Subgroups — #13082567

Order 1408.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623094	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623092	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623091	C₂	1	2	yes	maximal, complemented
7	#10623090	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623087	C₂	1	2	yes	maximal, complemented
9	#10623085	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623083	C₂	1	2	yes	maximal, complemented
11	#10623079	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623076	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623069	C₂	1	2	yes	maximal, complemented
14	D₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#4341	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623065	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623064	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623063	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623059	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623026	C₂	1	2	yes	maximal, complemented
21	#10623025	C₂	1	2	yes	maximal, complemented
22	C₂×#66938	C₂	1	2	yes	maximal, complemented
23	#10623021	C₂	1	2	yes	maximal, complemented
24	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₁	C₂²	1	2	yes	—
26	C₂×#4341	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
28	C₂×#4339	C₂²	1	2	yes	complemented
29	C₂²×Dic₂₂	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
37	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	#67006	C₂²	1	2	yes	—
41	#67006	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
43	#66993	C₂²	1	1	yes	characteristic
44	#66992	C₂²	1	2	yes	—
45	#66992	C₂²	1	2	yes	complemented
46	#66991	C₂²	1	1	yes	characteristic
47	#66991	C₂²	1	1	yes	characteristic, complemented
48	#66990	C₂²	1	2	yes	—
49	#66989	C₂²	1	1	yes	characteristic, complemented
50	#66988	C₂²	1	2	yes	complemented
51	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
52	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
53	#66983	C₂²	1	1	yes	characteristic
54	#66983	C₂²	1	2	yes	complemented
55	#66983	C₂²	1	2	yes	complemented
56	#66982	C₂²	1	2	yes	complemented
57	#66982	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	complemented
65	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	complemented
66	#66979	C₂²	1	2	yes	complemented
67	#66977	C₂²	1	2	yes	complemented
68	#66977	C₂²	1	2	yes	complemented
69	#66977	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×Dic₁₁	C₂²	1	2	yes	complemented
71	#66951	C₂²	1	1	yes	characteristic, complemented
72	#66951	C₂²	1	2	yes	complemented
73	#66950	C₂²	1	1	yes	characteristic, complemented
74	#66949	C₂²	1	1	yes	characteristic, complemented
75	#66949	C₂²	1	2	yes	complemented
76	#66948	C₂²	1	1	yes	characteristic, complemented
77	#66947	C₂²	1	1	yes	characteristic, complemented
78	#66946	C₂²	1	1	yes	characteristic, complemented
79	#66945	C₂²	1	1	yes	characteristic, complemented
80	#66945	C₂²	1	1	yes	characteristic, complemented
81	#66942	C₂²	1	1	yes	characteristic, complemented
82	#66941	C₂²	1	1	yes	characteristic, complemented
83	#66941	C₂²	1	1	yes	characteristic, complemented
84	#66940	C₂²	1	1	yes	characteristic, complemented
85	#66939	C₂²	1	2	yes	complemented
