Subgroups — #13082415

Order 1408.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 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	#10623260	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623258	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623221	C₂	1	1	yes	maximal, characteristic, complemented
5	#10623221	C₂	1	1	yes	maximal, characteristic, complemented
6	#10623220	C₂	1	1	yes	maximal, characteristic, complemented
7	#10623219	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623167	C₂	1	2	yes	maximal, complemented
9	#10623167	C₂	1	2	yes	maximal, complemented
10	#10623165	C₂	1	2	yes	maximal, complemented
11	#10623165	C₂	1	2	yes	maximal, complemented
12	#10623163	C₂	1	2	yes	maximal, complemented
13	D₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	#10623110	C₂	1	1	yes	maximal, characteristic, complemented
15	#10623109	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623076	C₂	1	1	yes	maximal, characteristic
17	#10623076	C₂	1	1	yes	maximal, characteristic
18	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic
19	#10623070	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623070	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623042	C₂	1	2	yes	maximal, complemented
23	C₂×#66949	C₂	1	2	yes	maximal, complemented
24	C₂×Q₈×D₁₁	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₁	C₂²	1	2	yes	—
27	C₂²×Dic₂₂	C₂²	1	2	yes	complemented
28	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
38	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
39	#66999	C₂²	1	2	yes	—
40	#66999	C₂²	1	1	yes	characteristic
41	#66999	C₂²	1	2	yes	complemented
42	#66999	C₂²	1	2	yes	complemented
43	#66997	C₂²	1	2	yes	complemented
44	#66997	C₂²	1	1	yes	characteristic, complemented
45	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
46	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
47	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	—
51	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
52	C₂×(C₂×D₁₁)⋊C₄	C₂²	1	2	yes	—
53	#66977	C₂²	1	2	yes	complemented
54	#66977	C₂²	1	2	yes	complemented
55	#66977	C₂²	1	2	yes	complemented
56	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
57	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
58	#66950	C₂²	1	1	yes	characteristic
59	#66950	C₂²	1	2	yes	—
60	#66950	C₂²	1	2	yes	complemented
61	#66950	C₂²	1	2	yes	complemented
62	#66949	C₂²	1	2	yes	—
63	#66949	C₂²	1	1	yes	characteristic
64	#66949	C₂²	1	2	yes	—
65	#66949	C₂²	1	2	yes	—
66	#66949	C₂²	1	1	yes	characteristic
67	#66949	C₂²	1	2	yes	—
68	#66949	C₂²	1	2	yes	complemented
69	#66949	C₂²	1	2	yes	complemented
70	#66949	C₂²	1	2	yes	complemented
71	#66949	C₂²	1	2	yes	complemented
72	#66949	C₂²	1	2	yes	complemented
73	#66949	C₂²	1	2	yes	complemented
74	#66949	C₂²	1	2	yes	complemented
75	#66949	C₂²	1	2	yes	complemented
76	#66946	C₂²	1	1	yes	characteristic
77	#66946	C₂²	1	1	yes	characteristic
78	#66946	C₂²	1	1	yes	characteristic
