Subgroups — C₁₁×#23339 #14600532

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1923	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1923	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#1916	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#1817	C₂	1	1	yes	maximal, characteristic
15	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#391	C₄	1	1	yes	characteristic
34	C₁₁×#389	C₄	1	1	yes	characteristic
35	C₁₁×#387	C₄	1	1	yes	characteristic
36	C₁₁×#387	C₄	1	1	yes	characteristic
37	C₁₁×#385	C₄	1	1	yes	characteristic
38	C₁₁×#385	C₄	1	1	yes	characteristic
39	C₁₁×#380	C₄	1	1	yes	characteristic
40	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₁×#336	C₂²	1	1	yes	characteristic
46	C₁₁×#336	C₂²	1	1	yes	characteristic
47	C₁₁×#336	C₂²	1	1	yes	characteristic
48	C₁₁×#336	C₂²	1	1	yes	characteristic
49	C₁₁×#336	C₂²	1	1	yes	characteristic
50	C₁₁×#336	C₂²	1	1	yes	characteristic
51	C₁₁×#336	C₂²	1	1	yes	characteristic
52	C₁₁×#336	C₂²	1	1	yes	characteristic
53	C₁₁×#336	C₂²	1	1	yes	characteristic
54	C₁₁×#336	C₂²	1	1	yes	characteristic
55	C₁₁×#336	C₂²	1	1	yes	characteristic
56	C₁₁×#336	C₂²	1	1	yes	characteristic
57	C₁₁×#336	C₂²	1	1	yes	characteristic
58	C₁₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×C₂²⋊Q₈	—	2	4	no	—
72	C₄×Q₈×C₁₁	—	4	1	no	—
73	C₄×Q₈×C₁₁	—	4	1	no	—
74	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	—	4	1	no	—
88	C₂×C₄²×C₁₁	—	4	1	no	—
89	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
97	C₁₁×C₄⋊C₈	—	4	1	no	—
98	C₁₁×C₄⋊C₈	—	4	1	no	—
99	C₁₁×C₄⋊C₈	—	4	1	no	—
100	C₁₁×C₄⋊C₈	—	4	1	no	—
101	C₁₁×C₄⋊C₈	—	4	1	no	—
102	C₁₁×C₄⋊C₈	—	4	1	no	—
103	C₁₁×C₂²⋊C₈	—	4	1	no	—
104	C₁₁×C₂²⋊C₈	—	4	1	no	—
105	C₁₁×C₂²⋊C₈	—	4	1	no	—
106	C₁₁×C₂²⋊C₈	—	4	1	no	—
107	C₁₁×#97	—	4	1	no	—
108	C₁₁×#97	—	4	1	no	—
109	C₄×C₈×C₁₁	—	4	1	no	—
110	C₄×C₈×C₁₁	—	4	1	no	—
111	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
120	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
121	#23339	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₁	—	2	2	no	—
124	C₂×Q₈×C₁₁	—	2	2	no	—
125	C₂×Q₈×C₁₁	—	4	1	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	2	no	—
128	C₂²×C₄×C₁₁	—	2	2	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	—	2	1	no	—
135	C₂²×C₄×C₁₁	—	4	1	no	—
136	C₂²×C₄×C₁₁	—	4	1	no	—
137	C₂²×C₄×C₁₁	—	4	1	no	—
138	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
152	C₂×C₈×C₁₁	—	2	1	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	—	2	1	no	—
157	C₂×C₈×C₁₁	—	2	1	no	—
158	C₂×C₈×C₁₁	—	2	1	no	—
159	C₂×C₈×C₁₁	—	2	1	no	—
160	C₂×C₈×C₁₁	—	2	1	no	—
161	C₂×C₈×C₁₁	—	2	1	no	—
162	C₂×C₈×C₁₁	—	2	1	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	2	1	no	—
165	C₂×C₈×C₁₁	—	2	1	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	1	no	—
168	C₂×C₈×C₁₁	—	2	1	no	—
169	C₂×C₈×C₁₁	—	2	1	no	—
170	C₂×C₈×C₁₁	—	2	1	no	—
171	C₂×C₈×C₁₁	—	2	1	no	—
172	C₂×C₈×C₁₁	—	2	1	no	—
173	C₂×C₈×C₁₁	—	2	1	no	—
174	C₂×C₈×C₁₁	—	2	1	no	—
175	C₂×C₈×C₁₁	—	2	1	no	—
176	C₁₁×C₄⋊C₄	—	2	2	no	—
177	C₁₁×C₄⋊C₄	—	2	2	no	—
178	C₁₁×C₄⋊C₄	—	2	2	no	—