86	#66938	C₂²	1	2	yes	—
87	#66938	C₂²	1	1	yes	characteristic
88	#66938	C₂²	1	2	yes	complemented
89	#66938	C₂²	1	2	yes	complemented
90	#66938	C₂²	1	2	yes	complemented
91	#66938	C₂²	1	2	yes	complemented
92	#66938	C₂²	1	2	yes	complemented
93	#66938	C₂²	1	2	yes	complemented
94	#66938	C₂²	1	2	yes	complemented
95	#66937	C₂²	1	1	yes	characteristic
96	#66937	C₂²	1	2	yes	complemented
97	#66937	C₂²	1	2	yes	complemented
98	#66936	C₂²	1	2	yes	complemented
99	#66936	C₂²	1	1	yes	characteristic, complemented
100	#66936	C₂²	1	2	yes	complemented
101	#66935	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
104	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
105	#66932	C₂²	1	2	yes	complemented
106	#66932	C₂²	1	2	yes	complemented
107	#66932	C₂²	1	1	yes	characteristic, complemented
108	#66931	C₂²	1	2	yes	complemented
109	#66931	C₂²	1	2	yes	complemented
110	#66930	C₂²	1	2	yes	complemented
111	#66929	C₂²	1	2	yes	complemented
112	#66928	C₂²	1	2	yes	complemented
113	#66928	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
116	#66925	C₂²	1	1	yes	characteristic, complemented
117	#66925	C₂²	1	2	yes	complemented
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
119	#66922	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	2	yes	complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₁	C₂³	1	2	yes	—
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁	—	2	4	no	—
126	C₂×D₄×C₁₁	C₂³	1	2	yes	—
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁	—	4	4	no	—
135	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
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	C₂²×Dic₁₁	C₂³	1	2	yes	—
145	C₂²×Dic₁₁	C₂³	1	2	yes	—
146	C₂²×Dic₁₁	C₂³	1	2	yes	—
147	#4341	—	2	4	no	—
148	D₄×D₁₁	—	2	4	no	—
149	#4339	—	4	4	no	—
150	C₂×D₄₄	C₂³	1	1	yes	characteristic
151	C₂×D₄₄	C₂³	1	1	yes	characteristic
152	C₂×D₄₄	C₂³	1	2	yes	—
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	2	yes	—
158	C₂×C₄×D₁₁	C₂³	1	2	yes	—
159	C₂×Dic₂₂	—	4	4	no	—
160	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
161	C₂×Dic₂₂	C₂³	1	2	yes	—
162	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₂	C₂³	1	2	yes	—
164	C₂×Dic₂₂	C₂³	1	2	yes	—
165	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₄²×C₁₁	C₂³	1	1	yes	characteristic
177	C₄²×C₁₁	C₂³	1	1	yes	characteristic
178	C₄²×C₁₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
201	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
209	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	Dic₁₁⋊C₄	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	2	yes	—
223	C₄×Dic₁₁	C₂³	1	2	yes	—
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	#3514	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	—	2	4	no	—
230	C₂³×C₁₁	—	4	2	no	—
231	C₂³×C₁₁	—	4	2	no	—
232	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₁	C₂⁴	1	2	yes	—
234	C₂³×C₁₁	C₂⁴	1	2	yes	—
235	C₂²×D₁₁	—	2	4	no	—
236	C₂²×D₁₁	—	4	2	no	—
237	C₂²×D₁₁	—	4	2	no	—
238	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₁	C₂⁴	1	2	yes	—
240	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₁	—	2	4	no	—
242	D₄×C₁₁	—	2	2	no	—
243	D₄×C₁₁	#41	1	4	yes	complemented
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	—	4	2	no	—
