Subgroups — #13083211

Order 1408.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623257	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623255	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623242	C₂	1	2	yes	maximal, complemented
5	#10623240	C₂	1	2	yes	maximal, complemented
6	#10623238	C₂	1	2	yes	maximal, complemented
7	#10623235	C₂	1	2	yes	maximal, complemented
8	#10623208	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623207	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623205	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623199	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623178	C₂	1	2	yes	maximal, complemented
13	#10623175	C₂	1	2	yes	maximal, complemented
14	#10623116	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623114	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623108	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623107	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623093	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623085	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623066	C₂	1	2	yes	maximal, complemented
23	#10623058	C₂	1	2	yes	maximal, complemented
24	C₂×#4343	C₂²	1	1	yes	characteristic
25	C₂×#4343	C₂²	1	1	yes	characteristic
26	C₂×#4343	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#4341	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#126	C₂²	1	2	yes	complemented
32	C₁₁×#126	C₂²	1	2	yes	complemented
33	C₁₁×#124	C₂²	1	1	yes	characteristic
34	C₁₁×#124	C₂²	1	1	yes	characteristic
35	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
38	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
40	C₁₁×#117	C₂²	1	2	yes	complemented
41	#67000	C₂²	1	1	yes	characteristic
42	#67000	C₂²	1	1	yes	characteristic
43	#67000	C₂²	1	2	yes	complemented
44	#66999	C₂²	1	1	yes	characteristic
45	#66999	C₂²	1	1	yes	characteristic, complemented
46	#66999	C₂²	1	1	yes	characteristic, complemented
47	#66997	C₂²	1	1	yes	characteristic, complemented
48	#66993	C₂²	1	1	yes	characteristic
49	#66991	C₂²	1	1	yes	characteristic
50	#66983	C₂²	1	2	yes	—
51	#66983	C₂²	1	2	yes	complemented
52	#66982	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
54	#66951	C₂²	1	2	yes	—
55	#66951	C₂²	1	1	yes	characteristic
56	#66951	C₂²	1	2	yes	complemented
57	#66951	C₂²	1	1	yes	characteristic, complemented
58	#66950	C₂²	1	1	yes	characteristic
59	#66950	C₂²	1	2	yes	complemented
60	#66949	C₂²	1	2	yes	complemented
61	#66949	C₂²	1	2	yes	complemented
62	#66948	C₂²	1	2	yes	—
63	#66948	C₂²	1	1	yes	characteristic
64	#66948	C₂²	1	2	yes	—
65	#66948	C₂²	1	1	yes	characteristic
66	#66948	C₂²	1	2	yes	complemented
67	#66948	C₂²	1	2	yes	complemented
