Subgroups — C₁₁×#23220 #14600413

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2366	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1982	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1936	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1926	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1864	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1762	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
15	C₂×C₄×D₄×C₁₁	—	2	1	no	—
16	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
17	C₁₁×#486	C₄	1	8	yes	complemented
18	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#102	C₂²	1	2	yes	—
22	C₂×C₁₁×#102	C₂²	1	2	yes	—
23	C₂×C₁₁×#102	C₂²	1	2	yes	—
24	C₂×C₁₁×#102	C₂²	1	2	yes	—
25	C₂×C₁₁×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×#391	—	2	1	no	—
28	C₁₁×#390	—	2	1	no	—
29	C₁₁×#390	C₂²	1	2	yes	—
30	C₁₁×#389	C₂²	1	2	yes	—
31	C₁₁×#387	—	2	2	no	—
32	C₁₁×#386	—	2	2	no	—
33	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₁×#340	C₂²	1	2	yes	—
38	C₁₁×#340	C₂²	1	1	yes	characteristic
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#340	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₁	—	2	1	no	—
43	C₂²×D₄×C₁₁	—	2	1	no	—
44	C₂²×D₄×C₁₁	—	2	1	no	—
45	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₁	—	2	2	no	—
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	—	2	2	no	—
51	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
52	C₁₁×#127	—	2	2	no	—
53	C₁₁×#127	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₁₁	—	4	4	no	—
55	C₄×D₄×C₁₁	—	2	4	no	—
56	C₄×D₄×C₁₁	—	4	2	no	—
57	C₄×D₄×C₁₁	—	4	4	no	—
58	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₁	—	2	1	no	—
71	C₂×C₄²×C₁₁	—	2	2	no	—
72	C₂×C₄²×C₁₁	—	2	1	no	—
73	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×#106	—	2	2	no	—
76	C₁₁×#106	—	2	2	no	—
77	C₁₁×C₄⋊C₈	—	2	2	no	—
78	C₁₁×#102	—	2	4	no	—
79	C₁₁×#102	—	4	2	no	—
80	C₁₁×#102	C₂×C₄	1	8	yes	complemented
81	C₁₁×#102	C₂×C₄	1	8	yes	complemented
82	C₁₁×#97	—	4	2	no	—
83	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
84	C₁₁×#95	—	2	1	no	—
85	C₁₁×#95	—	2	1	no	—
86	C₁₁×#95	—	2	2	no	—
87	C₁₁×#95	—	2	2	no	—
88	C₁₁×#95	D₄	1	2	yes	—
89	#23220	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₁	—	2	2	no	—
91	C₂×Q₈×C₁₁	—	2	4	no	—
92	C₂×Q₈×C₁₁	—	4	2	no	—
93	C₂×Q₈×C₁₁	—	4	2	no	—
94	C₂×D₄×C₁₁	—	2	4	no	—
95	C₂×D₄×C₁₁	—	2	4	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	2	no	—
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	2	2	no	—
101	C₂×D₄×C₁₁	—	4	2	no	—
102	C₂×D₄×C₁₁	—	4	2	no	—
103	C₂×D₄×C₁₁	—	8	1	no	—
104	C₂×D₄×C₁₁	—	8	1	no	—
105	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₁	—	2	1	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	4	4	no	—
112	C₂²×C₄×C₁₁	—	4	4	no	—
113	C₂²×C₄×C₁₁	—	8	2	no	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
128	C₁₁×C₄⋊C₄	—	2	4	no	—
129	C₁₁×C₄⋊C₄	—	2	2	no	—
130	C₁₁×C₄⋊C₄	—	2	2	no	—
131	C₁₁×C₄⋊C₄	—	2	2	no	—
132	C₁₁×C₄⋊C₄	—	2	1	no	—
133	C₁₁×C₄⋊C₄	—	2	1	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	1	no	—
136	C₁₁×C₄⋊C₄	—	2	1	no	—
137	C₁₁×C₄⋊C₄	—	2	1	no	—
138	C₁₁×C₄⋊C₄	—	4	4	no	—
139	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
140	C₁₁×C₄⋊C₄	#41	1	2	yes	—
141	C₁₁×C₄⋊C₄	#41	1	2	yes	—
142	C₁₁×C₂²⋊C₄	—	4	4	no	—
143	C₁₁×C₂²⋊C₄	—	4	4	no	—
144	C₁₁×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	—	4	4	no	—
148	C₄²×C₁₁	—	4	2	no	—
149	C₄²×C₁₁	—	4	2	no	—
150	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₁	#41	1	2	yes	—
