Subgroups — #13082360

Order 1408.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623259	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623255	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623239	C₂	1	2	yes	maximal, complemented
5	#10623236	C₂	1	2	yes	maximal, complemented
6	#10623236	C₂	1	2	yes	maximal, complemented
7	#10623233	C₂	1	2	yes	maximal, complemented
8	#10623225	C₂	1	2	yes	maximal, complemented
9	#10623224	C₂	1	2	yes	maximal, complemented
10	#10623224	C₂	1	2	yes	maximal, complemented
11	#10623222	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623221	C₂	1	2	yes	maximal, complemented
13	#10623220	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623174	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623158	C₂	1	1	yes	maximal, characteristic
16	D₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623156	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623111	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623109	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623105	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623103	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×#4343	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×#126	C₂²	1	2	yes	—
29	C₁₁×#126	C₂²	1	2	yes	—
30	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#125	C₂²	1	2	yes	complemented
32	C₁₁×#125	C₂²	1	2	yes	complemented
33	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
37	C₁₁×#117	C₂²	1	1	yes	characteristic
38	#67000	C₂²	1	1	yes	characteristic, complemented
39	#66999	C₂²	1	1	yes	characteristic
40	#66999	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
43	#66997	C₂²	1	1	yes	characteristic, complemented
44	#66983	C₂²	1	1	yes	characteristic
45	#66979	C₂²	1	1	yes	characteristic
46	#66977	C₂²	1	1	yes	characteristic
47	#66951	C₂²	1	2	yes	complemented
48	#66951	C₂²	1	2	yes	complemented
49	#66951	C₂²	1	2	yes	complemented
50	#66951	C₂²	1	2	yes	complemented
51	#66950	C₂²	1	2	yes	—
52	#66950	C₂²	1	2	yes	—
53	#66950	C₂²	1	1	yes	characteristic
54	#66950	C₂²	1	2	yes	complemented
55	#66949	C₂²	1	2	yes	—
56	#66949	C₂²	1	2	yes	—
57	#66949	C₂²	1	2	yes	—
58	#66949	C₂²	1	2	yes	complemented
59	#66949	C₂²	1	2	yes	complemented
60	#66949	C₂²	1	2	yes	complemented
61	#66948	C₂²	1	1	yes	characteristic
62	#66947	C₂²	1	2	yes	—
63	#66947	C₂²	1	2	yes	—
64	#66947	C₂²	1	2	yes	—
65	#66947	C₂²	1	2	yes	—
66	#66947	C₂²	1	2	yes	—
67	#66946	C₂²	1	2	yes	—
68	#66946	C₂²	1	2	yes	—
69	#66946	C₂²	1	2	yes	—
70	#66946	C₂²	1	1	yes	characteristic, complemented
71	#66945	C₂²	1	2	yes	—
72	#66945	C₂²	1	2	yes	—
73	#66945	C₂²	1	1	yes	characteristic
74	#66945	C₂²	1	1	yes	characteristic
75	#66945	C₂²	1	1	yes	characteristic
76	#66945	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
81	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
