Subgroups — #13082508

Order 1408.

1040 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623264	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623259	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623236	C₂	1	2	yes	maximal, complemented
5	#10623233	C₂	1	2	yes	maximal, complemented
6	#10623213	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623212	C₂	1	2	yes	maximal, complemented
8	#10623210	C₂	1	2	yes	maximal, complemented
9	D₁₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623195	C₂	1	2	yes	maximal, complemented
11	#10623189	C₂	1	2	yes	maximal, complemented
12	#10623172	C₂	1	2	yes	maximal, complemented
13	#10623168	C₂	1	2	yes	maximal, complemented
14	#10623159	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623155	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623138	C₂	1	1	yes	maximal, characteristic
17	#10623131	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623103	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623088	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	#10623053	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
26	C₂×#4339	C₂²	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×#126	C₂²	1	2	yes	complemented
29	C₁₁×#124	C₂²	1	1	yes	characteristic
30	C₁₁×#124	C₂²	1	2	yes	complemented
31	C₁₁×#123	C₂²	1	2	yes	complemented
32	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₁×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
38	#67000	C₂²	1	1	yes	characteristic
39	#67000	C₂²	1	2	yes	complemented
40	#66999	C₂²	1	2	yes	—
41	#66999	C₂²	1	2	yes	complemented
42	#66999	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₁	C₂²	1	2	yes	complemented
44	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
45	#66993	C₂²	1	2	yes	—
46	#66991	C₂²	1	1	yes	characteristic
47	#66990	C₂²	1	2	yes	—
48	#66989	C₂²	1	1	yes	characteristic
49	#66988	C₂²	1	2	yes	complemented
50	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₁	C₂²	1	2	yes	complemented
52	#66983	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
55	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
56	#66979	C₂²	1	2	yes	complemented
57	#66977	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
59	#66951	C₂²	1	2	yes	complemented
60	#66951	C₂²	1	2	yes	complemented
61	#66951	C₂²	1	2	yes	complemented
62	#66951	C₂²	1	2	yes	complemented
63	#66950	C₂²	1	2	yes	—
64	#66950	C₂²	1	1	yes	characteristic, complemented
65	#66949	C₂²	1	2	yes	complemented
66	#66948	C₂²	1	1	yes	characteristic
67	#66947	C₂²	1	2	yes	—
68	#66947	C₂²	1	2	yes	complemented
69	#66947	C₂²	1	2	yes	complemented
70	#66946	C₂²	1	1	yes	characteristic
