Subgroups — #13083131

Order 1408.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623264	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623256	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623235	C₂	1	2	yes	maximal, complemented
5	#10623235	C₂	1	2	yes	maximal, complemented
6	#10623214	C₂	1	2	yes	maximal, complemented
7	#10623207	C₂	1	2	yes	maximal, complemented
8	#10623205	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623188	C₂	1	2	yes	maximal, complemented
11	#10623184	C₂	1	2	yes	maximal, complemented
12	#10623178	C₂	1	2	yes	maximal, complemented
13	#10623164	C₂	1	1	yes	maximal, characteristic, complemented
14	#10623161	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623161	C₂	1	2	yes	maximal, complemented
16	#10623143	C₂	1	1	yes	maximal, characteristic, complemented
17	#10623140	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623116	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623107	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623090	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×D₄₄	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623059	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623056	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#4343	C₂²	1	2	yes	complemented
25	C₂×#4343	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₁	C₂²	1	2	yes	complemented
30	C₂×#4339	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₄₄	C₂²	1	2	yes	complemented
33	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#126	C₂²	1	2	yes	complemented
35	C₁₁×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×#124	C₂²	1	2	yes	complemented
37	C₁₁×#123	C₂²	1	2	yes	complemented
38	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₁×#121	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
43	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
44	#67000	C₂²	1	2	yes	complemented
45	#67000	C₂²	1	2	yes	complemented
46	#67000	C₂²	1	1	yes	characteristic, complemented
47	#67000	C₂²	1	1	yes	characteristic, complemented
48	#66999	C₂²	1	2	yes	complemented
49	#66993	C₂²	1	1	yes	characteristic
50	#66991	C₂²	1	2	yes	complemented
51	#66990	C₂²	1	2	yes	complemented
52	#66990	C₂²	1	2	yes	complemented
53	#66989	C₂²	1	1	yes	characteristic, complemented
54	#66983	C₂²	1	2	yes	complemented
55	#66982	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
59	#66951	C₂²	1	1	yes	characteristic, complemented
60	#66951	C₂²	1	2	yes	complemented
61	#66950	C₂²	1	1	yes	characteristic, complemented
62	#66950	C₂²	1	2	yes	complemented
63	#66949	C₂²	1	1	yes	characteristic, complemented
64	#66949	C₂²	1	2	yes	complemented
