Subgroups — C₁₁×#22289 #14599482

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1984	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1940	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1851	C₂	1	2	yes	maximal
7	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1753	C₂	1	2	yes	maximal
9	C₁₁×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
22	C₁₁×#391	C₄	1	1	yes	characteristic
23	C₁₁×#389	C₄	1	1	yes	characteristic
24	C₁₁×#387	C₄	1	2	yes	—
25	C₁₁×#385	C₄	1	2	yes	—
26	C₁₁×#380	C₄	1	1	yes	characteristic
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₁₁×#336	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
41	C₂×C₁₁×M₁₆	—	2	2	no	—
42	C₂×C₁₁×M₁₆	—	4	1	no	—
43	C₂×C₁₁×M₁₆	—	4	1	no	—
44	C₂×C₁₁×M₁₆	—	4	1	no	—
45	C₂×C₁₁×M₁₆	—	4	1	no	—
46	C₂×C₁₁×M₁₆	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₁₁×C₂²⋊Q₈	—	2	4	no	—
52	C₄×Q₈×C₁₁	—	4	1	no	—
53	C₄×Q₈×C₁₁	—	4	1	no	—
54	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₁	—	4	1	no	—
63	C₂×C₄²×C₁₁	—	4	1	no	—
64	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
70	C₁₁×C₄⋊C₈	—	4	2	no	—
71	C₁₁×C₄⋊C₈	—	4	1	no	—
72	C₁₁×C₄⋊C₈	—	4	1	no	—
73	C₁₁×C₄⋊C₈	—	4	2	no	—
74	C₁₁×C₂²⋊C₈	—	2	4	no	—
75	C₁₁×#97	—	4	2	no	—
76	C₄×C₈×C₁₁	—	4	2	no	—
77	C₁₁×#95	C₂×C₄	1	2	yes	—
78	C₁₁×#95	C₂×C₄	1	2	yes	—
79	C₁₁×#95	C₂×C₄	1	2	yes	—
80	C₁₁×#95	C₂×C₄	1	2	yes	—
81	C₁₁×#95	C₂×C₄	1	2	yes	—
82	#22289	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂×Q₈×C₁₁	—	4	1	no	—
85	C₂×Q₈×C₁₁	—	4	1	no	—
86	C₂×Q₈×C₁₁	M₁₆	1	4	yes	complemented
87	C₂²×C₄×C₁₁	—	2	1	no	—
88	C₂²×C₄×C₁₁	—	2	1	no	—
89	C₂²×C₄×C₁₁	—	2	1	no	—
90	C₂²×C₄×C₁₁	—	2	1	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	—	2	2	no	—
93	C₂²×C₄×C₁₁	—	4	1	no	—
94	C₂²×C₄×C₁₁	—	4	1	no	—
95	C₂²×C₄×C₁₁	—	4	1	no	—
96	C₂²×C₄×C₁₁	—	4	1	no	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₁	#41	1	2	yes	—
108	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
109	C₁₁×M₁₆	—	4	4	no	—
110	C₁₁×M₁₆	—	4	4	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	2	no	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	—	2	2	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	C₂×Q₈	1	4	yes	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	—	2	4	no	—
125	C₁₁×C₄⋊C₄	—	2	4	no	—
126	C₁₁×C₄⋊C₄	—	4	1	no	—
127	C₁₁×C₄⋊C₄	—	4	1	no	—
128	C₁₁×C₄⋊C₄	—	4	2	no	—
129	C₁₁×C₂²⋊C₄	—	2	4	no	—
130	C₁₁×C₂²⋊C₄	—	4	2	no	—
131	C₄²×C₁₁	—	2	2	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	—	2	1	no	—
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	2	2	no	—
136	C₄²×C₁₁	—	2	1	no	—
137	C₄²×C₁₁	—	2	1	no	—
138	C₄²×C₁₁	—	2	2	no	—
139	C₄²×C₁₁	—	4	1	no	—
140	C₄²×C₁₁	—	4	1	no	—
141	C₄×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
142	#1984	C₂×C₁₁	1	2	yes	complemented
143	#1940	C₂×C₁₁	1	2	yes	complemented
144	#1917	C₂×C₁₁	1	2	yes	complemented
145	#1916	C₂×C₁₁	1	2	yes	complemented
146	#1851	C₂×C₁₁	1	2	yes	—
147	#1797	C₂×C₁₁	1	1	yes	characteristic
