Subgroups — C₁₁×#61709 #14638902

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3505	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3346	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3344	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3316	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3314	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3239	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3117	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3092	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₁×#554	—	2	2	no	—
17	C₁₁×#554	—	2	2	no	—
18	C₁₁×#554	C₂²	1	4	yes	—
19	C₁₁×#554	C₂²	1	4	yes	complemented
20	C₁₁×#553	—	2	2	no	—
21	C₁₁×#553	C₂²	1	2	yes	—
22	C₁₁×#552	C₂²	1	2	yes	—
23	C₁₁×#551	—	2	2	no	—
24	C₁₁×#548	C₂²	1	2	yes	—
25	C₁₁×#546	C₂²	1	2	yes	—
26	C₁₁×#539	—	2	1	no	—
27	C₁₁×#538	—	2	1	no	—
28	C₁₁×#534	—	2	1	no	—
29	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#529	C₂²	1	2	yes	—
31	C₂×C₁₁×#125	—	2	1	no	—
32	C₁₁×#525	C₂²	1	2	yes	—
33	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₁×#121	C₂²	1	1	yes	characteristic
39	C₁₁×#518	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₁₁	—	2	1	no	—
42	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
43	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₁₁×#501	C₂²	1	4	yes	complemented
46	C₁₁×#489	C₂²	1	4	yes	complemented
47	C₁₁×#485	C₂²	1	4	yes	complemented
48	C₁₁×#484	C₂²	1	2	yes	complemented
49	C₁₁×#484	C₂²	1	2	yes	complemented
50	C₁₁×#484	C₂²	1	2	yes	complemented
51	C₁₁×#484	C₂²	1	4	yes	complemented
52	C₁₁×#484	C₂²	1	2	yes	complemented
53	C₁₁×#483	C₂²	1	2	yes	complemented
54	C₁₁×#483	C₂²	1	4	yes	complemented
55	C₁₁×#481	C₂²	1	2	yes	—
56	C₁₁×#481	C₂²	1	2	yes	—
57	C₁₁×#481	C₂²	1	2	yes	—
58	C₁₁×#481	C₂²	1	4	yes	complemented
59	C₁₁×#480	C₂²	1	4	yes	complemented
60	C₁₁×#479	C₂²	1	4	yes	complemented
61	C₁₁×#475	C₂²	1	4	yes	complemented
62	C₁₁×#474	C₂²	1	4	yes	complemented
63	C₁₁×#470	C₂²	1	4	yes	complemented
64	C₁₁×#468	C₂²	1	4	yes	complemented
65	C₁₁×#467	C₂²	1	4	yes	complemented
66	C₁₁×#465	C₂²	1	4	yes	complemented
67	C₁₁×#464	C₂²	1	4	yes	complemented
68	C₁₁×#452	C₂²	1	4	yes	complemented
69	C₁₁×#451	C₂²	1	2	yes	complemented
70	C₁₁×#451	C₂²	1	2	yes	complemented
71	C₁₁×#450	C₂²	1	2	yes	complemented
72	C₁₁×#448	C₂²	1	2	yes	—
73	C₁₁×#441	C₂²	1	4	yes	complemented
74	C₁₁×#440	C₂²	1	4	yes	complemented
75	C₁₁×#435	C₂²	1	4	yes	—
76	C₁₁×#435	C₂²	1	4	yes	complemented
77	C₁₁×#432	C₂²	1	2	yes	complemented
78	C₁₁×#428	C₂²	1	4	yes	complemented
79	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
80	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
81	C₁₁×#417	C₂²	1	4	yes	complemented
