Subgroups — C₁₁×#22066 #14599259

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2395	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1940	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1870	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1850	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₁	—	2	4	no	—
18	C₁₁×#424	—	2	4	no	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₁×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#400	C₄	1	1	yes	characteristic
30	C₁₁×#399	C₄	1	1	yes	characteristic
31	C₁₁×#398	C₄	1	1	yes	characteristic
32	C₁₁×#397	C₄	1	2	yes	—
33	C₁₁×#397	C₄	1	1	yes	characteristic
34	C₁₁×#394	C₄	1	2	yes	—
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₁₁×M₁₆	—	2	2	no	—
47	C₂×C₁₁×M₁₆	—	4	2	no	—
48	C₂²×C₈×C₁₁	—	2	2	no	—
49	C₂²×C₈×C₁₁	—	4	2	no	—
50	C₂²×C₈×C₁₁	—	4	2	no	—
51	C₂²×C₈×C₁₁	D₄	1	4	yes	—
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₁	—	2	2	no	—
59	C₄×D₄×C₁₁	—	2	2	no	—
60	C₁₁×#117	—	2	2	no	—
61	C₁₁×#117	—	2	2	no	—
62	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	—	2	4	no	—
77	C₁₁×C₄⋊C₈	—	2	4	no	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	4	2	no	—
80	C₁₁×C₂²⋊C₈	—	2	2	no	—
81	C₁₁×C₂²⋊C₈	—	2	2	no	—
82	C₁₁×C₂²⋊C₈	—	2	2	no	—
83	C₁₁×C₂²⋊C₈	—	4	2	no	—
84	C₁₁×#97	—	4	2	no	—
85	C₄×C₈×C₁₁	—	2	2	no	—
86	C₁₁×#95	C₂×C₄	1	2	yes	—
87	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#95	C₂×C₄	1	2	yes	—
89	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#95	C₂×C₄	1	2	yes	—
91	C₁₁×#95	C₂×C₄	1	2	yes	—
92	#22066	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	1	no	—
101	C₂²×C₄×C₁₁	—	2	1	no	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁	#41	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₁₁×M₁₆	—	4	4	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	4	4	no	—
129	C₂×C₈×C₁₁	—	4	4	no	—
130	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	2	no	—
135	C₁₁×C₄⋊C₄	—	2	4	no	—
136	C₁₁×C₄⋊C₄	—	4	2	no	—
137	C₁₁×C₂²⋊C₄	—	2	4	no	—
138	C₁₁×C₂²⋊C₄	—	2	2	no	—
139	C₁₁×C₂²⋊C₄	—	2	4	no	—
140	C₁₁×C₂²⋊C₄	—	2	2	no	—
141	C₁₁×C₂²⋊C₄	—	4	2	no	—
142	C₁₁×C₂²⋊C₄	—	4	2	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	—	2	2	no	—
148	C₄²×C₁₁	—	2	2	no	—
149	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
150	C₂×#424	C₂×C₁₁	1	1	yes	characteristic, complemented
151	#2395	C₂×C₁₁	1	1	yes	characteristic
152	#1940	C₂×C₁₁	1	2	yes	complemented
153	#1924	C₂×C₁₁	1	2	yes	complemented
154	#1916	C₂×C₁₁	1	2	yes	complemented
155	#1870	C₂×C₁₁	1	1	yes	characteristic
156	#1851	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1850	C₂×C₁₁	1	2	yes	complemented
158	#1818	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1752	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	—	2	1	no	—
161	C₂³×C₁₁	—	2	2	no	—
162	C₂³×C₁₁	—	2	2	no	—
163	C₂³×C₁₁	—	2	1	no	—
164	C₂³×C₁₁	—	2	1	no	—
165	C₂³×C₁₁	—	2	1	no	—
166	C₂³×C₁₁	—	2	2	no	—
167	C₂³×C₁₁	—	2	2	no	—
168	C₂³×C₁₁	C₄×D₄	1	2	yes	—
169	C₂³×C₁₁	#131	1	2	yes	—
170	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
171	D₄×C₁₁	—	2	8	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	4	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	2	2	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	4	1	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	4	2	no	—
197	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₁	#131	1	2	yes	—
199	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
202	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
203	C₈×C₁₁	—	2	2	no	—
204	C₈×C₁₁	—	2	2	no	—
205	C₈×C₁₁	—	4	1	no	—
206	C₈×C₁₁	—	4	2	no	—
207	C₈×C₁₁	—	4	1	no	—
208	C₈×C₁₁	—	4	2	no	—
209	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
213	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
214	C₈×D₄	—	2	4	no	—
215	#424	—	2	4	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
224	C₂×#97	C₂²×C₁₁	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
226	#400	C₄×C₁₁	1	1	yes	characteristic
227	#399	C₄×C₁₁	1	1	yes	characteristic
228	#398	C₄×C₁₁	1	1	yes	characteristic
