Subgroups — C₁₁×#36555 #14613748

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2864	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2587	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2538	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2522	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2497	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2454	C₂	1	2	yes	maximal
9	C₁₁×#2453	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2423	C₂	1	2	yes	maximal, complemented
11	C₁₁×#2360	C₂	1	2	yes	maximal, complemented
12	Q₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₁₁×#2345	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
16	C₄×C₁₁×#124	C₂	1	2	yes	maximal
17	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₁×#125	C₂²	1	2	yes	—
19	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
28	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
29	C₁₁×#400	C₂²	1	4	yes	—
30	C₁₁×#399	C₂²	1	4	yes	—
31	C₁₁×#398	C₂²	1	4	yes	—
32	C₁₁×#398	C₂²	1	4	yes	—
33	C₁₁×#396	C₂²	1	4	yes	—
34	C₁₁×#396	C₂²	1	4	yes	—
35	C₁₁×#391	C₂²	1	2	yes	—
36	C₁₁×#391	C₂²	1	1	yes	characteristic
37	C₁₁×#391	C₂²	1	2	yes	—
38	C₁₁×#390	C₂²	1	1	yes	characteristic
39	C₁₁×#390	C₂²	1	2	yes	—
40	C₁₁×#389	C₂²	1	2	yes	—
41	C₁₁×#389	C₂²	1	2	yes	—
42	C₁₁×#389	C₂²	1	4	yes	—
43	C₁₁×#389	C₂²	1	2	yes	—
44	C₁₁×#389	C₂²	1	2	yes	—
45	C₁₁×#389	C₂²	1	2	yes	—
46	C₁₁×#389	C₂²	1	2	yes	—
47	C₁₁×#389	C₂²	1	2	yes	—
48	C₁₁×#389	C₂²	1	2	yes	—
49	C₁₁×#389	C₂²	1	4	yes	—
50	C₁₁×#389	C₂²	1	2	yes	—
51	C₁₁×#388	C₂²	1	4	yes	—
52	C₁₁×#388	C₂²	1	4	yes	—
53	C₁₁×#388	C₂²	1	2	yes	—
54	C₁₁×#388	C₂²	1	2	yes	—
55	C₁₁×#387	C₂²	1	4	yes	—
56	C₁₁×#387	C₂²	1	4	yes	—
57	C₁₁×#387	C₂²	1	4	yes	—
58	C₁₁×#387	C₂²	1	4	yes	—
59	C₁₁×#387	C₂²	1	4	yes	—
60	C₁₁×#385	C₂²	1	4	yes	—
61	C₁₁×#385	C₂²	1	4	yes	—
62	C₁₁×#384	C₂²	1	2	yes	—
63	C₁₁×#384	C₂²	1	1	yes	characteristic
64	C₁₁×#384	C₂²	1	1	yes	characteristic
65	C₁₁×#382	C₂²	1	2	yes	—
66	C₁₁×#382	C₂²	1	1	yes	characteristic
67	C₁₁×#380	C₂²	1	2	yes	—
68	C₁₁×#380	C₂²	1	4	yes	—
69	C₁₁×#380	C₂²	1	2	yes	—
70	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄³×C₁₁	C₂²	1	1	yes	characteristic
82	C₄³×C₁₁	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
88	C₁₁×#125	—	4	4	no	—
89	C₁₁×#124	Q₈	1	8	yes	complemented
90	C₁₁×C₂²⋊Q₈	—	2	8	no	—
91	C₄×Q₈×C₁₁	—	2	4	no	—
92	C₄×Q₈×C₁₁	—	2	4	no	—
93	C₄×Q₈×C₁₁	—	2	4	no	—
94	C₄×Q₈×C₁₁	—	2	4	no	—
95	C₄×Q₈×C₁₁	—	4	4	no	—
96	C₄×D₄×C₁₁	—	2	4	no	—
97	C₄×D₄×C₁₁	—	4	4	no	—
98	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
144	C₁₁×#95	C₂³	1	2	yes	—
145	C₁₁×#95	C₂³	1	2	yes	—
146	C₁₁×#95	C₂³	1	4	yes	—
147	C₁₁×#95	C₂³	1	4	yes	—
148	C₁₁×#95	C₂³	1	2	yes	—
149	C₁₁×#95	C₂³	1	4	yes	—
150	C₁₁×#95	C₂³	1	2	yes	—
151	C₁₁×#95	C₂³	1	4	yes	—
152	C₁₁×#95	C₂³	1	2	yes	—
153	C₁₁×#95	C₂³	1	2	yes	—
154	C₁₁×#95	C₂³	1	2	yes	—
155	C₁₁×#95	C₂³	1	4	yes	—
156	C₁₁×#95	C₂³	1	4	yes	—