68	#66948	C₂²	1	1	yes	characteristic, complemented
69	#66947	C₂²	1	1	yes	characteristic
70	#66947	C₂²	1	2	yes	—
71	#66947	C₂²	1	2	yes	complemented
72	#66947	C₂²	1	2	yes	complemented
73	#66947	C₂²	1	2	yes	complemented
74	#66947	C₂²	1	2	yes	complemented
75	#66947	C₂²	1	2	yes	complemented
76	#66947	C₂²	1	2	yes	complemented
77	#66947	C₂²	1	1	yes	characteristic, complemented
78	#66946	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
80	#66943	C₂²	1	1	yes	characteristic, complemented
81	#66943	C₂²	1	1	yes	characteristic, complemented
82	#66942	C₂²	1	2	yes	complemented
83	#66939	C₂²	1	2	yes	—
84	#66938	C₂²	1	2	yes	complemented
85	#66937	C₂²	1	2	yes	—
86	#66937	C₂²	1	2	yes	—
87	#66937	C₂²	1	2	yes	—
88	#66937	C₂²	1	2	yes	complemented
89	#66937	C₂²	1	2	yes	complemented
90	#66937	C₂²	1	2	yes	complemented
91	#66937	C₂²	1	2	yes	complemented
92	#66936	C₂²	1	2	yes	—
93	#66936	C₂²	1	2	yes	complemented
94	#66935	C₂²	1	2	yes	—
95	#66935	C₂²	1	2	yes	—
96	#66935	C₂²	1	2	yes	—
97	#66935	C₂²	1	2	yes	—
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
102	#66931	C₂²	1	2	yes	complemented
103	#66929	C₂²	1	2	yes	—
104	#66928	C₂²	1	2	yes	—
105	#66928	C₂²	1	1	yes	characteristic
106	#66928	C₂²	1	1	yes	characteristic, complemented
107	#66927	C₂²	1	1	yes	characteristic
108	#66927	C₂²	1	2	yes	complemented
109	C₄×D₄₄	C₂²	1	1	yes	characteristic
110	C₄×D₄₄	C₂²	1	1	yes	characteristic
111	C₄×D₄₄	C₂²	1	1	yes	characteristic
112	C₄×D₄₄	C₂²	1	2	yes	complemented
113	C₄×D₄₄	C₂²	1	2	yes	complemented
114	C₄×D₄₄	C₂²	1	2	yes	complemented
115	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
117	#66925	C₂²	1	1	yes	characteristic
118	#66925	C₂²	1	2	yes	complemented
119	#66925	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
121	#66923	C₂²	1	2	yes	complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
134	C₂²×Dic₁₁	C₂³	1	2	yes	—
135	#4343	—	4	2	no	—
136	#4343	—	4	2	no	—
137	#4343	—	4	2	no	—
138	Q₈×D₁₁	—	4	2	no	—
139	#4341	—	4	2	no	—
140	D₄×D₁₁	—	4	2	no	—
141	C₂×D₄₄	C₂³	1	1	yes	characteristic
142	C₂×D₄₄	C₂³	1	1	yes	characteristic
143	C₂×D₄₄	C₂³	1	1	yes	characteristic
144	C₂×D₄₄	C₂³	1	1	yes	characteristic
145	C₂×D₄₄	C₂³	1	2	yes	—
146	C₂×D₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₄₄	C₂³	1	2	yes	—
148	C₂×D₄₄	C₂³	1	2	yes	—
149	C₂×D₄₄	C₂³	1	2	yes	—
150	C₂×D₄₄	C₂³	1	2	yes	—
151	C₂×D₄₄	C₂³	1	2	yes	—
152	C₂×D₄₄	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₁	C₂³	1	2	yes	—
159	C₂×C₄×D₁₁	C₂³	1	2	yes	—
160	C₂×C₄×D₁₁	C₂³	1	2	yes	—
161	C₂×C₄×D₁₁	C₂³	1	2	yes	—
162	C₂×C₄×D₁₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₁	C₂³	1	2	yes	—
164	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₂	C₂³	1	2	yes	—
