Subgroups — D₁₁×#542 #13081986

Order 1408.

1132 conjugacy classes of subgroups.

The subgroup lattice has 666 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	D₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623241	C₂	1	2	yes	maximal, complemented
5	D₁₁×#126	C₂	1	2	yes	maximal, complemented
6	#10623213	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₁×#124	C₂	1	2	yes	maximal, complemented
8	D₁₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623200	C₂	1	2	yes	maximal, complemented
10	#10623193	C₂	1	2	yes	maximal, complemented
11	D₁₁×#123	C₂	1	2	yes	maximal, complemented
12	#10623174	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623171	C₂	1	2	yes	maximal, complemented
14	D₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	D₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	D₁₁×#121	C₂	1	1	yes	maximal, characteristic
17	#10623134	C₂	1	1	yes	maximal, characteristic, complemented
18	#10623113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#10623092	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623065	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₁	C₂²	1	2	yes	—
26	C₂×D₄×D₁₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₁	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₁	C₂²	1	2	yes	—
30	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#126	C₂²	1	2	yes	complemented
32	C₁₁×#124	C₂²	1	2	yes	complemented
33	C₁₁×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#123	C₂²	1	2	yes	complemented
35	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₁×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
41	#67000	C₂²	1	2	yes	complemented
42	#67000	C₂²	1	1	yes	characteristic, complemented
43	#66999	C₂²	1	2	yes	complemented
44	#66999	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
46	#66997	C₂²	1	2	yes	complemented
47	#66992	C₂²	1	2	yes	—
48	#66991	C₂²	1	1	yes	characteristic
49	#66989	C₂²	1	1	yes	characteristic, complemented
50	#66989	C₂²	1	2	yes	complemented
51	#66988	C₂²	1	2	yes	complemented
52	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
53	#66983	C₂²	1	1	yes	characteristic
54	#66982	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
56	#66979	C₂²	1	1	yes	characteristic, complemented
57	#66977	C₂²	1	1	yes	characteristic, complemented
58	#66977	C₂²	1	2	yes	complemented
59	#66951	C₂²	1	2	yes	complemented
60	#66951	C₂²	1	2	yes	complemented
61	#66951	C₂²	1	2	yes	complemented
62	#66950	C₂²	1	2	yes	complemented
63	#66950	C₂²	1	1	yes	characteristic, complemented
64	#66949	C₂²	1	2	yes	complemented
65	#66949	C₂²	1	2	yes	complemented
66	#66949	C₂²	1	2	yes	complemented
67	#66948	C₂²	1	1	yes	characteristic
68	#66947	C₂²	1	2	yes	complemented
69	#66947	C₂²	1	2	yes	complemented