82	C₂×C₁₁×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
84	C₁₁×#407	C₂²	1	2	yes	complemented
85	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×C₁₁×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₁	—	2	1	no	—
89	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₁	—	2	1	no	—
92	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₁	—	2	1	no	—
95	C₂³×C₄×C₁₁	—	2	1	no	—
96	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
98	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
101	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
103	C₁₁×C₄⋊Q₈	—	2	2	no	—
104	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₁₁×#126	—	2	2	no	—
106	C₁₁×#126	—	2	2	no	—
107	C₁₁×#126	—	2	2	no	—
108	C₁₁×#125	—	2	4	no	—
109	C₁₁×#125	—	2	4	no	—
110	C₁₁×#125	—	2	2	no	—
111	C₁₁×#125	C₂³	1	2	yes	—
112	C₁₁×#124	—	2	2	no	—
113	C₁₁×#124	C₂³	1	2	yes	—
114	C₁₁×#123	—	2	2	no	—
115	C₁₁×#123	—	2	2	no	—
116	C₁₁×#123	—	2	2	no	—
117	C₁₁×#123	—	2	2	no	—
118	C₁₁×#123	—	2	2	no	—
119	C₁₁×C₂²⋊Q₈	—	2	1	no	—
120	C₁₁×C₂²⋊Q₈	—	2	1	no	—
121	C₁₁×C₂²⋊Q₈	—	2	1	no	—
122	C₁₁×C₂²⋊Q₈	—	2	1	no	—
123	C₁₁×C₂²⋊Q₈	—	2	2	no	—
124	C₁₁×C₂²⋊Q₈	—	2	2	no	—
125	C₁₁×C₂²⋊Q₈	—	2	4	no	—
126	C₁₁×C₂²⋊Q₈	—	2	4	no	—
127	C₁₁×C₂²⋊Q₈	—	2	4	no	—
128	C₁₁×C₂²⋊Q₈	—	2	4	no	—
129	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₁×#121	—	2	2	no	—
136	C₁₁×#121	—	2	2	no	—
137	C₁₁×#121	—	2	1	no	—
138	C₁₁×#121	—	2	1	no	—
139	C₁₁×#121	—	2	2	no	—
140	C₁₁×#121	C₂³	1	2	yes	—
141	C₁₁×#121	C₂³	1	2	yes	—
142	C₁₁×#121	C₂³	1	2	yes	—
143	C₁₁×#120	—	2	2	no	—
144	C₁₁×#120	—	2	2	no	—
145	C₄×Q₈×C₁₁	—	2	2	no	—
146	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
148	C₄×D₄×C₁₁	—	2	4	no	—
149	C₄×D₄×C₁₁	—	2	4	no	—
150	C₄×D₄×C₁₁	—	2	2	no	—
151	C₄×D₄×C₁₁	—	2	2	no	—
152	C₄×D₄×C₁₁	—	2	2	no	—
153	C₄×D₄×C₁₁	—	2	2	no	—
154	C₄×D₄×C₁₁	—	2	2	no	—
155	C₄×D₄×C₁₁	D₄	1	2	yes	—
156	C₄×D₄×C₁₁	D₄	1	2	yes	—
157	C₄×D₄×C₁₁	C₂³	1	2	yes	—
158	C₄×D₄×C₁₁	C₂³	1	2	yes	—
159	C₄×D₄×C₁₁	C₂³	1	2	yes	—
160	C₁₁×#117	—	2	2	no	—
161	C₁₁×#117	—	2	2	no	—
162	C₁₁×#117	C₂³	1	2	yes	—
163	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
166	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
180	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
187	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₁	—	2	1	no	—
190	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
191	C₁₁×#107	C₂³	1	4	yes	—
192	C₁₁×#107	C₂³	1	4	yes	—
193	C₁₁×#107	C₂³	1	4	yes	—
194	C₁₁×#106	C₂³	1	4	yes	—
195	C₁₁×#106	C₂³	1	4	yes	—
196	C₁₁×#106	C₂³	1	4	yes	—
197	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
198	C₁₁×#103	C₂³	1	4	yes	—
199	C₁₁×#103	C₂³	1	4	yes	—
200	C₁₁×#103	C₂³	1	4	yes	—
201	C₁₁×#103	C₂³	1	4	yes	—
202	C₁₁×#103	C₂³	1	4	yes	—
