Subgroups — #13082347

Order 1408.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623241	C₂	1	2	yes	maximal, complemented
3	#10623236	C₂	1	2	yes	maximal, complemented
4	#10623226	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623220	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623194	C₂	1	2	yes	maximal, complemented
7	#10623189	C₂	1	2	yes	maximal, complemented
8	#10623149	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623142	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623141	C₂	1	2	yes	maximal, complemented
11	#10623138	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623127	C₂	1	2	yes	maximal, complemented
14	#10623094	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623086	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623085	C₂	1	2	yes	maximal, complemented
17	#10623078	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623076	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623069	C₂	1	2	yes	maximal, complemented
20	#10623063	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623054	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623045	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#66945	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4341	C₂²	1	2	yes	complemented
25	C₂×#4341	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₁	C₂²	1	2	yes	—
28	C₂×#4339	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#126	C₂²	1	2	yes	complemented
31	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#123	C₂²	1	2	yes	complemented
33	C₁₁×#121	C₂²	1	1	yes	characteristic
34	C₁₁×#121	C₂²	1	2	yes	complemented
35	C₁₁×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#66993	C₂²	1	2	yes	complemented
42	#66992	C₂²	1	2	yes	—
43	#66992	C₂²	1	1	yes	characteristic, complemented
44	#66992	C₂²	1	2	yes	complemented
45	#66991	C₂²	1	1	yes	characteristic
46	#66991	C₂²	1	1	yes	characteristic, complemented
47	#66990	C₂²	1	1	yes	characteristic
48	#66990	C₂²	1	2	yes	—
49	#66988	C₂²	1	2	yes	complemented
50	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
51	D₄×Dic₁₁	C₂²	1	2	yes	complemented
52	#66983	C₂²	1	1	yes	characteristic
53	#66983	C₂²	1	2	yes	complemented
54	#66983	C₂²	1	1	yes	characteristic, complemented
55	#66983	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
60	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
61	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
62	#66979	C₂²	1	2	yes	complemented
63	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Dic₁₁	C₂²	1	2	yes	complemented
66	#66951	C₂²	1	2	yes	complemented
67	#66951	C₂²	1	2	yes	complemented
68	#66950	C₂²	1	2	yes	—
69	#66950	C₂²	1	2	yes	complemented
70	#66949	C₂²	1	2	yes	—
71	#66949	C₂²	1	1	yes	characteristic, complemented
72	#66948	C₂²	1	1	yes	characteristic
73	#66948	C₂²	1	1	yes	characteristic, complemented
