Subgroups — C₁₁×#36566 #14613759

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 580 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×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2589	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2580	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2574	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2465	C₂	1	4	yes	maximal, complemented
8	C₁₁×#2452	C₂	1	2	yes	maximal
9	C₁₁×#2451	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2368	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2351	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#2349	C₂	1	1	yes	maximal, characteristic
13	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₁×#124	C₂	1	2	yes	maximal
15	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
25	C₁₁×#400	C₂²	1	2	yes	—
26	C₁₁×#399	C₂²	1	2	yes	—
27	C₁₁×#398	C₂²	1	4	yes	—
28	C₁₁×#396	C₂²	1	4	yes	—
29	C₁₁×#395	C₂²	1	4	yes	—
30	C₁₁×#395	C₂²	1	2	yes	—
31	C₁₁×#393	C₂²	1	4	yes	—
32	C₁₁×#393	C₂²	1	2	yes	—
33	C₁₁×#391	C₂²	1	1	yes	characteristic
34	C₁₁×#391	C₂²	1	2	yes	—
35	C₁₁×#391	C₂²	1	4	yes	—
36	C₁₁×#391	C₂²	1	4	yes	—
37	C₁₁×#391	C₂²	1	4	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	2	yes	—
43	C₁₁×#389	C₂²	1	2	yes	—
44	C₁₁×#389	C₂²	1	4	yes	—
45	C₁₁×#388	C₂²	1	4	yes	—
46	C₁₁×#388	C₂²	1	4	yes	—
47	C₁₁×#388	C₂²	1	4	yes	—
48	C₁₁×#387	C₂²	1	4	yes	—
49	C₁₁×#387	C₂²	1	4	yes	—
50	C₁₁×#387	C₂²	1	4	yes	—
51	C₁₁×#387	C₂²	1	4	yes	—
52	C₁₁×#387	C₂²	1	4	yes	—
53	C₁₁×#387	C₂²	1	4	yes	—
54	C₁₁×#385	C₂²	1	4	yes	—
55	C₁₁×#385	C₂²	1	4	yes	—
56	C₁₁×#385	C₂²	1	4	yes	—
57	C₁₁×#382	C₂²	1	2	yes	—
58	C₁₁×#382	C₂²	1	1	yes	characteristic
59	C₁₁×#382	C₂²	1	2	yes	—
60	C₁₁×#382	C₂²	1	1	yes	characteristic
61	C₁₁×#382	C₂²	1	1	yes	characteristic
62	C₁₁×#380	C₂²	1	2	yes	—
63	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₂×C₁₁×#95	C₂²	1	2	yes	—
73	C₄³×C₁₁	C₂²	1	1	yes	characteristic
74	C₄³×C₁₁	C₂²	1	2	yes	—
75	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
81	C₁₁×C₄⋊Q₈	—	4	4	no	—
82	C₁₁×#124	Q₈	1	8	yes	complemented
83	C₁₁×C₂²⋊Q₈	—	2	16	no	—
84	C₄×Q₈×C₁₁	—	2	8	no	—
85	C₄×Q₈×C₁₁	—	2	4	no	—
86	C₄×Q₈×C₁₁	—	2	4	no	—
87	C₄×Q₈×C₁₁	—	4	4	no	—
88	C₄×D₄×C₁₁	—	2	4	no	—
89	C₄×D₄×C₁₁	—	4	4	no	—
90	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	yes	—
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
125	C₁₁×#95	C₂³	1	1	yes	characteristic
126	C₁₁×#95	C₂³	1	2	yes	—
127	C₁₁×#95	C₂³	1	4	yes	—
128	C₁₁×#95	C₂³	1	4	yes	—
129	C₁₁×#95	C₂³	1	4	yes	—
130	C₁₁×#95	C₂³	1	4	yes	—
131	C₁₁×#95	C₂³	1	4	yes	—
132	C₁₁×#95	C₂³	1	4	yes	—
133	C₁₁×#95	C₂³	1	4	yes	—
134	C₁₁×#95	C₂³	1	1	yes	characteristic
135	C₁₁×#95	C₂³	1	2	yes	—
136	C₁₁×#95	C₂³	1	2	yes	—
137	C₁₁×#95	C₂³	1	2	yes	—
138	C₁₁×#95	C₂³	1	2	yes	—
139	C₁₁×#95	C₂³	1	4	yes	—
140	C₁₁×#95	C₂³	1	2	yes	—
141	C₁₁×#95	C₂³	1	4	yes	—
142	C₁₁×#95	C₂³	1	4	yes	—
143	#36566	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
145	C₂×Q₈×C₁₁	—	2	4	no	—
146	C₂×Q₈×C₁₁	—	2	2	no	—
147	C₂×Q₈×C₁₁	—	2	2	no	—
148	C₂×Q₈×C₁₁	—	2	8	no	—
149	C₂×Q₈×C₁₁	—	2	2	no	—
150	C₂×Q₈×C₁₁	—	4	4	no	—
151	C₂×Q₈×C₁₁	—	4	4	no	—
152	C₂×Q₈×C₁₁	C₂×Q₈	1	4	yes	—
153	C₂×D₄×C₁₁	—	2	2	no	—
154	C₂×D₄×C₁₁	—	2	2	no	—
155	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	—
