Subgroups — C₁₁×#36562 #14613755

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#554	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2859	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2567	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2566	C₂	1	2	yes	maximal
7	C₁₁×#2565	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2556	C₂	1	8	yes	maximal, complemented
9	C₁₁×#2542	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#2429	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2360	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₁×#124	C₂	1	2	yes	maximal
13	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
14	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#557	—	2	8	no	—
16	C₁₁×#554	—	2	8	no	—
17	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#125	C₂²	1	2	yes	—
21	C₂×C₁₁×#125	C₂²	1	4	yes	—
22	C₂×C₁₁×#125	C₂²	1	2	yes	—
23	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
34	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₁×#399	C₂²	1	4	yes	—
36	C₁₁×#398	C₂²	1	8	yes	—
37	C₁₁×#396	C₂²	1	8	yes	—
38	C₁₁×#395	C₂²	1	4	yes	—
39	C₁₁×#391	C₂²	1	4	yes	—
40	C₁₁×#391	C₂²	1	4	yes	—
41	C₁₁×#391	C₂²	1	1	yes	characteristic
42	C₁₁×#391	C₂²	1	2	yes	—
43	C₁₁×#390	C₂²	1	2	yes	—
44	C₁₁×#390	C₂²	1	1	yes	characteristic
45	C₁₁×#389	C₂²	1	8	yes	—
46	C₁₁×#389	C₂²	1	4	yes	—
47	C₁₁×#389	C₂²	1	8	yes	—
48	C₁₁×#388	C₂²	1	8	yes	—
49	C₁₁×#388	C₂²	1	4	yes	—
50	C₁₁×#387	C₂²	1	8	yes	—
51	C₁₁×#385	C₂²	1	8	yes	—
52	C₁₁×#384	C₂²	1	2	yes	—
53	C₁₁×#384	C₂²	1	2	yes	—
54	C₁₁×#382	C₂²	1	1	yes	characteristic
55	C₁₁×#382	C₂²	1	2	yes	—
56	C₁₁×#382	C₂²	1	2	yes	—
57	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
60	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	—
63	C₄³×C₁₁	C₂²	1	2	yes	—
64	C₄³×C₁₁	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
72	C₁₁×C₄⋊Q₈	—	2	8	no	—
73	C₁₁×C₄⋊Q₈	—	2	4	no	—
74	C₁₁×C₄⋊Q₈	—	2	4	no	—
75	C₁₁×#125	—	2	16	no	—
76	C₁₁×#125	—	2	8	no	—
77	C₁₁×#125	—	2	8	no	—
78	C₁₁×#124	Q₈	1	8	yes	complemented
79	C₁₁×C₂²⋊Q₈	—	2	8	no	—
80	C₁₁×C₂²⋊Q₈	—	2	16	no	—
81	C₁₁×C₂²⋊Q₈	—	2	16	no	—
82	C₄×Q₈×C₁₁	—	2	8	no	—
83	C₄×Q₈×C₁₁	—	2	8	no	—
84	C₄×Q₈×C₁₁	—	2	8	no	—
85	C₄×Q₈×C₁₁	—	2	4	no	—
86	C₄×Q₈×C₁₁	D₄	1	8	yes	—
87	C₄×D₄×C₁₁	—	2	8	no	—
88	C₄×D₄×C₁₁	—	2	4	no	—
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	2	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	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	2	yes	—
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
124	C₁₁×#95	C₂³	1	4	yes	—
125	C₁₁×#95	C₂³	1	8	yes	—
126	C₁₁×#95	C₂³	1	4	yes	—
127	C₁₁×#95	C₂³	1	8	yes	—
128	C₁₁×#95	C₂³	1	4	yes	—
129	C₁₁×#95	C₂³	1	2	yes	—
130	C₁₁×#95	C₂³	1	8	yes	—
131	#36562	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
133	C₂×Q₈×C₁₁	—	2	2	no	—
134	C₂×Q₈×C₁₁	—	2	4	no	—
135	C₂×Q₈×C₁₁	—	2	4	no	—
136	C₂×Q₈×C₁₁	—	2	4	no	—
137	C₂×Q₈×C₁₁	—	2	8	no	—
138	C₂×Q₈×C₁₁	—	2	2	no	—
139	C₂×Q₈×C₁₁	—	4	4	no	—
140	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₁₁	C₂×Q₈	1	4	yes	—
142	C₂×D₄×C₁₁	—	2	2	no	—
143	C₂×D₄×C₁₁	—	2	2	no	—
144	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	—
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	—	4	8	no	—
