Subgroups — #13082343

Order 1408.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623247	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623246	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623222	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623220	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623192	C₂	1	2	yes	maximal, complemented
7	#10623190	C₂	1	2	yes	maximal, complemented
8	#10623189	C₂	1	2	yes	maximal, complemented
9	#10623186	C₂	1	2	yes	maximal, complemented
10	#10623150	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623147	C₂	1	2	yes	maximal, complemented
12	#10623143	C₂	1	2	yes	maximal, complemented
13	#10623141	C₂	1	2	yes	maximal, complemented
14	#10623137	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623134	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623132	C₂	1	2	yes	maximal, complemented
18	#10623088	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623079	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623077	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623076	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623065	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4341	C₂²	1	1	yes	characteristic
25	C₂×#4341	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₁	C₂²	1	2	yes	—
28	C₂×#4339	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#127	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#123	C₂²	1	2	yes	complemented
33	C₁₁×#123	C₂²	1	2	yes	complemented
34	C₁₁×#121	C₂²	1	1	yes	characteristic
35	C₁₁×#121	C₂²	1	2	yes	complemented
36	C₁₁×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₁×#121	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
41	#66993	C₂²	1	1	yes	characteristic, complemented
42	#66992	C₂²	1	2	yes	—
43	#66992	C₂²	1	2	yes	complemented
44	#66992	C₂²	1	2	yes	complemented
45	#66992	C₂²	1	2	yes	complemented
46	#66991	C₂²	1	1	yes	characteristic
47	#66991	C₂²	1	1	yes	characteristic, complemented
48	#66991	C₂²	1	2	yes	complemented
49	#66991	C₂²	1	2	yes	complemented
50	#66990	C₂²	1	2	yes	—
51	#66990	C₂²	1	2	yes	—
52	#66990	C₂²	1	2	yes	—
53	#66989	C₂²	1	1	yes	characteristic, complemented
54	#66989	C₂²	1	2	yes	complemented
55	#66989	C₂²	1	2	yes	complemented
56	#66988	C₂²	1	2	yes	complemented
57	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₁₁	C₂²	1	2	yes	complemented
60	D₄×Dic₁₁	C₂²	1	2	yes	complemented
61	#66983	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
66	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
67	#66979	C₂²	1	1	yes	characteristic, complemented
68	#66979	C₂²	1	2	yes	complemented
69	#66977	C₂²	1	1	yes	characteristic, complemented
70	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
71	#66951	C₂²	1	2	yes	complemented
72	#66951	C₂²	1	2	yes	complemented
73	#66950	C₂²	1	2	yes	—
74	#66950	C₂²	1	1	yes	characteristic, complemented
75	#66949	C₂²	1	2	yes	—
76	#66949	C₂²	1	2	yes	complemented
77	#66948	C₂²	1	1	yes	characteristic
78	#66947	C₂²	1	2	yes	complemented
79	#66946	C₂²	1	1	yes	characteristic, complemented
80	#66946	C₂²	1	2	yes	complemented
81	#66945	C₂²	1	1	yes	characteristic
82	#66945	C₂²	1	1	yes	characteristic