166	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₄²×C₁₁	C₂³	1	1	yes	characteristic
180	C₄²×C₁₁	C₂³	1	2	yes	—
181	C₄²×C₁₁	C₂³	1	1	yes	characteristic
182	C₄²×C₁₁	C₂³	1	1	yes	characteristic
183	C₄²×C₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
208	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₁	C₂³	1	2	yes	—
210	C₄⋊Dic₁₁	C₂³	1	2	yes	—
211	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
215	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	Dic₁₁⋊C₄	C₂³	1	2	yes	—
221	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₁₁⋊C₄	C₂³	1	2	yes	—
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
228	#3562	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	2	yes	—
230	C₂²×D₁₁	—	4	2	no	—
231	C₂²×D₁₁	—	4	2	no	—
232	C₂²×D₁₁	—	4	2	no	—
233	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₁	C₂⁴	1	2	yes	—
235	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁	C₂⁴	1	2	yes	—
238	Q₈×C₁₁	—	2	2	no	—
239	Q₈×C₁₁	—	2	2	no	—
240	Q₈×C₁₁	—	4	1	no	—
241	D₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	4	2	no	—
243	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₁₁	—	4	2	no	—
254	C₂²⋊D₁₁	—	4	2	no	—
255	C₂²⋊D₁₁	—	4	2	no	—
256	C₂²⋊D₁₁	—	4	2	no	—
257	C₂²⋊D₁₁	—	4	2	no	—
258	C₂×Dic₁₁	—	4	2	no	—
259	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁	C₂⁴	1	2	yes	—
264	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
266	D₄₄	—	2	2	no	—
267	D₄₄	—	2	2	no	—
268	D₄₄	—	4	2	no	—
269	D₄₄	—	4	2	no	—
270	D₄₄	—	4	1	no	—
271	D₄₄	—	4	2	no	—
272	D₄₄	—	4	1	no	—
273	D₄₄	—	4	2	no	—
274	D₄₄	—	4	1	no	—
275	D₄₄	—	4	2	no	—
276	D₄₄	—	4	2	no	—
277	D₄₄	—	4	2	no	—
278	C₄×D₁₁	—	2	2	no	—
279	C₄×D₁₁	—	2	2	no	—
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	4	2	no	—
282	C₄×D₁₁	—	4	2	no	—
283	C₄×D₁₁	—	4	1	no	—
284	C₄×D₁₁	—	4	1	no	—
285	C₄×D₁₁	—	4	2	no	—
286	C₄×D₁₁	—	4	2	no	—
287	C₄×D₁₁	—	4	2	no	—
288	C₄×D₁₁	—	4	2	no	—
289	Dic₂₂	—	2	2	no	—
290	Dic₂₂	—	4	2	no	—
291	#562	—	11	2	no	—
292	#560	—	11	2	no	—
293	#559	—	11	1	no	—
294	#556	D₁₁	1	1	yes	characteristic, complemented
295	#553	—	11	2	no	—
296	#551	—	11	2	no	—
297	#550	—	11	1	no	—
298	#548	—	11	1	no	—
299	#548	—	11	1	no	—
300	#547	—	11	1	no	—
301	#546	—	11	1	no	—
302	#546	—	11	1	no	—
303	#541	—	11	1	no	—
304	#540	—	11	1	no	—
305	#540	—	11	2	no	—
306	#539	—	11	2	no	—
307	#538	—	11	2	no	—
308	#538	—	11	2	no	—
309	#536	—	11	1	no	—
310	#535	—	11	1	no	—
311	#532	—	11	1	no	—
312	#529	—	11	1	no	—
313	#529	—	11	1	no	—
314	C₂²×C₁₁	—	2	2	no	—
315	C₂²×C₁₁	—	2	2	no	—
316	C₂²×C₁₁	—	2	2	no	—
317	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
318	C₂×D₁₁	—	2	1	no	—
319	C₂×D₁₁	—	2	2	no	—
320	C₂×D₁₁	—	2	1	no	—
321	C₂×D₁₁	—	2	1	no	—
322	C₂×D₁₁	—	2	2	no	—
323	C₂×D₁₁	—	2	1	no	—
324	C₂×D₁₁	—	2	1	no	—