247	C₂×C₄×C₁₁	—	4	2	no	—
248	C₂×C₄×C₁₁	—	4	2	no	—
249	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₁	—	2	4	no	—
258	C₂²⋊D₁₁	—	2	4	no	—
259	C₂²⋊D₁₁	—	2	4	no	—
260	C₂²⋊D₁₁	—	2	2	no	—
261	C₂²⋊D₁₁	—	4	2	no	—
262	C₂²⋊D₁₁	—	4	2	no	—
263	C₂²⋊D₁₁	—	4	2	no	—
264	C₂²⋊D₁₁	—	4	1	no	—
265	C₂²⋊D₁₁	—	4	2	no	—
266	C₂×Dic₁₁	—	2	4	no	—
267	C₂×Dic₁₁	—	2	4	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	2	yes	—
274	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
278	D₄₄	—	2	2	no	—
279	D₄₄	—	4	1	no	—
280	D₄₄	—	4	2	no	—
281	C₄×D₁₁	—	2	2	no	—
282	C₄×D₁₁	—	2	2	no	—
283	C₄×D₁₁	—	2	2	no	—
284	C₄×D₁₁	—	4	2	no	—
285	C₄×D₁₁	—	4	1	no	—
286	C₄×D₁₁	—	4	2	no	—
287	Dic₂₂	—	2	2	no	—
288	Dic₂₂	—	2	2	no	—
289	Dic₂₂	—	2	4	no	—
290	Dic₂₂	—	4	2	no	—
291	Dic₂₂	—	4	2	no	—
292	#559	—	11	1	no	—
293	#556	—	11	1	no	—
294	#555	—	11	1	no	—
295	#555	—	11	1	no	—
296	#551	—	11	2	no	—
297	#551	—	11	2	no	—
298	D₄×Q₈	—	11	1	no	—
299	#548	—	11	2	no	—
300	#546	—	11	1	no	—
301	#546	—	11	1	no	—
302	#546	—	11	2	no	—
303	D₄²	—	11	1	no	—
304	#542	—	11	1	no	—
305	#542	—	11	1	no	—
306	#538	—	11	2	no	—
307	#538	—	11	2	no	—
308	#532	—	11	1	no	—
309	#529	—	11	2	no	—
310	#529	—	11	1	no	—
311	C₂×#124	—	11	2	no	—
312	#518	—	11	1	no	—
313	#518	D₁₁	1	1	yes	characteristic, complemented
314	C₄×#41	—	11	1	no	—
315	C₂²×C₁₁	—	2	2	no	—
316	C₂²×C₁₁	—	2	2	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	2	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	1	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	2	1	no	—
323	C₂²×C₁₁	—	8	4	no	—
324	C₂²×C₁₁	C₂×#41	1	4	yes	—
325	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
326	C₂×D₁₁	—	2	1	no	—
327	C₂×D₁₁	—	2	2	no	—
328	C₂×D₁₁	—	2	1	no	—
329	C₂×D₁₁	—	2	1	no	—
330	C₂×D₁₁	—	2	2	no	—
331	C₂×D₁₁	—	2	1	no	—
332	C₂×D₁₁	—	2	1	no	—
333	C₂×D₁₁	—	2	2	no	—
334	C₂×D₁₁	—	2	1	no	—
335	C₂×D₁₁	—	8	4	no	—
336	C₄×C₁₁	—	2	1	no	—
337	C₄×C₁₁	—	2	1	no	—
338	C₄×C₁₁	—	2	2	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	1	no	—
341	C₄×C₁₁	—	2	2	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	C₂×#41	1	2	yes	—
344	Dic₁₁	—	2	2	no	—
345	Dic₁₁	—	2	1	no	—
346	Dic₁₁	—	2	1	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	2	no	—
349	Dic₁₁	—	2	2	no	—
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
353	C₂×#41	—	11	1	no	—
354	C₂×#41	—	11	2	no	—
355	C₂²×Q₈	—	11	2	no	—
356	C₂²×D₄	—	11	2	no	—
357	C₂²×D₄	—	11	1	no	—
358	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
359	C₄⋊Q₈	—	11	1	no	—
360	C₄⋊Q₈	—	11	1	no	—
361	C₄⋊Q₈	—	11	1	no	—
362	#127	—	11	1	no	—
363	#126	—	11	2	no	—
364	#126	—	11	1	no	—
365	#126	—	11	2	no	—
366	#126	—	11	1	no	—
367	#126	—	11	2	no	—
368	#126	—	11	2	no	—
369	#125	—	11	1	no	—
370	#124	—	11	1	no	—
371	#124	—	11	1	no	—
372	#124	—	11	2	no	—
373	#124	—	11	2	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	2	no	—
378	#124	—	11	2	no	—
379	#124	—	11	2	no	—
380	#124	—	11	2	no	—
381	#124	—	11	1	no	—
382	#123	—	11	2	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	1	no	—
386	#123	—	11	1	no	—
387	#123	—	11	2	no	—
388	#123	—	11	2	no	—
389	#123	—	11	2	no	—
390	C₂²⋊Q₈	—	11	2	no	—
391	C₂²⋊Q₈	—	11	1	no	—
392	C₂²⋊Q₈	—	11	2	no	—
393	C₂²⋊Q₈	—	11	1	no	—
394	C₂²⋊Q₈	—	11	1	no	—
