Subgroups — C₁₁×#21980 #14599173

Order 2816.

774 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	C₂×C₁₁×#433	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2298	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#1843	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
19	C₁₁×#433	—	2	4	no	—
20	C₁₁×#424	—	2	4	no	—
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
39	C₁₁×#388	C₄	1	1	yes	characteristic
40	C₁₁×#388	C₄	1	1	yes	characteristic
41	C₁₁×#388	C₄	1	1	yes	characteristic
42	C₁₁×#388	C₄	1	1	yes	characteristic
43	C₁₁×#387	C₄	1	1	yes	characteristic
44	C₁₁×#387	C₄	1	1	yes	characteristic
45	C₁₁×#387	C₄	1	1	yes	characteristic
46	C₁₁×#387	C₄	1	1	yes	characteristic
47	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₁₁×#376	C₂²	1	1	yes	characteristic
52	C₄³×C₁₁	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	C₁₁×#336	C₂²	1	1	yes	characteristic
60	C₁₁×#336	C₂²	1	1	yes	characteristic
61	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₂×C₁₁×M₁₆	—	2	2	no	—
63	C₂×C₁₁×M₁₆	—	4	1	no	—
64	C₂×C₁₁×M₁₆	—	4	1	no	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	—	4	1	no	—
67	C₂²×C₈×C₁₁	—	4	1	no	—
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	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×#117	D₄	1	4	yes	—
77	C₁₁×#117	Q₈	1	4	yes	—
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×C₄⋊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×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂×C₄	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	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
100	C₁₁×C₄⋊C₈	—	2	2	no	—
101	C₁₁×C₄⋊C₈	—	2	2	no	—
102	C₁₁×C₄⋊C₈	—	2	2	no	—
103	C₁₁×C₄⋊C₈	—	2	2	no	—
104	C₁₁×C₄⋊C₈	—	2	2	no	—
105	C₁₁×C₄⋊C₈	—	2	2	no	—
106	C₁₁×C₄⋊C₈	—	4	1	no	—
107	C₁₁×C₄⋊C₈	—	4	1	no	—
108	C₁₁×C₄⋊C₈	—	4	1	no	—
109	C₁₁×C₄⋊C₈	—	4	1	no	—
110	C₁₁×C₄⋊C₈	—	4	1	no	—
111	C₁₁×C₄⋊C₈	—	4	1	no	—
112	C₁₁×C₄⋊C₈	—	4	1	no	—
113	C₁₁×C₄⋊C₈	—	4	1	no	—
114	C₁₁×C₂²⋊C₈	—	2	2	no	—
115	C₁₁×C₂²⋊C₈	—	2	2	no	—
116	C₁₁×#97	—	2	2	no	—
117	C₄×C₈×C₁₁	—	2	2	no	—
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	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
122	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
123	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
124	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
125	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
126	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
127	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
128	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
129	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
130	#21980	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
152	C₁₁×M₁₆	—	4	4	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	C₂×C₈×C₁₁	—	2	1	no	—
177	C₂×C₈×C₁₁	—	4	4	no	—
178	C₁₁×C₄⋊C₄	—	2	2	no	—
179	C₁₁×C₄⋊C₄	—	2	2	no	—
180	C₁₁×C₄⋊C₄	—	4	1	no	—
181	C₁₁×C₄⋊C₄	—	4	1	no	—
182	C₁₁×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
183	C₁₁×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
184	C₁₁×C₂²⋊C₄	—	2	2	no	—
185	C₁₁×C₂²⋊C₄	—	2	2	no	—
186	C₁₁×C₂²⋊C₄	—	4	1	no	—
187	C₁₁×C₂²⋊C₄	—	4	1	no	—
188	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
189	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
190	C₄²×C₁₁	—	2	2	no	—
191	C₄²×C₁₁	—	2	2	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	—	4	1	no	—
201	C₄²×C₁₁	—	4	1	no	—
202	C₄²×C₁₁	C₂×D₄	1	2	yes	—
203	C₄²×C₁₁	C₂×D₄	1	2	yes	—
204	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
205	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
206	C₂×#433	C₂×C₁₁	1	1	yes	characteristic
207	C₂×#424	C₂×C₁₁	1	1	yes	characteristic
208	#2298	C₂×C₁₁	1	1	yes	characteristic
209	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
210	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
211	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
212	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
213	#1851	C₂×C₁₁	1	1	yes	characteristic
214	#1851	C₂×C₁₁	1	1	yes	characteristic
215	#1850	C₂×C₁₁	1	1	yes	characteristic
216	#1850	C₂×C₁₁	1	1	yes	characteristic
217	#1843	C₂×C₁₁	1	1	yes	characteristic, complemented
218	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#1832	C₂×C₁₁	1	1	yes	characteristic, complemented