203	C₁₁×#102	C₂³	1	4	yes	—
204	C₁₁×#102	C₂³	1	4	yes	—
205	C₁₁×#102	C₂³	1	4	yes	—
206	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₁₁×#97	C₂³	1	4	yes	—
212	#61709	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₁	—	2	1	no	—
214	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
216	C₁₁×#41	—	4	4	no	—
217	C₂×Q₈×C₁₁	—	2	1	no	—
218	C₂×Q₈×C₁₁	—	2	1	no	—
219	C₂×Q₈×C₁₁	—	2	4	no	—
220	C₂×Q₈×C₁₁	—	4	2	no	—
221	C₂×Q₈×C₁₁	—	4	2	no	—
222	C₂×Q₈×C₁₁	—	8	2	no	—
223	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₁	—	2	4	no	—
226	C₂×D₄×C₁₁	—	2	2	no	—
227	C₂×D₄×C₁₁	—	2	2	no	—
228	C₂×D₄×C₁₁	—	2	2	no	—
229	C₂×D₄×C₁₁	—	2	2	no	—
230	C₂×D₄×C₁₁	—	2	1	no	—
231	C₂×D₄×C₁₁	—	4	2	no	—
232	C₂×D₄×C₁₁	—	4	4	no	—
233	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₁	—	2	1	no	—
237	C₂²×C₄×C₁₁	—	2	1	no	—
238	C₂²×C₄×C₁₁	—	2	1	no	—
239	C₂²×C₄×C₁₁	—	2	1	no	—
240	C₂²×C₄×C₁₁	—	2	1	no	—
241	C₂²×C₄×C₁₁	—	2	1	no	—
242	C₂²×C₄×C₁₁	—	2	1	no	—
243	C₂²×C₄×C₁₁	—	2	4	no	—
244	C₂²×C₄×C₁₁	—	2	2	no	—
245	C₂²×C₄×C₁₁	—	2	2	no	—
246	C₂²×C₄×C₁₁	—	2	2	no	—
247	C₂²×C₄×C₁₁	—	2	2	no	—
248	C₂²×C₄×C₁₁	—	4	2	no	—
249	C₂²×C₄×C₁₁	—	4	2	no	—
250	C₂²×C₄×C₁₁	—	8	2	no	—
251	C₂²×C₄×C₁₁	—	8	2	no	—
252	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
263	C₁₁×Q₁₆	—	4	4	no	—
264	C₁₁×SD₁₆	—	4	4	no	—
265	C₁₁×M₁₆	—	4	4	no	—
266	C₂×C₈×C₁₁	—	4	2	no	—
267	C₂×C₈×C₁₁	—	4	2	no	—
268	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
269	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
270	C₁₁×C₄⋊C₄	—	2	1	no	—
271	C₁₁×C₄⋊C₄	—	2	4	no	—
272	C₁₁×C₄⋊C₄	—	2	2	no	—
273	C₁₁×C₄⋊C₄	—	2	2	no	—
274	C₁₁×C₄⋊C₄	—	2	1	no	—
275	C₁₁×C₄⋊C₄	—	2	1	no	—
276	C₁₁×C₄⋊C₄	—	2	2	no	—
277	C₁₁×C₄⋊C₄	—	2	4	no	—
278	C₁₁×C₄⋊C₄	—	2	4	no	—
279	C₁₁×C₄⋊C₄	—	2	2	no	—
280	C₁₁×C₄⋊C₄	—	2	4	no	—
281	C₁₁×C₄⋊C₄	—	2	2	no	—
282	C₁₁×C₄⋊C₄	—	2	2	no	—
283	C₁₁×C₄⋊C₄	—	2	1	no	—
284	C₁₁×C₄⋊C₄	—	2	1	no	—
285	C₁₁×C₄⋊C₄	—	2	2	no	—
286	C₁₁×C₄⋊C₄	—	2	2	no	—
287	C₁₁×C₄⋊C₄	—	2	2	no	—
288	C₁₁×C₄⋊C₄	—	2	2	no	—
289	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₁₁×C₂²⋊C₄	—	2	2	no	—
297	C₁₁×C₂²⋊C₄	—	2	2	no	—
298	C₁₁×C₂²⋊C₄	—	2	4	no	—
299	C₁₁×C₂²⋊C₄	—	2	2	no	—
300	C₁₁×C₂²⋊C₄	—	2	2	no	—
301	C₁₁×C₂²⋊C₄	—	2	2	no	—
302	C₁₁×C₂²⋊C₄	—	2	2	no	—
303	C₁₁×C₂²⋊C₄	—	2	2	no	—
304	C₁₁×C₂²⋊C₄	—	2	2	no	—
305	C₁₁×C₂²⋊C₄	—	2	2	no	—
306	C₁₁×C₂²⋊C₄	—	2	2	no	—
307	C₁₁×C₂²⋊C₄	—	2	2	no	—
308	C₁₁×C₂²⋊C₄	—	2	2	no	—
309	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
313	C₄²×C₁₁	—	2	4	no	—
314	C₄²×C₁₁	—	2	2	no	—
315	C₄²×C₁₁	—	2	2	no	—
316	C₄²×C₁₁	C₂×D₄	1	2	yes	—
317	C₄²×C₁₁	C₂⁴	1	2	yes	—
318	#3505	C₂×C₁₁	1	1	yes	characteristic
319	C₂×#554	C₂×C₁₁	1	1	yes	characteristic, complemented
320	#3346	C₂×C₁₁	1	4	yes	complemented
