Subgroups — C₁₁×#22509 #14599702

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1985	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1984	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1798	C₂	1	2	yes	maximal
9	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1750	C₂	1	2	yes	maximal
11	C₄×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#533	—	2	4	no	—
13	C₁₁×#533	—	2	4	no	—
14	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₁₁×#125	C₄	1	2	yes	—
17	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₁₁×C₂²⋊Q₈	C₄	1	2	yes	—
20	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
25	C₁₁×#446	—	2	4	no	—
26	C₈×Q₈×C₁₁	—	2	4	no	—
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
31	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#97	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
38	C₁₁×#336	C₂²	1	1	yes	characteristic
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	C₁₁×#336	C₂²	1	2	yes	—
44	C₁₁×#336	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×C₄⋊Q₈	—	2	4	no	—
58	C₁₁×C₄⋊Q₈	—	2	4	no	—
59	C₁₁×#125	—	2	8	no	—
60	C₁₁×C₂²⋊Q₈	—	2	4	no	—
61	C₁₁×C₂²⋊Q₈	—	2	4	no	—
62	C₁₁×C₂²⋊Q₈	—	2	8	no	—
63	C₄×Q₈×C₁₁	—	2	4	no	—
64	C₄×Q₈×C₁₁	—	2	4	no	—
65	C₄×Q₈×C₁₁	—	2	2	no	—
66	C₄×Q₈×C₁₁	—	2	2	no	—
67	C₄×Q₈×C₁₁	D₄	1	4	yes	—
68	C₄×Q₈×C₁₁	D₄	1	4	yes	—
69	C₁₁×#117	—	2	4	no	—
70	C₁₁×#117	—	2	4	no	—
71	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₁₁	—	2	2	no	—
83	C₂×C₄²×C₁₁	—	2	2	no	—
84	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
90	C₁₁×C₄⋊C₈	—	2	2	no	—
91	C₁₁×C₄⋊C₈	—	2	4	no	—
92	C₁₁×C₄⋊C₈	—	2	2	no	—
93	C₁₁×C₄⋊C₈	—	2	4	no	—
94	C₁₁×C₂²⋊C₈	—	2	2	no	—
95	C₁₁×C₂²⋊C₈	—	2	4	no	—
96	C₁₁×C₂²⋊C₈	Q₈	1	4	yes	complemented
97	C₁₁×#97	—	2	4	no	—
98	C₄×C₈×C₁₁	—	2	2	no	—
99	C₄×C₈×C₁₁	—	2	4	no	—
100	C₄×C₈×C₁₁	—	2	2	no	—
101	#22509	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₁	—	2	4	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	2	2	no	—
107	C₂×Q₈×C₁₁	—	2	4	no	—
108	C₂×Q₈×C₁₁	—	2	2	no	—
109	C₂×Q₈×C₁₁	—	2	2	no	—
110	C₂×Q₈×C₁₁	—	4	2	no	—
111	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	2	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	4	1	no	—
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₁	#41	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₁	—	2	1	no	—
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	1	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	1	no	—
146	C₂×C₈×C₁₁	—	2	1	no	—
147	C₂×C₈×C₁₁	—	2	2	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	2	no	—
150	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
151	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
152	C₁₁×C₄⋊C₄	—	2	4	no	—
153	C₁₁×C₄⋊C₄	—	2	4	no	—
154	C₁₁×C₄⋊C₄	—	2	4	no	—
155	C₁₁×C₄⋊C₄	—	2	4	no	—
156	C₁₁×C₄⋊C₄	—	2	4	no	—
157	C₁₁×C₄⋊C₄	—	2	4	no	—
158	C₁₁×C₄⋊C₄	—	2	2	no	—
159	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
160	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
161	C₁₁×C₂²⋊C₄	—	2	4	no	—
162	C₁₁×C₂²⋊C₄	—	2	4	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	—	2	2	no	—
168	C₄²×C₁₁	—	2	2	no	—
169	C₄²×C₁₁	C₂×D₄	1	2	yes	—
170	C₄²×C₁₁	C₂×D₄	1	2	yes	—
171	C₄²×C₁₁	C₂×D₄	1	4	yes	—
172	C₄²×C₁₁	C₂×D₄	1	4	yes	—
173	C₂×#533	C₂×C₁₁	1	1	yes	characteristic
174	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₂×C₈×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#1985	C₂×C₁₁	1	2	yes	complemented
177	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
178	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
