Subgroups — #13082364

Order 1408.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623263	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623260	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623227	C₂	1	2	yes	maximal, complemented
5	#10623224	C₂	1	2	yes	maximal, complemented
6	#10623173	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623172	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623171	C₂	1	2	yes	maximal, complemented
9	#10623170	C₂	1	2	yes	maximal, complemented
10	#10623168	C₂	1	2	yes	maximal, complemented
11	#10623159	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623153	C₂	1	2	yes	maximal, complemented
14	#10623112	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623103	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623087	C₂	1	2	yes	maximal, complemented
17	#10623078	C₂	1	1	yes	maximal, characteristic
18	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
19	#10623069	C₂	1	2	yes	maximal, complemented
20	#10623044	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623042	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#66945	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic
25	C₂×#4339	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×#125	C₂²	1	2	yes	complemented
29	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₁	C₂²	1	2	yes	—
35	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#67000	C₂²	1	2	yes	—
39	#66999	C₂²	1	2	yes	—
40	#66999	C₂²	1	1	yes	characteristic
41	#66999	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₁	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
44	#66997	C₂²	1	2	yes	complemented
45	#66992	C₂²	1	1	yes	characteristic
46	#66990	C₂²	1	1	yes	characteristic
47	#66988	C₂²	1	2	yes	—
48	#66982	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
54	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
55	#66979	C₂²	1	1	yes	characteristic, complemented
56	#66979	C₂²	1	2	yes	complemented
57	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
58	#66977	C₂²	1	1	yes	characteristic
59	#66977	C₂²	1	2	yes	—
60	#66977	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
62	#66951	C₂²	1	2	yes	—
63	#66951	C₂²	1	2	yes	—
64	#66951	C₂²	1	2	yes	—
65	#66951	C₂²	1	2	yes	complemented
66	#66951	C₂²	1	2	yes	complemented
67	#66950	C₂²	1	1	yes	characteristic
68	#66950	C₂²	1	1	yes	characteristic, complemented
69	#66949	C₂²	1	2	yes	—
70	#66949	C₂²	1	1	yes	characteristic
71	#66949	C₂²	1	2	yes	—
72	#66949	C₂²	1	2	yes	complemented
73	#66947	C₂²	1	1	yes	characteristic
74	#66947	C₂²	1	2	yes	—
75	#66947	C₂²	1	2	yes	—
76	#66946	C₂²	1	2	yes	—
77	#66945	C₂²	1	1	yes	characteristic
78	#66945	C₂²	1	1	yes	characteristic
79	#66945	C₂²	1	1	yes	characteristic
80	#66945	C₂²	1	1	yes	characteristic
81	#66945	C₂²	1	2	yes	—
82	#66945	C₂²	1	2	yes	—
83	#66945	C₂²	1	2	yes	—
84	#66945	C₂²	1	1	yes	characteristic, complemented
