Subgroups — #13082673

Order 1408.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623358	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623355	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623329	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623211	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623202	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623196	C₂	1	2	yes	maximal, complemented
9	#10623181	C₂	1	2	yes	maximal, complemented
10	#10623172	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623156	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623149	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623134	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623132	C₂	1	2	yes	maximal, complemented
15	#10623131	C₂	1	2	yes	maximal, complemented
16	#10623124	C₂	1	2	yes	maximal, complemented
17	#10623118	C₂	1	2	yes	maximal, complemented
18	#10623088	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623070	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#4341	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623026	C₂	1	2	yes	maximal, complemented
23	C₂×#66932	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×#4341	C₂²	1	1	yes	characteristic
27	C₁₁×#124	C₂²	1	1	yes	characteristic
28	C₁₁×#123	C₂²	1	2	yes	—
29	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₁×#121	C₂²	1	2	yes	—
31	C₁₁×#121	C₂²	1	1	yes	characteristic
32	C₁₁×#120	C₂²	1	2	yes	—
33	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
36	#67006	C₂²	1	2	yes	—
37	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
38	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	—
40	#66999	C₂²	1	1	yes	characteristic, complemented
41	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
43	#66997	C₂²	1	1	yes	characteristic, complemented
44	#66992	C₂²	1	2	yes	—
45	#66992	C₂²	1	2	yes	complemented
46	#66992	C₂²	1	2	yes	complemented
47	#66991	C₂²	1	1	yes	characteristic
48	#66991	C₂²	1	1	yes	characteristic
49	#66989	C₂²	1	1	yes	characteristic
50	#66989	C₂²	1	1	yes	characteristic
51	#66989	C₂²	1	2	yes	complemented
52	#66988	C₂²	1	2	yes	—
53	#66988	C₂²	1	2	yes	—
54	#66988	C₂²	1	2	yes	complemented
55	#66988	C₂²	1	2	yes	complemented
56	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
57	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₁	C₂²	1	2	yes	—
60	D₄×Dic₁₁	C₂²	1	2	yes	—
61	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
62	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
63	D₄×Dic₁₁	C₂²	1	2	yes	complemented
64	D₄×Dic₁₁	C₂²	1	2	yes	complemented
65	D₄×Dic₁₁	C₂²	1	2	yes	complemented
66	#66982	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
70	#66979	C₂²	1	1	yes	characteristic
71	#66979	C₂²	1	1	yes	characteristic
72	#66979	C₂²	1	2	yes	complemented
73	#66979	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	complemented
75	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
76	#66977	C₂²	1	1	yes	characteristic
77	#66977	C₂²	1	2	yes	complemented
78	#66977	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