70	#66946	C₂²	1	1	yes	characteristic, complemented
71	#66945	C₂²	1	1	yes	characteristic, complemented
72	#66945	C₂²	1	1	yes	characteristic, complemented
73	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
74	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
75	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
76	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
77	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
80	#66941	C₂²	1	2	yes	complemented
81	#66941	C₂²	1	1	yes	characteristic, complemented
82	#66941	C₂²	1	1	yes	characteristic, complemented
83	#66940	C₂²	1	1	yes	characteristic, complemented
84	#66940	C₂²	1	2	yes	complemented
85	#66939	C₂²	1	2	yes	complemented
86	#66938	C₂²	1	2	yes	complemented
87	#66938	C₂²	1	2	yes	complemented
88	#66938	C₂²	1	2	yes	complemented
89	#66938	C₂²	1	2	yes	complemented
90	#66938	C₂²	1	2	yes	complemented
91	#66938	C₂²	1	2	yes	complemented
92	#66937	C₂²	1	2	yes	—
93	#66936	C₂²	1	2	yes	complemented
94	#66936	C₂²	1	2	yes	complemented
95	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₁	C₂²	1	2	yes	—
103	#66932	C₂²	1	2	yes	complemented
104	#66932	C₂²	1	2	yes	complemented
105	#66932	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	#66930	C₂²	1	1	yes	characteristic, complemented
110	#66930	C₂²	1	1	yes	characteristic, complemented
111	#66929	C₂²	1	2	yes	complemented
112	#66928	C₂²	1	2	yes	complemented
113	#66928	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₄₄	C₂²	1	1	yes	characteristic, complemented
115	#66925	C₂²	1	1	yes	characteristic, complemented
116	#66925	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₁	C₂²	1	2	yes	—
118	C₄²×D₁₁	C₂²	1	1	yes	characteristic
119	C₄²×D₁₁	C₂²	1	1	yes	characteristic
120	#66922	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	2	yes	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	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
127	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
134	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₁	C₂³	1	2	yes	—
136	Q₈×D₁₁	—	2	4	no	—
137	Q₈×D₁₁	—	4	4	no	—
138	D₄×D₁₁	—	2	4	no	—
139	D₄×D₁₁	—	4	4	no	—
140	C₂×D₄₄	C₂³	1	1	yes	characteristic
141	C₂×D₄₄	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁	—	2	4	no	—
143	C₂×C₄×D₁₁	—	4	4	no	—
144	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂³	1	2	yes	—
147	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁	C₂³	1	2	yes	—
150	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₁	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₁	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁	C₂³	1	2	yes	—
156	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₂	C₂³	1	2	yes	—
159	C₂×Dic₂₂	C₂³	1	2	yes	—