321	#3344	C₂×C₁₁	1	4	yes	complemented
322	#3316	C₂×C₁₁	1	4	yes	complemented
323	#3314	C₂×C₁₁	1	4	yes	complemented
324	#3239	C₂×C₁₁	1	2	yes	complemented
325	#3196	C₂×C₁₁	1	2	yes	complemented
326	#3189	C₂×C₁₁	1	1	yes	characteristic, complemented
327	#3187	C₂×C₁₁	1	1	yes	characteristic, complemented
328	#3117	C₂×C₁₁	1	2	yes	complemented
329	#3092	C₂×C₁₁	1	2	yes	complemented
330	C₂×#484	C₂×C₁₁	1	1	yes	characteristic, complemented
331	C₂×#481	C₂×C₁₁	1	1	yes	characteristic, complemented
332	#2973	C₂×C₁₁	1	1	yes	characteristic, complemented
333	C₂³×C₁₁	—	2	2	no	—
334	C₂³×C₁₁	—	2	2	no	—
335	C₂³×C₁₁	—	4	1	no	—
336	C₂³×C₁₁	—	4	1	no	—
337	C₂³×C₁₁	—	4	1	no	—
338	C₂³×C₁₁	—	4	1	no	—
339	C₂³×C₁₁	—	4	2	no	—
340	C₂³×C₁₁	—	8	1	no	—
341	C₂³×C₁₁	—	8	1	no	—
342	C₂³×C₁₁	#137	1	4	yes	—
343	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
344	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
345	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
346	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₁₁	—	2	4	no	—
348	Q₈×C₁₁	—	2	4	no	—
349	Q₈×C₁₁	—	4	2	no	—
350	Q₈×C₁₁	—	8	1	no	—
351	Q₈×C₁₁	—	8	4	no	—
352	D₄×C₁₁	—	2	4	no	—
353	D₄×C₁₁	—	2	4	no	—
354	D₄×C₁₁	—	2	4	no	—
355	D₄×C₁₁	—	4	4	no	—
356	D₄×C₁₁	—	4	4	no	—
357	D₄×C₁₁	—	8	1	no	—
358	D₄×C₁₁	—	8	2	no	—
359	D₄×C₁₁	—	8	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	4	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	—	4	2	no	—
373	C₂×C₄×C₁₁	—	4	1	no	—
374	C₂×C₄×C₁₁	—	4	1	no	—
375	C₂×C₄×C₁₁	—	4	1	no	—
376	C₂×C₄×C₁₁	—	4	1	no	—
377	C₂×C₄×C₁₁	—	4	1	no	—
378	C₂×C₄×C₁₁	—	4	2	no	—
379	C₂×C₄×C₁₁	—	4	2	no	—
380	C₂×C₄×C₁₁	—	4	2	no	—
381	C₂×C₄×C₁₁	—	4	2	no	—
382	C₂×C₄×C₁₁	—	4	2	no	—
383	C₂×C₄×C₁₁	—	8	2	no	—
384	C₂×C₄×C₁₁	—	8	2	no	—
385	C₂×C₄×C₁₁	—	8	1	no	—
386	C₂×C₄×C₁₁	—	8	2	no	—
387	C₂×C₄×C₁₁	—	8	2	no	—
388	C₂×C₄×C₁₁	—	8	4	no	—
389	C₂×C₄×C₁₁	—	8	1	no	—
390	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
397	C₈×C₁₁	—	2	4	no	—
398	C₈×C₁₁	—	2	4	no	—
399	#554	—	2	2	no	—
400	#554	—	2	2	no	—
401	#554	C₂²×C₁₁	1	4	yes	—
402	#554	C₂²×C₁₁	1	4	yes	complemented
403	#553	—	2	2	no	—
404	#553	C₂²×C₁₁	1	2	yes	—
405	#552	C₂²×C₁₁	1	2	yes	—
406	#551	—	2	2	no	—
407	#548	C₂²×C₁₁	1	2	yes	—
408	#546	C₂²×C₁₁	1	2	yes	—
409	#539	—	2	1	no	—
410	#538	—	2	1	no	—
411	#534	—	2	1	no	—
412	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
413	#529	C₂²×C₁₁	1	2	yes	—
414	C₂×#125	—	2	1	no	—
415	#525	C₂²×C₁₁	1	2	yes	—
416	C₂×C₂²⋊Q₈	—	2	1	no	—
417	C₂×C₂²⋊Q₈	—	2	1	no	—
418	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
419	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
420	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
421	C₂×#121	C₂²×C₁₁	1	1	yes	characteristic
422	#518	—	2	1	no	—
