Subgroups — D₁₁×#3498 #15662088

Order 2816.

12982 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	#13082394	C₂	1	1	yes	maximal, characteristic, complemented
3	#13082393	C₂	1	4	yes	maximal, complemented
4	#13082392	C₂	1	3	yes	maximal, complemented
5	#13082391	C₂	1	6	yes	maximal, complemented
6	#13082390	C₂	1	2	yes	maximal, complemented
7	#13082389	C₂	1	3	yes	maximal, complemented
8	#13082388	C₂	1	12	yes	maximal, complemented
9	D₁₁×#550	C₂	1	4	yes	maximal, complemented
10	D₄²×D₁₁	C₂	1	12	yes	maximal, complemented
11	D₁₁×#535	C₂	1	6	yes	maximal, complemented
12	D₁₁×#532	C₂	1	3	yes	maximal, complemented
13	C₂×D₁₁×#127	C₂	1	3	yes	maximal, complemented
14	C₄×#41×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	D₁₁×H(5,𝔽₂)	—	2	32	no	—
18	C₂×#67042	C₂²	1	6	yes	complemented
19	C₂×#67042	C₂²	1	4	yes	complemented
20	C₂×#67042	C₂²	1	2	yes	complemented
21	C₂×#41×D₁₁	C₂²	1	1	yes	characteristic
22	C₂×#41×D₁₁	C₂²	1	6	yes	complemented
23	C₂×#41×D₁₁	C₂²	1	4	yes	complemented
24	C₂×#67037	C₂²	1	6	yes	complemented
25	C₂×#67037	C₂²	1	12	yes	complemented
26	C₂²×D₄×D₁₁	C₂²	1	6	yes	complemented
27	C₂²×D₄×D₁₁	C₂²	1	12	yes	complemented
28	C₂²×D₄×D₁₁	C₂²	1	12	yes	complemented
29	C₁₁×#550	C₂²	1	4	yes	complemented
30	D₄²×C₁₁	C₂²	1	12	yes	complemented
31	C₁₁×#535	C₂²	1	6	yes	complemented
32	C₁₁×#532	C₂²	1	3	yes	complemented
33	C₂×C₁₁×#127	C₂²	1	3	yes	complemented
34	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic, complemented
35	#10623365	C₂²	1	8	yes	complemented
36	#10623363	C₂²	1	6	yes	complemented
37	#10623361	C₂²	1	6	yes	complemented
38	#41×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
39	#10623336	C₂²	1	6	yes	complemented
40	C₂×#66993	C₂²	1	12	yes	complemented
41	C₂×#66993	C₂²	1	6	yes	complemented
42	D₄×C₂²⋊D₁₁	C₂²	1	24	yes	complemented
43	D₄×C₂²⋊D₁₁	C₂²	1	24	yes	complemented
44	#10623256	C₂²	1	3	yes	complemented
45	D₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	#10623249	C₂²	1	12	yes	complemented
47	#10623248	C₂²	1	12	yes	complemented
48	#10623247	C₂²	1	3	yes	complemented
49	#10623246	C₂²	1	12	yes	complemented
50	D₁₁×#127	C₂²	1	3	yes	complemented
51	D₁₁×#127	C₂²	1	6	yes	complemented
52	D₁₁×#127	C₂²	1	12	yes	complemented
53	D₁₁×#127	C₂²	1	12	yes	complemented
54	D₁₁×#127	C₂²	1	6	yes	complemented
55	D₁₁×#127	C₂²	1	6	yes	complemented
56	#10623205	C₂²	1	12	yes	complemented
57	D₁₁×#124	C₂²	1	6	yes	complemented
58	#10623199	C₂²	1	6	yes	complemented
59	#10623140	C₂²	1	24	yes	complemented
60	#10623140	C₂²	1	24	yes	complemented
61	#10623138	C₂²	1	24	yes	complemented
62	D₁₁×#121	C₂²	1	12	yes	complemented
63	D₁₁×#121	C₂²	1	24	yes	complemented
64	#10623130	C₂²	1	24	yes	complemented
65	#10623127	C₂²	1	12	yes	complemented
66	#10623123	C₂²	1	24	yes	complemented
67	#10623121	C₂²	1	48	yes	complemented
68	D₁₁×#120	C₂²	1	24	yes	complemented
69	#10623108	C₂²	1	4	yes	complemented
70	C₄×#4343	C₂²	1	2	yes	complemented
71	C₄×Q₈×D₁₁	C₂²	1	2	yes	complemented
72	#10623084	C₂²	1	12	yes	complemented
73	D₄×D₄₄	C₂²	1	12	yes	complemented
74	D₄×D₄₄	C₂²	1	12	yes	complemented
75	#10623079	C₂²	1	12	yes	complemented
76	C₄×D₄×D₁₁	C₂²	1	12	yes	complemented
77	C₄×D₄×D₁₁	C₂²	1	6	yes	complemented
78	C₄×#4341	C₂²	1	6	yes	complemented
79	#10623056	C₂²	1	6	yes	complemented
80	#10623053	C₂²	1	3	yes	complemented
81	D₁₁×#117	C₂²	1	3	yes	complemented
82	#10623008	C₂²	1	3	yes	complemented
83	C₂×#66927	C₂²	1	3	yes	complemented
84	C₄×#4339	C₂²	1	3	yes	complemented
85	C₂×C₄²×D₁₁	C₂²	1	3	yes	complemented
86	C₂⁴×D₁₁	C₂³	1	12	yes	—
87	C₁₁×H(5,𝔽₂)	—	2	16	no	—
88	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
89	C₂×C₁₁×#41	C₂³	1	6	yes	complemented
90	C₂×C₁₁×#41	C₂³	1	4	yes	complemented
91	C₂²×D₄×C₁₁	C₂³	1	12	yes	complemented
92	C₂²×D₄×C₁₁	C₂³	1	6	yes	complemented
93	C₂²×D₄×C₁₁	C₂³	1	12	yes	complemented
94	C₂²×C₂²⋊D₁₁	C₂³	1	24	yes	complemented
95	C₂²×C₂²⋊D₁₁	C₂³	1	12	yes	complemented
96	C₂²×C₂²⋊D₁₁	C₂³	1	24	yes	complemented
97	#67042	—	2	16	no	—
98	#67042	—	2	32	no	—
99	#67042	—	2	48	no	—
100	#41×D₁₁	—	2	32	no	—
