Subgroups — #13082980

Order 1408.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623365	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623364	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623336	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623211	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623207	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623197	C₂	1	2	yes	maximal, complemented
9	#10623193	C₂	1	2	yes	maximal, complemented
10	#10623172	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623160	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623144	C₂	1	2	yes	maximal, complemented
13	#10623142	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623138	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623130	C₂	1	2	yes	maximal, complemented
16	#10623126	C₂	1	2	yes	maximal, complemented
17	#10623123	C₂	1	2	yes	maximal, complemented
18	#10623096	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623089	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623079	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623079	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623025	C₂	1	2	yes	maximal, complemented
23	#10623021	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₁	C₂²	1	2	yes	—
27	C₂×#4343	C₂²	1	1	yes	characteristic, complemented
28	C₂×#4341	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₂×#4339	C₂²	1	2	yes	complemented
31	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
32	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#124	C₂²	1	1	yes	characteristic
34	C₁₁×#123	C₂²	1	2	yes	complemented
35	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×#121	C₂²	1	1	yes	characteristic
37	C₁₁×#121	C₂²	1	2	yes	complemented
38	C₁₁×#120	C₂²	1	2	yes	complemented
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
42	#67006	C₂²	1	2	yes	—
43	#67006	C₂²	1	2	yes	complemented
44	#67006	C₂²	1	2	yes	complemented
45	#66999	C₂²	1	1	yes	characteristic, complemented
46	#66999	C₂²	1	1	yes	characteristic, complemented
47	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
48	#66993	C₂²	1	1	yes	characteristic
49	#66993	C₂²	1	1	yes	characteristic
50	#66993	C₂²	1	2	yes	complemented
51	#66993	C₂²	1	2	yes	complemented
52	#66993	C₂²	1	2	yes	complemented
53	#66992	C₂²	1	2	yes	—
54	#66992	C₂²	1	2	yes	complemented
55	#66992	C₂²	1	2	yes	complemented
56	#66992	C₂²	1	2	yes	complemented
57	#66991	C₂²	1	1	yes	characteristic
58	#66991	C₂²	1	1	yes	characteristic
59	#66991	C₂²	1	1	yes	characteristic
60	#66991	C₂²	1	1	yes	characteristic, complemented
61	#66991	C₂²	1	1	yes	characteristic, complemented
