Subgroups — C₁₁×#21424 #14598617

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1997	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1965	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1900	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×#100	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₁×#41	C₄	1	2	yes	—
9	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
10	C₁₁×#532	—	2	1	no	—
11	C₁₁×#532	—	2	1	no	—
12	C₁₁×#532	—	2	1	no	—
13	C₁₁×#532	—	2	1	no	—
14	C₁₁×#532	—	2	1	no	—
15	C₁₁×#532	—	2	1	no	—
16	C₁₁×#532	—	2	1	no	—
17	C₁₁×#532	—	2	1	no	—
18	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#124	C₄	1	2	yes	—
21	C₂×C₁₁×#121	C₄	1	2	yes	—
22	C₂×C₁₁×#121	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₁	C₄	1	2	yes	—
24	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#432	—	2	1	no	—
27	C₁₁×#432	—	2	1	no	—
28	C₁₁×#431	—	2	1	no	—
29	C₁₁×#431	—	2	1	no	—
30	C₁₁×#423	C₂²	1	2	yes	—
31	C₂×C₁₁×#100	C₂²	1	8	yes	—
32	C₁₁×#407	C₂²	1	2	yes	—
33	C₄×C₁₁×M₁₆	—	2	1	no	—
34	C₄×C₁₁×M₁₆	—	2	1	no	—
35	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
36	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
37	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
38	C₂×C₁₁×#97	—	2	1	no	—
39	C₂×C₄×C₈×C₁₁	—	2	1	no	—
40	C₁₁×#343	C₂²	1	8	yes	—
41	C₂×C₁₁×#41	—	2	2	no	—
42	C₂×C₁₁×#41	—	2	2	no	—
43	C₂×C₁₁×#41	—	2	2	no	—
44	C₂×C₁₁×#41	—	2	2	no	—
45	C₂×C₁₁×#41	—	4	8	no	—
46	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
48	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
49	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₁	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
55	C₂×C₁₁×M₁₆	—	2	2	no	—
56	C₂×C₁₁×M₁₆	—	2	8	no	—
57	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
58	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₁	—	2	2	no	—
60	C₁₁×C₄⋊Q₈	—	2	1	no	—
61	C₁₁×C₄⋊Q₈	—	2	1	no	—
62	C₁₁×C₄⋊Q₈	—	2	1	no	—
63	C₁₁×C₄⋊Q₈	—	2	1	no	—
64	C₁₁×#127	—	2	1	no	—
65	C₁₁×#127	—	2	1	no	—
66	C₁₁×#127	—	2	1	no	—
67	C₁₁×#127	—	2	1	no	—
68	C₁₁×#124	—	2	2	no	—
69	C₁₁×#124	—	2	2	no	—
70	C₁₁×#124	—	2	2	no	—
71	C₁₁×#124	—	2	2	no	—
72	C₁₁×#121	—	2	2	no	—
73	C₁₁×#121	—	2	2	no	—
74	C₁₁×#121	—	2	2	no	—
75	C₁₁×#121	—	2	2	no	—
76	C₁₁×#121	—	2	2	no	—
77	C₁₁×#121	—	2	2	no	—
78	C₁₁×#121	—	2	2	no	—
79	C₁₁×#121	—	2	2	no	—
80	C₄×D₄×C₁₁	—	2	2	no	—
81	C₄×D₄×C₁₁	—	2	2	no	—
82	C₄×D₄×C₁₁	—	2	2	no	—
83	C₄×D₄×C₁₁	—	2	2	no	—
84	C₄×D₄×C₁₁	—	2	2	no	—
85	C₄×D₄×C₁₁	—	2	2	no	—
86	C₄×D₄×C₁₁	—	2	2	no	—
87	C₄×D₄×C₁₁	—	2	2	no	—
88	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
91	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
104	C₁₁×C₄⋊C₈	—	2	2	no	—
105	C₁₁×C₄⋊C₈	—	2	2	no	—
106	C₁₁×#100	—	2	16	no	—
107	C₁₁×C₂²⋊C₈	—	2	2	no	—
108	C₁₁×C₂²⋊C₈	—	2	2	no	—
109	C₁₁×#97	—	2	2	no	—
110	C₁₁×#97	—	2	2	no	—
111	C₁₁×#97	—	2	2	no	—
112	C₄×C₈×C₁₁	—	2	2	no	—
113	C₄×C₈×C₁₁	—	2	2	no	—
114	C₄×C₈×C₁₁	—	2	2	no	—
115	#21424	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
118	C₁₁×#41	—	4	8	no	—
119	C₁₁×#41	—	4	8	no	—
120	C₁₁×#41	—	4	8	no	—
121	C₁₁×#41	—	4	8	no	—
122	C₂×Q₈×C₁₁	—	2	2	no	—