423	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
424	C₂×C₄×D₄	—	2	1	no	—
425	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
428	#501	C₂²×C₁₁	1	4	yes	complemented
429	#489	C₂²×C₁₁	1	4	yes	complemented
430	#485	C₂²×C₁₁	1	4	yes	complemented
431	#484	C₂²×C₁₁	1	4	yes	complemented
432	#484	C₂²×C₁₁	1	2	yes	complemented
433	#484	C₂²×C₁₁	1	2	yes	complemented
434	#484	C₂²×C₁₁	1	2	yes	complemented
435	#484	C₂²×C₁₁	1	2	yes	complemented
436	#483	C₂²×C₁₁	1	2	yes	complemented
437	#483	C₂²×C₁₁	1	4	yes	complemented
438	#481	C₂²×C₁₁	1	2	yes	—
439	#481	C₂²×C₁₁	1	2	yes	—
440	#481	C₂²×C₁₁	1	2	yes	—
441	#481	C₂²×C₁₁	1	4	yes	complemented
442	#480	C₂²×C₁₁	1	4	yes	complemented
443	#479	C₂²×C₁₁	1	4	yes	complemented
444	#475	C₂²×C₁₁	1	4	yes	complemented
445	#474	C₂²×C₁₁	1	4	yes	complemented
446	#470	C₂²×C₁₁	1	4	yes	complemented
447	#468	C₂²×C₁₁	1	4	yes	complemented
448	#467	C₂²×C₁₁	1	4	yes	complemented
449	#465	C₂²×C₁₁	1	4	yes	complemented
450	#464	C₂²×C₁₁	1	4	yes	complemented
451	#452	C₂²×C₁₁	1	4	yes	complemented
452	#451	C₂²×C₁₁	1	2	yes	complemented
453	#451	C₂²×C₁₁	1	2	yes	complemented
454	#450	C₂²×C₁₁	1	2	yes	complemented
455	#448	C₂²×C₁₁	1	2	yes	—
456	#441	C₂²×C₁₁	1	4	yes	complemented
457	#440	C₂²×C₁₁	1	4	yes	complemented
458	#435	C₂²×C₁₁	1	4	yes	—
459	#435	C₂²×C₁₁	1	4	yes	complemented
460	#432	C₂²×C₁₁	1	2	yes	complemented
461	#428	C₂²×C₁₁	1	4	yes	complemented
462	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
463	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
464	#417	C₂²×C₁₁	1	4	yes	complemented
465	C₂×#103	C₂²×C₁₁	1	2	yes	complemented
466	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
467	#407	C₂²×C₁₁	1	2	yes	complemented
468	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
470	C₂²×C₁₁	—	2	1	no	—
471	C₂²×C₁₁	—	2	1	no	—
472	C₂²×C₁₁	—	2	1	no	—
473	C₂²×C₁₁	—	2	1	no	—
474	C₂²×C₁₁	—	2	1	no	—
475	C₂²×C₁₁	—	2	1	no	—
476	C₂²×C₁₁	—	2	2	no	—
477	C₂²×C₁₁	—	2	2	no	—
478	C₂²×C₁₁	—	2	2	no	—
479	C₂²×C₁₁	—	4	4	no	—
480	C₂²×C₁₁	—	4	4	no	—
481	C₂²×C₁₁	—	4	2	no	—
482	C₂²×C₁₁	—	4	2	no	—
483	C₂²×C₁₁	—	4	2	no	—
484	C₂²×C₁₁	—	16	2	no	—
485	C₂²×C₁₁	C₂×#137	1	2	yes	—
486	C₂²×C₁₁	C₂×#137	1	2	yes	—
487	C₂²×C₁₁	C₂×#137	1	2	yes	—
488	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₁₁	—	2	2	no	—
490	C₄×C₁₁	—	2	1	no	—
491	C₄×C₁₁	—	2	2	no	—
492	C₄×C₁₁	—	2	1	no	—
493	C₄×C₁₁	—	2	1	no	—
494	C₄×C₁₁	—	2	2	no	—
495	C₄×C₁₁	—	4	2	no	—
496	C₄×C₁₁	—	4	2	no	—
497	C₄×C₁₁	—	4	2	no	—
498	C₄×C₁₁	—	4	2	no	—
499	C₄×C₁₁	—	4	2	no	—
500	C₄×C₁₁	—	4	2	no	—
501	C₄×C₁₁	—	4	2	no	—
502	C₄×C₁₁	#585	1	2	yes	—
503	C₂×#41	C₂³×C₁₁	1	2	yes	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
514	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