79	#66945	C₂²	1	1	yes	characteristic
80	#66945	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
83	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
84	C₄⋊C₄×D₁₁	C₂²	1	2	yes	complemented
85	#66943	C₂²	1	1	yes	characteristic, complemented
86	#66943	C₂²	1	1	yes	characteristic, complemented
87	#66942	C₂²	1	2	yes	complemented
88	#66942	C₂²	1	1	yes	characteristic, complemented
89	#66942	C₂²	1	1	yes	characteristic, complemented
90	#66942	C₂²	1	2	yes	complemented
91	#66941	C₂²	1	1	yes	characteristic, complemented
92	#66941	C₂²	1	1	yes	characteristic, complemented
93	#66941	C₂²	1	1	yes	characteristic, complemented
94	#66941	C₂²	1	2	yes	complemented
95	#66941	C₂²	1	1	yes	characteristic, complemented
96	#66941	C₂²	1	1	yes	characteristic, complemented
97	#66940	C₂²	1	2	yes	complemented
98	#66940	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
105	#66931	C₂²	1	2	yes	complemented
106	#66931	C₂²	1	2	yes	complemented
107	#66931	C₂²	1	2	yes	complemented
108	#66931	C₂²	1	2	yes	complemented
109	#66931	C₂²	1	2	yes	complemented
110	#66931	C₂²	1	2	yes	complemented
111	C₄×D₄₄	C₂²	1	1	yes	characteristic
112	C₄×D₄₄	C₂²	1	1	yes	characteristic
113	C₄×D₄₄	C₂²	1	1	yes	characteristic
114	#66925	C₂²	1	1	yes	characteristic
115	#66925	C₂²	1	1	yes	characteristic
116	C₄²×D₁₁	C₂²	1	1	yes	characteristic
117	#66923	C₂²	1	1	yes	characteristic, complemented
118	#66923	C₂²	1	1	yes	characteristic, complemented
119	#66922	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₂	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	C₂³×D₁₁	C₂³	1	2	yes	—
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	2	yes	—
128	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
131	C₂²×Dic₁₁	C₂³	1	2	yes	—
132	C₂²×Dic₁₁	C₂³	1	2	yes	—
133	C₂²×Dic₁₁	C₂³	1	2	yes	—
134	Q₈×D₁₁	—	4	4	no	—
135	D₄×D₁₁	Q₈	1	8	yes	complemented
136	C₂×D₄₄	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₁	—	4	4	no	—
138	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₂	—	4	4	no	—
149	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
151	C₂×Dic₂₂	C₂³	1	2	yes	—
152	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₂	C₂³	1	2	yes	—
154	C₂×Dic₂₂	C₂³	1	2	yes	—
155	C₂×Dic₂₂	C₂³	1	2	yes	—
156	C₂×Dic₂₂	C₂³	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₄²×C₁₁	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	1	yes	characteristic
173	C₄²×C₁₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
177	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
185	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
193	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₁	C₂³	1	2	yes	—
195	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₁	C₂³	1	2	yes	—
197	C₄⋊Dic₁₁	C₂³	1	2	yes	—
198	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
213	Dic₁₁⋊C₄	C₂³	1	2	yes	—
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	Dic₁₁⋊C₄	C₂³	1	2	yes	—
217	Dic₁₁⋊C₄	C₂³	1	2	yes	—
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	C₄×Dic₁₁	C₂³	1	2	yes	—