83	#66945	C₂²	1	1	yes	characteristic
84	#66945	C₂²	1	2	yes	complemented
85	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
88	#66943	C₂²	1	1	yes	characteristic, complemented
89	#66942	C₂²	1	2	yes	complemented
90	#66941	C₂²	1	1	yes	characteristic, complemented
91	#66941	C₂²	1	2	yes	complemented
92	#66940	C₂²	1	1	yes	characteristic, complemented
93	#66939	C₂²	1	2	yes	complemented
94	#66938	C₂²	1	2	yes	complemented
95	#66938	C₂²	1	2	yes	complemented
96	#66937	C₂²	1	2	yes	—
97	#66937	C₂²	1	2	yes	complemented
98	#66936	C₂²	1	2	yes	—
99	#66936	C₂²	1	2	yes	complemented
100	#66936	C₂²	1	2	yes	complemented
101	#66936	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
109	#66932	C₂²	1	2	yes	complemented
110	#66932	C₂²	1	2	yes	complemented
111	#66931	C₂²	1	2	yes	complemented
112	#66930	C₂²	1	1	yes	characteristic, complemented
113	#66930	C₂²	1	1	yes	characteristic, complemented
114	#66930	C₂²	1	2	yes	complemented
115	#66928	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	1	yes	characteristic
119	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
121	#66922	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	1	yes	characteristic
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	C₂³	1	2	yes	—
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂×D₄×C₁₁	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
141	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₁	C₂³	1	2	yes	—
143	C₂²×Dic₁₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₁	C₂³	1	2	yes	—
145	#4341	—	2	4	no	—
146	#4341	—	4	4	no	—
147	D₄×D₁₁	—	2	4	no	—
148	D₄×D₁₁	—	4	4	no	—
149	#4339	—	4	4	no	—
150	C₂×D₄₄	C₂³	1	1	yes	characteristic
151	C₂×D₄₄	C₂³	1	2	yes	—
152	C₂×C₄×D₁₁	—	2	4	no	—
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	1	yes	characteristic
159	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
164	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₂	C₂³	1	2	yes	—
166	C₂×Dic₂₂	C₂³	1	2	yes	—
167	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
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	1	yes	characteristic
194	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
202	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₁	C₂³	1	2	yes	—
205	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₁	C₂³	1	2	yes	—
208	C₄⋊Dic₁₁	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	C₄×Dic₁₁	C₂³	1	2	yes	—
220	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	2	yes	—
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	#3494	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₁	C₂⁴	1	2	yes	—
231	C₂³×C₁₁	C₂⁴	1	2	yes	—
232	C₂²×D₁₁	—	2	2	no	—
233	C₂²×D₁₁	—	2	2	no	—
234	C₂²×D₁₁	—	2	4	no	—
235	C₂²×D₁₁	—	4	1	no	—
236	C₂²×D₁₁	—	4	2	no	—
237	C₂²×D₁₁	—	4	2	no	—
238	C₂²×D₁₁	C₂⁴	1	2	yes	—
239	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₁	—	2	2	no	—
242	D₄×C₁₁	—	2	2	no	—
243	D₄×C₁₁	—	4	2	no	—
244	D₄×C₁₁	—	4	2	no	—
245	D₄×C₁₁	—	4	2	no	—
246	D₄×C₁₁	—	4	2	no	—
247	C₂×C₄×C₁₁	—	2	2	no	—
248	C₂×C₄×C₁₁	—	4	2	no	—
249	C₂×C₄×C₁₁	—	4	2	no	—
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₁	—	2	4	no	—
259	C₂²⋊D₁₁	—	2	4	no	—
260	C₂²⋊D₁₁	—	2	4	no	—
