Subgroups — C₁₁×#59951 #14637144

Order 2816.

1664 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2769	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2731	C₂	1	2	yes	maximal
3	C₁₁×#2593	C₂	1	2	yes	maximal
4	C₁₁×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2532	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2529	C₂	1	4	yes	maximal, complemented
8	C₁₁×#2492	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2429	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2415	C₂	1	2	yes	maximal
11	C₁₁×#2369	C₂	1	2	yes	maximal, complemented
12	C₁₁×#2362	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2347	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
15	C₁₁×#2295	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#117	C₂²	1	2	yes	—
26	C₁₁×#400	C₂²	1	4	yes	—
27	C₁₁×#400	C₂²	1	2	yes	—
28	C₁₁×#400	C₂²	1	2	yes	—
29	C₁₁×#398	C₂²	1	4	yes	—
30	C₁₁×#398	C₂²	1	2	yes	—
31	C₁₁×#398	C₂²	1	2	yes	—
32	C₁₁×#397	C₂²	1	4	yes	—
33	C₁₁×#396	C₂²	1	4	yes	—
34	C₁₁×#394	C₂²	1	4	yes	—
35	C₁₁×#393	C₂²	1	4	yes	—
36	C₁₁×#391	C₂²	1	2	yes	—
37	C₁₁×#391	C₂²	1	2	yes	—
38	C₁₁×#391	C₂²	1	2	yes	—
39	C₁₁×#391	C₂²	1	4	yes	—
40	C₁₁×#391	C₂²	1	2	yes	—
41	C₁₁×#391	C₂²	1	2	yes	—
42	C₁₁×#391	C₂²	1	1	yes	characteristic
43	C₁₁×#390	C₂²	1	1	yes	characteristic
44	C₁₁×#389	C₂²	1	4	yes	—
45	C₁₁×#389	C₂²	1	2	yes	—
46	C₁₁×#389	C₂²	1	4	yes	—
47	C₁₁×#389	C₂²	1	2	yes	—
48	C₁₁×#389	C₂²	1	2	yes	—
49	C₁₁×#388	C₂²	1	4	yes	—
50	C₁₁×#388	C₂²	1	4	yes	—
51	C₁₁×#388	C₂²	1	4	yes	—
52	C₁₁×#388	C₂²	1	4	yes	—
53	C₁₁×#388	C₂²	1	4	yes	—
54	C₁₁×#388	C₂²	1	2	yes	—
55	C₁₁×#388	C₂²	1	4	yes	—
56	C₁₁×#388	C₂²	1	2	yes	—
57	C₁₁×#388	C₂²	1	4	yes	—
58	C₁₁×#387	C₂²	1	4	yes	—
59	C₁₁×#387	C₂²	1	4	yes	—
60	C₁₁×#387	C₂²	1	4	yes	—
61	C₁₁×#383	C₂²	1	4	yes	—
62	C₁₁×#382	C₂²	1	1	yes	characteristic
63	C₁₁×#382	C₂²	1	2	yes	—
64	C₁₁×#380	C₂²	1	2	yes	—
65	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
68	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₁₁×#376	C₂²	1	4	yes	—
74	C₄³×C₁₁	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
76	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
77	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
80	C₁₁×C₄⋊Q₈	—	2	8	no	—
81	C₁₁×C₄⋊Q₈	—	4	2	no	—
82	C₁₁×C₄⋊Q₈	—	4	2	no	—
83	C₁₁×#124	—	2	4	no	—
84	C₁₁×C₂²⋊Q₈	—	2	8	no	—
85	C₁₁×C₂²⋊Q₈	—	4	4	no	—
86	C₄×Q₈×C₁₁	—	2	8	no	—
87	C₄×Q₈×C₁₁	—	4	2	no	—
88	C₄×D₄×C₁₁	—	4	2	no	—
89	C₁₁×#117	—	2	8	no	—
