Subgroups — #13082924

Order 1408.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623365	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623360	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623322	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66983	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623198	C₂	1	2	yes	maximal, complemented
7	#10623197	C₂	1	2	yes	maximal, complemented
8	#10623174	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623173	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623161	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623160	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623150	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623142	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623140	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623138	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623123	C₂	1	2	yes	maximal, complemented
17	#10623120	C₂	1	2	yes	maximal, complemented
18	#10623093	C₂	1	2	yes	maximal, complemented
19	#10623091	C₂	1	2	yes	maximal, complemented
20	#10623087	C₂	1	2	yes	maximal, complemented
21	#10623085	C₂	1	2	yes	maximal, complemented
22	#10623063	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623061	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
27	C₂×#4343	C₂²	1	1	yes	characteristic, complemented
28	C₂×#4341	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₁	C₂²	1	2	yes	—
30	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₄₄	C₂²	1	1	yes	characteristic
33	C₁₁×#123	C₂²	1	2	yes	complemented
34	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×#121	C₂²	1	1	yes	characteristic
37	C₁₁×#121	C₂²	1	1	yes	characteristic, complemented
38	C₁₁×#120	C₂²	1	2	yes	complemented
39	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
41	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
42	#67006	C₂²	1	1	yes	characteristic
43	#67006	C₂²	1	1	yes	characteristic, complemented
44	#67000	C₂²	1	1	yes	characteristic, complemented
45	#66999	C₂²	1	1	yes	characteristic, complemented
46	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
47	#66993	C₂²	1	2	yes	complemented
48	#66993	C₂²	1	2	yes	complemented
49	#66993	C₂²	1	1	yes	characteristic, complemented
50	#66992	C₂²	1	2	yes	complemented
51	#66992	C₂²	1	2	yes	complemented
52	#66991	C₂²	1	2	yes	complemented
53	#66991	C₂²	1	2	yes	complemented
54	#66991	C₂²	1	1	yes	characteristic, complemented
55	#66990	C₂²	1	2	yes	—
56	#66990	C₂²	1	2	yes	complemented
57	#66990	C₂²	1	2	yes	complemented
58	#66988	C₂²	1	2	yes	complemented
59	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
60	#66983	C₂²	1	1	yes	characteristic
61	#66983	C₂²	1	1	yes	characteristic
62	#66983	C₂²	1	1	yes	characteristic
