Subgroups — C₁₁×#34141 #14611334

Order 2816.

3298 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×#41	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2367	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2366	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2365	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2364	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2361	C₂	1	4	yes	maximal, complemented
8	C₁₁×#2297	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2293	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2290	C₂	1	4	yes	maximal, complemented
11	C₄²×D₄×C₁₁	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₁×#41	C₂²	1	2	yes	—
15	C₁₁×#532	C₄	1	16	yes	complemented
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#124	C₂²	1	2	yes	—
19	C₂×C₁₁×#121	C₂²	1	2	yes	—
20	C₂×C₁₁×#121	C₂²	1	2	yes	—
21	C₄×C₁₁×#41	—	2	16	no	—
22	C₂×C₄×Q₈×C₁₁	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	—
24	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
28	C₂×C₁₁×#117	C₂²	1	4	yes	—
29	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₁	C₂²	1	4	yes	—
34	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#391	C₂²	1	4	yes	—
36	C₁₁×#390	C₂²	1	4	yes	—
37	C₁₁×#390	C₂²	1	4	yes	—
38	C₁₁×#389	C₂²	1	4	yes	—
39	C₁₁×#388	C₂²	1	8	yes	—
40	C₁₁×#388	C₂²	1	8	yes	—
41	C₁₁×#387	C₂²	1	8	yes	—
42	C₁₁×#386	C₂²	1	8	yes	—
43	C₁₁×#386	C₂²	1	8	yes	—
44	C₁₁×#385	C₂²	1	8	yes	—
45	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
52	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
53	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
54	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	—
57	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
58	C₁₁×#376	C₂²	1	2	yes	—
59	C₂×C₁₁×#95	C₂²	1	2	yes	—
60	C₄³×C₁₁	C₂²	1	2	yes	—
61	C₂×C₁₁×#41	—	2	8	no	—
62	C₂×C₁₁×#41	—	2	8	no	—
63	C₂×C₁₁×#41	C₂×C₄	1	16	yes	complemented
64	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
71	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
76	C₁₁×#127	C₂×C₄	1	8	yes	complemented
77	C₁₁×#124	C₂×C₄	1	16	yes	complemented
78	C₁₁×#121	C₂×C₄	1	16	yes	complemented
79	C₁₁×#121	C₂×C₄	1	16	yes	complemented
80	C₄×Q₈×C₁₁	—	2	16	no	—
81	C₄×D₄×C₁₁	—	2	16	no	—
82	C₄×D₄×C₁₁	—	2	16	no	—
83	C₄×D₄×C₁₁	—	2	32	no	—
84	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	complemented
85	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	complemented
86	C₁₁×#117	—	2	4	no	—
87	C₁₁×#117	—	2	16	no	—
88	C₁₁×#117	D₄	1	8	yes	complemented
89	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
90	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₁	—	2	8	no	—
106	C₂×C₄²×C₁₁	—	2	16	no	—
107	C₂×C₄²×C₁₁	C₂×C₄	1	8	yes	complemented
108	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
109	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₁₁×#95	C₂³	1	2	yes	—
121	C₁₁×#95	C₂³	1	4	yes	—
122	C₁₁×#95	C₂³	1	2	yes	—
123	C₁₁×#95	C₂³	1	4	yes	—
124	C₁₁×#95	C₂³	1	4	yes	—
125	C₁₁×#95	C₂³	1	8	yes	—
126	C₁₁×#95	C₂³	1	8	yes	—
127	#34141	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
129	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₁₁×#41	—	2	64	no	—
131	C₂×Q₈×C₁₁	—	2	4	no	—
132	C₂×Q₈×C₁₁	—	2	4	no	—
133	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
134	C₂×D₄×C₁₁	—	2	8	no	—
135	C₂×D₄×C₁₁	—	2	8	no	—
136	C₂×D₄×C₁₁	—	2	4	no	—
137	C₂×D₄×C₁₁	—	2	8	no	—
138	C₂×D₄×C₁₁	—	2	4	no	—
139	C₂×D₄×C₁₁	—	4	4	no	—
