Subgroups — C₁₁×#22546 #14599739

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1983	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1982	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1959	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1802	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1762	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#559	—	2	4	no	—
13	C₁₁×#559	C₄	1	8	yes	complemented
14	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#124	—	2	1	no	—
16	C₂×C₁₁×#124	C₂²	1	2	yes	—
17	C₂×C₁₁×#123	—	2	2	no	—
18	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁	—	2	1	no	—
22	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
23	C₁₁×#446	—	2	4	no	—
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#103	C₂²	1	2	yes	—
29	C₂×C₁₁×#102	C₂²	1	2	yes	—
30	C₂×C₁₁×#102	C₂²	1	2	yes	—
31	C₂×C₁₁×#102	C₂²	1	2	yes	—
32	C₂×C₁₁×#102	C₂²	1	2	yes	—
33	C₂×C₁₁×#97	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#389	—	2	1	no	—
36	C₁₁×#389	—	2	2	no	—
37	C₁₁×#384	C₂²	1	1	yes	characteristic
38	C₁₁×#384	C₂²	1	2	yes	—
39	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
41	C₁₁×#340	C₂²	1	1	yes	characteristic
42	C₁₁×#340	C₂²	1	1	yes	characteristic
43	C₁₁×#340	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₁	—	2	1	no	—
47	C₂²×D₄×C₁₁	—	2	1	no	—
48	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#127	—	2	2	no	—
54	C₁₁×#127	C₂×C₄	1	4	yes	—
55	C₁₁×#124	—	2	8	no	—
56	C₁₁×#124	—	2	4	no	—
57	C₁₁×#124	C₂×C₄	1	8	yes	—
58	C₁₁×#123	—	2	16	no	—
59	C₄×Q₈×C₁₁	—	2	2	no	—
60	C₄×Q₈×C₁₁	—	4	4	no	—
61	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₁	D₄	1	4	yes	—
64	C₄×D₄×C₁₁	—	2	8	no	—
65	C₄×D₄×C₁₁	—	2	4	no	—
66	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
67	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₁₁	—	2	1	no	—
82	C₂×C₄²×C₁₁	—	2	2	no	—
83	C₂×C₄²×C₁₁	—	2	1	no	—
84	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	—	2	2	no	—
87	C₁₁×C₄⋊C₈	—	2	4	no	—
88	C₁₁×#103	—	2	2	no	—
89	C₁₁×#103	—	2	2	no	—
90	C₁₁×#103	—	4	2	no	—
91	C₁₁×#102	—	2	4	no	—
92	C₁₁×#102	—	2	4	no	—
93	C₁₁×#102	—	4	2	no	—
94	C₁₁×#102	—	4	2	no	—
95	C₁₁×#97	—	2	4	no	—
96	C₄×C₈×C₁₁	—	2	2	no	—
97	C₁₁×#95	—	2	2	no	—
98	C₁₁×#95	—	2	1	no	—
99	#22546	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₁	—	2	2	no	—
101	C₂×Q₈×C₁₁	—	2	2	no	—
102	C₂×Q₈×C₁₁	—	2	2	no	—
103	C₂×Q₈×C₁₁	—	2	1	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	—	2	1	no	—
106	C₂×Q₈×C₁₁	—	2	1	no	—
107	C₂×Q₈×C₁₁	—	2	1	no	—
108	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
109	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₁₁	—	2	4	no	—
111	C₂×D₄×C₁₁	—	2	4	no	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	2	2	no	—
115	C₂×D₄×C₁₁	—	2	2	no	—
116	C₂×D₄×C₁₁	—	2	2	no	—
117	C₂×D₄×C₁₁	—	4	2	no	—
118	C₂×D₄×C₁₁	—	4	2	no	—
119	C₂×D₄×C₁₁	—	8	1	no	—
120	C₂×D₄×C₁₁	—	8	1	no	—
121	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	1	no	—
125	C₂²×C₄×C₁₁	—	2	8	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	8	2	no	—
129	C₂²×C₄×C₁₁	—	8	2	no	—
130	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	#41	1	2	yes	—
144	C₁₁×C₄⋊C₄	—	2	4	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	2	1	no	—
150	C₁₁×C₄⋊C₄	—	2	2	no	—
151	C₁₁×C₄⋊C₄	—	4	4	no	—
152	C₁₁×C₄⋊C₄	—	4	2	no	—
153	C₁₁×C₄⋊C₄	—	8	2	no	—
154	C₁₁×C₄⋊C₄	—	8	1	no	—
155	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
156	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
158	C₁₁×C₄⋊C₄	#41	1	2	yes	—
159	C₁₁×C₂²⋊C₄	—	2	8	no	—
160	C₁₁×C₂²⋊C₄	—	2	8	no	—
161	C₁₁×C₂²⋊C₄	—	2	8	no	—
162	C₄²×C₁₁	—	2	4	no	—
163	C₄²×C₁₁	—	4	4	no	—
164	C₄²×C₁₁	—	4	2	no	—
165	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
166	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
167	C₄²×C₁₁	C₂×D₄	1	2	yes	—
168	C₄²×C₁₁	C₂×D₄	1	4	yes	—
169	C₂×#559	C₂×C₁₁	1	1	yes	characteristic
170	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