63	#66983	C₂²	1	1	yes	characteristic, complemented
64	#66983	C₂²	1	2	yes	complemented
65	#66983	C₂²	1	1	yes	characteristic, complemented
66	#66983	C₂²	1	2	yes	complemented
67	#66983	C₂²	1	1	yes	characteristic, complemented
68	#66983	C₂²	1	2	yes	complemented
69	#66982	C₂²	1	1	yes	characteristic, complemented
70	#66982	C₂²	1	1	yes	characteristic, complemented
71	#66982	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
77	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	complemented
78	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	complemented
79	#66979	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
81	#66977	C₂²	1	1	yes	characteristic, complemented
82	#66977	C₂²	1	1	yes	characteristic, complemented
83	#66951	C₂²	1	2	yes	complemented
84	#66951	C₂²	1	2	yes	complemented
85	#66950	C₂²	1	2	yes	complemented
86	#66949	C₂²	1	2	yes	complemented
87	#66948	C₂²	1	1	yes	characteristic, complemented
88	#66948	C₂²	1	1	yes	characteristic, complemented
89	#66948	C₂²	1	2	yes	complemented
90	#66948	C₂²	1	2	yes	complemented
91	#66947	C₂²	1	2	yes	complemented
92	#66946	C₂²	1	1	yes	characteristic, complemented
93	#66946	C₂²	1	1	yes	characteristic, complemented
94	#66945	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
96	#66943	C₂²	1	1	yes	characteristic, complemented
97	#66943	C₂²	1	2	yes	complemented
98	#66941	C₂²	1	1	yes	characteristic, complemented
99	#66939	C₂²	1	2	yes	—
100	#66939	C₂²	1	2	yes	complemented
101	#66938	C₂²	1	2	yes	complemented
102	#66938	C₂²	1	2	yes	complemented
103	#66938	C₂²	1	2	yes	complemented
104	#66937	C₂²	1	2	yes	complemented
105	#66937	C₂²	1	2	yes	complemented
106	#66937	C₂²	1	2	yes	complemented
107	#66937	C₂²	1	2	yes	complemented
108	#66937	C₂²	1	2	yes	complemented
109	#66936	C₂²	1	2	yes	complemented
110	#66936	C₂²	1	2	yes	complemented
111	#66936	C₂²	1	2	yes	complemented
112	#66936	C₂²	1	2	yes	complemented
113	#66935	C₂²	1	2	yes	complemented
114	#66935	C₂²	1	2	yes	complemented
115	#66935	C₂²	1	2	yes	complemented
116	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
117	#66931	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	#66929	C₂²	1	2	yes	complemented
120	#66928	C₂²	1	2	yes	complemented
121	C₄×D₄₄	C₂²	1	2	yes	complemented
122	#66925	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₂³×D₁₁	C₂³	1	2	yes	—
126	C₁₁×#41	—	4	2	no	—
127	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂×D₄×C₁₁	C₂³	1	2	yes	—
131	C₂×D₄×C₁₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₁	—	4	2	no	—
133	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	—	4	4	no	—
141	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
155	C₂²×Dic₁₁	C₂³	1	2	yes	—
156	C₂²×Dic₁₁	C₂³	1	2	yes	—
157	#4343	—	4	2	no	—
158	#4341	—	4	4	no	—
159	D₄×D₁₁	—	4	4	no	—
