Subgroups — #13082683

Order 1408.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 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	#10623262	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623257	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623240	C₂	1	2	yes	maximal, complemented
5	#10623239	C₂	1	2	yes	maximal, complemented
6	#10623235	C₂	1	2	yes	maximal, complemented
7	D₁₁×#126	C₂	1	2	yes	maximal, complemented
8	#10623213	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623211	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623207	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623207	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623169	C₂	1	2	yes	maximal, complemented
13	#10623168	C₂	1	2	yes	maximal, complemented
14	#10623115	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623112	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623110	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623105	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#4343	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623089	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623076	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623059	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×D₄×D₁₁	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×#126	C₂²	1	2	yes	complemented
30	C₁₁×#124	C₂²	1	1	yes	characteristic
31	C₁₁×#124	C₂²	1	1	yes	characteristic
32	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
34	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
35	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#117	C₂²	1	2	yes	complemented
38	#67000	C₂²	1	1	yes	characteristic
39	#66999	C₂²	1	1	yes	characteristic
40	#66999	C₂²	1	1	yes	characteristic
41	#66999	C₂²	1	1	yes	characteristic, complemented
42	#66999	C₂²	1	1	yes	characteristic, complemented
43	#66999	C₂²	1	2	yes	complemented
44	#66999	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
47	#66991	C₂²	1	1	yes	characteristic
48	#66991	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
50	#66982	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
54	#66951	C₂²	1	1	yes	characteristic
55	#66951	C₂²	1	2	yes	—
56	#66951	C₂²	1	2	yes	—
57	#66951	C₂²	1	2	yes	—
58	#66951	C₂²	1	2	yes	complemented
59	#66951	C₂²	1	1	yes	characteristic, complemented
60	#66949	C₂²	1	2	yes	complemented
61	#66949	C₂²	1	2	yes	complemented
62	#66948	C₂²	1	1	yes	characteristic
63	#66948	C₂²	1	2	yes	complemented
64	#66947	C₂²	1	2	yes	—
65	#66947	C₂²	1	1	yes	characteristic
66	#66947	C₂²	1	1	yes	characteristic, complemented
67	#66947	C₂²	1	2	yes	complemented
68	#66947	C₂²	1	2	yes	complemented
69	#66946	C₂²	1	1	yes	characteristic
70	#66946	C₂²	1	2	yes	complemented
71	#66946	C₂²	1	2	yes	complemented
72	#66945	C₂²	1	1	yes	characteristic
73	#66945	C₂²	1	2	yes	complemented
74	#66945	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
76	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
79	#66943	C₂²	1	1	yes	characteristic, complemented