160	C₂×Dic₂₂	C₂³	1	2	yes	—
161	C₂×Dic₂₂	C₂³	1	2	yes	—
162	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
168	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₄²×C₁₁	C₂³	1	1	yes	characteristic
177	C₄²×C₁₁	C₂³	1	2	yes	—
178	C₄²×C₁₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
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	2	yes	—
191	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₁)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₁	C₂³	1	2	yes	—
202	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₁	C₂³	1	2	yes	—
204	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₁	C₂³	1	2	yes	—
206	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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	C₂×#542	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₁	C₂⁴	1	2	yes	—
231	C₂²×D₁₁	—	2	2	no	—
232	C₂²×D₁₁	—	2	4	no	—
233	C₂²×D₁₁	—	2	4	no	—
234	C₂²×D₁₁	—	2	2	no	—
235	C₂²×D₁₁	—	2	2	no	—
236	C₂²×D₁₁	—	2	4	no	—
237	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₁	C₂⁴	1	2	yes	—
239	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
240	Q₈×C₁₁	—	2	2	no	—
241	Q₈×C₁₁	—	4	2	no	—
242	D₄×C₁₁	—	2	2	no	—
243	D₄×C₁₁	—	4	2	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₁	—	2	4	no	—
256	C₂²⋊D₁₁	—	4	2	no	—
257	C₂²⋊D₁₁	—	4	2	no	—
258	C₂×Dic₁₁	—	2	2	no	—
259	C₂×Dic₁₁	—	4	2	no	—
260	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁	C₂⁴	1	2	yes	—
265	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
269	D₄₄	—	2	2	no	—
270	D₄₄	—	4	2	no	—
271	C₄×D₁₁	—	2	2	no	—
272	C₄×D₁₁	—	2	4	no	—
273	C₄×D₁₁	—	2	2	no	—
274	C₄×D₁₁	—	2	4	no	—
275	C₄×D₁₁	—	2	4	no	—
276	C₄×D₁₁	—	2	2	no	—
277	C₄×D₁₁	—	2	2	no	—
278	C₄×D₁₁	—	2	2	no	—
279	C₄×D₁₁	—	2	2	no	—
280	C₄×D₁₁	—	2	2	no	—
281	C₄×D₁₁	—	4	2	no	—
282	C₄×D₁₁	—	4	2	no	—
283	C₄×D₁₁	#41	1	4	yes	—
284	Dic₂₂	—	2	2	no	—
285	Dic₂₂	—	2	4	no	—
286	Dic₂₂	—	4	2	no	—
287	Dic₂₂	—	4	2	no	—
288	Dic₂₂	—	4	2	no	—
289	#542	—	11	1	no	—
290	#542	—	11	2	no	—
291	#542	—	11	2	no	—
292	#542	—	11	1	no	—
293	#542	—	11	2	no	—
294	#542	—	11	2	no	—
295	#542	—	11	1	no	—
296	#542	—	11	1	no	—
297	#542	—	11	1	no	—
298	#542	—	11	1	no	—
299	#542	—	11	1	no	—
300	#542	D₁₁	1	1	yes	characteristic, direct product factor
301	C₂×C₄⋊Q₈	—	11	1	no	—
302	C₂×#126	—	11	2	no	—
303	C₂×#124	—	11	1	no	—
304	C₂×#124	—	11	2	no	—
305	C₂×#123	—	11	2	no	—
306	C₂×C₂²⋊Q₈	—	11	2	no	—
307	C₂×C₂²⋊Q₈	—	11	1	no	—
308	C₂×#121	—	11	1	no	—
309	C₂×C₄×Q₈	—	11	1	no	—
310	C₂×C₄×D₄	—	11	1	no	—
311	C₂×#117	—	11	1	no	—
312	C₂²×C₁₁	—	2	1	no	—
313	C₂²×C₁₁	—	2	2	no	—
314	C₂²×C₁₁	—	2	2	no	—
315	C₂²×C₁₁	—	2	1	no	—
316	C₂²×C₁₁	—	2	1	no	—
317	C₂²×C₁₁	—	2	2	no	—
318	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
319	C₂×D₁₁	—	2	1	no	—