179	C₁₁×C₄⋊C₄	—	4	1	no	—
180	C₁₁×C₄⋊C₄	—	4	1	no	—
181	C₁₁×C₄⋊C₄	—	4	1	no	—
182	C₁₁×C₄⋊C₄	—	4	1	no	—
183	C₁₁×C₄⋊C₄	—	4	1	no	—
184	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
185	C₁₁×C₂²⋊C₄	—	2	2	no	—
186	C₁₁×C₂²⋊C₄	—	2	2	no	—
187	C₁₁×C₂²⋊C₄	—	2	2	no	—
188	C₁₁×C₂²⋊C₄	—	2	2	no	—
189	C₄²×C₁₁	—	2	1	no	—
190	C₄²×C₁₁	—	2	1	no	—
191	C₄²×C₁₁	—	2	1	no	—
192	C₄²×C₁₁	—	2	1	no	—
193	C₄²×C₁₁	—	2	1	no	—
194	C₄²×C₁₁	—	2	1	no	—
195	C₄²×C₁₁	—	2	1	no	—
196	C₄²×C₁₁	—	2	1	no	—
197	C₄²×C₁₁	—	2	1	no	—
198	C₄²×C₁₁	—	2	1	no	—
199	C₄²×C₁₁	—	2	1	no	—
200	C₄²×C₁₁	—	2	1	no	—
201	C₄²×C₁₁	—	4	1	no	—
202	C₄²×C₁₁	—	4	1	no	—
203	C₄×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
204	#1985	C₂×C₁₁	1	1	yes	characteristic, complemented
205	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
206	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
207	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#1924	C₂×C₁₁	1	1	yes	characteristic
209	#1924	C₂×C₁₁	1	1	yes	characteristic
210	#1923	C₂×C₁₁	1	1	yes	characteristic
211	#1923	C₂×C₁₁	1	1	yes	characteristic
212	#1917	C₂×C₁₁	1	1	yes	characteristic, complemented
213	#1917	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
215	#1916	C₂×C₁₁	1	1	yes	characteristic, complemented
216	#1817	C₂×C₁₁	1	1	yes	characteristic
217	#1797	C₂×C₁₁	1	1	yes	characteristic
218	C₂³×C₁₁	—	2	1	no	—
219	C₂³×C₁₁	—	2	1	no	—
220	C₂³×C₁₁	—	2	1	no	—
221	C₂³×C₁₁	—	2	1	no	—
222	C₂³×C₁₁	—	2	1	no	—
223	C₂³×C₁₁	—	2	1	no	—
224	C₂³×C₁₁	#131	1	2	yes	—
225	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
226	Q₈×C₁₁	—	4	4	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	2	1	no	—
229	C₂×C₄×C₁₁	—	2	1	no	—
230	C₂×C₄×C₁₁	—	2	1	no	—
231	C₂×C₄×C₁₁	—	2	1	no	—
232	C₂×C₄×C₁₁	—	2	1	no	—
233	C₂×C₄×C₁₁	—	2	1	no	—
234	C₂×C₄×C₁₁	—	2	1	no	—
235	C₂×C₄×C₁₁	—	2	1	no	—
236	C₂×C₄×C₁₁	—	2	1	no	—
237	C₂×C₄×C₁₁	—	2	1	no	—
238	C₂×C₄×C₁₁	—	2	1	no	—
239	C₂×C₄×C₁₁	—	2	1	no	—
240	C₂×C₄×C₁₁	—	2	1	no	—
241	C₂×C₄×C₁₁	—	2	1	no	—
242	C₂×C₄×C₁₁	—	2	1	no	—
243	C₂×C₄×C₁₁	—	2	1	no	—
244	C₂×C₄×C₁₁	—	2	1	no	—
245	C₂×C₄×C₁₁	—	2	1	no	—
246	C₂×C₄×C₁₁	—	2	1	no	—
247	C₂×C₄×C₁₁	—	2	1	no	—
248	C₂×C₄×C₁₁	—	2	1	no	—
249	C₂×C₄×C₁₁	—	2	1	no	—
250	C₂×C₄×C₁₁	—	2	1	no	—
251	C₂×C₄×C₁₁	—	2	1	no	—
252	C₂×C₄×C₁₁	—	2	1	no	—
253	C₂×C₄×C₁₁	—	2	1	no	—
254	C₂×C₄×C₁₁	—	2	1	no	—
255	C₂×C₄×C₁₁	—	2	1	no	—
256	C₂×C₄×C₁₁	—	2	1	no	—
257	C₂×C₄×C₁₁	—	2	1	no	—
258	C₂×C₄×C₁₁	—	2	1	no	—
259	C₂×C₄×C₁₁	—	2	1	no	—
260	C₂×C₄×C₁₁	—	2	1	no	—
261	C₂×C₄×C₁₁	—	2	1	no	—
262	C₂×C₄×C₁₁	—	4	4	no	—
263	C₂×C₄×C₁₁	—	4	4	no	—
264	C₂×C₄×C₁₁	—	4	1	no	—
265	C₂×C₄×C₁₁	—	4	1	no	—
266	C₂×C₄×C₁₁	—	4	1	no	—
267	C₂×C₄×C₁₁	—	4	1	no	—
268	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
269	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
270	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
271	C₂×C₄×C₁₁	#131	1	2	yes	—
272	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
278	C₈×C₁₁	—	4	1	no	—
279	C₈×C₁₁	—	4	1	no	—
280	C₈×C₁₁	—	4	1	no	—
281	C₈×C₁₁	—	4	1	no	—
282	C₈×C₁₁	—	4	1	no	—
