Subgroups — C₁₁×#34965 #14612158

Order 2816.

3114 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2603	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2566	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2544	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2504	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2435	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2433	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#2411	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₁×#127	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₁×#124	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₁×#120	C₂	1	4	yes	maximal, complemented
15	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
18	C₂×C₁₁×#127	C₂²	1	2	yes	—
19	C₁₁×#529	—	2	8	no	—
20	C₂×C₁₁×#126	C₂²	1	2	yes	complemented
21	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₁×#124	C₂²	1	2	yes	—
23	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₁×#123	C₂²	1	2	yes	—
25	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#120	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₁	—	2	8	no	—
30	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	complemented
37	C₂×C₁₁×#117	C₂²	1	2	yes	—
38	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
39	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
42	C₁₁×#398	C₂²	1	4	yes	complemented
43	C₁₁×#397	C₂²	1	4	yes	complemented
44	C₁₁×#396	C₂²	1	8	yes	complemented
45	C₁₁×#394	C₂²	1	4	yes	—
46	C₁₁×#394	C₂²	1	8	yes	complemented
47	C₁₁×#392	C₂²	1	4	yes	—
48	C₁₁×#391	C₂²	1	2	yes	complemented
49	C₁₁×#390	C₂²	1	2	yes	—
50	C₁₁×#390	C₂²	1	2	yes	—
51	C₁₁×#390	C₂²	1	8	yes	complemented
52	C₁₁×#390	C₂²	1	2	yes	complemented
53	C₁₁×#388	C₂²	1	8	yes	complemented
54	C₁₁×#386	C₂²	1	4	yes	—
55	C₁₁×#386	C₂²	1	8	yes	complemented
56	C₁₁×#385	C₂²	1	4	yes	—
57	C₁₁×#385	C₂²	1	8	yes	complemented
58	C₁₁×#384	C₂²	1	2	yes	complemented
59	C₁₁×#382	C₂²	1	2	yes	complemented
60	C₁₁×#379	C₂²	1	4	yes	—
61	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
62	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	complemented
67	C₁₁×#376	C₂²	1	2	yes	complemented
68	C₄³×C₁₁	C₂²	1	2	yes	complemented
69	C₂⁵×C₁₁	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₁	—	2	8	no	—
72	C₂²×D₄×C₁₁	—	2	4	no	—
73	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
77	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₁	—	2	8	no	—
79	C₂³×C₄×C₁₁	—	4	8	no	—
80	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
87	C₁₁×#127	—	2	8	no	—
88	C₁₁×#126	—	2	8	no	—
89	C₁₁×#125	—	2	4	no	—
90	C₁₁×#124	—	2	8	no	—
91	C₁₁×#124	—	2	4	no	—
92	C₁₁×#123	—	2	8	no	—
93	C₁₁×C₂²⋊Q₈	—	2	4	no	—
94	C₁₁×#121	—	2	4	no	—
95	C₁₁×#120	—	2	16	no	—
96	C₄×Q₈×C₁₁	—	2	4	no	—
97	C₄×D₄×C₁₁	—	2	8	no	—
98	C₄×D₄×C₁₁	—	2	8	no	—
99	C₄×D₄×C₁₁	—	2	8	no	—
100	C₄×D₄×C₁₁	—	2	8	no	—
101	C₄×D₄×C₁₁	—	2	8	no	—
102	C₄×D₄×C₁₁	—	2	4	no	—
103	C₄×D₄×C₁₁	—	4	16	no	—
104	C₁₁×#117	—	2	8	no	—
105	C₁₁×#117	—	2	8	no	—
106	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
117	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
118	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