140	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
141	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
142	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
143	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
144	C₂²×C₄×C₁₁	—	2	8	no	—
145	C₂²×C₄×C₁₁	—	2	4	no	—
146	C₂²×C₄×C₁₁	—	2	8	no	—
147	C₂²×C₄×C₁₁	—	2	8	no	—
148	C₂²×C₄×C₁₁	—	2	16	no	—
149	C₂²×C₄×C₁₁	—	2	8	no	—
150	C₂²×C₄×C₁₁	—	2	16	no	—
151	C₂²×C₄×C₁₁	—	4	2	no	—
152	C₂²×C₄×C₁₁	—	4	8	no	—
153	C₂²×C₄×C₁₁	—	4	4	no	—
154	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₁₁	C₂²×C₄	1	16	yes	—
156	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₁	#41	1	4	yes	—
160	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
171	C₁₁×C₄⋊C₄	—	2	16	no	—
172	C₁₁×C₄⋊C₄	—	2	8	no	—
173	C₁₁×C₄⋊C₄	—	2	4	no	—
174	C₁₁×C₄⋊C₄	—	2	4	no	—
175	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
176	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
177	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
178	C₁₁×C₄⋊C₄	#41	1	8	yes	complemented
179	C₁₁×C₂²⋊C₄	—	2	4	no	—
180	C₁₁×C₂²⋊C₄	—	2	16	no	—
181	C₁₁×C₂²⋊C₄	—	2	16	no	—
182	C₁₁×C₂²⋊C₄	—	4	8	no	—
183	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
184	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
185	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
186	C₄²×C₁₁	—	2	4	no	—
187	C₄²×C₁₁	—	2	4	no	—
188	C₄²×C₁₁	—	2	16	no	—
189	C₄²×C₁₁	—	2	8	no	—
190	C₄²×C₁₁	—	2	4	no	—
191	C₄²×C₁₁	—	2	8	no	—
192	C₄²×C₁₁	—	4	4	no	—
193	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
194	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
195	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
196	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
197	C₄²×C₁₁	C₂×D₄	1	8	yes	—
198	C₂×#532	C₂×C₁₁	1	1	yes	characteristic
199	C₂×C₄×#41	C₂×C₁₁	1	2	yes	complemented
200	#2367	C₂×C₁₁	1	4	yes	complemented
201	#2366	C₂×C₁₁	1	2	yes	complemented
202	#2365	C₂×C₁₁	1	2	yes	complemented
203	#2364	C₂×C₁₁	1	4	yes	complemented
204	#2361	C₂×C₁₁	1	4	yes	complemented
205	#2297	C₂×C₁₁	1	2	yes	complemented
206	#2293	C₂×C₁₁	1	2	yes	complemented
207	#2290	C₂×C₁₁	1	4	yes	complemented
208	C₄²×D₄	C₂×C₁₁	1	2	yes	complemented
209	C₄×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
210	C₂×C₄×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
211	C₂³×C₁₁	—	2	2	no	—
212	C₂³×C₁₁	—	2	2	no	—
213	C₂³×C₁₁	—	2	4	no	—
214	C₂³×C₁₁	—	2	8	no	—
215	C₂³×C₁₁	—	2	4	no	—
216	C₂³×C₁₁	—	2	8	no	—
217	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
218	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
219	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₁	C₂×#41	1	2	yes	—
221	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
222	Q₈×C₁₁	—	2	16	no	—
223	D₄×C₁₁	—	2	32	no	—
224	D₄×C₁₁	—	2	16	no	—
225	D₄×C₁₁	—	2	16	no	—
226	D₄×C₁₁	—	4	8	no	—
227	C₂×C₄×C₁₁	—	2	4	no	—
228	C₂×C₄×C₁₁	—	2	4	no	—
229	C₂×C₄×C₁₁	—	2	4	no	—
230	C₂×C₄×C₁₁	—	2	2	no	—
231	C₂×C₄×C₁₁	—	2	4	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	4	no	—
234	C₂×C₄×C₁₁	—	2	4	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	32	no	—
237	C₂×C₄×C₁₁	—	2	8	no	—
238	C₂×C₄×C₁₁	—	2	4	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	4	no	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	4	no	—
243	C₂×C₄×C₁₁	—	2	4	no	—
244	C₂×C₄×C₁₁	—	4	4	no	—
245	C₂×C₄×C₁₁	—	4	32	no	—
246	C₂×C₄×C₁₁	—	4	16	no	—
247	C₂×C₄×C₁₁	C₄×D₄	1	16	yes	complemented
248	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
