Subgroups — C₁₁×#60708 #14637901

Order 2816.

1860 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3495	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3181	C₂	1	4	yes	maximal, complemented
3	C₁₁×#3178	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3177	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3175	C₂	1	2	yes	maximal, complemented
6	C₁₁×#3170	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3168	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3056	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3050	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₁×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₁×#137	C₂²	1	2	yes	—
19	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#556	—	2	2	no	—
24	C₁₁×#554	—	2	2	no	—
25	C₁₁×#552	—	2	4	no	—
26	C₁₁×#552	—	2	2	no	—
27	C₁₁×#552	—	2	2	no	—
28	C₁₁×#551	—	2	4	no	—
29	C₁₁×#544	C₂²	1	2	yes	—
30	C₁₁×#542	C₂²	1	4	yes	—
31	C₁₁×#541	C₂²	1	4	yes	—
32	C₁₁×#536	C₂²	1	2	yes	—
33	C₁₁×#533	C₂²	1	4	yes	—
34	C₁₁×#529	C₂²	1	4	yes	—
35	C₁₁×#525	C₂²	1	2	yes	—
36	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₁₁×#520	C₂²	1	2	yes	—
38	C₁₁×#519	C₂²	1	2	yes	—
39	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
40	C₁₁×#501	C₂²	1	4	yes	complemented
41	C₁₁×#500	C₂²	1	2	yes	complemented
42	C₁₁×#499	C₂²	1	2	yes	complemented
43	C₁₁×#497	C₂²	1	4	yes	complemented
44	C₁₁×#495	C₂²	1	2	yes	complemented
45	C₁₁×#494	C₂²	1	2	yes	complemented
46	C₁₁×#491	C₂²	1	4	yes	complemented
47	C₁₁×#489	C₂²	1	4	yes	complemented
48	C₁₁×#488	C₂²	1	4	yes	complemented
49	C₁₁×#487	C₂²	1	4	yes	complemented
50	C₁₁×#470	C₂²	1	4	yes	—
51	C₁₁×#468	C₂²	1	4	yes	—
52	C₁₁×#467	C₂²	1	2	yes	—
53	C₁₁×#467	C₂²	1	1	yes	characteristic
54	C₁₁×#467	C₂²	1	4	yes	—
55	C₁₁×#467	C₂²	1	2	yes	—
56	C₁₁×#467	C₂²	1	1	yes	characteristic
57	C₁₁×#467	C₂²	1	2	yes	—
58	C₁₁×#467	C₂²	1	2	yes	—
59	C₁₁×#466	C₂²	1	1	yes	characteristic
60	C₁₁×#466	C₂²	1	1	yes	characteristic
61	C₁₁×#465	C₂²	1	4	yes	—
62	C₁₁×#465	C₂²	1	2	yes	—
63	C₁₁×#465	C₂²	1	2	yes	—
64	C₁₁×#441	C₂²	1	4	yes	complemented
65	C₁₁×#441	C₂²	1	4	yes	complemented
66	C₁₁×#440	C₂²	1	4	yes	complemented
67	C₁₁×#440	C₂²	1	4	yes	complemented
68	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	complemented
69	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	complemented
70	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	complemented
71	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
72	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
73	C₄×C₁₁×D₈	C₂²	1	2	yes	complemented
74	C₁₁×#428	C₂²	1	2	yes	—
75	C₁₁×#427	C₂²	1	1	yes	characteristic
76	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
77	C₁₁×#419	C₂²	1	2	yes	—
78	C₁₁×#417	C₂²	1	2	yes	—
