Subgroups — #13082346

Order 1408.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623360	C₂	1	2	yes	maximal, complemented
3	#10623355	C₂	1	2	yes	maximal, complemented
4	#10623264	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623260	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623250	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623246	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623210	C₂	1	2	yes	maximal, complemented
9	#10623201	C₂	1	2	yes	maximal, complemented
10	#10623141	C₂	1	2	yes	maximal, complemented
11	#10623137	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623132	C₂	1	2	yes	maximal, complemented
14	#10623131	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623127	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623093	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623092	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623087	C₂	1	2	yes	maximal, complemented
19	#10623077	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623076	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623071	C₂	1	2	yes	maximal, complemented
22	#10623010	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#66925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₁×#41	C₂²	1	2	yes	complemented
25	C₂×#4341	C₂²	1	1	yes	characteristic
26	C₂×#4341	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₁	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#127	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×#124	C₂²	1	2	yes	complemented
33	C₁₁×#121	C₂²	1	1	yes	characteristic
34	C₁₁×#121	C₂²	1	1	yes	characteristic, complemented
35	C₁₁×#121	C₂²	1	2	yes	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	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic, complemented
40	#67000	C₂²	1	2	yes	complemented
41	#66999	C₂²	1	2	yes	—
42	#66999	C₂²	1	2	yes	complemented
43	#66997	C₂²	1	2	yes	complemented
44	#66993	C₂²	1	1	yes	characteristic, complemented
45	#66992	C₂²	1	2	yes	—
46	#66992	C₂²	1	2	yes	complemented
47	#66992	C₂²	1	2	yes	complemented
48	#66992	C₂²	1	2	yes	complemented
49	#66992	C₂²	1	2	yes	complemented
50	#66992	C₂²	1	2	yes	complemented
51	#66991	C₂²	1	1	yes	characteristic
52	#66991	C₂²	1	1	yes	characteristic, complemented
53	#66990	C₂²	1	2	yes	—
54	#66990	C₂²	1	2	yes	—
55	#66990	C₂²	1	2	yes	—
56	#66989	C₂²	1	1	yes	characteristic, complemented
57	#66988	C₂²	1	2	yes	complemented
58	#66988	C₂²	1	2	yes	complemented
59	#66988	C₂²	1	2	yes	complemented
60	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
61	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₁₁	C₂²	1	2	yes	complemented
63	D₄×Dic₁₁	C₂²	1	2	yes	complemented
64	#66983	C₂²	1	1	yes	characteristic
65	#66983	C₂²	1	2	yes	complemented
66	#66982	C₂²	1	2	yes	complemented
67	#66982	C₂²	1	2	yes	complemented
68	#66982	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	1	yes	characteristic
73	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	1	yes	characteristic
74	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
75	#66977	C₂²	1	1	yes	characteristic, complemented
76	#66977	C₂²	1	2	yes	complemented
77	C₂×Dic₁₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₂×Dic₁₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