320	C₂×D₁₁	—	2	2	no	—
321	C₂×D₁₁	—	2	2	no	—
322	C₂×D₁₁	—	2	1	no	—
323	C₂×D₁₁	—	2	1	no	—
324	C₂×D₁₁	—	2	2	no	—
325	C₂×D₁₁	—	4	4	no	—
326	C₂×D₁₁	—	4	8	no	—
327	C₂×D₁₁	C₂×#41	1	2	yes	—
328	C₂×D₁₁	H(5,𝔽₂)	1	2	yes	—
329	C₂×D₁₁	2₋¹⁺⁴	1	2	yes	—
330	C₄×C₁₁	—	2	1	no	—
331	C₄×C₁₁	—	2	2	no	—
332	C₄×C₁₁	—	2	1	no	—
333	C₄×C₁₁	—	2	2	no	—
334	C₄×C₁₁	—	2	2	no	—
335	C₄×C₁₁	—	2	1	no	—
336	C₄×C₁₁	—	2	1	no	—
337	C₄×C₁₁	—	2	1	no	—
338	C₄×C₁₁	C₂×#41	1	2	yes	—
339	Dic₁₁	—	2	2	no	—
340	Dic₁₁	—	2	1	no	—
341	Dic₁₁	—	2	1	no	—
342	Dic₁₁	—	2	2	no	—
343	Dic₁₁	—	2	2	no	—
344	Dic₁₁	—	2	1	no	—
345	Dic₁₁	—	2	1	no	—
346	Dic₁₁	—	2	1	no	—
347	Dic₁₁	C₂×#41	1	2	yes	—
348	C₂²×Q₈	—	11	1	no	—
349	C₂²×Q₈	—	11	2	no	—
350	C₂²×D₄	—	11	1	no	—
351	C₂²×D₄	—	11	2	no	—
352	C₂³×C₄	—	11	1	no	—
353	C₂³×C₄	—	11	2	no	—
354	C₄⋊Q₈	—	11	2	no	—
355	C₄⋊Q₈	—	11	2	no	—
356	C₄⋊Q₈	—	11	1	no	—
357	C₄⋊Q₈	—	11	1	no	—
358	C₄⋊Q₈	—	11	1	no	—
359	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
360	#126	—	11	2	no	—
361	#126	—	11	2	no	—
362	#126	—	11	2	no	—
363	#126	—	11	2	no	—
364	#126	—	11	2	no	—
365	#126	—	11	2	no	—
366	#126	—	11	2	no	—
367	#126	C₂×D₁₁	1	2	yes	complemented
368	#124	—	11	1	no	—
369	#124	—	11	2	no	—
370	#124	—	11	1	no	—
371	#124	—	11	2	no	—
372	#124	—	11	2	no	—
373	#124	—	11	2	no	—
374	#124	—	11	2	no	—
375	#124	—	11	2	no	—
376	#124	—	11	2	no	—
377	#124	—	11	2	no	—
378	#124	—	11	1	no	—
379	#124	—	11	2	no	—
380	#124	C₂×D₁₁	1	1	yes	characteristic, complemented
381	#124	C₂×D₁₁	1	2	yes	complemented
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	#123	—	11	2	no	—
389	#123	C₂×D₁₁	1	2	yes	complemented
390	C₂²⋊Q₈	—	11	2	no	—
391	C₂²⋊Q₈	—	11	1	no	—
392	C₂²⋊Q₈	—	11	2	no	—
393	C₂²⋊Q₈	—	11	1	no	—
394	C₂²⋊Q₈	—	11	2	no	—
395	C₂²⋊Q₈	—	11	2	no	—
396	C₂²⋊Q₈	—	11	2	no	—
397	C₂²⋊Q₈	—	11	2	no	—
398	C₂²⋊Q₈	—	11	1	no	—
399	C₂²⋊Q₈	—	11	2	no	—
400	C₂²⋊Q₈	—	11	2	no	—
401	C₂²⋊Q₈	—	11	2	no	—
402	C₂²⋊Q₈	C₂×D₁₁	1	2	yes	complemented
403	C₂²⋊Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
404	#121	—	11	1	no	—
405	#121	—	11	2	no	—
406	#121	—	11	1	no	—
407	#121	—	11	1	no	—
408	#121	—	11	2	no	—
409	#121	C₂×D₁₁	1	1	yes	characteristic
410	C₄×Q₈	—	11	1	no	—
411	C₄×Q₈	—	11	2	no	—
412	C₄×Q₈	—	11	1	no	—
413	C₄×Q₈	—	11	2	no	—
414	C₄×Q₈	—	11	1	no	—
415	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	2	no	—
420	C₄×D₄	—	11	1	no	—
421	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
422	#117	—	11	1	no	—
423	#117	—	11	1	no	—
424	#117	—	11	1	no	—
425	#117	—	11	1	no	—
426	#117	—	11	1	no	—
427	#117	—	11	1	no	—
428	#117	—	11	1	no	—
429	#117	C₂×D₁₁	1	1	yes	characteristic, complemented
430	C₂×C₄⋊C₄	—	11	1	no	—
431	C₂×C₄⋊C₄	—	11	1	no	—
432	C₂×C₄⋊C₄	—	11	1	no	—
433	C₂×C₄⋊C₄	—	11	1	no	—
434	C₂×C₄⋊C₄	—	11	2	no	—