82	#66943	C₂²	1	2	yes	complemented
83	#66943	C₂²	1	1	yes	characteristic, complemented
84	#66943	C₂²	1	2	yes	complemented
85	#66942	C₂²	1	2	yes	complemented
86	#66942	C₂²	1	2	yes	complemented
87	#66942	C₂²	1	2	yes	complemented
88	#66941	C₂²	1	2	yes	complemented
89	#66941	C₂²	1	1	yes	characteristic, complemented
90	#66940	C₂²	1	2	yes	complemented
91	#66940	C₂²	1	2	yes	complemented
92	#66940	C₂²	1	1	yes	characteristic, complemented
93	#66938	C₂²	1	2	yes	—
94	#66938	C₂²	1	2	yes	—
95	#66936	C₂²	1	2	yes	—
96	#66936	C₂²	1	2	yes	—
97	#66935	C₂²	1	2	yes	—
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
102	#66932	C₂²	1	2	yes	—
103	#66932	C₂²	1	2	yes	—
104	#66931	C₂²	1	2	yes	—
105	#66930	C₂²	1	1	yes	characteristic
106	#66930	C₂²	1	1	yes	characteristic
107	#66928	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₄₄	C₂²	1	2	yes	—
109	C₄×D₄₄	C₂²	1	2	yes	—
110	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
111	#66925	C₂²	1	2	yes	—
112	#66925	C₂²	1	2	yes	—
113	#66925	C₂²	1	1	yes	characteristic
114	#66925	C₂²	1	1	yes	characteristic
115	#66925	C₂²	1	2	yes	complemented
116	#66925	C₂²	1	2	yes	complemented
117	C₄²×D₁₁	C₂²	1	1	yes	characteristic
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic
119	#66922	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₂	C₂²	1	2	yes	complemented
121	C₄×Dic₂₂	C₂²	1	2	yes	complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
128	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
129	#4343	—	2	4	no	—
130	Q₈×D₁₁	—	2	4	no	—
131	C₂×D₄₄	C₂³	1	2	yes	—
132	C₂×D₄₄	C₂³	1	2	yes	—
133	C₂×D₄₄	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₁	—	2	4	no	—
135	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₁	C₂³	1	2	yes	—
139	C₂×C₄×D₁₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
149	C₂×Dic₂₂	C₂³	1	2	yes	—
150	C₂×Dic₂₂	C₂³	1	2	yes	—
151	C₂×Dic₂₂	C₂³	1	2	yes	—
152	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
155	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₄²×C₁₁	C₂³	1	1	yes	characteristic
169	C₄²×C₁₁	C₂³	1	2	yes	—
170	C₄²×C₁₁	C₂³	1	2	yes	—
171	C₄²×C₁₁	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
181	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₁	C₂³	1	2	yes	—
193	C₄⋊Dic₁₁	C₂³	1	2	yes	—
194	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₁	C₂³	1	2	yes	—
196	C₄⋊Dic₁₁	C₂³	1	2	yes	—
197	C₄⋊Dic₁₁	C₂³	1	2	yes	—
198	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
200	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₁₁⋊C₄	C₂³	1	2	yes	—
202	Dic₁₁⋊C₄	C₂³	1	2	yes	—
203	Dic₁₁⋊C₄	C₂³	1	2	yes	—
204	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	2	yes	—
213	Dic₁₁⋊C₄	C₂³	1	2	yes	—
214	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₁	C₂³	1	2	yes	—
216	C₄×Dic₁₁	C₂³	1	2	yes	—
217	C₄×Dic₁₁	C₂³	1	2	yes	—