90	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	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	2	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	2	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
113	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₁	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	2	yes	—
132	C₁₁×#95	C₂³	1	2	yes	—
133	C₁₁×#95	C₂³	1	2	yes	—
134	C₁₁×#95	C₂³	1	2	yes	—
135	C₁₁×#95	C₂³	1	4	yes	—
136	C₁₁×#95	C₂³	1	2	yes	—
137	C₁₁×#95	C₂³	1	4	yes	—
138	C₁₁×#95	C₂³	1	2	yes	—
139	C₁₁×#95	C₂³	1	4	yes	—
140	C₁₁×#95	C₂³	1	4	yes	—
141	C₁₁×#95	C₂³	1	4	yes	—
142	C₁₁×#95	C₂³	1	4	yes	—
143	C₁₁×#95	C₂³	1	4	yes	—
144	#59951	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
146	C₂×Q₈×C₁₁	—	2	4	no	—
147	C₂×Q₈×C₁₁	—	2	4	no	—
148	C₂×Q₈×C₁₁	—	2	4	no	—
149	C₂×Q₈×C₁₁	—	2	4	no	—
150	C₂×Q₈×C₁₁	—	4	1	no	—
151	C₂×Q₈×C₁₁	—	4	1	no	—
152	C₂×Q₈×C₁₁	—	4	2	no	—
153	C₂×Q₈×C₁₁	—	4	2	no	—
154	C₂×Q₈×C₁₁	#41	1	4	yes	—
155	C₂×D₄×C₁₁	—	2	2	no	—
156	C₂×D₄×C₁₁	—	4	1	no	—
157	C₂×D₄×C₁₁	—	4	1	no	—
158	C₂²×C₄×C₁₁	—	2	4	no	—
159	C₂²×C₄×C₁₁	—	2	4	no	—
160	C₂²×C₄×C₁₁	—	2	4	no	—
161	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	4	no	—
176	C₁₁×C₄⋊C₄	—	2	8	no	—
177	C₁₁×C₄⋊C₄	—	2	8	no	—
178	C₁₁×C₄⋊C₄	—	2	8	no	—
179	C₁₁×C₄⋊C₄	—	2	8	no	—
180	C₁₁×C₄⋊C₄	—	2	4	no	—
181	C₁₁×C₄⋊C₄	—	2	8	no	—
182	C₁₁×C₄⋊C₄	—	4	1	no	—
183	C₁₁×C₄⋊C₄	—	4	1	no	—
184	C₁₁×C₄⋊C₄	—	4	1	no	—
185	C₁₁×C₄⋊C₄	—	4	1	no	—
186	C₁₁×C₄⋊C₄	—	4	4	no	—
187	C₁₁×C₄⋊C₄	—	4	2	no	—
188	C₁₁×C₄⋊C₄	—	4	2	no	—
189	C₁₁×C₄⋊C₄	—	4	2	no	—
190	C₁₁×C₄⋊C₄	#41	1	8	yes	—
191	C₁₁×C₂²⋊C₄	—	2	8	no	—
192	C₁₁×C₂²⋊C₄	—	2	8	no	—
193	C₁₁×C₂²⋊C₄	—	2	4	no	—
194	C₁₁×C₂²⋊C₄	—	2	4	no	—
195	C₁₁×C₂²⋊C₄	—	2	4	no	—
196	C₁₁×C₂²⋊C₄	—	2	4	no	—
197	C₁₁×C₂²⋊C₄	—	4	4	no	—
198	C₁₁×C₂²⋊C₄	—	4	2	no	—
199	C₁₁×C₂²⋊C₄	—	4	4	no	—
200	C₄²×C₁₁	—	2	8	no	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	—	2	8	no	—
203	C₄²×C₁₁	—	2	2	no	—
204	C₄²×C₁₁	—	2	4	no	—
205	C₄²×C₁₁	—	2	2	no	—
206	C₄²×C₁₁	—	2	2	no	—
207	C₄²×C₁₁	—	2	2	no	—
208	C₄²×C₁₁	—	2	4	no	—
209	C₄²×C₁₁	—	4	1	no	—
210	C₄²×C₁₁	—	4	4	no	—
211	C₄²×C₁₁	—	4	2	no	—
212	#2769	C₂×C₁₁	1	2	yes	complemented
213	#2731	C₂×C₁₁	1	2	yes	—
214	#2593	C₂×C₁₁	1	2	yes	—
215	#2568	C₂×C₁₁	1	1	yes	characteristic, complemented
216	#2546	C₂×C₁₁	1	1	yes	characteristic, complemented
217	#2532	C₂×C₁₁	1	4	yes	complemented
218	#2529	C₂×C₁₁	1	4	yes	complemented
219	#2492	C₂×C₁₁	1	2	yes	complemented
220	#2429	C₂×C₁₁	1	2	yes	complemented
221	#2415	C₂×C₁₁	1	2	yes	—
222	#2369	C₂×C₁₁	1	2	yes	complemented
223	#2362	C₂×C₁₁	1	2	yes	complemented
224	#2347	C₂×C₁₁	1	2	yes	complemented