226	#3501	—	11	1	no	maximal, Sylow
227	C₂³×C₁₁	C₂⁴	1	2	yes	—
228	C₂²×D₁₁	—	4	2	no	—
229	C₂²×D₁₁	—	4	2	no	—
230	C₂²×D₁₁	C₂×Q₈	1	8	yes	complemented
231	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁	C₂⁴	1	2	yes	—
233	Q₈×C₁₁	—	4	2	no	—
234	Q₈×C₁₁	—	4	1	no	—
235	D₄×C₁₁	C₂×Q₈	1	4	yes	complemented
236	C₂×C₄×C₁₁	—	4	2	no	—
237	C₂×C₄×C₁₁	—	4	2	no	—
238	C₂×C₄×C₁₁	—	4	2	no	—
239	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
249	C₂²⋊D₁₁	C₂×Q₈	1	8	yes	complemented
250	C₂×Dic₁₁	—	2	4	no	—
251	C₂×Dic₁₁	—	4	2	no	—
252	C₂×Dic₁₁	—	4	2	no	—
253	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₁	C₂⁴	1	2	yes	—
256	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
263	D₄₄	C₂×Q₈	1	4	yes	complemented
264	C₄×D₁₁	—	2	2	no	—
265	C₄×D₁₁	—	2	4	no	—
266	C₄×D₁₁	—	4	2	no	—
267	C₄×D₁₁	—	4	2	no	—
268	C₄×D₁₁	—	4	1	no	—
269	C₄×D₁₁	—	4	2	no	—
270	C₄×D₁₁	—	4	2	no	—
271	C₄×D₁₁	—	4	2	no	—
272	C₄×D₁₁	—	4	2	no	—
273	C₄×D₁₁	C₂×Q₈	1	4	yes	complemented
274	Dic₂₂	—	2	2	no	—
275	Dic₂₂	—	2	4	no	—
276	Dic₂₂	—	2	2	no	—
277	Dic₂₂	—	4	2	no	—
278	Dic₂₂	—	4	2	no	—
279	Dic₂₂	—	4	2	no	—
280	Dic₂₂	—	4	1	no	—
281	Dic₂₂	—	4	2	no	—
282	#554	—	11	1	no	—
283	#554	—	11	1	no	—
284	#554	—	11	2	no	—
285	#554	—	11	2	no	—
286	#554	—	11	1	no	—
287	#554	—	11	1	no	—
288	#554	—	11	1	no	—
289	#554	—	11	2	no	—
290	#554	D₁₁	1	1	yes	characteristic, complemented
291	D₄×Q₈	—	11	1	no	—
292	D₄×Q₈	—	11	2	no	—
293	D₄×Q₈	—	11	1	no	—
294	#544	—	11	1	no	—
295	#544	—	11	1	no	—
296	#543	—	11	2	no	—
297	#543	—	11	2	no	—
298	#533	—	11	1	no	—
299	#533	—	11	1	no	—
300	C₂×C₂²⋊Q₈	—	11	2	no	—
301	C₂×C₂²⋊Q₈	—	11	2	no	—
302	#518	—	11	1	no	—
303	#518	—	11	1	no	—
304	C₂×C₄×D₄	—	11	1	no	—
305	C₂²×C₁₁	—	2	2	no	—
306	C₂²×C₁₁	—	2	2	no	—
307	C₂²×C₁₁	C₂²×Q₈	1	4	yes	—
308	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₁	—	2	1	no	—
310	C₂×D₁₁	—	2	2	no	—
311	C₂×D₁₁	—	2	1	no	—
312	C₂×D₁₁	—	2	2	no	—
313	C₂×D₁₁	—	4	8	no	—
314	C₂×D₁₁	C₂²×Q₈	1	2	yes	—
315	C₂×D₁₁	C₂²×Q₈	1	4	yes	—
316	C₄×C₁₁	—	2	1	no	—
317	C₄×C₁₁	—	2	1	no	—
318	C₄×C₁₁	—	2	2	no	—
319	C₄×C₁₁	—	2	2	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	1	no	—
325	C₄×C₁₁	C₂²×Q₈	1	2	yes	—
326	Dic₁₁	—	2	1	no	—
327	Dic₁₁	—	2	2	no	—
328	Dic₁₁	—	2	1	no	—
329	Dic₁₁	—	2	2	no	—
330	Dic₁₁	—	2	1	no	—
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	—	2	2	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	C₂²×Q₈	1	2	yes	—
335	Dic₁₁	H(5,𝔽₂)	1	2	yes	—
336	C₂²×Q₈	—	11	2	no	—
337	C₂²×Q₈	—	11	2	no	—
338	C₂²×D₄	—	11	1	no	—
339	C₂³×C₄	—	11	2	no	—
340	C₄⋊Q₈	—	11	1	no	—
341	C₄⋊Q₈	—	11	2	no	—
342	C₄⋊Q₈	—	11	1	no	—
343	C₄⋊Q₈	—	11	1	no	—
344	C₄⋊Q₈	—	11	1	no	—
345	C₄⋊Q₈	—	11	2	no	—
346	C₄⋊Q₈	—	11	1	no	—
347	C₄⋊Q₈	—	11	1	no	—
348	C₄⋊Q₈	—	11	1	no	—
349	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
350	#125	—	11	1	no	—
351	#125	—	11	1	no	—
352	#125	—	11	2	no	—
353	#125	—	11	2	no	—
354	#125	—	11	1	no	—
355	#125	—	11	1	no	—
356	#125	—	11	1	no	—
357	#125	—	11	1	no	—