71	#66946	C₂²	1	1	yes	characteristic
72	#66946	C₂²	1	1	yes	characteristic
73	#66945	C₂²	1	1	yes	characteristic
74	#66945	C₂²	1	1	yes	characteristic
75	#66945	C₂²	1	2	yes	—
76	#66945	C₂²	1	2	yes	complemented
77	#66943	C₂²	1	1	yes	characteristic, complemented
78	#66943	C₂²	1	1	yes	characteristic, complemented
79	#66941	C₂²	1	2	yes	complemented
80	#66940	C₂²	1	1	yes	characteristic, complemented
81	#66940	C₂²	1	2	yes	complemented
82	#66940	C₂²	1	1	yes	characteristic, complemented
83	#66940	C₂²	1	1	yes	characteristic, complemented
84	#66940	C₂²	1	2	yes	complemented
85	#66939	C₂²	1	2	yes	complemented
86	#66939	C₂²	1	2	yes	complemented
87	#66938	C₂²	1	2	yes	—
88	#66938	C₂²	1	2	yes	—
89	#66938	C₂²	1	2	yes	—
90	#66938	C₂²	1	2	yes	complemented
91	#66938	C₂²	1	2	yes	complemented
92	#66938	C₂²	1	2	yes	complemented
93	#66936	C₂²	1	2	yes	—
94	#66936	C₂²	1	2	yes	complemented
95	#66936	C₂²	1	2	yes	complemented
96	#66935	C₂²	1	2	yes	—
97	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	(C₂²⋊D₁₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
106	#66932	C₂²	1	2	yes	complemented
107	#66932	C₂²	1	2	yes	complemented
108	#66932	C₂²	1	2	yes	complemented
109	#66931	C₂²	1	2	yes	complemented
110	#66930	C₂²	1	2	yes	complemented
111	#66928	C₂²	1	1	yes	characteristic
112	C₄×D₄₄	C₂²	1	1	yes	characteristic
113	C₄×D₄₄	C₂²	1	2	yes	complemented
114	#66925	C₂²	1	2	yes	—
115	#66925	C₂²	1	1	yes	characteristic
116	#66925	C₂²	1	2	yes	complemented
117	#66925	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic
119	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
120	#66922	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	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	2	yes	—
126	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₁	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
135	C₂²×Dic₁₁	C₂³	1	2	yes	—
136	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
138	Q₈×D₁₁	—	2	4	no	—
139	D₄×D₁₁	—	2	4	no	—
140	#4339	—	2	4	no	—
141	C₂×D₄₄	C₂³	1	1	yes	characteristic
142	C₂×D₄₄	C₂³	1	1	yes	characteristic
143	C₂×D₄₄	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₁	C₂³	1	2	yes	—
152	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₂	C₂³	1	2	yes	—
155	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₂	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₄²×C₁₁	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	2	yes	—
173	C₄²×C₁₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
179	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
195	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₁	C₂³	1	2	yes	—
197	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₁	C₂³	1	2	yes	—