101	#41×D₁₁	—	2	48	no	—
102	#41×D₁₁	D₄	1	16	yes	complemented
103	C₂×#4343	C₂³	1	1	yes	characteristic
104	C₂×#4343	C₂³	1	6	yes	complemented
105	C₂×#4343	C₂³	1	4	yes	complemented
106	C₂×Q₈×D₁₁	C₂³	1	2	yes	—
107	C₂×Q₈×D₁₁	C₂³	1	1	yes	characteristic
108	#67037	—	2	96	no	—
109	#67037	—	2	48	no	—
110	C₂×#4341	C₂³	1	3	yes	—
111	C₂×#4341	C₂³	1	6	yes	complemented
112	C₂×#4341	C₂³	1	12	yes	complemented
113	C₂×#4341	C₂³	1	12	yes	complemented
114	C₂×D₄×D₁₁	—	2	96	no	—
115	C₂×D₄×D₁₁	—	2	48	no	—
116	C₂×D₄×D₁₁	—	4	48	no	—
117	C₂×D₄×D₁₁	C₂³	1	12	yes	—
118	C₂×D₄×D₁₁	C₂³	1	6	yes	—
119	C₂×D₄×D₁₁	C₂³	1	12	yes	—
120	C₂×D₄×D₁₁	C₂³	1	12	yes	—
121	C₂×D₄×D₁₁	C₂³	1	24	yes	—
122	C₂×D₄×D₁₁	C₂³	1	3	yes	—
123	C₂×D₄×D₁₁	C₂³	1	12	yes	complemented
124	C₂×D₄×D₁₁	C₂³	1	12	yes	complemented
125	C₂×D₄×D₁₁	C₂³	1	12	yes	complemented
126	C₂×D₄×D₁₁	C₂³	1	12	yes	complemented
127	C₂×D₄×D₁₁	C₂³	1	24	yes	complemented
128	C₂×D₄×D₁₁	C₂³	1	24	yes	complemented
129	C₂×D₄×D₁₁	C₂³	1	24	yes	complemented
130	C₂×#4339	C₂³	1	3	yes	—
131	C₂×#4339	C₂³	1	6	yes	complemented
132	C₂×#4339	C₂³	1	12	yes	complemented
133	C₂×#4339	C₂³	1	12	yes	complemented
134	C₂²×D₄₄	C₂³	1	6	yes	complemented
135	C₂²×D₄₄	C₂³	1	12	yes	complemented
136	C₂²×D₄₄	C₂³	1	12	yes	complemented
137	C₂²×C₄×D₁₁	C₂³	1	6	yes	—
138	C₂²×C₄×D₁₁	C₂³	1	12	yes	—
139	C₂²×C₄×D₁₁	C₂³	1	3	yes	—
140	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
141	C₁₁×#127	C₂³	1	3	yes	complemented
142	C₁₁×#127	C₂³	1	6	yes	complemented
143	C₁₁×#127	C₂³	1	12	yes	complemented
144	C₁₁×#124	C₂³	1	6	yes	complemented
145	C₁₁×#121	C₂³	1	12	yes	complemented
146	C₁₁×#121	C₂³	1	24	yes	complemented
147	C₁₁×#120	C₂³	1	24	yes	complemented
148	C₄×Q₈×C₁₁	C₂³	1	2	yes	complemented
149	C₄×D₄×C₁₁	C₂³	1	6	yes	complemented
150	C₄×D₄×C₁₁	C₂³	1	12	yes	complemented
151	C₁₁×#117	C₂³	1	3	yes	complemented
152	C₂×C₄²×C₁₁	C₂³	1	3	yes	complemented
153	#67006	C₂³	1	24	yes	complemented
154	#67000	C₂³	1	6	yes	complemented
155	Q₈×Dic₁₁	C₂³	1	2	yes	complemented
156	#66997	C₂³	1	2	yes	complemented
157	#66993	C₂³	1	12	yes	complemented
158	#66993	C₂³	1	6	yes	complemented
159	#66993	C₂³	1	12	yes	complemented
160	#66993	C₂³	1	24	yes	complemented
161	#66993	C₂³	1	24	yes	complemented
162	#66993	C₂³	1	24	yes	complemented
163	#66993	C₂³	1	24	yes	complemented
164	#66992	C₂³	1	48	yes	complemented
165	#66992	C₂³	1	24	yes	complemented
166	#66991	C₂³	1	12	yes	complemented
167	#66991	C₂³	1	24	yes	complemented
168	#66990	C₂³	1	48	yes	complemented
169	#66990	C₂³	1	24	yes	complemented
170	#66989	C₂³	1	6	yes	complemented
171	D₄×Dic₁₁	C₂³	1	12	yes	complemented
172	D₄×Dic₁₁	C₂³	1	6	yes	complemented
173	#66983	C₂³	1	12	yes	complemented
174	#66983	C₂³	1	24	yes	complemented
175	C₄×C₂²⋊D₁₁	C₂³	1	12	yes	complemented
176	C₄×C₂²⋊D₁₁	C₂³	1	24	yes	complemented
177	#66979	C₂³	1	3	yes	complemented
178	C₂×C₄×Dic₁₁	C₂³	1	3	yes	complemented
179	C₂×C₄×Dic₁₁	C₂³	1	6	yes	complemented
180	#66948	C₂³	1	12	yes	complemented
181	#66948	C₂³	1	24	yes	complemented
182	#66946	C₂³	1	12	yes	complemented
183	#66946	C₂³	1	6	yes	complemented
184	#66945	C₂³	1	6	yes	complemented
185	C₄⋊C₄×D₁₁	C₂³	1	4	yes	—
186	C₄⋊C₄×D₁₁	C₂³	1	6	yes	—
187	#66941	C₂³	1	4	yes	complemented
188	#66940	C₂³	1	6	yes	complemented
189	#66938	C₂³	1	24	yes	complemented
190	#66937	C₂³	1	24	yes	complemented
191	#66937	C₂³	1	48	yes	complemented
192	#66935	C₂³	1	24	yes	complemented
193	#66935	C₂³	1	48	yes	complemented
194	(C₂²⋊D₁₁)⋊C₄	C₂³	1	12	yes	complemented
195	(C₂²⋊D₁₁)⋊C₄	C₂³	1	24	yes	complemented
196	C₂²⋊C₄×D₁₁	C₂³	1	6	yes	—
197	C₂²⋊C₄×D₁₁	C₂³	1	24	yes	—
198	#66930	C₂³	1	6	yes	complemented
199	#66928	C₂³	1	6	yes	complemented
200	#66927	C₂³	1	3	yes	complemented
201	#66927	C₂³	1	6	yes	complemented
202	#66927	C₂³	1	12	yes	complemented
203	C₄×D₄₄	C₂³	1	6	yes	complemented
204	C₄×D₄₄	C₂³	1	12	yes	complemented
205	#66925	C₂³	1	6	yes	complemented
206	C₄²×D₁₁	C₂³	1	1	yes	characteristic
207	C₄²×D₁₁	C₂³	1	3	yes	—
208	C₄²×D₁₁	C₂³	1	6	yes	—
209	C₄²×D₁₁	C₂³	1	3	yes	complemented
210	C₄²×D₁₁	C₂³	1	3	yes	complemented
211	C₄²×D₁₁	C₂³	1	6	yes	complemented
