Subgroups — C₁₁×#34521 #14611714

Order 2816.

2008 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#563	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2383	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2373	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2372	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2371	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2369	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2368	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2362	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2359	C₂	1	2	yes	maximal
11	C₁₁×#2335	C₂	1	2	yes	maximal
12	C₁₁×#2334	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2330	C₂	1	2	yes	maximal, complemented
14	C₁₁×#2329	C₂	1	2	yes	maximal, complemented
15	C₁₁×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₁×#2326	C₂	1	1	yes	maximal, characteristic
17	C₁₁×#2323	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₁×#126	C₂	1	2	yes	maximal, complemented
20	C₁₁×#563	C₄	1	16	yes	complemented
21	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#126	C₂²	1	2	yes	—
24	C₂×C₁₁×#126	C₂²	1	2	yes	—
25	C₂×C₁₁×#125	C₂²	1	2	yes	—
26	C₂×C₁₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#123	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#117	C₂²	1	2	yes	—
35	C₁₁×#391	C₂²	1	2	yes	—
36	C₁₁×#391	C₂²	1	1	yes	characteristic
37	C₁₁×#391	C₂²	1	1	yes	characteristic
38	C₁₁×#391	C₂²	1	1	yes	characteristic
39	C₁₁×#391	C₂²	1	1	yes	characteristic
40	C₁₁×#391	C₂²	1	1	yes	characteristic
41	C₁₁×#391	C₂²	1	2	yes	—
42	C₁₁×#390	C₂²	1	1	yes	characteristic
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	2	yes	—
50	C₁₁×#389	C₂²	1	2	yes	—
51	C₁₁×#388	C₂²	1	2	yes	—
52	C₁₁×#388	C₂²	1	2	yes	—
53	C₁₁×#388	C₂²	1	2	yes	—
54	C₁₁×#388	C₂²	1	2	yes	—
55	C₁₁×#388	C₂²	1	2	yes	—
56	C₁₁×#388	C₂²	1	2	yes	—
57	C₁₁×#388	C₂²	1	2	yes	—
58	C₁₁×#388	C₂²	1	2	yes	—
59	C₁₁×#388	C₂²	1	2	yes	—
60	C₁₁×#388	C₂²	1	2	yes	—
61	C₁₁×#387	C₂²	1	2	yes	—
62	C₁₁×#387	C₂²	1	2	yes	—
63	C₁₁×#387	C₂²	1	2	yes	—
64	C₁₁×#387	C₂²	1	2	yes	—
65	C₁₁×#387	C₂²	1	2	yes	—
66	C₁₁×#387	C₂²	1	2	yes	—
67	C₁₁×#387	C₂²	1	2	yes	—
68	C₁₁×#387	C₂²	1	2	yes	—
69	C₁₁×#387	C₂²	1	2	yes	—
70	C₁₁×#387	C₂²	1	2	yes	—
71	C₁₁×#387	C₂²	1	2	yes	—
72	C₁₁×#387	C₂²	1	2	yes	—
73	C₁₁×#387	C₂²	1	2	yes	—
74	C₁₁×#387	C₂²	1	2	yes	—
75	C₁₁×#387	C₂²	1	2	yes	—
76	C₁₁×#387	C₂²	1	2	yes	—
77	C₁₁×#386	C₂²	1	2	yes	—
78	C₁₁×#385	C₂²	1	2	yes	—
79	C₁₁×#385	C₂²	1	2	yes	—
80	C₁₁×#385	C₂²	1	2	yes	—
81	C₁₁×#385	C₂²	1	2	yes	—
82	C₁₁×#385	C₂²	1	2	yes	—
83	C₁₁×#384	C₂²	1	1	yes	characteristic
84	C₁₁×#384	C₂²	1	1	yes	characteristic
85	C₁₁×#383	C₂²	1	2	yes	—
86	C₁₁×#382	C₂²	1	1	yes	characteristic
87	C₁₁×#380	C₂²	1	2	yes	—
