Subgroups — C₁₁×#21098 #14598291

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2879	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1938	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1937	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
17	C₁₁×#424	—	2	2	no	—
18	C₁₁×#424	C₂²	1	4	yes	complemented
19	C₁₁×#423	—	2	2	no	—
20	C₁₁×#421	—	2	4	no	—
21	C₂×C₁₁×#104	C₂²	1	4	yes	—
22	C₁₁×#416	C₄	1	4	yes	complemented
23	C₁₁×#416	C₂²	1	2	yes	—
24	C₁₁×#416	C₂²	1	2	yes	—
25	C₂×C₁₁×#103	C₄	1	2	yes	complemented
26	C₂×C₁₁×#102	C₄	1	2	yes	complemented
27	C₁₁×#408	—	2	2	no	—
28	C₁₁×#408	C₂²	1	4	yes	—
29	C₁₁×#407	—	2	2	no	—
30	C₁₁×#405	—	2	4	no	—
31	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
33	C₁₁×#341	C₂²	1	2	yes	complemented
34	C₁₁×#341	C₂²	1	2	yes	complemented
35	C₁₁×#339	C₂²	1	4	yes	complemented
36	C₂×C₁₁×#41	—	2	1	no	—
37	C₂×C₁₁×#41	—	2	1	no	—
38	C₂×C₁₁×#41	—	2	2	no	—
39	C₂×C₁₁×#41	—	2	2	no	—
40	C₂×C₁₁×#41	—	2	2	no	—
41	C₂×C₁₁×#41	—	2	2	no	—
42	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
43	C₂×C₁₁×#41	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₁	—	2	1	no	—
46	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	—	2	1	no	—
48	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×C₁₁×M₁₆	—	2	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	—	2	1	no	—
52	C₂×C₁₁×M₁₆	—	2	1	no	—
53	C₂×C₁₁×M₁₆	—	2	2	no	—
54	C₂×C₁₁×M₁₆	—	2	2	no	—
55	C₂×C₁₁×M₁₆	—	2	2	no	—
56	C₂×C₁₁×M₁₆	—	2	2	no	—
57	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
58	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
59	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₁	—	2	2	no	—
62	C₂²×C₈×C₁₁	—	2	2	no	—
63	C₂²×C₈×C₁₁	—	2	1	no	—
64	C₂²×C₈×C₁₁	—	2	1	no	—
65	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	—	2	1	no	—
72	C₁₁×#117	—	2	2	no	—
73	C₁₁×#117	C₂×C₄	1	2	yes	—
74	C₁₁×#117	D₄	1	4	yes	—
75	C₁₁×#117	C₂³	1	2	yes	—
76	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₁	—	2	1	no	—
81	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
82	C₁₁×C₄⋊C₈	—	2	8	no	—
83	C₁₁×#104	—	2	8	no	—
84	C₁₁×#103	C₂×C₄	1	4	yes	—
85	C₁₁×#103	C₂×C₄	1	4	yes	—
86	C₁₁×#102	C₂×C₄	1	4	yes	—
87	C₁₁×#102	C₂×C₄	1	4	yes	—
88	C₁₁×C₂²⋊C₈	—	2	8	no	—
89	C₁₁×#97	—	2	4	no	—
90	C₄×C₈×C₁₁	—	2	4	no	—
91	#21098	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₁	—	2	1	no	—
93	C₂⁴×C₁₁	#41	1	1	yes	characteristic
94	C₁₁×#41	—	2	4	no	—
95	C₁₁×#41	—	2	4	no	—
96	C₁₁×#41	—	2	2	no	—
97	C₁₁×#41	—	2	2	no	—
98	C₁₁×#41	—	2	2	no	—
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	4	2	no	—
101	C₁₁×#41	—	4	2	no	—
102	C₁₁×#41	—	4	2	no	—
103	C₁₁×#41	—	4	2	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	2	2	no	—
107	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	2	1	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	4	2	no	—
115	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	2	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	4	2	no	—
122	C₂²×C₄×C₁₁	—	4	2	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	#41	1	2	yes	—
129	C₂²×C₄×C₁₁	#41	1	2	yes	—
130	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	#41	1	2	yes	—
132	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₁₁×M₁₆	—	2	4	no	—
134	C₁₁×M₁₆	—	2	4	no	—
135	C₁₁×M₁₆	—	2	2	no	—
136	C₁₁×M₁₆	—	2	2	no	—
137	C₁₁×M₁₆	—	2	2	no	—
138	C₁₁×M₁₆	—	2	2	no	—
139	C₁₁×M₁₆	—	4	2	no	—
140	C₁₁×M₁₆	—	4	2	no	—
141	C₂×C₈×C₁₁	—	2	4	no	—
142	C₂×C₈×C₁₁	—	2	4	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	1	no	—
146	C₂×C₈×C₁₁	—	2	2	no	—
147	C₂×C₈×C₁₁	—	2	2	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	2	no	—
151	C₂×C₈×C₁₁	—	4	2	no	—
152	C₂×C₈×C₁₁	—	4	2	no	—
153	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
156	C₁₁×C₄⋊C₄	—	2	2	no	—
157	C₁₁×C₄⋊C₄	—	2	4	no	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