225	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
226	#2295	C₂×C₁₁	1	2	yes	complemented
227	C₂³×C₁₁	—	2	2	no	—
228	C₂³×C₁₁	—	2	2	no	—
229	C₂³×C₁₁	—	2	2	no	—
230	C₂³×C₁₁	—	2	2	no	—
231	C₂³×C₁₁	—	2	2	no	—
232	C₂³×C₁₁	—	2	2	no	—
233	C₂³×C₁₁	—	2	2	no	—
234	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
235	Q₈×C₁₁	—	4	4	no	—
236	Q₈×C₁₁	—	4	8	no	—
237	Q₈×C₁₁	—	8	4	no	—
238	D₄×C₁₁	—	4	4	no	—
239	C₂×C₄×C₁₁	—	2	2	no	—
240	C₂×C₄×C₁₁	—	2	4	no	—
241	C₂×C₄×C₁₁	—	2	1	no	—
242	C₂×C₄×C₁₁	—	2	1	no	—
243	C₂×C₄×C₁₁	—	2	1	no	—
244	C₂×C₄×C₁₁	—	2	4	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	1	no	—
247	C₂×C₄×C₁₁	—	2	1	no	—
248	C₂×C₄×C₁₁	—	2	1	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	2	4	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	4	no	—
254	C₂×C₄×C₁₁	—	2	4	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	2	1	no	—
258	C₂×C₄×C₁₁	—	2	1	no	—
259	C₂×C₄×C₁₁	—	2	1	no	—
260	C₂×C₄×C₁₁	—	2	4	no	—
261	C₂×C₄×C₁₁	—	2	2	no	—
262	C₂×C₄×C₁₁	—	2	4	no	—
263	C₂×C₄×C₁₁	—	2	2	no	—
264	C₂×C₄×C₁₁	—	2	2	no	—
265	C₂×C₄×C₁₁	—	2	2	no	—
266	C₂×C₄×C₁₁	—	2	2	no	—
267	C₂×C₄×C₁₁	—	2	4	no	—
268	C₂×C₄×C₁₁	—	2	4	no	—
269	C₂×C₄×C₁₁	—	2	4	no	—
270	C₂×C₄×C₁₁	—	4	8	no	—
271	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
272	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
276	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
278	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
279	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
284	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₁	1	2	yes	—
288	#400	C₂²×C₁₁	1	2	yes	—
289	#400	C₂²×C₁₁	1	2	yes	—
290	#400	C₂²×C₁₁	1	4	yes	—
291	#398	C₂²×C₁₁	1	2	yes	—
292	#398	C₂²×C₁₁	1	4	yes	—
293	#398	C₂²×C₁₁	1	2	yes	—
294	#397	C₂²×C₁₁	1	4	yes	—
295	#396	C₂²×C₁₁	1	4	yes	—
296	#394	C₂²×C₁₁	1	4	yes	—
297	#393	C₂²×C₁₁	1	4	yes	—
298	#391	C₂²×C₁₁	1	2	yes	—
299	#391	C₂²×C₁₁	1	2	yes	—
300	#391	C₂²×C₁₁	1	2	yes	—
301	#391	C₂²×C₁₁	1	1	yes	characteristic
302	#391	C₂²×C₁₁	1	4	yes	—
303	#391	C₂²×C₁₁	1	2	yes	—
304	#391	C₂²×C₁₁	1	2	yes	—
305	#390	C₂²×C₁₁	1	1	yes	characteristic
306	#389	C₂²×C₁₁	1	2	yes	—
307	#389	C₂²×C₁₁	1	2	yes	—
308	#389	C₂²×C₁₁	1	4	yes	—
309	#389	C₂²×C₁₁	1	4	yes	—
310	#389	C₂²×C₁₁	1	2	yes	—
311	#388	C₂²×C₁₁	1	4	yes	—
312	#388	C₂²×C₁₁	1	4	yes	—
313	#388	C₂²×C₁₁	1	4	yes	—
314	#388	C₂²×C₁₁	1	4	yes	—
315	#388	C₂²×C₁₁	1	4	yes	—
316	#388	C₂²×C₁₁	1	4	yes	—
317	#388	C₂²×C₁₁	1	4	yes	—
318	#388	C₂²×C₁₁	1	2	yes	—
319	#388	C₂²×C₁₁	1	2	yes	—
320	#387	C₂²×C₁₁	1	4	yes	—