79	C₁₁×#416	C₂²	1	2	yes	—
80	C₂×C₁₁×#103	C₂²	1	2	yes	—
81	C₁₁×#405	C₂²	1	1	yes	characteristic
82	C₁₁×#405	C₂²	1	2	yes	—
83	C₁₁×#405	C₂²	1	2	yes	—
84	C₁₁×#405	C₂²	1	1	yes	characteristic
85	C₁₁×#405	C₂²	1	1	yes	characteristic
86	C₁₁×#405	C₂²	1	1	yes	characteristic
87	C₂×C₁₁×#97	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
89	C₂×C₁₁×#41	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
92	C₁₁×#137	—	2	8	no	—
93	C₁₁×#135	—	2	4	no	—
94	C₂×C₁₁×Q₁₆	—	2	4	no	—
95	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
97	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
102	C₂×C₁₁×M₁₆	—	2	4	no	—
103	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
105	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₁	—	2	4	no	—
107	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
109	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
114	C₁₁×C₄⋊Q₈	—	2	2	no	—
115	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₁×#126	—	2	4	no	—
118	C₁₁×#126	—	2	4	no	—
119	C₁₁×#126	—	2	4	no	—
120	C₁₁×#126	—	2	4	no	—
121	C₁₁×#125	—	2	4	no	—
122	C₁₁×#125	—	2	4	no	—
123	C₁₁×#125	—	2	2	no	—
124	C₁₁×#125	—	2	4	no	—
125	C₁₁×#125	C₂³	1	4	yes	—
126	C₁₁×#124	—	2	4	no	—
127	C₁₁×#124	C₂³	1	4	yes	—
128	C₁₁×#123	—	2	2	no	—
129	C₁₁×#123	—	2	4	no	—
130	C₁₁×#123	—	2	4	no	—
131	C₁₁×#123	—	2	4	no	—
132	C₁₁×C₂²⋊Q₈	—	2	2	no	—
133	C₁₁×C₂²⋊Q₈	—	2	2	no	—
134	C₁₁×C₂²⋊Q₈	—	2	4	no	—
135	C₁₁×C₂²⋊Q₈	—	2	2	no	—
136	C₁₁×C₂²⋊Q₈	—	2	2	no	—
137	C₁₁×C₂²⋊Q₈	—	2	4	no	—
138	C₁₁×C₂²⋊Q₈	—	2	4	no	—
139	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₁×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₁₁×#121	C₂³	1	2	yes	—
144	C₁₁×#121	C₂³	1	2	yes	—
145	C₁₁×#120	—	2	2	no	—
146	C₄×Q₈×C₁₁	—	2	2	no	—
147	C₄×Q₈×C₁₁	—	2	2	no	—
148	C₄×Q₈×C₁₁	—	2	4	no	—
149	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
152	C₄×D₄×C₁₁	—	2	2	no	—
153	C₄×D₄×C₁₁	—	2	2	no	—
154	C₄×D₄×C₁₁	—	2	4	no	—
155	C₄×D₄×C₁₁	—	2	4	no	—
156	C₄×D₄×C₁₁	C₂³	1	4	yes	—
157	C₁₁×#117	—	2	4	no	—
158	C₁₁×#117	—	2	2	no	—
159	C₁₁×#117	—	2	4	no	—
160	C₁₁×#117	—	2	4	no	—
161	C₁₁×#117	D₄	1	1	yes	characteristic
162	C₁₁×#117	D₄	1	2	yes	—
163	C₁₁×#117	D₄	1	1	yes	characteristic
164	C₁₁×#117	C₂³	1	2	yes	—
165	C₁₁×#117	C₂³	1	1	yes	characteristic
166	C₁₁×#117	C₂³	1	1	yes	characteristic
167	C₁₁×#117	C₂³	1	2	yes	—
168	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
169	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
170	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
172	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
174	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
175	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
176	C₁₁×#107	C₂³	1	1	yes	characteristic