212	#66922	C₂³	1	1	yes	characteristic, complemented
213	C₄×Dic₂₂	C₂³	1	6	yes	complemented
214	C₂×#3498	—	11	1	no	maximal, Sylow
215	C₂⁴×C₁₁	C₂⁴	1	12	yes	—
216	C₂³×D₁₁	—	2	48	no	—
217	C₂³×D₁₁	—	4	48	no	—
218	C₂³×D₁₁	C₂⁴	1	12	yes	—
219	C₂³×D₁₁	C₂⁴	1	3	yes	—
220	C₂³×D₁₁	C₂⁴	1	12	yes	—
221	C₂³×D₁₁	C₂⁴	1	24	yes	—
222	C₁₁×#41	—	2	16	no	—
223	C₁₁×#41	—	2	24	no	—
224	C₁₁×#41	C₂×D₄	1	8	yes	complemented
225	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₁	C₂⁴	1	1	yes	characteristic
227	C₂×D₄×C₁₁	—	2	48	no	—
228	C₂×D₄×C₁₁	—	2	24	no	—
229	C₂×D₄×C₁₁	—	4	24	no	—
230	C₂×D₄×C₁₁	C₂⁴	1	12	yes	—
231	C₂×D₄×C₁₁	C₂⁴	1	6	yes	—
232	C₂×D₄×C₁₁	C₂⁴	1	12	yes	—
233	C₂×D₄×C₁₁	C₂⁴	1	12	yes	—
234	C₂×D₄×C₁₁	C₂⁴	1	24	yes	—
235	C₂×D₄×C₁₁	C₂⁴	1	3	yes	—
236	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
237	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
238	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
239	C₂×C₂²⋊D₁₁	—	2	96	no	—
240	C₂×C₂²⋊D₁₁	—	2	48	no	—
241	C₂×C₂²⋊D₁₁	—	4	48	no	—
242	C₂×C₂²⋊D₁₁	C₂⁴	1	24	yes	—
243	C₂×C₂²⋊D₁₁	C₂⁴	1	12	yes	—
244	C₂×C₂²⋊D₁₁	C₂⁴	1	12	yes	—
245	C₂×C₂²⋊D₁₁	C₂⁴	1	24	yes	—
246	C₂×C₂²⋊D₁₁	C₂⁴	1	12	yes	—
247	C₂×C₂²⋊D₁₁	C₂⁴	1	48	yes	—
248	C₂×C₂²⋊D₁₁	C₂⁴	1	6	yes	—
249	C₂²×Dic₁₁	C₂⁴	1	6	yes	—
250	C₂²×Dic₁₁	C₂⁴	1	12	yes	—
251	C₂²×Dic₁₁	C₂⁴	1	3	yes	—
252	#4343	—	2	24	no	—
253	#4343	—	2	16	no	—
254	#4343	C₂×D₄	1	8	yes	complemented
255	Q₈×D₁₁	—	2	8	no	—
256	Q₈×D₁₁	C₂×D₄	1	8	yes	complemented
257	#4341	—	2	48	no	—
258	#4341	—	2	24	no	—
259	#4341	—	2	48	no	—
260	#4341	C₂×D₄	1	24	yes	complemented
261	D₄×D₁₁	—	2	96	no	—
262	D₄×D₁₁	—	2	48	no	—
263	D₄×D₁₁	—	2	48	no	—
264	D₄×D₁₁	—	2	24	no	—
265	D₄×D₁₁	—	2	48	no	—
266	D₄×D₁₁	—	2	48	no	—
267	D₄×D₁₁	—	2	48	no	—
268	D₄×D₁₁	—	2	48	no	—
269	D₄×D₁₁	—	2	48	no	—
270	D₄×D₁₁	—	4	48	no	—
271	D₄×D₁₁	—	4	48	no	—
272	D₄×D₁₁	—	4	48	no	—
273	D₄×D₁₁	C₂×D₄	1	24	yes	complemented
274	#4339	—	2	48	no	—
275	#4339	—	2	48	no	—
276	#4339	—	2	24	no	—
277	#4339	C₂×D₄	1	24	yes	complemented
278	C₂×D₄₄	—	2	48	no	—
279	C₂×D₄₄	—	2	24	no	—
280	C₂×D₄₄	—	4	24	no	—
281	C₂×D₄₄	C₂⁴	1	12	yes	—
282	C₂×D₄₄	C₂⁴	1	6	yes	—
283	C₂×D₄₄	C₂⁴	1	12	yes	—
284	C₂×D₄₄	C₂⁴	1	12	yes	—
285	C₂×D₄₄	C₂⁴	1	24	yes	—
286	C₂×D₄₄	C₂⁴	1	3	yes	—
287	C₂×C₄×D₁₁	—	2	48	no	—
288	C₂×C₄×D₁₁	—	2	24	no	—
289	C₂×C₄×D₁₁	C₂×D₄	1	24	yes	complemented
290	C₂×C₄×D₁₁	C₂⁴	1	6	yes	—
291	C₂×C₄×D₁₁	C₂⁴	1	6	yes	—
292	C₂×C₄×D₁₁	C₂⁴	1	6	yes	—
293	C₂×C₄×D₁₁	C₂⁴	1	12	yes	—
294	C₂×C₄×D₁₁	C₂⁴	1	4	yes	—
295	C₂×C₄×D₁₁	C₂⁴	1	12	yes	—
296	C₂×C₄×D₁₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×D₁₁	C₂⁴	1	3	yes	—
298	C₂×C₄×D₁₁	C₂⁴	1	3	yes	—
299	C₂×C₄×D₁₁	C₂⁴	1	3	yes	—
300	C₂×C₄×D₁₁	C₂⁴	1	2	yes	—
301	C₂×Dic₂₂	C₂⁴	1	2	yes	—
302	C₂×Dic₂₂	C₂⁴	1	4	yes	—
303	C₂×Dic₂₂	C₂⁴	1	3	yes	—
304	C₁₁×C₄⋊C₄	C₂⁴	1	6	yes	—
305	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₁₁×C₂²⋊C₄	C₂⁴	1	6	yes	—
307	C₁₁×C₂²⋊C₄	C₂⁴	1	24	yes	—
308	C₄²×C₁₁	C₂⁴	1	6	yes	—
309	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₁₁	C₂⁴	1	3	yes	—
311	C₂²⋊Dic₁₁	C₂⁴	1	6	yes	—
312	C₂²⋊Dic₁₁	C₂⁴	1	24	yes	—
313	(C₂×D₁₁)⋊C₄	C₂⁴	1	12	yes	—
314	(C₂×D₁₁)⋊C₄	C₂⁴	1	24	yes	—
315	(C₂×D₁₁)⋊C₄	C₂⁴	1	24	yes	—
316	C₄⋊Dic₁₁	C₂⁴	1	6	yes	—
317	C₄⋊Dic₁₁	C₂⁴	1	4	yes	—
318	Dic₁₁⋊C₄	C₂⁴	1	12	yes	—
319	Dic₁₁⋊C₄	C₂⁴	1	8	yes	—
320	C₄×Dic₁₁	C₂⁴	1	6	yes	—
321	C₄×Dic₁₁	C₂⁴	1	2	yes	—
322	C₄×Dic₁₁	C₂⁴	1	1	yes	characteristic
323	C₄×Dic₁₁	C₂⁴	1	3	yes	—
324	C₄×Dic₁₁	C₂⁴	1	6	yes	—
325	C₄×Dic₁₁	C₂⁴	1	6	yes	—
326	C₄×Dic₁₁	C₂⁴	1	6	yes	—
327	C₂²×H(5,𝔽₂)	—	11	2	no	—
328	#3498	—	11	2	no	—
329	#3498	—	11	4	no	—
330	#3498	—	11	12	no	—
331	#3498	—	11	6	no	—
332	#3498	—	11	3	no	—
333	#3498	—	11	3	no	—
334	#3498	—	11	1	no	—
335	#3498	D₁₁	1	1	yes	characteristic, direct product factor
336	C₂×#550	—	11	4	no	—
337	C₂×D₄²	—	11	12	no	—
338	C₂×#535	—	11	6	no	—
339	C₂×#532	—	11	3	no	—
340	C₂²×#127	—	11	3	no	—
341	C₂×C₄×#41	—	11	1	no	—
342	C₂³×C₁₁	—	2	24	no	—
343	C₂³×C₁₁	—	4	24	no	—
344	C₂³×C₁₁	C₂⁵	1	12	yes	—
345	C₂³×C₁₁	C₂⁵	1	3	yes	—
346	C₂²×D₁₁	—	2	12	no	—
347	C₂²×D₁₁	—	2	24	no	—
348	C₂²×D₁₁	—	2	24	no	—