124	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
125	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
129	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
130	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₁	D₄	1	8	yes	complemented
132	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
141	C₁₁×#95	C₂³	1	4	yes	—
142	C₁₁×#95	C₂³	1	2	yes	—
143	C₁₁×#95	C₂³	1	2	yes	—
144	C₁₁×#95	C₂³	1	8	yes	—
145	C₁₁×#95	C₂³	1	8	yes	—
146	#34965	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂⁴×C₁₁	—	2	4	no	—
148	C₂⁴×C₁₁	—	2	8	no	—
149	C₂⁴×C₁₁	—	2	8	no	—
150	C₂⁴×C₁₁	—	4	4	no	—
151	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
152	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
153	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₁₁	—	2	2	no	—
155	C₂×Q₈×C₁₁	—	2	4	no	—
156	C₂×D₄×C₁₁	—	2	32	no	—
157	C₂×D₄×C₁₁	—	2	8	no	—
158	C₂×D₄×C₁₁	—	2	4	no	—
159	C₂×D₄×C₁₁	—	2	8	no	—
160	C₂×D₄×C₁₁	—	2	16	no	—
161	C₂×D₄×C₁₁	—	2	4	no	—
162	C₂×D₄×C₁₁	—	2	4	no	—
163	C₂×D₄×C₁₁	—	2	2	no	—
164	C₂×D₄×C₁₁	—	2	4	no	—
165	C₂×D₄×C₁₁	—	2	16	no	—
166	C₂×D₄×C₁₁	—	2	4	no	—
167	C₂×D₄×C₁₁	—	4	8	no	—
168	C₂×D₄×C₁₁	#41	1	8	yes	—
169	C₂²×C₄×C₁₁	—	2	4	no	—
170	C₂²×C₄×C₁₁	—	2	4	no	—
171	C₂²×C₄×C₁₁	—	2	4	no	—
172	C₂²×C₄×C₁₁	—	2	4	no	—
173	C₂²×C₄×C₁₁	—	2	4	no	—
174	C₂²×C₄×C₁₁	—	2	8	no	—
175	C₂²×C₄×C₁₁	—	2	8	no	—
176	C₂²×C₄×C₁₁	—	2	8	no	—
177	C₂²×C₄×C₁₁	—	2	16	no	—
178	C₂²×C₄×C₁₁	—	4	8	no	—
179	C₂²×C₄×C₁₁	—	4	4	no	—
180	C₂²×C₄×C₁₁	—	4	32	no	—
181	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
196	C₁₁×C₄⋊C₄	—	2	4	no	—
197	C₁₁×C₄⋊C₄	—	2	4	no	—
198	C₁₁×C₄⋊C₄	—	2	4	no	—
199	C₁₁×C₄⋊C₄	—	2	4	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	4	no	—
202	C₁₁×C₄⋊C₄	—	2	2	no	—
203	C₁₁×C₄⋊C₄	—	2	4	no	—
204	C₁₁×C₄⋊C₄	—	2	8	no	—
205	C₁₁×C₄⋊C₄	—	4	8	no	—
206	C₁₁×C₂²⋊C₄	—	2	4	no	—
207	C₁₁×C₂²⋊C₄	—	2	4	no	—
208	C₁₁×C₂²⋊C₄	—	2	16	no	—
209	C₁₁×C₂²⋊C₄	—	2	8	no	—
210	C₁₁×C₂²⋊C₄	—	2	8	no	—
211	C₁₁×C₂²⋊C₄	—	2	4	no	—
212	C₁₁×C₂²⋊C₄	—	2	4	no	—
213	C₁₁×C₂²⋊C₄	—	2	4	no	—
214	C₁₁×C₂²⋊C₄	—	2	4	no	—
215	C₁₁×C₂²⋊C₄	—	2	16	no	—
216	C₁₁×C₂²⋊C₄	—	4	8	no	—
217	C₁₁×C₂²⋊C₄	—	4	8	no	—
218	C₁₁×C₂²⋊C₄	#41	1	8	yes	—
219	C₄²×C₁₁	—	2	4	no	—
220	C₄²×C₁₁	—	2	8	no	—
221	C₄²×C₁₁	—	2	4	no	—
222	C₄²×C₁₁	—	2	4	no	—
223	C₄²×C₁₁	—	2	8	no	—
224	C₄²×C₁₁	C₂×D₄	1	4	yes	—
225	C₄²×C₁₁	C₂×D₄	1	4	yes	—
226	C₄²×C₁₁	C₂×D₄	1	4	yes	—
227	C₄²×C₁₁	C₂×D₄	1	4	yes	—
228	C₂×#529	C₂×C₁₁	1	1	yes	characteristic, complemented
229	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
230	#2603	C₂×C₁₁	1	4	yes	complemented
231	#2566	C₂×C₁₁	1	2	yes	complemented
232	#2544	C₂×C₁₁	1	2	yes	complemented
233	#2504	C₂×C₁₁	1	1	yes	characteristic, complemented
234	#2502	C₂×C₁₁	1	1	yes	characteristic, complemented
235	#2435	C₂×C₁₁	1	1	yes	characteristic, complemented
236	#2433	C₂×C₁₁	1	1	yes	characteristic
237	#2411	C₂×C₁₁	1	4	yes	complemented
238	#2392	C₂×C₁₁	1	4	yes	complemented
239	C₄×#127	C₂×C₁₁	1	2	yes	complemented
240	C₄×#124	C₂×C₁₁	1	2	yes	complemented
241	C₄×#120	C₂×C₁₁	1	4	yes	complemented
242	C₄×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