160	D₄×D₁₁	—	4	2	no	—
161	#4339	—	4	2	no	—
162	C₂×D₄₄	—	4	2	no	—
163	C₂×D₄₄	C₂³	1	1	yes	characteristic
164	C₂×D₄₄	C₂³	1	1	yes	characteristic
165	C₂×D₄₄	C₂³	1	2	yes	—
166	C₂×D₄₄	C₂³	1	2	yes	—
167	C₂×D₄₄	C₂³	1	1	yes	characteristic
168	C₂×D₄₄	C₂³	1	2	yes	—
169	C₂×D₄₄	C₂³	1	2	yes	—
170	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₁₁	C₂³	1	2	yes	—
173	C₂×C₄×D₁₁	C₂³	1	2	yes	—
174	C₂×C₄×D₁₁	C₂³	1	2	yes	—
175	C₂×C₄×D₁₁	C₂³	1	2	yes	—
176	C₂×Dic₂₂	C₂³	1	2	yes	—
177	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
178	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
181	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₄²×C₁₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₁₁	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	1	yes	characteristic
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	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
207	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
212	C₄⋊Dic₁₁	C₂³	1	2	yes	—
213	C₄⋊Dic₁₁	C₂³	1	2	yes	—
214	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₁	C₂³	1	2	yes	—
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	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₁₁⋊C₄	C₂³	1	2	yes	—
221	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₁₁⋊C₄	C₂³	1	2	yes	—
223	Dic₁₁⋊C₄	C₂³	1	2	yes	—
224	Dic₁₁⋊C₄	C₂³	1	2	yes	—
225	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	2	yes	—
228	C₄×Dic₁₁	C₂³	1	2	yes	—
229	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
231	#3542	—	11	1	no	maximal, Sylow
232	C₂³×C₁₁	—	2	2	no	—
233	C₂³×C₁₁	—	4	1	no	—
234	C₂³×C₁₁	—	4	1	no	—
235	C₂³×C₁₁	C₂⁴	1	2	yes	—
236	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
238	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₁	—	2	4	no	—
240	C₂²×D₁₁	—	4	2	no	—
241	C₂²×D₁₁	—	4	2	no	—
242	C₂²×D₁₁	—	4	2	no	—
243	C₂²×D₁₁	—	4	2	no	—
244	C₂²×D₁₁	—	4	2	no	—
245	C₂²×D₁₁	C₂⁴	1	2	yes	—
246	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
247	C₂²×D₁₁	C₂⁴	1	2	yes	—
248	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
249	Q₈×C₁₁	—	2	2	no	—
250	D₄×C₁₁	—	2	4	no	—
251	D₄×C₁₁	—	2	2	no	—
252	D₄×C₁₁	—	4	2	no	—
253	D₄×C₁₁	—	4	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	2	no	—
257	C₂×C₄×C₁₁	—	4	1	no	—
258	C₂×C₄×C₁₁	—	4	1	no	—
259	C₂×C₄×C₁₁	—	4	1	no	—
260	C₂×C₄×C₁₁	—	4	2	no	—
261	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
266	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
268	C₂²⋊D₁₁	—	2	2	no	—
269	C₂²⋊D₁₁	—	2	2	no	—
270	C₂²⋊D₁₁	—	4	1	no	—
271	C₂²⋊D₁₁	—	4	1	no	—
272	C₂²⋊D₁₁	—	4	2	no	—
273	C₂²⋊D₁₁	—	4	2	no	—
274	C₂²⋊D₁₁	—	4	2	no	—
275	C₂²⋊D₁₁	—	4	2	no	—
276	C₂²⋊D₁₁	—	4	2	no	—
277	C₂²⋊D₁₁	—	4	2	no	—
278	C₂²⋊D₁₁	—	4	2	no	—
279	C₂²⋊D₁₁	—	4	1	no	—
280	C₂²⋊D₁₁	—	4	2	no	—
281	C₂²⋊D₁₁	—	4	1	no	—