261	C₂²⋊D₁₁	—	2	4	no	—
262	C₂²⋊D₁₁	—	4	2	no	—
263	C₂²⋊D₁₁	—	4	2	no	—
264	C₂²⋊D₁₁	—	4	2	no	—
265	C₂×Dic₁₁	—	2	2	no	—
266	C₂×Dic₁₁	—	2	4	no	—
267	C₂×Dic₁₁	—	4	2	no	—
268	C₂×Dic₁₁	—	4	2	no	—
269	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₁	C₂⁴	1	2	yes	—
273	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₁	C₂⁴	1	2	yes	—
277	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
278	D₄₄	—	2	4	no	—
279	D₄₄	—	2	2	no	—
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	2	2	no	—
282	C₄×D₁₁	—	2	2	no	—
283	C₄×D₁₁	—	2	2	no	—
284	C₄×D₁₁	—	2	2	no	—
285	C₄×D₁₁	—	4	2	no	—
286	C₄×D₁₁	—	4	1	no	—
287	C₄×D₁₁	—	4	1	no	—
288	C₄×D₁₁	—	4	2	no	—
289	C₄×D₁₁	—	4	2	no	—
290	C₄×D₁₁	#41	1	4	yes	complemented
291	Dic₂₂	—	2	2	no	—
292	Dic₂₂	—	4	2	no	—
293	Dic₂₂	—	4	2	no	—
294	#555	—	11	2	no	—
295	#553	—	11	2	no	—
296	#553	—	11	2	no	—
297	#551	—	11	2	no	—
298	#551	—	11	2	no	—
299	#547	—	11	2	no	—
300	#546	—	11	2	no	—
301	#546	—	11	2	no	—
302	#544	—	11	1	no	—
303	#542	—	11	1	no	—
304	#542	—	11	1	no	—
305	#540	—	11	1	no	—
306	#540	D₁₁	1	1	yes	characteristic, complemented
307	#535	—	11	1	no	—
308	#532	—	11	1	no	—
309	#532	—	11	1	no	—
310	#529	—	11	1	no	—
311	#529	—	11	1	no	—
312	#525	—	11	1	no	—
313	C₂×#121	—	11	1	no	—
314	#520	—	11	1	no	—
315	#518	—	11	1	no	—
316	C₂×#117	—	11	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	2	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	2	no	—
321	C₂²×C₁₁	—	2	1	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	1	no	—
325	C₂²×C₁₁	—	2	2	no	—
326	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
327	C₂×D₁₁	—	2	1	no	—
328	C₂×D₁₁	—	2	1	no	—
329	C₂×D₁₁	—	2	1	no	—
330	C₂×D₁₁	—	2	1	no	—
331	C₂×D₁₁	—	2	2	no	—
332	C₂×D₁₁	—	2	2	no	—
333	C₂×D₁₁	—	2	2	no	—
334	C₂×D₁₁	—	4	4	no	—
335	C₂×D₁₁	—	8	4	no	—
336	C₂×D₁₁	C₂×#41	1	2	yes	—
337	C₂×D₁₁	H(5,𝔽₂)	1	2	yes	—
338	C₄×C₁₁	—	2	1	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	2	no	—
341	C₄×C₁₁	—	2	1	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	—	2	2	no	—
344	C₄×C₁₁	—	2	1	no	—
345	C₄×C₁₁	C₂×#41	1	2	yes	—
346	Dic₁₁	—	2	2	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	1	no	—
349	Dic₁₁	—	2	2	no	—
350	Dic₁₁	—	2	2	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	1	no	—
353	Dic₁₁	—	2	1	no	—
354	Dic₁₁	C₂×#41	1	2	yes	—
355	C₂×#41	—	11	1	no	—
356	C₂×#41	—	11	2	no	—
357	C₂×#41	—	11	2	no	—
358	C₂²×D₄	—	11	1	no	—
359	C₂²×D₄	—	11	2	no	—
360	C₂³×C₄	—	11	1	no	—
361	C₄⋊Q₈	—	11	1	no	—
362	C₄⋊Q₈	—	11	2	no	—
363	C₄⋊Q₈	—	11	1	no	—
364	#127	—	11	1	no	—
365	#127	C₂×D₁₁	1	1	yes	characteristic, complemented
366	#126	—	11	2	no	—
367	#126	—	11	2	no	—
368	#126	—	11	2	no	—
369	#126	—	11	2	no	—
370	#125	—	11	1	no	—
371	#125	—	11	2	no	—
372	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
373	#124	—	11	1	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	2	no	—
378	#124	—	11	1	no	—
379	#123	—	11	2	no	—
380	#123	—	11	2	no	—
381	#123	—	11	2	no	—
382	#123	—	11	2	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	2	no	—
386	#123	C₂×D₁₁	1	2	yes	complemented
387	#123	C₂×D₁₁	1	2	yes	complemented
388	C₂²⋊Q₈	—	11	1	no	—
389	C₂²⋊Q₈	—	11	1	no	—
390	C₂²⋊Q₈	—	11	2	no	—
391	C₂²⋊Q₈	—	11	2	no	—