81	#66951	C₂²	1	2	yes	complemented
82	#66950	C₂²	1	1	yes	characteristic, complemented
83	#66949	C₂²	1	2	yes	—
84	#66948	C₂²	1	1	yes	characteristic
85	#66947	C₂²	1	2	yes	complemented
86	#66946	C₂²	1	1	yes	characteristic, complemented
87	#66945	C₂²	1	1	yes	characteristic
88	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
89	#66943	C₂²	1	1	yes	characteristic, complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66941	C₂²	1	1	yes	characteristic, complemented
92	#66940	C₂²	1	1	yes	characteristic, complemented
93	#66938	C₂²	1	2	yes	complemented
94	#66938	C₂²	1	2	yes	complemented
95	#66937	C₂²	1	2	yes	—
96	#66937	C₂²	1	2	yes	complemented
97	#66936	C₂²	1	2	yes	—
98	#66936	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
105	#66932	C₂²	1	2	yes	complemented
106	#66932	C₂²	1	2	yes	complemented
107	#66930	C₂²	1	2	yes	complemented
108	#66930	C₂²	1	2	yes	complemented
109	#66929	C₂²	1	2	yes	complemented
110	#66928	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
112	#66925	C₂²	1	1	yes	characteristic
113	#66925	C₂²	1	1	yes	characteristic
114	#66925	C₂²	1	1	yes	characteristic
115	#66925	C₂²	1	1	yes	characteristic
116	#66925	C₂²	1	1	yes	characteristic, complemented
117	#66925	C₂²	1	1	yes	characteristic, complemented
118	#66925	C₂²	1	1	yes	characteristic, complemented
119	#66925	C₂²	1	1	yes	characteristic, complemented
120	#66925	C₂²	1	2	yes	complemented
121	#66923	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	1	yes	characteristic
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₁₁×#41	—	4	4	no	—
126	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
127	C₂×D₄×C₁₁	C₂³	1	2	yes	—
128	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₁	C₂³	1	2	yes	—
132	C₂×D₄×C₁₁	C₂³	1	2	yes	—
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	2	yes	—
137	C₂²×C₄×C₁₁	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	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	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
145	C₂²×Dic₁₁	C₂³	1	2	yes	—
146	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₁	C₂³	1	2	yes	—
150	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
151	#4341	—	2	4	no	—
152	#4341	—	4	4	no	—
153	D₄×D₁₁	—	2	4	no	—
154	D₄×D₁₁	—	4	4	no	—
155	C₂×D₄₄	C₂³	1	1	yes	characteristic
156	C₂×D₄₄	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁	—	2	4	no	—
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	1	yes	characteristic
165	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₂	C₂³	1	2	yes	—
167	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₄²×C₁₁	C₂³	1	1	yes	characteristic
175	C₄²×C₁₁	C₂³	1	1	yes	characteristic
176	C₄²×C₁₁	C₂³	1	1	yes	characteristic
177	C₄²×C₁₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
185	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₁)⋊C₄	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	1	yes	characteristic
192	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
196	(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	2	yes	—
201	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₁	C₂³	1	2	yes	—
204	C₄⋊Dic₁₁	C₂³	1	2	yes	—
205	Dic₁₁⋊C₄	C₂³	1	2	yes	—