80	#66942	C₂²	1	2	yes	complemented
81	#66942	C₂²	1	2	yes	complemented
82	#66942	C₂²	1	2	yes	complemented
83	#66939	C₂²	1	2	yes	complemented
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	complemented
88	#66936	C₂²	1	2	yes	—
89	#66936	C₂²	1	2	yes	—
90	#66936	C₂²	1	2	yes	complemented
91	#66935	C₂²	1	2	yes	—
92	#66935	C₂²	1	2	yes	—
93	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
98	#66932	C₂²	1	2	yes	complemented
99	#66932	C₂²	1	2	yes	complemented
100	#66932	C₂²	1	2	yes	complemented
101	#66931	C₂²	1	2	yes	complemented
102	#66930	C₂²	1	2	yes	complemented
103	#66929	C₂²	1	2	yes	—
104	#66928	C₂²	1	2	yes	—
105	C₄×D₄₄	C₂²	1	1	yes	characteristic
106	C₄×D₄₄	C₂²	1	1	yes	characteristic
107	C₄×D₄₄	C₂²	1	1	yes	characteristic
108	C₄×D₄₄	C₂²	1	1	yes	characteristic
109	C₄×D₄₄	C₂²	1	1	yes	characteristic
110	C₄×D₄₄	C₂²	1	2	yes	complemented
111	C₄×D₄₄	C₂²	1	2	yes	complemented
112	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
113	#66925	C₂²	1	1	yes	characteristic
114	#66925	C₂²	1	2	yes	complemented
115	#66925	C₂²	1	2	yes	complemented
116	#66925	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₁	C₂²	1	2	yes	complemented
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
119	#66923	C₂²	1	1	yes	characteristic, complemented
120	#66923	C₂²	1	1	yes	characteristic, complemented
121	#66922	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	2	yes	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	C₂²×Dic₁₁	C₂³	1	2	yes	—
133	#4343	—	2	4	no	—
134	#4343	—	2	4	no	—
135	D₄×D₁₁	—	2	4	no	—
136	C₂×D₄₄	C₂³	1	2	yes	—
137	C₂×D₄₄	C₂³	1	2	yes	—
138	C₂×D₄₄	C₂³	1	1	yes	characteristic
139	C₂×D₄₄	C₂³	1	1	yes	characteristic
140	C₂×D₄₄	C₂³	1	1	yes	characteristic
141	C₂×D₄₄	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₁	C₂³	1	2	yes	—
148	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁	C₂³	1	2	yes	—
150	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁	C₂³	1	2	yes	—
152	C₂×C₄×D₁₁	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁	C₂³	1	2	yes	—
154	C₂×Dic₂₂	C₂³	1	2	yes	—
155	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
163	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₁₁	C₂³	1	2	yes	—
169	C₄²×C₁₁	C₂³	1	1	yes	characteristic
170	C₄²×C₁₁	C₂³	1	1	yes	characteristic
171	C₄²×C₁₁	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
176	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
186	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	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	2	yes	—
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
196	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₁	C₂³	1	2	yes	—
200	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₁	C₂³	1	2	yes	—
203	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₁	C₂³	1	2	yes	—
205	Dic₁₁⋊C₄	C₂³	1	2	yes	—
206	Dic₁₁⋊C₄	C₂³	1	2	yes	—
207	Dic₁₁⋊C₄	C₂³	1	2	yes	—
208	Dic₁₁⋊C₄	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	C₄×Dic₁₁	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	2	yes	—
