Subgroups — #13082485

Order 1408.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623365	C₂	1	2	yes	maximal, complemented
3	#10623360	C₂	1	2	yes	maximal, complemented
4	#10623259	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623256	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623247	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623212	C₂	1	2	yes	maximal, complemented
9	#10623207	C₂	1	2	yes	maximal, complemented
10	#10623150	C₂	1	2	yes	maximal, complemented
11	#10623143	C₂	1	2	yes	maximal, complemented
12	#10623138	C₂	1	2	yes	maximal, complemented
13	#10623130	C₂	1	2	yes	maximal, complemented
14	#10623093	C₂	1	2	yes	maximal, complemented
15	#10623090	C₂	1	2	yes	maximal, complemented
16	#10623085	C₂	1	2	yes	maximal, complemented
17	#10623076	C₂	1	2	yes	maximal, complemented
18	#10623008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#4339	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₁×#41	C₂²	1	2	yes	complemented
21	C₂×#4343	C₂²	1	2	yes	complemented
22	C₂×#4341	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₁	C₂²	1	2	yes	—
24	C₂×D₄×D₁₁	C₂²	1	2	yes	—
25	C₂×D₄×D₁₁	C₂²	1	2	yes	—
26	C₂×#4339	C₂²	1	1	yes	characteristic
27	C₂×#4339	C₂²	1	2	yes	complemented
28	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₁×#127	C₂²	1	1	yes	characteristic
30	C₁₁×#124	C₂²	1	2	yes	complemented
31	C₁₁×#121	C₂²	1	2	yes	complemented
32	C₁₁×#121	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
34	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
35	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	#67000	C₂²	1	2	yes	complemented
37	#66999	C₂²	1	2	yes	—
38	Q₈×Dic₁₁	C₂²	1	2	yes	complemented
39	#66993	C₂²	1	2	yes	—
40	#66993	C₂²	1	2	yes	—
41	#66993	C₂²	1	2	yes	—
42	#66993	C₂²	1	4	yes	complemented
43	#66992	C₂²	1	4	yes	complemented
44	#66991	C₂²	1	2	yes	complemented
45	#66991	C₂²	1	2	yes	complemented
46	#66991	C₂²	1	4	yes	complemented
47	#66990	C₂²	1	4	yes	—
48	#66989	C₂²	1	2	yes	complemented
49	D₄×Dic₁₁	C₂²	1	2	yes	complemented
50	D₄×Dic₁₁	C₂²	1	2	yes	complemented
51	#66983	C₂²	1	2	yes	complemented
52	#66983	C₂²	1	2	yes	complemented
53	#66983	C₂²	1	4	yes	complemented
54	#66982	C₂²	1	4	yes	complemented
55	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₁	C₂²	1	4	yes	complemented
60	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	4	yes	—
61	#66979	C₂²	1	1	yes	characteristic, complemented
62	#66950	C₂²	1	2	yes	—
63	#66948	C₂²	1	2	yes	complemented
64	#66948	C₂²	1	2	yes	complemented
65	#66946	C₂²	1	2	yes	complemented
66	#66946	C₂²	1	2	yes	complemented
67	#66945	C₂²	1	2	yes	—
68	#66943	C₂²	1	2	yes	complemented
69	#66940	C₂²	1	2	yes	complemented
70	#66939	C₂²	1	4	yes	complemented
71	#66938	C₂²	1	4	yes	complemented
72	#66937	C₂²	1	4	yes	complemented
73	#66936	C₂²	1	4	yes	complemented
74	#66936	C₂²	1	4	yes	complemented