282	C₂×Dic₁₁	—	2	4	no	—
283	C₂×Dic₁₁	—	4	2	no	—
284	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₁	C₂⁴	1	2	yes	—
287	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₁₁	C₂⁴	1	2	yes	—
292	D₄₄	—	2	2	no	—
293	D₄₄	—	2	2	no	—
294	D₄₄	—	4	2	no	—
295	D₄₄	—	4	2	no	—
296	D₄₄	—	4	1	no	—
297	D₄₄	—	4	2	no	—
298	D₄₄	—	4	2	no	—
299	C₄×D₁₁	—	2	2	no	—
300	C₄×D₁₁	—	2	2	no	—
301	C₄×D₁₁	—	4	2	no	—
302	C₄×D₁₁	—	4	2	no	—
303	C₄×D₁₁	—	4	2	no	—
304	C₄×D₁₁	—	4	2	no	—
305	Dic₂₂	—	4	1	no	—
306	Dic₂₂	—	4	2	no	—
307	#562	—	11	2	no	—
308	#560	—	11	2	no	—
309	#555	—	11	1	no	—
310	#553	—	11	1	no	—
311	#552	—	11	1	no	—
312	#551	—	11	2	no	—
313	#550	—	11	1	no	—
314	#547	—	11	1	no	—
315	#546	—	11	1	no	—
316	#546	—	11	1	no	—
317	#546	—	11	2	no	—
318	D₄²	—	11	1	no	—
319	#542	—	11	1	no	—
320	#540	—	11	1	no	—
321	#540	—	11	2	no	—
322	#538	—	11	2	no	—
323	#537	—	11	1	no	—
324	#535	—	11	1	no	—
325	#535	—	11	2	no	—
326	#534	—	11	2	no	—
327	#525	—	11	1	no	—
328	#525	D₁₁	1	1	yes	characteristic, complemented
329	C₂×#121	—	11	1	no	—
330	C₂²×C₁₁	—	2	1	no	—
331	C₂²×C₁₁	—	2	1	no	—
332	C₂²×C₁₁	—	2	1	no	—
333	C₂²×C₁₁	—	2	1	no	—
334	C₂²×C₁₁	—	2	2	no	—
335	C₂²×C₁₁	—	2	2	no	—
336	C₂²×C₁₁	—	2	1	no	—
337	C₂²×C₁₁	—	2	1	no	—
338	C₂²×C₁₁	—	2	1	no	—
339	C₂²×C₁₁	—	2	2	no	—
340	C₂²×C₁₁	—	2	1	no	—
341	C₂²×C₁₁	—	4	4	no	—
342	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
343	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
344	C₂×D₁₁	—	2	2	no	—
345	C₂×D₁₁	—	2	2	no	—
346	C₂×D₁₁	—	2	1	no	—
347	C₂×D₁₁	—	2	2	no	—
348	C₂×D₁₁	—	2	1	no	—
349	C₂×D₁₁	—	2	2	no	—
350	C₂×D₁₁	—	2	1	no	—
351	C₂×D₁₁	—	2	1	no	—
352	C₂×D₁₁	—	2	2	no	—
353	C₂×D₁₁	—	2	1	no	—
354	C₂×D₁₁	—	2	2	no	—
355	C₂×D₁₁	—	2	1	no	—
356	C₂×D₁₁	—	8	4	no	—
357	C₂×D₁₁	—	8	4	no	—
358	C₄×C₁₁	—	2	1	no	—
359	C₄×C₁₁	—	2	1	no	—
360	C₄×C₁₁	—	2	1	no	—
361	C₄×C₁₁	—	2	2	no	—
362	C₄×C₁₁	—	2	2	no	—
363	C₄×C₁₁	—	2	2	no	—
364	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
365	Dic₁₁	—	2	1	no	—
366	Dic₁₁	—	2	1	no	—
367	Dic₁₁	—	2	1	no	—
368	Dic₁₁	—	2	2	no	—
369	Dic₁₁	—	2	1	no	—
370	Dic₁₁	—	2	2	no	—
371	Dic₁₁	—	2	1	no	—
372	Dic₁₁	—	2	1	no	—
373	C₂×#41	—	11	1	no	—
374	C₂×#41	—	11	2	no	—
375	C₂×#41	—	11	1	no	—
376	C₂×#41	C₂×D₁₁	1	1	yes	characteristic, complemented
377	C₂²×D₄	—	11	2	no	—
378	C₂²×D₄	—	11	2	no	—
379	C₂²×D₄	—	11	1	no	—
380	C₂²×D₄	—	11	1	no	—
381	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic, complemented
382	C₄⋊Q₈	—	11	1	no	—
383	#127	—	11	2	no	—
384	#127	—	11	2	no	—
385	#127	—	11	1	no	—
386	#126	—	11	2	no	—
387	#126	—	11	2	no	—
388	#126	—	11	2	no	—
389	#125	—	11	1	no	—
390	#125	—	11	2	no	—
391	#124	—	11	1	no	—
392	#124	—	11	2	no	—
393	#124	—	11	2	no	—
394	#124	—	11	2	no	—
395	#124	—	11	2	no	—
396	#123	—	11	2	no	—
397	#123	—	11	1	no	—