177	C₁₁×#107	C₂³	1	2	yes	—
178	C₁₁×#107	C₂³	1	1	yes	characteristic
179	C₁₁×#107	C₂³	1	4	yes	—
180	C₁₁×#107	C₂³	1	2	yes	—
181	C₁₁×#106	C₂³	1	4	yes	—
182	C₁₁×#106	C₂³	1	2	yes	—
183	C₁₁×#103	C₂³	1	4	yes	—
184	C₁₁×#103	C₂³	1	4	yes	—
185	C₁₁×#103	C₂³	1	2	yes	—
186	C₁₁×#103	C₂³	1	4	yes	—
187	C₁₁×#103	C₂³	1	4	yes	—
188	C₁₁×#103	C₂³	1	4	yes	—
189	C₁₁×#103	C₂³	1	2	yes	—
190	C₁₁×#102	C₂³	1	2	yes	—
191	C₁₁×#102	C₂³	1	4	yes	—
192	C₁₁×#102	C₂³	1	2	yes	—
193	C₁₁×#97	C₂³	1	2	yes	—
194	C₁₁×#97	C₂³	1	2	yes	—
195	C₁₁×#97	C₂³	1	2	yes	—
196	C₁₁×#97	C₂³	1	2	yes	—
197	C₄×C₈×C₁₁	C₂³	1	2	yes	—
198	C₄×C₈×C₁₁	C₂³	1	2	yes	—
199	C₄×C₈×C₁₁	C₂³	1	2	yes	—
200	C₄×C₈×C₁₁	C₂³	1	2	yes	—
201	#60708	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
203	C₁₁×#41	—	2	4	no	—
204	C₁₁×#41	—	2	4	no	—
205	C₂×Q₈×C₁₁	—	2	2	no	—
206	C₂×Q₈×C₁₁	—	2	4	no	—
207	C₂×Q₈×C₁₁	—	2	4	no	—
208	C₂×Q₈×C₁₁	—	2	4	no	—
209	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
210	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₁	—	2	2	no	—
212	C₂×D₄×C₁₁	—	2	2	no	—
213	C₂×D₄×C₁₁	—	2	2	no	—
214	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₁	—	2	2	no	—
216	C₂²×C₄×C₁₁	—	2	2	no	—
217	C₂²×C₄×C₁₁	—	2	2	no	—
218	C₂²×C₄×C₁₁	—	2	2	no	—
219	C₂²×C₄×C₁₁	—	2	2	no	—
220	C₂²×C₄×C₁₁	—	2	4	no	—
221	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
229	C₁₁×Q₁₆	—	2	4	no	—
230	C₁₁×Q₁₆	—	2	4	no	—
231	C₁₁×Q₁₆	—	2	2	no	—
232	C₁₁×Q₁₆	—	2	8	no	—
233	C₁₁×SD₁₆	—	2	4	no	—
234	C₁₁×SD₁₆	—	2	8	no	—
235	C₁₁×D₈	—	2	2	no	—
236	C₁₁×M₁₆	—	2	4	no	—
237	C₁₁×M₁₆	—	2	2	no	—
238	C₁₁×M₁₆	#41	1	4	yes	—
239	C₂×C₈×C₁₁	—	2	2	no	—
240	C₂×C₈×C₁₁	—	2	2	no	—
241	C₂×C₈×C₁₁	—	2	2	no	—
242	C₂×C₈×C₁₁	—	2	2	no	—
243	C₂×C₈×C₁₁	—	2	4	no	—
244	C₂×C₈×C₁₁	—	2	2	no	—
245	C₂×C₈×C₁₁	#41	1	4	yes	—
246	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₁₁×C₄⋊C₄	—	2	2	no	—
253	C₁₁×C₄⋊C₄	—	2	4	no	—
254	C₁₁×C₄⋊C₄	—	2	4	no	—
255	C₁₁×C₄⋊C₄	—	2	4	no	—
256	C₁₁×C₄⋊C₄	—	2	4	no	—
257	C₁₁×C₄⋊C₄	—	2	4	no	—
258	C₁₁×C₄⋊C₄	—	2	4	no	—
259	C₁₁×C₄⋊C₄	—	2	4	no	—
260	C₁₁×C₄⋊C₄	—	2	4	no	—
261	C₁₁×C₄⋊C₄	—	2	2	no	—
262	C₁₁×C₄⋊C₄	—	2	4	no	—
263	C₁₁×C₄⋊C₄	—	2	2	no	—
264	C₁₁×C₄⋊C₄	—	2	4	no	—
265	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
268	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
270	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
271	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
273	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₁₁×C₂²⋊C₄	—	2	4	no	—
275	C₁₁×C₂²⋊C₄	—	2	4	no	—
276	C₁₁×C₂²⋊C₄	—	2	2	no	—
277	C₁₁×C₂²⋊C₄	—	2	2	no	—
278	C₁₁×C₂²⋊C₄	—	2	2	no	—
279	C₁₁×C₂²⋊C₄	—	2	2	no	—
280	C₁₁×C₂²⋊C₄	—	2	4	no	—
281	C₁₁×C₂²⋊C₄	—	2	4	no	—
282	C₁₁×C₂²⋊C₄	—	2	2	no	—
283	C₁₁×C₂²⋊C₄	—	2	4	no	—
284	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