85	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
87	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
88	#66943	C₂²	1	1	yes	characteristic, complemented
89	#66943	C₂²	1	2	yes	complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66942	C₂²	1	2	yes	complemented
92	#66942	C₂²	1	2	yes	complemented
93	#66942	C₂²	1	2	yes	complemented
94	#66942	C₂²	1	2	yes	complemented
95	#66941	C₂²	1	1	yes	characteristic, complemented
96	#66941	C₂²	1	2	yes	complemented
97	#66940	C₂²	1	2	yes	complemented
98	#66940	C₂²	1	1	yes	characteristic, complemented
99	#66940	C₂²	1	2	yes	complemented
100	#66940	C₂²	1	2	yes	complemented
101	#66939	C₂²	1	2	yes	—
102	#66938	C₂²	1	2	yes	—
103	#66938	C₂²	1	2	yes	complemented
104	#66937	C₂²	1	1	yes	characteristic
105	#66936	C₂²	1	1	yes	characteristic
106	#66936	C₂²	1	2	yes	—
107	#66935	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
109	#66932	C₂²	1	2	yes	complemented
110	#66932	C₂²	1	2	yes	complemented
111	#66931	C₂²	1	2	yes	—
112	#66931	C₂²	1	1	yes	characteristic
113	#66930	C₂²	1	2	yes	—
114	#66930	C₂²	1	2	yes	—
115	#66929	C₂²	1	2	yes	—
116	C₄×D₄₄	C₂²	1	1	yes	characteristic
117	#66925	C₂²	1	1	yes	characteristic
118	#66925	C₂²	1	2	yes	—
119	#66925	C₂²	1	2	yes	complemented
120	#66923	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	2	yes	complemented
123	C₂³×D₁₁	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
126	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₁	C₂³	1	2	yes	—
136	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
137	Q₈×D₁₁	—	2	4	no	—
138	#4339	—	2	4	no	—
139	C₂×D₄₄	C₂³	1	1	yes	characteristic
140	C₂×D₄₄	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₁	—	2	4	no	—
142	C₂×C₄×D₁₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₁	C₂³	1	2	yes	—
148	C₂×C₄×D₁₁	C₂³	1	2	yes	—
149	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₂	C₂³	1	2	yes	—
151	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
152	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₂	C₂³	1	2	yes	—
154	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
155	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₄²×C₁₁	C₂³	1	1	yes	characteristic
169	C₄²×C₁₁	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
176	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
190	C₄⋊Dic₁₁	C₂³	1	2	yes	—
191	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	2	yes	—
198	C₄⋊Dic₁₁	C₂³	1	2	yes	—
199	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₁₁⋊C₄	C₂³	1	2	yes	—
201	Dic₁₁⋊C₄	C₂³	1	2	yes	—
202	Dic₁₁⋊C₄	C₂³	1	2	yes	—
203	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
211	Dic₁₁⋊C₄	C₂³	1	2	yes	—
212	Dic₁₁⋊C₄	C₂³	1	2	yes	—
213	Dic₁₁⋊C₄	C₂³	1	2	yes	—
214	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₁	C₂³	1	2	yes	—
216	C₄×Dic₁₁	C₂³	1	2	yes	—
217	C₄×Dic₁₁	C₂³	1	2	yes	—
218	C₄×Dic₁₁	C₂³	1	2	yes	—
