Subgroups — C₁₁×#18060 #14595253

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#2974	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1592	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1583	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1582	C₂	1	2	yes	maximal, complemented
7	C₁₁×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1490	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#446	—	2	2	no	—
16	C₁₁×#446	C₂²	1	2	yes	complemented
17	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
18	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
21	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
22	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
24	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
25	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
26	C₁₁×#436	C₂²	1	2	yes	—
27	C₁₁×#435	—	2	2	no	—
28	C₈×D₄×C₁₁	C₂²	1	2	yes	—
29	C₁₁×#432	—	2	1	no	—
30	C₁₁×#432	C₂²	1	1	yes	characteristic
31	C₁₁×#432	C₂²	1	1	yes	characteristic
32	C₁₁×#431	—	2	1	no	—
33	C₁₁×#431	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#106	C₄	1	1	yes	characteristic
35	C₂×C₁₁×#103	C₄	1	1	yes	characteristic
36	C₂×C₁₁×#102	C₄	1	1	yes	characteristic
37	C₁₁×#407	—	2	1	no	—
38	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
39	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#335	C₂²	1	2	yes	complemented
42	C₁₁×#334	C₂²	1	2	yes	complemented
43	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
45	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₁×#322	C₂²	1	2	yes	complemented
48	C₁₁×#322	C₂²	1	2	yes	complemented
49	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₁	—	2	1	no	—
52	C₂×C₁₁×SD₁₆	—	2	4	no	—
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×M₁₆	—	2	1	no	—
58	C₂×C₁₁×M₁₆	—	2	2	no	—
59	C₂²×C₈×C₁₁	—	2	2	no	—
60	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₁	—	2	1	no	—
63	C₄×Q₈×C₁₁	—	2	1	no	—
64	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₁	—	2	1	no	—
69	C₄×D₄×C₁₁	—	2	1	no	—
70	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₁	—	2	1	no	—
79	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
80	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
81	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
82	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
83	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	—	2	2	no	—
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
87	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
89	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
94	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
95	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
96	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₁×C₂²⋊C₈	—	2	1	no	—
98	C₁₁×C₂²⋊C₈	—	2	1	no	—
99	C₁₁×C₂²⋊C₈	—	2	2	no	—
100	C₁₁×C₂²⋊C₈	—	2	2	no	—
101	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
102	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
103	C₁₁×#97	—	2	2	no	—
104	C₁₁×#97	—	2	1	no	—
105	C₁₁×#97	—	2	1	no	—
106	C₁₁×#97	—	2	1	no	—
107	C₄×C₈×C₁₁	—	2	2	no	—
108	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₁₁	C₂³	1	2	yes	—
111	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₁	C₂³	1	2	yes	—
114	#18060	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₁	—	2	1	no	—
116	C₂×Q₈×C₁₁	—	2	1	no	—
117	C₂×Q₈×C₁₁	—	2	2	no	—
118	C₂×Q₈×C₁₁	—	4	1	no	—
119	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₁	—	2	2	no	—
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	—	4	1	no	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	8	2	no	—
134	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
137	C₁₁×SD₁₆	—	2	2	no	—
138	C₁₁×SD₁₆	—	2	2	no	—
139	C₁₁×SD₁₆	—	2	2	no	—
140	C₁₁×SD₁₆	M₁₆	1	4	yes	complemented
141	C₁₁×M₁₆	—	4	2	no	—
142	C₁₁×M₁₆	—	8	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	2	no	—
147	C₂×C₈×C₁₁	—	4	1	no	—
148	C₂×C₈×C₁₁	—	8	2	no	—
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
155	C₁₁×C₄⋊C₄	—	2	1	no	—
156	C₁₁×C₄⋊C₄	—	2	1	no	—
157	C₁₁×C₄⋊C₄	—	2	1	no	—
158	C₁₁×C₄⋊C₄	—	2	1	no	—
159	C₁₁×C₄⋊C₄	—	2	1	no	—
160	C₁₁×C₄⋊C₄	—	2	1	no	—
161	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
162	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₁₁×C₂²⋊C₄	—	2	1	no	—
166	C₁₁×C₂²⋊C₄	—	2	1	no	—
167	C₁₁×C₂²⋊C₄	—	2	1	no	—
168	C₁₁×C₂²⋊C₄	—	2	1	no	—
169	C₄²×C₁₁	—	2	1	no	—
170	C₄²×C₁₁	—	2	1	no	—
171	C₄²×C₁₁	—	2	1	no	—
172	C₄²×C₁₁	—	2	1	no	—