398	#123	—	11	1	no	—
399	#123	—	11	2	no	—
400	#123	—	11	2	no	—
401	#123	—	11	2	no	—
402	#123	—	11	2	no	—
403	#123	—	11	2	no	—
404	#123	—	11	2	no	—
405	#123	—	11	2	no	—
406	#123	—	11	2	no	—
407	#123	C₂×D₁₁	1	2	yes	complemented
408	C₂²⋊Q₈	—	11	1	no	—
409	C₂²⋊Q₈	—	11	1	no	—
410	C₂²⋊Q₈	—	11	1	no	—
411	C₂²⋊Q₈	—	11	2	no	—
412	C₂²⋊Q₈	—	11	2	no	—
413	C₂²⋊Q₈	—	11	2	no	—
414	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
415	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
416	#121	—	11	2	no	—
417	#121	—	11	2	no	—
418	#121	—	11	2	no	—
419	#121	—	11	2	no	—
420	#121	—	11	1	no	—
421	#121	—	11	1	no	—
422	#121	—	11	1	no	—
423	#121	—	11	2	no	—
424	#121	—	11	1	no	—
425	#121	—	11	1	no	—
426	#121	—	11	2	no	—
427	#121	—	11	1	no	—
428	#121	—	11	1	no	—
429	#121	—	11	2	no	—
430	#121	—	11	1	no	—
431	#121	—	11	1	no	—
432	#121	—	11	2	no	—
433	#121	—	11	2	no	—
434	#121	—	11	2	no	—
435	#121	—	11	2	no	—
436	#121	—	11	2	no	—
437	#121	—	11	2	no	—
438	#121	—	11	2	no	—
439	#121	C₂×D₁₁	1	1	yes	characteristic
440	#121	C₂×D₁₁	1	1	yes	characteristic, complemented
441	#120	—	11	1	no	—
442	#120	—	11	1	no	—
443	#120	—	11	2	no	—
444	#120	—	11	2	no	—
445	#120	—	11	2	no	—
446	#120	—	11	2	no	—
447	#120	—	11	2	no	—
448	#120	—	11	2	no	—
449	#120	C₂×D₁₁	1	2	yes	complemented
450	C₄×Q₈	—	11	1	no	—
451	C₄×D₄	—	11	1	no	—
452	C₄×D₄	—	11	1	no	—
453	C₄×D₄	—	11	1	no	—
454	C₄×D₄	—	11	1	no	—
455	C₄×D₄	—	11	1	no	—
456	C₄×D₄	—	11	2	no	—
457	C₄×D₄	—	11	1	no	—
458	C₄×D₄	—	11	1	no	—
459	C₄×D₄	—	11	2	no	—
460	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
461	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
462	#117	—	11	1	no	—
463	#117	—	11	1	no	—
464	#117	—	11	2	no	—
465	#117	—	11	2	no	—
466	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
467	C₂×C₄⋊C₄	—	11	1	no	—
468	C₂×C₄⋊C₄	—	11	1	no	—
469	C₂×C₂²⋊C₄	—	11	2	no	—
470	C₂×C₂²⋊C₄	—	11	2	no	—
471	C₂×C₂²⋊C₄	—	11	2	no	—
472	C₂×C₁₁	—	2	2	no	—
473	C₂×C₁₁	—	4	2	no	—
474	C₂×C₁₁	—	4	1	no	—
475	C₂×C₁₁	—	4	1	no	—
476	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₁₁	#585	1	1	yes	characteristic
479	D₁₁	—	4	1	no	—
480	D₁₁	—	4	2	no	—
481	D₁₁	—	4	2	no	—
482	D₁₁	—	4	1	no	—
483	C₂⁴	—	11	2	no	—
484	C₂⁴	—	11	2	no	—
485	C₂⁴	C₂²×D₁₁	1	1	yes	characteristic
486	#41	—	4	2	no	—
487	#41	—	44	2	no	—
488	#41	—	44	4	no	—
489	#41	—	44	2	no	—
490	C₂×Q₈	—	11	1	no	—
491	C₂×Q₈	—	11	2	no	—
492	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
493	C₂×D₄	—	11	1	no	—
494	C₂×D₄	—	11	1	no	—
495	C₂×D₄	—	11	1	no	—
496	C₂×D₄	—	11	2	no	—
497	C₂×D₄	—	11	1	no	—
498	C₂×D₄	—	11	1	no	—
499	C₂×D₄	—	11	2	no	—
500	C₂×D₄	—	11	2	no	—
501	C₂×D₄	—	11	2	no	—
502	C₂×D₄	—	11	2	no	—
503	C₂×D₄	—	11	1	no	—
504	C₂×D₄	—	11	2	no	—
505	C₂×D₄	—	11	2	no	—
506	C₂×D₄	—	11	2	no	—
507	C₂×D₄	—	11	1	no	—