88	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₁₁×#376	C₂²	1	1	yes	characteristic
104	C₁₁×#376	C₂²	1	1	yes	characteristic
105	C₁₁×#376	C₂²	1	2	yes	—
106	C₂×C₁₁×#95	C₂²	1	2	yes	—
107	C₄³×C₁₁	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
115	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
116	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
117	C₁₁×#126	C₂×C₄	1	16	yes	complemented
118	C₁₁×#126	C₂×C₄	1	16	yes	complemented
119	C₁₁×#125	C₂×C₄	1	16	yes	complemented
120	C₁₁×#124	C₂×C₄	1	8	yes	—
121	C₁₁×#123	C₂×C₄	1	16	yes	—
122	C₁₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
123	C₁₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
124	C₄×Q₈×C₁₁	—	4	2	no	—
125	C₄×Q₈×C₁₁	—	4	2	no	—
126	C₄×Q₈×C₁₁	—	4	2	no	—
127	C₄×D₄×C₁₁	—	4	2	no	—
128	C₁₁×#117	—	4	4	no	—
129	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
183	C₁₁×#95	C₂³	1	2	yes	—
184	C₁₁×#95	C₂³	1	2	yes	—
185	C₁₁×#95	C₂³	1	2	yes	—
186	C₁₁×#95	C₂³	1	2	yes	—
187	C₁₁×#95	C₂³	1	2	yes	—
188	C₁₁×#95	C₂³	1	2	yes	—
189	C₁₁×#95	C₂³	1	2	yes	—
190	C₁₁×#95	C₂³	1	2	yes	—
191	C₁₁×#95	C₂³	1	2	yes	—
192	C₁₁×#95	C₂³	1	2	yes	—
193	C₁₁×#95	C₂³	1	2	yes	—
194	C₁₁×#95	C₂³	1	2	yes	—
195	C₁₁×#95	C₂³	1	2	yes	—
196	C₁₁×#95	C₂³	1	2	yes	—
197	C₁₁×#95	C₂³	1	2	yes	—
198	C₁₁×#95	C₂³	1	2	yes	—
199	C₁₁×#95	C₂³	1	2	yes	—
200	C₁₁×#95	C₂³	1	2	yes	—
201	C₁₁×#95	C₂³	1	2	yes	—
202	C₁₁×#95	C₂³	1	2	yes	—
203	C₁₁×#95	C₂³	1	2	yes	—
204	C₁₁×#95	C₂³	1	2	yes	—
205	C₁₁×#95	C₂³	1	2	yes	—
206	C₁₁×#95	C₂³	1	2	yes	—
207	C₁₁×#95	C₂³	1	2	yes	—
208	C₁₁×#95	C₂³	1	2	yes	—
209	#34521	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₁₁	—	4	1	no	—
212	C₂×Q₈×C₁₁	—	4	1	no	—
213	C₂×Q₈×C₁₁	—	4	1	no	—
214	C₂×Q₈×C₁₁	—	4	1	no	—
215	C₂×Q₈×C₁₁	—	4	1	no	—
216	C₂×Q₈×C₁₁	—	4	1	no	—
217	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
218	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
219	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
220	C₂×D₄×C₁₁	—	4	1	no	—
221	C₂×D₄×C₁₁	—	4	1	no	—
222	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
223	C₂²×C₄×C₁₁	—	2	4	no	—
224	C₂²×C₄×C₁₁	—	4	2	no	—
225	C₂²×C₄×C₁₁	—	4	2	no	—
226	C₂²×C₄×C₁₁	—	4	2	no	—
227	C₂²×C₄×C₁₁	—	4	2	no	—
228	C₂²×C₄×C₁₁	—	4	2	no	—
229	C₂²×C₄×C₁₁	—	4	2	no	—
230	C₂²×C₄×C₁₁	—	4	2	no	—
231	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
232	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
250	C₁₁×C₄⋊C₄	—	2	4	no	—
251	C₁₁×C₄⋊C₄	—	2	4	no	—
252	C₁₁×C₄⋊C₄	—	4	2	no	—
253	C₁₁×C₄⋊C₄	—	4	2	no	—
254	C₁₁×C₄⋊C₄	—	4	2	no	—
255	C₁₁×C₄⋊C₄	—	4	2	no	—
256	C₁₁×C₄⋊C₄	—	4	2	no	—
257	C₁₁×C₄⋊C₄	—	4	2	no	—
258	C₁₁×C₄⋊C₄	—	4	2	no	—
259	C₁₁×C₄⋊C₄	—	4	1	no	—
260	C₁₁×C₄⋊C₄	—	4	2	no	—
261	C₁₁×C₄⋊C₄	—	4	1	no	—
262	C₁₁×C₄⋊C₄	—	4	1	no	—
