₁×#22587 #14599780

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#416	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2880	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1937	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1826	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1789	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1764	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
16	C₁₁×#433	—	2	2	no	—
17	C₁₁×#432	—	2	1	no	—
18	C₁₁×#431	—	2	1	no	—
19	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
20	C₁₁×#424	C₂²	1	2	yes	complemented
21	C₂×C₁₁×#104	C₂²	1	2	yes	—
22	C₂×C₁₁×#104	C₂²	1	2	yes	—
23	C₁₁×#416	C₄	1	1	yes	characteristic, complemented
24	C₁₁×#416	C₄	1	1	yes	characteristic, complemented
25	C₁₁×#416	C₄	1	1	yes	characteristic, complemented
26	C₁₁×#416	C₄	1	1	yes	characteristic, complemented
27	C₁₁×#416	C₂²	1	1	yes	characteristic
28	C₁₁×#416	C₂²	1	1	yes	characteristic
29	C₁₁×#416	C₂²	1	1	yes	characteristic
30	C₁₁×#416	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#103	C₄	1	1	yes	characteristic, complemented
32	C₂×C₁₁×#103	C₄	1	1	yes	characteristic, complemented
33	C₂×C₁₁×#102	C₄	1	1	yes	characteristic, complemented
34	C₂×C₁₁×#102	C₄	1	1	yes	characteristic, complemented
35	C₁₁×#408	—	2	2	no	—
36	C₁₁×#408	C₂²	1	2	yes	—
37	C₁₁×#407	—	2	1	no	—
38	C₁₁×#407	C₂²	1	1	yes	characteristic
39	C₁₁×#407	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
41	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₁×#405	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
44	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₁×#341	C₂²	1	2	yes	complemented
46	C₁₁×#339	C₂²	1	2	yes	complemented
47	C₁₁×#339	C₂²	1	2	yes	complemented
48	C₁₁×#336	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	—	2	1	no	—
50	C₂×C₁₁×#41	—	2	1	no	—
51	C₂×C₁₁×#41	—	2	4	no	—
52	C₂×C₁₁×#41	—	4	2	no	—
53	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
56	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₁	—	2	1	no	—
59	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁	—	2	1	no	—
61	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₁₁×#131	—	2	4	no	—
63	C₁₁×#131	—	4	2	no	—
64	C₂×C₁₁×M₁₆	—	2	2	no	—
65	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₁	—	2	2	no	—
68	C₂²×C₈×C₁₁	—	4	2	no	—
69	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
76	C₁₁×#117	—	2	1	no	—
77	C₁₁×#117	—	2	1	no	—
78	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
79	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
80	C₁₁×#117	C₂³	1	1	yes	characteristic
81	C₁₁×#117	C₂³	1	1	yes	characteristic
82	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₁	—	2	1	no	—
87	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
88	C₁₁×#108	—	4	2	no	—
89	C₁₁×C₄⋊C₈	—	2	2	no	—
90	C₁₁×C₄⋊C₈	—	2	2	no	—
91	C₁₁×#104	—	2	4	no	—
92	C₁₁×#104	—	4	2	no	—
93	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
96	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
97	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
98	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
99	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
100	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
101	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