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	#3521	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	C₂⁴	1	2	yes	—
227	C₂²×D₁₁	—	2	4	no	—
228	C₂²×D₁₁	—	4	2	no	—
229	C₂²×D₁₁	—	4	2	no	—
230	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₁	C₂⁴	1	2	yes	—
234	Q₈×C₁₁	—	2	2	no	—
235	Q₈×C₁₁	—	2	2	no	—
236	Q₈×C₁₁	—	4	1	no	—
237	D₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	4	2	no	—
239	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₁	—	2	4	no	—
250	C₂²⋊D₁₁	—	4	2	no	—
251	C₂²⋊D₁₁	—	4	2	no	—
252	C₂×Dic₁₁	—	4	2	no	—
253	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁	C₂⁴	1	2	yes	—
258	C₂×Dic₁₁	C₂⁴	1	2	yes	—
259	C₂×Dic₁₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
261	D₄₄	—	2	4	no	—
262	D₄₄	—	2	4	no	—
263	D₄₄	—	4	1	no	—
264	D₄₄	—	4	1	no	—
265	D₄₄	—	4	1	no	—
266	D₄₄	#41	1	4	yes	—
267	C₄×D₁₁	—	2	4	no	—
268	C₄×D₁₁	—	2	4	no	—
269	C₄×D₁₁	—	2	2	no	—
270	C₄×D₁₁	—	2	2	no	—
271	C₄×D₁₁	—	2	2	no	—
272	C₄×D₁₁	—	4	2	no	—
273	C₄×D₁₁	—	4	2	no	—
274	C₄×D₁₁	—	4	2	no	—
275	C₄×D₁₁	—	4	1	no	—
276	C₄×D₁₁	—	4	2	no	—
277	C₄×D₁₁	—	4	2	no	—
278	C₄×D₁₁	—	4	1	no	—
279	Dic₂₂	—	4	2	no	—
280	#556	—	11	1	no	—
281	#556	D₁₁	1	1	yes	characteristic, complemented
282	#554	—	11	1	no	—
283	#553	—	11	2	no	—
284	#553	—	11	1	no	—
285	#552	—	11	2	no	—
286	#552	—	11	1	no	—
287	#551	—	11	2	no	—
288	#551	—	11	2	no	—
289	#547	—	11	1	no	—
290	#546	—	11	1	no	—
291	#546	—	11	1	no	—
292	#542	—	11	1	no	—
293	#541	—	11	1	no	—
294	#539	—	11	2	no	—
295	#538	—	11	2	no	—
296	#529	—	11	1	no	—
297	#529	—	11	1	no	—
298	#529	—	11	2	no	—
299	C₂×#126	—	11	2	no	—
300	#520	—	11	1	no	—
301	#518	—	11	1	no	—
302	C₄×#41	—	11	1	no	—
303	C₂²×C₁₁	—	2	2	no	—
304	C₂²×C₁₁	—	2	2	no	—
305	C₂²×C₁₁	—	2	2	no	—
306	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₁	—	2	2	no	—
308	C₂×D₁₁	—	2	2	no	—
309	C₂×D₁₁	—	2	1	no	—
310	C₂×D₁₁	—	2	1	no	—
311	C₂×D₁₁	—	2	1	no	—
312	C₂×D₁₁	—	2	1	no	—
313	C₂×D₁₁	—	2	1	no	—
314	C₂×D₁₁	—	2	1	no	—
315	C₂×D₁₁	—	2	1	no	—
316	C₂×D₁₁	—	2	1	no	—
317	C₂×D₁₁	—	2	1	no	—
318	C₂×D₁₁	—	8	4	no	—
319	C₂×D₁₁	C₂×#41	1	4	yes	—
320	C₄×C₁₁	—	2	2	no	—
321	C₄×C₁₁	—	2	2	no	—
322	C₄×C₁₁	—	2	1	no	—
323	C₄×C₁₁	—	2	2	no	—
324	C₄×C₁₁	—	2	1	no	—
325	C₄×C₁₁	—	2	1	no	—
326	C₄×C₁₁	—	2	1	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	—	2	1	no	—
329	C₄×C₁₁	C₂×#41	1	2	yes	—
330	Dic₁₁	—	2	1	no	—
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	—	2	1	no	—
333	Dic₁₁	—	2	2	no	—
334	Dic₁₁	—	2	2	no	—
335	Dic₁₁	—	2	1	no	—
336	Dic₁₁	—	2	2	no	—
337	Dic₁₁	—	2	1	no	—
338	C₂×#41	—	11	1	no	—
339	C₂×#41	—	11	1	no	—
340	C₂²×D₄	—	11	1	no	—
341	C₄⋊Q₈	—	11	1	no	—
342	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
343	#126	—	11	1	no	—
344	#126	—	11	2	no	—
345	#126	—	11	2	no	—
346	#126	—	11	1	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	C₂×D₁₁	1	2	yes	complemented
354	#126	C₂×D₁₁	1	2	yes	complemented
355	#125	—	11	2	no	—
356	#125	—	11	1	no	—
357	#125	—	11	2	no	—
358	#125	—	11	2	no	—
359	#125	—	11	1	no	—
360	#125	—	11	1	no	—
361	#124	—	11	1	no	—
362	#124	—	11	2	no	—
363	#124	—	11	2	no	—
