Subgroups — C₁₁×#22783 #14599976

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1937	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1876	C₂	1	2	yes	maximal
7	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
19	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
20	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
21	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
22	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
23	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
24	C₁₁×#433	—	2	2	no	—
25	C₁₁×#432	—	2	1	no	—
26	C₁₁×#431	—	2	1	no	—
27	C₁₁×#427	C₂²	1	1	yes	characteristic
28	C₁₁×#424	—	2	2	no	—
29	C₁₁×#424	C₂²	1	2	yes	—
30	C₁₁×#423	—	2	1	no	—
31	C₁₁×#423	C₂²	1	1	yes	characteristic
32	C₁₁×#423	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₂×C₁₁×#104	C₂²	1	2	yes	—
37	C₁₁×#416	C₂²	1	1	yes	characteristic
38	C₁₁×#416	C₂²	1	1	yes	characteristic
39	C₁₁×#408	C₂²	1	2	yes	—
40	C₁₁×#405	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₁×#341	C₂²	1	2	yes	—
45	C₁₁×#341	C₂²	1	2	yes	—
46	C₁₁×#339	C₂²	1	2	yes	—
47	C₁₁×#339	C₂²	1	2	yes	—
48	C₁₁×#336	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
51	C₁₁×#135	—	2	2	no	—
52	C₁₁×#135	—	2	2	no	—
53	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
57	C₁₁×#131	—	2	4	no	—
58	C₁₁×#131	—	4	2	no	—
59	C₂×C₁₁×M₁₆	—	2	2	no	—
60	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₁	—	2	2	no	—
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
66	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	1	no	—
72	C₄×D₄×C₁₁	—	2	1	no	—
73	C₄×D₄×C₁₁	—	2	1	no	—
74	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
78	C₁₁×#117	—	2	1	no	—
79	C₁₁×#117	—	2	1	no	—
80	C₁₁×#117	C₂³	1	1	yes	characteristic
81	C₁₁×#117	C₂³	1	1	yes	characteristic
82	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₁₁	—	2	1	no	—
84	C₂×C₄²×C₁₁	—	2	1	no	—
85	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
91	C₁₁×C₄⋊C₈	—	2	2	no	—
92	C₁₁×C₄⋊C₈	—	2	2	no	—
93	C₁₁×C₄⋊C₈	—	2	1	no	—
94	C₁₁×C₄⋊C₈	—	2	1	no	—
95	C₁₁×C₄⋊C₈	—	2	1	no	—
96	C₁₁×C₄⋊C₈	—	2	1	no	—
97	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
98	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
99	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
100	C₁₁×#104	—	2	4	no	—
101	C₁₁×#104	—	4	2	no	—
102	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
103	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
104	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
105	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
106	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
107	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
108	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
109	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
110	C₁₁×C₂²⋊C₈	—	2	2	no	—
111	C₁₁×C₂²⋊C₈	—	2	2	no	—
112	C₁₁×#97	—	2	2	no	—
113	C₄×C₈×C₁₁	—	2	2	no	—
114	C₄×C₈×C₁₁	—	4	2	no	—
115	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
117	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
119	C₁₁×#95	—	2	1	no	—
120	#22783	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₁₁×#41	—	2	1	no	—
122	C₁₁×#41	—	2	1	no	—
123	C₁₁×#41	—	2	1	no	—
124	C₁₁×#41	—	2	1	no	—
125	C₁₁×#41	—	2	1	no	—
126	C₁₁×#41	—	2	1	no	—
127	C₁₁×#41	#41	1	2	yes	—
128	C₁₁×#41	#41	1	2	yes	—
129	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₁	—	2	1	no	—
132	C₂×D₄×C₁₁	—	2	1	no	—
133	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	—	2	1	no	—
136	C₂²×C₄×C₁₁	—	2	2	no	—
137	C₂²×C₄×C₁₁	—	2	1	no	—
138	C₂²×C₄×C₁₁	—	2	1	no	—
139	C₂²×C₄×C₁₁	—	2	1	no	—
140	C₂²×C₄×C₁₁	—	2	1	no	—
141	C₂²×C₄×C₁₁	—	2	1	no	—
142	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
145	C₁₁×Q₁₆	—	2	2	no	—