62	#66991	C₂²	1	1	yes	characteristic, complemented
63	#66991	C₂²	1	2	yes	complemented
64	#66990	C₂²	1	2	yes	—
65	#66990	C₂²	1	2	yes	complemented
66	#66989	C₂²	1	2	yes	complemented
67	#66988	C₂²	1	2	yes	complemented
68	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
69	#66983	C₂²	1	1	yes	characteristic
70	#66983	C₂²	1	2	yes	complemented
71	#66983	C₂²	1	2	yes	complemented
72	#66983	C₂²	1	1	yes	characteristic, complemented
73	#66982	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
79	#66979	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
81	#66977	C₂²	1	2	yes	complemented
82	#66951	C₂²	1	2	yes	complemented
83	#66951	C₂²	1	2	yes	complemented
84	#66949	C₂²	1	2	yes	complemented
85	#66948	C₂²	1	1	yes	characteristic, complemented
86	#66948	C₂²	1	1	yes	characteristic, complemented
87	#66948	C₂²	1	2	yes	complemented
88	#66945	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
90	#66941	C₂²	1	1	yes	characteristic, complemented
91	#66941	C₂²	1	1	yes	characteristic, complemented
92	#66940	C₂²	1	2	yes	complemented
93	#66938	C₂²	1	2	yes	—
94	#66938	C₂²	1	1	yes	characteristic, complemented
95	#66938	C₂²	1	2	yes	complemented
96	#66938	C₂²	1	2	yes	complemented
97	#66938	C₂²	1	1	yes	characteristic, complemented
98	#66937	C₂²	1	1	yes	characteristic
99	#66937	C₂²	1	2	yes	complemented
100	#66937	C₂²	1	2	yes	complemented
101	#66937	C₂²	1	2	yes	complemented
102	#66937	C₂²	1	2	yes	complemented
103	#66937	C₂²	1	1	yes	characteristic, complemented
104	#66937	C₂²	1	2	yes	complemented
105	#66936	C₂²	1	2	yes	complemented
106	#66936	C₂²	1	2	yes	complemented
107	#66936	C₂²	1	2	yes	complemented
108	#66936	C₂²	1	2	yes	complemented
109	#66935	C₂²	1	2	yes	complemented
110	#66935	C₂²	1	2	yes	complemented
111	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
112	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
114	#66932	C₂²	1	2	yes	complemented
115	#66932	C₂²	1	2	yes	complemented
116	#66932	C₂²	1	2	yes	complemented
117	#66931	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
122	#66923	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₁	C₂³	1	2	yes	—
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₁₁×#41	—	4	2	no	—
126	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	—	4	2	no	—
128	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁	C₂³	1	2	yes	—
131	C₂×D₄×C₁₁	C₂³	1	2	yes	—
132	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₁	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	—	4	4	no	—
139	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₁	C₂³	1	2	yes	—
156	C₂²×Dic₁₁	C₂³	1	2	yes	—