156	C₂²×C₄×C₁₁	—	2	4	no	—
157	C₂²×C₄×C₁₁	—	2	8	no	—
158	C₂²×C₄×C₁₁	—	4	4	no	—
159	C₂²×C₄×C₁₁	—	4	4	no	—
160	C₂²×C₄×C₁₁	—	4	4	no	—
161	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
175	C₁₁×C₄⋊C₄	—	2	2	no	—
176	C₁₁×C₄⋊C₄	—	2	4	no	—
177	C₁₁×C₄⋊C₄	—	2	4	no	—
178	C₁₁×C₄⋊C₄	—	2	4	no	—
179	C₁₁×C₄⋊C₄	—	2	4	no	—
180	C₁₁×C₄⋊C₄	—	2	2	no	—
181	C₁₁×C₄⋊C₄	—	2	2	no	—
182	C₁₁×C₄⋊C₄	—	2	8	no	—
183	C₁₁×C₄⋊C₄	—	2	8	no	—
184	C₁₁×C₄⋊C₄	—	2	4	no	—
185	C₁₁×C₄⋊C₄	—	2	4	no	—
186	C₁₁×C₄⋊C₄	—	4	4	no	—
187	C₁₁×C₄⋊C₄	—	4	4	no	—
188	C₁₁×C₄⋊C₄	—	4	4	no	—
189	C₁₁×C₄⋊C₄	—	4	4	no	—
190	C₁₁×C₄⋊C₄	#41	1	8	yes	—
191	C₁₁×C₂²⋊C₄	—	2	4	no	—
192	C₁₁×C₂²⋊C₄	—	2	8	no	—
193	C₁₁×C₂²⋊C₄	—	2	8	no	—
194	C₁₁×C₂²⋊C₄	—	4	4	no	—
195	C₁₁×C₂²⋊C₄	—	4	4	no	—
196	C₁₁×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
197	C₄²×C₁₁	—	2	4	no	—
198	C₄²×C₁₁	—	2	4	no	—
199	C₄²×C₁₁	—	2	4	no	—
200	C₄²×C₁₁	—	2	4	no	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	—	2	4	no	—
203	C₄²×C₁₁	—	2	2	no	—
204	C₄²×C₁₁	—	4	2	no	—
205	C₄²×C₁₁	—	4	2	no	—
206	C₄²×C₁₁	—	4	2	no	—
207	C₄²×C₁₁	—	4	4	no	—
208	C₄²×C₁₁	C₂×Q₈	1	4	yes	—
209	C₄²×C₁₁	#41	1	4	yes	—
210	#2864	C₂×C₁₁	1	2	yes	complemented
211	#2862	C₂×C₁₁	1	1	yes	characteristic, complemented
212	#2589	C₂×C₁₁	1	4	yes	complemented
213	#2581	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#2580	C₂×C₁₁	1	1	yes	characteristic
215	#2574	C₂×C₁₁	1	4	yes	complemented
216	#2465	C₂×C₁₁	1	4	yes	complemented
217	#2452	C₂×C₁₁	1	2	yes	—
218	#2451	C₂×C₁₁	1	2	yes	complemented
219	#2368	C₂×C₁₁	1	4	yes	complemented
220	#2351	C₂×C₁₁	1	1	yes	characteristic, complemented
221	#2349	C₂×C₁₁	1	1	yes	characteristic
222	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
223	C₄×#124	C₂×C₁₁	1	2	yes	—
224	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
225	C₂³×C₁₁	—	2	4	no	—
226	C₂³×C₁₁	—	2	2	no	—
227	C₂³×C₁₁	—	2	2	no	—
228	C₂³×C₁₁	—	2	4	no	—
229	C₂³×C₁₁	C₂²×Q₈	1	4	yes	—
230	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
231	Q₈×C₁₁	—	2	8	no	—
232	Q₈×C₁₁	—	2	8	no	—
233	Q₈×C₁₁	—	8	8	no	—
234	D₄×C₁₁	—	2	8	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	2	2	no	—
240	C₂×C₄×C₁₁	—	2	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	2	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	2	no	—
248	C₂×C₄×C₁₁	—	2	2	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	4	no	—
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	4	no	—
253	C₂×C₄×C₁₁	—	2	4	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	2	no	—
259	C₂×C₄×C₁₁	—	2	2	no	—
260	C₂×C₄×C₁₁	—	2	4	no	—
261	C₂×C₄×C₁₁	—	2	4	no	—
262	C₂×C₄×C₁₁	—	2	4	no	—
263	C₂×C₄×C₁₁	—	8	4	no	—
264	C₂×C₄×C₁₁	—	8	8	no	—
265	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
266	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
267	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
268	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
269	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
270	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
271	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
272	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
276	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
277	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