159	C₁₁×C₂²⋊C₄	—	2	2	no	—
160	C₁₁×C₂²⋊C₄	—	2	4	no	—
161	C₁₁×C₂²⋊C₄	—	2	2	no	—
162	C₄²×C₁₁	—	2	2	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	C₂×D₄	1	4	yes	—
166	#2905	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂×#421	C₂×C₁₁	1	1	yes	characteristic
168	C₂×#416	C₂×C₁₁	1	1	yes	characteristic
169	#2879	C₂×C₁₁	1	1	yes	characteristic
170	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#1938	C₂×C₁₁	1	4	yes	complemented
172	#1937	C₂×C₁₁	1	4	yes	complemented
173	C₂×#341	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1733	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₂³×C₁₁	—	2	2	no	—
176	C₂³×C₁₁	—	4	2	no	—
177	C₂³×C₁₁	—	4	2	no	—
178	C₂³×C₁₁	—	8	2	no	—
179	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
180	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
181	C₂³×C₁₁	#123	1	2	yes	—
182	C₂³×C₁₁	#126	1	2	yes	—
183	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
184	Q₈×C₁₁	—	2	2	no	—
185	Q₈×C₁₁	—	2	2	no	—
186	Q₈×C₁₁	—	4	2	no	—
187	D₄×C₁₁	—	2	2	no	—
188	D₄×C₁₁	—	2	2	no	—
189	D₄×C₁₁	—	4	2	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	4	4	no	—
192	D₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	2	4	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	4	no	—
196	C₂×C₄×C₁₁	—	4	4	no	—
197	C₂×C₄×C₁₁	—	4	2	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	4	no	—
201	C₂×C₄×C₁₁	—	8	2	no	—
202	C₂×C₄×C₁₁	#117	1	2	yes	—
203	C₂×C₄×C₁₁	#117	1	2	yes	—
204	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	#121	1	2	yes	—
209	C₂×C₄×C₁₁	#121	1	2	yes	—
210	C₂×C₄×C₁₁	#123	1	2	yes	—
211	C₂×C₄×C₁₁	#124	1	2	yes	—
212	C₂×C₄×C₁₁	#124	1	2	yes	—
213	C₂×C₄×C₁₁	#126	1	2	yes	—
214	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	4	no	—
223	C₈×C₁₁	—	4	2	no	—
224	C₈×C₁₁	—	4	2	no	—
225	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
226	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
230	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
231	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
232	#424	—	2	2	no	—
233	#424	C₂²×C₁₁	1	4	yes	complemented
234	#423	—	2	2	no	—
235	#421	—	2	4	no	—
236	C₂×#104	C₂²×C₁₁	1	4	yes	—
237	#416	C₄×C₁₁	1	4	yes	complemented
238	#416	C₂²×C₁₁	1	2	yes	—
239	#416	C₂²×C₁₁	1	2	yes	—
240	C₂×#103	C₄×C₁₁	1	2	yes	complemented
241	C₂×#102	C₄×C₁₁	1	2	yes	complemented
242	#408	—	2	2	no	—
243	#408	C₂²×C₁₁	1	4	yes	—
244	#407	—	2	2	no	—
245	#405	—	2	4	no	—
246	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
247	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
248	#341	C₂²×C₁₁	1	2	yes	complemented
249	#341	C₂²×C₁₁	1	2	yes	complemented
250	#339	C₂²×C₁₁	1	4	yes	complemented
251	C₂²×C₁₁	—	2	2	no	—
252	C₂²×C₁₁	—	2	2	no	—
253	C₂²×C₁₁	—	2	2	no	—
254	C₂²×C₁₁	—	4	2	no	—
255	C₂²×C₁₁	—	4	2	no	—
256	C₂²×C₁₁	—	4	4	no	—
257	C₂²×C₁₁	—	4	2	no	—
258	C₂²×C₁₁	—	8	4	no	—
259	C₂²×C₁₁	#388	1	2	yes	—
260	C₂²×C₁₁	#388	1	2	yes	—
261	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₁₁	C₂×#123	1	1	yes	characteristic
263	C₂²×C₁₁	C₂×#126	1	1	yes	characteristic
264	C₄×C₁₁	—	4	4	no	—
265	C₄×C₁₁	—	4	4	no	—
266	C₄×C₁₁	—	4	2	no	—
267	C₄×C₁₁	#388	1	2	yes	—
268	C₄×C₁₁	#388	1	2	yes	—
269	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
270	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
272	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
273	C₂×#41	—	2	1	no	—
274	C₂×#41	—	2	1	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
280	C₂×#41	C₂³×C₁₁	1	2	yes	—
281	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
295	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
296	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
297	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
303	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