74	#66948	C₂²	1	2	yes	complemented
75	#66947	C₂²	1	1	yes	characteristic
76	#66947	C₂²	1	2	yes	complemented
77	#66947	C₂²	1	2	yes	complemented
78	#66946	C₂²	1	2	yes	complemented
79	#66946	C₂²	1	1	yes	characteristic, complemented
80	#66945	C₂²	1	2	yes	—
81	#66945	C₂²	1	1	yes	characteristic
82	#66945	C₂²	1	1	yes	characteristic
83	#66945	C₂²	1	2	yes	complemented
84	#66945	C₂²	1	1	yes	characteristic, complemented
85	#66945	C₂²	1	1	yes	characteristic, complemented
86	#66945	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
88	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
89	#66943	C₂²	1	1	yes	characteristic, complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66941	C₂²	1	2	yes	complemented
92	#66941	C₂²	1	1	yes	characteristic, complemented
93	#66939	C₂²	1	2	yes	complemented
94	#66939	C₂²	1	2	yes	complemented
95	#66939	C₂²	1	2	yes	complemented
96	#66938	C₂²	1	2	yes	complemented
97	#66938	C₂²	1	2	yes	complemented
98	#66938	C₂²	1	2	yes	complemented
99	#66938	C₂²	1	2	yes	complemented
100	#66937	C₂²	1	2	yes	—
101	#66937	C₂²	1	2	yes	complemented
102	#66937	C₂²	1	1	yes	characteristic, complemented
103	#66936	C₂²	1	1	yes	characteristic
104	#66936	C₂²	1	2	yes	complemented
105	#66935	C₂²	1	2	yes	—
106	#66935	C₂²	1	1	yes	characteristic
107	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
108	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
109	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
112	#66932	C₂²	1	2	yes	complemented
113	#66931	C₂²	1	2	yes	complemented
114	#66931	C₂²	1	1	yes	characteristic, complemented
115	#66928	C₂²	1	2	yes	complemented
116	C₄×D₄₄	C₂²	1	2	yes	—
117	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
119	#66925	C₂²	1	1	yes	characteristic
120	#66925	C₂²	1	2	yes	complemented
121	#66922	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	2	yes	complemented
123	C₂³×D₁₁	C₂³	1	1	yes	characteristic
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁	C₂³	1	2	yes	—
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
142	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₁	C₂³	1	2	yes	—
145	C₂²×Dic₁₁	C₂³	1	2	yes	—
146	#4341	—	4	4	no	—
147	#4341	—	4	4	no	—
148	D₄×D₁₁	—	2	4	no	—
149	D₄×D₁₁	—	4	4	no	—
150	#4339	—	2	4	no	—
151	C₂×D₄₄	C₂³	1	1	yes	characteristic
152	C₂×D₄₄	C₂³	1	1	yes	characteristic
153	C₂×D₄₄	C₂³	1	1	yes	characteristic
154	C₂×D₄₄	C₂³	1	2	yes	—
155	C₂×D₄₄	C₂³	1	2	yes	—
156	C₂×C₄×D₁₁	—	2	4	no	—
157	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₁	C₂³	1	2	yes	—
162	C₂×C₄×D₁₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₁	C₂³	1	2	yes	—
164	C₂×C₄×D₁₁	C₂³	1	2	yes	—
165	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₂	C₂³	1	2	yes	—
168	C₂×Dic₂₂	C₂³	1	2	yes	—
169	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₄²×C₁₁	C₂³	1	2	yes	—
183	C₄²×C₁₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	2	yes	—