283	C₈×C₁₁	—	4	1	no	—
284	C₈×C₁₁	—	4	1	no	—
285	C₈×C₁₁	—	4	1	no	—
286	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
290	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
299	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
300	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
303	#391	C₄×C₁₁	1	1	yes	characteristic
304	#389	C₄×C₁₁	1	1	yes	characteristic
305	#387	C₄×C₁₁	1	1	yes	characteristic
306	#387	C₄×C₁₁	1	1	yes	characteristic
307	#385	C₄×C₁₁	1	1	yes	characteristic
308	#385	C₄×C₁₁	1	1	yes	characteristic
309	#380	C₄×C₁₁	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
315	#336	C₂²×C₁₁	1	1	yes	characteristic
316	#336	C₂²×C₁₁	1	1	yes	characteristic
317	#336	C₂²×C₁₁	1	1	yes	characteristic
318	#336	C₂²×C₁₁	1	1	yes	characteristic
319	#336	C₂²×C₁₁	1	1	yes	characteristic
320	#336	C₂²×C₁₁	1	1	yes	characteristic
321	#336	C₂²×C₁₁	1	1	yes	characteristic
322	#336	C₂²×C₁₁	1	1	yes	characteristic
323	#336	C₂²×C₁₁	1	1	yes	characteristic
324	#336	C₂²×C₁₁	1	1	yes	characteristic
325	#336	C₂²×C₁₁	1	1	yes	characteristic
326	#336	C₂²×C₁₁	1	1	yes	characteristic
327	#336	C₂²×C₁₁	1	1	yes	characteristic
328	#336	C₂²×C₁₁	1	1	yes	characteristic
329	C₂²×C₁₁	—	2	2	no	—
330	C₂²×C₁₁	—	2	2	no	—
331	C₂²×C₁₁	—	2	2	no	—
332	C₂²×C₁₁	—	4	1	no	—
333	C₂²×C₁₁	—	4	1	no	—
334	C₂²×C₁₁	—	4	1	no	—
335	C₂²×C₁₁	—	4	1	no	—
336	C₂²×C₁₁	#518	1	1	yes	characteristic
337	C₂²×C₁₁	#519	1	1	yes	characteristic
338	C₂²×C₁₁	#520	1	1	yes	characteristic
339	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
340	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
341	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
342	C₂²×C₁₁	#568	1	1	yes	characteristic
343	C₄×C₁₁	—	2	2	no	—
344	C₄×C₁₁	—	2	2	no	—
345	C₄×C₁₁	—	2	2	no	—
346	C₄×C₁₁	—	2	2	no	—
347	C₄×C₁₁	—	4	1	no	—
348	C₄×C₁₁	—	4	1	no	—
349	C₄×C₁₁	—	4	1	no	—
350	C₄×C₁₁	—	4	1	no	—
351	C₄×C₁₁	—	4	1	no	—
352	C₄×C₁₁	—	4	1	no	—
353	C₄×C₁₁	—	4	1	no	—
354	C₄×C₁₁	—	4	1	no	—
355	C₄×C₁₁	—	4	1	no	—
356	C₄×C₁₁	#562	1	1	yes	characteristic
357	C₄×C₁₁	#562	1	1	yes	characteristic
358	C₄×C₁₁	#563	1	1	yes	characteristic
359	C₄×C₁₁	#563	1	1	yes	characteristic
360	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
361	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
362	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
372	C₂²⋊Q₈	—	2	4	no	—
373	C₄×Q₈	—	4	1	no	—
374	C₄×Q₈	—	4	1	no	—
375	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
388	C₂×C₄²	—	4	1	no	—
389	C₂×C₄²	—	4	1	no	—
390	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
391	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
398	C₄⋊C₈	—	4	1	no	—
399	C₄⋊C₈	—	4	1	no	—
400	C₄⋊C₈	—	4	1	no	—
401	C₄⋊C₈	—	4	1	no	—
402	C₄⋊C₈	—	4	1	no	—
403	C₄⋊C₈	—	4	1	no	—
404	C₂²⋊C₈	—	4	1	no	—
405	C₂²⋊C₈	—	4	1	no	—
406	C₂²⋊C₈	—	4	1	no	—
407	C₂²⋊C₈	—	4	1	no	—
408	#97	—	4	1	no	—
409	#97	—	4	1	no	—
410	C₄×C₈	—	4	1	no	—
411	C₄×C₈	—	4	1	no	—
412	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
413	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