65	#66948	C₂²	1	1	yes	characteristic
66	#66948	C₂²	1	2	yes	complemented
67	#66948	C₂²	1	2	yes	complemented
68	#66948	C₂²	1	2	yes	complemented
69	#66948	C₂²	1	1	yes	characteristic, complemented
70	#66948	C₂²	1	1	yes	characteristic, complemented
71	#66948	C₂²	1	2	yes	complemented
72	#66948	C₂²	1	2	yes	complemented
73	#66947	C₂²	1	2	yes	complemented
74	#66947	C₂²	1	2	yes	complemented
75	#66947	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
80	#66946	C₂²	1	1	yes	characteristic, complemented
81	#66946	C₂²	1	1	yes	characteristic, complemented
82	#66946	C₂²	1	1	yes	characteristic, complemented
83	#66942	C₂²	1	1	yes	characteristic, complemented
84	#66940	C₂²	1	1	yes	characteristic, complemented
85	#66938	C₂²	1	2	yes	complemented
86	#66938	C₂²	1	2	yes	complemented
87	#66938	C₂²	1	1	yes	characteristic, complemented
88	#66938	C₂²	1	2	yes	complemented
89	#66938	C₂²	1	2	yes	complemented
90	#66937	C₂²	1	1	yes	characteristic
91	#66937	C₂²	1	2	yes	complemented
92	#66937	C₂²	1	2	yes	complemented
93	#66937	C₂²	1	2	yes	complemented
94	#66937	C₂²	1	2	yes	complemented
95	#66936	C₂²	1	2	yes	complemented
96	#66936	C₂²	1	2	yes	complemented
97	#66936	C₂²	1	1	yes	characteristic, complemented
98	#66935	C₂²	1	2	yes	complemented
99	#66935	C₂²	1	2	yes	complemented
100	#66935	C₂²	1	2	yes	complemented
101	#66935	C₂²	1	2	yes	complemented
102	#66935	C₂²	1	2	yes	complemented
103	#66935	C₂²	1	2	yes	complemented
104	#66935	C₂²	1	2	yes	complemented
105	#66935	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	complemented
110	#66932	C₂²	1	1	yes	characteristic, complemented
111	#66928	C₂²	1	2	yes	complemented
112	#66928	C₂²	1	2	yes	complemented
113	#66928	C₂²	1	1	yes	characteristic, complemented
114	#66928	C₂²	1	1	yes	characteristic, complemented
115	#66927	C₂²	1	1	yes	characteristic
116	#66927	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄₄	C₂²	1	2	yes	complemented
118	C₄×D₄₄	C₂²	1	2	yes	complemented
119	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
120	#66925	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₁₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁	C₂³	1	2	yes	—
124	C₂³×D₁₁	C₂³	1	2	yes	—
125	C₂³×D₁₁	C₂³	1	2	yes	—
126	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
128	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
139	#4343	—	4	2	no	—
140	#4343	—	4	4	no	—
141	Q₈×D₁₁	—	4	2	no	—
142	D₄×D₁₁	—	4	2	no	—
143	D₄×D₁₁	—	4	2	no	—
144	D₄×D₁₁	—	4	4	no	—
145	#4339	—	4	2	no	—
146	C₂×D₄₄	—	4	2	no	—
147	C₂×D₄₄	—	4	4	no	—
148	C₂×D₄₄	C₂³	1	2	yes	—
149	C₂×D₄₄	C₂³	1	1	yes	characteristic
150	C₂×D₄₄	C₂³	1	1	yes	characteristic
151	C₂×D₄₄	C₂³	1	1	yes	characteristic