80	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₁₁	C₂²	1	2	yes	complemented
82	#66951	C₂²	1	2	yes	complemented
83	#66950	C₂²	1	1	yes	characteristic, complemented
84	#66945	C₂²	1	1	yes	characteristic, complemented
85	#66943	C₂²	1	1	yes	characteristic, complemented
86	#66943	C₂²	1	1	yes	characteristic, complemented
87	#66943	C₂²	1	2	yes	complemented
88	#66942	C₂²	1	2	yes	complemented
89	#66942	C₂²	1	2	yes	complemented
90	#66941	C₂²	1	1	yes	characteristic, complemented
91	#66940	C₂²	1	1	yes	characteristic, complemented
92	#66940	C₂²	1	2	yes	complemented
93	#66939	C₂²	1	2	yes	complemented
94	#66938	C₂²	1	2	yes	—
95	#66936	C₂²	1	1	yes	characteristic
96	#66936	C₂²	1	1	yes	characteristic, complemented
97	#66936	C₂²	1	2	yes	complemented
98	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
100	#66932	C₂²	1	1	yes	characteristic
101	#66932	C₂²	1	2	yes	—
102	#66932	C₂²	1	2	yes	—
103	#66932	C₂²	1	2	yes	—
104	#66932	C₂²	1	2	yes	—
105	#66932	C₂²	1	2	yes	complemented
106	#66932	C₂²	1	2	yes	complemented
107	#66932	C₂²	1	2	yes	complemented
108	#66932	C₂²	1	2	yes	complemented
109	#66932	C₂²	1	1	yes	characteristic, complemented
110	#66932	C₂²	1	2	yes	complemented
111	#66931	C₂²	1	2	yes	complemented
112	#66931	C₂²	1	2	yes	complemented
113	#66931	C₂²	1	2	yes	complemented
114	#66931	C₂²	1	2	yes	complemented
115	#66930	C₂²	1	2	yes	complemented
116	#66930	C₂²	1	2	yes	complemented
117	#66930	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
120	#66923	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₁	C₂³	1	2	yes	—
124	C₁₁×#41	—	2	4	no	—
125	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₁	—	2	4	no	—
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	2	yes	—
131	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₁	C₂³	1	2	yes	—
142	C₂²×Dic₁₁	C₂³	1	2	yes	—
143	C₂²×Dic₁₁	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	C₂²×Dic₁₁	C₂³	1	2	yes	—
148	#4341	—	2	4	no	—
149	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
152	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₂	C₂³	1	2	yes	—
155	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₄²×C₁₁	C₂³	1	1	yes	characteristic
166	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
183	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₁	C₂³	1	2	yes	—
193	C₄⋊Dic₁₁	C₂³	1	2	yes	—
194	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₁	C₂³	1	2	yes	—
196	C₄⋊Dic₁₁	C₂³	1	2	yes	—
197	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
199	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₁₁⋊C₄	C₂³	1	2	yes	—
201	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₁₁⋊C₄	C₂³	1	2	yes	—
203	Dic₁₁⋊C₄	C₂³	1	2	yes	—
204	Dic₁₁⋊C₄	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	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	2	yes	—
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₁	C₂³	1	2	yes	—
215	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
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	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₁	C₂³	1	2	yes	—
221	C₄×Dic₁₁	C₂³	1	2	yes	—
222	C₄×Dic₁₁	C₂³	1	2	yes	—