307	#117	—	2	1	no	—
308	#117	—	2	1	no	—
309	#117	—	2	2	no	—
310	#117	C₂×C₄×C₁₁	1	2	yes	—
311	#117	D₄×C₁₁	1	4	yes	—
312	#117	C₂³×C₁₁	1	2	yes	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
319	C₄⋊C₈	—	2	8	no	—
320	#104	—	2	8	no	—
321	#103	C₂×C₄×C₁₁	1	4	yes	—
322	#103	C₂×C₄×C₁₁	1	4	yes	—
323	#102	C₂×C₄×C₁₁	1	4	yes	—
324	#102	C₂×C₄×C₁₁	1	4	yes	—
325	C₂²⋊C₈	—	2	8	no	—
326	#97	—	2	4	no	—
327	C₄×C₈	—	2	4	no	—
328	C₂×C₁₁	—	2	1	no	—
329	C₂×C₁₁	—	2	2	no	—
330	C₂×C₁₁	—	2	1	no	—
331	C₂×C₁₁	—	2	2	no	—
332	C₂×C₁₁	—	8	2	no	—
333	C₂×C₁₁	C₂×#388	1	1	yes	characteristic
334	C₂×C₁₁	#2957	1	2	yes	—
335	C₂⁴	—	2	1	no	—
336	C₂⁴	C₁₁×#41	1	1	yes	characteristic
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
371	C₂²×C₄	C₁₁×#41	1	2	yes	—
372	C₂²×C₄	C₁₁×#41	1	2	yes	—
373	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
374	C₂²×C₄	C₁₁×#41	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	2	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
397	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	C₂×D₄×C₁₁	1	4	yes	—
409	C₁₁	#21098	1	1	yes	characteristic, direct product factor, Sylow
410	C₂³	—	2	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
415	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
416	C₂³	C₁₁×#123	1	2	yes	—
417	C₂³	C₁₁×#126	1	2	yes	—
418	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	4	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	C₁₁×#117	1	2	yes	—
438	C₂×C₄	C₁₁×#117	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
442	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
443	C₂×C₄	C₁₁×#121	1	2	yes	—
444	C₂×C₄	C₁₁×#121	1	2	yes	—
445	C₂×C₄	C₁₁×#123	1	2	yes	—
446	C₂×C₄	C₁₁×#124	1	2	yes	—
447	C₂×C₄	C₁₁×#124	1	2	yes	—
448	C₂×C₄	C₁₁×#126	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₁₁×#388	1	2	yes	—
469	C₂²	C₁₁×#388	1	2	yes	—
470	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
471	C₂²	C₂×C₁₁×#123	1	1	yes	characteristic
472	C₂²	C₂×C₁₁×#126	1	1	yes	characteristic
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	2	no	—
476	C₄	C₁₁×#388	1	2	yes	—
477	C₄	C₁₁×#388	1	2	yes	—
478	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
479	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
480	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
481	C₄	C₂×C₁₁×#124	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	2	1	no	—
486	C₂	—	8	2	no	—
487	C₂	C₂×C₁₁×#388	1	1	yes	characteristic
488	C₂	C₁₁×#2957	1	2	yes	—

	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 ◁ C₂²×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2905	C₂	semidirect
5. C₂×C₁₁×#405	C₂	semidirect
6. C₁₁×#1938	C₂	semidirect
7. C₁₁×#1937	C₂	semidirect
8. C₂×C₁₁×#341	C₂	semidirect
9. C₁₁×#1733	C₂	semidirect
18. C₁₁×#424	C₂²	semidirect
22. C₁₁×#416	C₄	semidirect
25. C₂×C₁₁×#103	C₄	semidirect
26. C₂×C₁₁×#102	C₄	semidirect
31. C₂×C₁₁×#97	C₂²	semidirect
32. C₂×C₄×C₈×C₁₁	C₂²	semidirect
33. C₁₁×#341	C₂²	semidirect
34. C₁₁×#341	C₂²	semidirect
35. C₁₁×#339	C₂²	semidirect
91. #21098	C₁₁	direct (N × H)
166. #2905	C₂×C₁₁	semidirect
170. C₂×#405	C₂×C₁₁	semidirect
171. #1938	C₂×C₁₁	semidirect
172. #1937	C₂×C₁₁	semidirect
173. C₂×#341	C₂×C₁₁	semidirect
174. #1733	C₂×C₁₁	semidirect
233. #424	C₂²×C₁₁	semidirect
237. #416	C₄×C₁₁	semidirect
240. C₂×#103	C₄×C₁₁	semidirect
241. C₂×#102	C₄×C₁₁	semidirect
246. C₂×#97	C₂²×C₁₁	semidirect
247. C₂×C₄×C₈	C₂²×C₁₁	semidirect
248. #341	C₂²×C₁₁	semidirect
249. #341	C₂²×C₁₁	semidirect
250. #339	C₂²×C₁₁	semidirect
409. C₁₁	#21098	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×#2905	2
C₂×C₁₁×#421	2
C₂×C₁₁×#416	2
C₁₁×#2879	2
C₂×C₁₁×#405	2
C₁₁×#1938	2
C₁₁×#1937	2
C₂×C₁₁×#341	2
C₁₁×#1733	2
#21098	11

Subgroups — C11×#21098 #14598291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21098 #14598291