435	C₂×C₄⋊C₄	—	11	2	no	—
436	C₂×C₄⋊C₄	—	11	2	no	—
437	C₂×C₂²⋊C₄	—	11	1	no	—
438	C₂×C₂²⋊C₄	—	11	1	no	—
439	C₂×C₂²⋊C₄	—	11	2	no	—
440	C₂×C₂²⋊C₄	—	11	2	no	—
441	C₂×C₂²⋊C₄	—	11	2	no	—
442	C₂×C₂²⋊C₄	—	11	2	no	—
443	C₂×C₂²⋊C₄	—	11	2	no	—
444	C₂×C₄²	—	11	1	no	—
445	C₂×C₄²	—	11	1	no	—
446	C₂×C₄²	—	11	2	no	—
447	C₂×C₁₁	—	4	1	no	—
448	C₂×C₁₁	—	4	2	no	—
449	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
450	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
452	D₁₁	—	4	1	no	—
453	D₁₁	—	4	2	no	—
454	D₁₁	#542	1	4	yes	direct product factor
455	C₂⁴	—	11	1	no	—
456	C₂⁴	—	11	2	no	—
457	C₂×Q₈	—	11	2	no	—
458	C₂×Q₈	—	11	1	no	—
459	C₂×Q₈	—	11	2	no	—
460	C₂×Q₈	—	11	2	no	—
461	C₂×Q₈	—	11	2	no	—
462	C₂×Q₈	—	22	4	no	—
463	C₂×Q₈	—	44	4	no	—
464	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₁₁	1	2	yes	—
466	C₂×D₄	—	11	2	no	—
467	C₂×D₄	—	11	2	no	—
468	C₂×D₄	—	11	2	no	—
469	C₂×D₄	—	11	1	no	—
470	C₂×D₄	—	11	2	no	—
471	C₂×D₄	—	22	4	no	—
472	C₂×D₄	—	44	4	no	—
473	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
474	C₂×D₄	C₂²×D₁₁	1	2	yes	—
475	C₂²×C₄	—	11	1	no	—
476	C₂²×C₄	—	11	1	no	—
477	C₂²×C₄	—	11	2	no	—
478	C₂²×C₄	—	11	1	no	—
479	C₂²×C₄	—	11	1	no	—
480	C₂²×C₄	—	11	2	no	—
481	C₂²×C₄	—	11	1	no	—
482	C₂²×C₄	—	11	1	no	—
483	C₂²×C₄	—	11	2	no	—
484	C₂²×C₄	—	11	1	no	—
485	C₂²×C₄	—	11	2	no	—
486	C₂²×C₄	—	11	1	no	—
487	C₂²×C₄	—	11	1	no	—
488	C₂²×C₄	—	11	2	no	—
489	C₂²×C₄	—	11	2	no	—
490	C₂²×C₄	—	22	4	no	—
491	C₂²×C₄	—	44	4	no	—
492	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
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	2	no	—
503	C₄⋊C₄	—	11	1	no	—
504	C₄⋊C₄	—	11	2	no	—
505	C₄⋊C₄	—	11	2	no	—
506	C₄⋊C₄	—	11	2	no	—
507	C₄⋊C₄	—	11	2	no	—
508	C₄⋊C₄	—	11	2	no	—
509	C₄⋊C₄	—	11	2	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	2	no	—
512	C₄⋊C₄	—	11	2	no	—
513	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
520	C₂²⋊C₄	—	11	1	no	—
521	C₂²⋊C₄	—	11	1	no	—
522	C₂²⋊C₄	—	11	2	no	—
523	C₂²⋊C₄	—	11	2	no	—
524	C₂²⋊C₄	—	11	2	no	—
525	C₂²⋊C₄	—	11	2	no	—
526	C₂²⋊C₄	—	11	2	no	—
527	C₂²⋊C₄	—	11	1	no	—
528	C₂²⋊C₄	—	11	1	no	—
529	C₂²⋊C₄	—	11	1	no	—
530	C₂²⋊C₄	—	11	1	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	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	2	no	—
541	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
548	C₄²	—	11	1	no	—
549	C₄²	—	11	1	no	—
550	C₄²	—	11	1	no	—
551	C₄²	—	11	1	no	—
552	C₄²	—	11	1	no	—
553	C₄²	—	11	1	no	—
554	C₄²	—	11	2	no	—
555	C₄²	—	11	2	no	—
556	C₄²	—	11	2	no	—
557	C₄²	C₂²×D₁₁	1	1	yes	characteristic
558	C₄²	C₂²×D₁₁	1	1	yes	characteristic
559	C₄²	C₂²×D₁₁	1	2	yes	—
560	C₁₁	C₂×#542	1	1	yes	characteristic, complemented, Sylow
561	C₂³	—	11	1	no	—
562	C₂³	—	11	1	no	—
563	C₂³	—	11	2	no	—