220	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
221	C₂³×C₁₁	—	2	1	no	—
222	C₂³×C₁₁	—	2	1	no	—
223	C₂³×C₁₁	—	2	1	no	—
224	C₂³×C₁₁	—	2	1	no	—
225	C₂³×C₁₁	—	2	1	no	—
226	C₂³×C₁₁	—	2	1	no	—
227	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
228	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
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	2	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	2	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	—	2	1	no	—
263	C₂×C₄×C₁₁	—	2	1	no	—
264	C₂×C₄×C₁₁	—	2	1	no	—
265	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
266	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
267	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
268	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
269	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
270	C₂×C₄×C₁₁	#131	1	2	yes	—
271	C₂×C₄×C₁₁	#131	1	2	yes	—
272	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
274	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₁₁	H(5,𝔽₂)	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	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
287	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
289	#433	—	2	4	no	—
290	#424	—	2	4	no	—
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×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
300	C₂×C₄⋊C₈	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	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
307	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
309	#388	C₄×C₁₁	1	1	yes	characteristic
310	#388	C₄×C₁₁	1	1	yes	characteristic
311	#388	C₄×C₁₁	1	1	yes	characteristic
312	#388	C₄×C₁₁	1	1	yes	characteristic
313	#387	C₄×C₁₁	1	1	yes	characteristic
314	#387	C₄×C₁₁	1	1	yes	characteristic
315	#387	C₄×C₁₁	1	1	yes	characteristic
316	#387	C₄×C₁₁	1	1	yes	characteristic
317	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
321	#376	C₂²×C₁₁	1	1	yes	characteristic
322	C₄³	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	#336	C₂²×C₁₁	1	1	yes	characteristic
330	#336	C₂²×C₁₁	1	1	yes	characteristic
331	C₂²×C₁₁	—	2	2	no	—
332	C₂²×C₁₁	—	2	2	no	—
333	C₂²×C₁₁	—	2	2	no	—
334	C₂²×C₁₁	—	4	1	no	—
335	C₂²×C₁₁	—	4	1	no	—
336	C₂²×C₁₁	—	4	1	no	—
337	C₂²×C₁₁	—	4	1	no	—
338	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
339	C₂²×C₁₁	#520	1	1	yes	characteristic
340	C₂²×C₁₁	#520	1	1	yes	characteristic
341	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
342	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
343	C₂²×C₁₁	#568	1	1	yes	characteristic
344	C₂²×C₁₁	#568	1	1	yes	characteristic
345	C₄×C₁₁	—	2	2	no	—
346	C₄×C₁₁	—	2	2	no	—
347	C₄×C₁₁	—	2	2	no	—
348	C₄×C₁₁	—	2	2	no	—
349	C₄×C₁₁	—	2	2	no	—
350	C₄×C₁₁	—	2	2	no	—
351	C₄×C₁₁	—	2	2	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	—	4	1	no	—
357	C₄×C₁₁	—	4	1	no	—
358	C₄×C₁₁	#535	1	1	yes	characteristic
359	C₄×C₁₁	#536	1	1	yes	characteristic
360	C₄×C₁₁	#544	1	1	yes	characteristic
361	C₄×C₁₁	#544	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	4	1	no	—
365	C₂×M₁₆	—	4	1	no	—
366	C₂²×C₈	—	2	2	no	—
367	C₂²×C₈	—	4	1	no	—
368	C₂²×C₈	—	4	1	no	—
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×C₈	C₂³×C₁₁	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
377	#117	D₄×C₁₁	1	4	yes	—
378	#117	Q₈×C₁₁	1	4	yes	—
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×C₄⋊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×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
391	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
392	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
393	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
394	C₂×C₄²	C₂×C₄×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	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
401	C₄⋊C₈	—	2	2	no	—
402	C₄⋊C₈	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	C₄⋊C₈	—	2	2	no	—
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	4	1	no	—
408	C₄⋊C₈	—	4	1	no	—
409	C₄⋊C₈	—	4	1	no	—
410	C₄⋊C₈	—	4	1	no	—
411	C₄⋊C₈	—	4	1	no	—
412	C₄⋊C₈	—	4	1	no	—
413	C₄⋊C₈	—	4	1	no	—
414	C₄⋊C₈	—	4	1	no	—
415	C₂²⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	#97	—	2	2	no	—
418	C₄×C₈	—	2	2	no	—
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	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