157	C₁₁×#95	C₂³	1	4	yes	—
158	C₁₁×#95	C₂³	1	4	yes	—
159	#36555	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
161	C₂×Q₈×C₁₁	—	2	2	no	—
162	C₂×Q₈×C₁₁	—	2	2	no	—
163	C₂×Q₈×C₁₁	—	2	2	no	—
164	C₂×Q₈×C₁₁	—	2	2	no	—
165	C₂×Q₈×C₁₁	C₂×Q₈	1	4	yes	—
166	C₂×Q₈×C₁₁	#41	1	4	yes	—
167	C₂×D₄×C₁₁	—	2	2	no	—
168	C₂×D₄×C₁₁	—	2	2	no	—
169	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	—
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	8	no	—
174	C₂²×C₄×C₁₁	—	4	4	no	—
175	C₂²×C₄×C₁₁	—	4	4	no	—
176	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₁	C₂⁴	1	2	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	C₁₁×C₄⋊C₄	—	2	8	no	—
193	C₁₁×C₄⋊C₄	—	2	4	no	—
194	C₁₁×C₄⋊C₄	—	2	2	no	—
195	C₁₁×C₄⋊C₄	—	2	4	no	—
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	2	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	2	no	—
202	C₁₁×C₄⋊C₄	—	2	4	no	—
203	C₁₁×C₄⋊C₄	—	2	8	no	—
204	C₁₁×C₄⋊C₄	—	2	4	no	—
205	C₁₁×C₄⋊C₄	—	2	4	no	—
206	C₁₁×C₄⋊C₄	—	4	2	no	—
207	C₁₁×C₄⋊C₄	—	4	2	no	—
208	C₁₁×C₄⋊C₄	—	4	4	no	—
209	C₁₁×C₄⋊C₄	—	4	4	no	—
210	C₁₁×C₄⋊C₄	—	4	4	no	—
211	C₁₁×C₄⋊C₄	—	4	4	no	—
212	C₁₁×C₄⋊C₄	—	4	4	no	—
213	C₁₁×C₄⋊C₄	#41	1	4	yes	—
214	C₁₁×C₂²⋊C₄	—	2	4	no	—
215	C₁₁×C₂²⋊C₄	—	2	8	no	—
216	C₁₁×C₂²⋊C₄	—	4	4	no	—
217	C₁₁×C₂²⋊C₄	—	4	2	no	—
218	C₁₁×C₂²⋊C₄	—	4	2	no	—
219	C₁₁×C₂²⋊C₄	—	4	4	no	—
220	C₁₁×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
221	C₁₁×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
222	C₄²×C₁₁	—	2	4	no	—
223	C₄²×C₁₁	—	2	4	no	—
224	C₄²×C₁₁	—	2	2	no	—
225	C₄²×C₁₁	—	2	2	no	—
226	C₄²×C₁₁	—	2	4	no	—
227	C₄²×C₁₁	—	2	4	no	—
228	C₄²×C₁₁	—	2	4	no	—
229	C₄²×C₁₁	—	2	2	no	—
230	C₄²×C₁₁	—	4	1	no	—
231	C₄²×C₁₁	—	4	1	no	—
232	C₄²×C₁₁	—	4	2	no	—
233	C₄²×C₁₁	—	4	2	no	—
234	C₄²×C₁₁	—	4	4	no	—
235	C₄²×C₁₁	C₂×Q₈	1	4	yes	—
236	C₄²×C₁₁	#41	1	4	yes	—
237	#2864	C₂×C₁₁	1	2	yes	complemented
238	#2859	C₂×C₁₁	1	1	yes	characteristic, complemented
239	#2587	C₂×C₁₁	1	4	yes	complemented
240	#2582	C₂×C₁₁	1	1	yes	characteristic, complemented
241	#2538	C₂×C₁₁	1	1	yes	characteristic
242	#2522	C₂×C₁₁	1	4	yes	complemented
243	#2497	C₂×C₁₁	1	2	yes	complemented
244	#2454	C₂×C₁₁	1	2	yes	—
245	#2453	C₂×C₁₁	1	2	yes	complemented
246	#2423	C₂×C₁₁	1	2	yes	complemented
247	#2360	C₂×C₁₁	1	2	yes	complemented
248	Q₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
249	D₄×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
250	#2345	C₂×C₁₁	1	2	yes	complemented
251	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
252	C₄×#124	C₂×C₁₁	1	2	yes	—
253	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
254	C₂³×C₁₁	—	2	2	no	—
255	C₂³×C₁₁	—	2	2	no	—
256	C₂³×C₁₁	—	2	2	no	—
257	C₂³×C₁₁	—	2	2	no	—
258	C₂³×C₁₁	—	2	2	no	—
259	C₂³×C₁₁	—	2	2	no	—
260	C₂³×C₁₁	C₂²×Q₈	1	4	yes	—
261	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
262	Q₈×C₁₁	—	2	8	no	—
263	Q₈×C₁₁	—	2	8	no	—
264	D₄×C₁₁	—	2	8	no	—
265	C₂×C₄×C₁₁	—	2	1	no	—