263	C₁₁×C₄⋊C₄	—	4	1	no	—
264	C₁₁×C₄⋊C₄	—	4	1	no	—
265	C₁₁×C₄⋊C₄	—	4	1	no	—
266	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
267	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
268	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
269	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
270	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
271	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
272	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
273	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
274	C₁₁×C₂²⋊C₄	—	2	4	no	—
275	C₁₁×C₂²⋊C₄	—	2	4	no	—
276	C₁₁×C₂²⋊C₄	—	4	2	no	—
277	C₁₁×C₂²⋊C₄	—	4	2	no	—
278	C₁₁×C₂²⋊C₄	—	4	2	no	—
279	C₁₁×C₂²⋊C₄	—	4	2	no	—
280	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
281	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
282	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
283	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
284	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
285	C₄²×C₁₁	—	2	4	no	—
286	C₄²×C₁₁	—	2	2	no	—
287	C₄²×C₁₁	—	2	2	no	—
288	C₄²×C₁₁	—	2	2	no	—
289	C₄²×C₁₁	—	2	4	no	—
290	C₄²×C₁₁	—	2	4	no	—
291	C₄²×C₁₁	—	4	2	no	—
292	C₄²×C₁₁	—	4	2	no	—
293	C₄²×C₁₁	—	4	1	no	—
294	C₄²×C₁₁	—	4	2	no	—
295	C₄²×C₁₁	—	4	2	no	—
296	C₄²×C₁₁	—	4	2	no	—
297	C₄²×C₁₁	—	4	1	no	—
298	C₄²×C₁₁	—	4	1	no	—
299	C₄²×C₁₁	—	4	2	no	—
300	C₄²×C₁₁	—	4	2	no	—
301	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
302	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
303	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
304	C₂×#563	C₂×C₁₁	1	1	yes	characteristic
305	#2383	C₂×C₁₁	1	2	yes	complemented
306	#2381	C₂×C₁₁	1	1	yes	characteristic, complemented
307	#2373	C₂×C₁₁	1	2	yes	complemented
308	#2372	C₂×C₁₁	1	1	yes	characteristic
309	#2371	C₂×C₁₁	1	2	yes	complemented
310	#2369	C₂×C₁₁	1	1	yes	characteristic, complemented
311	#2368	C₂×C₁₁	1	2	yes	complemented
312	#2362	C₂×C₁₁	1	2	yes	complemented
313	#2359	C₂×C₁₁	1	2	yes	—
314	#2335	C₂×C₁₁	1	2	yes	—
315	#2334	C₂×C₁₁	1	2	yes	complemented
316	#2330	C₂×C₁₁	1	2	yes	complemented
317	#2329	C₂×C₁₁	1	2	yes	complemented
318	#2327	C₂×C₁₁	1	1	yes	characteristic, complemented
319	#2326	C₂×C₁₁	1	1	yes	characteristic
320	#2323	C₂×C₁₁	1	2	yes	complemented
321	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
322	C₄×#126	C₂×C₁₁	1	2	yes	complemented
323	C₂³×C₁₁	—	2	2	no	—
324	C₂³×C₁₁	—	2	2	no	—
325	C₂³×C₁₁	—	2	2	no	—
326	C₂³×C₁₁	—	2	2	no	—
327	C₂³×C₁₁	—	2	2	no	—
328	C₂³×C₁₁	—	2	2	no	—
329	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
330	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
331	Q₈×C₁₁	—	4	4	no	—
332	Q₈×C₁₁	—	4	4	no	—
333	Q₈×C₁₁	—	4	4	no	—
334	D₄×C₁₁	—	4	4	no	—
335	C₂×C₄×C₁₁	—	2	2	no	—