285	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
286	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
287	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
288	C₄²×C₁₁	—	2	4	no	—
289	C₄²×C₁₁	—	2	4	no	—
290	C₄²×C₁₁	—	2	4	no	—
291	C₄²×C₁₁	—	2	2	no	—
292	C₄²×C₁₁	C₂×D₄	1	2	yes	—
293	C₄²×C₁₁	C₂×D₄	1	2	yes	—
294	C₄²×C₁₁	C₂⁴	1	2	yes	—
295	C₄²×C₁₁	C₂⁴	1	2	yes	—
296	#3495	C₂×C₁₁	1	2	yes	complemented
297	#3181	C₂×C₁₁	1	4	yes	complemented
298	#3178	C₂×C₁₁	1	4	yes	complemented
299	#3177	C₂×C₁₁	1	2	yes	complemented
300	#3175	C₂×C₁₁	1	2	yes	complemented
301	#3170	C₂×C₁₁	1	2	yes	complemented
302	#3168	C₂×C₁₁	1	2	yes	complemented
303	#3164	C₂×C₁₁	1	1	yes	characteristic, complemented
304	#3156	C₂×C₁₁	1	1	yes	characteristic, complemented
305	#3137	C₂×C₁₁	1	2	yes	complemented
306	#3056	C₂×C₁₁	1	2	yes	complemented
307	#3050	C₂×C₁₁	1	1	yes	characteristic
308	C₂×#467	C₂×C₁₁	1	1	yes	characteristic, complemented
309	#2951	C₂×C₁₁	1	1	yes	characteristic, complemented
310	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
311	#2947	C₂×C₁₁	1	2	yes	complemented
312	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
313	C₂³×C₁₁	—	2	2	no	—
314	C₂³×C₁₁	—	2	2	no	—
315	C₂³×C₁₁	—	2	2	no	—
316	C₂³×C₁₁	—	4	1	no	—
317	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
318	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₁₁	—	2	4	no	—
321	Q₈×C₁₁	—	2	2	no	—
322	Q₈×C₁₁	—	2	4	no	—
323	Q₈×C₁₁	—	2	2	no	—
324	Q₈×C₁₁	—	4	4	no	—
325	Q₈×C₁₁	—	8	4	no	—
326	D₄×C₁₁	—	2	2	no	—
327	D₄×C₁₁	—	2	2	no	—
328	D₄×C₁₁	—	4	4	no	—
329	D₄×C₁₁	—	4	4	no	—
330	D₄×C₁₁	—	8	2	no	—
331	C₂×C₄×C₁₁	—	2	2	no	—
332	C₂×C₄×C₁₁	—	2	4	no	—
333	C₂×C₄×C₁₁	—	2	2	no	—
334	C₂×C₄×C₁₁	—	2	2	no	—
335	C₂×C₄×C₁₁	—	2	1	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	4	no	—
342	C₂×C₄×C₁₁	—	2	2	no	—
343	C₂×C₄×C₁₁	—	2	4	no	—
344	C₂×C₄×C₁₁	—	4	2	no	—
345	C₂×C₄×C₁₁	—	4	4	no	—
346	C₂×C₄×C₁₁	—	4	4	no	—
347	C₂×C₄×C₁₁	—	8	4	no	—
348	C₂×C₄×C₁₁	—	8	2	no	—
349	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
357	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
358	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
359	C₈×C₁₁	—	2	1	no	—
360	C₈×C₁₁	—	2	1	no	—
361	C₈×C₁₁	—	2	2	no	—
362	C₈×C₁₁	C₂×#41	1	2	yes	—
363	C₈×C₁₁	C₂×#41	1	2	yes	—
364	C₈×C₁₁	C₂×#41	1	4	yes	—
365	C₂×#137	C₂²×C₁₁	1	2	yes	—
366	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
367	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
368	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
369	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
370	#556	—	2	2	no	—
371	#554	—	2	2	no	—
372	#552	—	2	4	no	—
373	#552	—	2	2	no	—
374	#552	—	2	2	no	—
375	#551	—	2	4	no	—
376	#544	C₂²×C₁₁	1	2	yes	—
