Subgroups — C₁₁×#22268 #14599461

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1957	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1880	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1877	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₁	—	2	1	no	—
15	C₂×C₄×D₄×C₁₁	—	2	1	no	—
16	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
17	C₁₁×#492	C₄	1	8	yes	complemented
18	C₂×C₁₁×#103	C₂²	1	4	yes	—
19	C₂×C₁₁×#102	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
22	C₁₁×#391	C₂²	1	2	yes	—
23	C₁₁×#390	—	2	1	no	—
24	C₁₁×#390	—	2	1	no	—
25	C₁₁×#390	C₂²	1	2	yes	—
26	C₁₁×#389	—	2	1	no	—
27	C₁₁×#389	—	2	1	no	—
28	C₁₁×#384	C₂²	1	1	yes	characteristic
29	C₁₁×#384	C₂²	1	1	yes	characteristic
30	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
31	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
32	C₄³×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#340	C₂²	1	4	yes	—
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₁	—	2	1	no	—
38	C₂²×D₄×C₁₁	—	2	1	no	—
39	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₁	—	2	2	no	—
41	C₂×C₁₁×SD₁₆	—	4	4	no	—
42	C₂×C₁₁×SD₁₆	—	4	4	no	—
43	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₁₁×C₄⋊Q₈	—	2	2	no	—
47	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
48	C₁₁×#127	—	2	2	no	—
49	C₁₁×#127	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₁₁	—	4	4	no	—
51	C₄×D₄×C₁₁	—	4	4	no	—
52	C₄×D₄×C₁₁	—	4	4	no	—
53	C₄×D₄×C₁₁	—	4	4	no	—
54	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₄²×C₁₁	—	2	2	no	—
67	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#103	—	4	4	no	—
75	C₁₁×#102	—	4	4	no	—
76	C₄×C₈×C₁₁	—	2	2	no	—
77	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
78	C₁₁×#95	—	2	2	no	—
79	C₁₁×#95	—	2	2	no	—
80	#22268	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₁	—	2	2	no	—
82	C₂×Q₈×C₁₁	—	2	2	no	—
83	C₂×Q₈×C₁₁	—	2	4	no	—
84	C₂×Q₈×C₁₁	—	2	4	no	—
85	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
86	C₂×D₄×C₁₁	—	2	4	no	—
87	C₂×D₄×C₁₁	—	2	4	no	—
88	C₂×D₄×C₁₁	—	2	2	no	—
89	C₂×D₄×C₁₁	—	2	4	no	—
90	C₂×D₄×C₁₁	—	2	4	no	—
91	C₂×D₄×C₁₁	—	4	2	no	—
92	C₂×D₄×C₁₁	—	4	2	no	—
93	C₂×D₄×C₁₁	—	4	2	no	—
94	C₂×D₄×C₁₁	—	4	2	no	—
95	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	—	2	2	no	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	4	4	no	—
100	C₂²×C₄×C₁₁	—	4	4	no	—
101	C₂²×C₄×C₁₁	—	4	4	no	—
102	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
109	C₁₁×SD₁₆	—	4	16	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
116	C₁₁×C₄⋊C₄	—	2	4	no	—
117	C₁₁×C₄⋊C₄	—	2	4	no	—
118	C₁₁×C₄⋊C₄	—	2	4	no	—
119	C₁₁×C₄⋊C₄	—	2	4	no	—
120	C₁₁×C₄⋊C₄	—	4	4	no	—
121	C₁₁×C₄⋊C₄	—	4	2	no	—
122	C₁₁×C₄⋊C₄	—	4	2	no	—
123	C₁₁×C₄⋊C₄	—	4	2	no	—
124	C₁₁×C₄⋊C₄	—	4	2	no	—
125	C₁₁×C₂²⋊C₄	—	4	4	no	—
126	C₁₁×C₂²⋊C₄	—	4	4	no	—
127	C₁₁×C₂²⋊C₄	—	4	4	no	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	—	2	2	no	—
131	C₄²×C₁₁	—	2	2	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	—	4	4	no	—
134	C₄²×C₁₁	SD₁₆	1	4	yes	complemented
135	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₁	#41	1	2	yes	—
137	C₂×#492	C₂×C₁₁	1	1	yes	characteristic
138	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
139	C₄×#127	C₂×C₁₁	1	1	yes	characteristic
140	#1957	C₂×C₁₁	1	1	yes	characteristic
141	#1956	C₂×C₁₁	1	1	yes	characteristic, complemented
142	#1880	C₂×C₁₁	1	4	yes	complemented
143	#1877	C₂×C₁₁	1	4	yes	complemented
144	#1834	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂³×C₁₁	—	2	4	no	—
147	C₂³×C₁₁	—	4	2	no	—
148	C₂³×C₁₁	—	4	2	no	—