152	C₂×D₄₄	C₂³	1	1	yes	characteristic
153	C₂×D₄₄	C₂³	1	2	yes	—
154	C₂×D₄₄	C₂³	1	2	yes	—
155	C₂×D₄₄	C₂³	1	2	yes	—
156	C₂×D₄₄	C₂³	1	2	yes	—
157	C₂×D₄₄	C₂³	1	2	yes	—
158	C₂×D₄₄	C₂³	1	2	yes	—
159	C₂×D₄₄	C₂³	1	2	yes	—
160	C₂×D₄₄	C₂³	1	2	yes	—
161	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₁	C₂³	1	2	yes	—
166	C₂×C₄×D₁₁	C₂³	1	2	yes	—
167	C₂×C₄×D₁₁	C₂³	1	2	yes	—
168	C₂×C₄×D₁₁	C₂³	1	2	yes	—
169	C₂×C₄×D₁₁	C₂³	1	2	yes	—
170	C₂×C₄×D₁₁	C₂³	1	2	yes	—
171	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
172	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
173	C₂×Dic₂₂	C₂³	1	2	yes	—
174	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
180	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
187	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₄²×C₁₁	C₂³	1	1	yes	characteristic
189	C₄²×C₁₁	C₂³	1	1	yes	characteristic
190	C₄²×C₁₁	C₂³	1	2	yes	—
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	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	1	yes	characteristic
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	2	yes	—
204	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
212	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₁₁)⋊C₄	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	2	yes	—
219	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₁₁⋊C₄	C₂³	1	2	yes	—
225	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₁	C₂³	1	2	yes	—
231	#3558	—	11	1	no	maximal, Sylow
232	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₁	C₂⁴	1	2	yes	—
234	C₂²×D₁₁	—	2	4	no	—
235	C₂²×D₁₁	—	4	2	no	—
236	C₂²×D₁₁	—	4	2	no	—
237	C₂²×D₁₁	—	4	2	no	—
238	C₂²×D₁₁	—	4	2	no	—
239	C₂²×D₁₁	—	4	2	no	—
240	C₂²×D₁₁	—	4	2	no	—
241	C₂²×D₁₁	—	4	2	no	—
242	C₂²×D₁₁	—	4	2	no	—
243	C₂²×D₁₁	C₂⁴	1	2	yes	—
244	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₁	C₂⁴	1	2	yes	—
246	C₂²×D₁₁	C₂⁴	1	2	yes	—
247	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
248	Q₈×C₁₁	—	2	2	no	—
249	Q₈×C₁₁	—	4	2	no	—
250	D₄×C₁₁	—	2	2	no	—
251	D₄×C₁₁	—	4	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	4	2	no	—
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
261	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₁₁	—	2	2	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	C₂²⋊D₁₁	—	4	1	no	—
269	C₂²⋊D₁₁	—	4	2	no	—
270	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
277	D₄₄	—	2	2	no	—
278	D₄₄	—	2	4	no	—
279	D₄₄	—	2	4	no	—
280	D₄₄	—	2	2	no	—
281	D₄₄	—	2	2	no	—
282	D₄₄	—	2	2	no	—
283	D₄₄	—	4	2	no	—
284	D₄₄	—	4	2	no	—
285	D₄₄	—	4	2	no	—
286	D₄₄	—	4	2	no	—
287	D₄₄	—	4	2	no	—
288	D₄₄	—	4	2	no	—
289	D₄₄	—	4	2	no	—
290	C₄×D₁₁	—	2	2	no	—
291	C₄×D₁₁	—	2	2	no	—
292	C₄×D₁₁	—	2	2	no	—