223	C₄×Dic₁₁	C₂³	1	2	yes	—
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	#3521	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	—	2	4	no	—
227	C₂³×C₁₁	—	4	2	no	—
228	C₂³×C₁₁	—	4	2	no	—
229	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₁	C₂⁴	1	2	yes	—
231	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₁	C₂⁴	1	2	yes	—
233	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
234	Q₈×C₁₁	—	2	2	no	—
235	D₄×C₁₁	—	2	4	no	—
236	D₄×C₁₁	—	2	4	no	—
237	D₄×C₁₁	—	2	2	no	—
238	D₄×C₁₁	—	4	2	no	—
239	D₄×C₁₁	—	4	1	no	—
240	D₄×C₁₁	#41	1	4	yes	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	4	2	no	—
245	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₁	—	2	4	no	—
253	C₂²⋊D₁₁	—	4	1	no	—
254	C₂²⋊D₁₁	—	4	1	no	—
255	C₂²⋊D₁₁	—	4	2	no	—
256	C₂×Dic₁₁	—	2	4	no	—
257	C₂×Dic₁₁	—	4	2	no	—
258	C₂×Dic₁₁	—	4	2	no	—
259	C₂×Dic₁₁	—	4	2	no	—
260	C₂×Dic₁₁	—	4	2	no	—
261	C₂×Dic₁₁	—	4	2	no	—
262	C₂×Dic₁₁	—	4	2	no	—
263	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₁	C₂⁴	1	2	yes	—
266	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₁	C₂⁴	1	2	yes	—
269	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₁	C₂⁴	1	2	yes	—
271	C₂×Dic₁₁	C₂⁴	1	2	yes	—
272	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
274	C₄×D₁₁	—	2	2	no	—
275	C₄×D₁₁	—	4	1	no	—
276	C₄×D₁₁	—	4	1	no	—
277	Dic₂₂	—	2	2	no	—
278	Dic₂₂	—	4	2	no	—
279	Dic₂₂	—	4	1	no	—
280	#556	—	11	1	no	—
281	#556	—	11	1	no	—
282	#554	—	11	1	no	—
283	#553	—	11	2	no	—
284	#553	—	11	1	no	—
285	#552	—	11	2	no	—
286	#552	—	11	1	no	—
287	#551	—	11	2	no	—
288	#551	—	11	2	no	—
289	#547	—	11	1	no	—
290	#546	—	11	1	no	—
291	#546	D₁₁	1	1	yes	characteristic, complemented
292	#542	—	11	1	no	—
293	#541	—	11	1	no	—
294	#539	—	11	2	no	—
295	#538	—	11	2	no	—
296	#529	—	11	1	no	—
297	#529	—	11	2	no	—
298	#529	—	11	1	no	—
299	C₂×#126	—	11	2	no	—
300	#520	—	11	1	no	—
301	#518	—	11	1	no	—
302	C₄×#41	—	11	1	no	—
303	C₂²×C₁₁	—	2	2	no	—
304	C₂²×C₁₁	—	2	2	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	—	2	1	no	—
307	C₂²×C₁₁	—	2	2	no	—
308	C₂²×C₁₁	—	2	1	no	—
309	C₂²×C₁₁	—	2	1	no	—
310	C₂²×C₁₁	—	2	2	no	—
311	C₂²×C₁₁	—	2	1	no	—
312	C₂²×C₁₁	—	2	1	no	—
313	C₂²×C₁₁	—	2	2	no	—
314	C₂²×C₁₁	—	8	4	no	—
315	C₂²×C₁₁	C₂×#41	1	4	yes	—
316	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
317	C₂×D₁₁	—	2	1	no	—
318	C₂×D₁₁	—	2	1	no	—
319	C₂×D₁₁	—	2	1	no	—
320	C₄×C₁₁	—	2	1	no	—
321	C₄×C₁₁	—	2	1	no	—
322	C₄×C₁₁	—	2	2	no	—
323	C₄×C₁₁	—	2	1	no	—
324	C₄×C₁₁	—	2	2	no	—
325	C₄×C₁₁	—	2	1	no	—
326	C₄×C₁₁	C₂×#41	1	2	yes	—
327	Dic₁₁	—	2	2	no	—
328	Dic₁₁	—	2	1	no	—
329	Dic₁₁	—	2	1	no	—
330	Dic₁₁	—	2	1	no	—
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	—	2	2	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	—	2	1	no	—
335	Dic₁₁	—	2	2	no	—
336	Dic₁₁	—	2	2	no	—
337	Dic₁₁	—	2	1	no	—
338	C₂×#41	—	11	1	no	—
339	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
340	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
341	C₄⋊Q₈	—	11	1	no	—
342	C₄⋊Q₈	—	11	1	no	—
343	#126	—	11	2	no	—
344	#126	—	11	1	no	—
345	#126	—	11	2	no	—
346	#126	—	11	2	no	—