364	#124	C₂×D₁₁	1	1	yes	characteristic
365	#124	C₂×D₁₁	1	1	yes	characteristic
366	#123	—	11	2	no	—
367	#123	—	11	2	no	—
368	#123	—	11	1	no	—
369	#123	—	11	1	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	C₂²⋊Q₈	—	11	1	no	—
377	C₂²⋊Q₈	—	11	1	no	—
378	C₂²⋊Q₈	—	11	2	no	—
379	C₂²⋊Q₈	—	11	1	no	—
380	C₂²⋊Q₈	—	11	1	no	—
381	C₂²⋊Q₈	—	11	1	no	—
382	C₂²⋊Q₈	—	11	2	no	—
383	C₂²⋊Q₈	—	11	2	no	—
384	C₂²⋊Q₈	—	11	2	no	—
385	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
386	#121	—	11	1	no	—
387	#121	—	11	1	no	—
388	#121	—	11	1	no	—
389	#121	—	11	2	no	—
390	#121	—	11	2	no	—
391	#121	—	11	2	no	—
392	#121	—	11	2	no	—
393	#120	—	11	2	no	—
394	#120	—	11	2	no	—
395	C₄×Q₈	—	11	1	no	—
396	C₄×Q₈	—	11	1	no	—
397	C₄×Q₈	—	11	2	no	—
398	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
399	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
400	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
401	C₄×D₄	—	11	1	no	—
402	C₄×D₄	—	11	2	no	—
403	C₄×D₄	—	11	2	no	—
404	C₄×D₄	—	11	1	no	—
405	C₄×D₄	—	11	2	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	2	no	—
411	C₄×D₄	—	11	1	no	—
412	C₄×D₄	—	11	2	no	—
413	C₄×D₄	—	11	1	no	—
414	C₄×D₄	—	11	1	no	—
415	C₄×D₄	—	11	1	no	—
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
418	#117	—	11	2	no	—
419	#117	—	11	1	no	—
420	#117	—	11	1	no	—
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	C₂×D₁₁	1	2	yes	complemented
427	C₂×C₄⋊C₄	—	11	2	no	—
428	C₂×C₄⋊C₄	—	11	1	no	—
429	C₂×C₄⋊C₄	—	11	2	no	—
430	C₂×C₄⋊C₄	—	11	2	no	—
431	C₂×C₂²⋊C₄	—	11	2	no	—
432	C₂×C₂²⋊C₄	—	11	2	no	—
433	C₂×C₂²⋊C₄	—	11	2	no	—
434	C₂×C₂²⋊C₄	—	11	2	no	—
435	C₂×C₄²	—	11	2	no	—
436	C₂×C₄²	—	11	1	no	—
437	C₂×C₁₁	—	4	2	no	—
438	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
439	C₂×C₁₁	#585	1	1	yes	characteristic
440	C₂×C₁₁	#585	1	1	yes	characteristic
441	D₁₁	—	2	4	no	—
442	D₁₁	—	4	1	no	—
443	D₁₁	—	4	1	no	—
444	D₁₁	—	4	1	no	—
445	C₂⁴	—	11	2	no	—
446	#41	—	22	4	no	—
447	#41	—	22	4	no	—
448	C₂×Q₈	—	11	2	no	—
449	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
450	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
451	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
452	C₂×D₄	—	11	2	no	—
453	C₂×D₄	—	11	2	no	—
454	C₂×D₄	—	11	2	no	—
455	C₂×D₄	—	11	1	no	—
456	C₂×D₄	—	11	2	no	—
457	C₂×D₄	—	11	2	no	—
458	C₂×D₄	—	11	1	no	—
459	C₂×D₄	—	11	1	no	—
460	C₂×D₄	—	11	1	no	—
461	C₂×D₄	—	22	4	no	—
462	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
463	C₂²×C₄	—	11	2	no	—
464	C₂²×C₄	—	11	2	no	—
465	C₂²×C₄	—	11	1	no	—
466	C₂²×C₄	—	11	2	no	—
467	C₂²×C₄	—	11	1	no	—
468	C₂²×C₄	—	11	1	no	—
469	C₂²×C₄	—	11	2	no	—
470	C₂²×C₄	—	11	2	no	—
471	C₂²×C₄	—	11	1	no	—
472	C₂²×C₄	—	11	1	no	—
473	C₂²×C₄	—	11	2	no	—
474	C₂²×C₄	—	11	2	no	—
475	C₂²×C₄	—	11	2	no	—
476	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
477	C₄⋊C₄	—	11	1	no	—
478	C₄⋊C₄	—	11	2	no	—
479	C₄⋊C₄	—	11	1	no	—
480	C₄⋊C₄	—	11	2	no	—
481	C₄⋊C₄	—	11	2	no	—
482	C₄⋊C₄	—	11	1	no	—
483	C₄⋊C₄	—	11	2	no	—
484	C₄⋊C₄	—	11	2	no	—
485	C₄⋊C₄	—	11	2	no	—
486	C₄⋊C₄	—	11	2	no	—
487	C₄⋊C₄	—	11	1	no	—