146	C₁₁×SD₁₆	—	2	2	no	—
147	C₁₁×SD₁₆	—	2	2	no	—
148	C₁₁×D₈	—	2	2	no	—
149	C₁₁×M₁₆	—	2	2	no	—
150	C₁₁×M₁₆	—	2	2	no	—
151	C₁₁×M₁₆	—	2	2	no	—
152	C₁₁×M₁₆	—	2	2	no	—
153	C₁₁×M₁₆	—	4	4	no	—
154	C₂×C₈×C₁₁	—	2	2	no	—
155	C₂×C₈×C₁₁	—	2	2	no	—
156	C₂×C₈×C₁₁	—	2	2	no	—
157	C₂×C₈×C₁₁	—	2	1	no	—
158	C₂×C₈×C₁₁	—	2	1	no	—
159	C₂×C₈×C₁₁	—	2	1	no	—
160	C₂×C₈×C₁₁	—	2	2	no	—
161	C₂×C₈×C₁₁	—	2	1	no	—
162	C₂×C₈×C₁₁	—	4	4	no	—
163	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
169	C₁₁×C₄⋊C₄	—	2	4	no	—
170	C₁₁×C₄⋊C₄	—	2	1	no	—
171	C₁₁×C₄⋊C₄	—	2	1	no	—
172	C₁₁×C₄⋊C₄	—	2	1	no	—
173	C₁₁×C₄⋊C₄	—	2	1	no	—
174	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
175	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
177	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
178	C₁₁×C₂²⋊C₄	—	2	1	no	—
179	C₁₁×C₂²⋊C₄	—	2	1	no	—
180	C₁₁×C₂²⋊C₄	—	2	1	no	—
181	C₁₁×C₂²⋊C₄	—	2	1	no	—
182	C₁₁×C₂²⋊C₄	—	2	1	no	—
183	C₁₁×C₂²⋊C₄	—	2	1	no	—
184	C₄²×C₁₁	—	2	1	no	—
185	C₄²×C₁₁	—	2	1	no	—
186	C₄²×C₁₁	—	2	1	no	—
187	C₄²×C₁₁	—	2	1	no	—
188	C₄²×C₁₁	—	2	1	no	—
189	C₄²×C₁₁	—	2	1	no	—
190	C₄²×C₁₁	—	2	2	no	—
191	C₄²×C₁₁	—	2	2	no	—
192	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
196	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
197	#2925	C₂×C₁₁	1	1	yes	characteristic, complemented
198	#2906	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#1937	C₂×C₁₁	1	2	yes	complemented
200	#1922	C₂×C₁₁	1	2	yes	complemented
201	#1876	C₂×C₁₁	1	2	yes	—
202	#1837	C₂×C₁₁	1	1	yes	characteristic, complemented
203	#1806	C₂×C₁₁	1	1	yes	characteristic, complemented
204	#1806	C₂×C₁₁	1	1	yes	characteristic, complemented
205	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
206	#1764	C₂×C₁₁	1	2	yes	complemented
207	C₂³×C₁₁	—	2	1	no	—
208	C₂³×C₁₁	—	2	1	no	—
209	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
210	Q₈×C₁₁	—	2	1	no	—
211	Q₈×C₁₁	—	2	1	no	—
212	Q₈×C₁₁	—	2	1	no	—
213	Q₈×C₁₁	#117	1	2	yes	—
214	D₄×C₁₁	—	2	2	no	—
215	D₄×C₁₁	—	2	2	no	—
216	D₄×C₁₁	—	2	1	no	—
217	D₄×C₁₁	—	2	1	no	—
218	D₄×C₁₁	—	2	1	no	—
219	D₄×C₁₁	—	4	1	no	—
220	D₄×C₁₁	—	4	1	no	—
221	D₄×C₁₁	#117	1	2	yes	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	2	4	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	2	1	no	—
229	C₂×C₄×C₁₁	—	2	1	no	—
230	C₂×C₄×C₁₁	—	2	1	no	—
231	C₂×C₄×C₁₁	—	2	1	no	—
232	C₂×C₄×C₁₁	—	4	1	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	4	2	no	—
235	C₂×C₄×C₁₁	—	4	1	no	—
236	C₂×C₄×C₁₁	—	4	1	no	—
237	C₂×C₄×C₁₁	—	4	2	no	—
238	C₂×C₄×C₁₁	—	4	2	no	—
239	C₂×C₄×C₁₁	—	8	1	no	—
240	C₂×C₄×C₁₁	—	8	1	no	—
241	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₁₁	—	2	1	no	—
252	C₈×C₁₁	—	2	1	no	—
253	C₈×C₁₁	—	2	1	no	—
254	C₈×C₁₁	—	2	1	no	—
255	C₈×C₁₁	—	2	2	no	—
256	C₈×C₁₁	—	2	2	no	—
257	C₈×C₁₁	—	4	2	no	—
258	C₈×C₁₁	—	4	2	no	—
259	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
260	C₂×#131	C₂²×C₁₁	1	2	yes	—
261	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
262	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
263	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
264	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
265	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
266	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
267	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
268	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
269	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
270	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
271	#433	—	2	2	no	—
272	#432	—	2	1	no	—
273	#431	—	2	1	no	—
274	#427	C₂²×C₁₁	1	1	yes	characteristic
275	#424	—	2	2	no	—
276	#424	C₂²×C₁₁	1	2	yes	—
277	#423	—	2	1	no	—
278	#423	C₂²×C₁₁	1	1	yes	characteristic
279	#423	C₂²×C₁₁	1	1	yes	characteristic