148	#1753	C₂×C₁₁	1	2	yes	—
149	#1728	C₂×C₁₁	1	1	yes	characteristic
150	C₂³×C₁₁	—	2	1	no	—
151	C₂³×C₁₁	—	2	1	no	—
152	C₂³×C₁₁	—	2	1	no	—
153	C₂³×C₁₁	—	2	1	no	—
154	C₂³×C₁₁	—	2	1	no	—
155	C₂³×C₁₁	—	2	1	no	—
156	C₂³×C₁₁	C₄×Q₈	1	2	yes	—
157	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
158	Q₈×C₁₁	—	4	4	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	4	4	no	—
187	C₂×C₄×C₁₁	—	4	4	no	—
188	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
189	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
190	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₁₁	#131	1	2	yes	—
192	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₁	—	2	4	no	—
199	C₈×C₁₁	—	4	2	no	—
200	C₈×C₁₁	—	4	2	no	—
201	C₈×C₁₁	—	4	2	no	—
202	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
203	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
212	C₂×#97	C₂²×C₁₁	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
214	#391	C₄×C₁₁	1	1	yes	characteristic
215	#389	C₄×C₁₁	1	1	yes	characteristic
216	#387	C₄×C₁₁	1	2	yes	—
217	#385	C₄×C₁₁	1	2	yes	—
218	#380	C₄×C₁₁	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
220	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
221	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
222	#336	C₂²×C₁₁	1	2	yes	—
223	#336	C₂²×C₁₁	1	2	yes	—
224	#336	C₂²×C₁₁	1	2	yes	—
225	#336	C₂²×C₁₁	1	2	yes	—
226	#336	C₂²×C₁₁	1	2	yes	—
227	#336	C₂²×C₁₁	1	2	yes	—
228	#336	C₂²×C₁₁	1	2	yes	—
229	C₂²×C₁₁	—	2	2	no	—
230	C₂²×C₁₁	—	2	2	no	—
231	C₂²×C₁₁	—	2	2	no	—
232	C₂²×C₁₁	—	4	1	no	—
233	C₂²×C₁₁	—	4	1	no	—
234	C₂²×C₁₁	—	4	1	no	—
235	C₂²×C₁₁	—	4	1	no	—
236	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
237	C₂²×C₁₁	#518	1	1	yes	characteristic
238	C₂²×C₁₁	#520	1	1	yes	characteristic
239	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
240	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
241	C₂²×C₁₁	#568	1	1	yes	characteristic
242	C₂²×C₁₁	#568	1	1	yes	characteristic
243	C₄×C₁₁	—	2	2	no	—
244	C₄×C₁₁	—	2	2	no	—
245	C₄×C₁₁	—	2	4	no	—
246	C₄×C₁₁	—	2	2	no	—
247	C₄×C₁₁	—	4	1	no	—
248	C₄×C₁₁	—	4	2	no	—
249	C₄×C₁₁	—	4	1	no	—
250	C₄×C₁₁	—	4	2	no	—
251	C₄×C₁₁	—	4	2	no	—
252	C₄×C₁₁	#538	1	1	yes	characteristic
253	C₄×C₁₁	#539	1	1	yes	characteristic
254	C₄×C₁₁	#543	1	1	yes	characteristic
255	C₄×C₁₁	#544	1	1	yes	characteristic
256	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	4	1	no	—
262	C₂×M₁₆	—	4	1	no	—
263	C₂×M₁₆	—	4	1	no	—
264	C₂×M₁₆	—	4	1	no	—
265	C₂×M₁₆	Q₈×C₁₁	1	4	yes	complemented
266	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₄×Q₈	—	4	1	no	—
272	C₄×Q₈	—	4	1	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
281	C₂×C₄²	—	4	1	no	—
282	C₂×C₄²	—	4	1	no	—
283	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
289	C₄⋊C₈	—	4	2	no	—
290	C₄⋊C₈	—	4	1	no	—
291	C₄⋊C₈	—	4	1	no	—
292	C₄⋊C₈	—	4	2	no	—
293	C₂²⋊C₈	—	2	4	no	—
294	#97	—	4	2	no	—
295	C₄×C₈	—	4	2	no	—
296	#95	C₂×C₄×C₁₁	1	2	yes	—