199	C₄⋊Dic₁₁	C₂³	1	2	yes	—
200	C₄⋊Dic₁₁	C₂³	1	2	yes	—
201	C₄⋊Dic₁₁	C₂³	1	2	yes	—
202	Dic₁₁⋊C₄	C₂³	1	2	yes	—
203	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₁₁⋊C₄	C₂³	1	2	yes	—
205	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₁₁⋊C₄	C₂³	1	2	yes	—
207	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₁⋊C₄	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	C₄×Dic₁₁	C₂³	1	2	yes	—
213	C₄×Dic₁₁	C₂³	1	2	yes	—
214	C₄×Dic₁₁	C₂³	1	2	yes	—
215	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₁	C₂³	1	2	yes	—
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	#3510	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	C₂⁴	1	2	yes	—
227	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₁	—	2	4	no	—
229	C₂²×D₁₁	—	4	2	no	—
230	C₂²×D₁₁	—	4	2	no	—
231	C₂²×D₁₁	C₂⁴	1	2	yes	—
232	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
234	Q₈×C₁₁	—	2	2	no	—
235	Q₈×C₁₁	—	4	2	no	—
236	D₄×C₁₁	—	2	2	no	—
237	D₄×C₁₁	—	4	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	4	2	no	—
240	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₁	—	2	2	no	—
250	C₂²⋊D₁₁	—	2	2	no	—
251	C₂²⋊D₁₁	—	2	4	no	—
252	C₂²⋊D₁₁	—	4	2	no	—
253	C₂²⋊D₁₁	—	4	2	no	—
254	C₂×Dic₁₁	—	4	2	no	—
255	C₂×Dic₁₁	—	4	1	no	—
256	C₂×Dic₁₁	—	4	1	no	—
257	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₁	C₂⁴	1	2	yes	—
262	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₁	C₂⁴	1	2	yes	—
264	C₂×Dic₁₁	C₂⁴	1	2	yes	—
265	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
266	D₄₄	—	2	2	no	—
267	D₄₄	—	2	2	no	—
268	D₄₄	—	4	2	no	—
269	C₄×D₁₁	—	2	4	no	—
270	C₄×D₁₁	—	2	2	no	—
271	C₄×D₁₁	—	4	2	no	—
272	C₄×D₁₁	—	4	1	no	—
273	C₄×D₁₁	—	4	2	no	—
274	C₄×D₁₁	—	4	1	no	—
275	C₄×D₁₁	—	4	1	no	—
276	C₄×D₁₁	—	4	1	no	—
277	C₄×D₁₁	#41	1	4	yes	—
278	Dic₂₂	—	2	2	no	—
279	Dic₂₂	—	2	2	no	—
280	Dic₂₂	—	2	4	no	—
281	Dic₂₂	—	4	2	no	—
282	#559	—	11	2	no	—
283	#559	—	11	2	no	—
284	#556	—	11	2	no	—
285	#556	—	11	2	no	—
286	#551	—	11	2	no	—
287	#551	—	11	2	no	—
288	#551	—	11	2	no	—
289	#551	—	11	2	no	—
290	#542	—	11	1	no	—
291	#542	—	11	1	no	—
292	#542	—	11	1	no	—
293	#542	D₁₁	1	1	yes	characteristic, complemented
294	#536	—	11	1	no	—
295	#535	—	11	1	no	—
296	#533	—	11	1	no	—
297	#529	—	11	1	no	—
298	#529	—	11	1	no	—
299	#529	—	11	1	no	—
300	#529	—	11	1	no	—
301	C₂×#124	—	11	1	no	—
302	#519	—	11	1	no	—
303	#518	—	11	1	no	—
304	C₄×#41	—	11	1	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	—	2	2	no	—
307	C₂²×C₁₁	—	2	2	no	—
308	C₂²×C₁₁	—	2	1	no	—
309	C₂²×C₁₁	—	2	2	no	—
310	C₂²×C₁₁	—	2	1	no	—
311	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
312	C₂×D₁₁	—	2	1	no	—