243	C₂³×C₁₁	—	2	2	no	—
244	C₂³×C₁₁	—	2	2	no	—
245	C₂³×C₁₁	—	2	16	no	—
246	C₂³×C₁₁	—	2	4	no	—
247	C₂³×C₁₁	—	2	8	no	—
248	C₂³×C₁₁	—	2	4	no	—
249	C₂³×C₁₁	—	2	8	no	—
250	C₂³×C₁₁	—	2	2	no	—
251	C₂³×C₁₁	—	2	4	no	—
252	C₂³×C₁₁	—	2	4	no	—
253	C₂³×C₁₁	—	2	4	no	—
254	C₂³×C₁₁	—	4	32	no	—
255	C₂³×C₁₁	—	4	8	no	—
256	C₂³×C₁₁	—	4	8	no	—
257	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
258	C₂³×C₁₁	C₂×#41	1	8	yes	—
259	C₂³×C₁₁	C₂×#41	1	4	yes	—
260	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
261	Q₈×C₁₁	—	4	4	no	—
262	D₄×C₁₁	—	2	16	no	—
263	D₄×C₁₁	—	2	16	no	—
264	D₄×C₁₁	—	4	32	no	—
265	D₄×C₁₁	—	4	8	no	—
266	D₄×C₁₁	—	4	4	no	—
267	C₂×C₄×C₁₁	—	2	8	no	—
268	C₂×C₄×C₁₁	—	2	2	no	—
269	C₂×C₄×C₁₁	—	2	4	no	—
270	C₂×C₄×C₁₁	—	2	2	no	—
271	C₂×C₄×C₁₁	—	2	2	no	—
272	C₂×C₄×C₁₁	—	2	4	no	—
273	C₂×C₄×C₁₁	—	2	2	no	—
274	C₂×C₄×C₁₁	—	2	8	no	—
275	C₂×C₄×C₁₁	—	2	8	no	—
276	C₂×C₄×C₁₁	—	2	2	no	—
277	C₂×C₄×C₁₁	—	2	2	no	—
278	C₂×C₄×C₁₁	—	2	2	no	—
279	C₂×C₄×C₁₁	—	2	4	no	—
280	C₂×C₄×C₁₁	—	2	4	no	—
281	C₂×C₄×C₁₁	—	2	4	no	—
282	C₂×C₄×C₁₁	—	2	4	no	—
283	C₂×C₄×C₁₁	—	2	4	no	—
284	C₂×C₄×C₁₁	—	2	4	no	—
285	C₂×C₄×C₁₁	—	2	4	no	—
286	C₂×C₄×C₁₁	—	2	8	no	—
287	C₂×C₄×C₁₁	—	4	16	no	—
288	C₂×C₄×C₁₁	—	4	8	no	—
289	C₂×C₄×C₁₁	—	4	8	no	—
290	C₂×C₄×C₁₁	—	4	16	no	—
291	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
298	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
299	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
300	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
301	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
302	C₂×#127	C₂²×C₁₁	1	2	yes	—
303	#529	—	2	8	no	—
304	C₂×#126	C₂²×C₁₁	1	2	yes	complemented
305	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic, complemented
306	C₂×#124	C₂²×C₁₁	1	2	yes	—
307	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic, complemented
308	C₂×#123	C₂²×C₁₁	1	2	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
310	C₂×#121	C₂²×C₁₁	1	1	yes	characteristic
311	C₂×#120	C₂²×C₁₁	1	4	yes	—
312	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
313	C₂×C₄×D₄	—	2	8	no	—
314	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
315	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
316	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
317	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
319	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
320	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	complemented
321	C₂×#117	C₂²×C₁₁	1	2	yes	—
322	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
323	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
325	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
326	#398	C₂²×C₁₁	1	4	yes	complemented
327	#397	C₂²×C₁₁	1	4	yes	complemented
328	#396	C₂²×C₁₁	1	8	yes	complemented
329	#394	C₂²×C₁₁	1	4	yes	—
330	#394	C₂²×C₁₁	1	8	yes	complemented
331	#392	C₂²×C₁₁	1	4	yes	—
332	#391	C₂²×C₁₁	1	2	yes	complemented
333	#390	C₂²×C₁₁	1	2	yes	—
334	#390	C₂²×C₁₁	1	2	yes	—
335	#390	C₂²×C₁₁	1	8	yes	complemented
336	#390	C₂²×C₁₁	1	2	yes	complemented
337	#388	C₂²×C₁₁	1	8	yes	complemented
338	#386	C₂²×C₁₁	1	4	yes	—
339	#386	C₂²×C₁₁	1	8	yes	complemented