488	C₄⋊C₄	—	11	1	no	—
489	C₄⋊C₄	—	11	1	no	—
490	C₄⋊C₄	—	11	1	no	—
491	C₄⋊C₄	—	11	1	no	—
492	C₄⋊C₄	—	11	2	no	—
493	C₄⋊C₄	—	11	2	no	—
494	C₄⋊C₄	—	11	2	no	—
495	C₄⋊C₄	—	11	1	no	—
496	C₄⋊C₄	—	11	2	no	—
497	C₄⋊C₄	—	11	1	no	—
498	C₄⋊C₄	—	11	2	no	—
499	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
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	1	no	—
514	C₂²⋊C₄	—	11	1	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	1	no	—
520	C₂²⋊C₄	—	11	2	no	—
521	C₂²⋊C₄	—	11	2	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	1	no	—
524	C₂²⋊C₄	—	11	1	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	—	11	1	no	—
527	C₂²⋊C₄	—	11	1	no	—
528	C₂²⋊C₄	—	11	2	no	—
529	C₂²⋊C₄	—	11	1	no	—
530	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
535	C₄²	—	11	1	no	—
536	C₄²	—	11	1	no	—
537	C₄²	—	11	1	no	—
538	C₄²	—	11	2	no	—
539	C₄²	—	11	2	no	—
540	C₄²	—	11	2	no	—
541	C₄²	—	11	2	no	—
542	C₄²	C₂²×D₁₁	1	2	yes	—
543	C₄²	C₂²×D₁₁	1	1	yes	characteristic
544	C₄²	C₂²×D₁₁	1	2	yes	—
545	C₄²	C₂²×D₁₁	1	1	yes	characteristic
546	C₄²	C₂²×D₁₁	1	1	yes	characteristic
547	C₁₁	#3521	1	1	yes	characteristic, complemented, Sylow
548	C₂³	—	11	2	no	—
549	C₂³	—	11	1	no	—
550	C₂³	—	11	1	no	—
551	C₂³	—	11	1	no	—
552	C₂³	—	22	4	no	—
553	C₂³	—	44	2	no	—
554	C₂³	—	44	2	no	—
555	C₂³	C₂³×D₁₁	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	44	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	11	4	no	—
562	D₄	—	22	4	no	—
563	D₄	—	22	4	no	—
564	D₄	—	22	4	no	—
565	D₄	—	44	1	no	—
566	D₄	—	44	1	no	—
567	D₄	—	44	1	no	—
568	D₄	—	44	2	no	—
569	D₄	—	44	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	11	1	no	—
572	C₂×C₄	—	11	1	no	—
573	C₂×C₄	—	11	1	no	—
574	C₂×C₄	—	11	2	no	—
575	C₂×C₄	—	11	1	no	—
576	C₂×C₄	—	11	2	no	—
577	C₂×C₄	—	11	2	no	—
578	C₂×C₄	—	11	1	no	—
579	C₂×C₄	—	22	4	no	—
580	C₂×C₄	—	22	4	no	—
581	C₂×C₄	—	22	2	no	—
582	C₂×C₄	—	22	2	no	—
583	C₂×C₄	—	22	2	no	—
584	C₂×C₄	—	44	2	no	—
585	C₂×C₄	—	44	2	no	—
586	C₂×C₄	—	44	2	no	—
587	C₂×C₄	—	44	1	no	—
588	C₂×C₄	—	44	1	no	—
589	C₂×C₄	—	44	2	no	—
590	C₂×C₄	—	44	2	no	—
591	C₂×C₄	—	44	2	no	—
592	C₂×C₄	C₂³×D₁₁	1	2	yes	—
593	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₁	1	2	yes	—
595	C₂×C₄	C₂³×D₁₁	1	2	yes	—
596	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
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	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	11	4	no	—
606	C₂²	—	22	2	no	—
607	C₂²	—	22	2	no	—
608	C₂²	—	22	1	no	—
609	C₂²	—	22	1	no	—
610	C₂²	—	22	1	no	—
611	C₂²	—	22	1	no	—
612	C₂²	—	22	1	no	—
613	C₂²	—	22	1	no	—
614	C₂²	—	22	1	no	—
615	C₂²	—	22	1	no	—
616	C₂²	—	22	1	no	—
617	C₂²	—	88	4	no	—
618	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	22	1	no	—
629	C₄	—	22	1	no	—
630	C₄	—	22	1	no	—
631	C₄	—	22	1	no	—
632	C₄	—	22	2	no	—
633	C₄	—	22	1	no	—
634	C₄	—	22	2	no	—
635	C₄	—	22	2	no	—
636	C₄	#41×D₁₁	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	22	4	no	—
639	C₂	—	44	1	no	—
640	C₂	—	44	1	no	—
641	C₂	—	44	1	no	—
642	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