103	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
104	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
105	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
106	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
107	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
108	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
109	C₁₁×C₂²⋊C₈	—	2	1	no	—
110	C₁₁×C₂²⋊C₈	—	2	1	no	—
111	C₁₁×C₂²⋊C₈	—	2	1	no	—
112	C₁₁×C₂²⋊C₈	—	2	1	no	—
113	C₁₁×C₂²⋊C₈	—	2	2	no	—
114	C₁₁×C₂²⋊C₈	—	2	2	no	—
115	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
116	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
118	C₁₁×#97	—	2	2	no	—
119	C₄×C₈×C₁₁	—	2	2	no	—
120	C₄×C₈×C₁₁	—	4	2	no	—
121	C₁₁×#95	—	2	1	no	—
122	#22587	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₁	—	2	1	no	—
124	C₂⁴×C₁₁	#41	1	1	yes	characteristic
125	C₁₁×#41	—	2	2	no	—
126	C₁₁×#41	—	2	2	no	—
127	C₁₁×#41	—	2	2	no	—
128	C₁₁×#41	—	2	2	no	—
129	C₁₁×#41	—	2	2	no	—
130	C₁₁×#41	—	4	4	no	—
131	C₁₁×#41	—	4	1	no	—
132	C₁₁×#41	—	4	1	no	—
133	C₁₁×#41	—	4	4	no	—
134	C₁₁×#41	#41	1	4	yes	—
135	C₂×Q₈×C₁₁	—	2	1	no	—
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	—	4	1	no	—
138	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×D₄×C₁₁	—	2	1	no	—
141	C₂×D₄×C₁₁	—	2	2	no	—
142	C₂×D₄×C₁₁	—	2	1	no	—
143	C₂×D₄×C₁₁	—	2	1	no	—
144	C₂×D₄×C₁₁	—	2	1	no	—
145	C₂×D₄×C₁₁	—	2	1	no	—
146	C₂×D₄×C₁₁	—	4	1	no	—
147	C₂×D₄×C₁₁	—	4	4	no	—
148	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₁	—	2	1	no	—
151	C₂²×C₄×C₁₁	—	2	2	no	—
152	C₂²×C₄×C₁₁	—	2	2	no	—
153	C₂²×C₄×C₁₁	—	2	1	no	—
154	C₂²×C₄×C₁₁	—	2	1	no	—
155	C₂²×C₄×C₁₁	—	2	2	no	—
156	C₂²×C₄×C₁₁	—	2	1	no	—
157	C₂²×C₄×C₁₁	—	2	1	no	—
158	C₂²×C₄×C₁₁	—	2	1	no	—
159	C₂²×C₄×C₁₁	—	2	1	no	—
160	C₂²×C₄×C₁₁	—	4	4	no	—
161	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
167	C₁₁×M₁₆	—	2	2	no	—
168	C₁₁×M₁₆	—	2	2	no	—
169	C₁₁×M₁₆	—	2	2	no	—
170	C₁₁×M₁₆	—	2	2	no	—
171	C₁₁×M₁₆	—	4	4	no	—
172	C₂×C₈×C₁₁	—	2	2	no	—
173	C₂×C₈×C₁₁	—	2	2	no	—
174	C₂×C₈×C₁₁	—	2	2	no	—
175	C₂×C₈×C₁₁	—	2	2	no	—
176	C₂×C₈×C₁₁	—	2	2	no	—
177	C₂×C₈×C₁₁	—	2	2	no	—
178	C₂×C₈×C₁₁	—	4	1	no	—
179	C₂×C₈×C₁₁	—	4	1	no	—
180	C₂×C₈×C₁₁	—	4	1	no	—
181	C₂×C₈×C₁₁	—	4	1	no	—
182	C₂×C₈×C₁₁	—	4	4	no	—
183	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
189	C₁₁×C₄⋊C₄	—	2	1	no	—
190	C₁₁×C₄⋊C₄	—	2	1	no	—
191	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₁₁×C₂²⋊C₄	—	2	4	no	—
196	C₁₁×C₂²⋊C₄	—	2	1	no	—
197	C₁₁×C₂²⋊C₄	—	2	1	no	—
198	C₁₁×C₂²⋊C₄	—	2	1	no	—
199	C₁₁×C₂²⋊C₄	—	2	1	no	—
200	C₄²×C₁₁	—	2	1	no	—
201	C₄²×C₁₁	—	2	1	no	—
202	C₄²×C₁₁	—	2	1	no	—
203	C₄²×C₁₁	—	2	1	no	—
204	C₄²×C₁₁	—	2	2	no	—
205	C₄²×C₁₁	—	2	2	no	—
206	#2924	C₂×C₁₁	1	1	yes	characteristic, complemented
207	C₂×#416	C₂×C₁₁	1	1	yes	characteristic
208	#2880	C₂×C₁₁	1	1	yes	characteristic
209	#1937	C₂×C₁₁	1	2	yes	complemented
210	#1929	C₂×C₁₁	1	2	yes	complemented
211	#1866	C₂×C₁₁	1	2	yes	complemented
212	#1826	C₂×C₁₁	1	1	yes	characteristic, complemented
213	#1810	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#1789	C₂×C₁₁	1	1	yes	characteristic
215	#1764	C₂×C₁₁	1	2	yes	complemented
216	C₈×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
217	C₂³×C₁₁	—	2	1	no	—
218	C₂³×C₁₁	—	2	2	no	—
219	C₂³×C₁₁	—	2	2	no	—