340	#385	C₂²×C₁₁	1	4	yes	—
341	#385	C₂²×C₁₁	1	8	yes	complemented
342	#384	C₂²×C₁₁	1	2	yes	complemented
343	#382	C₂²×C₁₁	1	2	yes	complemented
344	#379	C₂²×C₁₁	1	4	yes	—
345	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
346	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
347	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	complemented
351	#376	C₂²×C₁₁	1	2	yes	complemented
352	C₄³	C₂²×C₁₁	1	2	yes	complemented
353	C₂²×C₁₁	—	2	2	no	—
354	C₂²×C₁₁	—	2	2	no	—
355	C₂²×C₁₁	—	2	8	no	—
356	C₂²×C₁₁	—	2	8	no	—
357	C₂²×C₁₁	—	2	16	no	—
358	C₂²×C₁₁	—	4	32	no	—
359	C₂²×C₁₁	—	4	4	no	—
360	C₂²×C₁₁	—	4	4	no	—
361	C₂²×C₁₁	—	4	8	no	—
362	C₂²×C₁₁	—	4	2	no	—
363	C₂²×C₁₁	—	4	2	no	—
364	C₂²×C₁₁	—	4	2	no	—
365	C₂²×C₁₁	—	4	8	no	—
366	C₂²×C₁₁	#532	1	4	yes	—
367	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
368	C₂²×C₁₁	C₂²×#41	1	2	yes	—
369	C₂²×C₁₁	C₂²×#41	1	2	yes	—
370	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
371	C₄×C₁₁	—	2	2	no	—
372	C₄×C₁₁	—	2	2	no	—
373	C₄×C₁₁	—	2	2	no	—
374	C₄×C₁₁	—	2	2	no	—
375	C₄×C₁₁	—	2	8	no	—
376	C₄×C₁₁	—	4	2	no	—
377	C₄×C₁₁	—	4	2	no	—
378	C₄×C₁₁	—	4	2	no	—
379	C₄×C₁₁	—	4	4	no	—
380	C₄×C₁₁	—	4	4	no	—
381	C₄×C₁₁	#525	1	4	yes	—
382	C₄×C₁₁	#535	1	4	yes	—
383	C₂⁵	C₂³×C₁₁	1	2	yes	—
384	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
385	C₂²×D₄	—	2	8	no	—
386	C₂²×D₄	—	2	4	no	—
387	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
388	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
389	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
391	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	4	8	no	—
394	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
396	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
401	#127	—	2	8	no	—
402	#126	—	2	8	no	—
403	#125	—	2	4	no	—
404	#124	—	2	8	no	—
405	#124	—	2	4	no	—
406	#123	—	2	8	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	#121	—	2	4	no	—
409	#120	—	2	16	no	—
410	C₄×Q₈	—	2	4	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	8	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	—	4	16	no	—
418	#117	—	2	8	no	—
419	#117	—	2	8	no	—
420	C₂×C₄⋊C₄	—	2	4	no	—
421	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
431	C₂×C₂²⋊C₄	—	2	8	no	—
432	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
445	C₂×C₄²	D₄×C₁₁	1	8	yes	complemented
446	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
447	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
448	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
449	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
450	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
451	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
455	#95	C₂³×C₁₁	1	4	yes	—
456	#95	C₂³×C₁₁	1	2	yes	—
457	#95	C₂³×C₁₁	1	2	yes	—
458	#95	C₂³×C₁₁	1	8	yes	—
459	#95	C₂³×C₁₁	1	8	yes	—
460	C₂×C₁₁	—	2	4	no	—
461	C₂×C₁₁	—	4	8	no	—
462	C₂×C₁₁	—	8	2	no	—
463	C₂×C₁₁	C₂×#525	1	1	yes	characteristic
464	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
465	C₂×C₁₁	C₂×#535	1	1	yes	characteristic
466	C₂×C₁₁	#3481	1	4	yes	—
467	C₂⁴	—	2	4	no	—
468	C₂⁴	—	2	8	no	—