395	C₂²⋊Q₈	—	11	2	no	—
396	C₂²⋊Q₈	—	11	2	no	—
397	C₂²⋊Q₈	—	11	2	no	—
398	#121	—	11	2	no	—
399	#121	—	11	1	no	—
400	#121	—	11	2	no	—
401	#121	—	11	1	no	—
402	#121	—	11	2	no	—
403	#121	—	11	2	no	—
404	#121	—	11	1	no	—
405	#121	—	11	1	no	—
406	#121	—	11	1	no	—
407	#121	—	11	2	no	—
408	#121	—	11	2	no	—
409	#120	—	11	2	no	—
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×Q₈	—	11	2	no	—
416	C₄×Q₈	—	11	1	no	—
417	C₄×D₄	—	11	1	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	1	no	—
422	C₄×D₄	—	11	1	no	—
423	C₄×D₄	—	11	2	no	—
424	C₄×D₄	—	11	2	no	—
425	C₄×D₄	—	11	1	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	2	no	—
428	C₄×D₄	—	11	1	no	—
429	C₄×D₄	—	11	1	no	—
430	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
431	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
432	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
433	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
434	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
435	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
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	2	no	—
442	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
443	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
444	C₂×C₂²⋊C₄	—	11	2	no	—
445	C₂×C₂²⋊C₄	—	11	2	no	—
446	C₂×C₂²⋊C₄	—	11	2	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	complemented
449	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	complemented
450	C₂×C₄²	—	11	2	no	—
451	C₂×C₄²	—	11	1	no	—
452	C₂×C₁₁	—	2	4	no	—
453	C₂×C₁₁	—	4	2	no	—
454	C₂×C₁₁	—	4	1	no	—
455	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
456	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₁₁	#585	1	1	yes	characteristic
458	D₁₁	—	4	1	no	—
459	D₁₁	—	4	2	no	—
460	D₁₁	—	4	1	no	—
461	C₂⁴	—	11	2	no	—
462	C₂⁴	C₂²×D₁₁	1	2	yes	—
463	#41	—	22	4	no	—
464	#41	—	44	4	no	—
465	C₂×Q₈	—	11	1	no	—
466	C₂×Q₈	—	11	1	no	—
467	C₂×Q₈	—	11	2	no	—
468	C₂×Q₈	—	11	2	no	—
469	C₂×Q₈	—	11	2	no	—
470	C₂×Q₈	—	44	4	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	11	2	no	—
473	C₂×D₄	—	11	2	no	—
474	C₂×D₄	—	11	1	no	—
475	C₂×D₄	—	11	2	no	—
476	C₂×D₄	—	11	1	no	—
477	C₂×D₄	—	11	2	no	—
478	C₂×D₄	—	11	2	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	11	1	no	—
482	C₂×D₄	—	11	1	no	—
483	C₂×D₄	—	11	2	no	—
484	C₂×D₄	—	22	4	no	—
485	C₂×D₄	—	44	4	no	—
486	C₂×D₄	C₂²×D₁₁	1	2	yes	—
487	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	11	2	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	1	no	—
493	C₂²×C₄	—	11	1	no	—
494	C₂²×C₄	—	11	1	no	—
495	C₂²×C₄	—	11	1	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	2	no	—
498	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
503	C₄⋊C₄	—	11	1	no	—
504	C₄⋊C₄	—	11	1	no	—
505	C₄⋊C₄	—	11	1	no	—
506	C₄⋊C₄	—	11	1	no	—
507	C₄⋊C₄	—	11	1	no	—
508	C₄⋊C₄	—	11	1	no	—
509	C₄⋊C₄	—	11	2	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	2	no	—
512	C₄⋊C₄	—	11	2	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	1	no	—
520	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
524	C₂²⋊C₄	—	11	1	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	—	11	2	no	—
527	C₂²⋊C₄	—	11	2	no	—
528	C₂²⋊C₄	—	11	2	no	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	—	11	2	no	—