266	C₂×C₄×C₁₁	—	2	1	no	—
267	C₂×C₄×C₁₁	—	2	2	no	—
268	C₂×C₄×C₁₁	—	2	2	no	—
269	C₂×C₄×C₁₁	—	2	2	no	—
270	C₂×C₄×C₁₁	—	2	2	no	—
271	C₂×C₄×C₁₁	—	2	2	no	—
272	C₂×C₄×C₁₁	—	2	1	no	—
273	C₂×C₄×C₁₁	—	2	1	no	—
274	C₂×C₄×C₁₁	—	2	1	no	—
275	C₂×C₄×C₁₁	—	2	1	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	1	no	—
280	C₂×C₄×C₁₁	—	2	2	no	—
281	C₂×C₄×C₁₁	—	2	1	no	—
282	C₂×C₄×C₁₁	—	2	4	no	—
283	C₂×C₄×C₁₁	—	2	2	no	—
284	C₂×C₄×C₁₁	—	2	2	no	—
285	C₂×C₄×C₁₁	—	2	2	no	—
286	C₂×C₄×C₁₁	—	2	4	no	—
287	C₂×C₄×C₁₁	—	2	2	no	—
288	C₂×C₄×C₁₁	—	2	1	no	—
289	C₂×C₄×C₁₁	—	2	1	no	—
290	C₂×C₄×C₁₁	—	2	4	no	—
291	C₂×C₄×C₁₁	—	2	4	no	—
292	C₂×C₄×C₁₁	—	2	2	no	—
293	C₂×C₄×C₁₁	—	2	1	no	—
294	C₂×C₄×C₁₁	—	2	1	no	—
295	C₂×C₄×C₁₁	—	2	2	no	—
296	C₂×C₄×C₁₁	—	2	2	no	—
297	C₂×C₄×C₁₁	—	2	2	no	—
298	C₂×C₄×C₁₁	—	2	2	no	—
299	C₂×C₄×C₁₁	—	2	4	no	—
300	C₂×C₄×C₁₁	—	2	4	no	—
301	C₂×C₄×C₁₁	—	4	8	no	—
302	C₂×C₄×C₁₁	—	8	8	no	—
303	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
304	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
305	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
306	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
308	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
310	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
315	C₂×#125	C₂²×C₁₁	1	2	yes	—
316	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
317	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
318	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
325	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
326	#400	C₂²×C₁₁	1	4	yes	—
327	#399	C₂²×C₁₁	1	4	yes	—
328	#398	C₂²×C₁₁	1	4	yes	—
329	#398	C₂²×C₁₁	1	4	yes	—
330	#396	C₂²×C₁₁	1	4	yes	—
331	#396	C₂²×C₁₁	1	4	yes	—
332	#391	C₂²×C₁₁	1	2	yes	—
333	#391	C₂²×C₁₁	1	2	yes	—
334	#391	C₂²×C₁₁	1	1	yes	characteristic
335	#390	C₂²×C₁₁	1	1	yes	characteristic
336	#390	C₂²×C₁₁	1	2	yes	—
337	#389	C₂²×C₁₁	1	2	yes	—
338	#389	C₂²×C₁₁	1	2	yes	—
339	#389	C₂²×C₁₁	1	2	yes	—
340	#389	C₂²×C₁₁	1	4	yes	—
341	#389	C₂²×C₁₁	1	4	yes	—
342	#389	C₂²×C₁₁	1	2	yes	—
343	#389	C₂²×C₁₁	1	2	yes	—
344	#389	C₂²×C₁₁	1	2	yes	—
345	#389	C₂²×C₁₁	1	2	yes	—
346	#389	C₂²×C₁₁	1	2	yes	—
347	#389	C₂²×C₁₁	1	2	yes	—
348	#388	C₂²×C₁₁	1	2	yes	—
349	#388	C₂²×C₁₁	1	4	yes	—
350	#388	C₂²×C₁₁	1	4	yes	—
351	#388	C₂²×C₁₁	1	2	yes	—
352	#387	C₂²×C₁₁	1	4	yes	—
353	#387	C₂²×C₁₁	1	4	yes	—
354	#387	C₂²×C₁₁	1	4	yes	—
355	#387	C₂²×C₁₁	1	4	yes	—
356	#387	C₂²×C₁₁	1	4	yes	—
357	#385	C₂²×C₁₁	1	4	yes	—
358	#385	C₂²×C₁₁	1	4	yes	—
359	#384	C₂²×C₁₁	1	1	yes	characteristic
360	#384	C₂²×C₁₁	1	1	yes	characteristic
361	#384	C₂²×C₁₁	1	2	yes	—
362	#382	C₂²×C₁₁	1	2	yes	—
363	#382	C₂²×C₁₁	1	1	yes	characteristic
364	#380	C₂²×C₁₁	1	4	yes	—
365	#380	C₂²×C₁₁	1	2	yes	—
366	#380	C₂²×C₁₁	1	2	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
378	C₄³	C₂²×C₁₁	1	1	yes	characteristic
379	C₄³	C₂²×C₁₁	1	2	yes	—
380	C₂²×C₁₁	—	2	4	no	—
381	C₂²×C₁₁	—	2	4	no	—
382	C₂²×C₁₁	—	2	4	no	—