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	#3495	—	11	1	no	maximal, Sylow
226	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₁	—	2	2	no	—
229	C₂²×D₁₁	—	2	2	no	—
230	C₂²×D₁₁	—	4	1	no	—
231	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
234	Q₈×C₁₁	—	2	2	no	—
235	Q₈×C₁₁	—	4	2	no	—
236	D₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	4	2	no	—
240	C₂×C₄×C₁₁	—	4	2	no	—
241	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₁	—	2	2	no	—
251	C₂²⋊D₁₁	—	2	2	no	—
252	C₂²⋊D₁₁	—	2	2	no	—
253	C₂²⋊D₁₁	—	4	1	no	—
254	C₂×Dic₁₁	—	2	4	no	—
255	C₂×Dic₁₁	—	2	2	no	—
256	C₂×Dic₁₁	C₂⁴	1	2	yes	—
257	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₁	C₂⁴	1	2	yes	—
261	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁	C₂⁴	1	2	yes	—
264	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
265	D₄₄	—	2	2	no	—
266	D₄₄	—	4	1	no	—
267	C₄×D₁₁	—	2	2	no	—
268	C₄×D₁₁	—	2	4	no	—
269	C₄×D₁₁	—	2	2	no	—
270	C₄×D₁₁	—	2	2	no	—
271	C₄×D₁₁	—	2	2	no	—
272	C₄×D₁₁	—	4	2	no	—
273	C₄×D₁₁	—	4	2	no	—
274	C₄×D₁₁	#41	1	4	yes	—
275	Dic₂₂	—	2	2	no	—
276	Dic₂₂	—	2	2	no	—
277	Dic₂₂	—	2	4	no	—
278	Dic₂₂	—	4	2	no	—
279	#556	—	11	1	no	—
280	#556	—	11	1	no	—
281	#554	—	11	1	no	—
282	#554	D₁₁	1	1	yes	characteristic, complemented
283	#552	—	11	2	no	—
284	#552	—	11	1	no	—
285	#552	—	11	2	no	—
286	#552	—	11	1	no	—
287	#552	—	11	1	no	—
288	#552	—	11	1	no	—
289	#551	—	11	2	no	—
290	#551	—	11	2	no	—
291	#544	—	11	1	no	—
292	#542	—	11	2	no	—
293	#541	—	11	2	no	—
294	#536	—	11	1	no	—
295	#533	—	11	2	no	—
296	#529	—	11	2	no	—
297	#525	—	11	1	no	—
298	C₂×C₂²⋊Q₈	—	11	1	no	—
299	#520	—	11	1	no	—
300	#519	—	11	1	no	—
301	C₂×#117	—	11	1	no	—
302	C₂²×C₁₁	—	2	1	no	—
303	C₂²×C₁₁	—	2	1	no	—
304	C₂²×C₁₁	—	2	1	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	—	2	1	no	—
307	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
308	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₁	—	2	1	no	—
310	C₂×D₁₁	—	2	1	no	—
311	C₂×D₁₁	—	2	1	no	—
312	C₂×D₁₁	—	2	1	no	—
313	C₂×D₁₁	—	2	1	no	—
314	C₂×D₁₁	—	2	1	no	—
315	C₂×D₁₁	—	2	1	no	—
316	C₂×D₁₁	—	2	1	no	—
317	C₂×D₁₁	—	4	4	no	—
318	C₂×D₁₁	C₂×#41	1	2	yes	—
319	C₄×C₁₁	—	2	1	no	—
320	C₄×C₁₁	—	2	1	no	—
321	C₄×C₁₁	—	2	2	no	—
322	C₄×C₁₁	—	2	1	no	—
323	C₄×C₁₁	—	2	2	no	—
324	C₄×C₁₁	—	2	2	no	—
325	C₄×C₁₁	—	2	2	no	—
326	C₄×C₁₁	—	2	1	no	—
327	C₄×C₁₁	C₂×#41	1	2	yes	—
328	Dic₁₁	—	2	2	no	—
329	Dic₁₁	—	2	1	no	—
330	Dic₁₁	—	2	1	no	—
331	Dic₁₁	—	2	2	no	—
332	Dic₁₁	—	2	2	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	—	2	1	no	—
335	Dic₁₁	—	2	2	no	—
336	Dic₁₁	C₂×#41	1	2	yes	—
337	C₂×#41	—	11	1	no	—
338	C₂²×Q₈	—	11	1	no	—
339	C₂³×C₄	—	11	1	no	—
340	C₄⋊Q₈	—	11	2	no	—
341	C₄⋊Q₈	—	11	2	no	—
342	C₄⋊Q₈	—	11	1	no	—
343	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
344	#126	—	11	2	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	#125	—	11	2	no	—
353	#125	—	11	2	no	—
354	#125	—	11	2	no	—
355	#125	—	11	2	no	—