220	C₂³×C₁₁	—	2	1	no	—
221	C₂³×C₁₁	—	4	1	no	—
222	C₂³×C₁₁	—	4	2	no	—
223	C₂³×C₁₁	—	4	2	no	—
224	C₂³×C₁₁	—	8	1	no	—
225	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
227	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
228	Q₈×C₁₁	—	2	1	no	—
229	Q₈×C₁₁	—	2	1	no	—
230	Q₈×C₁₁	—	2	1	no	—
231	Q₈×C₁₁	—	4	2	no	—
232	Q₈×C₁₁	#117	1	2	yes	—
233	D₄×C₁₁	—	2	4	no	—
234	D₄×C₁₁	—	2	1	no	—
235	D₄×C₁₁	—	2	1	no	—
236	D₄×C₁₁	—	2	1	no	—
237	D₄×C₁₁	—	4	2	no	—
238	D₄×C₁₁	—	4	2	no	—
239	D₄×C₁₁	—	4	2	no	—
240	D₄×C₁₁	—	4	2	no	—
241	D₄×C₁₁	#117	1	2	yes	—
242	C₂×C₄×C₁₁	—	2	1	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	2	1	no	—
245	C₂×C₄×C₁₁	—	2	1	no	—
246	C₂×C₄×C₁₁	—	2	1	no	—
247	C₂×C₄×C₁₁	—	2	1	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	4	no	—
252	C₂×C₄×C₁₁	—	2	1	no	—
253	C₂×C₄×C₁₁	—	2	1	no	—
254	C₂×C₄×C₁₁	—	2	1	no	—
255	C₂×C₄×C₁₁	—	2	1	no	—
256	C₂×C₄×C₁₁	—	2	1	no	—
257	C₂×C₄×C₁₁	—	4	2	no	—
258	C₂×C₄×C₁₁	—	4	2	no	—
259	C₂×C₄×C₁₁	—	4	2	no	—
260	C₂×C₄×C₁₁	—	4	2	no	—
261	C₂×C₄×C₁₁	—	4	2	no	—
262	C₂×C₄×C₁₁	—	4	2	no	—
263	C₂×C₄×C₁₁	—	4	2	no	—
264	C₂×C₄×C₁₁	—	8	1	no	—
265	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
270	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₁₁	—	2	1	no	—
272	C₈×C₁₁	—	2	1	no	—
273	C₈×C₁₁	—	2	1	no	—
274	C₈×C₁₁	—	2	1	no	—
275	C₈×C₁₁	—	2	2	no	—
276	C₈×C₁₁	—	2	2	no	—
277	C₈×C₁₁	—	4	2	no	—
278	C₈×C₁₁	—	4	2	no	—
279	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×#131	C₂²×C₁₁	1	2	yes	—
281	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
283	#433	—	2	2	no	—
284	#432	—	2	1	no	—
285	#431	—	2	1	no	—
286	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
287	#424	C₂²×C₁₁	1	2	yes	complemented
288	C₂×#104	C₂²×C₁₁	1	2	yes	—
289	C₂×#104	C₂²×C₁₁	1	2	yes	—
290	#416	C₄×C₁₁	1	1	yes	characteristic, complemented
291	#416	C₄×C₁₁	1	1	yes	characteristic, complemented
292	#416	C₄×C₁₁	1	1	yes	characteristic, complemented
293	#416	C₄×C₁₁	1	1	yes	characteristic, complemented
294	#416	C₂²×C₁₁	1	1	yes	characteristic
295	#416	C₂²×C₁₁	1	1	yes	characteristic
296	#416	C₂²×C₁₁	1	1	yes	characteristic
297	#416	C₂²×C₁₁	1	1	yes	characteristic
298	C₂×#103	C₄×C₁₁	1	1	yes	characteristic, complemented
299	C₂×#103	C₄×C₁₁	1	1	yes	characteristic, complemented
300	C₂×#102	C₄×C₁₁	1	1	yes	characteristic, complemented
301	C₂×#102	C₄×C₁₁	1	1	yes	characteristic, complemented
302	#408	—	2	2	no	—
303	#408	C₂²×C₁₁	1	2	yes	—
304	#407	—	2	1	no	—
305	#407	C₂²×C₁₁	1	1	yes	characteristic
306	#407	C₂²×C₁₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	—	2	1	no	—
308	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
309	#405	C₂²×C₁₁	1	2	yes	complemented
310	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
311	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
312	#341	C₂²×C₁₁	1	2	yes	complemented
313	#339	C₂²×C₁₁	1	2	yes	complemented
314	#339	C₂²×C₁₁	1	2	yes	complemented
315	#336	C₂²×C₁₁	1	2	yes	complemented
316	C₂²×C₁₁	—	2	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	1	no	—
319	C₂²×C₁₁	—	2	1	no	—
320	C₂²×C₁₁	—	2	1	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	2	1	no	—
323	C₂²×C₁₁	—	2	1	no	—
324	C₂²×C₁₁	—	4	4	no	—
325	C₂²×C₁₁	—	4	1	no	—
326	C₂²×C₁₁	—	4	1	no	—
327	C₂²×C₁₁	—	4	1	no	—