249	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
250	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
252	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
253	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
254	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
255	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
256	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
259	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
262	C₂²×#41	C₂²×C₁₁	1	2	yes	—
263	#532	C₄×C₁₁	1	16	yes	complemented
264	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
266	C₂×#124	C₂²×C₁₁	1	2	yes	—
267	C₂×#121	C₂²×C₁₁	1	2	yes	—
268	C₂×#121	C₂²×C₁₁	1	2	yes	—
269	C₄×#41	—	2	16	no	—
270	C₂×C₄×Q₈	C₂²×C₁₁	1	4	yes	—
271	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	—
272	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
273	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
274	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
275	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
276	C₂×#117	C₂²×C₁₁	1	4	yes	—
277	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
280	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
281	C₂²×C₄²	C₂²×C₁₁	1	4	yes	—
282	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
283	#391	C₂²×C₁₁	1	4	yes	—
284	#390	C₂²×C₁₁	1	4	yes	—
285	#390	C₂²×C₁₁	1	4	yes	—
286	#389	C₂²×C₁₁	1	4	yes	—
287	#388	C₂²×C₁₁	1	8	yes	—
288	#388	C₂²×C₁₁	1	8	yes	—
289	#387	C₂²×C₁₁	1	8	yes	—
290	#386	C₂²×C₁₁	1	8	yes	—
291	#386	C₂²×C₁₁	1	8	yes	—
292	#385	C₂²×C₁₁	1	8	yes	—
293	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
294	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
306	#376	C₂²×C₁₁	1	2	yes	—
307	C₂×#95	C₂²×C₁₁	1	2	yes	—
308	C₄³	C₂²×C₁₁	1	2	yes	—
309	C₂²×C₁₁	—	2	2	no	—
310	C₂²×C₁₁	—	2	2	no	—
311	C₂²×C₁₁	—	2	4	no	—
312	C₂²×C₁₁	—	2	4	no	—
313	C₂²×C₁₁	—	2	8	no	—
314	C₂²×C₁₁	—	2	8	no	—
315	C₂²×C₁₁	—	2	8	no	—
316	C₂²×C₁₁	—	4	8	no	—
317	C₂²×C₁₁	—	4	8	no	—
318	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
319	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
320	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
322	C₂²×C₁₁	C₂²×#41	1	2	yes	—
323	C₂²×C₁₁	#585	1	2	yes	—
324	C₄×C₁₁	—	2	8	no	—
325	C₄×C₁₁	—	2	2	no	—
326	C₄×C₁₁	—	2	2	no	—
327	C₄×C₁₁	—	2	2	no	—
328	C₄×C₁₁	—	2	8	no	—
329	C₄×C₁₁	—	2	8	no	—
330	C₄×C₁₁	—	4	4	no	—
331	C₄×C₁₁	—	4	4	no	—
332	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
333	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
334	C₄×C₁₁	C₄×#41	1	4	yes	complemented
335	C₂×#41	—	2	8	no	—
336	C₂×#41	—	2	8	no	—
337	C₂×#41	C₂×C₄×C₁₁	1	16	yes	complemented
338	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
339	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
343	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
344	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
345	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
347	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
349	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	complemented
350	#127	C₂×C₄×C₁₁	1	8	yes	complemented
351	#124	C₂×C₄×C₁₁	1	16	yes	complemented
352	#121	C₂×C₄×C₁₁	1	16	yes	complemented
353	#121	C₂×C₄×C₁₁	1	16	yes	complemented
354	C₄×Q₈	—	2	16	no	—
355	C₄×D₄	—	2	16	no	—
356	C₄×D₄	—	2	16	no	—
357	C₄×D₄	—	2	32	no	—
358	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	complemented
359	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	complemented