179	#1984	C₂×C₁₁	1	2	yes	complemented
180	#1798	C₂×C₁₁	1	2	yes	—
181	#1797	C₂×C₁₁	1	1	yes	characteristic
182	#1750	C₂×C₁₁	1	2	yes	—
183	C₄×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic
184	C₂³×C₁₁	—	2	1	no	—
185	C₂³×C₁₁	—	2	1	no	—
186	C₂³×C₁₁	—	2	1	no	—
187	C₂³×C₁₁	—	2	1	no	—
188	C₂³×C₁₁	—	2	1	no	—
189	C₂³×C₁₁	—	2	1	no	—
190	C₂³×C₁₁	C₄×Q₈	1	2	yes	—
191	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
192	Q₈×C₁₁	—	2	8	no	—
193	Q₈×C₁₁	—	4	8	no	—
194	Q₈×C₁₁	—	4	4	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	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	1	no	—
204	C₂×C₄×C₁₁	—	2	2	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	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	—	2	1	no	—
213	C₂×C₄×C₁₁	—	2	1	no	—
214	C₂×C₄×C₁₁	—	2	2	no	—
215	C₂×C₄×C₁₁	—	2	2	no	—
216	C₂×C₄×C₁₁	—	2	2	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	4	4	no	—
219	C₂×C₄×C₁₁	—	4	4	no	—
220	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
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	C₄×Q₈	1	2	yes	—
225	C₂×C₄×C₁₁	#131	1	2	yes	—
226	C₂×C₄×C₁₁	#131	1	2	yes	—
227	C₂×C₄×C₁₁	#131	1	2	yes	—
228	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈×C₁₁	—	2	2	no	—
235	C₈×C₁₁	—	2	2	no	—
236	C₈×C₁₁	—	4	1	no	—
237	C₈×C₁₁	—	4	2	no	—
238	C₈×C₁₁	—	4	1	no	—
239	C₈×C₁₁	—	4	2	no	—
240	#533	—	2	4	no	—
241	#533	—	2	4	no	—
242	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
244	C₂×#125	C₄×C₁₁	1	2	yes	—
245	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₄×C₁₁	1	2	yes	—
248	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₁	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
253	#446	—	2	4	no	—
254	C₈×Q₈	—	2	4	no	—
255	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×#97	C₂²×C₁₁	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
266	#336	C₂²×C₁₁	1	2	yes	—
267	#336	C₂²×C₁₁	1	2	yes	—
268	#336	C₂²×C₁₁	1	2	yes	—
269	#336	C₂²×C₁₁	1	1	yes	characteristic
270	#336	C₂²×C₁₁	1	2	yes	—
271	#336	C₂²×C₁₁	1	2	yes	—
272	#336	C₂²×C₁₁	1	1	yes	characteristic
273	C₂²×C₁₁	—	2	2	no	—
274	C₂²×C₁₁	—	2	2	no	—
275	C₂²×C₁₁	—	2	2	no	—
276	C₂²×C₁₁	—	4	1	no	—
277	C₂²×C₁₁	—	4	1	no	—
278	C₂²×C₁₁	—	4	1	no	—
279	C₂²×C₁₁	—	4	1	no	—
280	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
282	C₂²×C₁₁	#519	1	1	yes	characteristic
283	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
284	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
285	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
286	C₂²×C₁₁	#568	1	1	yes	characteristic
287	C₄×C₁₁	—	2	2	no	—
288	C₄×C₁₁	—	2	4	no	—
289	C₄×C₁₁	—	2	2	no	—
290	C₄×C₁₁	—	2	2	no	—
291	C₄×C₁₁	—	2	4	no	—
292	C₄×C₁₁	—	4	1	no	—
293	C₄×C₁₁	—	4	2	no	—
294	C₄×C₁₁	—	4	2	no	—
295	C₄×C₁₁	#408	1	4	yes	—
296	C₄×C₁₁	#548	1	1	yes	characteristic
297	C₄×C₁₁	#548	1	1	yes	characteristic
298	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
299	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
300	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
302	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
307	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	4	no	—
314	#125	—	2	8	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	4	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	D₄×C₁₁	1	4	yes	—
323	C₄×Q₈	D₄×C₁₁	1	4	yes	—
324	#117	—	2	4	no	—
325	#117	—	2	4	no	—
326	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
330	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
333	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