377	#542	C₂²×C₁₁	1	4	yes	—
378	#541	C₂²×C₁₁	1	4	yes	—
379	#536	C₂²×C₁₁	1	2	yes	—
380	#533	C₂²×C₁₁	1	4	yes	—
381	#529	C₂²×C₁₁	1	4	yes	—
382	#525	C₂²×C₁₁	1	2	yes	—
383	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
384	#520	C₂²×C₁₁	1	2	yes	—
385	#519	C₂²×C₁₁	1	2	yes	—
386	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
387	#501	C₂²×C₁₁	1	4	yes	complemented
388	#500	C₂²×C₁₁	1	2	yes	complemented
389	#499	C₂²×C₁₁	1	2	yes	complemented
390	#497	C₂²×C₁₁	1	4	yes	complemented
391	#495	C₂²×C₁₁	1	2	yes	complemented
392	#494	C₂²×C₁₁	1	2	yes	complemented
393	#491	C₂²×C₁₁	1	4	yes	complemented
394	#489	C₂²×C₁₁	1	4	yes	complemented
395	#488	C₂²×C₁₁	1	4	yes	complemented
396	#487	C₂²×C₁₁	1	4	yes	complemented
397	#470	C₂²×C₁₁	1	4	yes	—
398	#468	C₂²×C₁₁	1	4	yes	—
399	#467	C₂²×C₁₁	1	2	yes	—
400	#467	C₂²×C₁₁	1	1	yes	characteristic
401	#467	C₂²×C₁₁	1	4	yes	—
402	#467	C₂²×C₁₁	1	2	yes	—
403	#467	C₂²×C₁₁	1	1	yes	characteristic
404	#467	C₂²×C₁₁	1	2	yes	—
405	#467	C₂²×C₁₁	1	2	yes	—
406	#466	C₂²×C₁₁	1	1	yes	characteristic
407	#466	C₂²×C₁₁	1	1	yes	characteristic
408	#465	C₂²×C₁₁	1	4	yes	—
409	#465	C₂²×C₁₁	1	2	yes	—
410	#465	C₂²×C₁₁	1	2	yes	—
411	#441	C₂²×C₁₁	1	4	yes	complemented
412	#441	C₂²×C₁₁	1	4	yes	complemented
413	#440	C₂²×C₁₁	1	4	yes	complemented
414	#440	C₂²×C₁₁	1	4	yes	complemented
415	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	complemented
416	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	complemented
417	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	complemented
418	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
419	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
420	C₄×D₈	C₂²×C₁₁	1	2	yes	complemented
421	#428	C₂²×C₁₁	1	2	yes	—
422	#427	C₂²×C₁₁	1	1	yes	characteristic
423	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
424	#419	C₂²×C₁₁	1	2	yes	—
425	#417	C₂²×C₁₁	1	2	yes	—
426	#416	C₂²×C₁₁	1	2	yes	—
427	C₂×#103	C₂²×C₁₁	1	2	yes	—
428	#405	C₂²×C₁₁	1	1	yes	characteristic
429	#405	C₂²×C₁₁	1	1	yes	characteristic
430	#405	C₂²×C₁₁	1	2	yes	—
431	#405	C₂²×C₁₁	1	2	yes	—
432	#405	C₂²×C₁₁	1	1	yes	characteristic
433	#405	C₂²×C₁₁	1	1	yes	characteristic
434	C₂×#97	C₂²×C₁₁	1	2	yes	—
435	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
436	C₂²×C₁₁	—	2	1	no	—
437	C₂²×C₁₁	—	2	1	no	—
438	C₂²×C₁₁	—	2	1	no	—
439	C₂²×C₁₁	—	2	1	no	—
440	C₂²×C₁₁	—	2	1	no	—
441	C₂²×C₁₁	—	2	1	no	—
442	C₂²×C₁₁	—	2	1	no	—
443	C₂²×C₁₁	—	4	4	no	—
444	C₂²×C₁₁	—	4	2	no	—
445	C₂²×C₁₁	—	4	2	no	—
446	C₂²×C₁₁	—	4	2	no	—
447	C₂²×C₁₁	#532	1	2	yes	—
448	C₂²×C₁₁	#578	1	2	yes	—
449	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
450	C₄×C₁₁	—	2	2	no	—
451	C₄×C₁₁	—	2	2	no	—
452	C₄×C₁₁	—	2	1	no	—
453	C₄×C₁₁	—	2	1	no	—