75	#66935	C₂²	1	4	yes	—
76	(C₂²⋊D₁₁)⋊C₄	C₂²	1	4	yes	complemented
77	C₂²⋊C₄×D₁₁	C₂²	1	4	yes	—
78	#66928	C₂²	1	2	yes	complemented
79	#66927	C₂²	1	1	yes	characteristic
80	C₄×D₄₄	C₂²	1	1	yes	characteristic
81	C₄×D₄₄	C₂²	1	1	yes	characteristic
82	C₄×D₄₄	C₂²	1	2	yes	complemented
83	C₄×D₄₄	C₂²	1	2	yes	complemented
84	#66925	C₂²	1	1	yes	characteristic
85	#66925	C₂²	1	1	yes	characteristic, complemented
86	C₄²×D₁₁	C₂²	1	1	yes	characteristic
87	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
88	#66922	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
91	C₂³×D₁₁	C₂³	1	4	yes	—
92	C₁₁×#41	—	4	4	no	—
93	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
94	C₂×D₄×C₁₁	C₂³	1	2	yes	—
95	C₂×D₄×C₁₁	C₂³	1	2	yes	—
96	C₂×D₄×C₁₁	C₂³	1	2	yes	—
97	C₂×D₄×C₁₁	C₂³	1	4	yes	—
98	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₁	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₁	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₁	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₁	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₁₁	C₂³	1	4	yes	—
109	C₂²×Dic₁₁	C₂³	1	4	yes	—
110	#4343	—	4	4	no	—
111	#4341	—	4	4	no	—
112	D₄×D₁₁	—	2	8	no	—
113	D₄×D₁₁	—	4	4	no	—
114	D₄×D₁₁	—	4	4	no	—
115	#4339	—	2	4	no	—
116	#4339	—	4	4	no	—
117	C₂×D₄₄	C₂³	1	1	yes	characteristic
118	C₂×D₄₄	C₂³	1	2	yes	—
119	C₂×D₄₄	C₂³	1	2	yes	—
120	C₂×D₄₄	C₂³	1	2	yes	—
121	C₂×D₄₄	C₂³	1	4	yes	—
122	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₁₁	C₂³	1	4	yes	—
128	C₂×C₄×D₁₁	C₂³	1	4	yes	—
129	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₂	C₂³	1	2	yes	—
132	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
133	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
134	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₄²×C₁₁	C₂³	1	1	yes	characteristic
137	C₄²×C₁₁	C₂³	1	1	yes	characteristic
138	C₄²×C₁₁	C₂³	1	1	yes	characteristic
139	C₄²×C₁₁	C₂³	1	1	yes	characteristic
140	C₂²⋊Dic₁₁	C₂³	1	4	yes	—
141	C₂²⋊Dic₁₁	C₂³	1	4	yes	—
142	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
143	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
144	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
145	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
146	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
147	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
148	(C₂×D₁₁)⋊C₄	C₂³	1	4	yes	—
149	(C₂×D₁₁)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₁₁)⋊C₄	C₂³	1	4	yes	—
151	(C₂×D₁₁)⋊C₄	C₂³	1	4	yes	—
152	(C₂×D₁₁)⋊C₄	C₂³	1	4	yes	—
153	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₁	C₂³	1	2	yes	—
156	C₄⋊Dic₁₁	C₂³	1	2	yes	—
157	C₄⋊Dic₁₁	C₂³	1	4	yes	—
158	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₁⋊C₄	C₂³	1	4	yes	—
163	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
164	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
165	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