508	C₂×D₄	—	11	1	no	—
509	C₂×D₄	—	11	2	no	—
510	C₂×D₄	—	11	1	no	—
511	C₂×D₄	—	11	2	no	—
512	C₂×D₄	—	11	2	no	—
513	C₂×D₄	—	11	2	no	—
514	C₂×D₄	—	44	2	no	—
515	C₂×D₄	—	44	2	no	—
516	C₂×D₄	—	44	4	no	—
517	C₂×D₄	—	44	4	no	—
518	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₁₁	1	2	yes	—
520	C₂×D₄	C₂²×D₁₁	1	2	yes	—
521	C₂×D₄	C₂²×D₁₁	1	2	yes	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	11	2	no	—
524	C₂²×C₄	—	11	2	no	—
525	C₂²×C₄	—	11	1	no	—
526	C₂²×C₄	—	11	1	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	C₂²×D₁₁	1	1	yes	characteristic
532	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
533	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
534	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
535	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
536	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
538	C₄⋊C₄	—	11	1	no	—
539	C₄⋊C₄	—	11	1	no	—
540	C₄⋊C₄	—	11	2	no	—
541	C₄⋊C₄	—	11	2	no	—
542	C₄⋊C₄	—	11	1	no	—
543	C₄⋊C₄	—	11	2	no	—
544	C₄⋊C₄	—	11	2	no	—
545	C₄⋊C₄	—	11	1	no	—
546	C₄⋊C₄	—	11	1	no	—
547	C₄⋊C₄	—	11	2	no	—
548	C₄⋊C₄	—	11	1	no	—
549	C₄⋊C₄	—	11	1	no	—
550	C₄⋊C₄	—	11	2	no	—
551	C₄⋊C₄	—	11	1	no	—
552	C₄⋊C₄	—	11	2	no	—
553	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
557	C₂²⋊C₄	—	11	1	no	—
558	C₂²⋊C₄	—	11	1	no	—
559	C₂²⋊C₄	—	11	1	no	—
560	C₂²⋊C₄	—	11	1	no	—
561	C₂²⋊C₄	—	11	1	no	—
562	C₂²⋊C₄	—	11	2	no	—
563	C₂²⋊C₄	—	11	1	no	—
564	C₂²⋊C₄	—	11	2	no	—
565	C₂²⋊C₄	—	11	2	no	—
566	C₂²⋊C₄	—	11	1	no	—
567	C₂²⋊C₄	—	11	2	no	—
568	C₂²⋊C₄	—	11	2	no	—
569	C₂²⋊C₄	—	11	2	no	—
570	C₂²⋊C₄	—	11	2	no	—
571	C₂²⋊C₄	—	11	2	no	—
572	C₂²⋊C₄	—	11	2	no	—
573	C₂²⋊C₄	—	11	2	no	—
574	C₂²⋊C₄	—	11	2	no	—
575	C₂²⋊C₄	—	11	2	no	—
576	C₂²⋊C₄	—	11	1	no	—
577	C₂²⋊C₄	—	11	1	no	—
578	C₂²⋊C₄	—	11	2	no	—
579	C₂²⋊C₄	—	11	2	no	—
580	C₂²⋊C₄	—	11	1	no	—
581	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
586	C₄²	—	11	2	no	—
587	C₄²	—	11	1	no	—
588	C₄²	—	11	1	no	—
589	C₄²	—	11	2	no	—
590	C₄²	C₂²×D₁₁	1	2	yes	—
591	C₁₁	#3542	1	1	yes	characteristic, complemented, Sylow
592	C₂³	—	2	2	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	11	1	no	—
596	C₂³	—	11	2	no	—
597	C₂³	—	11	2	no	—
598	C₂³	—	11	1	no	—
599	C₂³	—	22	4	no	—
600	C₂³	—	44	2	no	—
601	C₂³	—	44	2	no	—
602	C₂³	—	44	2	no	—
603	C₂³	—	44	2	no	—
604	C₂³	—	44	2	no	—
605	C₂³	C₂³×D₁₁	1	2	yes	—
606	C₂³	C₂³×D₁₁	1	1	yes	characteristic
607	C₂³	C₂³×D₁₁	1	1	yes	characteristic
608	C₂³	C₂³×D₁₁	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	44	1	no	—
611	Q₈	—	44	2	no	—
612	D₄	—	2	4	no	—
613	D₄	—	2	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	22	2	no	—
617	D₄	—	22	2	no	—
618	D₄	—	22	2	no	—
619	D₄	—	22	2	no	—
620	D₄	—	44	2	no	—
621	D₄	—	44	2	no	—
622	D₄	—	44	1	no	—
623	D₄	—	44	2	no	—
624	D₄	—	44	2	no	—