454	C₄×C₁₁	—	2	2	no	—
455	C₄×C₁₁	—	2	2	no	—
456	C₄×C₁₁	—	4	4	no	—
457	C₄×C₁₁	—	4	2	no	—
458	C₄×C₁₁	—	4	2	no	—
459	C₄×C₁₁	—	4	4	no	—
460	C₄×C₁₁	—	4	2	no	—
461	C₄×C₁₁	#532	1	2	yes	—
462	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
463	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
464	C₂×#41	C₂³×C₁₁	1	2	yes	—
465	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
466	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
467	#137	—	2	8	no	—
468	#135	—	2	4	no	—
469	C₂×Q₁₆	—	2	4	no	—
470	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
471	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
472	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
473	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
475	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
476	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
477	C₂×M₁₆	—	2	4	no	—
478	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
480	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
481	C₂²×C₈	—	2	4	no	—
482	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
488	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
492	#126	—	2	4	no	—
493	#126	—	2	4	no	—
494	#126	—	2	4	no	—
495	#126	—	2	4	no	—
496	#125	—	2	4	no	—
497	#125	—	2	4	no	—
498	#125	—	2	2	no	—
499	#125	—	2	4	no	—
500	#125	C₂³×C₁₁	1	4	yes	—
501	#124	—	2	4	no	—
502	#124	C₂³×C₁₁	1	4	yes	—
503	#123	—	2	2	no	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
515	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
516	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
517	C₂²⋊Q₈	C₂³×C₁₁	1	2	yes	—
518	#121	C₂³×C₁₁	1	2	yes	—
519	#121	C₂³×C₁₁	1	2	yes	—
520	#120	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	4	no	—
524	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
525	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
526	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	C₂³×C₁₁	1	4	yes	—
532	#117	—	2	4	no	—
533	#117	—	2	2	no	—
534	#117	—	2	4	no	—
535	#117	—	2	4	no	—
536	#117	D₄×C₁₁	1	1	yes	characteristic
537	#117	D₄×C₁₁	1	2	yes	—
538	#117	D₄×C₁₁	1	1	yes	characteristic
539	#117	C₂³×C₁₁	1	2	yes	—
540	#117	C₂³×C₁₁	1	1	yes	characteristic
541	#117	C₂³×C₁₁	1	1	yes	characteristic
542	#117	C₂³×C₁₁	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	—	2	2	no	—
545	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
546	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
551	#107	C₂³×C₁₁	1	2	yes	—
552	#107	C₂³×C₁₁	1	2	yes	—
553	#107	C₂³×C₁₁	1	1	yes	characteristic
554	#107	C₂³×C₁₁	1	1	yes	characteristic
555	#107	C₂³×C₁₁	1	4	yes	—
556	#106	C₂³×C₁₁	1	2	yes	—
557	#106	C₂³×C₁₁	1	4	yes	—
558	#103	C₂³×C₁₁	1	4	yes	—
559	#103	C₂³×C₁₁	1	4	yes	—
560	#103	C₂³×C₁₁	1	2	yes	—