347	#126	—	11	2	no	—
348	#126	—	11	2	no	—
349	#126	—	11	2	no	—
350	#126	—	11	2	no	—
351	#126	—	11	2	no	—
352	#126	—	11	1	no	—
353	#126	—	11	2	no	—
354	#126	—	11	2	no	—
355	#125	—	11	2	no	—
356	#125	—	11	1	no	—
357	#125	—	11	2	no	—
358	#125	—	11	2	no	—
359	#125	—	11	1	no	—
360	#125	—	11	1	no	—
361	#124	—	11	2	no	—
362	#124	—	11	1	no	—
363	#124	—	11	1	no	—
364	#124	—	11	2	no	—
365	#124	C₂×D₁₁	1	1	yes	characteristic
366	#123	—	11	2	no	—
367	#123	—	11	2	no	—
368	#123	—	11	2	no	—
369	#123	—	11	2	no	—
370	#123	—	11	2	no	—
371	#123	—	11	2	no	—
372	#123	—	11	1	no	—
373	#123	—	11	1	no	—
374	#123	—	11	2	no	—
375	#123	C₂×D₁₁	1	2	yes	—
376	C₂²⋊Q₈	—	11	1	no	—
377	C₂²⋊Q₈	—	11	2	no	—
378	C₂²⋊Q₈	—	11	1	no	—
379	C₂²⋊Q₈	—	11	1	no	—
380	C₂²⋊Q₈	—	11	1	no	—
381	C₂²⋊Q₈	—	11	2	no	—
382	C₂²⋊Q₈	—	11	2	no	—
383	C₂²⋊Q₈	—	11	2	no	—
384	C₂²⋊Q₈	—	11	2	no	—
385	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
386	#121	—	11	1	no	—
387	#121	—	11	1	no	—
388	#121	—	11	2	no	—
389	#121	—	11	2	no	—
390	#121	—	11	2	no	—
391	#121	C₂×D₁₁	1	2	yes	—
392	#121	C₂×D₁₁	1	1	yes	characteristic
393	#120	—	11	2	no	—
394	#120	C₂×D₁₁	1	2	yes	—
395	C₄×Q₈	—	11	1	no	—
396	C₄×Q₈	—	11	1	no	—
397	C₄×Q₈	—	11	1	no	—
398	C₄×Q₈	—	11	2	no	—
399	C₄×Q₈	—	11	1	no	—
400	C₄×Q₈	—	11	1	no	—
401	C₄×D₄	—	11	1	no	—
402	C₄×D₄	—	11	2	no	—
403	C₄×D₄	—	11	1	no	—
404	C₄×D₄	—	11	1	no	—
405	C₄×D₄	—	11	2	no	—
406	C₄×D₄	—	11	1	no	—
407	C₄×D₄	—	11	2	no	—
408	C₄×D₄	—	11	1	no	—
409	C₄×D₄	—	11	2	no	—
410	C₄×D₄	—	11	2	no	—
411	C₄×D₄	—	11	2	no	—
412	C₄×D₄	—	11	1	no	—
413	C₄×D₄	—	11	1	no	—
414	C₄×D₄	—	11	2	no	—
415	C₄×D₄	—	11	2	no	—
416	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
417	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
418	#117	—	11	1	no	—
419	#117	—	11	1	no	—
420	#117	—	11	1	no	—
421	#117	—	11	2	no	—
422	#117	—	11	1	no	—
423	#117	—	11	2	no	—
424	#117	—	11	2	no	—
425	#117	—	11	2	no	—
426	#117	—	11	2	no	—
427	C₂×C₄⋊C₄	—	11	2	no	—
428	C₂×C₄⋊C₄	—	11	1	no	—
429	C₂×C₄⋊C₄	—	11	2	no	—
430	C₂×C₄⋊C₄	—	11	2	no	—
431	C₂×C₂²⋊C₄	—	11	2	no	—
432	C₂×C₂²⋊C₄	—	11	2	no	—
433	C₂×C₂²⋊C₄	—	11	2	no	—
434	C₂×C₂²⋊C₄	C₂×D₁₁	1	2	yes	—
435	C₂×C₄²	—	11	2	no	—
436	C₂×C₄²	—	11	1	no	—
437	C₂×C₁₁	—	2	4	no	—
438	C₂×C₁₁	—	4	1	no	—
439	C₂×C₁₁	—	4	2	no	—
440	C₂×C₁₁	—	4	1	no	—
441	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
442	C₂×C₁₁	#585	1	1	yes	characteristic
443	C₂×C₁₁	#585	1	1	yes	characteristic
444	D₁₁	—	4	1	no	—
445	C₂⁴	C₂²×D₁₁	1	2	yes	—
446	#41	—	2	4	no	—
447	#41	—	22	4	no	—
448	C₂×Q₈	—	11	1	no	—
449	C₂×Q₈	—	11	1	no	—
450	C₂×Q₈	—	11	2	no	—
451	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	11	2	no	—
454	C₂×D₄	—	11	1	no	—
455	C₂×D₄	—	11	2	no	—
456	C₂×D₄	—	11	1	no	—
457	C₂×D₄	C₂²×D₁₁	1	2	yes	—
458	C₂×D₄	C₂²×D₁₁	1	2	yes	—
459	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
460	C₂×D₄	C₂²×D₁₁	1	2	yes	—
461	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
462	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
463	C₂²×C₄	—	11	2	no	—
464	C₂²×C₄	—	11	2	no	—
465	C₂²×C₄	—	11	2	no	—
466	C₂²×C₄	—	11	2	no	—
467	C₂²×C₄	—	11	2	no	—