328	C₂²×C₁₁	—	4	1	no	—
329	C₂²×C₁₁	—	4	1	no	—
330	C₂²×C₁₁	—	8	4	no	—
331	C₂²×C₁₁	#443	1	2	yes	—
332	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₁₁	#551	1	2	yes	—
334	C₄×C₁₁	—	2	1	no	—
335	C₄×C₁₁	—	2	1	no	—
336	C₄×C₁₁	—	2	2	no	—
337	C₄×C₁₁	—	4	4	no	—
338	C₄×C₁₁	—	4	1	no	—
339	C₄×C₁₁	—	4	1	no	—
340	C₄×C₁₁	—	4	1	no	—
341	C₄×C₁₁	—	4	1	no	—
342	C₄×C₁₁	—	4	1	no	—
343	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
344	C₄×C₁₁	#518	1	1	yes	characteristic
345	C₄×C₁₁	#546	1	2	yes	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
351	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
352	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
353	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
354	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
359	#131	—	2	4	no	—
360	#131	—	4	2	no	—
361	C₂×M₁₆	—	2	2	no	—
362	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
363	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
364	C₂²×C₈	—	2	2	no	—
365	C₂²×C₈	—	4	2	no	—
366	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
367	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
368	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
369	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
376	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
377	#117	C₂³×C₁₁	1	1	yes	characteristic
378	#117	C₂³×C₁₁	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
385	#108	—	4	2	no	—
386	C₄⋊C₈	—	2	2	no	—
387	C₄⋊C₈	—	2	2	no	—
388	#104	—	2	4	no	—
389	#104	—	4	2	no	—
390	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
391	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
392	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
393	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
394	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
395	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
396	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
397	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
398	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
399	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
400	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
401	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
402	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
403	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
404	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
405	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂²⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
413	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
414	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
415	#97	—	2	2	no	—
416	C₄×C₈	—	2	2	no	—
417	C₄×C₈	—	4	2	no	—
418	#95	—	2	1	no	—
419	C₂×C₁₁	—	2	2	no	—
420	C₂×C₁₁	—	2	2	no	—
421	C₂×C₁₁	—	4	1	no	—
422	C₂×C₁₁	—	4	2	no	—
423	C₂×C₁₁	—	8	1	no	—
424	C₂×C₁₁	#2342	1	1	yes	characteristic
425	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
426	C₂×C₁₁	#2957	1	1	yes	characteristic
427	C₂⁴	—	2	1	no	—
428	C₂⁴	C₁₁×#41	1	1	yes	characteristic
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	4	4	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	4	no	—
438	#41	C₁₁×#41	1	4	yes	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