321	#387	C₂²×C₁₁	1	4	yes	—
322	#387	C₂²×C₁₁	1	4	yes	—
323	#383	C₂²×C₁₁	1	4	yes	—
324	#382	C₂²×C₁₁	1	2	yes	—
325	#382	C₂²×C₁₁	1	1	yes	characteristic
326	#380	C₂²×C₁₁	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
331	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
335	#376	C₂²×C₁₁	1	4	yes	—
336	C₄³	C₂²×C₁₁	1	1	yes	characteristic
337	C₂²×C₁₁	—	4	2	no	—
338	C₂²×C₁₁	—	4	2	no	—
339	C₂²×C₁₁	—	4	2	no	—
340	C₂²×C₁₁	—	4	2	no	—
341	C₂²×C₁₁	—	4	2	no	—
342	C₂²×C₁₁	—	4	2	no	—
343	C₂²×C₁₁	—	4	2	no	—
344	C₂²×C₁₁	C₂²×#41	1	2	yes	—
345	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	2	yes	—
348	C₂²×C₁₁	#585	1	1	yes	characteristic
349	C₄×C₁₁	—	2	8	no	—
350	C₄×C₁₁	—	2	2	no	—
351	C₄×C₁₁	—	2	2	no	—
352	C₄×C₁₁	—	2	2	no	—
353	C₄×C₁₁	—	2	4	no	—
354	C₄×C₁₁	—	4	2	no	—
355	C₄×C₁₁	—	4	4	no	—
356	C₄×C₁₁	—	4	2	no	—
357	C₄×C₁₁	—	4	4	no	—
358	C₄×C₁₁	—	4	4	no	—
359	C₄×C₁₁	—	4	1	no	—
360	C₄×C₁₁	—	4	1	no	—
361	C₄×C₁₁	—	4	1	no	—
362	C₄×C₁₁	#555	1	4	yes	—
363	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
364	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
365	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
368	C₄⋊Q₈	—	2	8	no	—
369	C₄⋊Q₈	—	4	2	no	—
370	C₄⋊Q₈	—	4	2	no	—
371	#124	—	2	4	no	—
372	C₂²⋊Q₈	—	2	8	no	—
373	C₂²⋊Q₈	—	4	4	no	—
374	C₄×Q₈	—	2	8	no	—
375	C₄×Q₈	—	4	2	no	—
376	C₄×D₄	—	4	2	no	—
377	#117	—	2	8	no	—
378	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	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	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
404	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
409	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
411	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
412	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
414	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
415	#95	C₂³×C₁₁	1	4	yes	—
416	#95	C₂³×C₁₁	1	4	yes	—
417	#95	C₂³×C₁₁	1	4	yes	—
418	#95	C₂³×C₁₁	1	4	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	2	yes	—
423	#95	C₂³×C₁₁	1	4	yes	—
424	#95	C₂³×C₁₁	1	2	yes	—
425	#95	C₂³×C₁₁	1	4	yes	—
426	#95	C₂³×C₁₁	1	2	yes	—
427	#95	C₂³×C₁₁	1	4	yes	—
428	#95	C₂³×C₁₁	1	4	yes	—
429	#95	C₂³×C₁₁	1	4	yes	—
430	#95	C₂³×C₁₁	1	4	yes	—
431	#95	C₂³×C₁₁	1	4	yes	—
432	C₂×C₁₁	—	8	2	no	—
433	C₂×C₁₁	C₂×#555	1	1	yes	characteristic
434	C₂×C₁₁	#3482	1	2	yes	—
435	C₂×C₁₁	#3505	1	1	yes	characteristic
436	C₂×C₁₁	#3516	1	2	yes	—
437	C₂×C₁₁	#3550	1	1	yes	characteristic