152	C₂×#486	C₂×C₁₁	1	1	yes	characteristic
153	#2366	C₂×C₁₁	1	1	yes	characteristic
154	#2365	C₂×C₁₁	1	1	yes	characteristic, complemented
155	#1988	C₂×C₁₁	1	1	yes	characteristic, complemented
156	#1982	C₂×C₁₁	1	1	yes	characteristic
157	#1936	C₂×C₁₁	1	2	yes	complemented
158	#1926	C₂×C₁₁	1	2	yes	complemented
159	#1864	C₂×C₁₁	1	2	yes	complemented
160	C₄×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
161	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
162	#1762	C₂×C₁₁	1	2	yes	complemented
163	C₂³×C₁₁	—	2	4	no	—
164	C₂³×C₁₁	—	4	2	no	—
165	C₂³×C₁₁	—	4	2	no	—
166	C₂³×C₁₁	—	4	2	no	—
167	C₂³×C₁₁	—	4	2	no	—
168	C₂³×C₁₁	—	4	2	no	—
169	C₂³×C₁₁	—	4	2	no	—
170	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₁	—	4	8	no	—
172	D₄×C₁₁	—	2	4	no	—
173	D₄×C₁₁	—	2	4	no	—
174	D₄×C₁₁	—	4	2	no	—
175	D₄×C₁₁	—	4	2	no	—
176	D₄×C₁₁	—	4	8	no	—
177	D₄×C₁₁	—	8	4	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	4	1	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	4	1	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	4	1	no	—
194	C₂×C₄×C₁₁	—	4	1	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	4	1	no	—
197	C₂×C₄×C₁₁	—	4	1	no	—
198	C₂×C₄×C₁₁	—	4	1	no	—
199	C₂×C₄×C₁₁	—	4	1	no	—
200	C₂×C₄×C₁₁	—	4	1	no	—
201	C₂×C₄×C₁₁	—	8	8	no	—
202	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₁	—	2	2	no	—
213	C₈×C₁₁	—	2	2	no	—
214	C₈×C₁₁	—	4	2	no	—
215	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
216	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
217	C₂×C₄×Q₈	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
220	#486	C₄×C₁₁	1	8	yes	complemented
221	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×#102	C₂²×C₁₁	1	2	yes	—
225	C₂×#102	C₂²×C₁₁	1	2	yes	—
226	C₂×#102	C₂²×C₁₁	1	2	yes	—
227	C₂×#102	C₂²×C₁₁	1	2	yes	—
228	C₂×#97	C₂²×C₁₁	1	2	yes	—
229	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
230	#391	—	2	1	no	—
231	#390	—	2	1	no	—
232	#390	C₂²×C₁₁	1	2	yes	—
233	#389	C₂²×C₁₁	1	2	yes	—
234	#387	—	2	2	no	—
235	#386	—	2	2	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
240	#340	C₂²×C₁₁	1	2	yes	—
241	#340	C₂²×C₁₁	1	2	yes	—
242	#340	C₂²×C₁₁	1	1	yes	characteristic
243	#340	C₂²×C₁₁	1	1	yes	characteristic
244	#336	C₂²×C₁₁	1	2	yes	—
245	C₂²×C₁₁	—	4	4	no	—
246	C₂²×C₁₁	—	4	4	no	—
247	C₂²×C₁₁	—	4	4	no	—
248	C₂²×C₁₁	—	8	2	no	—
249	C₂²×C₁₁	—	8	2	no	—
250	C₂²×C₁₁	—	8	2	no	—
251	C₂²×C₁₁	—	8	2	no	—
252	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₁₁	#546	1	1	yes	characteristic
254	C₂²×C₁₁	#548	1	1	yes	characteristic
255	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₁₁	#577	1	1	yes	characteristic
258	C₂²×C₁₁	#577	1	1	yes	characteristic
259	C₄×C₁₁	—	2	2	no	—
260	C₄×C₁₁	—	4	2	no	—
261	C₄×C₁₁	—	4	2	no	—
262	C₄×C₁₁	—	4	4	no	—
263	C₄×C₁₁	—	4	2	no	—
264	C₄×C₁₁	—	4	2	no	—
265	C₄×C₁₁	—	8	1	no	—
266	C₄×C₁₁	—	8	1	no	—
267	C₄×C₁₁	#442	1	4	yes	—
268	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
269	C₄×C₁₁	#520	1	1	yes	characteristic
270	C₄×C₁₁	#556	1	1	yes	characteristic
271	C₄×C₁₁	#559	1	1	yes	characteristic
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
282	#127	—	2	2	no	—
283	#127	C₂×C₄×C₁₁	1	4	yes	—
284	C₄×Q₈	—	4	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	4	2	no	—
287	C₄×D₄	—	4	4	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
305	#106	—	2	2	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	4	no	—
309	#102	—	4	2	no	—
310	#102	C₂×C₄×C₁₁	1	8	yes	complemented
311	#102	C₂×C₄×C₁₁	1	8	yes	complemented