166	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
167	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
168	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
169	C₄×Dic₁₁	C₂³	1	4	yes	—
170	#3508	—	11	1	no	maximal, Sylow
171	C₂³×C₁₁	C₂⁴	1	4	yes	—
172	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
173	C₂²×D₁₁	—	2	8	no	—
174	C₂²×D₁₁	—	4	4	no	—
175	C₂²×D₁₁	—	4	4	no	—
176	C₂²×D₁₁	C₂⁴	1	4	yes	—
177	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
178	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
179	Q₈×C₁₁	—	2	4	no	—
180	D₄×C₁₁	—	2	4	no	—
181	D₄×C₁₁	—	2	4	no	—
182	D₄×C₁₁	—	2	4	no	—
183	D₄×C₁₁	—	4	4	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	4	4	no	—
188	C₂×C₄×C₁₁	C₂⁴	1	4	yes	—
189	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
195	C₂²⋊D₁₁	—	2	2	no	—
196	C₂²⋊D₁₁	—	2	2	no	—
197	C₂²⋊D₁₁	—	2	8	no	—
198	C₂²⋊D₁₁	—	4	4	no	—
199	C₂²⋊D₁₁	—	4	4	no	—
200	C₂²⋊D₁₁	—	4	4	no	—
201	C₂²⋊D₁₁	—	4	4	no	—
202	C₂×Dic₁₁	—	4	4	no	—
203	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
207	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
208	C₂×Dic₁₁	C₂⁴	1	4	yes	—
209	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
210	D₄₄	—	2	2	no	—
211	D₄₄	—	2	4	no	—
212	D₄₄	—	2	4	no	—
213	D₄₄	—	2	4	no	—
214	D₄₄	—	4	4	no	—
215	C₄×D₁₁	—	2	2	no	—
216	C₄×D₁₁	—	2	2	no	—
217	C₄×D₁₁	—	2	2	no	—
218	C₄×D₁₁	—	2	2	no	—
219	C₄×D₁₁	—	2	2	no	—
220	C₄×D₁₁	—	4	4	no	—
221	C₄×D₁₁	—	4	4	no	—
222	C₄×D₁₁	#41	1	4	yes	complemented
223	Dic₂₂	—	2	4	no	—
224	Dic₂₂	—	2	2	no	—
225	#559	—	11	2	no	—
226	#559	—	11	2	no	—
227	#550	—	11	2	no	—
228	#550	—	11	2	no	—
229	#546	—	11	2	no	—
230	#546	—	11	2	no	—
231	#546	—	11	2	no	—
232	#546	—	11	2	no	—
233	#540	—	11	2	no	—
234	#540	—	11	2	no	—
235	#535	—	11	2	no	—
236	#533	—	11	1	no	—
237	#532	—	11	1	no	—
238	#532	—	11	1	no	—
239	#532	—	11	1	no	—
240	#532	D₁₁	1	1	yes	characteristic, complemented
241	C₂×#127	—	11	1	no	—
242	#518	—	11	2	no	—
243	C₄×#41	—	11	1	no	—
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	—	2	4	no	—
246	C₂²×C₁₁	—	2	1	no	—
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	—	2	4	no	—
249	C₂²×C₁₁	—	2	4	no	—
250	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
251	C₂×D₁₁	—	2	1	no	—
252	C₂×D₁₁	—	2	1	no	—
253	C₂×D₁₁	—	2	4	no	—
254	C₂×D₁₁	—	2	1	no	—
255	C₂×D₁₁	—	2	4	no	—
256	C₂×D₁₁	—	2	4	no	—
257	C₂×D₁₁	—	2	1	no	—
258	C₂×D₁₁	—	2	1	no	—
259	C₂×D₁₁	—	8	8	no	—
260	C₂×D₁₁	C₂×#41	1	2	yes	—
261	C₄×C₁₁	—	2	1	no	—
262	C₄×C₁₁	—	2	1	no	—
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	2	4	no	—
265	C₄×C₁₁	C₂×#41	1	2	yes	—
266	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
267	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
268	Dic₁₁	—	2	1	no	—
269	Dic₁₁	—	2	4	no	—
270	Dic₁₁	—	2	1	no	—
271	Dic₁₁	—	2	1	no	—
272	Dic₁₁	—	2	1	no	—
273	Dic₁₁	—	2	1	no	—