293	C₄×D₁₁	—	4	1	no	—
294	C₄×D₁₁	—	4	2	no	—
295	C₄×D₁₁	—	4	2	no	—
296	C₄×D₁₁	—	4	2	no	—
297	C₄×D₁₁	—	4	2	no	—
298	C₄×D₁₁	—	4	2	no	—
299	C₄×D₁₁	—	4	2	no	—
300	Dic₂₂	—	2	2	no	—
301	Dic₂₂	—	4	1	no	—
302	Dic₂₂	—	4	2	no	—
303	#562	—	11	2	no	—
304	H(3,𝔽₄)	—	11	2	no	—
305	#559	—	11	1	no	—
306	#559	—	11	1	no	—
307	#548	—	11	1	no	—
308	#548	—	11	1	no	—
309	#546	—	11	2	no	—
310	#546	—	11	2	no	—
311	#546	—	11	1	no	—
312	#546	—	11	1	no	—
313	D₄²	—	11	1	no	—
314	D₄²	—	11	1	no	—
315	#542	—	11	1	no	—
316	#542	D₁₁	1	1	yes	characteristic, complemented
317	#538	—	11	2	no	—
318	#538	—	11	2	no	—
319	#538	—	11	2	no	—
320	#535	—	11	1	no	—
321	#535	—	11	1	no	—
322	#534	—	11	2	no	—
323	#532	—	11	1	no	—
324	#529	—	11	1	no	—
325	C₂×#124	—	11	1	no	—
326	C₂²×C₁₁	—	2	1	no	—
327	C₂²×C₁₁	—	2	2	no	—
328	C₂²×C₁₁	—	2	2	no	—
329	C₂²×C₁₁	—	2	1	no	—
330	C₂²×C₁₁	—	2	2	no	—
331	C₂²×C₁₁	—	2	1	no	—
332	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
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	1	no	—
338	C₂×D₁₁	—	2	2	no	—
339	C₂×D₁₁	—	2	2	no	—
340	C₂×D₁₁	—	2	2	no	—
341	C₂×D₁₁	—	2	2	no	—
342	C₂×D₁₁	—	2	2	no	—
343	C₂×D₁₁	—	2	2	no	—
344	C₂×D₁₁	—	2	1	no	—
345	C₂×D₁₁	—	2	2	no	—
346	C₂×D₁₁	—	2	2	no	—
347	C₂×D₁₁	—	8	4	no	—
348	C₂×D₁₁	—	8	4	no	—
349	C₂×D₁₁	—	8	4	no	—
350	C₂×D₁₁	H(5,𝔽₂)	1	2	yes	—
351	C₄×C₁₁	—	2	1	no	—
352	C₄×C₁₁	—	2	1	no	—
353	C₄×C₁₁	—	2	2	no	—
354	C₄×C₁₁	—	2	2	no	—
355	C₄×C₁₁	—	2	2	no	—
356	C₄×C₁₁	—	2	1	no	—
357	C₄×C₁₁	—	2	1	no	—
358	C₄×C₁₁	—	2	1	no	—
359	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
360	Dic₁₁	—	2	2	no	—
361	Dic₁₁	—	2	1	no	—
362	Dic₁₁	—	2	1	no	—
363	Dic₁₁	—	2	1	no	—
364	Dic₁₁	—	2	1	no	—
365	Dic₁₁	—	2	1	no	—
366	Dic₁₁	—	2	1	no	—
367	C₂×#41	—	11	2	no	—
368	C₂×#41	—	11	1	no	—
369	C₂×#41	—	11	1	no	—
370	C₂²×Q₈	—	11	1	no	—
371	C₂²×D₄	—	11	1	no	—
372	C₂²×D₄	—	11	2	no	—
373	C₂²×D₄	—	11	1	no	—
374	C₂²×D₄	—	11	2	no	—
375	C₂²×D₄	—	11	1	no	—
376	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
377	#127	—	11	1	no	—
378	#127	—	11	1	no	—
379	#127	—	11	1	no	—
380	#126	—	11	1	no	—
381	#126	—	11	2	no	—
382	#126	—	11	1	no	—
383	#126	C₂×D₁₁	1	2	yes	complemented
384	#125	—	11	1	no	—
385	#124	—	11	1	no	—
386	#124	—	11	2	no	—
387	#124	—	11	1	no	—
388	#124	—	11	2	no	—
389	#124	—	11	1	no	—
390	#124	—	11	2	no	—
391	#124	—	11	2	no	—
392	#124	—	11	1	no	—
393	#124	—	11	2	no	—
394	#124	—	11	2	no	—
395	#124	—	11	1	no	—
396	#124	—	11	1	no	—
397	#124	—	11	2	no	—
398	#124	—	11	2	no	—
399	#124	C₂×D₁₁	1	1	yes	characteristic, complemented
400	#124	C₂×D₁₁	1	2	yes	complemented
401	#123	—	11	2	no	—
402	#123	—	11	1	no	—
403	#123	—	11	2	no	—
404	#123	—	11	2	no	—
405	#123	—	11	2	no	—