157	#4343	—	4	2	no	—
158	#4341	—	4	4	no	—
159	D₄×D₁₁	—	4	2	no	—
160	#4339	—	4	2	no	—
161	#4339	—	4	2	no	—
162	#4339	—	4	4	no	—
163	C₂×D₄₄	C₂³	1	1	yes	characteristic
164	C₂×D₄₄	C₂³	1	1	yes	characteristic
165	C₂×D₄₄	C₂³	1	1	yes	characteristic
166	C₂×D₄₄	C₂³	1	2	yes	—
167	C₂×D₄₄	C₂³	1	2	yes	—
168	C₂×D₄₄	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₁₁	C₂³	1	2	yes	—
175	C₂×C₄×D₁₁	C₂³	1	2	yes	—
176	C₂×C₄×D₁₁	C₂³	1	2	yes	—
177	C₂×Dic₂₂	C₂³	1	2	yes	—
178	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
179	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
180	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₄²×C₁₁	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
195	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
196	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
197	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
199	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
200	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₁	C₂³	1	2	yes	—
216	C₄⋊Dic₁₁	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₁₁⋊C₄	C₂³	1	2	yes	—
222	Dic₁₁⋊C₄	C₂³	1	2	yes	—
223	Dic₁₁⋊C₄	C₂³	1	2	yes	—
224	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	C₄×Dic₁₁	C₂³	1	2	yes	—
229	C₄×Dic₁₁	C₂³	1	2	yes	—
230	C₄×Dic₁₁	C₂³	1	2	yes	—
231	#3546	—	11	1	no	maximal, Sylow
232	C₂³×C₁₁	—	4	2	no	—
233	C₂³×C₁₁	—	4	2	no	—
234	C₂³×C₁₁	—	4	2	no	—
235	C₂³×C₁₁	C₂⁴	1	2	yes	—
236	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₁	C₂⁴	1	2	yes	—
238	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₁	—	4	2	no	—
240	C₂²×D₁₁	—	4	2	no	—
241	C₂²×D₁₁	—	4	2	no	—
242	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₁	C₂⁴	1	2	yes	—
244	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
246	Q₈×C₁₁	—	2	2	no	—
247	D₄×C₁₁	—	2	2	no	—
248	D₄×C₁₁	—	2	2	no	—
249	D₄×C₁₁	—	4	2	no	—
250	D₄×C₁₁	—	4	2	no	—
251	D₄×C₁₁	—	4	1	no	—
252	D₄×C₁₁	—	4	2	no	—
253	C₂×C₄×C₁₁	—	2	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	4	2	no	—
256	C₂×C₄×C₁₁	—	4	2	no	—
257	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₁	—	2	4	no	—
265	C₂²⋊D₁₁	—	2	2	no	—
266	C₂²⋊D₁₁	—	2	2	no	—
267	C₂²⋊D₁₁	—	4	2	no	—
268	C₂²⋊D₁₁	—	4	1	no	—
269	C₂²⋊D₁₁	—	4	1	no	—
270	C₂²⋊D₁₁	—	4	1	no	—
271	C₂²⋊D₁₁	—	4	1	no	—
272	C₂²⋊D₁₁	—	4	2	no	—
273	C₂²⋊D₁₁	—	4	2	no	—
274	C₂²⋊D₁₁	—	4	2	no	—
275	C₂²⋊D₁₁	—	4	2	no	—
276	C₂²⋊D₁₁	—	4	2	no	—
277	C₂²⋊D₁₁	—	4	2	no	—
278	C₂²⋊D₁₁	—	4	2	no	—
279	C₂²⋊D₁₁	—	4	2	no	—
280	C₂×Dic₁₁	—	2	4	no	—
281	C₂×Dic₁₁	—	4	2	no	—
282	C₂×Dic₁₁	C₂⁴	1	2	yes	—
283	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₁	C₂⁴	1	2	yes	—
287	C₂×Dic₁₁	C₂⁴	1	2	yes	—