325	C₂×D₁₁	—	2	2	no	—
326	C₂×D₁₁	—	2	2	no	—
327	C₂×D₁₁	—	2	1	no	—
328	C₂×D₁₁	—	2	1	no	—
329	C₂×D₁₁	—	2	2	no	—
330	C₂×D₁₁	—	2	1	no	—
331	C₂×D₁₁	—	2	2	no	—
332	C₂×D₁₁	—	2	1	no	—
333	C₂×D₁₁	—	8	4	no	—
334	C₄×C₁₁	—	2	2	no	—
335	C₄×C₁₁	—	2	2	no	—
336	C₄×C₁₁	—	2	1	no	—
337	C₄×C₁₁	—	2	2	no	—
338	C₄×C₁₁	—	2	1	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	1	no	—
341	C₄×C₁₁	—	2	1	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
344	Dic₁₁	—	2	2	no	—
345	Dic₁₁	—	2	1	no	—
346	Dic₁₁	—	2	1	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	2	no	—
349	Dic₁₁	—	2	1	no	—
350	Dic₁₁	—	2	1	no	—
351	C₂×#41	—	11	1	no	—
352	C₂×#41	—	11	1	no	—
353	C₂×#41	—	11	1	no	—
354	C₂×#41	—	11	1	no	—
355	C₂²×Q₈	—	11	1	no	—
356	C₂²×D₄	—	11	1	no	—
357	C₄⋊Q₈	—	11	1	no	—
358	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
359	#127	—	11	1	no	—
360	#127	—	11	1	no	—
361	#127	—	11	2	no	—
362	#126	—	11	2	no	—
363	#126	—	11	1	no	—
364	#126	—	11	1	no	—
365	#126	—	11	2	no	—
366	#126	—	11	2	no	—
367	#126	C₂×D₁₁	1	2	yes	complemented
368	#126	C₂×D₁₁	1	2	yes	complemented
369	#125	—	11	1	no	—
370	#125	—	11	1	no	—
371	#125	—	11	2	no	—
372	#125	—	11	2	no	—
373	#124	—	11	1	no	—
374	#124	—	11	1	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	1	no	—
378	#124	—	11	1	no	—
379	#124	—	11	2	no	—
380	#124	C₂×D₁₁	1	1	yes	characteristic
381	#124	C₂×D₁₁	1	1	yes	characteristic
382	#123	—	11	2	no	—
383	#123	—	11	1	no	—
384	#123	—	11	1	no	—
385	#123	—	11	2	no	—
386	#123	—	11	2	no	—
387	#123	—	11	2	no	—
388	#123	—	11	2	no	—
389	#123	—	11	2	no	—
390	#123	—	11	2	no	—
391	#123	—	11	2	no	—
392	#123	—	11	2	no	—
393	#123	—	11	2	no	—
394	#123	—	11	2	no	—
395	C₂²⋊Q₈	—	11	1	no	—
396	C₂²⋊Q₈	—	11	1	no	—
397	C₂²⋊Q₈	—	11	1	no	—
398	C₂²⋊Q₈	—	11	2	no	—
399	C₂²⋊Q₈	—	11	2	no	—
400	C₂²⋊Q₈	—	11	2	no	—
401	C₂²⋊Q₈	—	11	1	no	—
402	C₂²⋊Q₈	—	11	2	no	—
403	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
404	#121	—	11	1	no	—
405	#121	—	11	2	no	—
406	#121	—	11	2	no	—
407	#121	—	11	1	no	—
408	#121	—	11	1	no	—
409	#121	—	11	2	no	—
410	#121	—	11	2	no	—
411	#121	—	11	2	no	—
412	#121	—	11	2	no	—
413	#121	—	11	1	no	—
414	#121	—	11	2	no	—
415	#121	—	11	2	no	—
416	#121	—	11	2	no	—
417	#121	—	11	2	no	—
418	#121	—	11	2	no	—
419	#121	—	11	2	no	—
420	#121	—	11	2	no	—
421	#120	—	11	2	no	—
422	#120	—	11	2	no	—
423	#120	—	11	2	no	—
424	#120	—	11	2	no	—
425	C₄×Q₈	—	11	1	no	—
426	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
427	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
428	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
429	C₄×D₄	—	11	2	no	—
430	C₄×D₄	—	11	2	no	—
431	C₄×D₄	—	11	2	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	2	no	—
434	C₄×D₄	—	11	1	no	—