173	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₁	#41	1	1	yes	characteristic
176	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
177	#2984	C₂×C₁₁	1	1	yes	characteristic, complemented
178	#2974	C₂×C₁₁	1	1	yes	characteristic
179	C₂×C₄×SD₁₆	C₂×C₁₁	1	1	yes	characteristic
180	#1592	C₂×C₁₁	1	2	yes	complemented
181	#1583	C₂×C₁₁	1	2	yes	complemented
182	#1582	C₂×C₁₁	1	2	yes	complemented
183	SD₁₆⋊C₈	C₂×C₁₁	1	2	yes	complemented
184	#1568	C₂×C₁₁	1	1	yes	characteristic, complemented
185	#1491	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#1490	C₂×C₁₁	1	1	yes	characteristic
187	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂³×C₁₁	—	2	1	no	—
189	C₂³×C₁₁	—	2	1	no	—
190	C₂³×C₁₁	—	4	2	no	—
191	C₂³×C₁₁	—	4	2	no	—
192	C₂³×C₁₁	—	8	1	no	—
193	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
194	Q₈×C₁₁	—	2	1	no	—
195	Q₈×C₁₁	—	2	1	no	—
196	Q₈×C₁₁	—	2	1	no	—
197	Q₈×C₁₁	—	4	2	no	—
198	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
199	D₄×C₁₁	—	2	1	no	—
200	D₄×C₁₁	—	2	1	no	—
201	D₄×C₁₁	—	2	1	no	—
202	D₄×C₁₁	—	4	2	no	—
203	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	2	1	no	—
211	C₂×C₄×C₁₁	—	2	1	no	—
212	C₂×C₄×C₁₁	—	2	1	no	—
213	C₂×C₄×C₁₁	—	2	1	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	2	no	—
216	C₂×C₄×C₁₁	—	4	2	no	—
217	C₂×C₄×C₁₁	—	4	2	no	—
218	C₂×C₄×C₁₁	—	8	1	no	—
219	C₂×C₄×C₁₁	—	8	1	no	—
220	C₂×C₄×C₁₁	—	8	1	no	—
221	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₁	—	2	1	no	—
228	C₈×C₁₁	—	2	1	no	—
229	C₈×C₁₁	—	2	1	no	—
230	C₈×C₁₁	—	2	2	no	—
231	C₈×C₁₁	—	2	2	no	—
232	C₈×C₁₁	—	4	2	no	—
233	C₈×C₁₁	—	4	2	no	—
234	C₈×C₁₁	—	4	2	no	—
235	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
236	C₂²×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
239	#446	—	2	2	no	—
240	#446	C₂²×C₁₁	1	2	yes	complemented
241	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
242	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
243	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
244	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
245	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
246	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
247	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
248	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
249	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
250	#436	C₂²×C₁₁	1	2	yes	—
251	#435	—	2	2	no	—
252	C₈×D₄	C₂²×C₁₁	1	2	yes	—
253	#432	—	2	1	no	—
254	#432	C₂²×C₁₁	1	1	yes	characteristic
255	#432	C₂²×C₁₁	1	1	yes	characteristic
256	#431	—	2	1	no	—
257	#431	C₂²×C₁₁	1	1	yes	characteristic
258	C₂×#106	C₄×C₁₁	1	1	yes	characteristic
259	C₂×#103	C₄×C₁₁	1	1	yes	characteristic
260	C₂×#102	C₄×C₁₁	1	1	yes	characteristic
261	#407	—	2	1	no	—
262	C₂×C₂²⋊C₈	—	2	1	no	—
263	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
265	#335	C₂²×C₁₁	1	2	yes	complemented
266	#334	C₂²×C₁₁	1	2	yes	complemented
267	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	complemented
268	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	complemented
269	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
270	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
271	#322	C₂²×C₁₁	1	2	yes	complemented
272	#322	C₂²×C₁₁	1	2	yes	complemented
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	—	2	1	no	—
275	C₂²×C₁₁	—	2	2	no	—
276	C₂²×C₁₁	—	4	1	no	—
277	C₂²×C₁₁	—	4	1	no	—
278	C₂²×C₁₁	—	4	1	no	—
279	C₂²×C₁₁	—	4	1	no	—
280	C₂²×C₁₁	—	4	1	no	—
281	C₂²×C₁₁	—	8	4	no	—
282	C₂²×C₁₁	#444	1	2	yes	—
283	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₁₁	—	2	1	no	—
285	C₄×C₁₁	—	2	2	no	—
286	C₄×C₁₁	—	2	1	no	—
287	C₄×C₁₁	—	2	1	no	—
288	C₄×C₁₁	—	2	1	no	—
289	C₄×C₁₁	—	4	1	no	—
290	C₄×C₁₁	—	4	1	no	—
291	C₄×C₁₁	—	4	1	no	—
292	C₄×C₁₁	—	4	1	no	—
293	C₄×C₁₁	—	4	1	no	—
294	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
295	C₄×C₁₁	#568	1	1	yes	characteristic
296	C₄×C₁₁	#577	1	2	yes	—
297	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
298	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
314	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
315	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
319	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
320	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
321	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
328	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
329	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
330	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