643	C₂	#10623453	1	1	yes	characteristic
644	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	#3521
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. #10623262	C₂	semidirect
3. #10623257	C₂	semidirect
4. #10623240	C₂	semidirect
5. #10623239	C₂	semidirect
6. #10623235	C₂	semidirect
7. D₁₁×#126	C₂	semidirect
8. #10623213	C₂	semidirect
9. #10623211	C₂	semidirect
10. #10623207	C₂	semidirect
11. #10623207	C₂	semidirect
12. #10623169	C₂	semidirect
13. #10623168	C₂	semidirect
14. #10623115	C₂	semidirect
15. #10623112	C₂	semidirect
16. #10623111	C₂	semidirect
17. #10623110	C₂	semidirect
18. #10623105	C₂	semidirect
19. C₄×#4343	C₂	semidirect
20. #10623089	C₂	semidirect
21. #10623076	C₂	semidirect
22. #10623059	C₂	semidirect
23. #10623058	C₂	semidirect
27. C₁₁×C₄⋊Q₈	C₂²	semidirect
28. C₁₁×#126	C₂²	semidirect
29. C₁₁×#126	C₂²	semidirect
32. C₁₁×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₁	C₂²	semidirect
34. C₄×Q₈×C₁₁	C₂²	semidirect
35. C₄×Q₈×C₁₁	C₂²	semidirect
37. C₁₁×#117	C₂²	semidirect
41. #66999	C₂²	semidirect
42. #66999	C₂²	semidirect
43. #66999	C₂²	semidirect
44. #66999	C₂²	semidirect
45. Q₈×Dic₁₁	C₂²	semidirect
46. Q₈×Dic₁₁	C₂²	semidirect
50. #66982	C₂²	semidirect
52. C₄×C₂²⋊D₁₁	C₂²	semidirect
58. #66951	C₂²	semidirect
59. #66951	C₂²	semidirect
60. #66949	C₂²	semidirect
61. #66949	C₂²	semidirect
63. #66948	C₂²	semidirect
66. #66947	C₂²	semidirect
67. #66947	C₂²	semidirect
68. #66947	C₂²	semidirect
70. #66946	C₂²	semidirect
71. #66946	C₂²	semidirect
73. #66945	C₂²	semidirect
74. #66945	C₂²	semidirect
75. C₄⋊C₄×D₁₁	C₂²	semidirect
76. C₄⋊C₄×D₁₁	C₂²	semidirect
77. C₄⋊C₄×D₁₁	C₂²	semidirect
78. C₄⋊C₄×D₁₁	C₂²	semidirect
79. #66943	C₂²	semidirect
80. #66942	C₂²	semidirect
81. #66942	C₂²	semidirect
82. #66942	C₂²	semidirect
83. #66939	C₂²	semidirect
84. #66938	C₂²	semidirect
87. #66937	C₂²	semidirect
90. #66936	C₂²	semidirect
94. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
98. #66932	C₂²	semidirect
99. #66932	C₂²	semidirect
100. #66932	C₂²	semidirect
101. #66931	C₂²	semidirect
102. #66930	C₂²	semidirect
110. C₄×D₄₄	C₂²	semidirect
111. C₄×D₄₄	C₂²	semidirect
112. C₄×D₄₄	C₂²	semidirect
114. #66925	C₂²	semidirect
115. #66925	C₂²	semidirect
116. #66925	C₂²	semidirect
117. C₄²×D₁₁	C₂²	semidirect
118. C₄²×D₁₁	C₂²	semidirect
119. #66923	C₂²	semidirect
120. #66923	C₂²	semidirect
121. #66922	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
281. #556	D₁₁	semidirect
342. C₄⋊Q₈	C₂×D₁₁	semidirect
353. #126	C₂×D₁₁	semidirect
354. #126	C₂×D₁₁	semidirect
385. C₂²⋊Q₈	C₂×D₁₁	semidirect
398. C₄×Q₈	C₂×D₁₁	semidirect
399. C₄×Q₈	C₂×D₁₁	semidirect
400. C₄×Q₈	C₂×D₁₁	semidirect
426. #117	C₂×D₁₁	semidirect
547. C₁₁	#3521	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
#10623262	2
#10623257	2
#10623240	2
#10623239	2
#10623235	2
D₁₁×#126	2
#10623213	2
#10623211	2
#10623207	2
#10623169	2
#10623168	2
#10623115	2
#10623112	2
#10623111	2
#10623110	2
#10623105	2
C₄×#4343	2
#10623089	2
#10623076	2
#10623059	2
#10623058	2
#3521	11