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
206	C₄⋊Dic₁₁	C₂³	1	2	yes	—
207	C₄⋊Dic₁₁	C₂³	1	2	yes	—
208	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₁	C₂³	1	2	yes	—
213	C₄⋊Dic₁₁	C₂³	1	2	yes	—
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₁₁⋊C₄	C₂³	1	2	yes	—
222	C₄×Dic₁₁	C₂³	1	2	yes	—
223	C₄×Dic₁₁	C₂³	1	2	yes	—
224	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₁	C₂³	1	2	yes	—
226	C₄×Dic₁₁	C₂³	1	2	yes	—
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	#3494	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	2	yes	—
230	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	—	2	2	no	—
233	C₂²×D₁₁	—	2	2	no	—
234	C₂²×D₁₁	—	2	4	no	—
235	C₂²×D₁₁	—	4	1	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	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
242	D₄×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	2	no	—
244	D₄×C₁₁	—	2	2	no	—
245	D₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	2	2	no	—
248	C₂×C₄×C₁₁	—	4	2	no	—
249	C₂×C₄×C₁₁	—	4	2	no	—
250	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₁	—	2	4	no	—
259	C₂²⋊D₁₁	—	2	2	no	—
260	C₂²⋊D₁₁	—	2	2	no	—
261	C₂²⋊D₁₁	—	2	2	no	—
262	C₂²⋊D₁₁	—	2	4	no	—
263	C₂²⋊D₁₁	—	4	2	no	—
264	C₂²⋊D₁₁	—	4	2	no	—
265	C₂²⋊D₁₁	—	4	2	no	—
266	C₂²⋊D₁₁	—	4	1	no	—
267	C₂×Dic₁₁	—	2	4	no	—
268	C₂×Dic₁₁	—	2	2	no	—
269	C₂×Dic₁₁	—	4	2	no	—
270	C₂×Dic₁₁	—	4	2	no	—
271	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁	C₂⁴	1	2	yes	—
274	C₂×Dic₁₁	C₂⁴	1	2	yes	—
275	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₁	C₂⁴	1	2	yes	—
277	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
279	D₄₄	—	2	2	no	—
280	D₄₄	—	2	2	no	—
281	D₄₄	—	4	1	no	—
282	D₄₄	—	4	2	no	—
283	D₄₄	—	4	2	no	—
284	C₄×D₁₁	—	2	2	no	—
285	C₄×D₁₁	—	2	2	no	—
286	C₄×D₁₁	—	2	2	no	—
287	C₄×D₁₁	—	2	2	no	—
288	C₄×D₁₁	—	4	2	no	—
289	C₄×D₁₁	—	4	2	no	—
290	C₄×D₁₁	—	4	2	no	—
291	C₄×D₁₁	—	4	2	no	—
292	C₄×D₁₁	#41	1	4	yes	complemented
293	Dic₂₂	—	2	2	no	—
294	Dic₂₂	—	4	2	no	—
295	Dic₂₂	—	4	2	no	—
296	#555	—	11	1	no	—
297	#555	—	11	1	no	—
298	#553	—	11	1	no	—
299	#553	—	11	1	no	—
300	#553	—	11	1	no	—
301	#553	D₁₁	1	1	yes	characteristic, complemented
302	#551	—	11	2	no	—
303	#551	—	11	2	no	—
304	#547	—	11	1	no	—
305	#547	—	11	1	no	—
306	#546	—	11	2	no	—
307	#546	—	11	2	no	—
308	#544	—	11	1	no	—
309	#542	—	11	2	no	—
310	#540	—	11	2	no	—
311	#535	—	11	1	no	—
312	#532	—	11	2	no	—
313	#529	—	11	2	no	—
314	#525	—	11	1	no	—
315	C₂×#121	—	11	1	no	—
316	#520	—	11	1	no	—
317	#518	—	11	1	no	—
318	C₂×#117	—	11	1	no	—
319	C₂²×C₁₁	—	2	1	no	—
320	C₂²×C₁₁	—	2	1	no	—
321	C₂²×C₁₁	—	2	1	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	1	no	—
325	C₂²×C₁₁	—	2	2	no	—
326	C₂²×C₁₁	—	2	1	no	—
327	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
328	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
329	C₂×D₁₁	—	2	1	no	—