360	#117	—	2	4	no	—
361	#117	—	2	16	no	—
362	#117	D₄×C₁₁	1	8	yes	complemented
363	C₂×C₄⋊C₄	—	2	8	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
379	C₂×C₄²	—	2	8	no	—
380	C₂×C₄²	—	2	16	no	—
381	C₂×C₄²	C₂×C₄×C₁₁	1	8	yes	complemented
382	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
385	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
386	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
387	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
389	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
394	#95	C₂³×C₁₁	1	2	yes	—
395	#95	C₂³×C₁₁	1	4	yes	—
396	#95	C₂³×C₁₁	1	2	yes	—
397	#95	C₂³×C₁₁	1	4	yes	—
398	#95	C₂³×C₁₁	1	4	yes	—
399	#95	C₂³×C₁₁	1	8	yes	—
400	#95	C₂³×C₁₁	1	8	yes	—
401	C₂×C₁₁	—	2	4	no	—
402	C₂×C₁₁	—	4	8	no	—
403	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
404	C₂×C₁₁	C₂×C₄×#41	1	1	yes	characteristic
405	C₂×C₁₁	#3428	1	1	yes	characteristic
406	C₂×C₁₁	D₄×#41	1	2	yes	—
407	C₂×C₁₁	#3480	1	2	yes	—
408	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
409	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
410	#41	—	2	64	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
421	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
422	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
423	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	2	16	no	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	8	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
435	C₂²×C₄	C₂²×C₄×C₁₁	1	16	yes	—
436	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
437	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
438	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
439	C₂²×C₄	C₁₁×#41	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
451	C₄⋊C₄	—	2	16	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
456	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
457	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
458	C₄⋊C₄	C₁₁×#41	1	8	yes	complemented
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	2	16	no	—
462	C₂²⋊C₄	—	4	8	no	—
463	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
464	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
465	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	16	no	—
469	C₄²	—	2	8	no	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	8	no	—
472	C₄²	—	4	4	no	—
473	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
474	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
475	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
476	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
477	C₄²	C₂×D₄×C₁₁	1	8	yes	—
478	C₁₁	#34141	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	8	no	—
485	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
486	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
487	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
488	C₂³	C₂×C₁₁×#41	1	2	yes	—
489	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	D₄	—	2	32	no	—
492	D₄	—	2	16	no	—
493	D₄	—	2	16	no	—
494	D₄	—	4	8	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	32	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	32	no	—
514	C₂×C₄	—	4	16	no	—
515	C₂×C₄	C₄×D₄×C₁₁	1	16	yes	complemented
516	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
517	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
518	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
519	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