313	C₂×D₁₁	—	2	1	no	—
314	C₂×D₁₁	—	2	2	no	—
315	C₂×D₁₁	—	2	1	no	—
316	C₂×D₁₁	—	2	2	no	—
317	C₂×D₁₁	—	2	2	no	—
318	C₂×D₁₁	—	2	1	no	—
319	C₂×D₁₁	—	2	1	no	—
320	C₂×D₁₁	—	8	4	no	—
321	C₂×D₁₁	C₂×#41	1	2	yes	—
322	C₄×C₁₁	—	2	1	no	—
323	C₄×C₁₁	—	2	2	no	—
324	C₄×C₁₁	—	2	1	no	—
325	C₄×C₁₁	—	2	2	no	—
326	C₄×C₁₁	—	2	2	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	—	2	1	no	—
329	C₄×C₁₁	—	2	1	no	—
330	C₄×C₁₁	C₂×#41	1	2	yes	—
331	Dic₁₁	—	2	2	no	—
332	Dic₁₁	—	2	1	no	—
333	Dic₁₁	—	2	2	no	—
334	Dic₁₁	—	2	2	no	—
335	Dic₁₁	—	2	1	no	—
336	Dic₁₁	—	2	1	no	—
337	Dic₁₁	—	2	1	no	—
338	Dic₁₁	—	2	1	no	—
339	Dic₁₁	C₂×#41	1	2	yes	—
340	C₂×#41	—	11	1	no	—
341	C₂²×Q₈	—	11	1	no	—
342	C₂²×D₄	—	11	1	no	—
343	C₄⋊Q₈	—	11	2	no	—
344	C₄⋊Q₈	—	11	1	no	—
345	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
346	#127	—	11	2	no	—
347	#126	—	11	2	no	—
348	#126	—	11	2	no	—
349	#126	—	11	2	no	—
350	#126	—	11	2	no	—
351	#126	—	11	2	no	—
352	#126	—	11	2	no	—
353	#126	—	11	2	no	—
354	#126	C₂×D₁₁	1	2	yes	complemented
355	#125	—	11	1	no	—
356	#125	—	11	1	no	—
357	#124	—	11	1	no	—
358	#124	—	11	2	no	—
359	#124	—	11	1	no	—
360	#124	—	11	2	no	—
361	#124	—	11	2	no	—
362	#124	—	11	2	no	—
363	#124	—	11	2	no	—
364	#124	—	11	2	no	—
365	#124	—	11	2	no	—
366	#124	—	11	1	no	—
367	#124	C₂×D₁₁	1	1	yes	characteristic
368	#124	C₂×D₁₁	1	2	yes	complemented
369	#123	—	11	2	no	—
370	#123	—	11	2	no	—
371	#123	—	11	2	no	—
372	#123	—	11	2	no	—
373	#123	—	11	2	no	—
374	#123	—	11	2	no	—
375	#123	—	11	2	no	—
376	#123	—	11	2	no	—
377	#123	—	11	2	no	—
378	#123	C₂×D₁₁	1	2	yes	complemented
379	C₂²⋊Q₈	—	11	1	no	—
380	C₂²⋊Q₈	—	11	2	no	—
381	C₂²⋊Q₈	—	11	2	no	—
382	C₂²⋊Q₈	—	11	1	no	—
383	C₂²⋊Q₈	—	11	1	no	—
384	C₂²⋊Q₈	—	11	2	no	—
385	C₂²⋊Q₈	—	11	2	no	—
386	C₂²⋊Q₈	—	11	2	no	—
387	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
388	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
389	#121	—	11	1	no	—
390	#121	—	11	1	no	—
391	#121	—	11	1	no	—
392	#121	C₂×D₁₁	1	1	yes	characteristic
393	#120	—	11	2	no	—
394	#120	—	11	2	no	—
395	C₄×Q₈	—	11	1	no	—
396	C₄×Q₈	—	11	2	no	—
397	C₄×Q₈	—	11	1	no	—
398	C₄×Q₈	—	11	1	no	—
399	C₄×Q₈	—	11	1	no	—
400	C₄×Q₈	—	11	2	no	—
401	C₄×Q₈	—	11	2	no	—
402	C₄×Q₈	—	11	1	no	—
403	C₄×Q₈	—	11	2	no	—
404	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
405	C₄×D₄	—	11	1	no	—
406	C₄×D₄	—	11	2	no	—
407	C₄×D₄	—	11	2	no	—
408	C₄×D₄	—	11	2	no	—
409	C₄×D₄	—	11	1	no	—
410	C₄×D₄	—	11	1	no	—
411	C₄×D₄	—	11	1	no	—
412	C₄×D₄	—	11	1	no	—
413	C₄×D₄	—	11	1	no	—
414	C₄×D₄	—	11	1	no	—
415	C₄×D₄	—	11	1	no	—
416	C₄×D₄	—	11	2	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
421	#117	—	11	2	no	—
422	#117	—	11	1	no	—