356	#125	—	11	2	no	—
357	#125	—	11	2	no	—
358	#125	—	11	1	no	—
359	#125	—	11	1	no	—
360	#125	C₂×D₁₁	1	2	yes	complemented
361	#124	—	11	2	no	—
362	#124	—	11	2	no	—
363	#124	—	11	2	no	—
364	#123	—	11	2	no	—
365	#123	—	11	2	no	—
366	#123	—	11	1	no	—
367	#123	—	11	2	no	—
368	#123	—	11	2	no	—
369	#123	—	11	1	no	—
370	#123	—	11	2	no	—
371	#123	—	11	2	no	—
372	C₂²⋊Q₈	—	11	1	no	—
373	C₂²⋊Q₈	—	11	1	no	—
374	C₂²⋊Q₈	—	11	2	no	—
375	C₂²⋊Q₈	—	11	1	no	—
376	C₂²⋊Q₈	—	11	2	no	—
377	C₂²⋊Q₈	—	11	1	no	—
378	C₂²⋊Q₈	—	11	2	no	—
379	C₂²⋊Q₈	—	11	1	no	—
380	C₂²⋊Q₈	—	11	1	no	—
381	C₂²⋊Q₈	—	11	1	no	—
382	C₂²⋊Q₈	—	11	2	no	—
383	C₂²⋊Q₈	—	11	2	no	—
384	C₂²⋊Q₈	—	11	2	no	—
385	C₂²⋊Q₈	—	11	1	no	—
386	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
387	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	—
388	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
389	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
390	#121	—	11	1	no	—
391	#121	—	11	1	no	—
392	#120	—	11	1	no	—
393	#120	—	11	1	no	—
394	C₄×Q₈	—	11	1	no	—
395	C₄×Q₈	—	11	2	no	—
396	C₄×Q₈	—	11	2	no	—
397	C₄×Q₈	—	11	1	no	—
398	C₄×Q₈	—	11	2	no	—
399	C₄×Q₈	—	11	2	no	—
400	C₄×Q₈	—	11	2	no	—
401	C₄×Q₈	—	11	1	no	—
402	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
403	C₄×D₄	—	11	2	no	—
404	C₄×D₄	—	11	2	no	—
405	C₄×D₄	—	11	1	no	—
406	C₄×D₄	—	11	1	no	—
407	C₄×D₄	—	11	2	no	—
408	C₄×D₄	—	11	2	no	—
409	C₄×D₄	—	11	1	no	—
410	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
411	C₄×D₄	C₂×D₁₁	1	2	yes	—
412	#117	—	11	1	no	—
413	#117	—	11	2	no	—
414	#117	—	11	1	no	—
415	#117	—	11	1	no	—
416	#117	—	11	2	no	—
417	#117	—	11	1	no	—
418	#117	—	11	2	no	—
419	#117	—	11	1	no	—
420	#117	—	11	2	no	—
421	#117	—	11	1	no	—
422	#117	—	11	2	no	—
423	#117	—	11	2	no	—
424	#117	—	11	1	no	—
425	#117	—	11	2	no	—
426	#117	—	11	2	no	—
427	C₂×C₄⋊C₄	—	11	1	no	—
428	C₂×C₄⋊C₄	—	11	1	no	—
429	C₂×C₄⋊C₄	—	11	1	no	—
430	C₂×C₄⋊C₄	—	11	2	no	—
431	C₂×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic, complemented
433	C₂×C₂²⋊C₄	—	11	2	no	—
434	C₂×C₂²⋊C₄	—	11	2	no	—
435	C₂×C₄²	—	11	2	no	—
436	C₂×C₁₁	—	2	2	no	—
437	C₂×C₁₁	—	4	1	no	—
438	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
439	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂×C₁₁	#585	1	1	yes	characteristic
441	D₁₁	—	2	2	no	—
442	D₁₁	—	4	1	no	—
443	D₁₁	—	4	1	no	—
444	C₂⁴	—	11	1	no	—
445	#41	—	22	4	no	—
446	C₂×Q₈	—	11	1	no	—
447	C₂×Q₈	—	11	2	no	—
448	C₂×Q₈	—	11	1	no	—
449	C₂×Q₈	—	11	2	no	—
450	C₂×Q₈	—	22	4	no	—
451	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
453	C₂×D₄	—	11	1	no	—
454	C₂×D₄	—	11	1	no	—
455	C₂×D₄	—	11	1	no	—
456	C₂×D₄	—	11	1	no	—
457	C₂×D₄	—	11	1	no	—
458	C₂×D₄	—	11	1	no	—
459	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
460	C₂²×C₄	—	11	1	no	—
461	C₂²×C₄	—	11	1	no	—
462	C₂²×C₄	—	11	2	no	—
463	C₂²×C₄	—	11	2	no	—
464	C₂²×C₄	—	11	1	no	—
465	C₂²×C₄	—	11	1	no	—