149	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
162	C₁₁×C₄⋊C₄	—	2	8	no	—
163	C₁₁×C₄⋊C₄	—	2	4	no	—
164	C₁₁×C₄⋊C₄	—	2	2	no	—
165	C₁₁×C₄⋊C₄	—	2	4	no	—
166	C₁₁×C₄⋊C₄	—	2	4	no	—
167	C₁₁×C₄⋊C₄	—	2	2	no	—
168	C₁₁×C₄⋊C₄	—	2	8	no	—
169	C₁₁×C₄⋊C₄	—	2	8	no	—
170	C₁₁×C₄⋊C₄	—	2	4	no	—
171	C₁₁×C₄⋊C₄	—	2	8	no	—
172	C₁₁×C₄⋊C₄	—	2	8	no	—
173	C₁₁×C₄⋊C₄	—	2	4	no	—
174	C₁₁×C₄⋊C₄	—	2	8	no	—
175	C₁₁×C₄⋊C₄	—	2	16	no	—
176	C₁₁×C₄⋊C₄	—	4	8	no	—
177	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
179	C₁₁×C₄⋊C₄	#41	1	8	yes	—
180	C₁₁×C₂²⋊C₄	—	2	4	no	—
181	C₁₁×C₂²⋊C₄	—	2	8	no	—
182	C₁₁×C₂²⋊C₄	—	2	16	no	—
183	C₁₁×C₂²⋊C₄	—	4	4	no	—
184	C₁₁×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
185	C₄²×C₁₁	—	2	8	no	—
186	C₄²×C₁₁	—	2	4	no	—
187	C₄²×C₁₁	—	2	8	no	—
188	C₄²×C₁₁	—	2	4	no	—
189	C₄²×C₁₁	—	2	4	no	—
190	C₄²×C₁₁	—	2	2	no	—
191	C₄²×C₁₁	—	4	4	no	—
192	C₄²×C₁₁	—	4	2	no	—
193	C₄²×C₁₁	C₂×D₄	1	8	yes	—
194	C₄²×C₁₁	C₂×D₄	1	4	yes	—
195	C₄²×C₁₁	C₂×Q₈	1	4	yes	—
196	C₂×#557	C₂×C₁₁	1	1	yes	characteristic, complemented
197	C₂×#554	C₂×C₁₁	1	1	yes	characteristic
198	#2862	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#2859	C₂×C₁₁	1	2	yes	complemented
200	#2567	C₂×C₁₁	1	1	yes	characteristic, complemented
201	#2566	C₂×C₁₁	1	2	yes	—
202	#2565	C₂×C₁₁	1	2	yes	complemented
203	#2556	C₂×C₁₁	1	8	yes	complemented
204	#2542	C₂×C₁₁	1	1	yes	characteristic
205	#2429	C₂×C₁₁	1	4	yes	complemented
206	#2360	C₂×C₁₁	1	4	yes	complemented
207	C₄×#124	C₂×C₁₁	1	2	yes	—
208	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
209	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
210	C₂³×C₁₁	—	2	2	no	—
211	C₂³×C₁₁	—	2	4	no	—
212	C₂³×C₁₁	—	2	2	no	—
213	C₂³×C₁₁	—	2	4	no	—
214	C₂³×C₁₁	C₂²×Q₈	1	4	yes	—
215	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
216	Q₈×C₁₁	—	2	8	no	—
217	Q₈×C₁₁	—	2	8	no	—
218	Q₈×C₁₁	—	4	8	no	—
219	Q₈×C₁₁	—	8	4	no	—
220	D₄×C₁₁	—	2	8	no	—
221	C₂×C₄×C₁₁	—	2	2	no	—
222	C₂×C₄×C₁₁	—	2	2	no	—
223	C₂×C₄×C₁₁	—	2	4	no	—
224	C₂×C₄×C₁₁	—	2	4	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	2	2	no	—
227	C₂×C₄×C₁₁	—	2	4	no	—
228	C₂×C₄×C₁₁	—	2	4	no	—
229	C₂×C₄×C₁₁	—	2	2	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	2	no	—
235	C₂×C₄×C₁₁	—	2	8	no	—
236	C₂×C₄×C₁₁	—	2	4	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	8	no	—
241	C₂×C₄×C₁₁	—	4	8	no	—
242	C₂×C₄×C₁₁	—	8	8	no	—
243	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
249	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
250	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
251	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
252	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
253	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
254	#557	—	2	8	no	—
255	#554	—	2	8	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
259	C₂×#125	C₂²×C₁₁	1	2	yes	—
260	C₂×#125	C₂²×C₁₁	1	2	yes	—
261	C₂×#125	C₂²×C₁₁	1	4	yes	—
262	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
266	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
267	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
270	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