336	C₂×C₄×C₁₁	—	2	1	no	—
337	C₂×C₄×C₁₁	—	2	1	no	—
338	C₂×C₄×C₁₁	—	2	1	no	—
339	C₂×C₄×C₁₁	—	2	2	no	—
340	C₂×C₄×C₁₁	—	2	2	no	—
341	C₂×C₄×C₁₁	—	2	2	no	—
342	C₂×C₄×C₁₁	—	2	2	no	—
343	C₂×C₄×C₁₁	—	2	2	no	—
344	C₂×C₄×C₁₁	—	2	2	no	—
345	C₂×C₄×C₁₁	—	2	2	no	—
346	C₂×C₄×C₁₁	—	2	2	no	—
347	C₂×C₄×C₁₁	—	2	2	no	—
348	C₂×C₄×C₁₁	—	2	2	no	—
349	C₂×C₄×C₁₁	—	2	2	no	—
350	C₂×C₄×C₁₁	—	2	1	no	—
351	C₂×C₄×C₁₁	—	2	1	no	—
352	C₂×C₄×C₁₁	—	2	1	no	—
353	C₂×C₄×C₁₁	—	2	2	no	—
354	C₂×C₄×C₁₁	—	2	1	no	—
355	C₂×C₄×C₁₁	—	2	2	no	—
356	C₂×C₄×C₁₁	—	2	1	no	—
357	C₂×C₄×C₁₁	—	2	1	no	—
358	C₂×C₄×C₁₁	—	2	2	no	—
359	C₂×C₄×C₁₁	—	2	2	no	—
360	C₂×C₄×C₁₁	—	2	2	no	—
361	C₂×C₄×C₁₁	—	2	2	no	—
362	C₂×C₄×C₁₁	—	2	2	no	—
363	C₂×C₄×C₁₁	—	2	2	no	—
364	C₂×C₄×C₁₁	—	2	2	no	—
365	C₂×C₄×C₁₁	—	2	2	no	—
366	C₂×C₄×C₁₁	—	2	2	no	—
367	C₂×C₄×C₁₁	—	2	2	no	—
368	C₂×C₄×C₁₁	—	2	2	no	—
369	C₂×C₄×C₁₁	—	2	2	no	—
370	C₂×C₄×C₁₁	—	2	2	no	—
371	C₂×C₄×C₁₁	—	2	2	no	—
372	C₂×C₄×C₁₁	—	2	2	no	—
373	C₂×C₄×C₁₁	—	2	2	no	—
374	C₂×C₄×C₁₁	—	2	2	no	—
375	C₂×C₄×C₁₁	—	4	8	no	—
376	C₂×C₄×C₁₁	—	8	4	no	—
377	C₂×C₄×C₁₁	—	8	4	no	—
378	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
379	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
380	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
382	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
388	#563	C₄×C₁₁	1	16	yes	complemented
389	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
390	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
391	C₂×#126	C₂²×C₁₁	1	2	yes	—
392	C₂×#126	C₂²×C₁₁	1	2	yes	—
393	C₂×#125	C₂²×C₁₁	1	2	yes	—
394	C₂×#124	C₂²×C₁₁	1	1	yes	characteristic
395	C₂×#123	C₂²×C₁₁	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
398	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
402	C₂×#117	C₂²×C₁₁	1	2	yes	—
403	#391	C₂²×C₁₁	1	1	yes	characteristic
404	#391	C₂²×C₁₁	1	1	yes	characteristic
405	#391	C₂²×C₁₁	1	2	yes	—
406	#391	C₂²×C₁₁	1	1	yes	characteristic
407	#391	C₂²×C₁₁	1	1	yes	characteristic
408	#391	C₂²×C₁₁	1	1	yes	characteristic
409	#391	C₂²×C₁₁	1	2	yes	—
410	#390	C₂²×C₁₁	1	1	yes	characteristic
411	#389	C₂²×C₁₁	1	2	yes	—
412	#389	C₂²×C₁₁	1	2	yes	—
413	#389	C₂²×C₁₁	1	2	yes	—
414	#389	C₂²×C₁₁	1	2	yes	—
415	#389	C₂²×C₁₁	1	2	yes	—
416	#389	C₂²×C₁₁	1	2	yes	—
417	#389	C₂²×C₁₁	1	2	yes	—
418	#389	C₂²×C₁₁	1	2	yes	—
419	#388	C₂²×C₁₁	1	2	yes	—
420	#388	C₂²×C₁₁	1	2	yes	—
421	#388	C₂²×C₁₁	1	2	yes	—
422	#388	C₂²×C₁₁	1	2	yes	—
423	#388	C₂²×C₁₁	1	2	yes	—
424	#388	C₂²×C₁₁	1	2	yes	—
425	#388	C₂²×C₁₁	1	2	yes	—
426	#388	C₂²×C₁₁	1	2	yes	—
427	#388	C₂²×C₁₁	1	2	yes	—
428	#388	C₂²×C₁₁	1	2	yes	—
429	#387	C₂²×C₁₁	1	2	yes	—
430	#387	C₂²×C₁₁	1	2	yes	—
431	#387	C₂²×C₁₁	1	2	yes	—
432	#387	C₂²×C₁₁	1	2	yes	—
433	#387	C₂²×C₁₁	1	2	yes	—