274	Dic₁₁	C₂×#41	1	2	yes	—
275	C₂×#41	—	11	2	no	—
276	C₂×#41	—	11	2	no	—
277	C₂×#41	—	11	1	no	—
278	C₂×#41	—	11	2	no	—
279	C₂×#41	C₂×D₁₁	1	2	yes	complemented
280	C₂²×D₄	—	11	2	no	—
281	C₂²×D₄	—	11	2	no	—
282	C₂²×D₄	—	11	2	no	—
283	C₄⋊Q₈	—	11	1	no	—
284	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
285	#127	—	11	2	no	—
286	#127	—	11	2	no	—
287	#127	—	11	2	no	—
288	#127	—	11	4	no	—
289	#127	—	11	1	no	—
290	#127	C₂×D₁₁	1	1	yes	characteristic
291	#125	—	11	2	no	—
292	#124	—	11	2	no	—
293	#124	—	11	2	no	—
294	#124	—	11	4	no	—
295	#124	—	11	2	no	—
296	#124	C₂×D₁₁	1	2	yes	complemented
297	#123	—	11	4	no	—
298	#123	—	11	4	no	—
299	#123	—	11	4	no	—
300	#123	—	11	4	no	—
301	C₂²⋊Q₈	—	11	2	no	—
302	C₂²⋊Q₈	—	11	2	no	—
303	#121	—	11	2	no	—
304	#121	—	11	2	no	—
305	#121	—	11	4	no	—
306	#121	—	11	4	no	—
307	#121	—	11	2	no	—
308	#121	—	11	2	no	—
309	#121	—	11	4	no	—
310	#121	—	11	2	no	—
311	#121	—	11	2	no	—
312	#121	—	11	4	no	—
313	#121	C₂×D₁₁	1	2	yes	complemented
314	#121	C₂×D₁₁	1	2	yes	complemented
315	#120	—	11	4	no	—
316	#120	—	11	4	no	—
317	C₄×Q₈	—	11	2	no	—
318	C₄×Q₈	—	11	2	no	—
319	C₄×Q₈	—	11	1	no	—
320	C₄×Q₈	—	11	1	no	—
321	C₄×D₄	—	11	2	no	—
322	C₄×D₄	—	11	2	no	—
323	C₄×D₄	—	11	1	no	—
324	C₄×D₄	—	11	1	no	—
325	C₄×D₄	—	11	1	no	—
326	C₄×D₄	—	11	1	no	—
327	C₄×D₄	—	11	4	no	—
328	C₄×D₄	—	11	2	no	—
329	C₄×D₄	—	11	2	no	—
330	C₄×D₄	—	11	4	no	—
331	C₄×D₄	—	11	1	no	—
332	C₄×D₄	—	11	1	no	—
333	C₄×D₄	—	11	2	no	—
334	C₄×D₄	—	11	2	no	—
335	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
336	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
337	#117	—	11	1	no	—
338	#117	—	11	2	no	—
339	#117	—	11	1	no	—
340	#117	—	11	1	no	—
341	C₂×C₂²⋊C₄	—	11	4	no	—
342	C₂×C₂²⋊C₄	—	11	4	no	—
343	C₂×C₄²	—	11	1	no	—
344	C₂×C₄²	—	11	1	no	—
345	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic, complemented
346	C₂×C₁₁	—	4	4	no	—
347	C₂×C₁₁	—	4	1	no	—
348	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
349	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	D₁₁	—	2	2	no	—
352	D₁₁	—	4	1	no	—
353	D₁₁	—	4	4	no	—
354	C₂⁴	—	11	4	no	—
355	#41	—	4	4	no	—
356	#41	—	22	4	no	—
357	#41	—	44	4	no	—
358	#41	—	44	4	no	—
359	#41	—	44	4	no	—
360	C₂×Q₈	—	11	1	no	—
361	C₂×Q₈	—	11	2	no	—
362	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
363	C₂×D₄	—	11	1	no	—
364	C₂×D₄	—	11	4	no	—
365	C₂×D₄	—	11	1	no	—
366	C₂×D₄	—	11	4	no	—
367	C₂×D₄	—	11	4	no	—
368	C₂×D₄	—	11	4	no	—
369	C₂×D₄	—	11	4	no	—
370	C₂×D₄	—	11	1	no	—
371	C₂×D₄	—	11	2	no	—
372	C₂×D₄	—	11	2	no	—
373	C₂×D₄	—	11	2	no	—
374	C₂×D₄	—	11	4	no	—
375	C₂×D₄	—	22	8	no	—
376	C₂×D₄	—	44	4	no	—
377	C₂×D₄	—	44	4	no	—
378	C₂×D₄	C₂²×D₁₁	1	2	yes	—
379	C₂×D₄	C₂²×D₁₁	1	2	yes	—
380	C₂×D₄	C₂²×D₁₁	1	2	yes	—
381	C₂×D₄	C₂²×D₁₁	1	4	yes	—
382	C₂²×C₄	—	11	1	no	—
383	C₂²×C₄	—	11	4	no	—
384	C₂²×C₄	—	11	1	no	—
385	C₂²×C₄	—	11	1	no	—
386	C₂²×C₄	—	11	1	no	—