423	#117	—	11	1	no	—
424	#117	—	11	2	no	—
425	#117	—	11	2	no	—
426	#117	—	11	2	no	—
427	#117	—	11	1	no	—
428	#117	—	11	1	no	—
429	#117	—	11	2	no	—
430	#117	—	11	2	no	—
431	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
432	C₂×C₂²⋊C₄	—	11	2	no	—
433	C₂×C₂²⋊C₄	—	11	2	no	—
434	C₂×C₂²⋊C₄	—	11	2	no	—
435	C₂×C₂²⋊C₄	—	11	2	no	—
436	C₂×C₄²	—	11	1	no	—
437	C₂×C₄²	—	11	1	no	—
438	C₂×C₄²	—	11	1	no	—
439	C₂×C₁₁	—	4	2	no	—
440	C₂×C₁₁	—	4	1	no	—
441	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
442	C₂×C₁₁	#585	1	1	yes	characteristic
443	C₂×C₁₁	#585	1	1	yes	characteristic
444	D₁₁	—	2	2	no	—
445	D₁₁	—	4	1	no	—
446	D₁₁	—	4	2	no	—
447	C₂⁴	—	11	2	no	—
448	#41	—	22	4	no	—
449	C₂×Q₈	—	11	1	no	—
450	C₂×Q₈	—	11	2	no	—
451	C₂×Q₈	—	11	1	no	—
452	C₂×Q₈	—	11	2	no	—
453	C₂×Q₈	—	22	4	no	—
454	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
455	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
456	C₂×D₄	—	11	1	no	—
457	C₂×D₄	—	11	2	no	—
458	C₂×D₄	—	11	1	no	—
459	C₂×D₄	—	11	2	no	—
460	C₂×D₄	—	11	2	no	—
461	C₂×D₄	—	11	1	no	—
462	C₂×D₄	—	11	1	no	—
463	C₂×D₄	—	11	2	no	—
464	C₂×D₄	—	22	4	no	—
465	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
466	C₂×D₄	C₂²×D₁₁	1	2	yes	—
467	C₂²×C₄	—	11	1	no	—
468	C₂²×C₄	—	11	1	no	—
469	C₂²×C₄	—	11	1	no	—
470	C₂²×C₄	—	11	2	no	—
471	C₂²×C₄	—	11	1	no	—
472	C₂²×C₄	—	11	2	no	—
473	C₂²×C₄	—	11	1	no	—
474	C₂²×C₄	—	11	1	no	—
475	C₂²×C₄	—	11	1	no	—
476	C₂²×C₄	—	11	1	no	—
477	C₂²×C₄	—	11	2	no	—
478	C₂²×C₄	—	11	2	no	—
479	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
481	C₄⋊C₄	—	11	2	no	—
482	C₄⋊C₄	—	11	2	no	—
483	C₄⋊C₄	—	11	1	no	—
484	C₄⋊C₄	—	11	1	no	—
485	C₄⋊C₄	—	11	1	no	—
486	C₄⋊C₄	—	11	1	no	—
487	C₄⋊C₄	—	11	1	no	—
488	C₄⋊C₄	—	11	1	no	—
489	C₄⋊C₄	—	11	2	no	—
490	C₄⋊C₄	—	11	2	no	—
491	C₄⋊C₄	—	11	2	no	—
492	C₄⋊C₄	—	11	2	no	—
493	C₄⋊C₄	—	11	2	no	—
494	C₄⋊C₄	—	11	2	no	—
495	C₄⋊C₄	—	11	2	no	—
496	C₄⋊C₄	—	11	2	no	—
497	C₄⋊C₄	—	11	2	no	—
498	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
505	C₂²⋊C₄	—	11	2	no	—
506	C₂²⋊C₄	—	11	2	no	—
507	C₂²⋊C₄	—	11	2	no	—
508	C₂²⋊C₄	—	11	2	no	—
509	C₂²⋊C₄	—	11	2	no	—
510	C₂²⋊C₄	—	11	1	no	—
511	C₂²⋊C₄	—	11	1	no	—
512	C₂²⋊C₄	—	11	2	no	—
513	C₂²⋊C₄	—	11	2	no	—
514	C₂²⋊C₄	—	11	2	no	—
515	C₂²⋊C₄	—	11	2	no	—
516	C₂²⋊C₄	—	11	2	no	—
517	C₂²⋊C₄	—	11	2	no	—
518	C₂²⋊C₄	—	11	2	no	—
519	C₂²⋊C₄	—	11	2	no	—
520	C₂²⋊C₄	—	11	1	no	—
521	C₂²⋊C₄	—	11	1	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	2	no	—
524	C₂²⋊C₄	—	11	2	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
531	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
533	C₄²	—	11	1	no	—
534	C₄²	—	11	1	no	—
535	C₄²	—	11	1	no	—
536	C₄²	—	11	1	no	—