516	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
517	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
518	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
521	#126	—	2	2	no	—
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#125	—	2	4	no	—
525	#125	—	2	4	no	—
526	#125	—	2	2	no	—
527	#125	C₂³×C₁₁	1	2	yes	—
528	#124	—	2	2	no	—
529	#124	C₂³×C₁₁	1	2	yes	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
546	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
547	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
548	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
549	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
550	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	2	no	—
556	#121	C₂³×C₁₁	1	2	yes	—
557	#121	C₂³×C₁₁	1	2	yes	—
558	#121	C₂³×C₁₁	1	2	yes	—
559	#120	—	2	2	no	—
560	#120	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
563	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	D₄×C₁₁	1	2	yes	—
572	C₄×D₄	D₄×C₁₁	1	2	yes	—
573	C₄×D₄	C₂³×C₁₁	1	2	yes	—
574	C₄×D₄	C₂³×C₁₁	1	2	yes	—
575	C₄×D₄	C₂³×C₁₁	1	2	yes	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	C₂³×C₁₁	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	2	no	—
603	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
605	C₂×C₄²	—	2	1	no	—
606	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
607	#107	C₂³×C₁₁	1	4	yes	—
608	#107	C₂³×C₁₁	1	4	yes	—
609	#107	C₂³×C₁₁	1	4	yes	—
610	#106	C₂³×C₁₁	1	4	yes	—
611	#106	C₂³×C₁₁	1	4	yes	—
612	#106	C₂³×C₁₁	1	4	yes	—
613	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
614	#103	C₂³×C₁₁	1	4	yes	—
615	#103	C₂³×C₁₁	1	4	yes	—
616	#103	C₂³×C₁₁	1	4	yes	—
617	#103	C₂³×C₁₁	1	4	yes	—
618	#103	C₂³×C₁₁	1	4	yes	—
619	#102	C₂³×C₁₁	1	4	yes	—
620	#102	C₂³×C₁₁	1	4	yes	—
621	#102	C₂³×C₁₁	1	4	yes	—
622	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
623	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
624	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
626	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
627	#97	C₂³×C₁₁	1	4	yes	—
628	C₂×C₁₁	—	2	2	no	—
629	C₂×C₁₁	—	2	2	no	—
630	C₂×C₁₁	—	2	2	no	—
631	C₂×C₁₁	—	4	2	no	—
632	C₂×C₁₁	—	8	2	no	—
633	C₂×C₁₁	#3485	1	1	yes	characteristic
634	C₂×C₁₁	C₂²×#137	1	1	yes	characteristic
635	C₂×C₁₁	#3585	1	1	yes	characteristic
636	C₂⁴	—	2	1	no	—
637	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
638	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
639	#41	—	4	4	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×Q₈	—	4	2	no	—
645	C₂×Q₈	—	8	2	no	—
646	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
647	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
657	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