330	C₂×D₁₁	—	2	1	no	—
331	C₂×D₁₁	—	2	1	no	—
332	C₂×D₁₁	—	2	2	no	—
333	C₂×D₁₁	—	2	1	no	—
334	C₂×D₁₁	—	2	1	no	—
335	C₂×D₁₁	—	2	2	no	—
336	C₂×D₁₁	—	2	1	no	—
337	C₂×D₁₁	—	2	2	no	—
338	C₂×D₁₁	—	2	1	no	—
339	C₂×D₁₁	—	2	1	no	—
340	C₂×D₁₁	—	4	4	no	—
341	C₂×D₁₁	—	8	4	no	—
342	C₂×D₁₁	C₂×#41	1	2	yes	—
343	C₄×C₁₁	—	2	1	no	—
344	C₄×C₁₁	—	2	1	no	—
345	C₄×C₁₁	—	2	1	no	—
346	C₄×C₁₁	—	2	2	no	—
347	C₄×C₁₁	—	2	2	no	—
348	C₄×C₁₁	—	2	1	no	—
349	C₄×C₁₁	—	2	2	no	—
350	C₄×C₁₁	C₂×#41	1	2	yes	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	1	no	—
353	Dic₁₁	—	2	2	no	—
354	Dic₁₁	—	2	1	no	—
355	Dic₁₁	—	2	2	no	—
356	Dic₁₁	—	2	2	no	—
357	Dic₁₁	—	2	1	no	—
358	Dic₁₁	C₂×#41	1	2	yes	—
359	C₂×#41	—	11	2	no	—
360	C₂×#41	—	11	2	no	—
361	C₂×#41	—	11	1	no	—
362	C₂²×D₄	—	11	1	no	—
363	C₂²×D₄	—	11	2	no	—
364	C₂³×C₄	—	11	1	no	—
365	C₄⋊Q₈	—	11	2	no	—
366	C₄⋊Q₈	—	11	1	no	—
367	C₄⋊Q₈	—	11	1	no	—
368	#127	—	11	2	no	—
369	#126	—	11	2	no	—
370	#126	—	11	2	no	—
371	#126	—	11	2	no	—
372	#126	C₂×D₁₁	1	2	yes	complemented
373	#125	—	11	2	no	—
374	#125	—	11	1	no	—
375	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
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	#123	—	11	2	no	—
382	#123	—	11	1	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	1	no	—
386	#123	—	11	2	no	—
387	#123	—	11	2	no	—
388	#123	—	11	2	no	—
389	#123	—	11	2	no	—
390	#123	C₂×D₁₁	1	2	yes	complemented
391	C₂²⋊Q₈	—	11	1	no	—
392	C₂²⋊Q₈	—	11	2	no	—
393	C₂²⋊Q₈	—	11	2	no	—
394	C₂²⋊Q₈	—	11	2	no	—
395	C₂²⋊Q₈	—	11	1	no	—
396	C₂²⋊Q₈	—	11	2	no	—
397	#121	—	11	2	no	—
398	#121	—	11	1	no	—
399	#121	—	11	1	no	—
400	#121	—	11	1	no	—
401	#121	—	11	2	no	—
402	#121	—	11	1	no	—
403	#121	—	11	2	no	—
404	#121	—	11	1	no	—
405	#121	—	11	2	no	—
406	#121	—	11	1	no	—
407	#121	—	11	1	no	—
408	#121	—	11	2	no	—
409	#121	—	11	2	no	—
410	#121	—	11	1	no	—
411	#121	—	11	2	no	—
412	#121	C₂×D₁₁	1	1	yes	characteristic
413	#121	C₂×D₁₁	1	2	yes	complemented
414	#121	C₂×D₁₁	1	1	yes	characteristic, complemented
415	#120	—	11	1	no	—
416	#120	—	11	2	no	—
417	#120	—	11	1	no	—
418	#120	—	11	2	no	—
419	C₄×Q₈	—	11	2	no	—
420	C₄×D₄	—	11	1	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	2	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	1	no	—
425	C₄×D₄	—	11	2	no	—
426	C₄×D₄	—	11	1	no	—
427	C₄×D₄	—	11	2	no	—
428	C₄×D₄	—	11	2	no	—
429	C₄×D₄	—	11	2	no	—
430	C₄×D₄	—	11	2	no	—
431	C₄×D₄	—	11	1	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	1	no	—
434	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
435	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
436	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
437	#117	—	11	2	no	—
438	#117	—	11	1	no	—
439	#117	—	11	1	no	—
440	#117	—	11	2	no	—
441	#117	—	11	2	no	—
442	#117	—	11	1	no	—
443	#117	—	11	1	no	—
444	#117	—	11	1	no	—
445	#117	—	11	1	no	—
446	#117	—	11	2	no	—