537	C₄²	—	11	1	no	—
538	C₄²	—	11	1	no	—
539	C₄²	—	11	1	no	—
540	C₄²	—	11	1	no	—
541	C₄²	—	11	2	no	—
542	C₄²	—	11	2	no	—
543	C₄²	—	11	2	no	—
544	C₄²	—	11	2	no	—
545	C₄²	—	11	2	no	—
546	C₄²	C₂²×D₁₁	1	1	yes	characteristic
547	C₄²	C₂²×D₁₁	1	1	yes	characteristic
548	C₄²	C₂²×D₁₁	1	2	yes	—
549	C₁₁	#3510	1	1	yes	characteristic, complemented, Sylow
550	C₂³	—	11	1	no	—
551	C₂³	—	11	2	no	—
552	C₂³	—	11	1	no	—
553	C₂³	—	22	4	no	—
554	C₂³	—	44	2	no	—
555	C₂³	—	44	2	no	—
556	C₂³	C₂³×D₁₁	1	2	yes	—
557	C₂³	C₂³×D₁₁	1	1	yes	characteristic
558	Q₈	—	2	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	22	4	no	—
561	Q₈	—	22	2	no	—
562	Q₈	—	22	2	no	—
563	Q₈	—	44	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	22	2	no	—
567	D₄	—	22	4	no	—
568	D₄	—	22	2	no	—
569	D₄	—	22	2	no	—
570	D₄	—	22	2	no	—
571	D₄	—	44	2	no	—
572	D₄	—	44	2	no	—
573	D₄	—	44	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	11	1	no	—
577	C₂×C₄	—	11	4	no	—
578	C₂×C₄	—	11	1	no	—
579	C₂×C₄	—	11	1	no	—
580	C₂×C₄	—	11	1	no	—
581	C₂×C₄	—	11	1	no	—
582	C₂×C₄	—	11	2	no	—
583	C₂×C₄	—	11	2	no	—
584	C₂×C₄	—	11	1	no	—
585	C₂×C₄	—	11	2	no	—
586	C₂×C₄	—	22	4	no	—
587	C₂×C₄	—	22	2	no	—
588	C₂×C₄	—	44	1	no	—
589	C₂×C₄	—	44	2	no	—
590	C₂×C₄	—	44	1	no	—
591	C₂×C₄	—	44	1	no	—
592	C₂×C₄	—	44	2	no	—
593	C₂×C₄	—	44	1	no	—
594	C₂×C₄	—	44	1	no	—
595	C₂×C₄	—	44	1	no	—
596	C₂×C₄	—	44	2	no	—
597	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₁	1	2	yes	—
599	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₁₁	1	2	yes	—
603	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₁	1	2	yes	—
605	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	11	2	no	—
613	C₂²	—	22	1	no	—
614	C₂²	—	22	1	no	—
615	C₂²	—	22	1	no	—
616	C₂²	—	22	2	no	—
617	C₂²	—	22	1	no	—
618	C₂²	—	22	2	no	—
619	C₂²	—	22	1	no	—
620	C₂²	—	22	2	no	—
621	C₂²	—	88	4	no	—
622	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	11	2	no	—
632	C₄	—	22	1	no	—
633	C₄	—	22	2	no	—
634	C₄	—	22	1	no	—
635	C₄	—	22	1	no	—
636	C₄	—	22	1	no	—
637	C₄	—	22	1	no	—
638	C₄	—	22	2	no	—
639	C₄	—	22	2	no	—
640	C₄	#41×D₁₁	1	2	yes	—
641	C₂	—	4	2	no	—
642	C₂	—	4	1	no	—
643	C₂	—	22	2	no	—
644	C₂	—	44	2	no	—
645	C₂	—	44	1	no	—
646	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
647	C₂	#10623455	1	1	yes	characteristic
648	C₂	#10623457	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#542	C₂
prime radical	#10623138	C₂
hypercenter	#542	D₁₁
hypocenter	C₁₁	#3510
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₁₁×#542	C₂	semidirect
2. #10623264	C₂	semidirect
3. #10623259	C₂	semidirect
4. #10623236	C₂	semidirect
5. #10623233	C₂	semidirect
6. #10623213	C₂	semidirect