406	#123	—	11	2	no	—
407	#123	—	11	1	no	—
408	#123	—	11	2	no	—
409	#123	—	11	2	no	—
410	#123	C₂×D₁₁	1	2	yes	complemented
411	C₂²⋊Q₈	—	11	2	no	—
412	C₂²⋊Q₈	—	11	1	no	—
413	C₂²⋊Q₈	—	11	2	no	—
414	C₂²⋊Q₈	—	11	2	no	—
415	C₂²⋊Q₈	—	11	1	no	—
416	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
418	#121	—	11	2	no	—
419	#121	—	11	2	no	—
420	#121	—	11	2	no	—
421	#121	—	11	1	no	—
422	#121	—	11	1	no	—
423	#121	—	11	2	no	—
424	#121	—	11	2	no	—
425	#121	—	11	2	no	—
426	#121	—	11	2	no	—
427	#121	—	11	1	no	—
428	#121	—	11	1	no	—
429	#121	—	11	2	no	—
430	#121	—	11	2	no	—
431	#121	—	11	2	no	—
432	#121	—	11	2	no	—
433	#121	C₂×D₁₁	1	1	yes	characteristic
434	#120	—	11	2	no	—
435	#120	—	11	2	no	—
436	#120	—	11	2	no	—
437	#120	—	11	2	no	—
438	#120	—	11	2	no	—
439	#120	—	11	2	no	—
440	#120	—	11	2	no	—
441	#120	—	11	2	no	—
442	#120	—	11	2	no	—
443	#120	—	11	2	no	—
444	C₄×Q₈	—	11	1	no	—
445	C₄×Q₈	—	11	1	no	—
446	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
447	C₄×D₄	—	11	1	no	—
448	C₄×D₄	—	11	1	no	—
449	C₄×D₄	—	11	2	no	—
450	C₄×D₄	—	11	2	no	—
451	C₄×D₄	—	11	1	no	—
452	C₄×D₄	—	11	1	no	—
453	C₄×D₄	—	11	2	no	—
454	C₄×D₄	—	11	1	no	—
455	C₄×D₄	—	11	1	no	—
456	C₄×D₄	—	11	2	no	—
457	C₄×D₄	—	11	2	no	—
458	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
459	#117	—	11	1	no	—
460	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
461	C₂×C₂²⋊C₄	—	11	2	no	—
462	C₂×C₂²⋊C₄	—	11	2	no	—
463	C₂×C₂²⋊C₄	—	11	2	no	—
464	C₂×C₂²⋊C₄	—	11	2	no	—
465	C₂×C₄²	—	11	1	no	—
466	C₂×C₁₁	—	4	2	no	—
467	C₂×C₁₁	—	4	1	no	—
468	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₁₁	#585	1	1	yes	characteristic
471	D₁₁	—	2	2	no	—
472	D₁₁	—	4	2	no	—
473	D₁₁	—	4	2	no	—
474	D₁₁	—	4	2	no	—
475	D₁₁	—	4	1	no	—
476	C₂⁴	—	11	2	no	—
477	C₂⁴	—	11	2	no	—
478	C₂⁴	—	11	2	no	—
479	#41	—	44	2	no	—
480	#41	—	44	4	no	—
481	#41	—	44	2	no	—
482	C₂×Q₈	—	11	1	no	—
483	C₂×Q₈	—	11	1	no	—
484	C₂×Q₈	—	11	2	no	—
485	C₂×Q₈	—	44	2	no	—
486	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
487	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
488	C₂×D₄	—	11	1	no	—
489	C₂×D₄	—	11	1	no	—
490	C₂×D₄	—	11	2	no	—
491	C₂×D₄	—	11	2	no	—
492	C₂×D₄	—	11	2	no	—
493	C₂×D₄	—	11	2	no	—
494	C₂×D₄	—	11	2	no	—
495	C₂×D₄	—	11	2	no	—
496	C₂×D₄	—	11	2	no	—
497	C₂×D₄	—	11	1	no	—
498	C₂×D₄	—	11	1	no	—
499	C₂×D₄	—	11	1	no	—
500	C₂×D₄	—	11	1	no	—
501	C₂×D₄	—	11	2	no	—
502	C₂×D₄	—	11	2	no	—
503	C₂×D₄	—	11	2	no	—
504	C₂×D₄	—	11	2	no	—
505	C₂×D₄	—	11	2	no	—
506	C₂×D₄	—	11	2	no	—
507	C₂×D₄	—	11	2	no	—
508	C₂×D₄	—	44	2	no	—
509	C₂×D₄	—	44	4	no	—
510	C₂×D₄	—	44	2	no	—
511	C₂×D₄	—	44	2	no	—
512	C₂×D₄	—	44	4	no	—
513	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