658	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	8	2	no	—
674	C₂²×C₄	—	8	2	no	—
675	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
686	Q₁₆	—	4	4	no	—
687	SD₁₆	—	4	4	no	—
688	M₁₆	—	4	4	no	—
689	C₂×C₈	—	4	2	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
692	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
714	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
733	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	C₂×D₄×C₁₁	1	2	yes	—
740	C₄²	C₂⁴×C₁₁	1	2	yes	—
741	C₁₁	#61709	1	1	yes	characteristic, direct product factor, Sylow
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	8	1	no	—
750	C₂³	—	8	1	no	—
751	C₂³	C₁₁×#137	1	4	yes	—
752	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
753	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
754	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
755	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	8	1	no	—
760	Q₈	—	8	4	no	—
761	D₄	—	2	4	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	2	no	—
768	D₄	—	8	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	1	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
805	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
806	C₈	—	2	4	no	—
807	C₈	—	2	4	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	16	2	no	—
823	C₂²	C₂×C₁₁×#137	1	2	yes	—
824	C₂²	C₂×C₁₁×#137	1	2	yes	—
825	C₂²	C₂×C₁₁×#137	1	2	yes	—
826	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	C₁₁×#585	1	2	yes	—
841	C₂	—	2	2	no	—
842	C₂	—	2	2	no	—
843	C₂	—	2	2	no	—
844	C₂	—	4	2	no	—
845	C₂	—	8	2	no	—
846	C₂	C₁₁×#3485	1	1	yes	characteristic
847	C₂	C₂²×C₁₁×#137	1	1	yes	characteristic
848	C₂	C₁₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#554	C₂	semidirect
3. C₁₁×#3346	C₂	semidirect
4. C₁₁×#3344	C₂	semidirect
5. C₁₁×#3316	C₂	semidirect
6. C₁₁×#3314	C₂	semidirect
7. C₁₁×#3239	C₂	semidirect
8. C₁₁×#3196	C₂	semidirect
9. C₁₁×#3189	C₂	semidirect
10. C₁₁×#3187	C₂	semidirect
11. C₁₁×#3117	C₂	semidirect
12. C₁₁×#3092	C₂	semidirect
13. C₂×C₁₁×#484	C₂	semidirect
14. C₂×C₁₁×#481	C₂	semidirect
15. C₁₁×#2973	C₂	semidirect
19. C₁₁×#554	C₂²	semidirect
29. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
44. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
45. C₁₁×#501	C₂²	semidirect
46. C₁₁×#489	C₂²	semidirect
47. C₁₁×#485	C₂²	semidirect
48. C₁₁×#484	C₂²	semidirect
49. C₁₁×#484	C₂²	semidirect
50. C₁₁×#484	C₂²	semidirect
51. C₁₁×#484	C₂²	semidirect
52. C₁₁×#484	C₂²	semidirect
53. C₁₁×#483	C₂²	semidirect
54. C₁₁×#483	C₂²	semidirect
58. C₁₁×#481	C₂²	semidirect
59. C₁₁×#480	C₂²	semidirect
60. C₁₁×#479	C₂²	semidirect
61. C₁₁×#475	C₂²	semidirect
62. C₁₁×#474	C₂²	semidirect