625	D₄	—	44	2	no	—
626	D₄	—	44	2	no	—
627	D₄	—	44	2	no	—
628	D₄	—	44	2	no	—
629	D₄	—	44	2	no	—
630	D₄	—	44	2	no	—
631	D₄	—	44	1	no	—
632	D₄	—	44	1	no	—
633	D₄	—	44	2	no	—
634	D₄	—	44	1	no	—
635	D₄	—	44	2	no	—
636	D₄	—	44	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	11	1	no	—
645	C₂×C₄	—	11	1	no	—
646	C₂×C₄	—	11	2	no	—
647	C₂×C₄	—	11	1	no	—
648	C₂×C₄	—	11	1	no	—
649	C₂×C₄	—	11	1	no	—
650	C₂×C₄	—	11	1	no	—
651	C₂×C₄	—	11	2	no	—
652	C₂×C₄	—	22	4	no	—
653	C₂×C₄	—	22	2	no	—
654	C₂×C₄	—	22	2	no	—
655	C₂×C₄	—	44	2	no	—
656	C₂×C₄	—	44	2	no	—
657	C₂×C₄	—	44	2	no	—
658	C₂×C₄	—	44	2	no	—
659	C₂×C₄	—	44	2	no	—
660	C₂×C₄	C₂³×D₁₁	1	2	yes	—
661	C₂×C₄	C₂³×D₁₁	1	2	yes	—
662	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₁	1	2	yes	—
664	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	22	1	no	—
680	C₂²	—	22	1	no	—
681	C₂²	—	22	2	no	—
682	C₂²	—	22	2	no	—
683	C₂²	—	22	1	no	—
684	C₂²	—	22	2	no	—
685	C₂²	—	22	1	no	—
686	C₂²	—	22	2	no	—
687	C₂²	—	22	2	no	—
688	C₂²	—	22	1	no	—
689	C₂²	—	22	2	no	—
690	C₂²	—	22	1	no	—
691	C₂²	—	88	4	no	—
692	C₂²	—	88	4	no	—
693	C₂²	#67042	1	2	yes	—
694	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	22	1	no	—
702	C₄	—	22	1	no	—
703	C₄	—	22	2	no	—
704	C₄	—	22	2	no	—
705	C₄	—	22	1	no	—
706	C₄	—	22	1	no	—
707	C₄	—	22	1	no	—
708	C₄	—	22	1	no	—
709	C₄	#67037	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	2	no	—
714	C₂	—	44	1	no	—
715	C₂	—	44	2	no	—
716	C₂	—	44	2	no	—
717	C₂	—	44	1	no	—
718	C₂	C₂×#67037	1	1	yes	characteristic
719	C₂	C₂×#67042	1	1	yes	characteristic
720	C₂	#10623453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#525	C₂
hypercenter	#525	D₁₁
hypocenter	C₁₁	#3542
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₁₁×#525	C₂	semidirect
2. #10623365	C₂	semidirect
3. #10623360	C₂	semidirect
4. #10623322	C₂	semidirect
5. C₂×#66983	C₂	semidirect
6. #10623198	C₂	semidirect
7. #10623197	C₂	semidirect
8. #10623174	C₂	semidirect
9. #10623173	C₂	semidirect
10. #10623161	C₂	semidirect
11. #10623160	C₂	semidirect
12. #10623150	C₂	semidirect
13. #10623142	C₂	semidirect
14. #10623140	C₂	semidirect
15. #10623138	C₂	semidirect
16. #10623123	C₂	semidirect
17. #10623120	C₂	semidirect
18. #10623093	C₂	semidirect
19. #10623091	C₂	semidirect
20. #10623087	C₂	semidirect
21. #10623085	C₂	semidirect
22. #10623063	C₂	semidirect
23. #10623061	C₂	semidirect
24. C₂×C₁₁×#41	C₂²	semidirect
25. C₂³×C₄×C₁₁	C₂²	semidirect
26. C₂²×C₂²⋊D₁₁	C₂²	semidirect
27. C₂×#4343	C₂²	semidirect
28. C₂×#4341	C₂²	semidirect
30. C₂×D₄×D₁₁	C₂²	semidirect
31. C₂×#4339	C₂²	semidirect
33. C₁₁×#123	C₂²	semidirect
34. C₁₁×C₂²⋊Q₈	C₂²	semidirect
35. C₁₁×C₂²⋊Q₈	C₂²	semidirect
37. C₁₁×#121	C₂²	semidirect
38. C₁₁×#120	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₄×D₄×C₁₁	C₂²	semidirect