206	Dic₁₁⋊C₄	C₂³	1	2	yes	—
207	Dic₁₁⋊C₄	C₂³	1	2	yes	—
208	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	Dic₁₁⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₁₁	C₂³	1	2	yes	—
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	Q₈×C₁₁	—	4	2	no	—
242	D₄×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	4	no	—
244	D₄×C₁₁	—	2	2	no	—
245	D₄×C₁₁	—	2	2	no	—
246	D₄×C₁₁	—	4	2	no	—
247	D₄×C₁₁	—	4	2	no	—
248	C₂×C₄×C₁₁	—	2	2	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	4	1	no	—
251	C₂×C₄×C₁₁	—	4	2	no	—
252	C₂×C₄×C₁₁	—	4	2	no	—
253	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₁	—	2	4	no	—
262	C₂²⋊D₁₁	—	2	4	no	—
263	C₂²⋊D₁₁	—	2	4	no	—
264	C₂²⋊D₁₁	—	4	2	no	—
265	C₂²⋊D₁₁	—	4	2	no	—
266	C₂²⋊D₁₁	—	4	2	no	—
267	C₂²⋊D₁₁	—	4	2	no	—
268	C₂×Dic₁₁	—	2	2	no	—
269	C₂×Dic₁₁	—	2	2	no	—
270	C₂×Dic₁₁	—	2	4	no	—
271	C₂×Dic₁₁	—	4	2	no	—
272	C₂×Dic₁₁	—	4	2	no	—
273	C₂×Dic₁₁	—	4	1	no	—
274	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₁	C₂⁴	1	2	yes	—
279	C₂×Dic₁₁	C₂⁴	1	2	yes	—
280	C₂×Dic₁₁	C₂⁴	1	2	yes	—
281	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
283	D₄₄	—	2	2	no	—
284	D₄₄	—	4	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	#41	1	4	yes	complemented
292	Dic₂₂	—	2	2	no	—
293	Dic₂₂	—	4	2	no	—
294	#555	—	11	2	no	—
295	#553	—	11	2	no	—
296	#553	—	11	2	no	—
297	#551	—	11	2	no	—
298	#551	—	11	2	no	—
299	#547	—	11	2	no	—
300	#546	—	11	2	no	—
301	#546	—	11	2	no	—
302	#544	—	11	1	no	—
303	#542	—	11	1	no	—
304	#542	—	11	1	no	—
305	#540	—	11	1	no	—
306	#540	—	11	1	no	—
307	#535	—	11	1	no	—
308	#532	—	11	1	no	—
309	#532	D₁₁	1	1	yes	characteristic, complemented
310	#529	—	11	1	no	—
311	#529	—	11	1	no	—
312	#525	—	11	1	no	—
313	C₂×#121	—	11	1	no	—
314	#520	—	11	1	no	—
315	#518	—	11	1	no	—
316	C₂×#117	—	11	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	1	no	—
319	C₂²×C₁₁	—	2	2	no	—
320	C₂²×C₁₁	—	2	2	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	2	no	—
325	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
326	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
327	C₂×D₁₁	—	2	1	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	2	no	—
333	C₂×D₁₁	—	2	2	no	—
334	C₂×D₁₁	—	2	1	no	—
335	C₂×D₁₁	—	4	4	no	—
336	C₂×D₁₁	—	8	4	no	—
337	C₂×D₁₁	C₂×#41	1	2	yes	—
338	C₄×C₁₁	—	2	1	no	—
339	C₄×C₁₁	—	2	1	no	—
340	C₄×C₁₁	—	2	1	no	—
341	C₄×C₁₁	—	2	2	no	—
342	C₄×C₁₁	—	2	2	no	—
343	C₄×C₁₁	—	2	1	no	—
344	C₄×C₁₁	—	2	1	no	—
345	C₄×C₁₁	C₂×#41	1	2	yes	—
346	Dic₁₁	—	2	2	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	1	no	—
349	Dic₁₁	—	2	2	no	—
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	2	no	—
352	Dic₁₁	—	2	1	no	—
353	Dic₁₁	—	2	1	no	—
354	Dic₁₁	C₂×#41	1	2	yes	—
355	C₂×#41	—	11	1	no	—
356	C₂×#41	—	11	2	no	—
357	C₂×#41	C₂×D₁₁	1	2	yes	complemented
358	C₂²×D₄	—	11	1	no	—
359	C₂²×D₄	—	11	2	no	—
360	C₂³×C₄	—	11	1	no	—
361	C₄⋊Q₈	—	11	2	no	—
362	C₄⋊Q₈	—	11	1	no	—
363	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
364	#127	—	11	1	no	—
365	#127	C₂×D₁₁	1	1	yes	characteristic, complemented
366	#126	—	11	2	no	—
367	#126	—	11	2	no	—
368	#126	—	11	2	no	—
369	#126	—	11	2	no	—
370	#125	—	11	1	no	—
371	#125	—	11	2	no	—
372	#125	—	11	1	no	—
373	#124	—	11	2	no	—