514	C₂×D₄	C₂²×D₁₁	1	2	yes	—
515	C₂²×C₄	—	11	1	no	—
516	C₂²×C₄	—	11	1	no	—
517	C₂²×C₄	—	11	1	no	—
518	C₂²×C₄	—	11	1	no	—
519	C₂²×C₄	—	11	2	no	—
520	C₂²×C₄	—	11	2	no	—
521	C₂²×C₄	—	11	2	no	—
522	C₂²×C₄	—	11	2	no	—
523	C₂²×C₄	—	11	2	no	—
524	C₂²×C₄	—	11	2	no	—
525	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
527	C₄⋊C₄	—	11	1	no	—
528	C₄⋊C₄	—	11	1	no	—
529	C₄⋊C₄	—	11	1	no	—
530	C₄⋊C₄	—	11	1	no	—
531	C₄⋊C₄	—	11	1	no	—
532	C₄⋊C₄	—	11	1	no	—
533	C₄⋊C₄	—	11	2	no	—
534	C₄⋊C₄	—	11	1	no	—
535	C₄⋊C₄	—	11	2	no	—
536	C₄⋊C₄	—	11	1	no	—
537	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
539	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
542	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
543	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
544	C₂²⋊C₄	—	11	1	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	1	no	—
548	C₂²⋊C₄	—	11	1	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	2	no	—
555	C₂²⋊C₄	—	11	1	no	—
556	C₂²⋊C₄	—	11	1	no	—
557	C₂²⋊C₄	—	11	1	no	—
558	C₂²⋊C₄	—	11	1	no	—
559	C₂²⋊C₄	—	11	2	no	—
560	C₂²⋊C₄	—	11	1	no	—
561	C₂²⋊C₄	—	11	2	no	—
562	C₂²⋊C₄	—	11	2	no	—
563	C₂²⋊C₄	—	11	2	no	—
564	C₂²⋊C₄	—	11	2	no	—
565	C₂²⋊C₄	—	11	2	no	—
566	C₂²⋊C₄	—	11	2	no	—
567	C₂²⋊C₄	—	11	2	no	—
568	C₂²⋊C₄	—	11	2	no	—
569	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
576	C₄²	—	11	1	no	—
577	C₄²	—	11	1	no	—
578	C₄²	—	11	1	no	—
579	C₄²	—	11	1	no	—
580	C₄²	—	11	2	no	—
581	C₄²	C₂²×D₁₁	1	1	yes	characteristic
582	C₄²	C₂²×D₁₁	1	1	yes	characteristic
583	C₄²	C₂²×D₁₁	1	2	yes	—
584	C₁₁	#3558	1	1	yes	characteristic, complemented, Sylow
585	C₂³	—	11	1	no	—
586	C₂³	—	11	1	no	—
587	C₂³	—	11	2	no	—
588	C₂³	—	11	2	no	—
589	C₂³	—	11	2	no	—
590	C₂³	—	22	4	no	—
591	C₂³	—	44	2	no	—
592	C₂³	—	44	2	no	—
593	C₂³	—	44	2	no	—
594	C₂³	—	44	2	no	—
595	C₂³	—	44	2	no	—
596	C₂³	—	44	2	no	—
597	C₂³	—	44	2	no	—
598	C₂³	—	44	2	no	—
599	C₂³	C₂³×D₁₁	1	1	yes	characteristic
600	C₂³	C₂³×D₁₁	1	2	yes	—
601	Q₈	—	2	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	22	2	no	—
604	Q₈	—	44	2	no	—
605	Q₈	—	44	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	22	2	no	—
609	D₄	—	22	4	no	—
610	D₄	—	22	4	no	—
611	D₄	—	22	2	no	—
612	D₄	—	22	2	no	—
613	D₄	—	22	2	no	—
614	D₄	—	22	2	no	—
615	D₄	—	44	2	no	—
616	D₄	—	44	2	no	—
617	D₄	—	44	2	no	—
618	D₄	—	44	2	no	—
619	D₄	—	44	2	no	—
620	D₄	—	44	2	no	—
621	D₄	—	44	2	no	—
622	D₄	—	44	2	no	—
623	D₄	—	44	2	no	—
624	D₄	—	44	2	no	—
625	D₄	—	44	2	no	—
626	D₄	—	44	1	no	—
627	D₄	—	44	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	11	1	no	—
631	C₂×C₄	—	11	1	no	—
632	C₂×C₄	—	11	1	no	—
633	C₂×C₄	—	11	1	no	—
634	C₂×C₄	—	11	2	no	—