438	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	C₁₁×#41	1	4	yes	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	4	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	C₁₁×#41	1	8	yes	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	4	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₄²	—	2	8	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	8	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	4	no	—
504	C₄²	—	4	2	no	—
505	C₁₁	#59951	1	1	yes	characteristic, direct product factor, Sylow
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
514	Q₈	—	4	4	no	—
515	Q₈	—	4	8	no	—
516	Q₈	—	8	4	no	—
517	D₄	—	4	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
551	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
552	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
553	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
554	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
555	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
556	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	C₂²×C₁₁×#41	1	2	yes	—
565	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
566	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	2	yes	—
568	C₂²	C₁₁×#585	1	1	yes	characteristic
569	C₄	—	2	8	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	C₁₁×#555	1	4	yes	—
583	C₂	—	8	2	no	—
584	C₂	C₂×C₁₁×#555	1	1	yes	characteristic
585	C₂	C₁₁×#3482	1	2	yes	—
586	C₂	C₁₁×#3505	1	1	yes	characteristic
587	C₂	C₁₁×#3516	1	2	yes	—
588	C₂	C₁₁×#3550	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×#2769	C₂	semidirect
4. C₁₁×#2568	C₂	semidirect
5. C₁₁×#2546	C₂	semidirect
6. C₁₁×#2532	C₂	semidirect
7. C₁₁×#2529	C₂	semidirect
8. C₁₁×#2492	C₂	semidirect
9. C₁₁×#2429	C₂	semidirect
11. C₁₁×#2369	C₂	semidirect
12. C₁₁×#2362	C₂	semidirect
13. C₁₁×#2347	C₂	semidirect
15. C₁₁×#2295	C₂	semidirect
144. #59951	C₁₁	direct (N × H)
212. #2769	C₂×C₁₁	semidirect
215. #2568	C₂×C₁₁	semidirect
216. #2546	C₂×C₁₁	semidirect
217. #2532	C₂×C₁₁	semidirect
218. #2529	C₂×C₁₁	semidirect
219. #2492	C₂×C₁₁	semidirect
220. #2429	C₂×C₁₁	semidirect
222. #2369	C₂×C₁₁	semidirect
223. #2362	C₂×C₁₁	semidirect
224. #2347	C₂×C₁₁	semidirect
226. #2295	C₂×C₁₁	semidirect
505. C₁₁	#59951	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×#2769	2
C₁₁×#2731	2
C₁₁×#2593	2
C₁₁×#2568	2
C₁₁×#2546	2
C₁₁×#2532	2
C₁₁×#2529	2
C₁₁×#2492	2
C₁₁×#2429	2
C₁₁×#2415	2
C₁₁×#2369	2
C₁₁×#2362	2
C₁₁×#2347	2
C₄×C₁₁×#124	2
C₁₁×#2295	2
#59951	11

Subgroups — C11×#59951 #14637144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#59951 #14637144