374	#124	—	11	1	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	1	no	—
378	#124	C₂×D₁₁	1	2	yes	complemented
379	#123	—	11	2	no	—
380	#123	—	11	2	no	—
381	#123	—	11	2	no	—
382	#123	—	11	2	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	2	no	—
386	#123	—	11	2	no	—
387	#123	—	11	2	no	—
388	C₂²⋊Q₈	—	11	2	no	—
389	C₂²⋊Q₈	—	11	2	no	—
390	C₂²⋊Q₈	—	11	1	no	—
391	C₂²⋊Q₈	—	11	2	no	—
392	C₂²⋊Q₈	—	11	1	no	—
393	C₂²⋊Q₈	—	11	2	no	—
394	#121	—	11	1	no	—
395	#121	—	11	2	no	—
396	#121	—	11	1	no	—
397	#121	—	11	2	no	—
398	#121	—	11	2	no	—
399	#121	—	11	2	no	—
400	#121	—	11	2	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	2	no	—
407	#121	C₂×D₁₁	1	1	yes	characteristic
408	#121	C₂×D₁₁	1	1	yes	characteristic, complemented
409	#121	C₂×D₁₁	1	2	yes	complemented
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×D₄	—	11	1	no	—
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	2	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	2	no	—
422	C₄×D₄	—	11	1	no	—
423	C₄×D₄	—	11	2	no	—
424	C₄×D₄	—	11	2	no	—
425	C₄×D₄	—	11	2	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	1	no	—
428	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
429	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₁₁	1	2	yes	complemented
431	#117	—	11	1	no	—
432	#117	—	11	2	no	—
433	#117	—	11	2	no	—
434	#117	—	11	1	no	—
435	#117	—	11	1	no	—
436	#117	—	11	1	no	—
437	#117	—	11	1	no	—
438	#117	—	11	1	no	—
439	#117	—	11	1	no	—
440	#117	—	11	1	no	—
441	#117	—	11	1	no	—
442	#117	—	11	2	no	—
443	C₂×C₄⋊C₄	—	11	1	no	—
444	C₂×C₄⋊C₄	—	11	1	no	—
445	C₂×C₄⋊C₄	—	11	2	no	—
446	C₂×C₄⋊C₄	—	11	1	no	—
447	C₂×C₂²⋊C₄	—	11	1	no	—
448	C₂×C₂²⋊C₄	—	11	1	no	—
449	C₂×C₂²⋊C₄	—	11	2	no	—
450	C₂×C₂²⋊C₄	—	11	2	no	—
451	C₂×C₂²⋊C₄	—	11	2	no	—
452	C₂×C₄²	—	11	1	no	—
453	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic, complemented
454	C₂×C₁₁	—	2	2	no	—
455	C₂×C₁₁	—	4	2	no	—
456	C₂×C₁₁	—	4	2	no	—
457	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
458	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₁₁	#585	1	1	yes	characteristic
460	D₁₁	—	2	2	no	—
461	D₁₁	—	4	1	no	—
462	D₁₁	—	4	2	no	—
463	C₂⁴	—	11	1	no	—
464	C₂⁴	—	11	2	no	—
465	#41	—	4	4	no	—
466	#41	—	22	4	no	—
467	#41	—	44	4	no	—
468	C₂×Q₈	—	11	1	no	—
469	C₂×Q₈	—	11	2	no	—
470	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
471	C₂×D₄	—	11	2	no	—
472	C₂×D₄	—	11	2	no	—
473	C₂×D₄	—	11	2	no	—
474	C₂×D₄	—	11	2	no	—
475	C₂×D₄	—	11	2	no	—
476	C₂×D₄	—	11	2	no	—
477	C₂×D₄	—	11	2	no	—
478	C₂×D₄	—	11	1	no	—
479	C₂×D₄	—	11	2	no	—
480	C₂×D₄	—	22	4	no	—
481	C₂×D₄	—	44	4	no	—
482	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₁	1	2	yes	—
485	C₂×D₄	C₂²×D₁₁	1	2	yes	—
486	C₂×D₄	C₂²×D₁₁	1	2	yes	—
487	C₂×D₄	C₂²×D₁₁	1	2	yes	—
488	C₂²×C₄	—	11	1	no	—
489	C₂²×C₄	—	11	1	no	—
490	C₂²×C₄	—	11	1	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	1	no	—
493	C₂²×C₄	—	11	2	no	—
494	C₂²×C₄	—	11	2	no	—
495	C₂²×C₄	—	11	1	no	—
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	—	22	4	no	—
502	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
506	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
507	C₄⋊C₄	—	11	1	no	—
508	C₄⋊C₄	—	11	2	no	—
509	C₄⋊C₄	—	11	1	no	—
510	C₄⋊C₄	—	11	1	no	—