564	C₂³	—	22	2	no	—
565	C₂³	—	22	4	no	—
566	C₂³	—	22	4	no	—
567	C₂³	—	22	2	no	—
568	C₂³	—	22	2	no	—
569	C₂³	—	22	4	no	—
570	C₂³	C₂³×D₁₁	1	1	yes	characteristic
571	C₂³	C₂³×D₁₁	1	2	yes	—
572	Q₈	—	2	2	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	22	4	no	—
575	Q₈	—	22	2	no	—
576	Q₈	—	44	2	no	—
577	Q₈	—	44	2	no	—
578	Q₈	—	44	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	22	4	no	—
582	D₄	—	22	2	no	—
583	D₄	—	44	2	no	—
584	D₄	—	44	2	no	—
585	D₄	—	44	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	11	1	no	—
589	C₂×C₄	—	11	4	no	—
590	C₂×C₄	—	11	1	no	—
591	C₂×C₄	—	11	1	no	—
592	C₂×C₄	—	11	2	no	—
593	C₂×C₄	—	11	1	no	—
594	C₂×C₄	—	11	1	no	—
595	C₂×C₄	—	11	2	no	—
596	C₂×C₄	—	11	1	no	—
597	C₂×C₄	—	11	2	no	—
598	C₂×C₄	—	22	2	no	—
599	C₂×C₄	—	22	2	no	—
600	C₂×C₄	—	22	2	no	—
601	C₂×C₄	—	22	4	no	—
602	C₂×C₄	—	22	4	no	—
603	C₂×C₄	—	22	4	no	—
604	C₂×C₄	—	22	2	no	—
605	C₂×C₄	—	22	2	no	—
606	C₂×C₄	—	22	2	no	—
607	C₂×C₄	—	22	2	no	—
608	C₂×C₄	—	22	2	no	—
609	C₂×C₄	—	44	2	no	—
610	C₂×C₄	—	44	2	no	—
611	C₂×C₄	—	44	2	no	—
612	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₁	1	2	yes	—
615	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₁	1	2	yes	—
618	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₁	1	2	yes	—
620	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	11	2	no	—
628	C₂²	—	11	2	no	—
629	C₂²	—	11	2	no	—
630	C₂²	—	22	1	no	—
631	C₂²	—	22	2	no	—
632	C₂²	—	22	2	no	—
633	C₂²	—	22	1	no	—
634	C₂²	—	22	1	no	—
635	C₂²	—	22	2	no	—
636	C₂²	—	44	4	no	—
637	C₂²	—	44	8	no	—
638	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	11	2	no	—
648	C₄	—	22	1	no	—
649	C₄	—	22	2	no	—
650	C₄	—	22	1	no	—
651	C₄	—	22	2	no	—
652	C₄	—	22	2	no	—
653	C₄	—	22	1	no	—
654	C₄	—	22	1	no	—
655	C₄	—	22	1	no	—
656	C₄	#41×D₁₁	1	2	yes	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	11	4	no	—
660	C₂	—	44	1	no	—
661	C₂	—	44	2	no	—
662	C₂	C₂×#41×D₁₁	1	1	yes	characteristic
663	C₂	D₁₁×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂	D₁₁×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	C₁₁×#542	C₂
prime radical	D₁₁×#121	C₂
hypercenter	#542	D₁₁
hypocenter	C₁₁	C₂×#542
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. D₁₁×C₄⋊Q₈	C₂	semidirect
4. #10623241	C₂	semidirect
5. D₁₁×#126	C₂	semidirect
6. #10623213	C₂	semidirect
7. D₁₁×#124	C₂	semidirect
8. D₁₁×#124	C₂	semidirect
9. #10623200	C₂	semidirect
10. #10623193	C₂	semidirect
11. D₁₁×#123	C₂	semidirect
12. #10623174	C₂	semidirect
13. #10623171	C₂	semidirect
14. D₁₁×C₂²⋊Q₈	C₂	semidirect
15. D₁₁×C₂²⋊Q₈	C₂	semidirect
17. #10623134	C₂	semidirect
18. #10623113	C₂	semidirect
19. C₄×Q₈×D₁₁	C₂	semidirect
20. #10623092	C₂	semidirect
21. C₄×D₄×D₁₁	C₂	semidirect
22. #10623065	C₂	semidirect