349	C₂²×D₁₁	—	2	48	no	—
350	C₂²×D₁₁	—	2	48	no	—
351	C₂²×D₁₁	—	4	24	no	—
352	C₂²×D₁₁	—	4	48	no	—
353	C₂²×D₁₁	—	8	96	no	—
354	C₂²×D₁₁	C₂²×D₄	1	12	yes	—
355	C₂²×D₁₁	C₂⁵	1	12	yes	—
356	C₂²×D₁₁	C₂⁵	1	3	yes	—
357	C₂²×D₁₁	C₂⁵	1	1	yes	characteristic
358	Q₈×C₁₁	—	2	4	no	—
359	Q₈×C₁₁	C₂²×D₄	1	4	yes	complemented
360	D₄×C₁₁	—	2	24	no	—
361	D₄×C₁₁	—	2	24	no	—
362	D₄×C₁₁	—	2	12	no	—
363	D₄×C₁₁	—	2	24	no	—
364	D₄×C₁₁	—	4	24	no	—
365	D₄×C₁₁	C₂²×D₄	1	12	yes	complemented
366	C₂×C₄×C₁₁	—	2	24	no	—
367	C₂×C₄×C₁₁	—	2	12	no	—
368	C₂×C₄×C₁₁	C₂²×D₄	1	12	yes	complemented
369	C₂×C₄×C₁₁	C₂⁵	1	6	yes	—
370	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
371	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
372	C₂×C₄×C₁₁	C₂⁵	1	3	yes	—
373	C₂×C₄×C₁₁	C₂⁵	1	2	yes	—
374	C₂²⋊D₁₁	—	2	24	no	—
375	C₂²⋊D₁₁	—	2	24	no	—
376	C₂²⋊D₁₁	—	2	24	no	—
377	C₂²⋊D₁₁	—	2	48	no	—
378	C₂²⋊D₁₁	—	2	48	no	—
379	C₂²⋊D₁₁	—	4	48	no	—
380	C₂²⋊D₁₁	C₂²×D₄	1	24	yes	complemented
381	C₂×Dic₁₁	—	2	24	no	—
382	C₂×Dic₁₁	—	2	12	no	—
383	C₂×Dic₁₁	C₂²×D₄	1	12	yes	complemented
384	C₂×Dic₁₁	C₂⁵	1	6	yes	—
385	C₂×Dic₁₁	C₂⁵	1	4	yes	—
386	C₂×Dic₁₁	C₂⁵	1	1	yes	characteristic
387	C₂×Dic₁₁	C₂⁵	1	3	yes	—
388	C₂×Dic₁₁	C₂⁵	1	2	yes	—
389	D₄₄	—	2	24	no	—
390	D₄₄	—	2	24	no	—
391	D₄₄	—	2	12	no	—
392	D₄₄	—	2	24	no	—
393	D₄₄	—	4	24	no	—
394	D₄₄	C₂²×D₄	1	12	yes	complemented
395	C₄×D₁₁	—	2	8	no	—
396	C₄×D₁₁	—	2	12	no	—
397	C₄×D₁₁	—	2	24	no	—
398	C₄×D₁₁	—	2	12	no	—
399	C₄×D₁₁	—	2	24	no	—
400	C₄×D₁₁	—	2	12	no	—
401	C₄×D₁₁	C₂²×D₄	1	12	yes	—
402	C₄×D₁₁	C₂²×D₄	1	4	yes	—
403	C₄×D₁₁	C₂²×D₄	1	12	yes	complemented
404	C₄×D₁₁	C₂²×D₄	1	12	yes	complemented
405	C₄×D₁₁	H(5,𝔽₂)	1	8	yes	complemented
406	Dic₂₂	—	2	4	no	—
407	Dic₂₂	—	2	8	no	—
408	Dic₂₂	C₂²×D₄	1	12	yes	complemented
409	C₂×H(5,𝔽₂)	—	11	2	no	—
410	C₂×H(5,𝔽₂)	—	11	4	no	—
411	C₂×H(5,𝔽₂)	—	11	6	no	—
412	C₂×H(5,𝔽₂)	—	11	12	no	—
413	C₂×H(5,𝔽₂)	—	11	6	no	—
414	C₂×H(5,𝔽₂)	—	22	32	no	—
415	C₂×H(5,𝔽₂)	C₂×D₁₁	1	2	yes	complemented
416	C₂²×#41	—	11	1	no	—
417	C₂²×#41	—	11	6	no	—
418	C₂²×#41	—	11	4	no	—
419	C₂³×D₄	—	11	6	no	—
420	C₂³×D₄	—	11	12	no	—
421	C₂³×D₄	—	11	12	no	—
422	#550	—	11	8	no	—
423	#550	—	11	12	no	—
424	#550	—	11	24	no	—
425	#550	—	11	4	no	—
426	#550	—	11	12	no	—
427	#550	C₂×D₁₁	1	4	yes	complemented
428	D₄²	—	11	24	no	—
429	D₄²	—	11	24	no	—
430	D₄²	—	11	12	no	—
431	D₄²	—	11	24	no	—
432	D₄²	—	11	24	no	—
433	D₄²	—	11	48	no	—
434	D₄²	—	11	12	no	—
435	D₄²	—	11	12	no	—
436	D₄²	C₂×D₁₁	1	12	yes	complemented
437	#535	—	11	6	no	—
438	#535	—	11	6	no	—
439	#535	—	11	12	no	—
440	#535	—	11	12	no	—
441	#535	—	11	24	no	—
442	#535	—	11	24	no	—
443	#535	—	11	6	no	—
444	#535	C₂×D₁₁	1	6	yes	complemented
445	#532	—	11	6	no	—
446	#532	—	11	3	no	—
447	#532	—	11	3	no	—
448	#532	—	11	6	no	—
449	#532	—	11	12	no	—
450	#532	—	11	12	no	—
451	#532	—	11	3	no	—
452	#532	C₂×D₁₁	1	3	yes	complemented
453	C₂×C₄⋊Q₈	—	11	1	no	—
454	C₂×#127	—	11	12	no	—
455	C₂×#127	—	11	6	no	—
456	C₂×#127	—	11	3	no	—
457	C₂×#127	—	11	6	no	—
458	C₂×#127	—	11	12	no	—
459	C₂×#127	—	11	12	no	—
460	C₂×#127	—	11	6	no	—
461	C₂×#127	—	11	6	no	—
462	C₂×#127	—	11	3	no	—
463	C₂×#127	C₂×D₁₁	1	3	yes	complemented
464	C₂×#124	—	11	6	no	—
465	C₂×#121	—	11	12	no	—
466	C₂×#121	—	11	24	no	—
467	C₂×#120	—	11	24	no	—
468	C₄×#41	—	11	1	no	—
469	C₄×#41	—	11	2	no	—
470	C₄×#41	—	11	6	no	—
471	C₄×#41	—	11	3	no	—
472	C₄×#41	—	11	3	no	—
473	C₄×#41	C₂×D₁₁	1	1	yes	characteristic, complemented
474	C₂×C₄×Q₈	—	11	2	no	—
475	C₂×C₄×D₄	—	11	6	no	—
476	C₂×C₄×D₄	—	11	12	no	—
477	C₂×#117	—	11	3	no	—
478	C₂²×C₄²	—	11	3	no	—
479	C₂²×C₁₁	—	2	6	no	—
480	C₂²×C₁₁	—	2	12	no	—
481	C₂²×C₁₁	—	2	24	no	—
482	C₂²×C₁₁	—	8	24	no	—
483	C₂²×C₁₁	C₂³×D₄	1	6	yes	—
484	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
485	C₂×D₁₁	—	2	6	no	—
486	C₂×D₁₁	—	2	24	no	—
487	C₂×D₁₁	—	2	12	no	—
488	C₂×D₁₁	—	2	24	no	—
489	C₂×D₁₁	—	4	48	no	—
490	C₂×D₁₁	—	8	48	no	—
491	C₂×D₁₁	—	8	24	no	—
492	C₂×D₁₁	C₂³×D₄	1	6	yes	—
493	C₂×D₁₁	C₂³×D₄	1	2	yes	—
494	C₂×D₁₁	C₂×H(5,𝔽₂)	1	4	yes	—
495	C₄×C₁₁	—	2	4	no	—
496	C₄×C₁₁	—	2	6	no	—