435	C₄×D₄	—	11	1	no	—
436	C₄×D₄	—	11	1	no	—
437	C₄×D₄	—	11	1	no	—
438	C₄×D₄	—	11	2	no	—
439	C₄×D₄	—	11	1	no	—
440	C₄×D₄	—	11	2	no	—
441	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
442	#117	—	11	1	no	—
443	#117	—	11	1	no	—
444	#117	—	11	2	no	—
445	#117	C₂×D₁₁	1	2	yes	complemented
446	C₂×C₄⋊C₄	—	11	2	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	—	11	2	no	—
449	C₂×C₄²	—	11	1	no	—
450	C₂×C₁₁	—	4	2	no	—
451	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₁₁	#585	1	1	yes	characteristic
453	C₂×C₁₁	#585	1	1	yes	characteristic
454	D₁₁	—	4	1	no	—
455	D₁₁	—	4	1	no	—
456	D₁₁	—	4	2	no	—
457	D₁₁	—	4	2	no	—
458	D₁₁	—	4	1	no	—
459	C₂⁴	—	11	2	no	—
460	#41	—	44	2	no	—
461	#41	—	44	2	no	—
462	#41	—	44	2	no	—
463	#41	—	44	2	no	—
464	C₂×Q₈	—	11	1	no	—
465	C₂×Q₈	—	11	2	no	—
466	C₂×Q₈	—	44	2	no	—
467	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
470	C₂×D₄	—	11	2	no	—
471	C₂×D₄	—	11	2	no	—
472	C₂×D₄	—	11	2	no	—
473	C₂×D₄	—	11	2	no	—
474	C₂×D₄	—	11	2	no	—
475	C₂×D₄	—	11	1	no	—
476	C₂×D₄	—	11	1	no	—
477	C₂×D₄	—	11	1	no	—
478	C₂×D₄	—	11	1	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	11	2	no	—
482	C₂×D₄	—	11	2	no	—
483	C₂×D₄	—	11	1	no	—
484	C₂×D₄	—	11	2	no	—
485	C₂×D₄	—	11	2	no	—
486	C₂×D₄	—	11	2	no	—
487	C₂×D₄	—	44	2	no	—
488	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	11	1	no	—
491	C₂²×C₄	—	11	1	no	—
492	C₂²×C₄	—	11	1	no	—
493	C₂²×C₄	—	11	1	no	—
494	C₂²×C₄	—	11	1	no	—
495	C₂²×C₄	—	11	2	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	2	no	—
498	C₂²×C₄	—	11	2	no	—
499	C₂²×C₄	—	11	2	no	—
500	C₂²×C₄	—	11	2	no	—
501	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
502	C₄⋊C₄	—	11	1	no	—
503	C₄⋊C₄	—	11	2	no	—
504	C₄⋊C₄	—	11	2	no	—
505	C₄⋊C₄	—	11	1	no	—
506	C₄⋊C₄	—	11	1	no	—
507	C₄⋊C₄	—	11	2	no	—
508	C₄⋊C₄	—	11	1	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	1	no	—
511	C₄⋊C₄	—	11	1	no	—
512	C₄⋊C₄	—	11	2	no	—
513	C₄⋊C₄	—	11	2	no	—
514	C₄⋊C₄	—	11	2	no	—
515	C₄⋊C₄	—	11	2	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	2	no	—
518	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
526	C₂²⋊C₄	—	11	2	no	—
527	C₂²⋊C₄	—	11	1	no	—
528	C₂²⋊C₄	—	11	1	no	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	—	11	2	no	—
531	C₂²⋊C₄	—	11	2	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	1	no	—
534	C₂²⋊C₄	—	11	1	no	—
535	C₂²⋊C₄	—	11	2	no	—
536	C₂²⋊C₄	—	11	1	no	—
537	C₂²⋊C₄	—	11	1	no	—
538	C₂²⋊C₄	—	11	1	no	—
539	C₂²⋊C₄	—	11	1	no	—
540	C₂²⋊C₄	—	11	2	no	—
541	C₂²⋊C₄	—	11	2	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	2	no	—
544	C₂²⋊C₄	—	11	1	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	1	no	—
549	C₂²⋊C₄	—	11	2	no	—
550	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