434	#387	C₂²×C₁₁	1	2	yes	—
435	#387	C₂²×C₁₁	1	2	yes	—
436	#387	C₂²×C₁₁	1	2	yes	—
437	#387	C₂²×C₁₁	1	2	yes	—
438	#387	C₂²×C₁₁	1	2	yes	—
439	#387	C₂²×C₁₁	1	2	yes	—
440	#387	C₂²×C₁₁	1	2	yes	—
441	#387	C₂²×C₁₁	1	2	yes	—
442	#387	C₂²×C₁₁	1	2	yes	—
443	#387	C₂²×C₁₁	1	2	yes	—
444	#387	C₂²×C₁₁	1	2	yes	—
445	#386	C₂²×C₁₁	1	2	yes	—
446	#385	C₂²×C₁₁	1	2	yes	—
447	#385	C₂²×C₁₁	1	2	yes	—
448	#385	C₂²×C₁₁	1	2	yes	—
449	#385	C₂²×C₁₁	1	2	yes	—
450	#385	C₂²×C₁₁	1	2	yes	—
451	#384	C₂²×C₁₁	1	1	yes	characteristic
452	#384	C₂²×C₁₁	1	1	yes	characteristic
453	#383	C₂²×C₁₁	1	2	yes	—
454	#382	C₂²×C₁₁	1	1	yes	characteristic
455	#380	C₂²×C₁₁	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
471	#376	C₂²×C₁₁	1	1	yes	characteristic
472	#376	C₂²×C₁₁	1	1	yes	characteristic
473	#376	C₂²×C₁₁	1	2	yes	—
474	C₂×#95	C₂²×C₁₁	1	2	yes	—
475	C₄³	C₂²×C₁₁	1	1	yes	characteristic
476	C₂²×C₁₁	—	2	4	no	—
477	C₂²×C₁₁	—	2	4	no	—
478	C₂²×C₁₁	—	2	4	no	—
479	C₂²×C₁₁	—	4	2	no	—
480	C₂²×C₁₁	—	4	2	no	—
481	C₂²×C₁₁	—	4	2	no	—
482	C₂²×C₁₁	—	4	2	no	—
483	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
484	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	2	yes	—
486	C₂²×C₁₁	#585	1	1	yes	characteristic
487	C₂²×C₁₁	#585	1	2	yes	—
488	C₄×C₁₁	—	2	4	no	—
489	C₄×C₁₁	—	2	4	no	—
490	C₄×C₁₁	—	2	2	no	—
491	C₄×C₁₁	—	2	2	no	—
492	C₄×C₁₁	—	2	2	no	—
493	C₄×C₁₁	—	2	4	no	—
494	C₄×C₁₁	—	2	4	no	—
495	C₄×C₁₁	—	2	4	no	—
496	C₄×C₁₁	—	2	2	no	—
497	C₄×C₁₁	—	2	4	no	—
498	C₄×C₁₁	—	4	2	no	—
499	C₄×C₁₁	—	4	1	no	—
500	C₄×C₁₁	—	4	2	no	—
501	C₄×C₁₁	—	4	1	no	—
502	C₄×C₁₁	—	4	2	no	—
503	C₄×C₁₁	—	4	1	no	—
504	C₄×C₁₁	—	4	2	no	—
505	C₄×C₁₁	—	4	2	no	—
506	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
508	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
511	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
512	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
513	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	complemented
514	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	complemented
515	#126	C₂×C₄×C₁₁	1	16	yes	complemented
516	#126	C₂×C₄×C₁₁	1	16	yes	complemented
517	#125	C₂×C₄×C₁₁	1	16	yes	complemented
518	#124	C₂×C₄×C₁₁	1	8	yes	—
519	#123	C₂×C₄×C₁₁	1	16	yes	—
520	C₂²⋊Q₈	C₂×C₄×C₁₁	1	16	yes	complemented
521	C₂²⋊Q₈	C₂×C₄×C₁₁	1	16	yes	complemented
522	C₄×Q₈	—	4	2	no	—
523	C₄×Q₈	—	4	2	no	—
524	C₄×Q₈	—	4	2	no	—
525	C₄×D₄	—	4	2	no	—
526	#117	—	4	4	no	—
527	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
576	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
581	#95	C₂³×C₁₁	1	2	yes	—
582	#95	C₂³×C₁₁	1	2	yes	—
583	#95	C₂³×C₁₁	1	2	yes	—
584	#95	C₂³×C₁₁	1	2	yes	—
585	#95	C₂³×C₁₁	1	2	yes	—
586	#95	C₂³×C₁₁	1	2	yes	—
587	#95	C₂³×C₁₁	1	2	yes	—
588	#95	C₂³×C₁₁	1	2	yes	—