497	C₄×C₁₁	C₂³×D₄	1	6	yes	—
498	C₄×C₁₁	C₂³×D₄	1	2	yes	—
499	C₄×C₁₁	C₂×H(5,𝔽₂)	1	4	yes	complemented
500	Dic₁₁	—	2	4	no	—
501	Dic₁₁	—	2	6	no	—
502	Dic₁₁	C₂³×D₄	1	2	yes	—
503	Dic₁₁	C₂³×D₄	1	6	yes	—
504	Dic₁₁	C₂×H(5,𝔽₂)	1	4	yes	complemented
505	C₂⁵	—	11	12	no	—
506	H(5,𝔽₂)	—	2	16	no	—
507	H(5,𝔽₂)	—	22	96	no	—
508	H(5,𝔽₂)	—	22	48	no	—
509	H(5,𝔽₂)	—	22	32	no	—
510	H(5,𝔽₂)	—	22	48	no	—
511	H(5,𝔽₂)	—	22	16	no	—
512	C₂×#41	—	11	16	no	—
513	C₂×#41	—	11	1	no	—
514	C₂×#41	—	11	6	no	—
515	C₂×#41	—	11	4	no	—
516	C₂×#41	—	11	3	no	—
517	C₂×#41	—	11	12	no	—
518	C₂×#41	—	11	6	no	—
519	C₂×#41	—	11	12	no	—
520	C₂×#41	—	11	3	no	—
521	C₂×#41	—	11	12	no	—
522	C₂×#41	—	11	6	no	—
523	C₂×#41	—	11	12	no	—
524	C₂×#41	—	22	48	no	—
525	C₂×#41	—	22	32	no	—
526	C₂×#41	C₂²×D₁₁	1	1	yes	characteristic
527	C₂×#41	C₂²×D₁₁	1	6	yes	complemented
528	C₂×#41	C₂²×D₁₁	1	4	yes	complemented
529	C₂²×Q₈	—	11	1	no	—
530	C₂²×Q₈	—	11	2	no	—
531	C₂²×D₄	—	11	3	no	—
532	C₂²×D₄	—	11	12	no	—
533	C₂²×D₄	—	11	24	no	—
534	C₂²×D₄	—	11	24	no	—
535	C₂²×D₄	—	11	12	no	—
536	C₂²×D₄	—	11	12	no	—
537	C₂²×D₄	—	11	12	no	—
538	C₂²×D₄	—	11	6	no	—
539	C₂²×D₄	—	11	12	no	—
540	C₂²×D₄	—	11	12	no	—
541	C₂²×D₄	—	11	24	no	—
542	C₂²×D₄	—	11	12	no	—
543	C₂²×D₄	—	11	12	no	—
544	C₂²×D₄	—	11	24	no	—
545	C₂²×D₄	—	11	24	no	—
546	C₂²×D₄	—	11	24	no	—
547	C₂²×D₄	—	11	6	no	—
548	C₂²×D₄	—	11	12	no	—
549	C₂²×D₄	—	11	12	no	—
550	C₂²×D₄	—	22	48	no	—
551	C₂²×D₄	—	22	96	no	—
552	C₂²×D₄	—	44	48	no	—
553	C₂²×D₄	C₂²×D₁₁	1	6	yes	complemented
554	C₂²×D₄	C₂²×D₁₁	1	12	yes	complemented
555	C₂²×D₄	C₂²×D₁₁	1	12	yes	complemented
556	C₂³×C₄	—	11	3	no	—
557	C₂³×C₄	—	11	6	no	—
558	C₂³×C₄	—	11	12	no	—
559	C₄⋊Q₈	—	11	2	no	—
560	C₄⋊Q₈	—	11	4	no	—
561	C₄⋊Q₈	—	11	1	no	—
562	C₄⋊Q₈	C₂²×D₁₁	1	1	yes	characteristic, complemented
563	#127	—	11	6	no	—
564	#127	—	11	12	no	—
565	#127	—	11	24	no	—
566	#127	—	11	12	no	—
567	#127	—	11	24	no	—
568	#127	—	11	24	no	—
569	#127	—	11	24	no	—
570	#127	—	11	3	no	—
571	#127	—	11	6	no	—
572	#127	—	11	12	no	—
573	#127	C₂²×D₁₁	1	3	yes	complemented
574	#127	C₂²×D₁₁	1	6	yes	complemented
575	#127	C₂²×D₁₁	1	12	yes	complemented
576	#124	—	11	6	no	—
577	#124	—	11	6	no	—
578	#124	—	11	24	no	—
579	#124	—	11	6	no	—
580	#124	C₂²×D₁₁	1	6	yes	complemented
581	#121	—	11	12	no	—
582	#121	—	11	24	no	—
583	#121	—	11	24	no	—
584	#121	—	11	48	no	—
585	#121	—	11	12	no	—
586	#121	—	11	24	no	—
587	#121	—	11	12	no	—
588	#121	—	11	24	no	—
589	#121	—	11	24	no	—
590	#121	—	11	48	no	—
591	#121	C₂²×D₁₁	1	12	yes	complemented
592	#121	C₂²×D₁₁	1	24	yes	complemented
593	#120	—	11	24	no	—
594	#120	—	11	24	no	—
595	#120	—	11	48	no	—
596	#120	—	11	48	no	—
597	#120	—	11	24	no	—
598	#120	C₂²×D₁₁	1	24	yes	complemented
599	C₄×Q₈	—	11	2	no	—
600	C₄×Q₈	—	11	6	no	—
601	C₄×Q₈	—	11	6	no	—
602	C₄×Q₈	C₂²×D₁₁	1	2	yes	complemented
603	C₄×D₄	—	11	6	no	—
604	C₄×D₄	—	11	12	no	—
605	C₄×D₄	—	11	12	no	—
606	C₄×D₄	—	11	24	no	—
607	C₄×D₄	—	11	6	no	—
608	C₄×D₄	—	11	12	no	—
609	C₄×D₄	—	11	12	no	—
610	C₄×D₄	—	11	24	no	—
611	C₄×D₄	—	11	6	no	—
612	C₄×D₄	—	11	12	no	—
613	C₄×D₄	C₂²×D₁₁	1	6	yes	complemented
614	C₄×D₄	C₂²×D₁₁	1	12	yes	complemented
615	#117	—	11	3	no	—
616	#117	—	11	6	no	—
617	#117	—	11	6	no	—
618	#117	—	11	6	no	—
619	#117	C₂²×D₁₁	1	3	yes	complemented
620	C₂×C₄⋊C₄	—	11	6	no	—
621	C₂×C₄⋊C₄	—	11	4	no	—
622	C₂×C₂²⋊C₄	—	11	6	no	—
623	C₂×C₂²⋊C₄	—	11	24	no	—
624	C₂×C₄²	—	11	6	no	—
625	C₂×C₄²	—	11	3	no	—
626	C₂×C₄²	—	11	3	no	—
627	C₂×C₄²	—	11	6	no	—
628	C₂×C₄²	—	11	6	no	—
629	C₂×C₄²	—	11	3	no	—
630	C₂×C₄²	—	11	3	no	—
631	C₂×C₄²	—	11	1	no	—
632	C₂×C₄²	C₂²×D₁₁	1	3	yes	complemented
633	C₂×C₁₁	—	2	6	no	—
634	C₂×C₁₁	—	4	12	no	—
635	C₂×C₁₁	C₂⁴×D₄	1	1	yes	characteristic
636	C₂×C₁₁	C₂²×H(5,𝔽₂)	1	2	yes	—
637	D₁₁	—	2	6	no	—
638	D₁₁	—	4	12	no	—
639	D₁₁	#3498	1	4	yes	direct product factor
640	C₂⁴	—	11	3	no	—
641	C₂⁴	—	11	12	no	—
642	C₂⁴	—	11	24	no	—
643	C₂⁴	—	11	12	no	—
644	C₂⁴	—	22	48	no	—
645	C₂⁴	—	44	48	no	—
646	C₂⁴	C₂³×D₁₁	1	12	yes	—
647	#41	—	2	16	no	—
648	#41	—	2	24	no	—
649	#41	—	11	8	no	—
650	#41	—	11	24	no	—
651	#41	—	11	24	no	—