555	C₄²	—	11	1	no	—
556	C₄²	—	11	1	no	—
557	C₄²	—	11	1	no	—
558	C₄²	—	11	2	no	—
559	C₄²	C₂²×D₁₁	1	1	yes	characteristic
560	C₄²	C₂²×D₁₁	1	2	yes	—
561	C₄²	C₂²×D₁₁	1	1	yes	characteristic
562	C₄²	C₂²×D₁₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₁	1	2	yes	—
564	C₁₁	#3562	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	11	1	no	—
566	C₂³	—	11	2	no	—
567	C₂³	—	11	1	no	—
568	C₂³	—	11	1	no	—
569	C₂³	—	11	2	no	—
570	C₂³	—	44	2	no	—
571	C₂³	—	44	2	no	—
572	C₂³	—	44	2	no	—
573	C₂³	C₂³×D₁₁	1	2	yes	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	22	2	no	—
578	Q₈	—	44	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	22	2	no	—
581	D₄	—	22	2	no	—
582	D₄	—	44	2	no	—
583	D₄	—	44	2	no	—
584	D₄	—	44	2	no	—
585	D₄	—	44	2	no	—
586	D₄	—	44	2	no	—
587	D₄	—	44	1	no	—
588	D₄	—	44	2	no	—
589	D₄	—	44	1	no	—
590	D₄	—	44	2	no	—
591	D₄	—	44	1	no	—
592	D₄	—	44	2	no	—
593	D₄	—	44	2	no	—
594	D₄	—	44	2	no	—
595	D₄	—	44	2	no	—
596	D₄	—	44	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	11	1	no	—
599	C₂×C₄	—	11	1	no	—
600	C₂×C₄	—	11	1	no	—
601	C₂×C₄	—	11	2	no	—
602	C₂×C₄	—	11	2	no	—
603	C₂×C₄	—	11	1	no	—
604	C₂×C₄	—	11	1	no	—
605	C₂×C₄	—	22	2	no	—
606	C₂×C₄	—	22	2	no	—
607	C₂×C₄	—	22	2	no	—
608	C₂×C₄	—	44	2	no	—
609	C₂×C₄	—	44	2	no	—
610	C₂×C₄	—	44	2	no	—
611	C₂×C₄	—	44	2	no	—
612	C₂×C₄	—	44	1	no	—
613	C₂×C₄	—	44	2	no	—
614	C₂×C₄	—	44	1	no	—
615	C₂×C₄	—	44	2	no	—
616	C₂×C₄	—	44	2	no	—
617	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₁	1	2	yes	—
622	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₁	1	2	yes	—
625	C₂×C₄	C₂³×D₁₁	1	2	yes	—
626	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	22	1	no	—
631	C₂²	—	22	1	no	—
632	C₂²	—	22	1	no	—
633	C₂²	—	22	2	no	—
634	C₂²	—	22	2	no	—
635	C₂²	—	22	1	no	—
636	C₂²	—	22	1	no	—
637	C₂²	—	22	2	no	—
638	C₂²	—	22	2	no	—
639	C₂²	—	22	1	no	—
640	C₂²	—	22	1	no	—
641	C₂²	—	22	2	no	—
642	C₂²	—	22	2	no	—
643	C₂²	—	22	1	no	—
644	C₂²	—	22	1	no	—
645	C₂²	—	88	4	no	—
646	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	22	1	no	—
657	C₄	—	22	1	no	—
658	C₄	—	22	1	no	—
659	C₄	—	22	2	no	—
660	C₄	—	22	1	no	—
661	C₄	—	22	2	no	—
662	C₄	—	22	1	no	—
663	C₄	#67042	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	44	1	no	—
666	C₂	—	44	2	no	—
667	C₂	—	44	1	no	—
668	C₂	—	44	1	no	—
669	C₂	—	44	2	no	—
670	C₂	C₂×#67042	1	1	yes	characteristic
671	C₂	#10623453	1	1	yes	characteristic
672	C₂	#10623457	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#556	C₂
hypercenter	#556	D₁₁
hypocenter	C₁₁	#3562
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₁×#556	C₂	semidirect
2. #10623257	C₂	semidirect
3. #10623255	C₂	semidirect
4. #10623242	C₂	semidirect
5. #10623240	C₂	semidirect