123	C₂×Q₈×C₁₁	—	2	2	no	—
124	C₂×Q₈×C₁₁	—	4	4	no	—
125	C₂×D₄×C₁₁	—	2	4	no	—
126	C₂×D₄×C₁₁	—	2	4	no	—
127	C₂×D₄×C₁₁	—	2	2	no	—
128	C₂×D₄×C₁₁	—	2	2	no	—
129	C₂×D₄×C₁₁	—	2	2	no	—
130	C₂×D₄×C₁₁	—	2	2	no	—
131	C₂×D₄×C₁₁	—	2	2	no	—
132	C₂×D₄×C₁₁	—	2	2	no	—
133	C₂×D₄×C₁₁	—	2	8	no	—
134	C₂×D₄×C₁₁	—	4	4	no	—
135	C₂×D₄×C₁₁	—	4	4	no	—
136	C₂×D₄×C₁₁	—	4	8	no	—
137	C₂²×C₄×C₁₁	—	2	4	no	—
138	C₂²×C₄×C₁₁	—	2	4	no	—
139	C₂²×C₄×C₁₁	—	2	4	no	—
140	C₂²×C₄×C₁₁	—	2	4	no	—
141	C₂²×C₄×C₁₁	—	4	2	no	—
142	C₂²×C₄×C₁₁	—	4	8	no	—
143	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
162	C₁₁×M₁₆	—	2	8	no	—
163	C₁₁×M₁₆	—	2	4	no	—
164	C₁₁×M₁₆	—	2	8	no	—
165	C₁₁×M₁₆	#41	1	8	yes	complemented
166	C₂×C₈×C₁₁	—	2	8	no	—
167	C₂×C₈×C₁₁	—	2	4	no	—
168	C₂×C₈×C₁₁	—	2	4	no	—
169	C₁₁×C₄⋊C₄	—	2	2	no	—
170	C₁₁×C₄⋊C₄	—	2	2	no	—
171	C₁₁×C₄⋊C₄	—	2	2	no	—
172	C₁₁×C₄⋊C₄	—	2	2	no	—
173	C₁₁×C₂²⋊C₄	—	2	4	no	—
174	C₁₁×C₂²⋊C₄	—	2	4	no	—
175	C₁₁×C₂²⋊C₄	—	2	4	no	—
176	C₁₁×C₂²⋊C₄	—	2	4	no	—
177	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
193	C₂×#532	C₂×C₁₁	1	1	yes	characteristic
194	#2920	C₂×C₁₁	1	1	yes	characteristic, complemented
195	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
196	#1997	C₂×C₁₁	1	2	yes	complemented
197	#1965	C₂×C₁₁	1	2	yes	complemented
198	#1900	C₂×C₁₁	1	4	yes	complemented
199	C₄×#100	C₂×C₁₁	1	4	yes	complemented
200	C₂³×C₁₁	—	2	2	no	—
201	C₂³×C₁₁	—	2	2	no	—
202	C₂³×C₁₁	—	2	4	no	—
203	C₂³×C₁₁	—	2	8	no	—
204	C₂³×C₁₁	—	4	1	no	—
205	C₂³×C₁₁	—	4	4	no	—
206	C₂³×C₁₁	—	4	4	no	—
207	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
210	Q₈×C₁₁	—	4	4	no	—
211	Q₈×C₁₁	—	4	4	no	—
212	D₄×C₁₁	—	4	4	no	—
213	D₄×C₁₁	—	4	4	no	—
214	D₄×C₁₁	—	4	8	no	—
215	D₄×C₁₁	—	4	8	no	—
216	D₄×C₁₁	—	4	4	no	—
217	D₄×C₁₁	—	4	4	no	—
218	D₄×C₁₁	—	4	4	no	—
219	D₄×C₁₁	—	4	4	no	—
220	C₂×C₄×C₁₁	—	2	2	no	—
221	C₂×C₄×C₁₁	—	2	2	no	—
222	C₂×C₄×C₁₁	—	2	2	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	2	2	no	—
227	C₂×C₄×C₁₁	—	2	2	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	4	no	—
234	C₂×C₄×C₁₁	—	4	1	no	—
235	C₂×C₄×C₁₁	—	4	1	no	—
236	C₂×C₄×C₁₁	—	4	1	no	—
237	C₂×C₄×C₁₁	—	4	8	no	—
238	C₂×C₄×C₁₁	—	4	8	no	—
239	C₂×C₄×C₁₁	—	4	4	no	—
240	C₂×C₄×C₁₁	#100	1	4	yes	complemented
241	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
254	C₈×C₁₁	—	2	8	no	—
255	C₈×C₁₁	—	4	4	no	—
256	C₂²×#41	C₄×C₁₁	1	2	yes	—
257	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
258	#532	—	2	1	no	—
259	#532	—	2	1	no	—
260	#532	—	2	1	no	—
261	#532	—	2	1	no	—
262	#532	—	2	1	no	—
263	#532	—	2	1	no	—
264	#532	—	2	1	no	—
265	#532	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
267	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×#124	C₄×C₁₁	1	2	yes	—
269	C₂×#121	C₄×C₁₁	1	2	yes	—
270	C₂×#121	C₂²×C₁₁	1	2	yes	—
271	C₂×C₄×D₄	C₄×C₁₁	1	2	yes	—
272	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
273	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
274	#432	—	2	1	no	—
275	#432	—	2	1	no	—
276	#431	—	2	1	no	—
277	#431	—	2	1	no	—
278	#423	C₂²×C₁₁	1	2	yes	—
279	C₂×#100	C₂²×C₁₁	1	8	yes	—
280	#407	C₂²×C₁₁	1	2	yes	—
281	C₄×M₁₆	—	2	1	no	—