423	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
424	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
425	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
426	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
427	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
428	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
429	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
430	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
431	C₂×C₁₁	—	4	2	no	—
432	C₂×C₁₁	#2317	1	1	yes	characteristic
433	C₂×C₁₁	#2906	1	1	yes	characteristic
434	C₂×C₁₁	#2906	1	1	yes	characteristic
435	C₂×C₁₁	#2992	1	1	yes	characteristic
436	C₂×C₁₁	#2993	1	1	yes	characteristic
437	C₂×C₁₁	#2994	1	1	yes	characteristic
438	C₂×C₁₁	#2995	1	1	yes	characteristic
439	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
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	C₂×D₄×C₁₁	1	2	yes	—
458	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
460	M₁₆	—	4	4	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	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	4	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
491	C₄⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
497	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	4	yes	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	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	—	4	1	no	—
509	C₄²	—	4	1	no	—
510	C₄²	C₂×D₄×C₁₁	1	2	yes	—
511	C₄²	C₂×D₄×C₁₁	1	2	yes	—
512	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
513	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
514	C₁₁	#21980	1	1	yes	characteristic, direct product factor, Sylow
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
522	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
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	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	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	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
560	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
561	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
562	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
563	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
564	C₂×C₄	C₁₁×#131	1	2	yes	—
565	C₂×C₄	C₁₁×#131	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
567	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
568	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₁₁×H(5,𝔽₂)	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	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
588	C₂²	C₁₁×#520	1	1	yes	characteristic
589	C₂²	C₁₁×#520	1	1	yes	characteristic
590	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
591	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
592	C₂²	C₁₁×#568	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	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	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×#535	1	1	yes	characteristic
608	C₄	C₁₁×#536	1	1	yes	characteristic
609	C₄	C₁₁×#544	1	1	yes	characteristic
610	C₄	C₁₁×#544	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	C₁₁×#2317	1	1	yes	characteristic
613	C₂	C₁₁×#2906	1	1	yes	characteristic
614	C₂	C₁₁×#2906	1	1	yes	characteristic
615	C₂	C₁₁×#2992	1	1	yes	characteristic
616	C₂	C₁₁×#2993	1	1	yes	characteristic
617	C₂	C₁₁×#2994	1	1	yes	characteristic
618	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
4. C₁₁×#1940	C₂	semidirect
5. C₁₁×#1940	C₂	semidirect
6. C₁₁×#1939	C₂	semidirect
7. C₁₁×#1939	C₂	semidirect
12. C₁₁×#1843	C₂	semidirect
13. C₁₁×#1842	C₂	semidirect
14. C₁₁×#1832	C₂	semidirect
15. C₁₁×#1831	C₂	semidirect
130. #21980	C₁₁	direct (N × H)
209. #1940	C₂×C₁₁	semidirect
210. #1940	C₂×C₁₁	semidirect
211. #1939	C₂×C₁₁	semidirect
212. #1939	C₂×C₁₁	semidirect
217. #1843	C₂×C₁₁	semidirect
218. #1842	C₂×C₁₁	semidirect
219. #1832	C₂×C₁₁	semidirect
220. #1831	C₂×C₁₁	semidirect
514. C₁₁	#21980	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×#433	2
C₂×C₁₁×#424	2
C₁₁×#2298	2
C₁₁×#1940	2
C₁₁×#1939	2
C₁₁×#1851	2
C₁₁×#1850	2
C₁₁×#1843	2
C₁₁×#1842	2
C₁₁×#1832	2
C₁₁×#1831	2
#21980	11

Subgroups — C11×#21980 #14599173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21980 #14599173