6. #10623238	C₂	semidirect
7. #10623235	C₂	semidirect
8. #10623208	C₂	semidirect
9. #10623207	C₂	semidirect
10. #10623205	C₂	semidirect
11. #10623199	C₂	semidirect
12. #10623178	C₂	semidirect
13. #10623175	C₂	semidirect
14. #10623116	C₂	semidirect
15. #10623114	C₂	semidirect
16. #10623111	C₂	semidirect
17. #10623111	C₂	semidirect
18. #10623108	C₂	semidirect
19. #10623107	C₂	semidirect
20. #10623093	C₂	semidirect
21. #10623085	C₂	semidirect
22. #10623066	C₂	semidirect
23. #10623058	C₂	semidirect
26. C₂×#4343	C₂²	semidirect
27. C₂×Q₈×D₁₁	C₂²	semidirect
30. C₁₁×C₄⋊Q₈	C₂²	semidirect
31. C₁₁×#126	C₂²	semidirect
32. C₁₁×#126	C₂²	semidirect
35. C₁₁×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₁	C₂²	semidirect
37. C₄×Q₈×C₁₁	C₂²	semidirect
38. C₄×Q₈×C₁₁	C₂²	semidirect
40. C₁₁×#117	C₂²	semidirect
43. #67000	C₂²	semidirect
45. #66999	C₂²	semidirect
46. #66999	C₂²	semidirect
47. #66997	C₂²	semidirect
51. #66983	C₂²	semidirect
52. #66982	C₂²	semidirect
56. #66951	C₂²	semidirect
57. #66951	C₂²	semidirect
59. #66950	C₂²	semidirect
60. #66949	C₂²	semidirect
61. #66949	C₂²	semidirect
66. #66948	C₂²	semidirect
67. #66948	C₂²	semidirect
68. #66948	C₂²	semidirect
71. #66947	C₂²	semidirect
72. #66947	C₂²	semidirect
73. #66947	C₂²	semidirect
74. #66947	C₂²	semidirect
75. #66947	C₂²	semidirect
76. #66947	C₂²	semidirect
77. #66947	C₂²	semidirect
78. #66946	C₂²	semidirect
79. C₄⋊C₄×D₁₁	C₂²	semidirect
80. #66943	C₂²	semidirect
81. #66943	C₂²	semidirect
82. #66942	C₂²	semidirect
84. #66938	C₂²	semidirect
88. #66937	C₂²	semidirect
89. #66937	C₂²	semidirect
90. #66937	C₂²	semidirect
91. #66937	C₂²	semidirect
93. #66936	C₂²	semidirect
98. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
102. #66931	C₂²	semidirect
106. #66928	C₂²	semidirect
108. #66927	C₂²	semidirect
112. C₄×D₄₄	C₂²	semidirect
113. C₄×D₄₄	C₂²	semidirect
114. C₄×D₄₄	C₂²	semidirect
115. C₄×D₄₄	C₂²	semidirect
116. C₄×D₄₄	C₂²	semidirect
118. #66925	C₂²	semidirect
119. #66925	C₂²	semidirect
120. C₄²×D₁₁	C₂²	semidirect
121. #66923	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
294. #556	D₁₁	semidirect
358. C₄⋊Q₈	C₂×D₁₁	semidirect
367. #126	C₂×D₁₁	semidirect
368. #126	C₂×D₁₁	semidirect
403. C₂²⋊Q₈	C₂×D₁₁	semidirect
426. C₄×Q₈	C₂×D₁₁	semidirect
427. C₄×Q₈	C₂×D₁₁	semidirect
428. C₄×Q₈	C₂×D₁₁	semidirect
445. #117	C₂×D₁₁	semidirect
564. C₁₁	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#556	2
#10623257	2
#10623255	2
#10623242	2
#10623240	2
#10623238	2
#10623235	2
#10623208	2
#10623207	2
#10623205	2
#10623199	2
#10623178	2
#10623175	2
#10623116	2
#10623114	2
#10623111	2
#10623108	2
#10623107	2
#10623093	2
#10623085	2
#10623066	2
#10623058	2
#3562	11