392	C₂²⋊Q₈	—	11	2	no	—
393	C₂²⋊Q₈	—	11	2	no	—
394	#121	—	11	1	no	—
395	#121	—	11	2	no	—
396	#121	—	11	1	no	—
397	#121	—	11	2	no	—
398	#121	—	11	2	no	—
399	#121	—	11	2	no	—
400	#121	—	11	2	no	—
401	#121	—	11	2	no	—
402	#121	—	11	1	no	—
403	#121	—	11	1	no	—
404	#121	—	11	2	no	—
405	#121	—	11	2	no	—
406	#121	C₂×D₁₁	1	1	yes	characteristic
407	#121	C₂×D₁₁	1	1	yes	characteristic, complemented
408	#121	C₂×D₁₁	1	2	yes	complemented
409	#121	C₂×D₁₁	1	2	yes	complemented
410	#120	—	11	2	no	—
411	#120	—	11	2	no	—
412	#120	—	11	2	no	—
413	C₄×Q₈	—	11	1	no	—
414	C₄×Q₈	—	11	1	no	—
415	C₄×D₄	—	11	1	no	—
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	2	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	2	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	2	no	—
425	C₄×D₄	—	11	2	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	2	no	—
428	C₄×D₄	—	11	1	no	—
429	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
431	#117	—	11	1	no	—
432	#117	—	11	2	no	—
433	#117	—	11	1	no	—
434	#117	—	11	1	no	—
435	#117	—	11	1	no	—
436	#117	—	11	2	no	—
437	#117	—	11	1	no	—
438	#117	—	11	1	no	—
439	#117	—	11	2	no	—
440	#117	—	11	1	no	—
441	#117	—	11	1	no	—
442	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
443	C₂×C₄⋊C₄	—	11	2	no	—
444	C₂×C₄⋊C₄	—	11	1	no	—
445	C₂×C₄⋊C₄	—	11	1	no	—
446	C₂×C₄⋊C₄	—	11	1	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	—	11	1	no	—
449	C₂×C₂²⋊C₄	—	11	1	no	—
450	C₂×C₂²⋊C₄	—	11	2	no	—
451	C₂×C₂²⋊C₄	—	11	2	no	—
452	C₂×C₄²	—	11	1	no	—
453	C₂×C₄²	—	11	1	no	—
454	C₂×C₁₁	—	4	1	no	—
455	C₂×C₁₁	—	4	2	no	—
456	C₂×C₁₁	—	4	2	no	—
457	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
458	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₁₁	#585	1	1	yes	characteristic
460	D₁₁	—	2	2	no	—
461	D₁₁	—	2	2	no	—
462	D₁₁	—	4	2	no	—
463	C₂⁴	—	11	1	no	—
464	C₂⁴	—	11	2	no	—
465	#41	—	22	4	no	—
466	#41	—	44	4	no	—
467	#41	—	44	4	no	—
468	C₂×Q₈	—	11	1	no	—
469	C₂×Q₈	—	11	2	no	—
470	C₂×Q₈	—	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	2	no	—
476	C₂×D₄	—	11	2	no	—
477	C₂×D₄	—	11	2	no	—
478	C₂×D₄	—	11	1	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	22	4	no	—
481	C₂×D₄	—	44	4	no	—
482	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₁	1	2	yes	—
485	C₂×D₄	C₂²×D₁₁	1	2	yes	—
486	C₂×D₄	C₂²×D₁₁	1	2	yes	—
487	C₂×D₄	C₂²×D₁₁	1	2	yes	—
488	C₂²×C₄	—	11	1	no	—
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	11	1	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	2	no	—
493	C₂²×C₄	—	11	1	no	—
494	C₂²×C₄	—	11	1	no	—
495	C₂²×C₄	—	11	1	no	—
496	C₂²×C₄	—	11	1	no	—
497	C₂²×C₄	—	11	1	no	—
498	C₂²×C₄	—	11	1	no	—
499	C₂²×C₄	—	11	1	no	—
500	C₂²×C₄	—	11	2	no	—
501	C₂²×C₄	—	11	2	no	—
502	C₂²×C₄	—	11	2	no	—
503	C₂²×C₄	—	22	4	no	—
504	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
506	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
507	C₄⋊C₄	—	11	1	no	—
508	C₄⋊C₄	—	11	2	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	1	no	—
511	C₄⋊C₄	—	11	1	no	—
512	C₄⋊C₄	—	11	1	no	—
513	C₄⋊C₄	—	11	1	no	—
514	C₄⋊C₄	—	11	1	no	—
515	C₄⋊C₄	—	11	2	no	—
516	C₄⋊C₄	—	11	2	no	—
517	C₄⋊C₄	—	11	2	no	—
518	C₄⋊C₄	—	11	1	no	—
519	C₄⋊C₄	—	11	2	no	—
520	C₄⋊C₄	—	11	2	no	—