272	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
274	#399	C₂²×C₁₁	1	4	yes	—
275	#398	C₂²×C₁₁	1	8	yes	—
276	#396	C₂²×C₁₁	1	8	yes	—
277	#395	C₂²×C₁₁	1	4	yes	—
278	#391	C₂²×C₁₁	1	1	yes	characteristic
279	#391	C₂²×C₁₁	1	2	yes	—
280	#391	C₂²×C₁₁	1	4	yes	—
281	#391	C₂²×C₁₁	1	4	yes	—
282	#390	C₂²×C₁₁	1	1	yes	characteristic
283	#390	C₂²×C₁₁	1	2	yes	—
284	#389	C₂²×C₁₁	1	4	yes	—
285	#389	C₂²×C₁₁	1	8	yes	—
286	#389	C₂²×C₁₁	1	8	yes	—
287	#388	C₂²×C₁₁	1	8	yes	—
288	#388	C₂²×C₁₁	1	4	yes	—
289	#387	C₂²×C₁₁	1	8	yes	—
290	#385	C₂²×C₁₁	1	8	yes	—
291	#384	C₂²×C₁₁	1	2	yes	—
292	#384	C₂²×C₁₁	1	2	yes	—
293	#382	C₂²×C₁₁	1	2	yes	—
294	#382	C₂²×C₁₁	1	1	yes	characteristic
295	#382	C₂²×C₁₁	1	2	yes	—
296	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
300	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	—
302	C₄³	C₂²×C₁₁	1	2	yes	—
303	C₄³	C₂²×C₁₁	1	1	yes	characteristic
304	C₂²×C₁₁	—	2	4	no	—
305	C₂²×C₁₁	—	2	8	no	—
306	C₂²×C₁₁	—	4	2	no	—
307	C₂²×C₁₁	—	4	2	no	—
308	C₂²×C₁₁	—	4	4	no	—
309	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
310	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
311	C₂²×C₁₁	C₂²×#41	1	2	yes	—
312	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂²×C₁₁	#585	1	2	yes	—
314	C₄×C₁₁	—	2	4	no	—
315	C₄×C₁₁	—	2	4	no	—
316	C₄×C₁₁	—	2	4	no	—
317	C₄×C₁₁	—	2	4	no	—
318	C₄×C₁₁	—	2	2	no	—
319	C₄×C₁₁	—	2	8	no	—
320	C₄×C₁₁	—	4	2	no	—
321	C₄×C₁₁	—	4	4	no	—
322	C₄×C₁₁	—	4	2	no	—
323	C₄×C₁₁	—	4	4	no	—
324	C₄×C₁₁	—	4	2	no	—
325	C₄×C₁₁	#532	1	4	yes	—
326	C₄×C₁₁	D₄×Q₈	1	4	yes	—
327	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
328	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
333	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
334	C₄⋊Q₈	—	2	8	no	—
335	C₄⋊Q₈	—	2	4	no	—
336	C₄⋊Q₈	—	2	4	no	—
337	#125	—	2	16	no	—
338	#125	—	2	8	no	—
339	#125	—	2	8	no	—
340	#124	Q₈×C₁₁	1	8	yes	complemented
341	C₂²⋊Q₈	—	2	8	no	—
342	C₂²⋊Q₈	—	2	16	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₄×Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	8	no	—
346	C₄×Q₈	—	2	8	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	D₄×C₁₁	1	8	yes	—
349	C₄×D₄	—	2	8	no	—
350	C₄×D₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	8	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
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	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
375	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
376	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
377	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
378	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
379	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
381	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
382	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
386	#95	C₂³×C₁₁	1	4	yes	—
387	#95	C₂³×C₁₁	1	8	yes	—
388	#95	C₂³×C₁₁	1	4	yes	—
389	#95	C₂³×C₁₁	1	8	yes	—
390	#95	C₂³×C₁₁	1	4	yes	—
391	#95	C₂³×C₁₁	1	2	yes	—
392	#95	C₂³×C₁₁	1	8	yes	—
393	C₂×C₁₁	—	4	4	no	—
394	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
395	C₂×C₁₁	C₂×D₄×Q₈	1	1	yes	characteristic
396	C₂×C₁₁	Q₈×#41	1	2	yes	—
397	C₂×C₁₁	#3500	1	1	yes	characteristic
398	C₂×C₁₁	#3515	1	2	yes	—