468	C₂²×C₄	—	11	2	no	—
469	C₂²×C₄	—	11	2	no	—
470	C₂²×C₄	—	11	1	no	—
471	C₂²×C₄	—	11	1	no	—
472	C₂²×C₄	—	11	1	no	—
473	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
477	C₄⋊C₄	—	11	1	no	—
478	C₄⋊C₄	—	11	2	no	—
479	C₄⋊C₄	—	11	1	no	—
480	C₄⋊C₄	—	11	1	no	—
481	C₄⋊C₄	—	11	1	no	—
482	C₄⋊C₄	—	11	2	no	—
483	C₄⋊C₄	—	11	2	no	—
484	C₄⋊C₄	—	11	1	no	—
485	C₄⋊C₄	—	11	2	no	—
486	C₄⋊C₄	—	11	2	no	—
487	C₄⋊C₄	—	11	2	no	—
488	C₄⋊C₄	—	11	2	no	—
489	C₄⋊C₄	—	11	2	no	—
490	C₄⋊C₄	—	11	2	no	—
491	C₄⋊C₄	—	11	1	no	—
492	C₄⋊C₄	—	11	1	no	—
493	C₄⋊C₄	—	11	1	no	—
494	C₄⋊C₄	—	11	1	no	—
495	C₄⋊C₄	—	11	1	no	—
496	C₄⋊C₄	—	11	2	no	—
497	C₄⋊C₄	—	11	2	no	—
498	C₄⋊C₄	—	11	2	no	—
499	C₄⋊C₄	—	11	2	no	—
500	C₄⋊C₄	—	11	2	no	—
501	C₄⋊C₄	—	11	1	no	—
502	C₄⋊C₄	—	11	2	no	—
503	C₄⋊C₄	—	11	1	no	—
504	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
507	C₂²⋊C₄	—	11	1	no	—
508	C₂²⋊C₄	—	11	2	no	—
509	C₂²⋊C₄	—	11	1	no	—
510	C₂²⋊C₄	—	11	1	no	—
511	C₂²⋊C₄	—	11	2	no	—
512	C₂²⋊C₄	—	11	2	no	—
513	C₂²⋊C₄	—	11	2	no	—
514	C₂²⋊C₄	—	11	2	no	—
515	C₂²⋊C₄	—	11	2	no	—
516	C₂²⋊C₄	—	11	2	no	—
517	C₂²⋊C₄	—	11	2	no	—
518	C₂²⋊C₄	—	11	2	no	—
519	C₂²⋊C₄	—	11	1	no	—
520	C₂²⋊C₄	—	11	1	no	—
521	C₂²⋊C₄	—	11	2	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	1	no	—
524	C₂²⋊C₄	—	11	2	no	—
525	C₂²⋊C₄	—	11	1	no	—
526	C₂²⋊C₄	—	11	2	no	—
527	C₂²⋊C₄	—	11	1	no	—
528	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
529	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
535	C₄²	—	11	1	no	—
536	C₄²	—	11	1	no	—
537	C₄²	—	11	1	no	—
538	C₄²	—	11	2	no	—
539	C₄²	—	11	2	no	—
540	C₄²	—	11	2	no	—
541	C₄²	—	11	2	no	—
542	C₄²	—	11	2	no	—
543	C₄²	—	11	2	no	—
544	C₄²	—	11	1	no	—
545	C₄²	—	11	1	no	—
546	C₄²	C₂²×D₁₁	1	1	yes	characteristic
547	C₁₁	#3521	1	1	yes	characteristic, complemented, Sylow
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	11	1	no	—
552	C₂³	C₂³×D₁₁	1	1	yes	characteristic
553	C₂³	C₂³×D₁₁	1	2	yes	—
554	C₂³	C₂³×D₁₁	1	1	yes	characteristic
555	C₂³	C₂³×D₁₁	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	22	2	no	—
558	Q₈	—	44	1	no	—
559	Q₈	—	44	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	2	no	—
565	D₄	—	22	4	no	—
566	D₄	—	44	2	no	—
567	D₄	—	44	1	no	—
568	D₄	—	44	1	no	—
569	D₄	#4341	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	11	1	no	—
575	C₂×C₄	—	11	1	no	—
576	C₂×C₄	—	11	2	no	—
577	C₂×C₄	—	11	1	no	—
578	C₂×C₄	—	11	1	no	—
579	C₂×C₄	—	11	2	no	—
580	C₂×C₄	—	11	1	no	—
581	C₂×C₄	—	11	1	no	—
582	C₂×C₄	—	11	2	no	—
583	C₂×C₄	—	11	2	no	—
584	C₂×C₄	—	11	1	no	—
585	C₂×C₄	—	22	4	no	—
586	C₂×C₄	—	22	2	no	—
587	C₂×C₄	—	44	1	no	—
588	C₂×C₄	—	44	1	no	—
589	C₂×C₄	—	44	2	no	—
590	C₂×C₄	—	44	2	no	—
591	C₂×C₄	—	44	2	no	—
592	C₂×C₄	—	44	2	no	—
593	C₂×C₄	—	44	2	no	—
594	C₂×C₄	—	44	2	no	—
595	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₁	1	2	yes	—
597	C₂×C₄	C₂³×D₁₁	1	2	yes	—
598	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	22	1	no	—
615	C₂²	—	22	1	no	—
616	C₂²	—	22	1	no	—
617	C₂²	C₂×#4341	1	4	yes	—
618	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	22	1	no	—
626	C₄	—	22	2	no	—
627	C₄	—	22	1	no	—