466	C₂²×C₄	—	11	1	no	—
467	C₂²×C₄	—	11	1	no	—
468	C₂²×C₄	—	11	2	no	—
469	C₂²×C₄	—	11	2	no	—
470	C₂²×C₄	—	22	4	no	—
471	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
475	C₄⋊C₄	—	11	1	no	—
476	C₄⋊C₄	—	11	1	no	—
477	C₄⋊C₄	—	11	1	no	—
478	C₄⋊C₄	—	11	2	no	—
479	C₄⋊C₄	—	11	2	no	—
480	C₄⋊C₄	—	11	2	no	—
481	C₄⋊C₄	—	11	2	no	—
482	C₄⋊C₄	—	11	2	no	—
483	C₄⋊C₄	—	11	2	no	—
484	C₄⋊C₄	—	11	1	no	—
485	C₄⋊C₄	—	11	1	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	2	no	—
492	C₄⋊C₄	—	11	2	no	—
493	C₄⋊C₄	—	11	2	no	—
494	C₄⋊C₄	—	11	2	no	—
495	C₄⋊C₄	—	11	1	no	—
496	C₄⋊C₄	—	11	1	no	—
497	C₄⋊C₄	—	11	1	no	—
498	C₄⋊C₄	—	11	2	no	—
499	C₄⋊C₄	—	11	2	no	—
500	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
509	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
510	C₂²⋊C₄	—	11	2	no	—
511	C₂²⋊C₄	—	11	1	no	—
512	C₂²⋊C₄	—	11	1	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	2	no	—
520	C₂²⋊C₄	—	11	2	no	—
521	C₂²⋊C₄	—	11	1	no	—
522	C₂²⋊C₄	—	11	1	no	—
523	C₂²⋊C₄	—	11	1	no	—
524	C₂²⋊C₄	—	11	2	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	—	11	1	no	—
527	C₂²⋊C₄	—	11	1	no	—
528	C₂²⋊C₄	—	11	1	no	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
534	C₄²	—	11	2	no	—
535	C₄²	—	11	2	no	—
536	C₄²	—	11	2	no	—
537	C₄²	—	11	2	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	1	no	—
544	C₄²	C₂²×D₁₁	1	2	yes	—
545	C₄²	C₂²×D₁₁	1	1	yes	characteristic
546	C₁₁	#3495	1	1	yes	characteristic, complemented, Sylow
547	C₂³	—	11	1	no	—
548	C₂³	—	11	1	no	—
549	C₂³	—	11	1	no	—
550	C₂³	—	22	2	no	—
551	C₂³	—	22	2	no	—
552	C₂³	—	44	1	no	—
553	C₂³	C₂³×D₁₁	1	1	yes	characteristic
554	C₂³	C₂³×D₁₁	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	22	4	no	—
558	Q₈	—	22	2	no	—
559	Q₈	—	22	2	no	—
560	Q₈	—	44	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	22	2	no	—
563	D₄	—	22	2	no	—
564	D₄	—	22	2	no	—
565	D₄	—	22	2	no	—
566	D₄	—	44	1	no	—
567	D₄	—	44	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	11	1	no	—
573	C₂×C₄	—	11	4	no	—
574	C₂×C₄	—	11	2	no	—
575	C₂×C₄	—	11	1	no	—
576	C₂×C₄	—	11	1	no	—
577	C₂×C₄	—	11	1	no	—
578	C₂×C₄	—	11	2	no	—
579	C₂×C₄	—	11	2	no	—
580	C₂×C₄	—	11	1	no	—
581	C₂×C₄	—	11	2	no	—
582	C₂×C₄	—	22	2	no	—
583	C₂×C₄	—	22	2	no	—
584	C₂×C₄	—	22	4	no	—
585	C₂×C₄	—	22	2	no	—
586	C₂×C₄	—	22	4	no	—
587	C₂×C₄	—	22	2	no	—
588	C₂×C₄	—	22	2	no	—
589	C₂×C₄	—	44	2	no	—
590	C₂×C₄	—	44	2	no	—
591	C₂×C₄	C₂³×D₁₁	1	2	yes	—
592	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₁	1	2	yes	—
594	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₁	1	2	yes	—
596	C₂×C₄	C₂³×D₁₁	1	2	yes	—
597	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	11	2	no	—
606	C₂²	—	22	1	no	—
607	C₂²	—	22	1	no	—
608	C₂²	—	22	1	no	—
609	C₂²	—	22	1	no	—
610	C₂²	—	22	1	no	—
611	C₂²	—	22	1	no	—
612	C₂²	—	22	1	no	—
613	C₂²	—	22	1	no	—
614	C₂²	—	44	4	no	—
615	C₂²	#67040	1	2	yes	—
616	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	11	2	no	—