511	C₄⋊C₄	—	11	1	no	—
512	C₄⋊C₄	—	11	1	no	—
513	C₄⋊C₄	—	11	1	no	—
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	1	no	—
521	C₄⋊C₄	—	11	2	no	—
522	C₄⋊C₄	—	11	2	no	—
523	C₄⋊C₄	—	11	2	no	—
524	C₄⋊C₄	—	11	2	no	—
525	C₄⋊C₄	—	11	2	no	—
526	C₄⋊C₄	—	11	2	no	—
527	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
530	C₂²⋊C₄	—	11	2	no	—
531	C₂²⋊C₄	—	11	2	no	—
532	C₂²⋊C₄	—	11	2	no	—
533	C₂²⋊C₄	—	11	2	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	2	no	—
536	C₂²⋊C₄	—	11	2	no	—
537	C₂²⋊C₄	—	11	1	no	—
538	C₂²⋊C₄	—	11	1	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	1	no	—
541	C₂²⋊C₄	—	11	1	no	—
542	C₂²⋊C₄	—	11	1	no	—
543	C₂²⋊C₄	—	11	1	no	—
544	C₂²⋊C₄	—	11	1	no	—
545	C₂²⋊C₄	—	11	1	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	C₂²×D₁₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
557	C₄²	—	11	1	no	—
558	C₄²	—	11	1	no	—
559	C₄²	—	11	1	no	—
560	C₄²	—	11	1	no	—
561	C₄²	—	11	2	no	—
562	C₄²	—	11	2	no	—
563	C₄²	—	11	2	no	—
564	C₄²	C₂²×D₁₁	1	1	yes	characteristic
565	C₄²	C₂²×D₁₁	1	1	yes	characteristic
566	C₄²	C₂²×D₁₁	1	1	yes	characteristic
567	C₄²	C₂²×D₁₁	1	1	yes	characteristic
568	C₁₁	#3494	1	1	yes	characteristic, complemented, Sylow
569	C₂³	—	11	1	no	—
570	C₂³	—	11	2	no	—
571	C₂³	—	11	1	no	—
572	C₂³	—	22	2	no	—
573	C₂³	—	22	4	no	—
574	C₂³	—	22	2	no	—
575	C₂³	—	44	1	no	—
576	C₂³	—	44	2	no	—
577	C₂³	—	44	2	no	—
578	C₂³	C₂³×D₁₁	1	2	yes	—
579	C₂³	C₂³×D₁₁	1	2	yes	—
580	C₂³	C₂³×D₁₁	1	1	yes	characteristic
581	Q₈	—	4	2	no	—
582	Q₈	—	22	2	no	—
583	Q₈	—	44	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	22	4	no	—
591	D₄	—	22	4	no	—
592	D₄	—	22	4	no	—
593	D₄	—	22	2	no	—
594	D₄	—	44	2	no	—
595	D₄	—	44	2	no	—
596	D₄	—	44	2	no	—
597	D₄	—	44	2	no	—
598	D₄	—	44	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	11	1	no	—
605	C₂×C₄	—	11	4	no	—
606	C₂×C₄	—	11	1	no	—
607	C₂×C₄	—	11	2	no	—
608	C₂×C₄	—	11	1	no	—
609	C₂×C₄	—	11	1	no	—
610	C₂×C₄	—	11	1	no	—
611	C₂×C₄	—	11	2	no	—
612	C₂×C₄	—	11	2	no	—
613	C₂×C₄	—	11	1	no	—
614	C₂×C₄	—	22	2	no	—
615	C₂×C₄	—	22	2	no	—
616	C₂×C₄	—	22	2	no	—
617	C₂×C₄	—	22	4	no	—
618	C₂×C₄	—	22	2	no	—
619	C₂×C₄	—	22	2	no	—
620	C₂×C₄	—	44	2	no	—
621	C₂×C₄	—	44	2	no	—
622	C₂×C₄	—	44	2	no	—
623	C₂×C₄	—	44	2	no	—
624	C₂×C₄	—	44	2	no	—
625	C₂×C₄	—	44	1	no	—
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	2	yes	—
630	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	11	2	no	—
643	C₂²	—	22	1	no	—
644	C₂²	—	22	1	no	—
645	C₂²	—	22	2	no	—
646	C₂²	—	22	1	no	—
647	C₂²	—	22	1	no	—
648	C₂²	—	22	2	no	—
649	C₂²	—	22	2	no	—
650	C₂²	—	22	1	no	—
651	C₂²	—	44	4	no	—
652	C₂²	—	88	4	no	—
653	C₂²	#67037	1	2	yes	—
654	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	11	2	no	—
663	C₄	—	22	1	no	—
664	C₄	—	22	1	no	—
665	C₄	—	22	2	no	—
666	C₄	—	22	1	no	—
667	C₄	—	22	2	no	—
668	C₄	—	22	1	no	—
669	C₄	—	22	2	no	—
670	C₄	—	22	1	no	—
671	C₄	#41×D₁₁	1	2	yes	—
672	C₂	—	2	2	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	22	2	no	—
676	C₂	—	44	1	no	—
677	C₂	—	44	2	no	—
678	C₂	C₂×#67037	1	1	yes	characteristic
679	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
680	C₂	#10623453	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#532	C₂
hypercenter	#532	D₁₁