288	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
290	D₄₄	—	2	2	no	—
291	D₄₄	—	4	1	no	—
292	D₄₄	—	4	1	no	—
293	D₄₄	—	4	1	no	—
294	D₄₄	—	4	2	no	—
295	D₄₄	—	4	2	no	—
296	C₄×D₁₁	—	2	2	no	—
297	C₄×D₁₁	—	2	2	no	—
298	C₄×D₁₁	—	2	2	no	—
299	C₄×D₁₁	—	2	2	no	—
300	C₄×D₁₁	—	4	1	no	—
301	C₄×D₁₁	—	4	2	no	—
302	C₄×D₁₁	—	4	2	no	—
303	C₄×D₁₁	—	4	2	no	—
304	Dic₂₂	—	2	4	no	—
305	Dic₂₂	—	4	1	no	—
306	Dic₂₂	—	4	1	no	—
307	#560	—	11	2	no	—
308	#560	—	11	2	no	—
309	#556	—	11	1	no	—
310	#553	—	11	1	no	—
311	#553	—	11	1	no	—
312	#550	—	11	1	no	—
313	#550	—	11	2	no	—
314	#547	—	11	1	no	—
315	#546	—	11	1	no	—
316	#546	—	11	2	no	—
317	#546	D₁₁	1	1	yes	characteristic, complemented
318	D₄²	—	11	1	no	—
319	#542	—	11	2	no	—
320	#538	—	11	2	no	—
321	#538	—	11	2	no	—
322	#537	—	11	1	no	—
323	#537	—	11	1	no	—
324	#535	—	11	1	no	—
325	#535	—	11	1	no	—
326	#535	—	11	2	no	—
327	#532	—	11	1	no	—
328	#532	—	11	1	no	—
329	#529	—	11	1	no	—
330	C₂²×C₁₁	—	2	1	no	—
331	C₂²×C₁₁	—	2	1	no	—
332	C₂²×C₁₁	—	2	2	no	—
333	C₂²×C₁₁	—	2	2	no	—
334	C₂²×C₁₁	—	2	2	no	—
335	C₂²×C₁₁	—	2	1	no	—
336	C₂²×C₁₁	—	2	2	no	—
337	C₂²×C₁₁	—	2	1	no	—
338	C₂²×C₁₁	—	2	1	no	—
339	C₂²×C₁₁	—	2	1	no	—
340	C₂²×C₁₁	—	2	2	no	—
341	C₂²×C₁₁	—	2	2	no	—
342	C₂²×C₁₁	—	8	4	no	—
343	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
344	C₂×D₁₁	—	2	1	no	—
345	C₂×D₁₁	—	2	1	no	—
346	C₂×D₁₁	—	2	2	no	—
347	C₂×D₁₁	—	2	2	no	—
348	C₂×D₁₁	—	2	1	no	—
349	C₂×D₁₁	—	2	1	no	—
350	C₂×D₁₁	—	2	1	no	—
351	C₂×D₁₁	—	2	1	no	—
352	C₂×D₁₁	—	2	1	no	—
353	C₂×D₁₁	—	2	2	no	—
354	C₂×D₁₁	—	2	1	no	—
355	C₂×D₁₁	—	2	1	no	—
356	C₂×D₁₁	—	8	4	no	—
357	C₄×C₁₁	—	2	1	no	—
358	C₄×C₁₁	—	2	1	no	—
359	C₄×C₁₁	—	2	1	no	—
360	C₄×C₁₁	—	2	2	no	—
361	C₄×C₁₁	—	2	2	no	—
362	C₄×C₁₁	—	2	1	no	—
363	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
364	Dic₁₁	—	2	2	no	—
365	Dic₁₁	—	2	1	no	—
366	Dic₁₁	—	2	1	no	—
367	Dic₁₁	—	2	1	no	—
368	Dic₁₁	—	2	2	no	—
369	Dic₁₁	—	2	1	no	—
370	Dic₁₁	—	2	2	no	—
371	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
372	C₂×#41	—	11	1	no	—
373	C₂×#41	—	11	2	no	—
374	C₂×#41	—	11	1	no	—
375	C₂×#41	—	11	1	no	—
376	C₂×#41	—	11	2	no	—
377	C₂×#41	C₂×D₁₁	1	1	yes	characteristic, complemented
378	C₂²×D₄	—	11	2	no	—
379	C₂²×D₄	—	11	1	no	—
380	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
381	C₄⋊Q₈	—	11	1	no	—
382	C₄⋊Q₈	—	11	1	no	—
383	#127	—	11	1	no	—
384	#127	—	11	1	no	—
385	#127	—	11	2	no	—
386	#127	—	11	2	no	—
387	#127	—	11	2	no	—
388	#126	—	11	2	no	—
389	#126	—	11	2	no	—
390	#126	—	11	2	no	—
391	#126	—	11	2	no	—
392	#126	—	11	2	no	—
393	#125	—	11	1	no	—
394	#124	—	11	2	no	—
395	#124	—	11	2	no	—
396	#124	—	11	1	no	—
397	#124	—	11	1	no	—