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	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	#3495	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₁	—	2	2	no	—
228	C₂²×D₁₁	—	2	2	no	—
229	C₂²×D₁₁	—	4	1	no	—
230	C₂²×D₁₁	C₂⁴	1	2	yes	—
231	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₁	—	2	2	no	—
234	Q₈×C₁₁	—	2	2	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂²⋊D₁₁	—	4	2	no	—
247	C₂×Dic₁₁	—	2	2	no	—
248	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₁	C₂⁴	1	2	yes	—
252	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₁	C₂⁴	1	2	yes	—
254	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₁	C₂⁴	1	2	yes	—
256	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
257	D₄₄	—	2	4	no	—
258	D₄₄	—	2	4	no	—
259	D₄₄	—	2	2	no	—
260	C₄×D₁₁	—	2	2	no	—
261	C₄×D₁₁	—	2	4	no	—
262	C₄×D₁₁	—	2	2	no	—
263	C₄×D₁₁	—	2	2	no	—
264	C₄×D₁₁	—	2	2	no	—
265	C₄×D₁₁	—	2	2	no	—
266	C₄×D₁₁	—	2	4	no	—
267	C₄×D₁₁	—	4	1	no	—
268	C₄×D₁₁	—	4	2	no	—
269	C₄×D₁₁	—	4	2	no	—
270	C₄×D₁₁	—	4	1	no	—
271	C₄×D₁₁	—	4	2	no	—
272	C₄×D₁₁	#41	1	4	yes	—
273	Dic₂₂	—	2	2	no	—
274	Dic₂₂	—	2	4	no	—
275	Dic₂₂	—	4	2	no	—
276	Dic₂₂	—	4	2	no	—
277	#556	—	11	2	no	—
278	#554	—	11	2	no	—
279	#552	—	11	2	no	—
280	#552	—	11	2	no	—
281	#552	—	11	2	no	—
282	#552	—	11	2	no	—
283	#551	—	11	2	no	—
284	#551	—	11	2	no	—
285	#544	—	11	1	no	—
286	#542	—	11	1	no	—
287	#542	—	11	1	no	—
288	#541	—	11	1	no	—
289	#541	D₁₁	1	1	yes	characteristic, complemented
290	#536	—	11	1	no	—
291	#533	—	11	1	no	—
292	#533	—	11	1	no	—
293	#529	—	11	1	no	—
294	#529	—	11	1	no	—
295	#525	—	11	1	no	—
296	C₂×C₂²⋊Q₈	—	11	1	no	—
297	#520	—	11	1	no	—
298	#519	—	11	1	no	—
299	C₂×#117	—	11	1	no	—
300	C₂²×C₁₁	—	2	1	no	—
301	C₂²×C₁₁	—	2	1	no	—
302	C₂²×C₁₁	—	2	1	no	—
303	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
304	C₂×D₁₁	—	2	1	no	—
305	C₂×D₁₁	—	2	1	no	—
306	C₂×D₁₁	—	2	1	no	—
307	C₂×D₁₁	—	2	1	no	—
308	C₂×D₁₁	—	2	2	no	—
309	C₂×D₁₁	—	2	2	no	—
310	C₂×D₁₁	—	2	2	no	—
311	C₂×D₁₁	—	4	4	no	—
312	C₂×D₁₁	C₂×#41	1	2	yes	—
313	C₂×D₁₁	2₋¹⁺⁴	1	2	yes	—
314	C₄×C₁₁	—	2	1	no	—
315	C₄×C₁₁	—	2	2	no	—
316	C₄×C₁₁	—	2	2	no	—
317	C₄×C₁₁	—	2	1	no	—
318	C₄×C₁₁	—	2	1	no	—
319	C₄×C₁₁	—	2	2	no	—
320	C₄×C₁₁	—	2	1	no	—
321	C₄×C₁₁	—	2	2	no	—
322	C₄×C₁₁	—	2	1	no	—
323	C₄×C₁₁	C₂×#41	1	2	yes	—
324	Dic₁₁	—	2	2	no	—
325	Dic₁₁	—	2	1	no	—
326	Dic₁₁	—	2	1	no	—
327	Dic₁₁	—	2	1	no	—
328	Dic₁₁	—	2	1	no	—
329	Dic₁₁	—	2	2	no	—
330	Dic₁₁	—	2	2	no	—
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	C₂×#41	1	2	yes	—
333	C₂×#41	—	11	1	no	—
334	C₂²×Q₈	—	11	1	no	—
335	C₂³×C₄	—	11	1	no	—
336	C₄⋊Q₈	—	11	1	no	—
337	C₄⋊Q₈	—	11	1	no	—
338	C₄⋊Q₈	—	11	2	no	—
339	C₄⋊Q₈	—	11	1	no	—
340	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
341	#126	—	11	2	no	—
342	#126	—	11	2	no	—
343	#126	—	11	2	no	—
344	#126	—	11	2	no	—
345	#126	—	11	2	no	—
346	#126	—	11	2	no	—
347	#126	C₂×D₁₁	1	2	yes	—
348	#126	C₂×D₁₁	1	2	yes	—