23. D₁₁×#117	C₂	semidirect
30. C₁₁×C₄⋊Q₈	C₂²	semidirect
31. C₁₁×#126	C₂²	semidirect
32. C₁₁×#124	C₂²	semidirect
33. C₁₁×#124	C₂²	semidirect
34. C₁₁×#123	C₂²	semidirect
35. C₁₁×C₂²⋊Q₈	C₂²	semidirect
36. C₁₁×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₁	C₂²	semidirect
39. C₄×D₄×C₁₁	C₂²	semidirect
40. C₁₁×#117	C₂²	semidirect
41. #67000	C₂²	semidirect
42. #67000	C₂²	semidirect
43. #66999	C₂²	semidirect
44. #66999	C₂²	semidirect
45. Q₈×Dic₁₁	C₂²	semidirect
46. #66997	C₂²	semidirect
49. #66989	C₂²	semidirect
50. #66989	C₂²	semidirect
51. #66988	C₂²	semidirect
52. D₄×Dic₁₁	C₂²	semidirect
54. #66982	C₂²	semidirect
55. C₄×C₂²⋊D₁₁	C₂²	semidirect
56. #66979	C₂²	semidirect
57. #66977	C₂²	semidirect
58. #66977	C₂²	semidirect
59. #66951	C₂²	semidirect
60. #66951	C₂²	semidirect
61. #66951	C₂²	semidirect
62. #66950	C₂²	semidirect
63. #66950	C₂²	semidirect
64. #66949	C₂²	semidirect
65. #66949	C₂²	semidirect
66. #66949	C₂²	semidirect
68. #66947	C₂²	semidirect
69. #66947	C₂²	semidirect
70. #66946	C₂²	semidirect
71. #66945	C₂²	semidirect
72. #66945	C₂²	semidirect
80. #66941	C₂²	semidirect
81. #66941	C₂²	semidirect
82. #66941	C₂²	semidirect
83. #66940	C₂²	semidirect
84. #66940	C₂²	semidirect
85. #66939	C₂²	semidirect
86. #66938	C₂²	semidirect
87. #66938	C₂²	semidirect
88. #66938	C₂²	semidirect
89. #66938	C₂²	semidirect
90. #66938	C₂²	semidirect
91. #66938	C₂²	semidirect
93. #66936	C₂²	semidirect
94. #66936	C₂²	semidirect
95. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
103. #66932	C₂²	semidirect
104. #66932	C₂²	semidirect
105. #66932	C₂²	semidirect
106. #66931	C₂²	semidirect
107. #66931	C₂²	semidirect
108. #66931	C₂²	semidirect
109. #66930	C₂²	semidirect
110. #66930	C₂²	semidirect
111. #66929	C₂²	semidirect
112. #66928	C₂²	semidirect
113. #66928	C₂²	semidirect
114. C₄×D₄₄	C₂²	semidirect
115. #66925	C₂²	semidirect
116. #66925	C₂²	semidirect
120. #66922	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
300. #542	D₁₁	direct (N × H)
359. C₄⋊Q₈	C₂×D₁₁	semidirect
367. #126	C₂×D₁₁	semidirect
380. #124	C₂×D₁₁	semidirect
381. #124	C₂×D₁₁	semidirect
389. #123	C₂×D₁₁	semidirect
402. C₂²⋊Q₈	C₂×D₁₁	semidirect
403. C₂²⋊Q₈	C₂×D₁₁	semidirect
415. C₄×Q₈	C₂×D₁₁	semidirect
421. C₄×D₄	C₂×D₁₁	semidirect
429. #117	C₂×D₁₁	semidirect
454. D₁₁	#542	direct (N × H)
560. C₁₁	C₂×#542	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
D₁₁×C₄⋊Q₈	2
#10623241	2
D₁₁×#126	2
#10623213	2
D₁₁×#124	2
#10623200	2
#10623193	2
D₁₁×#123	2
#10623174	2
#10623171	2
D₁₁×C₂²⋊Q₈	2
D₁₁×#121	2
#10623134	2
#10623113	2
C₄×Q₈×D₁₁	2
#10623092	2
C₄×D₄×D₁₁	2
#10623065	2
D₁₁×#117	2
C₂×#542	11

Subgroups — D11×#542 #13081986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#542 #13081986