398	#124	—	11	2	no	—
399	#124	—	11	2	no	—
400	#124	C₂×D₁₁	1	1	yes	characteristic
401	#123	—	11	2	no	—
402	#123	—	11	2	no	—
403	#123	—	11	2	no	—
404	#123	—	11	2	no	—
405	#123	—	11	2	no	—
406	#123	—	11	2	no	—
407	#123	C₂×D₁₁	1	2	yes	complemented
408	C₂²⋊Q₈	—	11	1	no	—
409	C₂²⋊Q₈	—	11	1	no	—
410	C₂²⋊Q₈	—	11	2	no	—
411	C₂²⋊Q₈	—	11	2	no	—
412	C₂²⋊Q₈	—	11	2	no	—
413	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
414	#121	—	11	1	no	—
415	#121	—	11	1	no	—
416	#121	—	11	1	no	—
417	#121	—	11	2	no	—
418	#121	—	11	1	no	—
419	#121	—	11	1	no	—
420	#121	—	11	2	no	—
421	#121	—	11	1	no	—
422	#121	—	11	2	no	—
423	#121	—	11	2	no	—
424	#121	—	11	2	no	—
425	#121	—	11	1	no	—
426	#121	—	11	1	no	—
427	#121	—	11	2	no	—
428	#121	—	11	2	no	—
429	#121	—	11	1	no	—
430	#121	—	11	1	no	—
431	#121	—	11	2	no	—
432	#121	—	11	1	no	—
433	#121	—	11	1	no	—
434	#121	—	11	2	no	—
435	#121	—	11	2	no	—
436	#121	—	11	2	no	—
437	#121	—	11	2	no	—
438	#121	—	11	2	no	—
439	#121	C₂×D₁₁	1	1	yes	characteristic
440	#121	C₂×D₁₁	1	2	yes	complemented
441	#120	—	11	2	no	—
442	#120	—	11	2	no	—
443	#120	—	11	2	no	—
444	#120	—	11	2	no	—
445	#120	—	11	2	no	—
446	#120	—	11	2	no	—
447	#120	—	11	2	no	—
448	#120	C₂×D₁₁	1	2	yes	complemented
449	C₄×Q₈	—	11	1	no	—
450	C₄×Q₈	—	11	2	no	—
451	C₄×D₄	—	11	1	no	—
452	C₄×D₄	—	11	2	no	—
453	C₄×D₄	—	11	1	no	—
454	C₄×D₄	—	11	1	no	—
455	C₄×D₄	—	11	2	no	—
456	C₄×D₄	—	11	2	no	—
457	C₄×D₄	—	11	2	no	—
458	C₄×D₄	—	11	2	no	—
459	C₄×D₄	—	11	1	no	—
460	C₄×D₄	—	11	1	no	—
461	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
462	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
463	#117	—	11	1	no	—
464	#117	—	11	1	no	—
465	#117	—	11	2	no	—
466	C₂×C₄⋊C₄	—	11	1	no	—
467	C₂×C₄⋊C₄	—	11	1	no	—
468	C₂×C₂²⋊C₄	—	11	2	no	—
469	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	complemented
470	C₂×C₄²	—	11	1	no	—
471	C₂×C₁₁	—	4	2	no	—
472	C₂×C₁₁	—	4	1	no	—
473	C₂×C₁₁	—	4	2	no	—
474	C₂×C₁₁	—	4	1	no	—
475	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₁₁	#585	1	1	yes	characteristic
478	D₁₁	—	4	1	no	—
479	D₁₁	—	4	1	no	—
480	D₁₁	—	4	2	no	—
481	D₁₁	—	4	1	no	—
482	C₂⁴	—	11	2	no	—
483	C₂⁴	C₂²×D₁₁	1	2	yes	—
484	#41	—	4	2	no	—
485	#41	—	44	2	no	—
486	#41	—	44	2	no	—
487	#41	—	44	4	no	—
488	#41	—	44	4	no	—
489	#41	—	44	2	no	—
490	C₂×Q₈	—	11	2	no	—
491	C₂×Q₈	—	11	1	no	—
492	C₂×Q₈	—	11	1	no	—
493	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	11	1	no	—
496	C₂×D₄	—	11	2	no	—
497	C₂×D₄	—	11	1	no	—
498	C₂×D₄	—	11	2	no	—
499	C₂×D₄	—	11	2	no	—
500	C₂×D₄	—	11	2	no	—
501	C₂×D₄	—	11	2	no	—
502	C₂×D₄	—	11	1	no	—
503	C₂×D₄	—	11	2	no	—
504	C₂×D₄	—	11	1	no	—