349	#125	—	11	1	no	—
350	#125	—	11	2	no	—
351	#125	—	11	2	no	—
352	#125	—	11	2	no	—
353	#125	—	11	2	no	—
354	#125	—	11	2	no	—
355	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
356	#125	C₂×D₁₁	1	2	yes	complemented
357	#125	C₂×D₁₁	1	2	yes	complemented
358	#124	—	11	1	no	—
359	#124	—	11	2	no	—
360	#124	—	11	2	no	—
361	#124	—	11	1	no	—
362	#123	—	11	2	no	—
363	#123	—	11	2	no	—
364	#123	—	11	2	no	—
365	#123	—	11	2	no	—
366	#123	—	11	2	no	—
367	#123	—	11	2	no	—
368	#123	—	11	2	no	—
369	C₂²⋊Q₈	—	11	1	no	—
370	C₂²⋊Q₈	—	11	1	no	—
371	C₂²⋊Q₈	—	11	1	no	—
372	C₂²⋊Q₈	—	11	1	no	—
373	C₂²⋊Q₈	—	11	2	no	—
374	C₂²⋊Q₈	—	11	2	no	—
375	C₂²⋊Q₈	—	11	2	no	—
376	C₂²⋊Q₈	—	11	2	no	—
377	C₂²⋊Q₈	—	11	2	no	—
378	C₂²⋊Q₈	—	11	2	no	—
379	C₂²⋊Q₈	—	11	2	no	—
380	C₂²⋊Q₈	—	11	2	no	—
381	C₂²⋊Q₈	—	11	2	no	—
382	C₂²⋊Q₈	—	11	2	no	—
383	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
385	#121	—	11	1	no	—
386	#121	—	11	1	no	—
387	#120	—	11	2	no	—
388	C₄×Q₈	—	11	1	no	—
389	C₄×Q₈	—	11	1	no	—
390	C₄×Q₈	—	11	1	no	—
391	C₄×Q₈	—	11	2	no	—
392	C₄×Q₈	—	11	2	no	—
393	C₄×Q₈	—	11	1	no	—
394	C₄×Q₈	—	11	2	no	—
395	C₄×Q₈	—	11	2	no	—
396	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
397	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
398	C₄×D₄	—	11	1	no	—
399	C₄×D₄	—	11	2	no	—
400	C₄×D₄	—	11	2	no	—
401	C₄×D₄	—	11	2	no	—
402	C₄×D₄	—	11	2	no	—
403	C₄×D₄	—	11	1	no	—
404	C₄×D₄	—	11	2	no	—
405	C₄×D₄	—	11	2	no	—
406	#117	—	11	1	no	—
407	#117	—	11	1	no	—
408	#117	—	11	1	no	—
409	#117	—	11	1	no	—
410	#117	—	11	2	no	—
411	#117	—	11	2	no	—
412	#117	—	11	2	no	—
413	#117	—	11	1	no	—
414	#117	—	11	1	no	—
415	#117	—	11	1	no	—
416	#117	—	11	1	no	—
417	#117	—	11	2	no	—
418	#117	—	11	2	no	—
419	#117	—	11	2	no	—
420	#117	—	11	2	no	—
421	#117	C₂×D₁₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	—	11	1	no	—
423	C₂×C₄⋊C₄	—	11	1	no	—
424	C₂×C₄⋊C₄	—	11	1	no	—
425	C₂×C₄⋊C₄	—	11	2	no	—
426	C₂×C₄⋊C₄	—	11	2	no	—
427	C₂×C₂²⋊C₄	—	11	1	no	—
428	C₂×C₂²⋊C₄	—	11	1	no	—
429	C₂×C₂²⋊C₄	—	11	2	no	—
430	C₂×C₄²	—	11	1	no	—
431	C₂×C₄²	—	11	1	no	—
432	C₂×C₁₁	—	4	1	no	—
433	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
434	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂×C₁₁	#585	1	1	yes	characteristic
436	D₁₁	—	2	2	no	—
437	D₁₁	—	2	2	no	—
438	D₁₁	—	4	2	no	—
439	C₂⁴	—	11	1	no	—
440	#41	—	22	4	no	—
441	C₂×Q₈	—	11	2	no	—
442	C₂×Q₈	—	11	1	no	—
443	C₂×Q₈	—	11	2	no	—
444	C₂×Q₈	—	11	2	no	—
445	C₂×Q₈	—	22	4	no	—
446	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
448	C₂×D₄	—	11	2	no	—
449	C₂×D₄	—	11	2	no	—
450	C₂×D₄	—	11	2	no	—
451	C₂×D₄	—	11	1	no	—
452	C₂²×C₄	—	11	1	no	—
453	C₂²×C₄	—	11	1	no	—
454	C₂²×C₄	—	11	1	no	—
455	C₂²×C₄	—	11	1	no	—
456	C₂²×C₄	—	11	1	no	—
457	C₂²×C₄	—	11	2	no	—
458	C₂²×C₄	—	11	1	no	—
459	C₂²×C₄	—	11	1	no	—
460	C₂²×C₄	—	11	2	no	—
461	C₂²×C₄	—	11	1	no	—
462	C₂²×C₄	—	11	1	no	—