358	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
359	#125	C₂×D₁₁	1	1	yes	characteristic, complemented
360	C₂²⋊Q₈	—	11	2	no	—
361	C₂²⋊Q₈	—	11	1	no	—
362	C₂²⋊Q₈	—	11	2	no	—
363	C₂²⋊Q₈	—	11	2	no	—
364	C₂²⋊Q₈	—	11	2	no	—
365	C₂²⋊Q₈	—	11	2	no	—
366	C₂²⋊Q₈	—	11	2	no	—
367	C₂²⋊Q₈	—	11	1	no	—
368	C₂²⋊Q₈	—	11	2	no	—
369	C₂²⋊Q₈	—	11	1	no	—
370	C₂²⋊Q₈	—	11	2	no	—
371	C₂²⋊Q₈	—	11	2	no	—
372	C₂²⋊Q₈	—	11	2	no	—
373	C₂²⋊Q₈	—	11	2	no	—
374	C₂²⋊Q₈	—	11	2	no	—
375	C₂²⋊Q₈	—	11	2	no	—
376	C₂²⋊Q₈	—	11	2	no	—
377	C₂²⋊Q₈	—	11	2	no	—
378	C₂²⋊Q₈	—	11	1	no	—
379	C₂²⋊Q₈	—	11	2	no	—
380	C₂²⋊Q₈	—	11	2	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	—	11	2	no	—
386	C₂²⋊Q₈	—	11	2	no	—
387	C₂²⋊Q₈	—	11	2	no	—
388	C₂²⋊Q₈	—	11	2	no	—
389	C₂²⋊Q₈	—	11	2	no	—
390	C₂²⋊Q₈	—	11	2	no	—
391	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
392	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
393	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
394	C₄×Q₈	—	11	2	no	—
395	C₄×Q₈	—	11	2	no	—
396	C₄×Q₈	—	11	1	no	—
397	C₄×Q₈	—	11	1	no	—
398	C₄×Q₈	—	11	1	no	—
399	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
400	C₄×D₄	—	11	1	no	—
401	C₄×D₄	—	11	1	no	—
402	C₄×D₄	—	11	1	no	—
403	C₄×D₄	—	11	2	no	—
404	C₄×D₄	—	11	2	no	—
405	C₄×D₄	—	11	2	no	—
406	C₄×D₄	—	11	1	no	—
407	C₄×D₄	—	11	1	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	1	no	—
415	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
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	1	no	—
422	C₂×C₄⋊C₄	—	11	2	no	—
423	C₂×C₄⋊C₄	—	11	2	no	—
424	C₂×C₄⋊C₄	—	11	1	no	—
425	C₂×C₄⋊C₄	—	11	2	no	—
426	C₂×C₄⋊C₄	—	11	2	no	—
427	C₂×C₄⋊C₄	—	11	2	no	—
428	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	complemented
429	C₂×C₂²⋊C₄	—	11	2	no	—
430	C₂×C₂²⋊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×C₄²	—	11	1	no	—
435	C₂×C₁₁	—	2	4	no	—
436	C₂×C₁₁	C₂³×Q₈	1	1	yes	characteristic
437	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₁₁	#585	1	1	yes	characteristic
439	D₁₁	—	2	2	no	—
440	D₁₁	—	2	4	no	—
441	C₂⁴	—	11	2	no	—
442	C₂×Q₈	—	11	2	no	—
443	C₂×Q₈	—	11	1	no	—
444	C₂×Q₈	—	11	1	no	—
445	C₂×Q₈	—	11	2	no	—
446	C₂×Q₈	—	11	1	no	—
447	C₂×Q₈	—	11	2	no	—
448	C₂×Q₈	—	11	2	no	—
449	C₂×Q₈	—	11	2	no	—
450	C₂×Q₈	—	44	4	no	—
451	C₂×Q₈	—	44	4	no	—
452	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
454	C₂×D₄	—	11	2	no	—
455	C₂×D₄	—	11	8	no	—
456	C₂×D₄	—	11	1	no	—
457	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
458	C₂²×C₄	—	11	1	no	—
459	C₂²×C₄	—	11	2	no	—
460	C₂²×C₄	—	11	2	no	—
461	C₂²×C₄	—	11	2	no	—
462	C₂²×C₄	—	11	1	no	—
463	C₂²×C₄	—	11	2	no	—
464	C₂²×C₄	—	11	1	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	2	no	—
471	C₂²×C₄	—	44	4	no	—
472	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
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	2	no	—
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	2	no	—
482	C₄⋊C₄	—	11	1	no	—
483	C₄⋊C₄	—	11	2	no	—