hypocenter	C₁₁	#3494
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₁₁×#532	C₂	semidirect
2. #10623360	C₂	semidirect
3. #10623355	C₂	semidirect
4. #10623264	C₂	semidirect
5. #10623260	C₂	semidirect
6. #10623250	C₂	semidirect
7. #10623246	C₂	semidirect
8. #10623210	C₂	semidirect
9. #10623201	C₂	semidirect
10. #10623141	C₂	semidirect
11. #10623137	C₂	semidirect
12. D₁₁×#121	C₂	semidirect
13. #10623132	C₂	semidirect
14. #10623131	C₂	semidirect
15. #10623127	C₂	semidirect
16. #10623093	C₂	semidirect
17. #10623092	C₂	semidirect
18. #10623087	C₂	semidirect
19. #10623077	C₂	semidirect
20. #10623076	C₂	semidirect
21. #10623071	C₂	semidirect
22. #10623010	C₂	semidirect
23. C₂×#66925	C₂	semidirect
24. C₂×C₁₁×#41	C₂²	semidirect
26. C₂×#4341	C₂²	semidirect
30. C₁₁×C₄⋊Q₈	C₂²	semidirect
31. C₁₁×#127	C₂²	semidirect
32. C₁₁×#124	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. C₂×C₄²×C₁₁	C₂²	semidirect
40. #67000	C₂²	semidirect
42. #66999	C₂²	semidirect
43. #66997	C₂²	semidirect
44. #66993	C₂²	semidirect
46. #66992	C₂²	semidirect
47. #66992	C₂²	semidirect
48. #66992	C₂²	semidirect
49. #66992	C₂²	semidirect
50. #66992	C₂²	semidirect
52. #66991	C₂²	semidirect
56. #66989	C₂²	semidirect
57. #66988	C₂²	semidirect
58. #66988	C₂²	semidirect
59. #66988	C₂²	semidirect
60. D₄×Dic₁₁	C₂²	semidirect
61. D₄×Dic₁₁	C₂²	semidirect
62. D₄×Dic₁₁	C₂²	semidirect
63. D₄×Dic₁₁	C₂²	semidirect
65. #66983	C₂²	semidirect
66. #66982	C₂²	semidirect
67. #66982	C₂²	semidirect
68. #66982	C₂²	semidirect
70. C₄×C₂²⋊D₁₁	C₂²	semidirect
71. C₄×C₂²⋊D₁₁	C₂²	semidirect
75. #66977	C₂²	semidirect
76. #66977	C₂²	semidirect
77. C₂×Dic₁₁⋊C₄	C₂²	semidirect
78. C₂×Dic₁₁⋊C₄	C₂²	semidirect
79. C₂×Dic₁₁⋊C₄	C₂²	semidirect
80. C₂×C₄×Dic₁₁	C₂²	semidirect
81. #66951	C₂²	semidirect
82. #66950	C₂²	semidirect
85. #66947	C₂²	semidirect
86. #66946	C₂²	semidirect
89. #66943	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66940	C₂²	semidirect
93. #66938	C₂²	semidirect
94. #66938	C₂²	semidirect
96. #66937	C₂²	semidirect
98. #66936	C₂²	semidirect
100. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
105. #66932	C₂²	semidirect
106. #66932	C₂²	semidirect
107. #66930	C₂²	semidirect
108. #66930	C₂²	semidirect
109. #66929	C₂²	semidirect
110. #66928	C₂²	semidirect
111. C₄×D₄₄	C₂²	semidirect
116. #66925	C₂²	semidirect
117. #66925	C₂²	semidirect
118. #66925	C₂²	semidirect
119. #66925	C₂²	semidirect
120. #66925	C₂²	semidirect
121. #66923	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
291. C₄×D₁₁	#41	semidirect
309. #532	D₁₁	semidirect
357. C₂×#41	C₂×D₁₁	semidirect
363. C₄⋊Q₈	C₂×D₁₁	semidirect
365. #127	C₂×D₁₁	semidirect
378. #124	C₂×D₁₁	semidirect
408. #121	C₂×D₁₁	semidirect
409. #121	C₂×D₁₁	semidirect
428. C₄×D₄	C₂×D₁₁	semidirect
429. C₄×D₄	C₂×D₁₁	semidirect
430. C₄×D₄	C₂×D₁₁	semidirect
453. C₂×C₄²	C₂×D₁₁	semidirect
568. 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×#532	2
#10623360	2
#10623355	2
#10623264	2
#10623260	2
#10623250	2
#10623246	2
#10623210	2
#10623201	2
#10623141	2
#10623137	2
D₁₁×#121	2
#10623132	2
#10623131	2
#10623127	2
#10623093	2
#10623092	2
#10623087	2
#10623077	2
#10623076	2
#10623071	2
#10623010	2
C₂×#66925	2
#3494	11