282	C₄×M₁₆	—	2	1	no	—
283	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
284	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
285	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
286	C₂×#97	—	2	1	no	—
287	C₂×C₄×C₈	—	2	1	no	—
288	#343	C₂²×C₁₁	1	8	yes	—
289	C₂²×C₁₁	—	2	1	no	—
290	C₂²×C₁₁	—	2	1	no	—
291	C₂²×C₁₁	—	2	1	no	—
292	C₂²×C₁₁	—	2	1	no	—
293	C₂²×C₁₁	—	2	1	no	—
294	C₂²×C₁₁	—	2	1	no	—
295	C₂²×C₁₁	—	2	1	no	—
296	C₂²×C₁₁	—	4	4	no	—
297	C₂²×C₁₁	—	4	4	no	—
298	C₂²×C₁₁	—	4	4	no	—
299	C₂²×C₁₁	—	4	4	no	—
300	C₂²×C₁₁	—	8	8	no	—
301	C₂²×C₁₁	C₂×#100	1	2	yes	—
302	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₁₁	C₄×#41	1	2	yes	—
304	C₄×C₁₁	—	2	1	no	—
305	C₄×C₁₁	—	2	1	no	—
306	C₄×C₁₁	—	2	1	no	—
307	C₄×C₁₁	—	2	1	no	—
308	C₄×C₁₁	—	2	1	no	—
309	C₄×C₁₁	—	2	1	no	—
310	C₄×C₁₁	—	2	1	no	—
311	C₄×C₁₁	—	4	4	no	—
312	C₄×C₁₁	C₂×#100	1	2	yes	—
313	C₄×C₁₁	C₂×#100	1	2	yes	—
314	C₄×C₁₁	#413	1	2	yes	—
315	C₄×C₁₁	#525	1	2	yes	—
316	C₄×C₁₁	#532	1	2	yes	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	4	8	no	—
322	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
323	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
324	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
325	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
326	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
327	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂³×C₄	C₂×C₄×C₁₁	1	4	yes	—
329	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	8	no	—
333	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
334	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	—	2	1	no	—
342	#127	—	2	1	no	—
343	#127	—	2	1	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#124	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
368	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
369	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
370	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
371	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
372	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
373	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
374	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
375	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
376	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	2	2	no	—
382	#100	—	2	16	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	#97	—	2	2	no	—
386	#97	—	2	2	no	—
387	#97	—	2	2	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	C₄×C₈	—	2	2	no	—
391	C₂×C₁₁	—	2	2	no	—
392	C₂×C₁₁	—	2	2	no	—
393	C₂×C₁₁	—	4	1	no	—
394	C₂×C₁₁	—	8	4	no	—
395	C₂×C₁₁	#2297	1	1	yes	characteristic
396	C₂×C₁₁	C₂²×#100	1	1	yes	characteristic
397	C₂×C₁₁	C₂×#413	1	1	yes	characteristic
398	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
399	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
400	#41	—	4	8	no	—
401	#41	—	4	8	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	8	no	—
425	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
426	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
427	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