484	C₄⋊C₄	—	11	2	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	2	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	1	no	—
497	C₄⋊C₄	—	11	1	no	—
498	C₄⋊C₄	—	11	1	no	—
499	C₄⋊C₄	—	11	1	no	—
500	C₄⋊C₄	—	11	2	no	—
501	C₄⋊C₄	—	11	1	no	—
502	C₄⋊C₄	—	11	1	no	—
503	C₄⋊C₄	—	11	2	no	—
504	C₄⋊C₄	—	11	1	no	—
505	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
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	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
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	1	no	—
521	C₂²⋊C₄	—	11	1	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	1	no	—
524	C₂²⋊C₄	—	11	1	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	—	11	2	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	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
534	C₄²	—	11	1	no	—
535	C₄²	—	11	1	no	—
536	C₄²	—	11	1	no	—
537	C₄²	—	11	2	no	—
538	C₄²	—	11	2	no	—
539	C₄²	—	11	1	no	—
540	C₄²	—	11	1	no	—
541	C₄²	C₂²×D₁₁	1	1	yes	characteristic
542	C₄²	C₂²×D₁₁	1	1	yes	characteristic
543	C₄²	C₂²×D₁₁	1	1	yes	characteristic
544	C₁₁	#3501	1	1	yes	characteristic, complemented, Sylow
545	C₂³	—	11	1	no	—
546	C₂³	—	11	2	no	—
547	C₂³	—	11	8	no	—
548	C₂³	—	44	2	no	—
549	C₂³	—	44	2	no	—
550	C₂³	C₂³×D₁₁	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	22	2	no	—
554	Q₈	—	22	4	no	—
555	Q₈	—	22	2	no	—
556	Q₈	—	44	2	no	—
557	Q₈	—	44	2	no	—
558	Q₈	—	44	2	no	—
559	Q₈	—	44	2	no	—
560	Q₈	—	44	1	no	—
561	D₄	—	11	8	no	—
562	D₄	—	11	4	no	—
563	D₄	Q₈×D₁₁	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	11	1	no	—
568	C₂×C₄	—	11	1	no	—
569	C₂×C₄	—	11	4	no	—
570	C₂×C₄	—	11	1	no	—
571	C₂×C₄	—	11	1	no	—
572	C₂×C₄	—	11	2	no	—
573	C₂×C₄	—	11	1	no	—
574	C₂×C₄	—	11	1	no	—
575	C₂×C₄	—	11	2	no	—
576	C₂×C₄	—	11	1	no	—
577	C₂×C₄	—	11	2	no	—
578	C₂×C₄	—	22	2	no	—
579	C₂×C₄	—	22	4	no	—
580	C₂×C₄	—	22	4	no	—
581	C₂×C₄	—	44	2	no	—
582	C₂×C₄	—	44	2	no	—
583	C₂×C₄	—	44	2	no	—
584	C₂×C₄	—	44	2	no	—
585	C₂×C₄	—	44	2	no	—
586	C₂×C₄	—	44	2	no	—
587	C₂×C₄	—	44	1	no	—
588	C₂×C₄	—	44	2	no	—
589	C₂×C₄	—	44	2	no	—
590	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₁	1	2	yes	—
593	C₂×C₄	C₂³×D₁₁	1	2	yes	—
594	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₁	1	2	yes	—
599	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	11	2	no	—
603	C₂²	—	11	4	no	—
604	C₂²	—	22	2	no	—
605	C₂²	—	22	1	no	—
606	C₂²	—	22	2	no	—
607	C₂²	—	22	1	no	—
608	C₂²	—	44	8	no	—
609	C₂²	C₂×Q₈×D₁₁	1	4	yes	—
610	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	11	2	no	—
621	C₄	—	11	2	no	—
622	C₄	—	22	1	no	—
623	C₄	—	22	2	no	—
624	C₄	—	22	1	no	—
625	C₄	—	22	1	no	—
626	C₄	—	22	2	no	—
627	C₄	—	22	1	no	—
628	C₄	—	22	2	no	—
629	C₄	—	22	1	no	—
630	C₄	C₂×Q₈×D₁₁	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	22	2	no	—
633	C₂	—	22	4	no	—
634	C₂	C₂²×Q₈×D₁₁	1	1	yes	characteristic
635	C₂	#10623453	1	1	yes	characteristic
636	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#554	C₂
prime radical	C₂×D₄×D₁₁	C₂²