447	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₄	—	11	1	no	—
449	C₂×C₄⋊C₄	—	11	1	no	—
450	C₂×C₄⋊C₄	—	11	1	no	—
451	C₂×C₄⋊C₄	—	11	1	no	—
452	C₂×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊C₄	—	11	2	no	—
454	C₂×C₂²⋊C₄	—	11	2	no	—
455	C₂×C₂²⋊C₄	—	11	2	no	—
456	C₂×C₂²⋊C₄	—	11	2	no	—
457	C₂×C₄²	—	11	2	no	—
458	C₂×C₁₁	—	2	2	no	—
459	C₂×C₁₁	—	4	2	no	—
460	C₂×C₁₁	—	4	1	no	—
461	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
462	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂×C₁₁	#585	1	1	yes	characteristic
464	D₁₁	—	2	2	no	—
465	D₁₁	—	4	1	no	—
466	D₁₁	—	4	1	no	—
467	D₁₁	—	4	2	no	—
468	C₂⁴	—	11	1	no	—
469	C₂⁴	—	11	2	no	—
470	#41	—	22	4	no	—
471	#41	—	44	4	no	—
472	#41	—	44	4	no	—
473	C₂×Q₈	—	11	1	no	—
474	C₂×Q₈	—	11	2	no	—
475	C₂×Q₈	—	11	2	no	—
476	C₂×D₄	—	11	1	no	—
477	C₂×D₄	—	11	2	no	—
478	C₂×D₄	—	11	1	no	—
479	C₂×D₄	—	11	1	no	—
480	C₂×D₄	—	11	2	no	—
481	C₂×D₄	—	11	1	no	—
482	C₂×D₄	—	11	2	no	—
483	C₂×D₄	—	11	2	no	—
484	C₂×D₄	—	11	2	no	—
485	C₂×D₄	—	11	1	no	—
486	C₂×D₄	—	11	1	no	—
487	C₂×D₄	—	11	1	no	—
488	C₂×D₄	—	11	2	no	—
489	C₂×D₄	—	11	2	no	—
490	C₂×D₄	—	22	4	no	—
491	C₂×D₄	—	44	4	no	—
492	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₁₁	1	2	yes	—
495	C₂×D₄	C₂²×D₁₁	1	2	yes	—
496	C₂²×C₄	—	11	1	no	—
497	C₂²×C₄	—	11	1	no	—
498	C₂²×C₄	—	11	2	no	—
499	C₂²×C₄	—	11	2	no	—
500	C₂²×C₄	—	11	2	no	—
501	C₂²×C₄	—	11	1	no	—
502	C₂²×C₄	—	11	1	no	—
503	C₂²×C₄	—	11	1	no	—
504	C₂²×C₄	—	11	1	no	—
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	—	22	4	no	—
510	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
514	C₄⋊C₄	—	11	1	no	—
515	C₄⋊C₄	—	11	1	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	2	no	—
518	C₄⋊C₄	—	11	2	no	—
519	C₄⋊C₄	—	11	2	no	—
520	C₄⋊C₄	—	11	2	no	—
521	C₄⋊C₄	—	11	1	no	—
522	C₄⋊C₄	—	11	1	no	—
523	C₄⋊C₄	—	11	1	no	—
524	C₄⋊C₄	—	11	1	no	—
525	C₄⋊C₄	—	11	2	no	—
526	C₄⋊C₄	—	11	2	no	—
527	C₄⋊C₄	—	11	2	no	—
528	C₄⋊C₄	—	11	2	no	—
529	C₄⋊C₄	—	11	1	no	—
530	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
535	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
536	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
537	C₂²⋊C₄	—	11	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	1	no	—
541	C₂²⋊C₄	—	11	1	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	1	no	—
544	C₂²⋊C₄	—	11	1	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	2	no	—
549	C₂²⋊C₄	—	11	2	no	—
550	C₂²⋊C₄	—	11	2	no	—
551	C₂²⋊C₄	—	11	2	no	—
552	C₂²⋊C₄	—	11	2	no	—
553	C₂²⋊C₄	—	11	2	no	—
554	C₂²⋊C₄	—	11	1	no	—
555	C₂²⋊C₄	—	11	2	no	—
556	C₂²⋊C₄	—	11	1	no	—
557	C₂²⋊C₄	—	11	1	no	—
558	C₂²⋊C₄	—	11	1	no	—
559	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
563	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
565	C₄²	—	11	2	no	—
566	C₄²	—	11	2	no	—
567	C₄²	—	11	2	no	—
568	C₄²	—	11	2	no	—
569	C₄²	—	11	2	no	—
570	C₄²	—	11	1	no	—
571	C₄²	C₂²×D₁₁	1	2	yes	—