41. C₁₁×#117	C₂²	semidirect
43. #67006	C₂²	semidirect
44. #67000	C₂²	semidirect
45. #66999	C₂²	semidirect
46. Q₈×Dic₁₁	C₂²	semidirect
47. #66993	C₂²	semidirect
48. #66993	C₂²	semidirect
49. #66993	C₂²	semidirect
50. #66992	C₂²	semidirect
51. #66992	C₂²	semidirect
52. #66991	C₂²	semidirect
53. #66991	C₂²	semidirect
54. #66991	C₂²	semidirect
56. #66990	C₂²	semidirect
57. #66990	C₂²	semidirect
58. #66988	C₂²	semidirect
59. D₄×Dic₁₁	C₂²	semidirect
63. #66983	C₂²	semidirect
64. #66983	C₂²	semidirect
65. #66983	C₂²	semidirect
66. #66983	C₂²	semidirect
67. #66983	C₂²	semidirect
68. #66983	C₂²	semidirect
69. #66982	C₂²	semidirect
70. #66982	C₂²	semidirect
71. #66982	C₂²	semidirect
73. C₄×C₂²⋊D₁₁	C₂²	semidirect
74. C₄×C₂²⋊D₁₁	C₂²	semidirect
75. C₄×C₂²⋊D₁₁	C₂²	semidirect
76. C₄×C₂²⋊D₁₁	C₂²	semidirect
77. C₂×(C₂×D₁₁)⋊C₄	C₂²	semidirect
78. C₂×(C₂×D₁₁)⋊C₄	C₂²	semidirect
79. #66979	C₂²	semidirect
80. C₂×C₄⋊Dic₁₁	C₂²	semidirect
81. #66977	C₂²	semidirect
82. #66977	C₂²	semidirect
83. #66951	C₂²	semidirect
84. #66951	C₂²	semidirect
85. #66950	C₂²	semidirect
86. #66949	C₂²	semidirect
87. #66948	C₂²	semidirect
88. #66948	C₂²	semidirect
89. #66948	C₂²	semidirect
90. #66948	C₂²	semidirect
91. #66947	C₂²	semidirect
92. #66946	C₂²	semidirect
93. #66946	C₂²	semidirect
94. #66945	C₂²	semidirect
95. C₄⋊C₄×D₁₁	C₂²	semidirect
96. #66943	C₂²	semidirect
97. #66943	C₂²	semidirect
98. #66941	C₂²	semidirect
100. #66939	C₂²	semidirect
101. #66938	C₂²	semidirect
102. #66938	C₂²	semidirect
103. #66938	C₂²	semidirect
104. #66937	C₂²	semidirect
105. #66937	C₂²	semidirect
106. #66937	C₂²	semidirect
107. #66937	C₂²	semidirect
108. #66937	C₂²	semidirect
109. #66936	C₂²	semidirect
110. #66936	C₂²	semidirect
111. #66936	C₂²	semidirect
112. #66936	C₂²	semidirect
113. #66935	C₂²	semidirect
114. #66935	C₂²	semidirect
115. #66935	C₂²	semidirect
116. C₂²⋊C₄×D₁₁	C₂²	semidirect
117. #66931	C₂²	semidirect
118. #66930	C₂²	semidirect
119. #66929	C₂²	semidirect
120. #66928	C₂²	semidirect
121. C₄×D₄₄	C₂²	semidirect
122. #66925	C₂²	semidirect
328. #525	D₁₁	semidirect
376. C₂×#41	C₂×D₁₁	semidirect
381. C₂³×C₄	C₂×D₁₁	semidirect
407. #123	C₂×D₁₁	semidirect
414. C₂²⋊Q₈	C₂×D₁₁	semidirect
415. C₂²⋊Q₈	C₂×D₁₁	semidirect
440. #121	C₂×D₁₁	semidirect
449. #120	C₂×D₁₁	semidirect
460. C₄×D₄	C₂×D₁₁	semidirect
461. C₄×D₄	C₂×D₁₁	semidirect
466. #117	C₂×D₁₁	semidirect
591. C₁₁	#3542	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#525	2
#10623365	2
#10623360	2
#10623322	2
C₂×#66983	2
#10623198	2
#10623197	2
#10623174	2
#10623173	2
#10623161	2
#10623160	2
#10623150	2
#10623142	2
#10623140	2
#10623138	2
#10623123	2
#10623120	2
#10623093	2
#10623091	2
#10623087	2
#10623085	2
#10623063	2
#10623061	2
#3542	11