520	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
521	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
522	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
524	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
526	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
527	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
528	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
529	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	8	no	—
538	C₂²	—	4	8	no	—
539	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
540	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
541	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
542	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
543	C₂²	C₂²×C₁₁×#41	1	2	yes	—
544	C₂²	C₁₁×#585	1	2	yes	—
545	C₄	—	2	8	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	8	no	—
550	C₄	—	2	8	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
554	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
555	C₄	C₄×C₁₁×#41	1	4	yes	complemented
556	C₂	—	2	4	no	—
557	C₂	—	4	8	no	—
558	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
559	C₂	C₂×C₄×C₁₁×#41	1	1	yes	characteristic
560	C₂	C₁₁×#3428	1	1	yes	characteristic
561	C₂	D₄×C₁₁×#41	1	2	yes	—
562	C₂	C₁₁×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂⁵
prime radical	C₂×C₁₁×#532	C₂
LCS	G ▷ C₂² ▷ 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×C₄×C₁₁×#41	C₂	semidirect
3. C₁₁×#2367	C₂	semidirect
4. C₁₁×#2366	C₂	semidirect
5. C₁₁×#2365	C₂	semidirect
6. C₁₁×#2364	C₂	semidirect
7. C₁₁×#2361	C₂	semidirect
8. C₁₁×#2297	C₂	semidirect
9. C₁₁×#2293	C₂	semidirect
10. C₁₁×#2290	C₂	semidirect
11. C₄²×D₄×C₁₁	C₂	semidirect
12. C₄×C₁₁×#117	C₂	semidirect
13. C₂×C₄×C₁₁×C₄⋊C₄	C₂	semidirect
15. C₁₁×#532	C₄	semidirect
63. C₂×C₁₁×#41	C₂×C₄	semidirect
75. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
76. C₁₁×#127	C₂×C₄	semidirect
77. C₁₁×#124	C₂×C₄	semidirect
78. C₁₁×#121	C₂×C₄	semidirect
79. C₁₁×#121	C₂×C₄	semidirect
84. C₄×D₄×C₁₁	C₂×C₄	semidirect
85. C₄×D₄×C₁₁	C₂×C₄	semidirect
88. C₁₁×#117	D₄	semidirect
107. C₂×C₄²×C₁₁	C₂×C₄	semidirect
127. #34141	C₁₁	direct (N × H)
178. C₁₁×C₄⋊C₄	#41	semidirect
199. C₂×C₄×#41	C₂×C₁₁	semidirect
200. #2367	C₂×C₁₁	semidirect
201. #2366	C₂×C₁₁	semidirect
202. #2365	C₂×C₁₁	semidirect
203. #2364	C₂×C₁₁	semidirect
204. #2361	C₂×C₁₁	semidirect
205. #2297	C₂×C₁₁	semidirect
206. #2293	C₂×C₁₁	semidirect
207. #2290	C₂×C₁₁	semidirect
208. C₄²×D₄	C₂×C₁₁	semidirect
209. C₄×#117	C₂×C₁₁	semidirect
210. C₂×C₄×C₄⋊C₄	C₂×C₁₁	semidirect
247. C₂×C₄×C₁₁	C₄×D₄	semidirect
263. #532	C₄×C₁₁	semidirect
334. C₄×C₁₁	C₄×#41	semidirect
337. C₂×#41	C₂×C₄×C₁₁	semidirect
349. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
350. #127	C₂×C₄×C₁₁	semidirect
351. #124	C₂×C₄×C₁₁	semidirect
352. #121	C₂×C₄×C₁₁	semidirect
353. #121	C₂×C₄×C₁₁	semidirect
358. C₄×D₄	C₂×C₄×C₁₁	semidirect
359. C₄×D₄	C₂×C₄×C₁₁	semidirect
362. #117	D₄×C₁₁	semidirect
381. C₂×C₄²	C₂×C₄×C₁₁	semidirect
458. C₄⋊C₄	C₁₁×#41	semidirect
478. C₁₁	#34141	direct (N × H)
515. C₂×C₄	C₄×D₄×C₁₁	semidirect
555. C₄	C₄×C₁₁×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#532	2
C₂×C₄×C₁₁×#41	2
C₁₁×#2367	2
C₁₁×#2366	2
C₁₁×#2365	2
C₁₁×#2364	2
C₁₁×#2361	2
C₁₁×#2297	2
C₁₁×#2293	2
C₁₁×#2290	2
C₄²×D₄×C₁₁	2
C₄×C₁₁×#117	2
C₂×C₄×C₁₁×C₄⋊C₄	2
#34141	11

Subgroups — C11×#34141 #14611334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34141 #14611334