572	C₄²	C₂²×D₁₁	1	1	yes	characteristic
573	C₁₁	#3494	1	1	yes	characteristic, complemented, Sylow
574	C₂³	—	11	1	no	—
575	C₂³	—	11	1	no	—
576	C₂³	—	11	2	no	—
577	C₂³	—	11	1	no	—
578	C₂³	—	22	2	no	—
579	C₂³	—	22	4	no	—
580	C₂³	—	22	2	no	—
581	C₂³	—	44	1	no	—
582	C₂³	—	44	2	no	—
583	C₂³	—	44	2	no	—
584	C₂³	C₂³×D₁₁	1	2	yes	—
585	C₂³	C₂³×D₁₁	1	1	yes	characteristic
586	C₂³	C₂³×D₁₁	1	1	yes	characteristic
587	Q₈	—	22	2	no	—
588	Q₈	—	44	2	no	—
589	Q₈	—	44	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	22	2	no	—
595	D₄	—	22	4	no	—
596	D₄	—	22	2	no	—
597	D₄	—	22	2	no	—
598	D₄	—	22	4	no	—
599	D₄	—	22	2	no	—
600	D₄	—	22	2	no	—
601	D₄	—	44	2	no	—
602	D₄	—	44	1	no	—
603	D₄	—	44	2	no	—
604	D₄	—	44	2	no	—
605	D₄	—	44	2	no	—
606	D₄	—	44	2	no	—
607	D₄	—	44	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	11	1	no	—
613	C₂×C₄	—	11	4	no	—
614	C₂×C₄	—	11	1	no	—
615	C₂×C₄	—	11	1	no	—
616	C₂×C₄	—	11	2	no	—
617	C₂×C₄	—	11	2	no	—
618	C₂×C₄	—	11	1	no	—
619	C₂×C₄	—	11	1	no	—
620	C₂×C₄	—	11	2	no	—
621	C₂×C₄	—	22	2	no	—
622	C₂×C₄	—	22	2	no	—
623	C₂×C₄	—	22	2	no	—
624	C₂×C₄	—	22	4	no	—
625	C₂×C₄	—	22	2	no	—
626	C₂×C₄	—	22	2	no	—
627	C₂×C₄	—	44	2	no	—
628	C₂×C₄	—	44	2	no	—
629	C₂×C₄	—	44	2	no	—
630	C₂×C₄	—	44	2	no	—
631	C₂×C₄	—	44	2	no	—
632	C₂×C₄	—	44	2	no	—
633	C₂×C₄	C₂³×D₁₁	1	2	yes	—
634	C₂×C₄	C₂³×D₁₁	1	2	yes	—
635	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₁	1	2	yes	—
639	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	11	2	no	—
650	C₂²	—	22	1	no	—
651	C₂²	—	22	1	no	—
652	C₂²	—	22	1	no	—
653	C₂²	—	22	1	no	—
654	C₂²	—	22	2	no	—
655	C₂²	—	22	1	no	—
656	C₂²	—	22	2	no	—
657	C₂²	—	22	1	no	—
658	C₂²	—	22	2	no	—
659	C₂²	—	22	1	no	—
660	C₂²	—	22	1	no	—
661	C₂²	—	44	4	no	—
662	C₂²	—	88	4	no	—
663	C₂²	#67042	1	2	yes	—
664	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	11	2	no	—
673	C₄	—	22	1	no	—
674	C₄	—	22	1	no	—
675	C₄	—	22	2	no	—
676	C₄	—	22	2	no	—
677	C₄	—	22	2	no	—
678	C₄	—	22	1	no	—
679	C₄	—	22	1	no	—
680	C₄	#41×D₁₁	1	2	yes	—
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	22	2	no	—
685	C₂	—	44	1	no	—
686	C₂	—	44	2	no	—
687	C₂	—	44	1	no	—
688	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
689	C₂	C₂×#67042	1	1	yes	characteristic
690	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#553	C₂
hypercenter	#553	D₁₁
hypocenter	C₁₁	#3494
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₁×#553	C₂	semidirect
2. #10623241	C₂	semidirect
3. #10623236	C₂	semidirect
4. #10623226	C₂	semidirect
5. #10623220	C₂	semidirect
6. #10623194	C₂	semidirect
7. #10623189	C₂	semidirect
8. #10623149	C₂	semidirect
9. #10623142	C₂	semidirect
10. #10623141	C₂	semidirect
11. #10623138	C₂	semidirect
12. D₁₁×#121	C₂	semidirect
13. #10623127	C₂	semidirect
14. #10623094	C₂	semidirect
15. #10623086	C₂	semidirect
16. #10623085	C₂	semidirect
17. #10623078	C₂	semidirect