387	C₂²×C₄	—	11	1	no	—
388	C₂²×C₄	—	11	1	no	—
389	C₂²×C₄	—	11	4	no	—
390	C₂²×C₄	—	11	4	no	—
391	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
392	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
395	C₄⋊C₄	—	11	1	no	—
396	C₄⋊C₄	—	11	1	no	—
397	C₄⋊C₄	—	11	2	no	—
398	C₄⋊C₄	—	11	1	no	—
399	C₄⋊C₄	—	11	1	no	—
400	C₄⋊C₄	—	11	1	no	—
401	C₄⋊C₄	—	11	1	no	—
402	C₄⋊C₄	—	11	2	no	—
403	C₄⋊C₄	—	11	4	no	—
404	C₄⋊C₄	—	11	4	no	—
405	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
406	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
407	C₂²⋊C₄	—	11	4	no	—
408	C₂²⋊C₄	—	11	1	no	—
409	C₂²⋊C₄	—	11	1	no	—
410	C₂²⋊C₄	—	11	4	no	—
411	C₂²⋊C₄	—	11	1	no	—
412	C₂²⋊C₄	—	11	1	no	—
413	C₂²⋊C₄	—	11	4	no	—
414	C₂²⋊C₄	—	11	4	no	—
415	C₂²⋊C₄	—	11	4	no	—
416	C₂²⋊C₄	—	11	1	no	—
417	C₂²⋊C₄	—	11	1	no	—
418	C₂²⋊C₄	—	11	4	no	—
419	C₂²⋊C₄	—	11	4	no	—
420	C₂²⋊C₄	C₂²×D₁₁	1	4	yes	—
421	C₂²⋊C₄	C₂²×D₁₁	1	4	yes	—
422	C₄²	—	11	1	no	—
423	C₄²	—	11	1	no	—
424	C₄²	—	11	1	no	—
425	C₄²	—	11	1	no	—
426	C₄²	—	11	1	no	—
427	C₄²	—	11	1	no	—
428	C₄²	—	11	4	no	—
429	C₄²	C₂²×D₁₁	1	1	yes	characteristic
430	C₄²	C₂²×D₁₁	1	1	yes	characteristic
431	C₄²	C₂²×D₁₁	1	1	yes	characteristic
432	C₄²	C₂²×D₁₁	1	1	yes	characteristic
433	C₁₁	#3508	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	11	1	no	—
435	C₂³	—	11	4	no	—
436	C₂³	—	11	1	no	—
437	C₂³	—	22	8	no	—
438	C₂³	—	44	4	no	—
439	C₂³	—	44	4	no	—
440	C₂³	C₂³×D₁₁	1	4	yes	—
441	C₂³	C₂³×D₁₁	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	22	2	no	—
444	Q₈	—	22	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	22	2	no	—
450	D₄	—	22	8	no	—
451	D₄	—	22	2	no	—
452	D₄	—	22	2	no	—
453	D₄	—	22	4	no	—
454	D₄	—	22	4	no	—
455	D₄	—	22	4	no	—
456	D₄	—	44	4	no	—
457	D₄	—	44	4	no	—
458	D₄	—	44	4	no	—
459	D₄	—	44	4	no	—
460	D₄	—	44	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	11	1	no	—
466	C₂×C₄	—	11	4	no	—
467	C₂×C₄	—	11	1	no	—
468	C₂×C₄	—	11	1	no	—
469	C₂×C₄	—	11	1	no	—
470	C₂×C₄	—	11	1	no	—
471	C₂×C₄	—	11	1	no	—
472	C₂×C₄	—	11	4	no	—
473	C₂×C₄	—	22	2	no	—
474	C₂×C₄	—	22	2	no	—
475	C₂×C₄	—	22	2	no	—
476	C₂×C₄	—	22	2	no	—
477	C₂×C₄	—	22	2	no	—
478	C₂×C₄	—	44	4	no	—
479	C₂×C₄	—	44	4	no	—
480	C₂×C₄	—	44	4	no	—
481	C₂×C₄	C₂³×D₁₁	1	4	yes	—
482	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
487	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	11	2	no	—
495	C₂²	—	22	1	no	—
496	C₂²	—	22	1	no	—
497	C₂²	—	22	1	no	—
498	C₂²	—	22	4	no	—
499	C₂²	—	22	1	no	—
500	C₂²	—	22	4	no	—
501	C₂²	—	22	1	no	—
502	C₂²	—	22	4	no	—
503	C₂²	—	88	8	no	—
504	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	4	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	11	2	no	—
510	C₄	—	22	1	no	—
511	C₄	—	22	1	no	—
512	C₄	—	22	1	no	—
513	C₄	—	22	1	no	—
514	C₄	—	22	1	no	—
515	C₄	—	22	4	no	—
516	C₄	#67037	1	2	yes	—
517	C₄	#41×D₁₁	1	2	yes	—