463	C₂²×C₄	—	11	2	no	—
464	C₂²×C₄	—	11	2	no	—
465	C₂²×C₄	—	11	2	no	—
466	C₂²×C₄	—	22	4	no	—
467	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
468	C₄⋊C₄	—	11	1	no	—
469	C₄⋊C₄	—	11	2	no	—
470	C₄⋊C₄	—	11	1	no	—
471	C₄⋊C₄	—	11	1	no	—
472	C₄⋊C₄	—	11	1	no	—
473	C₄⋊C₄	—	11	1	no	—
474	C₄⋊C₄	—	11	1	no	—
475	C₄⋊C₄	—	11	2	no	—
476	C₄⋊C₄	—	11	2	no	—
477	C₄⋊C₄	—	11	1	no	—
478	C₄⋊C₄	—	11	2	no	—
479	C₄⋊C₄	—	11	2	no	—
480	C₄⋊C₄	—	11	1	no	—
481	C₄⋊C₄	—	11	2	no	—
482	C₄⋊C₄	—	11	2	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	2	no	—
488	C₄⋊C₄	—	11	2	no	—
489	C₄⋊C₄	—	11	2	no	—
490	C₄⋊C₄	—	11	2	no	—
491	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
503	C₂²⋊C₄	—	11	1	no	—
504	C₂²⋊C₄	—	11	1	no	—
505	C₂²⋊C₄	—	11	2	no	—
506	C₂²⋊C₄	—	11	1	no	—
507	C₂²⋊C₄	—	11	1	no	—
508	C₂²⋊C₄	—	11	1	no	—
509	C₂²⋊C₄	—	11	1	no	—
510	C₂²⋊C₄	—	11	2	no	—
511	C₂²⋊C₄	—	11	2	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	2	no	—
521	C₂²⋊C₄	—	11	2	no	—
522	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
526	C₄²	—	11	1	no	—
527	C₄²	—	11	1	no	—
528	C₄²	—	11	1	no	—
529	C₄²	—	11	1	no	—
530	C₄²	—	11	1	no	—
531	C₄²	—	11	1	no	—
532	C₄²	—	11	2	no	—
533	C₄²	—	11	2	no	—
534	C₄²	—	11	2	no	—
535	C₄²	—	11	2	no	—
536	C₄²	—	11	2	no	—
537	C₄²	C₂²×D₁₁	1	1	yes	characteristic
538	C₄²	C₂²×D₁₁	1	1	yes	characteristic
539	C₄²	C₂²×D₁₁	1	2	yes	—
540	C₄²	C₂²×D₁₁	1	2	yes	—
541	C₁₁	#3495	1	1	yes	characteristic, complemented, Sylow
542	C₂³	—	11	1	no	—
543	C₂³	—	11	1	no	—
544	C₂³	—	11	2	no	—
545	C₂³	—	22	2	no	—
546	C₂³	—	22	2	no	—
547	C₂³	—	44	1	no	—
548	C₂³	C₂³×D₁₁	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	2	2	no	—
551	Q₈	—	22	4	no	—
552	Q₈	—	22	2	no	—
553	Q₈	—	44	2	no	—
554	Q₈	—	44	2	no	—
555	D₄	—	22	4	no	—
556	D₄	—	22	4	no	—
557	D₄	—	22	2	no	—
558	D₄	—	44	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	11	1	no	—
561	C₂×C₄	—	11	4	no	—
562	C₂×C₄	—	11	1	no	—
563	C₂×C₄	—	11	1	no	—
564	C₂×C₄	—	11	1	no	—
565	C₂×C₄	—	11	2	no	—
566	C₂×C₄	—	11	1	no	—
567	C₂×C₄	—	11	2	no	—
568	C₂×C₄	—	11	1	no	—
569	C₂×C₄	—	11	2	no	—
570	C₂×C₄	—	22	2	no	—
571	C₂×C₄	—	22	4	no	—
572	C₂×C₄	—	22	2	no	—
573	C₂×C₄	—	22	4	no	—
574	C₂×C₄	—	22	2	no	—
575	C₂×C₄	—	22	2	no	—
576	C₂×C₄	—	22	2	no	—
577	C₂×C₄	—	22	2	no	—
578	C₂×C₄	—	44	2	no	—
579	C₂×C₄	—	44	1	no	—
580	C₂×C₄	—	44	2	no	—
581	C₂×C₄	—	44	2	no	—
582	C₂×C₄	—	44	1	no	—
583	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₁	1	2	yes	—
585	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₁	1	2	yes	—
588	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₁	1	2	yes	—
590	C₂×C₄	C₂³×D₁₁	1	2	yes	—
591	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	11	2	no	—
597	C₂²	—	11	2	no	—
598	C₂²	—	22	1	no	—
599	C₂²	—	22	1	no	—
600	C₂²	—	22	1	no	—
601	C₂²	—	22	1	no	—
602	C₂²	—	22	2	no	—
603	C₂²	—	22	2	no	—
604	C₂²	—	22	2	no	—
605	C₂²	—	44	4	no	—