229	#397	C₄×C₁₁	1	2	yes	—
230	#397	C₄×C₁₁	1	1	yes	characteristic
231	#394	C₄×C₁₁	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
233	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
235	#336	C₂²×C₁₁	1	2	yes	—
236	#336	C₂²×C₁₁	1	2	yes	—
237	#336	C₂²×C₁₁	1	2	yes	—
238	#336	C₂²×C₁₁	1	2	yes	—
239	#336	C₂²×C₁₁	1	2	yes	—
240	C₂²×C₁₁	—	2	2	no	—
241	C₂²×C₁₁	—	2	2	no	—
242	C₂²×C₁₁	—	2	2	no	—
243	C₂²×C₁₁	—	2	2	no	—
244	C₂²×C₁₁	—	2	4	no	—
245	C₂²×C₁₁	—	4	1	no	—
246	C₂²×C₁₁	—	4	1	no	—
247	C₂²×C₁₁	—	4	2	no	—
248	C₂²×C₁₁	—	4	2	no	—
249	C₂²×C₁₁	—	4	2	no	—
250	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₁₁	#520	1	2	yes	—
252	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
253	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
254	C₂²×C₁₁	#568	1	2	yes	—
255	C₄×C₁₁	—	2	2	no	—
256	C₄×C₁₁	—	2	2	no	—
257	C₄×C₁₁	—	4	1	no	—
258	C₄×C₁₁	—	4	2	no	—
259	C₄×C₁₁	—	4	1	no	—
260	C₄×C₁₁	—	4	2	no	—
261	C₄×C₁₁	—	4	2	no	—
262	C₄×C₁₁	—	4	2	no	—
263	C₄×C₁₁	#534	1	1	yes	characteristic
264	C₄×C₁₁	#536	1	1	yes	characteristic
265	C₄×C₁₁	#539	1	2	yes	—
266	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	4	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	4	2	no	—
273	C₂²×C₈	—	4	2	no	—
274	C₂²×C₈	D₄×C₁₁	1	4	yes	—
275	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
290	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
299	C₄⋊C₈	—	2	4	no	—
300	C₄⋊C₈	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	4	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	4	2	no	—
307	#97	—	4	2	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	C₂×C₄×C₁₁	1	2	yes	—
310	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
311	#95	C₂×C₄×C₁₁	1	2	yes	—
312	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
313	#95	C₂×C₄×C₁₁	1	2	yes	—
314	#95	C₂×C₄×C₁₁	1	2	yes	—
315	C₂×C₁₁	—	4	2	no	—
316	C₂×C₁₁	—	4	2	no	—
317	C₂×C₁₁	#2322	1	1	yes	characteristic
318	C₂×C₁₁	#2929	1	1	yes	characteristic
319	C₂×C₁₁	#2932	1	1	yes	characteristic
320	C₂×C₁₁	#2992	1	2	yes	—
321	C₂×C₁₁	#2993	1	2	yes	—
322	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
323	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
342	C₂²×C₄	C₁₁×#41	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
344	M₁₆	—	4	4	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₁₁	#22066	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	C₄×D₄×C₁₁	1	2	yes	—
388	C₂³	C₁₁×#131	1	2	yes	—
389	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
417	C₂×C₄	C₁₁×#131	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
420	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
439	C₂²	C₁₁×#520	1	2	yes	—
440	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
441	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
442	C₂²	C₁₁×#568	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	C₁₁×#534	1	1	yes	characteristic
452	C₄	C₁₁×#536	1	1	yes	characteristic
453	C₄	C₁₁×#539	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₁₁×#2322	1	1	yes	characteristic
457	C₂	C₁₁×#2929	1	1	yes	characteristic
458	C₂	C₁₁×#2932	1	1	yes	characteristic
459	C₂	C₁₁×#2992	1	2	yes	—
460	C₂	C₁₁×#2993	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#424	C₂	semidirect
4. C₁₁×#1940	C₂	semidirect
5. C₁₁×#1924	C₂	semidirect
6. C₁₁×#1916	C₂	semidirect
8. C₁₁×#1851	C₂	semidirect
9. C₁₁×#1850	C₂	semidirect
10. C₁₁×#1818	C₂	semidirect
11. C₁₁×#1752	C₂	semidirect
92. #22066	C₁₁	direct (N × H)
150. C₂×#424	C₂×C₁₁	semidirect
152. #1940	C₂×C₁₁	semidirect
153. #1924	C₂×C₁₁	semidirect
154. #1916	C₂×C₁₁	semidirect
156. #1851	C₂×C₁₁	semidirect
157. #1850	C₂×C₁₁	semidirect
158. #1818	C₂×C₁₁	semidirect
159. #1752	C₂×C₁₁	semidirect
378. C₁₁	#22066	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×C₈×D₄×C₁₁	2
C₂×C₁₁×#424	2
C₁₁×#2395	2
C₁₁×#1940	2
C₁₁×#1924	2
C₁₁×#1916	2
C₁₁×#1870	2
C₁₁×#1851	2
C₁₁×#1850	2
C₁₁×#1818	2
C₁₁×#1752	2
#22066	11

Subgroups — C11×#22066 #14599259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22066 #14599259