171	Q₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
172	#1983	C₂×C₁₁	1	2	yes	complemented
173	#1982	C₂×C₁₁	1	1	yes	characteristic
174	#1959	C₂×C₁₁	1	2	yes	complemented
175	#1957	C₂×C₁₁	1	1	yes	characteristic
176	#1803	C₂×C₁₁	1	1	yes	characteristic, complemented
177	#1802	C₂×C₁₁	1	2	yes	complemented
178	#1762	C₂×C₁₁	1	2	yes	complemented
179	C₄×#103	C₂×C₁₁	1	1	yes	characteristic, complemented
180	C₂³×C₁₁	—	2	4	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	—	4	2	no	—
183	C₂³×C₁₁	—	4	2	no	—
184	C₂³×C₁₁	—	4	2	no	—
185	C₂³×C₁₁	—	4	2	no	—
186	C₂³×C₁₁	—	4	2	no	—
187	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₁	—	2	8	no	—
189	Q₈×C₁₁	—	2	2	no	—
190	Q₈×C₁₁	—	2	2	no	—
191	Q₈×C₁₁	—	4	1	no	—
192	Q₈×C₁₁	—	4	1	no	—
193	D₄×C₁₁	—	2	4	no	—
194	D₄×C₁₁	—	2	4	no	—
195	D₄×C₁₁	—	4	2	no	—
196	D₄×C₁₁	—	4	2	no	—
197	D₄×C₁₁	—	4	8	no	—
198	D₄×C₁₁	—	8	4	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	4	1	no	—
209	C₂×C₄×C₁₁	—	4	1	no	—
210	C₂×C₄×C₁₁	—	4	1	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	—	4	1	no	—
213	C₂×C₄×C₁₁	—	4	1	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	1	no	—
216	C₂×C₄×C₁₁	—	4	2	no	—
217	C₂×C₄×C₁₁	—	4	1	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	2	no	—
220	C₂×C₄×C₁₁	—	8	8	no	—
221	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
222	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
223	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₁₁	#137	1	2	yes	—
227	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
233	C₈×C₁₁	—	2	2	no	—
234	C₈×C₁₁	—	4	1	no	—
235	C₈×C₁₁	—	4	2	no	—
236	#559	—	2	4	no	—
237	#559	C₄×C₁₁	1	8	yes	complemented
238	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×#124	—	2	1	no	—
240	C₂×#124	C₂²×C₁₁	1	2	yes	—
241	C₂×#123	—	2	2	no	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
247	#446	—	2	4	no	—
248	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
252	C₂×#103	C₂²×C₁₁	1	2	yes	—
253	C₂×#102	C₂²×C₁₁	1	2	yes	—
254	C₂×#102	C₂²×C₁₁	1	2	yes	—
255	C₂×#102	C₂²×C₁₁	1	2	yes	—
256	C₂×#102	C₂²×C₁₁	1	2	yes	—
257	C₂×#97	C₂²×C₁₁	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
259	#389	—	2	1	no	—
260	#389	—	2	2	no	—
261	#384	C₂²×C₁₁	1	2	yes	—
262	#384	C₂²×C₁₁	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
265	#340	C₂²×C₁₁	1	1	yes	characteristic
266	#340	C₂²×C₁₁	1	2	yes	—
267	#340	C₂²×C₁₁	1	1	yes	characteristic
268	C₂²×C₁₁	—	4	4	no	—
269	C₂²×C₁₁	—	4	4	no	—
270	C₂²×C₁₁	—	4	4	no	—
271	C₂²×C₁₁	—	8	2	no	—
272	C₂²×C₁₁	—	8	2	no	—
273	C₂²×C₁₁	—	8	2	no	—
274	C₂²×C₁₁	—	8	2	no	—
275	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₁₁	#548	1	1	yes	characteristic
277	C₂²×C₁₁	#550	1	1	yes	characteristic
278	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₂²×C₁₁	C₂×#137	1	1	yes	characteristic
280	C₂²×C₁₁	#576	1	1	yes	characteristic
281	C₂²×C₁₁	#577	1	1	yes	characteristic
282	C₄×C₁₁	—	2	4	no	—
283	C₄×C₁₁	—	2	4	no	—
284	C₄×C₁₁	—	2	2	no	—
285	C₄×C₁₁	—	4	2	no	—
286	C₄×C₁₁	—	4	2	no	—
287	C₄×C₁₁	—	4	2	no	—
288	C₄×C₁₁	—	8	2	no	—
289	C₄×C₁₁	—	8	1	no	—
290	C₄×C₁₁	#417	1	4	yes	—
291	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
292	C₄×C₁₁	#520	1	1	yes	characteristic
293	C₄×C₁₁	#548	1	1	yes	characteristic
294	C₄×C₁₁	#550	1	1	yes	characteristic
295	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
296	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
300	C₂³×C₄	—	2	2	no	—
301	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
304	#127	—	2	2	no	—
305	#127	C₂×C₄×C₁₁	1	4	yes	—
306	#124	—	2	8	no	—
307	#124	—	2	4	no	—
308	#124	C₂×C₄×C₁₁	1	8	yes	—
309	#123	—	2	16	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	4	4	no	—
312	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	—
313	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	—
314	C₄×Q₈	D₄×C₁₁	1	4	yes	—