606	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	11	2	no	—
617	C₄	—	22	1	no	—
618	C₄	—	22	2	no	—
619	C₄	—	22	1	no	—
620	C₄	—	22	1	no	—
621	C₄	—	22	1	no	—
622	C₄	—	22	2	no	—
623	C₄	—	22	1	no	—
624	C₄	—	22	2	no	—
625	C₄	#41×D₁₁	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	22	2	no	—
628	C₂	—	22	2	no	—
629	C₂	—	44	2	no	—
630	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
631	C₂	D₁₁×2₋¹⁺⁴	1	1	yes	characteristic
632	C₂	#10623457	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#541	C₂
prime radical	#10623158	C₂
hypercenter	#541	D₁₁
hypocenter	C₁₁	#3495
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. C₁₁×#541	C₂	semidirect
2. #10623259	C₂	semidirect
3. #10623255	C₂	semidirect
4. #10623239	C₂	semidirect
5. #10623236	C₂	semidirect
6. #10623236	C₂	semidirect
7. #10623233	C₂	semidirect
8. #10623225	C₂	semidirect
9. #10623224	C₂	semidirect
10. #10623224	C₂	semidirect
11. #10623222	C₂	semidirect
12. #10623221	C₂	semidirect
13. #10623220	C₂	semidirect
14. #10623174	C₂	semidirect
16. D₁₁×C₂²⋊Q₈	C₂	semidirect
17. #10623156	C₂	semidirect
18. #10623111	C₂	semidirect
19. #10623109	C₂	semidirect
20. #10623105	C₂	semidirect
21. #10623103	C₂	semidirect
22. #10623065	C₂	semidirect
23. D₁₁×#117	C₂	semidirect
27. C₁₁×C₄⋊Q₈	C₂²	semidirect
30. C₁₁×#125	C₂²	semidirect
31. C₁₁×#125	C₂²	semidirect
32. C₁₁×#125	C₂²	semidirect
35. C₄×Q₈×C₁₁	C₂²	semidirect
36. C₄×Q₈×C₁₁	C₂²	semidirect
38. #67000	C₂²	semidirect
41. Q₈×Dic₁₁	C₂²	semidirect
42. Q₈×Dic₁₁	C₂²	semidirect
43. #66997	C₂²	semidirect
47. #66951	C₂²	semidirect
48. #66951	C₂²	semidirect
49. #66951	C₂²	semidirect
50. #66951	C₂²	semidirect
54. #66950	C₂²	semidirect
58. #66949	C₂²	semidirect
59. #66949	C₂²	semidirect
60. #66949	C₂²	semidirect
70. #66946	C₂²	semidirect
76. #66945	C₂²	semidirect
81. C₄⋊C₄×D₁₁	C₂²	semidirect
82. #66943	C₂²	semidirect
83. #66943	C₂²	semidirect
84. #66943	C₂²	semidirect
85. #66942	C₂²	semidirect
86. #66942	C₂²	semidirect
87. #66942	C₂²	semidirect
88. #66941	C₂²	semidirect
89. #66941	C₂²	semidirect
90. #66940	C₂²	semidirect
91. #66940	C₂²	semidirect
92. #66940	C₂²	semidirect
107. #66928	C₂²	semidirect
110. C₄×D₄₄	C₂²	semidirect
115. #66925	C₂²	semidirect
116. #66925	C₂²	semidirect
119. #66922	C₂²	semidirect
120. C₄×Dic₂₂	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
289. #541	D₁₁	semidirect
340. C₄⋊Q₈	C₂×D₁₁	semidirect
355. #125	C₂×D₁₁	semidirect
356. #125	C₂×D₁₁	semidirect
357. #125	C₂×D₁₁	semidirect
396. C₄×Q₈	C₂×D₁₁	semidirect
397. C₄×Q₈	C₂×D₁₁	semidirect
541. C₁₁	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#541	2
#10623259	2
#10623255	2
#10623239	2
#10623236	2
#10623233	2
#10623225	2
#10623224	2
#10623222	2
#10623221	2
#10623220	2
#10623174	2
#10623158	2
D₁₁×C₂²⋊Q₈	2
#10623156	2
#10623111	2
#10623109	2
#10623105	2
#10623103	2
#10623065	2
D₁₁×#117	2
#3495	11