531	C₂²⋊C₄	—	11	1	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	1	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	1	no	—
536	C₂²⋊C₄	—	11	1	no	—
537	C₂²⋊C₄	—	11	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	2	no	—
541	C₂²⋊C₄	—	11	2	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	2	no	—
544	C₂²⋊C₄	—	11	1	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	1	no	—
547	C₂²⋊C₄	—	11	1	no	—
548	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
555	C₄²	—	11	1	no	—
556	C₄²	—	11	2	no	—
557	C₄²	—	11	1	no	—
558	C₄²	—	11	2	no	—
559	C₄²	—	11	1	no	—
560	C₄²	—	11	2	no	—
561	C₄²	—	11	2	no	—
562	C₄²	—	11	1	no	—
563	C₄²	C₂²×D₁₁	1	1	yes	characteristic
564	C₄²	C₂²×D₁₁	1	2	yes	—
565	C₄²	C₂²×D₁₁	1	1	yes	characteristic
566	C₁₁	#3514	1	1	yes	characteristic, complemented, Sylow
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	11	1	no	—
571	C₂³	—	11	2	no	—
572	C₂³	—	11	1	no	—
573	C₂³	—	22	4	no	—
574	C₂³	—	44	2	no	—
575	C₂³	—	44	2	no	—
576	C₂³	C₂³×D₁₁	1	1	yes	characteristic
577	C₂³	C₂³×D₁₁	1	2	yes	—
578	C₂³	C₂³×D₁₁	1	2	yes	—
579	Q₈	—	22	2	no	—
580	Q₈	—	22	4	no	—
581	Q₈	—	22	2	no	—
582	Q₈	—	44	2	no	—
583	Q₈	—	44	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	22	2	no	—
587	D₄	—	22	4	no	—
588	D₄	—	22	4	no	—
589	D₄	—	22	4	no	—
590	D₄	—	22	2	no	—
591	D₄	—	44	2	no	—
592	D₄	—	44	1	no	—
593	D₄	—	44	2	no	—
594	D₄	—	44	2	no	—
595	D₄	—	44	2	no	—
596	D₄	—	44	1	no	—
597	D₄	—	44	2	no	—
598	D₄	#4339	1	4	yes	complemented
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	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	2	no	—
610	C₂×C₄	—	11	1	no	—
611	C₂×C₄	—	11	1	no	—
612	C₂×C₄	—	11	2	no	—
613	C₂×C₄	—	22	2	no	—
614	C₂×C₄	—	22	4	no	—
615	C₂×C₄	—	22	4	no	—
616	C₂×C₄	—	22	2	no	—
617	C₂×C₄	—	22	2	no	—
618	C₂×C₄	—	44	2	no	—
619	C₂×C₄	—	44	2	no	—
620	C₂×C₄	—	44	1	no	—
621	C₂×C₄	—	44	2	no	—
622	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₁	1	2	yes	—
624	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₁	1	2	yes	—
629	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	22	1	no	—
640	C₂²	—	22	1	no	—
641	C₂²	—	22	2	no	—
642	C₂²	—	22	1	no	—
643	C₂²	—	22	2	no	—
644	C₂²	—	22	1	no	—
645	C₂²	—	22	1	no	—
646	C₂²	—	22	2	no	—
647	C₂²	—	22	1	no	—
648	C₂²	—	88	4	no	—
649	C₂²	C₂×#4339	1	4	yes	—
650	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	11	2	no	—
659	C₄	—	22	1	no	—
660	C₄	—	22	1	no	—
661	C₄	—	22	2	no	—
662	C₄	—	22	2	no	—
663	C₄	—	22	2	no	—
664	C₄	—	22	1	no	—
665	C₄	—	22	1	no	—
666	C₄	—	22	1	no	—
667	C₄	C₂×#4339	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	44	1	no	—
672	C₂	—	44	2	no	—
673	C₂	—	44	1	no	—
674	C₂	C₂²×#4339	1	1	yes	characteristic
675	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#518	C₂
hypercenter	#518	D₁₁
hypocenter	C₁₁	#3514
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. C₁₁×#518	C₂	semidirect
2. #10623337	C₂	semidirect
3. D₄×C₂²⋊D₁₁	C₂	semidirect
4. #10623094	C₂	semidirect
5. #10623092	C₂	semidirect
6. #10623091	C₂	semidirect
7. #10623090	C₂	semidirect
8. #10623087	C₂	semidirect
9. #10623085	C₂	semidirect
10. #10623083	C₂	semidirect
11. #10623079	C₂	semidirect
12. #10623076	C₂	semidirect
13. #10623069	C₂	semidirect
14. D₄×Dic₂₂	C₂	semidirect