297	#95	C₂×C₄×C₁₁	1	2	yes	—
298	#95	C₂×C₄×C₁₁	1	2	yes	—
299	#95	C₂×C₄×C₁₁	1	2	yes	—
300	#95	C₂×C₄×C₁₁	1	2	yes	—
301	C₂×C₁₁	—	4	2	no	—
302	C₂×C₁₁	#2329	1	1	yes	characteristic
303	C₂×C₁₁	#2962	1	1	yes	characteristic
304	C₂×C₁₁	Q₈×M₁₆	1	1	yes	characteristic
305	C₂×C₁₁	#2973	1	1	yes	characteristic
306	C₂×C₁₁	#2976	1	1	yes	characteristic
307	C₂×C₁₁	#2991	1	1	yes	characteristic
308	C₂×C₁₁	#2995	1	1	yes	characteristic
309	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	C₁₁×M₁₆	1	4	yes	complemented
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
327	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
333	C₂²×C₄	C₁₁×#41	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
335	M₁₆	—	4	4	no	—
336	M₁₆	—	4	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₁₁	#22289	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	C₄×Q₈×C₁₁	1	2	yes	—
375	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
376	Q₈	—	4	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
407	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
408	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
409	C₂×C₄	C₁₁×#131	1	2	yes	—
410	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
411	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
412	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
428	C₂²	C₁₁×#518	1	1	yes	characteristic
429	C₂²	C₁₁×#520	1	1	yes	characteristic
430	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
431	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
432	C₂²	C₁₁×#568	1	1	yes	characteristic
433	C₂²	C₁₁×#568	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	C₁₁×#538	1	1	yes	characteristic
444	C₄	C₁₁×#539	1	1	yes	characteristic
445	C₄	C₁₁×#543	1	1	yes	characteristic
446	C₄	C₁₁×#544	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₁₁×#2329	1	1	yes	characteristic
449	C₂	C₁₁×#2962	1	1	yes	characteristic
450	C₂	Q₈×C₁₁×M₁₆	1	1	yes	characteristic
451	C₂	C₁₁×#2973	1	1	yes	characteristic
452	C₂	C₁₁×#2976	1	1	yes	characteristic
453	C₂	C₁₁×#2991	1	1	yes	characteristic
454	C₂	C₁₁×#2995	1	1	yes	characteristic

	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	C₂⁴×C₁₁	C₂²×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. C₁₁×#1984	C₂	semidirect
3. C₁₁×#1940	C₂	semidirect
4. C₁₁×#1917	C₂	semidirect
5. C₁₁×#1916	C₂	semidirect
46. C₂×C₁₁×M₁₆	Q₈	semidirect
82. #22289	C₁₁	direct (N × H)
86. C₂×Q₈×C₁₁	M₁₆	semidirect
142. #1984	C₂×C₁₁	semidirect
143. #1940	C₂×C₁₁	semidirect
144. #1917	C₂×C₁₁	semidirect
145. #1916	C₂×C₁₁	semidirect
265. C₂×M₁₆	Q₈×C₁₁	semidirect
312. C₂×Q₈	C₁₁×M₁₆	semidirect
367. C₁₁	#22289	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×C₂²⋊Q₈	2
C₁₁×#1984	2
C₁₁×#1940	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1851	2
C₁₁×#1797	2
C₁₁×#1753	2
C₁₁×#1728	2
#22289	11

Subgroups — C11×#22289 #14599482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22289 #14599482