652	#41	—	22	48	no	—
653	#41	—	22	48	no	—
654	#41	—	22	48	no	—
655	#41	—	22	24	no	—
656	#41	—	22	24	no	—
657	#41	—	22	48	no	—
658	#41	—	22	16	no	—
659	#41	—	22	24	no	—
660	#41	D₄×D₁₁	1	8	yes	complemented
661	C₂×Q₈	—	11	8	no	—
662	C₂×Q₈	—	11	3	no	—
663	C₂×Q₈	—	11	4	no	—
664	C₂×Q₈	—	11	2	no	—
665	C₂×Q₈	—	22	8	no	—
666	C₂×Q₈	C₂³×D₁₁	1	2	yes	—
667	C₂×Q₈	C₂³×D₁₁	1	1	yes	characteristic
668	C₂×D₄	—	2	48	no	—
669	C₂×D₄	—	2	24	no	—
670	C₂×D₄	—	4	24	no	—
671	C₂×D₄	—	11	6	no	—
672	C₂×D₄	—	11	24	no	—
673	C₂×D₄	—	11	24	no	—
674	C₂×D₄	—	11	12	no	—
675	C₂×D₄	—	11	12	no	—
676	C₂×D₄	—	11	24	no	—
677	C₂×D₄	—	11	12	no	—
678	C₂×D₄	—	11	48	no	—
679	C₂×D₄	—	11	3	no	—
680	C₂×D₄	—	11	12	no	—
681	C₂×D₄	—	11	12	no	—
682	C₂×D₄	—	11	12	no	—
683	C₂×D₄	—	11	6	no	—
684	C₂×D₄	—	11	24	no	—
685	C₂×D₄	—	22	48	no	—
686	C₂×D₄	—	22	24	no	—
687	C₂×D₄	—	22	48	no	—
688	C₂×D₄	—	22	48	no	—
689	C₂×D₄	—	22	48	no	—
690	C₂×D₄	—	22	48	no	—
691	C₂×D₄	—	22	48	no	—
692	C₂×D₄	—	22	96	no	—
693	C₂×D₄	—	22	48	no	—
694	C₂×D₄	—	22	48	no	—
695	C₂×D₄	—	22	96	no	—
696	C₂×D₄	—	22	48	no	—
697	C₂×D₄	—	22	24	no	—
698	C₂×D₄	—	44	24	no	—
699	C₂×D₄	—	44	48	no	—
700	C₂×D₄	—	44	48	no	—
701	C₂×D₄	—	44	48	no	—
702	C₂×D₄	—	44	48	no	—
703	C₂×D₄	C₂³×D₁₁	1	12	yes	—
704	C₂×D₄	C₂³×D₁₁	1	12	yes	—
705	C₂×D₄	C₂³×D₁₁	1	12	yes	—
706	C₂×D₄	C₂³×D₁₁	1	6	yes	—
707	C₂×D₄	C₂³×D₁₁	1	24	yes	—
708	C₂×D₄	C₂³×D₁₁	1	3	yes	—
709	C₂²×C₄	—	11	3	no	—
710	C₂²×C₄	—	11	24	no	—
711	C₂²×C₄	—	11	2	no	—
712	C₂²×C₄	—	11	1	no	—
713	C₂²×C₄	—	11	3	no	—
714	C₂²×C₄	—	11	3	no	—
715	C₂²×C₄	—	11	3	no	—
716	C₂²×C₄	—	11	6	no	—
717	C₂²×C₄	—	11	12	no	—
718	C₂²×C₄	—	11	6	no	—
719	C₂²×C₄	—	11	6	no	—
720	C₂²×C₄	—	11	6	no	—
721	C₂²×C₄	—	11	4	no	—
722	C₂²×C₄	—	11	12	no	—
723	C₂²×C₄	—	11	12	no	—
724	C₂²×C₄	—	22	48	no	—
725	C₂²×C₄	—	22	24	no	—
726	C₂²×C₄	C₂³×D₁₁	1	6	yes	—
727	C₂²×C₄	C₂³×D₁₁	1	12	yes	—
728	C₂²×C₄	C₂³×D₁₁	1	3	yes	—
729	C₄⋊C₄	—	11	12	no	—
730	C₄⋊C₄	—	11	6	no	—
731	C₄⋊C₄	—	11	8	no	—
732	C₄⋊C₄	—	11	4	no	—
733	C₄⋊C₄	C₂³×D₁₁	1	6	yes	—
734	C₄⋊C₄	C₂³×D₁₁	1	4	yes	—
735	C₂²⋊C₄	—	11	6	no	—
736	C₂²⋊C₄	—	11	24	no	—
737	C₂²⋊C₄	—	11	12	no	—
738	C₂²⋊C₄	—	11	24	no	—
739	C₂²⋊C₄	—	11	24	no	—
740	C₂²⋊C₄	C₂³×D₁₁	1	6	yes	—
741	C₂²⋊C₄	C₂³×D₁₁	1	24	yes	—
742	C₄²	—	11	1	no	—
743	C₄²	—	11	2	no	—
744	C₄²	—	11	6	no	—
745	C₄²	—	11	3	no	—
746	C₄²	—	11	6	no	—
747	C₄²	—	11	6	no	—
748	C₄²	—	11	6	no	—
749	C₄²	C₂³×D₁₁	1	1	yes	characteristic
750	C₄²	C₂³×D₁₁	1	3	yes	—
751	C₄²	C₂³×D₁₁	1	6	yes	—
752	C₁₁	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
753	C₂³	—	2	24	no	—
754	C₂³	—	4	24	no	—
755	C₂³	—	11	1	no	—
756	C₂³	—	11	12	no	—
757	C₂³	—	11	3	no	—
758	C₂³	—	11	12	no	—
759	C₂³	—	22	12	no	—
760	C₂³	—	22	24	no	—
761	C₂³	—	22	48	no	—
762	C₂³	—	22	48	no	—
763	C₂³	—	22	24	no	—
764	C₂³	—	44	24	no	—
765	C₂³	—	44	48	no	—
766	C₂³	—	88	96	no	—
767	C₂³	C₂⁴×D₁₁	1	12	yes	—
768	C₂³	C₂⁴×D₁₁	1	3	yes	—
769	Q₈	—	2	4	no	—
770	Q₈	—	11	12	no	—
771	Q₈	—	22	8	no	—
772	Q₈	—	22	4	no	—
773	Q₈	C₂×D₄×D₁₁	1	4	yes	complemented
774	D₄	—	2	24	no	—
775	D₄	—	2	24	no	—
776	D₄	—	2	12	no	—
777	D₄	—	2	24	no	—
778	D₄	—	4	24	no	—
779	D₄	—	11	24	no	—
780	D₄	—	11	12	no	—
781	D₄	—	22	24	no	—
782	D₄	—	22	24	no	—
783	D₄	—	22	48	no	—
784	D₄	—	22	48	no	—
785	D₄	—	22	24	no	—
786	D₄	—	22	24	no	—
787	D₄	—	22	24	no	—
788	D₄	—	22	12	no	—
789	D₄	—	22	24	no	—
790	D₄	—	44	24	no	—
791	D₄	—	44	48	no	—
792	D₄	C₂×D₄×D₁₁	1	12	yes	complemented
793	C₂×C₄	—	2	24	no	—
794	C₂×C₄	—	2	12	no	—
795	C₂×C₄	—	11	12	no	—
796	C₂×C₄	—	11	2	no	—
797	C₂×C₄	—	11	1	no	—
798	C₂×C₄	—	11	3	no	—
799	C₂×C₄	—	11	4	no	—
800	C₂×C₄	—	11	12	no	—
801	C₂×C₄	—	11	12	no	—
802	C₂×C₄	—	11	12	no	—
803	C₂×C₄	—	11	8	no	—
804	C₂×C₄	—	11	6	no	—
805	C₂×C₄	—	11	4	no	—
806	C₂×C₄	—	22	24	no	—
807	C₂×C₄	—	22	12	no	—
808	C₂×C₄	—	22	8	no	—
809	C₂×C₄	—	22	12	no	—
810	C₂×C₄	—	22	24	no	—
811	C₂×C₄	—	22	12	no	—
812	C₂×C₄	—	22	24	no	—
813	C₂×C₄	—	22	12	no	—
814	C₂×C₄	C₂×D₄×D₁₁	1	12	yes	complemented
815	C₂×C₄	C₂⁴×D₁₁	1	6	yes	—
816	C₂×C₄	C₂⁴×D₁₁	1	4	yes	—
817	C₂×C₄	C₂⁴×D₁₁	1	1	yes	characteristic
818	C₂×C₄	C₂⁴×D₁₁	1	3	yes	—