7. #10623212	C₂	semidirect
8. #10623210	C₂	semidirect
9. D₁₁×#124	C₂	semidirect
10. #10623195	C₂	semidirect
11. #10623189	C₂	semidirect
12. #10623172	C₂	semidirect
13. #10623168	C₂	semidirect
14. #10623159	C₂	semidirect
15. #10623155	C₂	semidirect
17. #10623131	C₂	semidirect
18. #10623111	C₂	semidirect
19. #10623103	C₂	semidirect
20. #10623088	C₂	semidirect
21. #10623076	C₂	semidirect
22. #10623065	C₂	semidirect
23. #10623053	C₂	semidirect
27. C₁₁×C₄⋊Q₈	C₂²	semidirect
28. C₁₁×#126	C₂²	semidirect
30. C₁₁×#124	C₂²	semidirect
31. C₁₁×#123	C₂²	semidirect
32. C₁₁×C₂²⋊Q₈	C₂²	semidirect
33. C₁₁×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₁₁	C₂²	semidirect
37. C₁₁×#117	C₂²	semidirect
39. #67000	C₂²	semidirect
41. #66999	C₂²	semidirect
42. #66999	C₂²	semidirect
43. Q₈×Dic₁₁	C₂²	semidirect
44. Q₈×Dic₁₁	C₂²	semidirect
49. #66988	C₂²	semidirect
51. D₄×Dic₁₁	C₂²	semidirect
54. C₄×C₂²⋊D₁₁	C₂²	semidirect
56. #66979	C₂²	semidirect
57. #66977	C₂²	semidirect
58. C₂×C₄×Dic₁₁	C₂²	semidirect
59. #66951	C₂²	semidirect
60. #66951	C₂²	semidirect
61. #66951	C₂²	semidirect
62. #66951	C₂²	semidirect
64. #66950	C₂²	semidirect
65. #66949	C₂²	semidirect
68. #66947	C₂²	semidirect
69. #66947	C₂²	semidirect
76. #66945	C₂²	semidirect
77. #66943	C₂²	semidirect
78. #66943	C₂²	semidirect
79. #66941	C₂²	semidirect
80. #66940	C₂²	semidirect
81. #66940	C₂²	semidirect
82. #66940	C₂²	semidirect
83. #66940	C₂²	semidirect
84. #66940	C₂²	semidirect
85. #66939	C₂²	semidirect
86. #66939	C₂²	semidirect
90. #66938	C₂²	semidirect
91. #66938	C₂²	semidirect
92. #66938	C₂²	semidirect
94. #66936	C₂²	semidirect
95. #66936	C₂²	semidirect
100. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
106. #66932	C₂²	semidirect
107. #66932	C₂²	semidirect
108. #66932	C₂²	semidirect
109. #66931	C₂²	semidirect
110. #66930	C₂²	semidirect
113. C₄×D₄₄	C₂²	semidirect
116. #66925	C₂²	semidirect
117. #66925	C₂²	semidirect
119. C₄²×D₁₁	C₂²	semidirect
120. #66922	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
293. #542	D₁₁	semidirect
345. C₄⋊Q₈	C₂×D₁₁	semidirect
354. #126	C₂×D₁₁	semidirect
368. #124	C₂×D₁₁	semidirect
378. #123	C₂×D₁₁	semidirect
387. C₂²⋊Q₈	C₂×D₁₁	semidirect
388. C₂²⋊Q₈	C₂×D₁₁	semidirect
404. C₄×Q₈	C₂×D₁₁	semidirect
431. #117	C₂×D₁₁	semidirect
549. C₁₁	#3510	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#542	2
#10623264	2
#10623259	2
#10623236	2
#10623233	2
#10623213	2
#10623212	2
#10623210	2
D₁₁×#124	2
#10623195	2
#10623189	2
#10623172	2
#10623168	2
#10623159	2
#10623155	2
#10623138	2
#10623131	2
#10623111	2
#10623103	2
#10623088	2
#10623076	2
#10623065	2
#10623053	2
#3510	11