428	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
429	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
430	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
431	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
432	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
444	M₁₆	—	2	8	no	—
445	M₁₆	—	2	4	no	—
446	M₁₆	—	2	8	no	—
447	M₁₆	C₁₁×#41	1	8	yes	complemented
448	C₂×C₈	—	2	8	no	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
460	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
461	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
462	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
463	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
464	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
465	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
466	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
475	C₁₁	#21424	1	1	yes	characteristic, direct product factor, Sylow
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	4	no	—
483	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
484	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
485	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
486	Q₈	—	4	4	no	—
487	Q₈	—	4	4	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	4	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	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	C₁₁×#100	1	4	yes	complemented
517	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
520	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
530	C₈	—	2	8	no	—
531	C₈	—	4	4	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	8	8	no	—
544	C₂²	C₂×C₁₁×#100	1	2	yes	—
545	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
546	C₂²	C₄×C₁₁×#41	1	2	yes	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	4	4	no	—
555	C₄	C₂×C₁₁×#100	1	2	yes	—
556	C₄	C₂×C₁₁×#100	1	2	yes	—
557	C₄	C₁₁×#413	1	2	yes	—
558	C₄	C₁₁×#525	1	2	yes	—
559	C₄	C₁₁×#532	1	2	yes	—
560	C₂	—	2	2	no	—
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	8	4	no	—
564	C₂	C₁₁×#2297	1	1	yes	characteristic
565	C₂	C₂²×C₁₁×#100	1	1	yes	characteristic
566	C₂	C₂×C₁₁×#413	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₁×#532	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2920	C₂	semidirect
3. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
4. C₁₁×#1997	C₂	semidirect
5. C₁₁×#1965	C₂	semidirect
6. C₁₁×#1900	C₂	semidirect
7. C₄×C₁₁×#100	C₂	semidirect
115. #21424	C₁₁	direct (N × H)
165. C₁₁×M₁₆	#41	semidirect
194. #2920	C₂×C₁₁	semidirect
195. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
196. #1997	C₂×C₁₁	semidirect
197. #1965	C₂×C₁₁	semidirect
198. #1900	C₂×C₁₁	semidirect
199. C₄×#100	C₂×C₁₁	semidirect
240. C₂×C₄×C₁₁	#100	semidirect
447. M₁₆	C₁₁×#41	semidirect
475. C₁₁	#21424	direct (N × H)
516. C₂×C₄	C₁₁×#100	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×#532	2
C₁₁×#2920	2
C₂×C₄×C₁₁×M₁₆	2
C₁₁×#1997	2
C₁₁×#1965	2
C₁₁×#1900	2
C₄×C₁₁×#100	2
#21424	11

Subgroups — C11×#21424 #14598617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21424 #14598617