63. C₁₁×#470	C₂²	semidirect
64. C₁₁×#468	C₂²	semidirect
65. C₁₁×#467	C₂²	semidirect
66. C₁₁×#465	C₂²	semidirect
67. C₁₁×#464	C₂²	semidirect
68. C₁₁×#452	C₂²	semidirect
69. C₁₁×#451	C₂²	semidirect
70. C₁₁×#451	C₂²	semidirect
71. C₁₁×#450	C₂²	semidirect
73. C₁₁×#441	C₂²	semidirect
74. C₁₁×#440	C₂²	semidirect
76. C₁₁×#435	C₂²	semidirect
77. C₁₁×#432	C₂²	semidirect
78. C₁₁×#428	C₂²	semidirect
79. C₂×C₁₁×#107	C₂²	semidirect
80. C₂×C₁₁×#106	C₂²	semidirect
81. C₁₁×#417	C₂²	semidirect
82. C₂×C₁₁×#103	C₂²	semidirect
83. C₂×C₁₁×#102	C₂²	semidirect
84. C₁₁×#407	C₂²	semidirect
212. #61709	C₁₁	direct (N × H)
319. C₂×#554	C₂×C₁₁	semidirect
320. #3346	C₂×C₁₁	semidirect
321. #3344	C₂×C₁₁	semidirect
322. #3316	C₂×C₁₁	semidirect
323. #3314	C₂×C₁₁	semidirect
324. #3239	C₂×C₁₁	semidirect
325. #3196	C₂×C₁₁	semidirect
326. #3189	C₂×C₁₁	semidirect
327. #3187	C₂×C₁₁	semidirect
328. #3117	C₂×C₁₁	semidirect
329. #3092	C₂×C₁₁	semidirect
330. C₂×#484	C₂×C₁₁	semidirect
331. C₂×#481	C₂×C₁₁	semidirect
332. #2973	C₂×C₁₁	semidirect
402. #554	C₂²×C₁₁	semidirect
412. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
420. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
423. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
427. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
428. #501	C₂²×C₁₁	semidirect
429. #489	C₂²×C₁₁	semidirect
430. #485	C₂²×C₁₁	semidirect
431. #484	C₂²×C₁₁	semidirect
432. #484	C₂²×C₁₁	semidirect
433. #484	C₂²×C₁₁	semidirect
434. #484	C₂²×C₁₁	semidirect
435. #484	C₂²×C₁₁	semidirect
436. #483	C₂²×C₁₁	semidirect
437. #483	C₂²×C₁₁	semidirect
441. #481	C₂²×C₁₁	semidirect
442. #480	C₂²×C₁₁	semidirect
443. #479	C₂²×C₁₁	semidirect
444. #475	C₂²×C₁₁	semidirect
445. #474	C₂²×C₁₁	semidirect
446. #470	C₂²×C₁₁	semidirect
447. #468	C₂²×C₁₁	semidirect
448. #467	C₂²×C₁₁	semidirect
449. #465	C₂²×C₁₁	semidirect
450. #464	C₂²×C₁₁	semidirect
451. #452	C₂²×C₁₁	semidirect
452. #451	C₂²×C₁₁	semidirect
453. #451	C₂²×C₁₁	semidirect
454. #450	C₂²×C₁₁	semidirect
456. #441	C₂²×C₁₁	semidirect
457. #440	C₂²×C₁₁	semidirect
459. #435	C₂²×C₁₁	semidirect
460. #432	C₂²×C₁₁	semidirect
461. #428	C₂²×C₁₁	semidirect
462. C₂×#107	C₂²×C₁₁	semidirect
463. C₂×#106	C₂²×C₁₁	semidirect
464. #417	C₂²×C₁₁	semidirect
465. C₂×#103	C₂²×C₁₁	semidirect
466. C₂×#102	C₂²×C₁₁	semidirect
467. #407	C₂²×C₁₁	semidirect
741. C₁₁	#61709	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×#3505	2
C₂×C₁₁×#554	2
C₁₁×#3346	2
C₁₁×#3344	2
C₁₁×#3316	2
C₁₁×#3314	2
C₁₁×#3239	2
C₁₁×#3196	2
C₁₁×#3189	2
C₁₁×#3187	2
C₁₁×#3117	2
C₁₁×#3092	2
C₂×C₁₁×#484	2
C₂×C₁₁×#481	2
C₁₁×#2973	2
#61709	11

Subgroups — C11×#61709 #14638902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61709 #14638902