561	#103	C₂³×C₁₁	1	2	yes	—
562	#103	C₂³×C₁₁	1	4	yes	—
563	#103	C₂³×C₁₁	1	4	yes	—
564	#103	C₂³×C₁₁	1	4	yes	—
565	#102	C₂³×C₁₁	1	2	yes	—
566	#102	C₂³×C₁₁	1	2	yes	—
567	#102	C₂³×C₁₁	1	4	yes	—
568	#97	C₂³×C₁₁	1	2	yes	—
569	#97	C₂³×C₁₁	1	2	yes	—
570	#97	C₂³×C₁₁	1	2	yes	—
571	#97	C₂³×C₁₁	1	2	yes	—
572	C₄×C₈	C₂³×C₁₁	1	2	yes	—
573	C₄×C₈	C₂³×C₁₁	1	2	yes	—
574	C₄×C₈	C₂³×C₁₁	1	2	yes	—
575	C₄×C₈	C₂³×C₁₁	1	2	yes	—
576	C₂×C₁₁	—	2	2	no	—
577	C₂×C₁₁	—	2	2	no	—
578	C₂×C₁₁	—	4	1	no	—
579	C₂×C₁₁	—	8	2	no	—
580	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
581	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
582	C₂×C₁₁	#3584	1	1	yes	characteristic
583	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
584	#41	—	2	4	no	—
585	#41	—	2	4	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
591	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
603	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
610	Q₁₆	—	2	4	no	—
611	Q₁₆	—	2	4	no	—
612	Q₁₆	—	2	2	no	—
613	Q₁₆	—	2	8	no	—
614	SD₁₆	—	2	4	no	—
615	SD₁₆	—	2	8	no	—
616	D₈	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	4	no	—
619	M₁₆	C₁₁×#41	1	4	yes	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	4	no	—
626	C₂×C₈	C₁₁×#41	1	4	yes	—
627	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
628	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
629	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
632	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
647	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
654	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
668	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	2	no	—
673	C₄²	C₂×D₄×C₁₁	1	2	yes	—
674	C₄²	C₂×D₄×C₁₁	1	2	yes	—
675	C₄²	C₂⁴×C₁₁	1	2	yes	—
676	C₄²	C₂⁴×C₁₁	1	2	yes	—
677	C₁₁	#60708	1	1	yes	characteristic, direct product factor, Sylow
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	1	no	—
682	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
685	Q₈	—	2	4	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	4	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	4	4	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	8	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
721	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
722	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
723	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	1	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×C₁₁×#41	1	2	yes	—
728	C₈	C₂×C₁₁×#41	1	2	yes	—
729	C₈	C₂×C₁₁×#41	1	4	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₁₁×#532	1	2	yes	—
742	C₂²	C₁₁×#578	1	2	yes	—
743	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	C₁₁×#532	1	2	yes	—
756	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