635	C₂×C₄	—	11	1	no	—
636	C₂×C₄	—	11	1	no	—
637	C₂×C₄	—	22	2	no	—
638	C₂×C₄	—	22	2	no	—
639	C₂×C₄	—	22	2	no	—
640	C₂×C₄	—	44	2	no	—
641	C₂×C₄	—	44	2	no	—
642	C₂×C₄	—	44	2	no	—
643	C₂×C₄	—	44	2	no	—
644	C₂×C₄	—	44	2	no	—
645	C₂×C₄	—	44	2	no	—
646	C₂×C₄	—	44	1	no	—
647	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₁	1	2	yes	—
650	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₁	1	2	yes	—
652	C₂×C₄	C₂³×D₁₁	1	2	yes	—
653	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	11	2	no	—
663	C₂²	—	22	1	no	—
664	C₂²	—	22	1	no	—
665	C₂²	—	22	1	no	—
666	C₂²	—	22	2	no	—
667	C₂²	—	22	2	no	—
668	C₂²	—	22	2	no	—
669	C₂²	—	22	2	no	—
670	C₂²	—	22	2	no	—
671	C₂²	—	22	2	no	—
672	C₂²	—	22	1	no	—
673	C₂²	—	22	2	no	—
674	C₂²	—	22	2	no	—
675	C₂²	—	22	2	no	—
676	C₂²	—	22	1	no	—
677	C₂²	—	88	4	no	—
678	C₂²	—	88	4	no	—
679	C₂²	—	88	4	no	—
680	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	22	1	no	—
690	C₄	—	22	1	no	—
691	C₄	—	22	2	no	—
692	C₄	—	22	1	no	—
693	C₄	—	22	1	no	—
694	C₄	—	22	1	no	—
695	C₄	—	22	1	no	—
696	C₄	#67042	1	2	yes	—
697	C₂	—	4	1	no	—
698	C₂	—	4	2	no	—
699	C₂	—	22	2	no	—
700	C₂	—	44	1	no	—
701	C₂	—	44	2	no	—
702	C₂	—	44	2	no	—
703	C₂	—	44	2	no	—
704	C₂	C₂×#67042	1	1	yes	characteristic
705	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂	#10623457	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#542	C₂
hypercenter	#542	D₁₁
hypocenter	C₁₁	#3558
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₁₁×#542	C₂	semidirect
2. #10623264	C₂	semidirect
3. #10623256	C₂	semidirect
4. #10623235	C₂	semidirect
5. #10623235	C₂	semidirect
6. #10623214	C₂	semidirect
7. #10623207	C₂	semidirect
8. #10623205	C₂	semidirect
9. D₁₁×#124	C₂	semidirect
10. #10623188	C₂	semidirect
11. #10623184	C₂	semidirect
12. #10623178	C₂	semidirect
13. #10623164	C₂	semidirect
14. #10623161	C₂	semidirect
15. #10623161	C₂	semidirect
16. #10623143	C₂	semidirect
17. #10623140	C₂	semidirect
18. #10623116	C₂	semidirect
19. #10623107	C₂	semidirect
20. #10623090	C₂	semidirect
21. D₄×D₄₄	C₂	semidirect
22. #10623059	C₂	semidirect
23. #10623056	C₂	semidirect
24. C₂×#4343	C₂²	semidirect
25. C₂×#4343	C₂²	semidirect
26. C₂×Q₈×D₁₁	C₂²	semidirect
28. C₂×D₄×D₁₁	C₂²	semidirect
29. C₂×D₄×D₁₁	C₂²	semidirect
30. C₂×#4339	C₂²	semidirect
31. C₂²×D₄₄	C₂²	semidirect
32. C₂²×D₄₄	C₂²	semidirect
33. C₁₁×C₄⋊Q₈	C₂²	semidirect
34. C₁₁×#126	C₂²	semidirect
35. C₁₁×#124	C₂²	semidirect
36. C₁₁×#124	C₂²	semidirect
37. C₁₁×#123	C₂²	semidirect
38. C₁₁×C₂²⋊Q₈	C₂²	semidirect
39. C₁₁×C₂²⋊Q₈	C₂²	semidirect
41. C₄×Q₈×C₁₁	C₂²	semidirect
42. C₄×D₄×C₁₁	C₂²	semidirect
43. C₁₁×#117	C₂²	semidirect
44. #67000	C₂²	semidirect