469	C₂⁴	—	2	8	no	—
470	C₂⁴	—	4	4	no	—
471	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
472	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
473	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×D₄	—	2	32	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	16	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	16	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	4	8	no	—
488	C₂×D₄	C₁₁×#41	1	8	yes	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	16	no	—
498	C₂²×C₄	—	4	8	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	—	4	32	no	—
501	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
502	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	4	8	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	2	16	no	—
529	C₂²⋊C₄	—	2	8	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	16	no	—
536	C₂²⋊C₄	—	4	8	no	—
537	C₂²⋊C₄	—	4	8	no	—
538	C₂²⋊C₄	C₁₁×#41	1	8	yes	—
539	C₄²	—	2	4	no	—
540	C₄²	—	2	8	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	4	no	—
543	C₄²	—	2	8	no	—
544	C₄²	C₂×D₄×C₁₁	1	4	yes	—
545	C₄²	C₂×D₄×C₁₁	1	4	yes	—
546	C₄²	C₂×D₄×C₁₁	1	4	yes	—
547	C₄²	C₂×D₄×C₁₁	1	4	yes	—
548	C₁₁	#34965	1	1	yes	characteristic, direct product factor, Sylow
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	16	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	8	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	8	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	4	32	no	—
561	C₂³	—	4	8	no	—
562	C₂³	—	4	8	no	—
563	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
564	C₂³	C₂×C₁₁×#41	1	8	yes	—
565	C₂³	C₂×C₁₁×#41	1	4	yes	—
566	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
567	Q₈	—	4	4	no	—
568	D₄	—	2	16	no	—
569	D₄	—	2	16	no	—
570	D₄	—	4	32	no	—
571	D₄	—	4	8	no	—
572	D₄	—	4	4	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	8	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	4	16	no	—
594	C₂×C₄	—	4	8	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	4	16	no	—
597	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
599	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
600	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
601	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
602	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
603	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
604	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
605	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	16	no	—
611	C₂²	—	4	32	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	8	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	8	no	—
619	C₂²	C₁₁×#532	1	4	yes	—
620	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
621	C₂²	C₂²×C₁₁×#41	1	2	yes	—
622	C₂²	C₂²×C₁₁×#41	1	2	yes	—
623	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	8	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	4	no	—
634	C₄	C₁₁×#525	1	4	yes	—
635	C₄	C₁₁×#535	1	4	yes	—
636	C₂	—	2	4	no	—
637	C₂	—	4	8	no	—
638	C₂	—	8	2	no	—
639	C₂	C₂×C₁₁×#525	1	1	yes	characteristic
640	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
641	C₂	C₂×C₁₁×#535	1	1	yes	characteristic