819	C₂×C₄	C₂⁴×D₁₁	1	2	yes	—
820	C₂²	—	2	6	no	—
821	C₂²	—	2	12	no	—
822	C₂²	—	2	24	no	—
823	C₂²	—	8	24	no	—
824	C₂²	—	11	2	no	—
825	C₂²	—	11	4	no	—
826	C₂²	—	11	6	no	—
827	C₂²	—	22	24	no	—
828	C₂²	—	22	6	no	—
829	C₂²	—	22	12	no	—
830	C₂²	—	22	24	no	—
831	C₂²	—	44	48	no	—
832	C₂²	—	88	24	no	—
833	C₂²	—	88	48	no	—
834	C₂²	C₂²×D₄×D₁₁	1	6	yes	—
835	C₂²	C₂⁵×D₁₁	1	1	yes	characteristic
836	C₄	—	2	4	no	—
837	C₄	—	2	6	no	—
838	C₄	—	11	2	no	—
839	C₄	—	11	6	no	—
840	C₄	—	11	4	no	—
841	C₄	—	22	4	no	—
842	C₄	—	22	6	no	—
843	C₄	C₂²×D₄×D₁₁	1	6	yes	—
844	C₄	C₂²×D₄×D₁₁	1	2	yes	—
845	C₄	D₁₁×H(5,𝔽₂)	1	4	yes	complemented
846	C₂	—	2	6	no	—
847	C₂	—	4	12	no	—
848	C₂	—	11	4	no	—
849	C₂	—	22	6	no	—
850	C₂	—	44	12	no	—
851	C₂	C₂³×D₄×D₁₁	1	1	yes	characteristic
852	C₂	C₂×D₁₁×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁶
Fitting	C₁₁×#3498	C₂
hypercenter	#3498	D₁₁
hypocenter	C₁₁	C₂×#3498
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #3498

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₁×H(5,𝔽₂)	C₂	semidirect
2. #13082394	C₂	semidirect
3. #13082393	C₂	semidirect
4. #13082392	C₂	semidirect
5. #13082391	C₂	semidirect
6. #13082390	C₂	semidirect
7. #13082389	C₂	semidirect
8. #13082388	C₂	semidirect
9. D₁₁×#550	C₂	semidirect
10. D₄²×D₁₁	C₂	semidirect
11. D₁₁×#535	C₂	semidirect
12. D₁₁×#532	C₂	semidirect
13. C₂×D₁₁×#127	C₂	semidirect
14. C₄×#41×D₁₁	C₂	semidirect
15. C₁₁×#3498	C₂	semidirect
16. C₂×C₁₁×H(5,𝔽₂)	C₂²	semidirect
18. C₂×#67042	C₂²	semidirect
19. C₂×#67042	C₂²	semidirect
20. C₂×#67042	C₂²	semidirect
22. C₂×#41×D₁₁	C₂²	semidirect
23. C₂×#41×D₁₁	C₂²	semidirect
24. C₂×#67037	C₂²	semidirect
25. C₂×#67037	C₂²	semidirect
26. C₂²×D₄×D₁₁	C₂²	semidirect
27. C₂²×D₄×D₁₁	C₂²	semidirect
28. C₂²×D₄×D₁₁	C₂²	semidirect
29. C₁₁×#550	C₂²	semidirect
30. D₄²×C₁₁	C₂²	semidirect
31. C₁₁×#535	C₂²	semidirect
32. C₁₁×#532	C₂²	semidirect
33. C₂×C₁₁×#127	C₂²	semidirect
34. C₄×C₁₁×#41	C₂²	semidirect
35. #10623365	C₂²	semidirect
36. #10623363	C₂²	semidirect
37. #10623361	C₂²	semidirect
38. #41×Dic₁₁	C₂²	semidirect
39. #10623336	C₂²	semidirect
40. C₂×#66993	C₂²	semidirect
41. C₂×#66993	C₂²	semidirect
42. D₄×C₂²⋊D₁₁	C₂²	semidirect
43. D₄×C₂²⋊D₁₁	C₂²	semidirect
44. #10623256	C₂²	semidirect
45. D₁₁×C₄⋊Q₈	C₂²	semidirect
46. #10623249	C₂²	semidirect
47. #10623248	C₂²	semidirect
48. #10623247	C₂²	semidirect
49. #10623246	C₂²	semidirect
50. D₁₁×#127	C₂²	semidirect
51. D₁₁×#127	C₂²	semidirect
52. D₁₁×#127	C₂²	semidirect
53. D₁₁×#127	C₂²	semidirect
54. D₁₁×#127	C₂²	semidirect
55. D₁₁×#127	C₂²	semidirect
56. #10623205	C₂²	semidirect
57. D₁₁×#124	C₂²	semidirect
58. #10623199	C₂²	semidirect
59. #10623140	C₂²	semidirect
60. #10623140	C₂²	semidirect
61. #10623138	C₂²	semidirect
62. D₁₁×#121	C₂²	semidirect
63. D₁₁×#121	C₂²	semidirect
64. #10623130	C₂²	semidirect
65. #10623127	C₂²	semidirect
66. #10623123	C₂²	semidirect
67. #10623121	C₂²	semidirect
68. D₁₁×#120	C₂²	semidirect
69. #10623108	C₂²	semidirect
70. C₄×#4343	C₂²	semidirect
71. C₄×Q₈×D₁₁	C₂²	semidirect
72. #10623084	C₂²	semidirect
73. D₄×D₄₄	C₂²	semidirect
74. D₄×D₄₄	C₂²	semidirect
75. #10623079	C₂²	semidirect
76. C₄×D₄×D₁₁	C₂²	semidirect
77. C₄×D₄×D₁₁	C₂²	semidirect
78. C₄×#4341	C₂²	semidirect
79. #10623056	C₂²	semidirect
80. #10623053	C₂²	semidirect
81. D₁₁×#117	C₂²	semidirect
82. #10623008	C₂²	semidirect
83. C₂×#66927	C₂²	semidirect
84. C₄×#4339	C₂²	semidirect
85. C₂×C₄²×D₁₁	C₂²	semidirect
89. C₂×C₁₁×#41	C₂³	semidirect
90. C₂×C₁₁×#41	C₂³	semidirect
91. C₂²×D₄×C₁₁	C₂³	semidirect
92. C₂²×D₄×C₁₁	C₂³	semidirect
93. C₂²×D₄×C₁₁	C₂³	semidirect
94. C₂²×C₂²⋊D₁₁	C₂³	semidirect
95. C₂²×C₂²⋊D₁₁	C₂³	semidirect
96. C₂²×C₂²⋊D₁₁	C₂³	semidirect
102. #41×D₁₁	D₄	semidirect
104. C₂×#4343	C₂³	semidirect
105. C₂×#4343	C₂³	semidirect
111. C₂×#4341	C₂³	semidirect
112. C₂×#4341	C₂³	semidirect
113. C₂×#4341	C₂³	semidirect
123. C₂×D₄×D₁₁	C₂³	semidirect
124. C₂×D₄×D₁₁	C₂³	semidirect
125. C₂×D₄×D₁₁	C₂³	semidirect
126. C₂×D₄×D₁₁	C₂³	semidirect
127. C₂×D₄×D₁₁	C₂³	semidirect
128. C₂×D₄×D₁₁	C₂³	semidirect