334	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
342	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
344	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	—	2	4	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	4	no	—
349	C₂²⋊C₈	—	2	4	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	Q₈×C₁₁	1	4	yes	complemented
352	#97	—	2	4	no	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	2	4	no	—
355	C₄×C₈	—	2	2	no	—
356	C₂×C₁₁	—	4	2	no	—
357	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×C₁₁	C₂×#408	1	1	yes	characteristic
359	C₂×C₁₁	#2880	1	1	yes	characteristic
360	C₂×C₁₁	#2960	1	1	yes	characteristic
361	C₂×C₁₁	#2962	1	1	yes	characteristic
362	C₂×C₁₁	#2985	1	1	yes	characteristic
363	C₂×C₁₁	#2986	1	1	yes	characteristic
364	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
394	C₂²×C₄	C₁₁×#41	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
413	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	8	yes	—
422	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	C₂×D₄×C₁₁	1	2	yes	—
432	C₄²	C₂×D₄×C₁₁	1	2	yes	—
433	C₄²	C₂×D₄×C₁₁	1	4	yes	—
434	C₄²	C₂×D₄×C₁₁	1	4	yes	—
435	C₁₁	#22509	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	C₄×Q₈×C₁₁	1	2	yes	—
443	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
444	Q₈	—	2	8	no	—
445	Q₈	—	4	8	no	—
446	Q₈	—	4	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
473	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
474	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
475	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
476	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
477	C₂×C₄	C₁₁×#131	1	2	yes	—
478	C₂×C₄	C₁₁×#131	1	2	yes	—
479	C₂×C₄	C₁₁×#131	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
482	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
484	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	1	no	—
491	C₈	—	4	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
500	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
501	C₂²	C₁₁×#519	1	1	yes	characteristic
502	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
503	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
504	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
505	C₂²	C₁₁×#568	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	C₁₁×#408	1	4	yes	—
515	C₄	C₁₁×#548	1	1	yes	characteristic
516	C₄	C₁₁×#548	1	1	yes	characteristic
517	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
518	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
521	C₂	C₂×C₁₁×#408	1	1	yes	characteristic
522	C₂	C₁₁×#2880	1	1	yes	characteristic
523	C₂	C₁₁×#2960	1	1	yes	characteristic
524	C₂	C₁₁×#2962	1	1	yes	characteristic
525	C₂	C₁₁×#2985	1	1	yes	characteristic
526	C₂	C₁₁×#2986	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. C₂×C₁₁×#446	C₂	semidirect
3. C₂×C₈×Q₈×C₁₁	C₂	semidirect
4. C₁₁×#1985	C₂	semidirect
5. C₁₁×#1984	C₂	semidirect
6. C₁₁×#1984	C₂	semidirect
7. C₁₁×#1984	C₂	semidirect
96. C₁₁×C₂²⋊C₈	Q₈	semidirect
101. #22509	C₁₁	direct (N × H)
174. C₂×#446	C₂×C₁₁	semidirect
175. C₂×C₈×Q₈	C₂×C₁₁	semidirect
176. #1985	C₂×C₁₁	semidirect
177. #1984	C₂×C₁₁	semidirect
178. #1984	C₂×C₁₁	semidirect
179. #1984	C₂×C₁₁	semidirect
351. C₂²⋊C₈	Q₈×C₁₁	semidirect
435. C₁₁	#22509	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×#533	2
C₂×C₁₁×#446	2
C₂×C₈×Q₈×C₁₁	2
C₁₁×#1985	2
C₁₁×#1984	2
C₁₁×#1798	2
C₁₁×#1797	2
C₁₁×#1750	2
C₄×C₁₁×C₂²⋊C₈	2
#22509	11

Subgroups — C11×#22509 #14599702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22509 #14599702