518	C₄	#67042	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	22	2	no	—
522	C₂	—	44	4	no	—
523	C₂	—	44	1	no	—
524	C₂	C₂×#67037	1	1	yes	characteristic
525	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
526	C₂	C₂×#67042	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#532	C₂
hypercenter	#532	D₁₁
hypocenter	C₁₁	#3508
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₁₁×#532	C₂	semidirect
2. #10623365	C₂	semidirect
3. #10623360	C₂	semidirect
4. #10623259	C₂	semidirect
5. #10623256	C₂	semidirect
6. #10623247	C₂	semidirect
7. D₁₁×#127	C₂	semidirect
8. #10623212	C₂	semidirect
9. #10623207	C₂	semidirect
10. #10623150	C₂	semidirect
11. #10623143	C₂	semidirect
12. #10623138	C₂	semidirect
13. #10623130	C₂	semidirect
14. #10623093	C₂	semidirect
15. #10623090	C₂	semidirect
16. #10623085	C₂	semidirect
17. #10623076	C₂	semidirect
18. #10623008	C₂	semidirect
19. C₄×#4339	C₂	semidirect
20. C₂×C₁₁×#41	C₂²	semidirect
21. C₂×#4343	C₂²	semidirect
22. C₂×#4341	C₂²	semidirect
27. C₂×#4339	C₂²	semidirect
28. C₁₁×C₄⋊Q₈	C₂²	semidirect
30. C₁₁×#124	C₂²	semidirect
31. C₁₁×#121	C₂²	semidirect
32. C₁₁×#121	C₂²	semidirect
33. C₄×D₄×C₁₁	C₂²	semidirect
34. C₄×D₄×C₁₁	C₂²	semidirect
35. C₂×C₄²×C₁₁	C₂²	semidirect
36. #67000	C₂²	semidirect
38. Q₈×Dic₁₁	C₂²	semidirect
42. #66993	C₂²	semidirect
43. #66992	C₂²	semidirect
44. #66991	C₂²	semidirect
45. #66991	C₂²	semidirect
46. #66991	C₂²	semidirect
48. #66989	C₂²	semidirect
49. D₄×Dic₁₁	C₂²	semidirect
50. D₄×Dic₁₁	C₂²	semidirect
51. #66983	C₂²	semidirect
52. #66983	C₂²	semidirect
53. #66983	C₂²	semidirect
54. #66982	C₂²	semidirect
57. C₄×C₂²⋊D₁₁	C₂²	semidirect
58. C₄×C₂²⋊D₁₁	C₂²	semidirect
59. C₄×C₂²⋊D₁₁	C₂²	semidirect
61. #66979	C₂²	semidirect
63. #66948	C₂²	semidirect
64. #66948	C₂²	semidirect
65. #66946	C₂²	semidirect
66. #66946	C₂²	semidirect
68. #66943	C₂²	semidirect
69. #66940	C₂²	semidirect
70. #66939	C₂²	semidirect
71. #66938	C₂²	semidirect
72. #66937	C₂²	semidirect
73. #66936	C₂²	semidirect
74. #66936	C₂²	semidirect
76. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
78. #66928	C₂²	semidirect
82. C₄×D₄₄	C₂²	semidirect
83. C₄×D₄₄	C₂²	semidirect
85. #66925	C₂²	semidirect
87. C₄²×D₁₁	C₂²	semidirect
88. #66922	C₂²	semidirect
89. C₄×Dic₂₂	C₂²	semidirect
90. C₄×Dic₂₂	C₂²	semidirect
222. C₄×D₁₁	#41	semidirect
240. #532	D₁₁	semidirect
279. C₂×#41	C₂×D₁₁	semidirect
284. C₄⋊Q₈	C₂×D₁₁	semidirect
296. #124	C₂×D₁₁	semidirect
313. #121	C₂×D₁₁	semidirect
314. #121	C₂×D₁₁	semidirect
335. C₄×D₄	C₂×D₁₁	semidirect
336. C₄×D₄	C₂×D₁₁	semidirect
345. C₂×C₄²	C₂×D₁₁	semidirect
433. C₁₁	#3508	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#532	2
#10623365	2
#10623360	2
#10623259	2
#10623256	2
#10623247	2
D₁₁×#127	2
#10623212	2
#10623207	2
#10623150	2
#10623143	2
#10623138	2
#10623130	2
#10623093	2
#10623090	2
#10623085	2
#10623076	2
#10623008	2
C₄×#4339	2
#3508	11