hypercenter	#554	D₁₁
hypocenter	C₁₁	#3501
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. #10623260	C₂	semidirect
3. #10623258	C₂	semidirect
4. #10623221	C₂	semidirect
5. #10623221	C₂	semidirect
6. #10623220	C₂	semidirect
7. #10623219	C₂	semidirect
8. #10623167	C₂	semidirect
9. #10623167	C₂	semidirect
10. #10623165	C₂	semidirect
11. #10623165	C₂	semidirect
12. #10623163	C₂	semidirect
13. D₁₁×C₂²⋊Q₈	C₂	semidirect
14. #10623110	C₂	semidirect
15. #10623109	C₂	semidirect
19. #10623070	C₂	semidirect
20. #10623070	C₂	semidirect
21. D₄×Dic₂₂	C₂	semidirect
22. #10623042	C₂	semidirect
23. C₂×#66949	C₂	semidirect
24. C₂×Q₈×D₁₁	C₂²	semidirect
27. C₂²×Dic₂₂	C₂²	semidirect
28. C₁₁×C₄⋊Q₈	C₂²	semidirect
29. C₁₁×#125	C₂²	semidirect
30. C₁₁×#125	C₂²	semidirect
31. C₁₁×C₂²⋊Q₈	C₂²	semidirect
32. C₁₁×C₂²⋊Q₈	C₂²	semidirect
33. C₁₁×C₂²⋊Q₈	C₂²	semidirect
34. C₄×Q₈×C₁₁	C₂²	semidirect
38. C₂×C₁₁×C₄⋊C₄	C₂²	semidirect
41. #66999	C₂²	semidirect
42. #66999	C₂²	semidirect
43. #66997	C₂²	semidirect
44. #66997	C₂²	semidirect
53. #66977	C₂²	semidirect
54. #66977	C₂²	semidirect
55. #66977	C₂²	semidirect
56. C₂×Dic₁₁⋊C₄	C₂²	semidirect
57. C₂×Dic₁₁⋊C₄	C₂²	semidirect
60. #66950	C₂²	semidirect
61. #66950	C₂²	semidirect
68. #66949	C₂²	semidirect
69. #66949	C₂²	semidirect
70. #66949	C₂²	semidirect
71. #66949	C₂²	semidirect
72. #66949	C₂²	semidirect
73. #66949	C₂²	semidirect
74. #66949	C₂²	semidirect
75. #66949	C₂²	semidirect
82. C₄⋊C₄×D₁₁	C₂²	semidirect
83. C₄⋊C₄×D₁₁	C₂²	semidirect
84. C₄⋊C₄×D₁₁	C₂²	semidirect
85. #66943	C₂²	semidirect
86. #66943	C₂²	semidirect
87. #66942	C₂²	semidirect
88. #66942	C₂²	semidirect
89. #66942	C₂²	semidirect
90. #66942	C₂²	semidirect
91. #66941	C₂²	semidirect
92. #66941	C₂²	semidirect
93. #66941	C₂²	semidirect
94. #66941	C₂²	semidirect
95. #66941	C₂²	semidirect
96. #66941	C₂²	semidirect
97. #66940	C₂²	semidirect
98. #66940	C₂²	semidirect
105. #66931	C₂²	semidirect
106. #66931	C₂²	semidirect
107. #66931	C₂²	semidirect
108. #66931	C₂²	semidirect
109. #66931	C₂²	semidirect
110. #66931	C₂²	semidirect
117. #66923	C₂²	semidirect
118. #66923	C₂²	semidirect
119. #66922	C₂²	semidirect
120. C₄×Dic₂₂	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
135. D₄×D₁₁	Q₈	semidirect
230. C₂²×D₁₁	C₂×Q₈	semidirect
235. D₄×C₁₁	C₂×Q₈	semidirect
249. C₂²⋊D₁₁	C₂×Q₈	semidirect
263. D₄₄	C₂×Q₈	semidirect
273. C₄×D₁₁	C₂×Q₈	semidirect
290. #554	D₁₁	semidirect
349. C₄⋊Q₈	C₂×D₁₁	semidirect
358. #125	C₂×D₁₁	semidirect
359. #125	C₂×D₁₁	semidirect
391. C₂²⋊Q₈	C₂×D₁₁	semidirect
392. C₂²⋊Q₈	C₂×D₁₁	semidirect
393. C₂²⋊Q₈	C₂×D₁₁	semidirect
399. C₄×Q₈	C₂×D₁₁	semidirect
428. C₂×C₄⋊C₄	C₂×D₁₁	semidirect
544. C₁₁	#3501	semidirect
563. D₄	Q₈×D₁₁	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
#10623260	2
#10623258	2
#10623221	2
#10623220	2
#10623219	2
#10623167	2
#10623165	2
#10623163	2
D₁₁×C₂²⋊Q₈	2
#10623110	2
#10623109	2
#10623076	2
C₄×D₄×D₁₁	2
#10623070	2
D₄×Dic₂₂	2
#10623042	2
C₂×#66949	2
#3501	11