331	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
335	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
336	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
337	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
338	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
339	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
340	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
341	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
342	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
343	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
344	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
350	C₂²⋊C₈	D₄×C₁₁	1	1	yes	characteristic
351	#97	—	2	2	no	—
352	#97	—	2	1	no	—
353	#97	—	2	1	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
357	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
358	C₄×C₈	C₂³×C₁₁	1	2	yes	—
359	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₁₁	1	2	yes	—
362	C₂×C₁₁	—	2	2	no	—
363	C₂×C₁₁	—	4	2	no	—
364	C₂×C₁₁	—	8	1	no	—
365	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
366	C₂×C₁₁	#2949	1	1	yes	characteristic
367	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
368	C₂⁴	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
373	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
378	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
389	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	2	2	no	—
392	SD₁₆	—	2	2	no	—
393	SD₁₆	C₁₁×M₁₆	1	4	yes	complemented
394	M₁₆	—	4	2	no	—
395	M₁₆	—	8	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	8	2	no	—
402	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
405	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
406	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
407	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
416	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
417	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
428	C₄²	C₁₁×#41	1	1	yes	characteristic
429	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
430	C₁₁	#18060	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	1	no	—
436	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
437	Q₈	—	2	1	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	4	2	no	—
441	Q₈	C₂×C₁₁×M₁₆	1	2	yes	—
442	D₄	—	2	1	no	—
443	D₄	—	2	1	no	—
444	D₄	—	2	1	no	—
445	D₄	—	4	2	no	—
446	D₄	C₂×C₁₁×M₁₆	1	2	yes	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	8	1	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
465	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
466	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
469	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	8	4	no	—
488	C₂²	C₁₁×#444	1	2	yes	—
489	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
501	C₄	C₁₁×#568	1	1	yes	characteristic
502	C₄	C₁₁×#577	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
507	C₂	C₁₁×#2949	1	1	yes	characteristic
508	C₂	C₂×C₁₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂²×D₄×C₁₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2984	C₂	semidirect
4. C₁₁×#1592	C₂	semidirect
5. C₁₁×#1583	C₂	semidirect
6. C₁₁×#1582	C₂	semidirect
7. C₁₁×SD₁₆⋊C₈	C₂	semidirect
8. C₁₁×#1568	C₂	semidirect
9. C₁₁×#1491	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
16. C₁₁×#446	C₂²	semidirect
17. C₈×Q₈×C₁₁	C₂²	semidirect
41. C₁₁×#335	C₂²	semidirect
42. C₁₁×#334	C₂²	semidirect
43. C₁₁×Q₈⋊C₈	C₂²	semidirect
44. C₁₁×Q₈⋊C₈	C₂²	semidirect
47. C₁₁×#322	C₂²	semidirect
48. C₁₁×#322	C₂²	semidirect
114. #18060	C₁₁	direct (N × H)
140. C₁₁×SD₁₆	M₁₆	semidirect
177. #2984	C₂×C₁₁	semidirect
180. #1592	C₂×C₁₁	semidirect
181. #1583	C₂×C₁₁	semidirect
182. #1582	C₂×C₁₁	semidirect
183. SD₁₆⋊C₈	C₂×C₁₁	semidirect
184. #1568	C₂×C₁₁	semidirect
185. #1491	C₂×C₁₁	semidirect
187. #1451	C₂×C₁₁	semidirect
240. #446	C₂²×C₁₁	semidirect
241. C₈×Q₈	C₂²×C₁₁	semidirect
265. #335	C₂²×C₁₁	semidirect
266. #334	C₂²×C₁₁	semidirect
267. Q₈⋊C₈	C₂²×C₁₁	semidirect
268. Q₈⋊C₈	C₂²×C₁₁	semidirect
271. #322	C₂²×C₁₁	semidirect
272. #322	C₂²×C₁₁	semidirect
393. SD₁₆	C₁₁×M₁₆	semidirect
430. C₁₁	#18060	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×#2984	2
C₁₁×#2974	2
C₂×C₄×C₁₁×SD₁₆	2
C₁₁×#1592	2
C₁₁×#1583	2
C₁₁×#1582	2
C₁₁×SD₁₆⋊C₈	2
C₁₁×#1568	2
C₁₁×#1491	2
C₁₁×#1490	2
C₁₁×#1451	2
#18060	11

Subgroups — C11×#18060 #14595253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18060 #14595253