414	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
415	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
416	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
417	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
418	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
419	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
420	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
421	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
422	C₂×C₁₁	—	4	2	no	—
423	C₂×C₁₁	#2378	1	1	yes	characteristic
424	C₂×C₁₁	#2974	1	1	yes	characteristic
425	C₂×C₁₁	#2976	1	1	yes	characteristic
426	C₂×C₁₁	#2984	1	1	yes	characteristic
427	C₂×C₁₁	#2985	1	1	yes	characteristic
428	C₂×C₁₁	#2989	1	1	yes	characteristic
429	C₂×C₁₁	#2994	1	1	yes	characteristic
430	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	—	4	1	no	—
511	C₁₁	#23339	1	1	yes	characteristic, direct product factor, Sylow
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₁₁×#131	1	2	yes	—
519	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
520	Q₈	—	4	4	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
563	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
564	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
565	C₂×C₄	C₁₁×#131	1	2	yes	—
566	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
570	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₁₁×#518	1	1	yes	characteristic
588	C₂²	C₁₁×#519	1	1	yes	characteristic
589	C₂²	C₁₁×#520	1	1	yes	characteristic
590	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
591	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
592	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
593	C₂²	C₁₁×#568	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	C₁₁×#562	1	1	yes	characteristic
608	C₄	C₁₁×#562	1	1	yes	characteristic
609	C₄	C₁₁×#563	1	1	yes	characteristic
610	C₄	C₁₁×#563	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	C₁₁×#2378	1	1	yes	characteristic
613	C₂	C₁₁×#2974	1	1	yes	characteristic
614	C₂	C₁₁×#2976	1	1	yes	characteristic
615	C₂	C₁₁×#2984	1	1	yes	characteristic
616	C₂	C₁₁×#2985	1	1	yes	characteristic
617	C₂	C₁₁×#2989	1	1	yes	characteristic
618	C₂	C₁₁×#2994	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×#1985	C₂	semidirect
3. C₁₁×#1984	C₂	semidirect
4. C₁₁×#1940	C₂	semidirect
5. C₁₁×#1939	C₂	semidirect
10. C₁₁×#1917	C₂	semidirect
11. C₁₁×#1917	C₂	semidirect
12. C₁₁×#1916	C₂	semidirect
13. C₁₁×#1916	C₂	semidirect
121. #23339	C₁₁	direct (N × H)
204. #1985	C₂×C₁₁	semidirect
205. #1984	C₂×C₁₁	semidirect
206. #1940	C₂×C₁₁	semidirect
207. #1939	C₂×C₁₁	semidirect
212. #1917	C₂×C₁₁	semidirect
213. #1917	C₂×C₁₁	semidirect
214. #1916	C₂×C₁₁	semidirect
215. #1916	C₂×C₁₁	semidirect
511. C₁₁	#23339	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×#1985	2
C₁₁×#1984	2
C₁₁×#1940	2
C₁₁×#1939	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1817	2
C₁₁×#1797	2
#23339	11

Subgroups — C11×#23339 #14600532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23339 #14600532