626	C₄	—	22	2	no	—
627	C₄	—	22	2	no	—
628	C₄	—	22	1	no	—
629	C₄	—	22	1	no	—
630	C₄	—	22	1	no	—
631	C₄	—	22	2	no	—
632	C₄	—	22	2	no	—
633	C₄	—	22	1	no	—
634	C₄	#41×D₁₁	1	2	yes	—
635	C₂	—	2	2	no	—
636	C₂	—	4	1	no	—
637	C₂	—	22	2	no	—
638	C₂	—	44	1	no	—
639	C₂	—	44	1	no	—
640	C₂	C₂×#67040	1	1	yes	characteristic
641	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
642	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#554	C₂
prime radical	#10623078	C₂
hypercenter	#554	D₁₁
hypocenter	C₁₁	#3495
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₁×#554	C₂	semidirect
2. #10623263	C₂	semidirect
3. #10623260	C₂	semidirect
4. #10623227	C₂	semidirect
5. #10623224	C₂	semidirect
6. #10623173	C₂	semidirect
7. #10623172	C₂	semidirect
8. #10623171	C₂	semidirect
9. #10623170	C₂	semidirect
10. #10623168	C₂	semidirect
11. #10623159	C₂	semidirect
12. D₁₁×C₂²⋊Q₈	C₂	semidirect
13. #10623153	C₂	semidirect
14. #10623112	C₂	semidirect
15. #10623103	C₂	semidirect
16. #10623087	C₂	semidirect
18. #10623072	C₂	semidirect
19. #10623069	C₂	semidirect
20. #10623044	C₂	semidirect
21. #10623042	C₂	semidirect
22. #10623035	C₂	semidirect
23. C₂×#66945	C₂	semidirect
27. C₁₁×C₄⋊Q₈	C₂²	semidirect
28. C₁₁×#125	C₂²	semidirect
31. C₁₁×C₂²⋊Q₈	C₂²	semidirect
32. C₁₁×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₁	C₂²	semidirect
37. C₂×C₁₁×C₄⋊C₄	C₂²	semidirect
41. #66999	C₂²	semidirect
42. Q₈×Dic₁₁	C₂²	semidirect
43. Q₈×Dic₁₁	C₂²	semidirect
44. #66997	C₂²	semidirect
53. C₄×C₂²⋊D₁₁	C₂²	semidirect
55. #66979	C₂²	semidirect
56. #66979	C₂²	semidirect
60. #66977	C₂²	semidirect
65. #66951	C₂²	semidirect
66. #66951	C₂²	semidirect
68. #66950	C₂²	semidirect
72. #66949	C₂²	semidirect
84. #66945	C₂²	semidirect
87. C₄⋊C₄×D₁₁	C₂²	semidirect
88. #66943	C₂²	semidirect
89. #66943	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66942	C₂²	semidirect
92. #66942	C₂²	semidirect
93. #66942	C₂²	semidirect
94. #66942	C₂²	semidirect
95. #66941	C₂²	semidirect
96. #66941	C₂²	semidirect
97. #66940	C₂²	semidirect
98. #66940	C₂²	semidirect
99. #66940	C₂²	semidirect
100. #66940	C₂²	semidirect
103. #66938	C₂²	semidirect
109. #66932	C₂²	semidirect
110. #66932	C₂²	semidirect
119. #66925	C₂²	semidirect
120. #66923	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
282. #554	D₁₁	semidirect
343. C₄⋊Q₈	C₂×D₁₁	semidirect
360. #125	C₂×D₁₁	semidirect
388. C₂²⋊Q₈	C₂×D₁₁	semidirect
389. C₂²⋊Q₈	C₂×D₁₁	semidirect
402. C₄×Q₈	C₂×D₁₁	semidirect
432. C₂×C₄⋊C₄	C₂×D₁₁	semidirect
546. C₁₁	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#554	2
#10623263	2
#10623260	2
#10623227	2
#10623224	2
#10623173	2
#10623172	2
#10623171	2
#10623170	2
#10623168	2
#10623159	2
D₁₁×C₂²⋊Q₈	2
#10623153	2
#10623112	2
#10623103	2
#10623087	2
#10623078	2
#10623072	2
#10623069	2
#10623044	2
#10623042	2
#10623035	2
C₂×#66945	2
#3495	11