521	C₄⋊C₄	—	11	2	no	—
522	C₄⋊C₄	—	11	2	no	—
523	C₄⋊C₄	—	11	2	no	—
524	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
530	C₂²⋊C₄	—	11	1	no	—
531	C₂²⋊C₄	—	11	1	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	2	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	2	no	—
536	C₂²⋊C₄	—	11	2	no	—
537	C₂²⋊C₄	—	11	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	1	no	—
540	C₂²⋊C₄	—	11	1	no	—
541	C₂²⋊C₄	—	11	2	no	—
542	C₂²⋊C₄	—	11	1	no	—
543	C₂²⋊C₄	—	11	1	no	—
544	C₂²⋊C₄	—	11	2	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	2	no	—
549	C₂²⋊C₄	—	11	2	no	—
550	C₂²⋊C₄	—	11	2	no	—
551	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
557	C₄²	—	11	1	no	—
558	C₄²	—	11	1	no	—
559	C₄²	—	11	1	no	—
560	C₄²	—	11	1	no	—
561	C₄²	—	11	1	no	—
562	C₄²	—	11	1	no	—
563	C₄²	—	11	2	no	—
564	C₄²	—	11	2	no	—
565	C₄²	—	11	2	no	—
566	C₄²	C₂²×D₁₁	1	1	yes	characteristic
567	C₄²	C₂²×D₁₁	1	1	yes	characteristic
568	C₁₁	#3494	1	1	yes	characteristic, complemented, Sylow
569	C₂³	—	11	1	no	—
570	C₂³	—	11	1	no	—
571	C₂³	—	11	2	no	—
572	C₂³	—	22	2	no	—
573	C₂³	—	22	2	no	—
574	C₂³	—	22	4	no	—
575	C₂³	—	44	1	no	—
576	C₂³	—	44	2	no	—
577	C₂³	—	44	2	no	—
578	C₂³	C₂³×D₁₁	1	1	yes	characteristic
579	C₂³	C₂³×D₁₁	1	2	yes	—
580	C₂³	C₂³×D₁₁	1	2	yes	—
581	Q₈	—	22	2	no	—
582	Q₈	—	44	2	no	—
583	Q₈	—	44	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	22	4	no	—
591	D₄	—	22	4	no	—
592	D₄	—	22	4	no	—
593	D₄	—	22	4	no	—
594	D₄	—	22	4	no	—
595	D₄	—	22	2	no	—
596	D₄	—	44	2	no	—
597	D₄	—	44	2	no	—
598	D₄	—	44	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	11	1	no	—
603	C₂×C₄	—	11	4	no	—
604	C₂×C₄	—	11	1	no	—
605	C₂×C₄	—	11	1	no	—
606	C₂×C₄	—	11	2	no	—
607	C₂×C₄	—	11	1	no	—
608	C₂×C₄	—	11	1	no	—
609	C₂×C₄	—	11	1	no	—
610	C₂×C₄	—	11	2	no	—
611	C₂×C₄	—	11	2	no	—
612	C₂×C₄	—	22	2	no	—
613	C₂×C₄	—	22	2	no	—
614	C₂×C₄	—	22	2	no	—
615	C₂×C₄	—	22	2	no	—
616	C₂×C₄	—	22	2	no	—
617	C₂×C₄	—	22	4	no	—
618	C₂×C₄	—	22	2	no	—
619	C₂×C₄	—	44	2	no	—
620	C₂×C₄	—	44	2	no	—
621	C₂×C₄	—	44	1	no	—
622	C₂×C₄	—	44	2	no	—
623	C₂×C₄	—	44	1	no	—
624	C₂×C₄	—	44	2	no	—
625	C₂×C₄	—	44	2	no	—
626	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₁	1	2	yes	—
631	C₂×C₄	C₂³×D₁₁	1	2	yes	—
632	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	11	2	no	—
644	C₂²	—	11	2	no	—
645	C₂²	—	22	1	no	—
646	C₂²	—	22	1	no	—
647	C₂²	—	22	1	no	—
648	C₂²	—	22	1	no	—
649	C₂²	—	22	2	no	—
650	C₂²	—	22	2	no	—
651	C₂²	—	22	2	no	—
652	C₂²	—	44	4	no	—
653	C₂²	—	88	4	no	—
654	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	11	2	no	—
663	C₄	—	22	1	no	—
664	C₄	—	22	2	no	—
665	C₄	—	22	1	no	—
666	C₄	—	22	1	no	—
667	C₄	—	22	2	no	—
668	C₄	—	22	2	no	—
669	C₄	—	22	1	no	—
670	C₄	—	22	1	no	—
671	C₄	#41×D₁₁	1	2	yes	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	22	2	no	—
676	C₂	—	22	2	no	—
677	C₂	—	44	2	no	—
678	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
679	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#540	C₂
hypercenter	#540	D₁₁
hypocenter	C₁₁	#3494
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. C₁₁×#540	C₂	semidirect
2. #10623247	C₂	semidirect
3. #10623246	C₂	semidirect
4. #10623222	C₂	semidirect