45. #67000	C₂²	semidirect
46. #67000	C₂²	semidirect
47. #67000	C₂²	semidirect
48. #66999	C₂²	semidirect
50. #66991	C₂²	semidirect
51. #66990	C₂²	semidirect
52. #66990	C₂²	semidirect
53. #66989	C₂²	semidirect
54. #66983	C₂²	semidirect
55. #66982	C₂²	semidirect
56. C₄×C₂²⋊D₁₁	C₂²	semidirect
57. C₄×C₂²⋊D₁₁	C₂²	semidirect
58. C₄×C₂²⋊D₁₁	C₂²	semidirect
59. #66951	C₂²	semidirect
60. #66951	C₂²	semidirect
61. #66950	C₂²	semidirect
62. #66950	C₂²	semidirect
63. #66949	C₂²	semidirect
64. #66949	C₂²	semidirect
66. #66948	C₂²	semidirect
67. #66948	C₂²	semidirect
68. #66948	C₂²	semidirect
69. #66948	C₂²	semidirect
70. #66948	C₂²	semidirect
71. #66948	C₂²	semidirect
72. #66948	C₂²	semidirect
73. #66947	C₂²	semidirect
74. #66947	C₂²	semidirect
75. #66947	C₂²	semidirect
76. #66947	C₂²	semidirect
77. #66947	C₂²	semidirect
78. #66946	C₂²	semidirect
79. #66946	C₂²	semidirect
80. #66946	C₂²	semidirect
81. #66946	C₂²	semidirect
82. #66946	C₂²	semidirect
83. #66942	C₂²	semidirect
84. #66940	C₂²	semidirect
85. #66938	C₂²	semidirect
86. #66938	C₂²	semidirect
87. #66938	C₂²	semidirect
88. #66938	C₂²	semidirect
89. #66938	C₂²	semidirect
91. #66937	C₂²	semidirect
92. #66937	C₂²	semidirect
93. #66937	C₂²	semidirect
94. #66937	C₂²	semidirect
95. #66936	C₂²	semidirect
96. #66936	C₂²	semidirect
97. #66936	C₂²	semidirect
98. #66935	C₂²	semidirect
99. #66935	C₂²	semidirect
100. #66935	C₂²	semidirect
101. #66935	C₂²	semidirect
102. #66935	C₂²	semidirect
103. #66935	C₂²	semidirect
104. #66935	C₂²	semidirect
105. #66935	C₂²	semidirect
106. C₂²⋊C₄×D₁₁	C₂²	semidirect
107. C₂²⋊C₄×D₁₁	C₂²	semidirect
108. C₂²⋊C₄×D₁₁	C₂²	semidirect
109. C₂²⋊C₄×D₁₁	C₂²	semidirect
110. #66932	C₂²	semidirect
111. #66928	C₂²	semidirect
112. #66928	C₂²	semidirect
113. #66928	C₂²	semidirect
114. #66928	C₂²	semidirect
116. #66927	C₂²	semidirect
117. C₄×D₄₄	C₂²	semidirect
118. C₄×D₄₄	C₂²	semidirect
119. C₄×D₄₄	C₂²	semidirect
120. #66925	C₂²	semidirect
121. C₄²×D₁₁	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
316. #542	D₁₁	semidirect
376. C₄⋊Q₈	C₂×D₁₁	semidirect
383. #126	C₂×D₁₁	semidirect
399. #124	C₂×D₁₁	semidirect
400. #124	C₂×D₁₁	semidirect
410. #123	C₂×D₁₁	semidirect
416. C₂²⋊Q₈	C₂×D₁₁	semidirect
417. C₂²⋊Q₈	C₂×D₁₁	semidirect
446. C₄×Q₈	C₂×D₁₁	semidirect
458. C₄×D₄	C₂×D₁₁	semidirect
460. #117	C₂×D₁₁	semidirect
584. C₁₁	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#542	2
#10623264	2
#10623256	2
#10623235	2
#10623214	2
#10623207	2
#10623205	2
D₁₁×#124	2
#10623188	2
#10623184	2
#10623178	2
#10623164	2
#10623161	2
#10623143	2
#10623140	2
#10623116	2
#10623107	2
#10623090	2
D₄×D₄₄	2
#10623059	2
#10623056	2
#3558	11