312	#97	—	4	2	no	—
313	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	D₄×C₁₁	1	2	yes	—
319	C₂×C₁₁	—	8	4	no	—
320	C₂×C₁₁	#2367	1	1	yes	characteristic
321	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
322	C₂×C₁₁	#2949	1	1	yes	characteristic
323	C₂×C₁₁	#3324	1	1	yes	characteristic
324	C₂×C₁₁	#3332	1	1	yes	characteristic
325	C₂×C₁₁	#3368	1	1	yes	characteristic
326	C₂×C₁₁	#3373	1	1	yes	characteristic
327	C₂⁴	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	1	no	—
341	C₂×D₄	—	8	1	no	—
342	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
364	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
377	C₄⋊C₄	C₁₁×#41	1	2	yes	—
378	C₄⋊C₄	C₁₁×#41	1	2	yes	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	4	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
388	C₄²	C₁₁×#41	1	2	yes	—
389	C₁₁	#23220	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
398	Q₈	—	4	8	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	8	no	—
404	D₄	—	8	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	8	8	no	—
429	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
430	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
431	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
432	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
437	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	4	2	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
450	C₂²	C₁₁×#546	1	1	yes	characteristic
451	C₂²	C₁₁×#548	1	1	yes	characteristic
452	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
453	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
454	C₂²	C₁₁×#577	1	1	yes	characteristic
455	C₂²	C₁₁×#577	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	1	no	—
463	C₄	—	8	1	no	—
464	C₄	C₁₁×#442	1	4	yes	—
465	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
466	C₄	C₁₁×#520	1	1	yes	characteristic
467	C₄	C₁₁×#556	1	1	yes	characteristic
468	C₄	C₁₁×#559	1	1	yes	characteristic
469	C₂	—	8	4	no	—
470	C₂	C₁₁×#2367	1	1	yes	characteristic
471	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
472	C₂	C₁₁×#2949	1	1	yes	characteristic
473	C₂	C₁₁×#3324	1	1	yes	characteristic
474	C₂	C₁₁×#3332	1	1	yes	characteristic
475	C₂	C₁₁×#3368	1	1	yes	characteristic
476	C₂	C₁₁×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2365	C₂	semidirect
4. C₁₁×#1988	C₂	semidirect
6. C₁₁×#1936	C₂	semidirect
7. C₁₁×#1926	C₂	semidirect
8. C₁₁×#1864	C₂	semidirect
9. C₄×C₁₁×#106	C₂	semidirect
10. C₁₁×#1770	C₂	semidirect
11. C₁₁×#1762	C₂	semidirect
17. C₁₁×#486	C₄	semidirect
51. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
80. C₁₁×#102	C₂×C₄	semidirect
81. C₁₁×#102	C₂×C₄	semidirect
83. C₄×C₈×C₁₁	C₂×C₄	semidirect
89. #23220	C₁₁	direct (N × H)
154. #2365	C₂×C₁₁	semidirect
155. #1988	C₂×C₁₁	semidirect
157. #1936	C₂×C₁₁	semidirect
158. #1926	C₂×C₁₁	semidirect
159. #1864	C₂×C₁₁	semidirect
160. C₄×#106	C₂×C₁₁	semidirect
161. #1770	C₂×C₁₁	semidirect
162. #1762	C₂×C₁₁	semidirect
220. #486	C₄×C₁₁	semidirect
281. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
310. #102	C₂×C₄×C₁₁	semidirect
311. #102	C₂×C₄×C₁₁	semidirect
313. C₄×C₈	C₂×C₄×C₁₁	semidirect
389. C₁₁	#23220	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#486	2
C₁₁×#2366	2
C₁₁×#2365	2
C₁₁×#1988	2
C₁₁×#1982	2
C₁₁×#1936	2
C₁₁×#1926	2
C₁₁×#1864	2
C₄×C₁₁×#106	2
C₁₁×#1770	2
C₁₁×#1762	2
#23220	11

Subgroups — C11×#23220 #14600413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23220 #14600413