5. #10623220	C₂	semidirect
6. #10623192	C₂	semidirect
7. #10623190	C₂	semidirect
8. #10623189	C₂	semidirect
9. #10623186	C₂	semidirect
10. #10623150	C₂	semidirect
11. #10623147	C₂	semidirect
12. #10623143	C₂	semidirect
13. #10623141	C₂	semidirect
14. #10623137	C₂	semidirect
15. D₁₁×#121	C₂	semidirect
16. #10623134	C₂	semidirect
17. #10623132	C₂	semidirect
18. #10623088	C₂	semidirect
19. #10623079	C₂	semidirect
20. #10623077	C₂	semidirect
21. #10623076	C₂	semidirect
22. #10623065	C₂	semidirect
23. D₁₁×#117	C₂	semidirect
25. C₂×#4341	C₂²	semidirect
28. C₂×#4339	C₂²	semidirect
30. C₁₁×#127	C₂²	semidirect
31. C₁₁×#125	C₂²	semidirect
32. C₁₁×#123	C₂²	semidirect
33. C₁₁×#123	C₂²	semidirect
35. C₁₁×#121	C₂²	semidirect
36. C₁₁×#121	C₂²	semidirect
37. C₁₁×#121	C₂²	semidirect
38. C₄×D₄×C₁₁	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₁₁×#117	C₂²	semidirect
41. #66993	C₂²	semidirect
43. #66992	C₂²	semidirect
44. #66992	C₂²	semidirect
45. #66992	C₂²	semidirect
47. #66991	C₂²	semidirect
48. #66991	C₂²	semidirect
49. #66991	C₂²	semidirect
53. #66989	C₂²	semidirect
54. #66989	C₂²	semidirect
55. #66989	C₂²	semidirect
56. #66988	C₂²	semidirect
57. D₄×Dic₁₁	C₂²	semidirect
58. D₄×Dic₁₁	C₂²	semidirect
59. D₄×Dic₁₁	C₂²	semidirect
60. D₄×Dic₁₁	C₂²	semidirect
63. C₄×C₂²⋊D₁₁	C₂²	semidirect
64. C₄×C₂²⋊D₁₁	C₂²	semidirect
65. C₄×C₂²⋊D₁₁	C₂²	semidirect
67. #66979	C₂²	semidirect
68. #66979	C₂²	semidirect
69. #66977	C₂²	semidirect
70. C₂×Dic₁₁⋊C₄	C₂²	semidirect
71. #66951	C₂²	semidirect
72. #66951	C₂²	semidirect
74. #66950	C₂²	semidirect
76. #66949	C₂²	semidirect
78. #66947	C₂²	semidirect
79. #66946	C₂²	semidirect
80. #66946	C₂²	semidirect
84. #66945	C₂²	semidirect
86. C₄⋊C₄×D₁₁	C₂²	semidirect
87. C₄⋊C₄×D₁₁	C₂²	semidirect
88. #66943	C₂²	semidirect
89. #66942	C₂²	semidirect
90. #66941	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66940	C₂²	semidirect
93. #66939	C₂²	semidirect
94. #66938	C₂²	semidirect
95. #66938	C₂²	semidirect
97. #66937	C₂²	semidirect
99. #66936	C₂²	semidirect
100. #66936	C₂²	semidirect
101. #66936	C₂²	semidirect
103. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
109. #66932	C₂²	semidirect
110. #66932	C₂²	semidirect
111. #66931	C₂²	semidirect
112. #66930	C₂²	semidirect
113. #66930	C₂²	semidirect
114. #66930	C₂²	semidirect
115. #66928	C₂²	semidirect
116. C₄×D₄₄	C₂²	semidirect
119. C₄²×D₁₁	C₂²	semidirect
120. C₄²×D₁₁	C₂²	semidirect
121. #66922	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
290. C₄×D₁₁	#41	semidirect
306. #540	D₁₁	semidirect
365. #127	C₂×D₁₁	semidirect
372. #125	C₂×D₁₁	semidirect
386. #123	C₂×D₁₁	semidirect
387. #123	C₂×D₁₁	semidirect
407. #121	C₂×D₁₁	semidirect
408. #121	C₂×D₁₁	semidirect
409. #121	C₂×D₁₁	semidirect
429. C₄×D₄	C₂×D₁₁	semidirect
430. C₄×D₄	C₂×D₁₁	semidirect
442. #117	C₂×D₁₁	semidirect
568. C₁₁	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#540	2
#10623247	2
#10623246	2
#10623222	2
#10623220	2
#10623192	2
#10623190	2
#10623189	2
#10623186	2
#10623150	2
#10623147	2
#10623143	2
#10623141	2
#10623137	2
D₁₁×#121	2
#10623134	2
#10623132	2
#10623088	2
#10623079	2
#10623077	2
#10623076	2
#10623065	2
D₁₁×#117	2
#3494	11