589	#95	C₂³×C₁₁	1	2	yes	—
590	#95	C₂³×C₁₁	1	2	yes	—
591	#95	C₂³×C₁₁	1	2	yes	—
592	#95	C₂³×C₁₁	1	2	yes	—
593	#95	C₂³×C₁₁	1	2	yes	—
594	#95	C₂³×C₁₁	1	2	yes	—
595	#95	C₂³×C₁₁	1	2	yes	—
596	#95	C₂³×C₁₁	1	2	yes	—
597	#95	C₂³×C₁₁	1	2	yes	—
598	#95	C₂³×C₁₁	1	2	yes	—
599	#95	C₂³×C₁₁	1	2	yes	—
600	#95	C₂³×C₁₁	1	2	yes	—
601	#95	C₂³×C₁₁	1	2	yes	—
602	#95	C₂³×C₁₁	1	2	yes	—
603	#95	C₂³×C₁₁	1	2	yes	—
604	#95	C₂³×C₁₁	1	2	yes	—
605	#95	C₂³×C₁₁	1	2	yes	—
606	#95	C₂³×C₁₁	1	2	yes	—
607	C₂×C₁₁	—	4	4	no	—
608	C₂×C₁₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂×C₁₁	C₄×2₋¹⁺⁴	1	2	yes	—
610	C₂×C₁₁	#3544	1	1	yes	characteristic
611	C₂×C₁₁	#3551	1	1	yes	characteristic
612	C₂×C₁₁	#3564	1	2	yes	—
613	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
614	C₂×Q₈	—	4	1	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	—	4	1	no	—
617	C₂×Q₈	—	4	1	no	—
618	C₂×Q₈	—	4	1	no	—
619	C₂×Q₈	—	4	1	no	—
620	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
621	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
622	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
635	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	1	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	1	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	1	no	—
661	C₄⋊C₄	—	4	1	no	—
662	C₄⋊C₄	—	4	1	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
670	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
671	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
672	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
673	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
674	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
675	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
676	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
684	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
685	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	1	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₄²	—	4	1	no	—
703	C₄²	—	4	1	no	—
704	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
705	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
706	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
707	C₁₁	#34521	1	1	yes	characteristic, direct product factor, Sylow
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
715	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
716	Q₈	—	4	4	no	—
717	Q₈	—	4	4	no	—
718	Q₈	—	4	4	no	—
719	D₄	—	4	4	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	8	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
764	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
765	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
766	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
767	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