383	C₂²×C₁₁	—	4	2	no	—
384	C₂²×C₁₁	—	4	2	no	—
385	C₂²×C₁₁	—	4	2	no	—
386	C₂²×C₁₁	—	4	2	no	—
387	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
388	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
389	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₁₁	#585	1	1	yes	characteristic
393	C₂²×C₁₁	#585	1	1	yes	characteristic
394	C₄×C₁₁	—	2	4	no	—
395	C₄×C₁₁	—	2	4	no	—
396	C₄×C₁₁	—	2	2	no	—
397	C₄×C₁₁	—	2	2	no	—
398	C₄×C₁₁	—	2	2	no	—
399	C₄×C₁₁	—	2	4	no	—
400	C₄×C₁₁	—	4	2	no	—
401	C₄×C₁₁	—	4	2	no	—
402	C₄×C₁₁	—	4	2	no	—
403	C₄×C₁₁	—	4	1	no	—
404	C₄×C₁₁	—	4	4	no	—
405	C₄×C₁₁	—	4	2	no	—
406	C₄×C₁₁	—	4	1	no	—
407	C₄×C₁₁	—	4	4	no	—
408	C₄×C₁₁	#529	1	4	yes	—
409	C₄×C₁₁	#554	1	4	yes	—
410	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
414	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
415	#125	—	4	4	no	—
416	#124	Q₈×C₁₁	1	8	yes	complemented
417	C₂²⋊Q₈	—	2	8	no	—
418	C₄×Q₈	—	2	4	no	—
419	C₄×Q₈	—	2	4	no	—
420	C₄×Q₈	—	2	4	no	—
421	C₄×Q₈	—	2	4	no	—
422	C₄×Q₈	—	4	4	no	—
423	C₄×D₄	—	2	4	no	—
424	C₄×D₄	—	4	4	no	—
425	C₂×C₄⋊C₄	—	2	8	no	—
426	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
456	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
457	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
458	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
465	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
471	#95	C₂³×C₁₁	1	2	yes	—
472	#95	C₂³×C₁₁	1	2	yes	—
473	#95	C₂³×C₁₁	1	4	yes	—
474	#95	C₂³×C₁₁	1	4	yes	—
475	#95	C₂³×C₁₁	1	2	yes	—
476	#95	C₂³×C₁₁	1	4	yes	—
477	#95	C₂³×C₁₁	1	2	yes	—
478	#95	C₂³×C₁₁	1	4	yes	—
479	#95	C₂³×C₁₁	1	2	yes	—
480	#95	C₂³×C₁₁	1	2	yes	—
481	#95	C₂³×C₁₁	1	2	yes	—
482	#95	C₂³×C₁₁	1	4	yes	—
483	#95	C₂³×C₁₁	1	4	yes	—
484	#95	C₂³×C₁₁	1	4	yes	—
485	#95	C₂³×C₁₁	1	4	yes	—
486	C₂×C₁₁	—	4	4	no	—
487	C₂×C₁₁	C₂×#529	1	1	yes	characteristic
488	C₂×C₁₁	C₂×#554	1	1	yes	characteristic
489	C₂×C₁₁	Q₈×#41	1	1	yes	characteristic
490	C₂×C₁₁	Q₈×#41	1	1	yes	characteristic
491	C₂×C₁₁	#3512	1	1	yes	characteristic
492	C₂×C₁₁	#3514	1	1	yes	characteristic
493	C₂×C₁₁	#3517	1	1	yes	characteristic
494	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	C₂×Q₈×C₁₁	1	4	yes	—
500	C₂×Q₈	C₁₁×#41	1	4	yes	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	4	4	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	—	4	4	no	—
547	C₄⋊C₄	C₁₁×#41	1	4	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	C₂×Q₈×C₁₁	1	8	yes	—
555	C₂²⋊C₄	C₂×Q₈×C₁₁	1	8	yes	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	2	no	—
564	C₄²	—	4	4	no	—
565	C₄²	—	4	1	no	—
566	C₄²	—	4	1	no	—
567	C₄²	—	4	2	no	—
568	C₄²	—	4	2	no	—
569	C₄²	C₂×Q₈×C₁₁	1	4	yes	—
570	C₄²	C₁₁×#41	1	4	yes	—
571	C₁₁	#36555	1	1	yes	characteristic, direct product factor, Sylow
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	C₂²×Q₈×C₁₁	1	4	yes	—
579	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
580	Q₈	—	2	8	no	—