757	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
763	C₂	C₂×C₁₁×#578	1	1	yes	characteristic
764	C₂	C₁₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3495	C₂	semidirect
2. C₁₁×#3181	C₂	semidirect
3. C₁₁×#3178	C₂	semidirect
4. C₁₁×#3177	C₂	semidirect
5. C₁₁×#3175	C₂	semidirect
6. C₁₁×#3170	C₂	semidirect
7. C₁₁×#3168	C₂	semidirect
8. C₁₁×#3164	C₂	semidirect
9. C₁₁×#3156	C₂	semidirect
10. C₁₁×#3137	C₂	semidirect
11. C₁₁×#3056	C₂	semidirect
13. C₂×C₁₁×#467	C₂	semidirect
14. C₁₁×#2951	C₂	semidirect
15. C₁₁×#2950	C₂	semidirect
16. C₁₁×#2947	C₂	semidirect
17. C₂×C₁₁×#405	C₂	semidirect
40. C₁₁×#501	C₂²	semidirect
41. C₁₁×#500	C₂²	semidirect
42. C₁₁×#499	C₂²	semidirect
43. C₁₁×#497	C₂²	semidirect
44. C₁₁×#495	C₂²	semidirect
45. C₁₁×#494	C₂²	semidirect
46. C₁₁×#491	C₂²	semidirect
47. C₁₁×#489	C₂²	semidirect
48. C₁₁×#488	C₂²	semidirect
49. C₁₁×#487	C₂²	semidirect
64. C₁₁×#441	C₂²	semidirect
65. C₁₁×#441	C₂²	semidirect
66. C₁₁×#440	C₂²	semidirect
67. C₁₁×#440	C₂²	semidirect
68. C₄×C₁₁×Q₁₆	C₂²	semidirect
69. C₄×C₁₁×Q₁₆	C₂²	semidirect
70. C₄×C₁₁×Q₁₆	C₂²	semidirect
71. C₄×C₁₁×Q₁₆	C₂²	semidirect
72. C₄×C₁₁×SD₁₆	C₂²	semidirect
73. C₄×C₁₁×D₈	C₂²	semidirect
201. #60708	C₁₁	direct (N × H)
296. #3495	C₂×C₁₁	semidirect
297. #3181	C₂×C₁₁	semidirect
298. #3178	C₂×C₁₁	semidirect
299. #3177	C₂×C₁₁	semidirect
300. #3175	C₂×C₁₁	semidirect
301. #3170	C₂×C₁₁	semidirect
302. #3168	C₂×C₁₁	semidirect
303. #3164	C₂×C₁₁	semidirect
304. #3156	C₂×C₁₁	semidirect
305. #3137	C₂×C₁₁	semidirect
306. #3056	C₂×C₁₁	semidirect
308. C₂×#467	C₂×C₁₁	semidirect
309. #2951	C₂×C₁₁	semidirect
310. #2950	C₂×C₁₁	semidirect
311. #2947	C₂×C₁₁	semidirect
312. C₂×#405	C₂×C₁₁	semidirect
387. #501	C₂²×C₁₁	semidirect
388. #500	C₂²×C₁₁	semidirect
389. #499	C₂²×C₁₁	semidirect
390. #497	C₂²×C₁₁	semidirect
391. #495	C₂²×C₁₁	semidirect
392. #494	C₂²×C₁₁	semidirect
393. #491	C₂²×C₁₁	semidirect
394. #489	C₂²×C₁₁	semidirect
395. #488	C₂²×C₁₁	semidirect
396. #487	C₂²×C₁₁	semidirect
411. #441	C₂²×C₁₁	semidirect
412. #441	C₂²×C₁₁	semidirect
413. #440	C₂²×C₁₁	semidirect
414. #440	C₂²×C₁₁	semidirect
415. C₄×Q₁₆	C₂²×C₁₁	semidirect
416. C₄×Q₁₆	C₂²×C₁₁	semidirect
417. C₄×Q₁₆	C₂²×C₁₁	semidirect
418. C₄×Q₁₆	C₂²×C₁₁	semidirect
419. C₄×SD₁₆	C₂²×C₁₁	semidirect
420. C₄×D₈	C₂²×C₁₁	semidirect
677. C₁₁	#60708	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×#3495	2
C₁₁×#3181	2
C₁₁×#3178	2
C₁₁×#3177	2
C₁₁×#3175	2
C₁₁×#3170	2
C₁₁×#3168	2
C₁₁×#3164	2
C₁₁×#3156	2
C₁₁×#3137	2
C₁₁×#3056	2
C₁₁×#3050	2
C₂×C₁₁×#467	2
C₁₁×#2951	2
C₁₁×#2950	2
C₁₁×#2947	2
C₂×C₁₁×#405	2
#60708	11

Subgroups — C11×#60708 #14637901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60708 #14637901