278	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
281	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
282	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
284	#400	C₂²×C₁₁	1	2	yes	—
285	#399	C₂²×C₁₁	1	2	yes	—
286	#398	C₂²×C₁₁	1	4	yes	—
287	#396	C₂²×C₁₁	1	4	yes	—
288	#395	C₂²×C₁₁	1	4	yes	—
289	#395	C₂²×C₁₁	1	2	yes	—
290	#393	C₂²×C₁₁	1	4	yes	—
291	#393	C₂²×C₁₁	1	2	yes	—
292	#391	C₂²×C₁₁	1	4	yes	—
293	#391	C₂²×C₁₁	1	2	yes	—
294	#391	C₂²×C₁₁	1	4	yes	—
295	#391	C₂²×C₁₁	1	4	yes	—
296	#391	C₂²×C₁₁	1	1	yes	characteristic
297	#390	C₂²×C₁₁	1	2	yes	—
298	#390	C₂²×C₁₁	1	1	yes	characteristic
299	#389	C₂²×C₁₁	1	2	yes	—
300	#389	C₂²×C₁₁	1	2	yes	—
301	#389	C₂²×C₁₁	1	4	yes	—
302	#389	C₂²×C₁₁	1	2	yes	—
303	#389	C₂²×C₁₁	1	2	yes	—
304	#388	C₂²×C₁₁	1	4	yes	—
305	#388	C₂²×C₁₁	1	4	yes	—
306	#388	C₂²×C₁₁	1	4	yes	—
307	#387	C₂²×C₁₁	1	4	yes	—
308	#387	C₂²×C₁₁	1	4	yes	—
309	#387	C₂²×C₁₁	1	4	yes	—
310	#387	C₂²×C₁₁	1	4	yes	—
311	#387	C₂²×C₁₁	1	4	yes	—
312	#387	C₂²×C₁₁	1	4	yes	—
313	#385	C₂²×C₁₁	1	4	yes	—
314	#385	C₂²×C₁₁	1	4	yes	—
315	#385	C₂²×C₁₁	1	4	yes	—
316	#382	C₂²×C₁₁	1	2	yes	—
317	#382	C₂²×C₁₁	1	1	yes	characteristic
318	#382	C₂²×C₁₁	1	1	yes	characteristic
319	#382	C₂²×C₁₁	1	2	yes	—
320	#382	C₂²×C₁₁	1	1	yes	characteristic
321	#380	C₂²×C₁₁	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
329	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
331	C₂×#95	C₂²×C₁₁	1	2	yes	—
332	C₄³	C₂²×C₁₁	1	1	yes	characteristic
333	C₄³	C₂²×C₁₁	1	2	yes	—
334	C₂²×C₁₁	—	2	4	no	—
335	C₂²×C₁₁	—	2	8	no	—
336	C₂²×C₁₁	—	4	2	no	—
337	C₂²×C₁₁	—	4	2	no	—
338	C₂²×C₁₁	—	4	4	no	—
339	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
340	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₁₁	C₂²×#41	1	2	yes	—
342	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₁₁	#585	1	2	yes	—
344	C₄×C₁₁	—	2	4	no	—
345	C₄×C₁₁	—	2	2	no	—
346	C₄×C₁₁	—	2	4	no	—
347	C₄×C₁₁	—	2	4	no	—
348	C₄×C₁₁	—	2	2	no	—
349	C₄×C₁₁	—	2	4	no	—
350	C₄×C₁₁	—	2	4	no	—
351	C₄×C₁₁	—	4	2	no	—
352	C₄×C₁₁	—	4	2	no	—
353	C₄×C₁₁	—	4	2	no	—
354	C₄×C₁₁	—	4	2	no	—
355	C₄×C₁₁	—	4	4	no	—
356	C₄×C₁₁	—	4	4	no	—
357	C₄×C₁₁	#554	1	4	yes	—
358	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
361	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
363	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
364	C₄⋊Q₈	—	4	4	no	—
365	#124	Q₈×C₁₁	1	8	yes	complemented
366	C₂²⋊Q₈	—	2	16	no	—
367	C₄×Q₈	—	2	8	no	—
368	C₄×Q₈	—	2	4	no	—
369	C₄×Q₈	—	2	4	no	—
370	C₄×Q₈	—	4	4	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	4	4	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
395	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
397	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
400	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
408	#95	C₂³×C₁₁	1	1	yes	characteristic
409	#95	C₂³×C₁₁	1	2	yes	—
410	#95	C₂³×C₁₁	1	4	yes	—
411	#95	C₂³×C₁₁	1	4	yes	—
412	#95	C₂³×C₁₁	1	4	yes	—
413	#95	C₂³×C₁₁	1	4	yes	—
414	#95	C₂³×C₁₁	1	4	yes	—
415	#95	C₂³×C₁₁	1	4	yes	—
416	#95	C₂³×C₁₁	1	4	yes	—
417	#95	C₂³×C₁₁	1	1	yes	characteristic
418	#95	C₂³×C₁₁	1	2	yes	—
419	#95	C₂³×C₁₁	1	2	yes	—
420	#95	C₂³×C₁₁	1	2	yes	—
421	#95	C₂³×C₁₁	1	2	yes	—
422	#95	C₂³×C₁₁	1	4	yes	—