642	C₂	C₁₁×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂⁵
prime radical	C₁₁×#2433	C₂
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
1. C₂×C₁₁×#529	C₂	semidirect
2. C₂²×C₄×D₄×C₁₁	C₂	semidirect
3. C₁₁×#2603	C₂	semidirect
4. C₁₁×#2566	C₂	semidirect
5. C₁₁×#2544	C₂	semidirect
6. C₁₁×#2504	C₂	semidirect
7. C₁₁×#2502	C₂	semidirect
8. C₁₁×#2435	C₂	semidirect
10. C₁₁×#2411	C₂	semidirect
11. C₁₁×#2392	C₂	semidirect
12. C₄×C₁₁×#127	C₂	semidirect
13. C₄×C₁₁×#124	C₂	semidirect
14. C₄×C₁₁×#120	C₂	semidirect
15. C₄×C₁₁×#117	C₂	semidirect
20. C₂×C₁₁×#126	C₂²	semidirect
21. C₂×C₁₁×#125	C₂²	semidirect
23. C₂×C₁₁×#124	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
35. C₂×C₄×D₄×C₁₁	C₂²	semidirect
36. C₂×C₄×D₄×C₁₁	C₂²	semidirect
38. C₂×C₁₁×#117	C₂²	semidirect
42. C₁₁×#398	C₂²	semidirect
43. C₁₁×#397	C₂²	semidirect
44. C₁₁×#396	C₂²	semidirect
46. C₁₁×#394	C₂²	semidirect
48. C₁₁×#391	C₂²	semidirect
51. C₁₁×#390	C₂²	semidirect
52. C₁₁×#390	C₂²	semidirect
53. C₁₁×#388	C₂²	semidirect
55. C₁₁×#386	C₂²	semidirect
57. C₁₁×#385	C₂²	semidirect
58. C₁₁×#384	C₂²	semidirect
59. C₁₁×#382	C₂²	semidirect
61. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
62. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
66. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
67. C₁₁×#376	C₂²	semidirect
68. C₄³×C₁₁	C₂²	semidirect
131. C₂×C₄²×C₁₁	D₄	semidirect
146. #34965	C₁₁	direct (N × H)
228. C₂×#529	C₂×C₁₁	semidirect
229. C₂²×C₄×D₄	C₂×C₁₁	semidirect
230. #2603	C₂×C₁₁	semidirect
231. #2566	C₂×C₁₁	semidirect
232. #2544	C₂×C₁₁	semidirect
233. #2504	C₂×C₁₁	semidirect
234. #2502	C₂×C₁₁	semidirect
235. #2435	C₂×C₁₁	semidirect
237. #2411	C₂×C₁₁	semidirect
238. #2392	C₂×C₁₁	semidirect
239. C₄×#127	C₂×C₁₁	semidirect
240. C₄×#124	C₂×C₁₁	semidirect
241. C₄×#120	C₂×C₁₁	semidirect
242. C₄×#117	C₂×C₁₁	semidirect
304. C₂×#126	C₂²×C₁₁	semidirect
305. C₂×#125	C₂²×C₁₁	semidirect
307. C₂×#124	C₂²×C₁₁	semidirect
312. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
319. C₂×C₄×D₄	C₂²×C₁₁	semidirect
320. C₂×C₄×D₄	C₂²×C₁₁	semidirect
322. C₂×#117	C₂²×C₁₁	semidirect
326. #398	C₂²×C₁₁	semidirect
327. #397	C₂²×C₁₁	semidirect
328. #396	C₂²×C₁₁	semidirect
330. #394	C₂²×C₁₁	semidirect
332. #391	C₂²×C₁₁	semidirect
335. #390	C₂²×C₁₁	semidirect
336. #390	C₂²×C₁₁	semidirect
337. #388	C₂²×C₁₁	semidirect
339. #386	C₂²×C₁₁	semidirect
341. #385	C₂²×C₁₁	semidirect
342. #384	C₂²×C₁₁	semidirect
343. #382	C₂²×C₁₁	semidirect
345. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
346. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
350. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
351. #376	C₂²×C₁₁	semidirect
352. C₄³	C₂²×C₁₁	semidirect
445. C₂×C₄²	D₄×C₁₁	semidirect
548. C₁₁	#34965	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×#529	2
C₂²×C₄×D₄×C₁₁	2
C₁₁×#2603	2
C₁₁×#2566	2
C₁₁×#2544	2
C₁₁×#2504	2
C₁₁×#2502	2
C₁₁×#2435	2
C₁₁×#2433	2
C₁₁×#2411	2
C₁₁×#2392	2
C₄×C₁₁×#127	2
C₄×C₁₁×#124	2
C₄×C₁₁×#120	2
C₄×C₁₁×#117	2
#34965	11

Subgroups — C11×#34965 #14612158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34965 #14612158