129. C₂×D₄×D₁₁	C₂³	semidirect
131. C₂×#4339	C₂³	semidirect
132. C₂×#4339	C₂³	semidirect
133. C₂×#4339	C₂³	semidirect
134. C₂²×D₄₄	C₂³	semidirect
135. C₂²×D₄₄	C₂³	semidirect
136. C₂²×D₄₄	C₂³	semidirect
140. C₁₁×C₄⋊Q₈	C₂³	semidirect
141. C₁₁×#127	C₂³	semidirect
142. C₁₁×#127	C₂³	semidirect
143. C₁₁×#127	C₂³	semidirect
144. C₁₁×#124	C₂³	semidirect
145. C₁₁×#121	C₂³	semidirect
146. C₁₁×#121	C₂³	semidirect
147. C₁₁×#120	C₂³	semidirect
148. C₄×Q₈×C₁₁	C₂³	semidirect
149. C₄×D₄×C₁₁	C₂³	semidirect
150. C₄×D₄×C₁₁	C₂³	semidirect
151. C₁₁×#117	C₂³	semidirect
152. C₂×C₄²×C₁₁	C₂³	semidirect
153. #67006	C₂³	semidirect
154. #67000	C₂³	semidirect
155. Q₈×Dic₁₁	C₂³	semidirect
156. #66997	C₂³	semidirect
157. #66993	C₂³	semidirect
158. #66993	C₂³	semidirect
159. #66993	C₂³	semidirect
160. #66993	C₂³	semidirect
161. #66993	C₂³	semidirect
162. #66993	C₂³	semidirect
163. #66993	C₂³	semidirect
164. #66992	C₂³	semidirect
165. #66992	C₂³	semidirect
166. #66991	C₂³	semidirect
167. #66991	C₂³	semidirect
168. #66990	C₂³	semidirect
169. #66990	C₂³	semidirect
170. #66989	C₂³	semidirect
171. D₄×Dic₁₁	C₂³	semidirect
172. D₄×Dic₁₁	C₂³	semidirect
173. #66983	C₂³	semidirect
174. #66983	C₂³	semidirect
175. C₄×C₂²⋊D₁₁	C₂³	semidirect
176. C₄×C₂²⋊D₁₁	C₂³	semidirect
177. #66979	C₂³	semidirect
178. C₂×C₄×Dic₁₁	C₂³	semidirect
179. C₂×C₄×Dic₁₁	C₂³	semidirect
180. #66948	C₂³	semidirect
181. #66948	C₂³	semidirect
182. #66946	C₂³	semidirect
183. #66946	C₂³	semidirect
184. #66945	C₂³	semidirect
187. #66941	C₂³	semidirect
188. #66940	C₂³	semidirect
189. #66938	C₂³	semidirect
190. #66937	C₂³	semidirect
191. #66937	C₂³	semidirect
192. #66935	C₂³	semidirect
193. #66935	C₂³	semidirect
194. (C₂²⋊D₁₁)⋊C₄	C₂³	semidirect
195. (C₂²⋊D₁₁)⋊C₄	C₂³	semidirect
198. #66930	C₂³	semidirect
199. #66928	C₂³	semidirect
200. #66927	C₂³	semidirect
201. #66927	C₂³	semidirect
202. #66927	C₂³	semidirect
203. C₄×D₄₄	C₂³	semidirect
204. C₄×D₄₄	C₂³	semidirect
205. #66925	C₂³	semidirect
209. C₄²×D₁₁	C₂³	semidirect
210. C₄²×D₁₁	C₂³	semidirect
211. C₄²×D₁₁	C₂³	semidirect
212. #66922	C₂³	semidirect
213. C₄×Dic₂₂	C₂³	semidirect
224. C₁₁×#41	C₂×D₄	semidirect
254. #4343	C₂×D₄	semidirect
256. Q₈×D₁₁	C₂×D₄	semidirect
260. #4341	C₂×D₄	semidirect
273. D₄×D₁₁	C₂×D₄	semidirect
277. #4339	C₂×D₄	semidirect
289. C₂×C₄×D₁₁	C₂×D₄	semidirect
335. #3498	D₁₁	direct (N × H)
359. Q₈×C₁₁	C₂²×D₄	semidirect
365. D₄×C₁₁	C₂²×D₄	semidirect
368. C₂×C₄×C₁₁	C₂²×D₄	semidirect
380. C₂²⋊D₁₁	C₂²×D₄	semidirect
383. C₂×Dic₁₁	C₂²×D₄	semidirect
394. D₄₄	C₂²×D₄	semidirect
403. C₄×D₁₁	C₂²×D₄	semidirect
404. C₄×D₁₁	C₂²×D₄	semidirect
405. C₄×D₁₁	H(5,𝔽₂)	semidirect
408. Dic₂₂	C₂²×D₄	semidirect
415. C₂×H(5,𝔽₂)	C₂×D₁₁	semidirect
427. #550	C₂×D₁₁	semidirect
436. D₄²	C₂×D₁₁	semidirect
444. #535	C₂×D₁₁	semidirect
452. #532	C₂×D₁₁	semidirect
463. C₂×#127	C₂×D₁₁	semidirect
473. C₄×#41	C₂×D₁₁	semidirect
499. C₄×C₁₁	C₂×H(5,𝔽₂)	semidirect
504. Dic₁₁	C₂×H(5,𝔽₂)	semidirect
527. C₂×#41	C₂²×D₁₁	semidirect
528. C₂×#41	C₂²×D₁₁	semidirect
553. C₂²×D₄	C₂²×D₁₁	semidirect
554. C₂²×D₄	C₂²×D₁₁	semidirect
555. C₂²×D₄	C₂²×D₁₁	semidirect
562. C₄⋊Q₈	C₂²×D₁₁	semidirect
573. #127	C₂²×D₁₁	semidirect
574. #127	C₂²×D₁₁	semidirect
575. #127	C₂²×D₁₁	semidirect
580. #124	C₂²×D₁₁	semidirect
591. #121	C₂²×D₁₁	semidirect
592. #121	C₂²×D₁₁	semidirect
598. #120	C₂²×D₁₁	semidirect
602. C₄×Q₈	C₂²×D₁₁	semidirect
613. C₄×D₄	C₂²×D₁₁	semidirect
614. C₄×D₄	C₂²×D₁₁	semidirect
619. #117	C₂²×D₁₁	semidirect
632. C₂×C₄²	C₂²×D₁₁	semidirect
639. D₁₁	#3498	direct (N × H)
660. #41	D₄×D₁₁	semidirect
752. C₁₁	C₂×#3498	semidirect
773. Q₈	C₂×D₄×D₁₁	semidirect
792. D₄	C₂×D₄×D₁₁	semidirect
814. C₂×C₄	C₂×D₄×D₁₁	semidirect
845. C₄	D₁₁×H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₁₁×H(5,𝔽₂)	2
#13082394	2
#13082393	2
#13082392	2
#13082391	2
#13082390	2
#13082389	2
#13082388	2
D₁₁×#550	2
D₄²×D₁₁	2
D₁₁×#535	2
D₁₁×#532	2
C₂×D₁₁×#127	2
C₄×#41×D₁₁	2
C₁₁×#3498	2
C₂×#3498	11

Subgroups — D11×#3498 #15662088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#3498 #15662088