628	C₄	—	22	2	no	—
629	C₄	—	22	2	no	—
630	C₄	—	22	1	no	—
631	C₄	—	22	1	no	—
632	C₄	—	22	1	no	—
633	C₄	—	22	1	no	—
634	C₄	—	22	2	no	—
635	C₄	—	22	1	no	—
636	C₄	C₂×#4341	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	44	1	no	—
642	C₂	C₂²×#4341	1	1	yes	characteristic
643	C₂	#10623453	1	1	yes	characteristic
644	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#546	C₂
hypercenter	#546	D₁₁
hypocenter	C₁₁	#3521
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₁₁×#546	C₂	semidirect
2. #10623358	C₂	semidirect
3. #10623355	C₂	semidirect
4. #10623337	C₂	semidirect
5. #10623329	C₂	semidirect
6. #10623211	C₂	semidirect
7. #10623202	C₂	semidirect
8. #10623196	C₂	semidirect
9. #10623181	C₂	semidirect
10. #10623172	C₂	semidirect
11. #10623156	C₂	semidirect
12. #10623149	C₂	semidirect
13. #10623134	C₂	semidirect
14. #10623132	C₂	semidirect
15. #10623131	C₂	semidirect
16. #10623124	C₂	semidirect
17. #10623118	C₂	semidirect
18. #10623088	C₂	semidirect
19. #10623072	C₂	semidirect
20. #10623070	C₂	semidirect
21. C₄×#4341	C₂	semidirect
22. #10623026	C₂	semidirect
23. C₂×#66932	C₂	semidirect
40. #66999	C₂²	semidirect
41. Q₈×Dic₁₁	C₂²	semidirect
42. Q₈×Dic₁₁	C₂²	semidirect
43. #66997	C₂²	semidirect
45. #66992	C₂²	semidirect
46. #66992	C₂²	semidirect
51. #66989	C₂²	semidirect
54. #66988	C₂²	semidirect
55. #66988	C₂²	semidirect
63. D₄×Dic₁₁	C₂²	semidirect
64. D₄×Dic₁₁	C₂²	semidirect
65. D₄×Dic₁₁	C₂²	semidirect
66. #66982	C₂²	semidirect
68. C₄×C₂²⋊D₁₁	C₂²	semidirect
69. C₄×C₂²⋊D₁₁	C₂²	semidirect
72. #66979	C₂²	semidirect
73. #66979	C₂²	semidirect
74. C₂×C₄⋊Dic₁₁	C₂²	semidirect
75. C₂×C₄⋊Dic₁₁	C₂²	semidirect
77. #66977	C₂²	semidirect
78. #66977	C₂²	semidirect
79. C₂×Dic₁₁⋊C₄	C₂²	semidirect
80. C₂×Dic₁₁⋊C₄	C₂²	semidirect
81. C₂×C₄×Dic₁₁	C₂²	semidirect
82. #66951	C₂²	semidirect
83. #66950	C₂²	semidirect
84. #66945	C₂²	semidirect
85. #66943	C₂²	semidirect
86. #66943	C₂²	semidirect
87. #66943	C₂²	semidirect
88. #66942	C₂²	semidirect
89. #66942	C₂²	semidirect
90. #66941	C₂²	semidirect
91. #66940	C₂²	semidirect
92. #66940	C₂²	semidirect
93. #66939	C₂²	semidirect
96. #66936	C₂²	semidirect
97. #66936	C₂²	semidirect
98. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
105. #66932	C₂²	semidirect
106. #66932	C₂²	semidirect
107. #66932	C₂²	semidirect
108. #66932	C₂²	semidirect
109. #66932	C₂²	semidirect
110. #66932	C₂²	semidirect
111. #66931	C₂²	semidirect
112. #66931	C₂²	semidirect
113. #66931	C₂²	semidirect
114. #66931	C₂²	semidirect
115. #66930	C₂²	semidirect
116. #66930	C₂²	semidirect
117. #66930	C₂²	semidirect
118. #66930	C₂²	semidirect
119. C₄²×D₁₁	C₂²	semidirect
120. #66923	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
291. #546	D₁₁	semidirect
547. C₁₁	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#546	2
#10623358	2
#10623355	2
#10623337	2
#10623329	2
#10623211	2
#10623202	2
#10623196	2
#10623181	2
#10623172	2
#10623156	2
#10623149	2
#10623134	2
#10623132	2
#10623131	2
#10623124	2
#10623118	2
#10623088	2
#10623072	2
#10623070	2
C₄×#4341	2
#10623026	2
C₂×#66932	2
#3521	11