15. C₄×#4341	C₂	semidirect
16. #10623065	C₂	semidirect
17. #10623064	C₂	semidirect
18. #10623063	C₂	semidirect
19. #10623059	C₂	semidirect
20. #10623026	C₂	semidirect
21. #10623025	C₂	semidirect
22. C₂×#66938	C₂	semidirect
23. #10623021	C₂	semidirect
28. C₂×#4339	C₂²	semidirect
29. C₂²×Dic₂₂	C₂²	semidirect
32. C₄×D₄×C₁₁	C₂²	semidirect
33. C₄×D₄×C₁₁	C₂²	semidirect
34. C₄×D₄×C₁₁	C₂²	semidirect
35. C₄×D₄×C₁₁	C₂²	semidirect
36. C₁₁×#117	C₂²	semidirect
37. C₁₁×#117	C₂²	semidirect
38. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₁₁×C₂²⋊C₄	C₂²	semidirect
41. #67006	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
45. #66992	C₂²	semidirect
47. #66991	C₂²	semidirect
49. #66989	C₂²	semidirect
50. #66988	C₂²	semidirect
54. #66983	C₂²	semidirect
55. #66983	C₂²	semidirect
56. #66982	C₂²	semidirect
57. #66982	C₂²	semidirect
59. C₄×C₂²⋊D₁₁	C₂²	semidirect
60. C₄×C₂²⋊D₁₁	C₂²	semidirect
61. C₄×C₂²⋊D₁₁	C₂²	semidirect
62. C₄×C₂²⋊D₁₁	C₂²	semidirect
63. C₄×C₂²⋊D₁₁	C₂²	semidirect
64. C₂×(C₂×D₁₁)⋊C₄	C₂²	semidirect
65. C₂×(C₂×D₁₁)⋊C₄	C₂²	semidirect
66. #66979	C₂²	semidirect
67. #66977	C₂²	semidirect
68. #66977	C₂²	semidirect
69. #66977	C₂²	semidirect
70. C₂×C₄×Dic₁₁	C₂²	semidirect
71. #66951	C₂²	semidirect
72. #66951	C₂²	semidirect
73. #66950	C₂²	semidirect
74. #66949	C₂²	semidirect
75. #66949	C₂²	semidirect
76. #66948	C₂²	semidirect
77. #66947	C₂²	semidirect
78. #66946	C₂²	semidirect
79. #66945	C₂²	semidirect
80. #66945	C₂²	semidirect
81. #66942	C₂²	semidirect
82. #66941	C₂²	semidirect
83. #66941	C₂²	semidirect
84. #66940	C₂²	semidirect
85. #66939	C₂²	semidirect
88. #66938	C₂²	semidirect
89. #66938	C₂²	semidirect
90. #66938	C₂²	semidirect
91. #66938	C₂²	semidirect
92. #66938	C₂²	semidirect
93. #66938	C₂²	semidirect
94. #66938	C₂²	semidirect
96. #66937	C₂²	semidirect
97. #66937	C₂²	semidirect
98. #66936	C₂²	semidirect
99. #66936	C₂²	semidirect
100. #66936	C₂²	semidirect
101. #66935	C₂²	semidirect
102. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
104. C₂²⋊C₄×D₁₁	C₂²	semidirect
105. #66932	C₂²	semidirect
106. #66932	C₂²	semidirect
107. #66932	C₂²	semidirect
108. #66931	C₂²	semidirect
109. #66931	C₂²	semidirect
110. #66930	C₂²	semidirect
111. #66929	C₂²	semidirect
112. #66928	C₂²	semidirect
113. #66928	C₂²	semidirect
114. C₄×D₄₄	C₂²	semidirect
115. C₄×D₄₄	C₂²	semidirect
116. #66925	C₂²	semidirect
117. #66925	C₂²	semidirect
118. C₄²×D₁₁	C₂²	semidirect
119. #66922	C₂²	semidirect
120. C₄×Dic₂₂	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
243. D₄×C₁₁	#41	semidirect
313. #518	D₁₁	semidirect
432. C₄×D₄	C₂×D₁₁	semidirect
433. C₄×D₄	C₂×D₁₁	semidirect
434. C₄×D₄	C₂×D₁₁	semidirect
435. C₄×D₄	C₂×D₁₁	semidirect
442. #117	C₂×D₁₁	semidirect
443. #117	C₂×D₁₁	semidirect
448. C₂×C₂²⋊C₄	C₂×D₁₁	semidirect
449. C₂×C₂²⋊C₄	C₂×D₁₁	semidirect
566. C₁₁	#3514	semidirect
598. D₄	#4339	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#518	2
#10623337	2
D₄×C₂²⋊D₁₁	2
#10623094	2
#10623092	2
#10623091	2
#10623090	2
#10623087	2
#10623085	2
#10623083	2
#10623079	2
#10623076	2
#10623069	2
D₄×Dic₂₂	2
C₄×#4341	2
#10623065	2
#10623064	2
#10623063	2
#10623059	2
#10623026	2
#10623025	2
C₂×#66938	2
#10623021	2
#3514	11