443	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
453	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
469	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	4	4	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	4	no	—
487	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
488	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
489	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
490	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
492	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₁₁	#22587	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	1	no	—
519	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
520	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
521	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	C₁₁×#117	1	2	yes	—
527	D₄	—	2	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	C₁₁×#117	1	2	yes	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
560	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
564	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	C₁₁×#443	1	2	yes	—
589	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
590	C₂²	C₁₁×#551	1	2	yes	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
601	C₄	C₁₁×#518	1	1	yes	characteristic
602	C₄	C₁₁×#546	1	2	yes	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	C₁₁×#2342	1	1	yes	characteristic
609	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
610	C₂	C₁₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2924	C₂	semidirect
4. C₁₁×#1937	C₂	semidirect
5. C₁₁×#1929	C₂	semidirect
6. C₁₁×#1866	C₂	semidirect
7. C₁₁×#1826	C₂	semidirect
8. C₁₁×#1810	C₂	semidirect
10. C₁₁×#1764	C₂	semidirect
11. C₈×C₁₁×C₂²⋊C₄	C₂	semidirect
19. C₂×C₁₁×#108	C₂²	semidirect
20. C₁₁×#424	C₂²	semidirect
23. C₁₁×#416	C₄	semidirect
24. C₁₁×#416	C₄	semidirect
25. C₁₁×#416	C₄	semidirect
26. C₁₁×#416	C₄	semidirect
31. C₂×C₁₁×#103	C₄	semidirect
32. C₂×C₁₁×#103	C₄	semidirect
33. C₂×C₁₁×#102	C₄	semidirect
34. C₂×C₁₁×#102	C₄	semidirect
42. C₁₁×#405	C₂²	semidirect
43. C₂×C₄×C₈×C₁₁	C₂²	semidirect
45. C₁₁×#341	C₂²	semidirect
46. C₁₁×#339	C₂²	semidirect
47. C₁₁×#339	C₂²	semidirect
48. C₁₁×#336	C₂²	semidirect
122. #22587	C₁₁	direct (N × H)
206. #2924	C₂×C₁₁	semidirect
209. #1937	C₂×C₁₁	semidirect
210. #1929	C₂×C₁₁	semidirect
211. #1866	C₂×C₁₁	semidirect
212. #1826	C₂×C₁₁	semidirect
213. #1810	C₂×C₁₁	semidirect
215. #1764	C₂×C₁₁	semidirect
216. C₈×C₂²⋊C₄	C₂×C₁₁	semidirect
286. C₂×#108	C₂²×C₁₁	semidirect
287. #424	C₂²×C₁₁	semidirect
290. #416	C₄×C₁₁	semidirect
291. #416	C₄×C₁₁	semidirect
292. #416	C₄×C₁₁	semidirect
293. #416	C₄×C₁₁	semidirect
298. C₂×#103	C₄×C₁₁	semidirect
299. C₂×#103	C₄×C₁₁	semidirect
300. C₂×#102	C₄×C₁₁	semidirect
301. C₂×#102	C₄×C₁₁	semidirect
309. #405	C₂²×C₁₁	semidirect
310. C₂×C₄×C₈	C₂²×C₁₁	semidirect
312. #341	C₂²×C₁₁	semidirect
313. #339	C₂²×C₁₁	semidirect
314. #339	C₂²×C₁₁	semidirect
315. #336	C₂²×C₁₁	semidirect
510. C₁₁	#22587	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×#2924	2
C₂×C₁₁×#416	2
C₁₁×#2880	2
C₁₁×#1937	2
C₁₁×#1929	2
C₁₁×#1866	2
C₁₁×#1826	2
C₁₁×#1810	2
C₁₁×#1789	2
C₁₁×#1764	2
C₈×C₁₁×C₂²⋊C₄	2
#22587	11

Subgroups — C11×#22587 #14599780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22587 #14599780