423	#95	C₂³×C₁₁	1	2	yes	—
424	#95	C₂³×C₁₁	1	4	yes	—
425	#95	C₂³×C₁₁	1	4	yes	—
426	C₂×C₁₁	—	4	4	no	—
427	C₂×C₁₁	#3444	1	1	yes	characteristic
428	C₂×C₁₁	C₂×#554	1	1	yes	characteristic
429	C₂×C₁₁	Q₈×#41	1	2	yes	—
430	C₂×C₁₁	#3510	1	1	yes	characteristic
431	C₂×C₁₁	#3514	1	2	yes	—
432	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	C₂×Q₈×C₁₁	1	4	yes	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	C₁₁×#41	1	8	yes	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	C₂×Q₈×C₁₁	1	16	yes	—
485	C₄²	—	2	4	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	4	4	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	2	no	—
495	C₄²	—	4	2	no	—
496	C₄²	C₂×Q₈×C₁₁	1	4	yes	—
497	C₄²	C₁₁×#41	1	4	yes	—
498	C₁₁	#36566	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	4	no	—
503	C₂³	C₂²×Q₈×C₁₁	1	4	yes	—
504	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
505	Q₈	—	2	8	no	—
506	Q₈	—	2	8	no	—
507	Q₈	—	8	8	no	—
508	D₄	—	2	8	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	—	8	8	no	—
539	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
540	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
541	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
542	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
543	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
544	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
545	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
546	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
547	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
548	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	C₂³×Q₈×C₁₁	1	1	yes	characteristic
555	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
556	C₂²	C₂²×C₁₁×#41	1	2	yes	—
557	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂²	C₁₁×#585	1	2	yes	—
559	C₄	—	2	4	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	4	no	—
562	C₄	—	2	4	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	2	no	—
572	C₄	C₁₁×#554	1	4	yes	—
573	C₂	—	4	4	no	—
574	C₂	C₁₁×#3444	1	1	yes	characteristic
575	C₂	C₂×C₁₁×#554	1	1	yes	characteristic
576	C₂	Q₈×C₁₁×#41	1	2	yes	—
577	C₂	C₁₁×#3510	1	1	yes	characteristic
578	C₂	C₁₁×#3514	1	2	yes	—

	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×#2862	C₂	semidirect
3. C₁₁×#2589	C₂	semidirect
4. C₁₁×#2581	C₂	semidirect
6. C₁₁×#2574	C₂	semidirect
7. C₁₁×#2465	C₂	semidirect
9. C₁₁×#2451	C₂	semidirect
10. C₁₁×#2368	C₂	semidirect
11. C₁₁×#2351	C₂	semidirect
15. C₄²×Q₈×C₁₁	C₂	semidirect
82. C₁₁×#124	Q₈	semidirect
143. #36566	C₁₁	direct (N × H)
210. #2864	C₂×C₁₁	semidirect
211. #2862	C₂×C₁₁	semidirect
212. #2589	C₂×C₁₁	semidirect
213. #2581	C₂×C₁₁	semidirect
215. #2574	C₂×C₁₁	semidirect
216. #2465	C₂×C₁₁	semidirect
218. #2451	C₂×C₁₁	semidirect
219. #2368	C₂×C₁₁	semidirect
220. #2351	C₂×C₁₁	semidirect
224. C₄²×Q₈	C₂×C₁₁	semidirect
365. #124	Q₈×C₁₁	semidirect
498. C₁₁	#36566	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×#2862	2
C₁₁×#2589	2
C₁₁×#2581	2
C₁₁×#2580	2
C₁₁×#2574	2
C₁₁×#2465	2
C₁₁×#2452	2
C₁₁×#2451	2
C₁₁×#2368	2
C₁₁×#2351	2
C₁₁×#2349	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36566	11

Subgroups — C11×#36566 #14613759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36566 #14613759