280	C₂×C₄⋊C₈	—	2	1	no	—
281	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×#104	C₂²×C₁₁	1	2	yes	—
283	C₂×#104	C₂²×C₁₁	1	2	yes	—
284	#416	C₂²×C₁₁	1	1	yes	characteristic
285	#416	C₂²×C₁₁	1	1	yes	characteristic
286	#408	C₂²×C₁₁	1	2	yes	—
287	#405	C₂²×C₁₁	1	2	yes	—
288	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
289	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
291	#341	C₂²×C₁₁	1	2	yes	—
292	#341	C₂²×C₁₁	1	2	yes	—
293	#339	C₂²×C₁₁	1	2	yes	—
294	#339	C₂²×C₁₁	1	2	yes	—
295	#336	C₂²×C₁₁	1	2	yes	—
296	C₂²×C₁₁	—	2	1	no	—
297	C₂²×C₁₁	—	2	1	no	—
298	C₂²×C₁₁	—	2	2	no	—
299	C₂²×C₁₁	—	4	1	no	—
300	C₂²×C₁₁	—	4	1	no	—
301	C₂²×C₁₁	—	4	1	no	—
302	C₂²×C₁₁	—	4	1	no	—
303	C₂²×C₁₁	—	4	1	no	—
304	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂²×C₁₁	#552	1	1	yes	characteristic
306	C₂²×C₁₁	#553	1	1	yes	characteristic
307	C₄×C₁₁	—	2	2	no	—
308	C₄×C₁₁	—	2	1	no	—
309	C₄×C₁₁	—	2	1	no	—
310	C₄×C₁₁	—	2	1	no	—
311	C₄×C₁₁	—	4	4	no	—
312	C₄×C₁₁	—	4	1	no	—
313	C₄×C₁₁	—	4	1	no	—
314	C₄×C₁₁	—	4	1	no	—
315	C₄×C₁₁	—	4	1	no	—
316	C₄×C₁₁	—	4	1	no	—
317	C₄×C₁₁	#443	1	2	yes	—
318	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
319	C₄×C₁₁	#520	1	1	yes	characteristic
320	C₄×C₁₁	#546	1	1	yes	characteristic
321	C₄×C₁₁	#548	1	1	yes	characteristic
322	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
323	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
324	#135	—	2	2	no	—
325	#135	—	2	2	no	—
326	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
330	#131	—	2	4	no	—
331	#131	—	4	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
334	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
339	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
340	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
341	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
342	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
348	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
349	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
350	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
351	#117	—	2	1	no	—
352	#117	—	2	1	no	—
353	#117	C₂³×C₁₁	1	1	yes	characteristic
354	#117	C₂³×C₁₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
359	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
360	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
361	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
362	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
363	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
364	C₄⋊C₈	—	2	2	no	—
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
371	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
372	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
373	#104	—	2	4	no	—
374	#104	—	4	2	no	—
375	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
376	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
377	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
378	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
379	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
380	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
381	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
382	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	#97	—	2	2	no	—
386	C₄×C₈	—	2	2	no	—
387	C₄×C₈	—	4	2	no	—
388	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
389	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
390	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
391	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
392	#95	—	2	1	no	—
393	C₂×C₁₁	—	2	1	no	—
394	C₂×C₁₁	—	2	1	no	—
395	C₂×C₁₁	—	4	2	no	—
396	C₂×C₁₁	—	8	1	no	—
397	C₂×C₁₁	#2352	1	1	yes	characteristic