768	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
769	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
770	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
771	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
772	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
781	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	2	yes	—
783	C₂²	C₁₁×#585	1	1	yes	characteristic
784	C₂²	C₁₁×#585	1	2	yes	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₂	—	4	4	no	—
804	C₂	C₄×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂	C₄×C₁₁×2₋¹⁺⁴	1	2	yes	—
806	C₂	C₁₁×#3544	1	1	yes	characteristic
807	C₂	C₁₁×#3551	1	1	yes	characteristic
808	C₂	C₁₁×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2383	C₂	semidirect
3. C₁₁×#2381	C₂	semidirect
4. C₁₁×#2373	C₂	semidirect
6. C₁₁×#2371	C₂	semidirect
7. C₁₁×#2369	C₂	semidirect
8. C₁₁×#2368	C₂	semidirect
9. C₁₁×#2362	C₂	semidirect
12. C₁₁×#2334	C₂	semidirect
13. C₁₁×#2330	C₂	semidirect
14. C₁₁×#2329	C₂	semidirect
15. C₁₁×#2327	C₂	semidirect
17. C₁₁×#2323	C₂	semidirect
18. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
19. C₄×C₁₁×#126	C₂	semidirect
20. C₁₁×#563	C₄	semidirect
115. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
116. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
117. C₁₁×#126	C₂×C₄	semidirect
118. C₁₁×#126	C₂×C₄	semidirect
119. C₁₁×#125	C₂×C₄	semidirect
122. C₁₁×C₂²⋊Q₈	C₂×C₄	semidirect
123. C₁₁×C₂²⋊Q₈	C₂×C₄	semidirect
209. #34521	C₁₁	direct (N × H)
305. #2383	C₂×C₁₁	semidirect
306. #2381	C₂×C₁₁	semidirect
307. #2373	C₂×C₁₁	semidirect
309. #2371	C₂×C₁₁	semidirect
310. #2369	C₂×C₁₁	semidirect
311. #2368	C₂×C₁₁	semidirect
312. #2362	C₂×C₁₁	semidirect
315. #2334	C₂×C₁₁	semidirect
316. #2330	C₂×C₁₁	semidirect
317. #2329	C₂×C₁₁	semidirect
318. #2327	C₂×C₁₁	semidirect
320. #2323	C₂×C₁₁	semidirect
321. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
322. C₄×#126	C₂×C₁₁	semidirect
388. #563	C₄×C₁₁	semidirect
513. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
514. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
515. #126	C₂×C₄×C₁₁	semidirect
516. #126	C₂×C₄×C₁₁	semidirect
517. #125	C₂×C₄×C₁₁	semidirect
520. C₂²⋊Q₈	C₂×C₄×C₁₁	semidirect
521. C₂²⋊Q₈	C₂×C₄×C₁₁	semidirect
707. C₁₁	#34521	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×#563	2
C₁₁×#2383	2
C₁₁×#2381	2
C₁₁×#2373	2
C₁₁×#2372	2
C₁₁×#2371	2
C₁₁×#2369	2
C₁₁×#2368	2
C₁₁×#2362	2
C₁₁×#2359	2
C₁₁×#2335	2
C₁₁×#2334	2
C₁₁×#2330	2
C₁₁×#2329	2
C₁₁×#2327	2
C₁₁×#2326	2
C₁₁×#2323	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#126	2
#34521	11

Subgroups — C11×#34521 #14611714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34521 #14611714