315	C₄×D₄	—	2	8	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	4	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#103	—	4	2	no	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	4	2	no	—
345	#102	—	4	2	no	—
346	#97	—	2	4	no	—
347	C₄×C₈	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	1	no	—
350	C₂×C₁₁	—	8	4	no	—
351	C₂×C₁₁	#2341	1	1	yes	characteristic
352	C₂×C₁₁	C₂×#417	1	1	yes	characteristic
353	C₂×C₁₁	#2897	1	1	yes	characteristic
354	C₂×C₁₁	#3373	1	1	yes	characteristic
355	C₂×C₁₁	#3375	1	1	yes	characteristic
356	C₂×C₁₁	#3399	1	1	yes	characteristic
357	C₂×C₁₁	#3400	1	1	yes	characteristic
358	C₂⁴	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
367	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	8	1	no	—
378	C₂×D₄	—	8	1	no	—
379	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	C₁₁×#41	1	2	yes	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	4	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	8	2	no	—
412	C₄⋊C₄	—	8	1	no	—
413	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
414	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	8	yes	—
415	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
416	C₄⋊C₄	C₁₁×#41	1	2	yes	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	4	4	no	—
422	C₄²	—	4	2	no	—
423	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
424	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
425	C₄²	C₂×D₄×C₁₁	1	2	yes	—
426	C₄²	C₂×D₄×C₁₁	1	4	yes	—
427	C₁₁	#22546	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
436	Q₈	—	2	8	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	8	no	—
446	D₄	—	8	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
470	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
471	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
472	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
473	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
474	C₂×C₄	C₁₁×#137	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
477	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
478	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
479	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	4	1	no	—
483	C₈	—	4	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
492	C₂²	C₁₁×#548	1	1	yes	characteristic
493	C₂²	C₁₁×#550	1	1	yes	characteristic
494	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
495	C₂²	C₂×C₁₁×#137	1	1	yes	characteristic
496	C₂²	C₁₁×#576	1	1	yes	characteristic
497	C₂²	C₁₁×#577	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	1	no	—
506	C₄	C₁₁×#417	1	4	yes	—
507	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
508	C₄	C₁₁×#520	1	1	yes	characteristic
509	C₄	C₁₁×#548	1	1	yes	characteristic
510	C₄	C₁₁×#550	1	1	yes	characteristic
511	C₂	—	8	4	no	—
512	C₂	C₁₁×#2341	1	1	yes	characteristic
513	C₂	C₂×C₁₁×#417	1	1	yes	characteristic
514	C₂	C₁₁×#2897	1	1	yes	characteristic
515	C₂	C₁₁×#3373	1	1	yes	characteristic
516	C₂	C₁₁×#3375	1	1	yes	characteristic
517	C₂	C₁₁×#3399	1	1	yes	characteristic
518	C₂	C₁₁×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#446	C₂	semidirect
3. Q₈×C₁₁×C₄⋊C₄	C₂	semidirect
4. C₁₁×#1983	C₂	semidirect
6. C₁₁×#1959	C₂	semidirect
8. C₁₁×#1803	C₂	semidirect
9. C₁₁×#1802	C₂	semidirect
10. C₁₁×#1762	C₂	semidirect
11. C₄×C₁₁×#103	C₂	semidirect
13. C₁₁×#559	C₄	semidirect
99. #22546	C₁₁	direct (N × H)
170. C₂×#446	C₂×C₁₁	semidirect
171. Q₈×C₄⋊C₄	C₂×C₁₁	semidirect
172. #1983	C₂×C₁₁	semidirect
174. #1959	C₂×C₁₁	semidirect
176. #1803	C₂×C₁₁	semidirect
177. #1802	C₂×C₁₁	semidirect
178. #1762	C₂×C₁₁	semidirect
179. C₄×#103	C₂×C₁₁	semidirect
237. #559	C₄×C₁₁	semidirect
427. C₁₁	#22546	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#559	2
C₂×C₁₁×#446	2
Q₈×C₁₁×C₄⋊C₄	2
C₁₁×#1983	2
C₁₁×#1982	2
C₁₁×#1959	2
C₁₁×#1957	2
C₁₁×#1803	2
C₁₁×#1802	2
C₁₁×#1762	2
C₄×C₁₁×#103	2
#22546	11

Subgroups — C11×#22546 #14599739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22546 #14599739