398	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
399	C₂×C₁₁	#2957	1	1	yes	characteristic
400	#41	—	2	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	1	no	—
406	#41	C₁₁×#41	1	2	yes	—
407	#41	C₁₁×#41	1	2	yes	—
408	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
409	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
413	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
422	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
424	Q₁₆	—	2	2	no	—
425	SD₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	D₈	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	4	4	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	4	4	no	—
442	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
443	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
444	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
445	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
447	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
454	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
472	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
475	C₁₁	#22783	1	1	yes	characteristic, direct product factor, Sylow
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	C₁₁×#117	1	2	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	C₁₁×#117	1	2	yes	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	1	no	—
509	C₂×C₄	—	8	1	no	—
510	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
511	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
512	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
513	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
516	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
517	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
518	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	4	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
537	C₂²	C₁₁×#552	1	1	yes	characteristic
538	C₂²	C₁₁×#553	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	C₁₁×#443	1	2	yes	—
550	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
551	C₄	C₁₁×#520	1	1	yes	characteristic
552	C₄	C₁₁×#546	1	1	yes	characteristic
553	C₄	C₁₁×#548	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	C₁₁×#2352	1	1	yes	characteristic
559	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
560	C₂	C₁₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2925	C₂	semidirect
3. C₁₁×#2906	C₂	semidirect
4. C₁₁×#1937	C₂	semidirect
5. C₁₁×#1922	C₂	semidirect
7. C₁₁×#1837	C₂	semidirect
8. C₁₁×#1806	C₂	semidirect
9. C₁₁×#1806	C₂	semidirect
10. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₁₁×#1764	C₂	semidirect
16. C₄×C₁₁×Q₁₆	C₄	semidirect
17. C₄×C₁₁×Q₁₆	C₄	semidirect
18. C₄×C₁₁×SD₁₆	C₄	semidirect
19. C₄×C₁₁×SD₁₆	C₄	semidirect
20. C₄×C₁₁×SD₁₆	C₄	semidirect
21. C₄×C₁₁×SD₁₆	C₄	semidirect
22. C₄×C₁₁×D₈	C₄	semidirect
23. C₄×C₁₁×D₈	C₄	semidirect
120. #22783	C₁₁	direct (N × H)
197. #2925	C₂×C₁₁	semidirect
198. #2906	C₂×C₁₁	semidirect
199. #1937	C₂×C₁₁	semidirect
200. #1922	C₂×C₁₁	semidirect
202. #1837	C₂×C₁₁	semidirect
203. #1806	C₂×C₁₁	semidirect
204. #1806	C₂×C₁₁	semidirect
205. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
206. #1764	C₂×C₁₁	semidirect
263. C₄×Q₁₆	C₄×C₁₁	semidirect
264. C₄×Q₁₆	C₄×C₁₁	semidirect
265. C₄×SD₁₆	C₄×C₁₁	semidirect
266. C₄×SD₁₆	C₄×C₁₁	semidirect
267. C₄×SD₁₆	C₄×C₁₁	semidirect
268. C₄×SD₁₆	C₄×C₁₁	semidirect
269. C₄×D₈	C₄×C₁₁	semidirect
270. C₄×D₈	C₄×C₁₁	semidirect
475. C₁₁	#22783	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#135	2
C₁₁×#2925	2
C₁₁×#2906	2
C₁₁×#1937	2
C₁₁×#1922	2
C₁₁×#1876	2
C₁₁×#1837	2
C₁₁×#1806	2
C₈×C₁₁×C₄⋊C₄	2
C₁₁×#1764	2
#22783	11

Subgroups — C11×#22783 #14599976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22783 #14599976