18. #10623076	C₂	semidirect
19. #10623069	C₂	semidirect
20. #10623063	C₂	semidirect
21. #10623054	C₂	semidirect
22. #10623045	C₂	semidirect
23. C₂×#66945	C₂	semidirect
24. C₂×#4341	C₂²	semidirect
25. C₂×#4341	C₂²	semidirect
30. C₁₁×#126	C₂²	semidirect
31. C₁₁×#125	C₂²	semidirect
32. C₁₁×#123	C₂²	semidirect
34. C₁₁×#121	C₂²	semidirect
35. C₁₁×#121	C₂²	semidirect
36. C₄×D₄×C₁₁	C₂²	semidirect
37. C₄×D₄×C₁₁	C₂²	semidirect
38. C₄×D₄×C₁₁	C₂²	semidirect
39. C₁₁×#117	C₂²	semidirect
40. C₂×C₁₁×C₄⋊C₄	C₂²	semidirect
41. #66993	C₂²	semidirect
43. #66992	C₂²	semidirect
44. #66992	C₂²	semidirect
46. #66991	C₂²	semidirect
49. #66988	C₂²	semidirect
50. D₄×Dic₁₁	C₂²	semidirect
51. D₄×Dic₁₁	C₂²	semidirect
53. #66983	C₂²	semidirect
54. #66983	C₂²	semidirect
55. #66983	C₂²	semidirect
56. C₄×C₂²⋊D₁₁	C₂²	semidirect
57. C₄×C₂²⋊D₁₁	C₂²	semidirect
58. C₄×C₂²⋊D₁₁	C₂²	semidirect
59. C₄×C₂²⋊D₁₁	C₂²	semidirect
62. #66979	C₂²	semidirect
63. C₂×C₄⋊Dic₁₁	C₂²	semidirect
64. C₂×C₄⋊Dic₁₁	C₂²	semidirect
65. C₂×C₄×Dic₁₁	C₂²	semidirect
66. #66951	C₂²	semidirect
67. #66951	C₂²	semidirect
69. #66950	C₂²	semidirect
71. #66949	C₂²	semidirect
73. #66948	C₂²	semidirect
74. #66948	C₂²	semidirect
76. #66947	C₂²	semidirect
77. #66947	C₂²	semidirect
78. #66946	C₂²	semidirect
79. #66946	C₂²	semidirect
83. #66945	C₂²	semidirect
84. #66945	C₂²	semidirect
85. #66945	C₂²	semidirect
86. #66945	C₂²	semidirect
88. C₄⋊C₄×D₁₁	C₂²	semidirect
89. #66943	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66941	C₂²	semidirect
93. #66939	C₂²	semidirect
94. #66939	C₂²	semidirect
95. #66939	C₂²	semidirect
96. #66938	C₂²	semidirect
97. #66938	C₂²	semidirect
98. #66938	C₂²	semidirect
99. #66938	C₂²	semidirect
101. #66937	C₂²	semidirect
102. #66937	C₂²	semidirect
104. #66936	C₂²	semidirect
108. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
109. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
112. #66932	C₂²	semidirect
113. #66931	C₂²	semidirect
114. #66931	C₂²	semidirect
115. #66928	C₂²	semidirect
117. C₄×D₄₄	C₂²	semidirect
118. C₄×D₄₄	C₂²	semidirect
120. #66925	C₂²	semidirect
121. #66922	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
292. C₄×D₁₁	#41	semidirect
301. #553	D₁₁	semidirect
372. #126	C₂×D₁₁	semidirect
375. #125	C₂×D₁₁	semidirect
390. #123	C₂×D₁₁	semidirect
413. #121	C₂×D₁₁	semidirect
414. #121	C₂×D₁₁	semidirect
434. C₄×D₄	C₂×D₁₁	semidirect
435. C₄×D₄	C₂×D₁₁	semidirect
436. C₄×D₄	C₂×D₁₁	semidirect
447. #117	C₂×D₁₁	semidirect
452. C₂×C₄⋊C₄	C₂×D₁₁	semidirect
573. C₁₁	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#553	2
#10623241	2
#10623236	2
#10623226	2
#10623220	2
#10623194	2
#10623189	2
#10623149	2
#10623142	2
#10623141	2
#10623138	2
D₁₁×#121	2
#10623127	2
#10623094	2
#10623086	2
#10623085	2
#10623078	2
#10623076	2
#10623069	2
#10623063	2
#10623054	2
#10623045	2
C₂×#66945	2
#3494	11