505	C₂×D₄	—	11	1	no	—
506	C₂×D₄	—	11	2	no	—
507	C₂×D₄	—	11	2	no	—
508	C₂×D₄	—	11	2	no	—
509	C₂×D₄	—	11	2	no	—
510	C₂×D₄	—	11	1	no	—
511	C₂×D₄	—	11	1	no	—
512	C₂×D₄	—	11	1	no	—
513	C₂×D₄	—	11	1	no	—
514	C₂×D₄	—	11	2	no	—
515	C₂×D₄	—	11	2	no	—
516	C₂×D₄	—	11	1	no	—
517	C₂×D₄	—	44	2	no	—
518	C₂×D₄	—	44	4	no	—
519	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₁₁	1	2	yes	—
523	C₂×D₄	C₂²×D₁₁	1	2	yes	—
524	C₂×D₄	C₂²×D₁₁	1	2	yes	—
525	C₂²×C₄	—	11	2	no	—
526	C₂²×C₄	—	11	2	no	—
527	C₂²×C₄	—	11	1	no	—
528	C₂²×C₄	—	11	1	no	—
529	C₂²×C₄	—	11	1	no	—
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	C₂²×D₁₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
538	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
539	C₄⋊C₄	—	11	1	no	—
540	C₄⋊C₄	—	11	1	no	—
541	C₄⋊C₄	—	11	2	no	—
542	C₄⋊C₄	—	11	2	no	—
543	C₄⋊C₄	—	11	1	no	—
544	C₄⋊C₄	—	11	2	no	—
545	C₄⋊C₄	—	11	2	no	—
546	C₄⋊C₄	—	11	1	no	—
547	C₄⋊C₄	—	11	2	no	—
548	C₄⋊C₄	—	11	1	no	—
549	C₄⋊C₄	—	11	2	no	—
550	C₄⋊C₄	—	11	1	no	—
551	C₄⋊C₄	—	11	2	no	—
552	C₄⋊C₄	—	11	2	no	—
553	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
556	C₂²⋊C₄	—	11	2	no	—
557	C₂²⋊C₄	—	11	2	no	—
558	C₂²⋊C₄	—	11	2	no	—
559	C₂²⋊C₄	—	11	1	no	—
560	C₂²⋊C₄	—	11	2	no	—
561	C₂²⋊C₄	—	11	2	no	—
562	C₂²⋊C₄	—	11	2	no	—
563	C₂²⋊C₄	—	11	2	no	—
564	C₂²⋊C₄	—	11	1	no	—
565	C₂²⋊C₄	—	11	1	no	—
566	C₂²⋊C₄	—	11	2	no	—
567	C₂²⋊C₄	—	11	2	no	—
568	C₂²⋊C₄	—	11	1	no	—
569	C₂²⋊C₄	—	11	1	no	—
570	C₂²⋊C₄	—	11	2	no	—
571	C₂²⋊C₄	—	11	2	no	—
572	C₂²⋊C₄	—	11	2	no	—
573	C₂²⋊C₄	—	11	2	no	—
574	C₂²⋊C₄	—	11	2	no	—
575	C₂²⋊C₄	—	11	1	no	—
576	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
580	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
582	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
583	C₄²	—	11	1	no	—
584	C₄²	—	11	1	no	—
585	C₄²	—	11	1	no	—
586	C₄²	—	11	2	no	—
587	C₄²	—	11	2	no	—
588	C₄²	—	11	2	no	—
589	C₄²	C₂²×D₁₁	1	1	yes	characteristic
590	C₁₁	#3546	1	1	yes	characteristic, complemented, Sylow
591	C₂³	—	4	2	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	11	1	no	—
595	C₂³	—	11	2	no	—
596	C₂³	—	11	1	no	—
597	C₂³	—	11	1	no	—
598	C₂³	—	44	2	no	—
599	C₂³	—	44	2	no	—
600	C₂³	—	44	2	no	—
601	C₂³	C₂³×D₁₁	1	2	yes	—
602	C₂³	C₂³×D₁₁	1	1	yes	characteristic
603	C₂³	C₂³×D₁₁	1	2	yes	—
604	C₂³	C₂³×D₁₁	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	22	4	no	—
607	Q₈	—	44	1	no	—
608	Q₈	—	44	1	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	22	2	no	—
616	D₄	—	22	4	no	—
617	D₄	—	22	2	no	—
618	D₄	—	22	2	no	—
619	D₄	—	44	1	no	—
620	D₄	—	44	1	no	—
621	D₄	—	44	2	no	—
622	D₄	—	44	2	no	—
623	D₄	—	44	1	no	—
624	D₄	—	44	2	no	—