581	Q₈	—	2	8	no	—
582	D₄	—	2	8	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	4	8	no	—
620	C₂×C₄	—	8	8	no	—
621	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
622	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
623	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
624	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
625	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
626	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
627	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
628	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
629	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
630	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
631	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
632	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	C₂³×Q₈×C₁₁	1	1	yes	characteristic
641	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
642	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
643	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
644	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂²	C₁₁×#585	1	1	yes	characteristic
646	C₂²	C₁₁×#585	1	1	yes	characteristic
647	C₄	—	2	4	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	4	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	4	no	—
661	C₄	C₁₁×#529	1	4	yes	—
662	C₄	C₁₁×#554	1	4	yes	—
663	C₂	—	4	4	no	—
664	C₂	C₂×C₁₁×#529	1	1	yes	characteristic
665	C₂	C₂×C₁₁×#554	1	1	yes	characteristic
666	C₂	Q₈×C₁₁×#41	1	1	yes	characteristic
667	C₂	Q₈×C₁₁×#41	1	1	yes	characteristic
668	C₂	C₁₁×#3512	1	1	yes	characteristic
669	C₂	C₁₁×#3514	1	1	yes	characteristic
670	C₂	C₁₁×#3517	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₁×#2864	C₂	semidirect
2. C₁₁×#2859	C₂	semidirect
3. C₁₁×#2587	C₂	semidirect
4. C₁₁×#2582	C₂	semidirect
6. C₁₁×#2522	C₂	semidirect
7. C₁₁×#2497	C₂	semidirect
9. C₁₁×#2453	C₂	semidirect
10. C₁₁×#2423	C₂	semidirect
11. C₁₁×#2360	C₂	semidirect
12. Q₈×C₁₁×C₄⋊C₄	C₂	semidirect
14. C₁₁×#2345	C₂	semidirect
17. C₄²×Q₈×C₁₁	C₂	semidirect
89. C₁₁×#124	Q₈	semidirect
159. #36555	C₁₁	direct (N × H)
237. #2864	C₂×C₁₁	semidirect
238. #2859	C₂×C₁₁	semidirect
239. #2587	C₂×C₁₁	semidirect
240. #2582	C₂×C₁₁	semidirect
242. #2522	C₂×C₁₁	semidirect
243. #2497	C₂×C₁₁	semidirect
245. #2453	C₂×C₁₁	semidirect
246. #2423	C₂×C₁₁	semidirect
247. #2360	C₂×C₁₁	semidirect
248. Q₈×C₄⋊C₄	C₂×C₁₁	semidirect
250. #2345	C₂×C₁₁	semidirect
253. C₄²×Q₈	C₂×C₁₁	semidirect
416. #124	Q₈×C₁₁	semidirect
571. C₁₁	#36555	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2864	2
C₁₁×#2859	2
C₁₁×#2587	2
C₁₁×#2582	2
C₁₁×#2538	2
C₁₁×#2522	2
C₁₁×#2497	2
C₁₁×#2454	2
C₁₁×#2453	2
C₁₁×#2423	2
C₁₁×#2360	2
Q₈×C₁₁×C₄⋊C₄	2
D₄×C₁₁×C₄⋊C₄	2
C₁₁×#2345	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36555	11

Subgroups — C11×#36555 #14613748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36555 #14613748