399	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
408	C₂×Q₈	C₂×Q₈×C₁₁	1	4	yes	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	4	8	no	—
416	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	16	no	—
443	C₄⋊C₄	—	4	8	no	—
444	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
446	C₄⋊C₄	C₁₁×#41	1	8	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	16	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	C₂×Q₈×C₁₁	1	16	yes	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	2	8	no	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	4	no	—
459	C₄²	—	4	2	no	—
460	C₄²	C₂×D₄×C₁₁	1	8	yes	—
461	C₄²	C₂×D₄×C₁₁	1	4	yes	—
462	C₄²	C₂×Q₈×C₁₁	1	4	yes	—
463	C₁₁	#36562	1	1	yes	characteristic, direct product factor, Sylow
464	C₂³	—	2	2	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	C₂²×Q₈×C₁₁	1	4	yes	—
469	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
470	Q₈	—	2	8	no	—
471	Q₈	—	2	8	no	—
472	Q₈	—	4	8	no	—
473	Q₈	—	8	4	no	—
474	D₄	—	2	8	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	8	8	no	—
497	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
498	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
499	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
502	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
503	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
504	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
505	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
506	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
507	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
514	C₂²	C₂³×Q₈×C₁₁	1	1	yes	characteristic
515	C₂²	C₂²×C₁₁×#41	1	2	yes	—
516	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
517	C₂²	C₁₁×#585	1	2	yes	—
518	C₄	—	2	4	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	8	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₁₁×#532	1	4	yes	—
530	C₄	D₄×Q₈×C₁₁	1	4	yes	—
531	C₂	—	4	4	no	—
532	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
533	C₂	C₂×D₄×Q₈×C₁₁	1	1	yes	characteristic
534	C₂	Q₈×C₁₁×#41	1	2	yes	—
535	C₂	C₁₁×#3500	1	1	yes	characteristic
536	C₂	C₁₁×#3515	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. C₂×C₁₁×#557	C₂	semidirect
3. C₁₁×#2862	C₂	semidirect
4. C₁₁×#2859	C₂	semidirect
5. C₁₁×#2567	C₂	semidirect
7. C₁₁×#2565	C₂	semidirect
8. C₁₁×#2556	C₂	semidirect
10. C₁₁×#2429	C₂	semidirect
11. C₁₁×#2360	C₂	semidirect
14. C₄²×Q₈×C₁₁	C₂	semidirect
78. C₁₁×#124	Q₈	semidirect
131. #36562	C₁₁	direct (N × H)
196. C₂×#557	C₂×C₁₁	semidirect
198. #2862	C₂×C₁₁	semidirect
199. #2859	C₂×C₁₁	semidirect
200. #2567	C₂×C₁₁	semidirect
202. #2565	C₂×C₁₁	semidirect
203. #2556	C₂×C₁₁	semidirect
205. #2429	C₂×C₁₁	semidirect
206. #2360	C₂×C₁₁	semidirect
209. C₄²×Q₈	C₂×C₁₁	semidirect
340. #124	Q₈×C₁₁	semidirect
463. C₁₁	#36562	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×#557	2
C₂×C₁₁×#554	2
C₁₁×#2862	2
C₁₁×#2859	2
C₁₁×#2567	2
C₁₁×#2566	2
C₁₁×#2565	2
C₁₁×#2556	2
C₁₁×#2542	2
C₁₁×#2429	2
C₁₁×#2360	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36562	11

Subgroups — C11×#36562 #14613755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36562 #14613755