625	D₄	—	44	2	no	—
626	D₄	—	44	2	no	—
627	D₄	—	44	1	no	—
628	D₄	—	44	1	no	—
629	D₄	—	44	1	no	—
630	D₄	—	44	1	no	—
631	D₄	—	44	2	no	—
632	D₄	—	44	2	no	—
633	D₄	—	44	2	no	—
634	D₄	—	44	2	no	—
635	D₄	—	44	2	no	—
636	D₄	—	44	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	11	1	no	—
642	C₂×C₄	—	11	2	no	—
643	C₂×C₄	—	11	1	no	—
644	C₂×C₄	—	11	1	no	—
645	C₂×C₄	—	11	1	no	—
646	C₂×C₄	—	11	2	no	—
647	C₂×C₄	—	11	1	no	—
648	C₂×C₄	—	11	2	no	—
649	C₂×C₄	—	22	2	no	—
650	C₂×C₄	—	22	4	no	—
651	C₂×C₄	—	22	2	no	—
652	C₂×C₄	—	22	2	no	—
653	C₂×C₄	—	22	2	no	—
654	C₂×C₄	—	44	2	no	—
655	C₂×C₄	—	44	2	no	—
656	C₂×C₄	—	44	2	no	—
657	C₂×C₄	—	44	1	no	—
658	C₂×C₄	—	44	2	no	—
659	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₁	1	2	yes	—
663	C₂×C₄	C₂³×D₁₁	1	2	yes	—
664	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	22	1	no	—
680	C₂²	—	22	1	no	—
681	C₂²	—	22	1	no	—
682	C₂²	—	22	2	no	—
683	C₂²	—	22	1	no	—
684	C₂²	—	22	1	no	—
685	C₂²	—	22	2	no	—
686	C₂²	—	22	1	no	—
687	C₂²	—	22	1	no	—
688	C₂²	—	22	1	no	—
689	C₂²	—	22	2	no	—
690	C₂²	—	22	1	no	—
691	C₂²	—	88	4	no	—
692	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	11	2	no	—
700	C₄	—	22	1	no	—
701	C₄	—	22	1	no	—
702	C₄	—	22	1	no	—
703	C₄	—	22	1	no	—
704	C₄	—	22	2	no	—
705	C₄	—	22	2	no	—
706	C₄	—	22	2	no	—
707	C₄	#67037	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	44	1	no	—
713	C₂	—	44	2	no	—
714	C₂	—	44	1	no	—
715	C₂	—	44	1	no	—
716	C₂	C₂×#67037	1	1	yes	characteristic
717	C₂	#10623453	1	1	yes	characteristic
718	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#546	C₂
hypercenter	#546	D₁₁
hypocenter	C₁₁	#3546
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₁₁×#546	C₂	semidirect
2. #10623365	C₂	semidirect
3. #10623364	C₂	semidirect
4. #10623336	C₂	semidirect
5. D₄×C₂²⋊D₁₁	C₂	semidirect
6. #10623211	C₂	semidirect
7. #10623207	C₂	semidirect
8. #10623197	C₂	semidirect
9. #10623193	C₂	semidirect
10. #10623172	C₂	semidirect
11. #10623160	C₂	semidirect
12. #10623144	C₂	semidirect
13. #10623142	C₂	semidirect
14. #10623138	C₂	semidirect
15. #10623130	C₂	semidirect
16. #10623126	C₂	semidirect
17. #10623123	C₂	semidirect
18. #10623096	C₂	semidirect
19. #10623089	C₂	semidirect
20. #10623079	C₂	semidirect
21. #10623079	C₂	semidirect
22. #10623025	C₂	semidirect
23. #10623021	C₂	semidirect
24. C₂×C₁₁×#41	C₂²	semidirect
27. C₂×#4343	C₂²	semidirect
28. C₂×#4341	C₂²	semidirect
30. C₂×#4339	C₂²	semidirect
31. C₂×#4339	C₂²	semidirect
32. C₂×#4339	C₂²	semidirect
34. C₁₁×#123	C₂²	semidirect
35. C₁₁×C₂²⋊Q₈	C₂²	semidirect
37. C₁₁×#121	C₂²	semidirect
38. C₁₁×#120	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₄×D₄×C₁₁	C₂²	semidirect
41. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
43. #67006	C₂²	semidirect
44. #67006	C₂²	semidirect
45. #66999	C₂²	semidirect
46. #66999	C₂²	semidirect
47. Q₈×Dic₁₁	C₂²	semidirect
50. #66993	C₂²	semidirect
51. #66993	C₂²	semidirect
52. #66993	C₂²	semidirect
54. #66992	C₂²	semidirect
55. #66992	C₂²	semidirect
56. #66992	C₂²	semidirect
60. #66991	C₂²	semidirect
61. #66991	C₂²	semidirect
62. #66991	C₂²	semidirect
63. #66991	C₂²	semidirect
65. #66990	C₂²	semidirect
66. #66989	C₂²	semidirect
67. #66988	C₂²	semidirect
70. #66983	C₂²	semidirect
71. #66983	C₂²	semidirect
72. #66983	C₂²	semidirect
73. #66982	C₂²	semidirect
75. C₄×C₂²⋊D₁₁	C₂²	semidirect
76. C₄×C₂²⋊D₁₁	C₂²	semidirect
77. C₄×C₂²⋊D₁₁	C₂²	semidirect
78. C₄×C₂²⋊D₁₁	C₂²	semidirect
79. #66979	C₂²	semidirect
80. C₂×C₄⋊Dic₁₁	C₂²	semidirect
81. #66977	C₂²	semidirect
82. #66951	C₂²	semidirect
83. #66951	C₂²	semidirect
84. #66949	C₂²	semidirect
85. #66948	C₂²	semidirect
86. #66948	C₂²	semidirect
87. #66948	C₂²	semidirect
88. #66945	C₂²	semidirect
89. C₄⋊C₄×D₁₁	C₂²	semidirect
90. #66941	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66940	C₂²	semidirect
94. #66938	C₂²	semidirect
95. #66938	C₂²	semidirect
96. #66938	C₂²	semidirect
97. #66938	C₂²	semidirect
99. #66937	C₂²	semidirect
100. #66937	C₂²	semidirect
101. #66937	C₂²	semidirect
102. #66937	C₂²	semidirect
103. #66937	C₂²	semidirect
104. #66937	C₂²	semidirect
105. #66936	C₂²	semidirect
106. #66936	C₂²	semidirect
107. #66936	C₂²	semidirect
108. #66936	C₂²	semidirect
109. #66935	C₂²	semidirect
110. #66935	C₂²	semidirect
111. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
112. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
113. C₂²⋊C₄×D₁₁	C₂²	semidirect
114. #66932	C₂²	semidirect
115. #66932	C₂²	semidirect
116. #66932	C₂²	semidirect
117. #66931	C₂²	semidirect
118. #66930	C₂²	semidirect
119. C₄×D₄₄	C₂²	semidirect
120. C₄×D₄₄	C₂²	semidirect
121. C₄²×D₁₁	C₂²	semidirect
122. #66923	C₂²	semidirect
317. #546	D₁₁	semidirect
377. C₂×#41	C₂×D₁₁	semidirect
407. #123	C₂×D₁₁	semidirect
413. C₂²⋊Q₈	C₂×D₁₁	semidirect
440. #121	C₂×D₁₁	semidirect
448. #120	C₂×D₁₁	semidirect
461. C₄×D₄	C₂×D₁₁	semidirect
462. C₄×D₄	C₂×D₁₁	semidirect
469. C₂×C₂²⋊C₄	C₂×D₁₁	semidirect
590. C₁₁	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#546	2
#10623365	2
#10623364	2
#10623336	2
D₄×C₂²⋊D₁₁	2
#10623211	2
#10623207	2
#10623197	2
#10623193	2
#10623172	2
#10623160	2
#10623144	2
#10623142	2
#10623138	2
#10623130	2
#10623126	2
#10623123	2
#10623096	2
#10623089	2
#10623079	2
#10623025	2
#10623021	2
#3546	11