149	C₂³×C₁₁	—	4	2	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	2	no	—
152	C₂³×C₁₁	—	4	2	no	—
153	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₁₁	—	2	8	no	—
155	Q₈×C₁₁	—	4	4	no	—
156	D₄×C₁₁	—	2	8	no	—
157	D₄×C₁₁	—	4	4	no	—
158	D₄×C₁₁	—	4	8	no	—
159	D₄×C₁₁	—	4	8	no	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	4	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	4	2	no	—
172	C₂×C₄×C₁₁	—	4	2	no	—
173	C₂×C₄×C₁₁	—	4	2	no	—
174	C₂×C₄×C₁₁	—	4	2	no	—
175	C₂×C₄×C₁₁	—	4	2	no	—
176	C₂×C₄×C₁₁	—	4	2	no	—
177	C₂×C₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	—	4	2	no	—
179	C₂×C₄×C₁₁	—	8	8	no	—
180	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₁	#135	1	2	yes	—
186	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₁₁	#137	1	2	yes	—
188	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
191	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
192	C₈×C₁₁	—	2	4	no	—
193	C₈×C₁₁	—	4	2	no	—
194	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
198	C₂×C₄×D₄	—	2	1	no	—
199	C₂×C₄×D₄	—	2	1	no	—
200	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
201	#492	C₄×C₁₁	1	8	yes	complemented
202	C₂×#103	C₂²×C₁₁	1	4	yes	—
203	C₂×#102	C₂²×C₁₁	1	4	yes	—
204	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
206	#391	C₂²×C₁₁	1	2	yes	—
207	#390	—	2	1	no	—
208	#390	—	2	1	no	—
209	#390	C₂²×C₁₁	1	2	yes	—
210	#389	—	2	1	no	—
211	#389	—	2	1	no	—
212	#384	C₂²×C₁₁	1	1	yes	characteristic
213	#384	C₂²×C₁₁	1	1	yes	characteristic
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	—	2	1	no	—
216	C₄³	C₂²×C₁₁	1	1	yes	characteristic
217	#340	C₂²×C₁₁	1	4	yes	—
218	#336	C₂²×C₁₁	1	2	yes	—
219	#336	C₂²×C₁₁	1	2	yes	—
220	C₂²×C₁₁	—	4	4	no	—
221	C₂²×C₁₁	—	4	4	no	—
222	C₂²×C₁₁	—	4	4	no	—
223	C₂²×C₁₁	—	8	2	no	—
224	C₂²×C₁₁	—	8	2	no	—
225	C₂²×C₁₁	—	8	2	no	—
226	C₂²×C₁₁	—	8	2	no	—
227	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₁	#535	1	1	yes	characteristic
229	C₂²×C₁₁	#535	1	1	yes	characteristic
230	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
231	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
232	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂²×C₁₁	C₂×#137	1	1	yes	characteristic
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	2	no	—
236	C₄×C₁₁	—	4	4	no	—
237	C₄×C₁₁	—	4	1	no	—
238	C₄×C₁₁	—	4	1	no	—
239	C₄×C₁₁	—	8	2	no	—
240	C₄×C₁₁	—	8	2	no	—
241	C₄×C₁₁	C₄×SD₁₆	1	4	yes	—
242	C₄×C₁₁	#440	1	4	yes	—
243	C₄×C₁₁	#518	1	2	yes	—
244	C₄×C₁₁	#540	1	2	yes	—
245	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂×SD₁₆	—	4	4	no	—
251	C₂×SD₁₆	—	4	4	no	—
252	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
253	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
257	#127	—	2	2	no	—
258	#127	C₂×C₄×C₁₁	1	4	yes	—
259	C₄×Q₈	—	4	4	no	—
260	C₄×D₄	—	4	4	no	—
261	C₄×D₄	—	4	4	no	—
262	C₄×D₄	—	4	4	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
283	#103	—	4	4	no	—
284	#102	—	4	4	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₂×C₁₁	—	8	4	no	—
290	C₂×C₁₁	#2328	1	1	yes	characteristic
291	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
292	C₂×C₁₁	C₂×#440	1	1	yes	characteristic
293	C₂×C₁₁	#3206	1	1	yes	characteristic
294	C₂×C₁₁	#3207	1	1	yes	characteristic
295	C₂×C₁₁	#3208	1	1	yes	characteristic
296	C₂×C₁₁	#3210	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
325	SD₁₆	—	4	16	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	4	no	—
350	C₄²	C₁₁×SD₁₆	1	4	yes	complemented
351	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
352	C₄²	C₁₁×#41	1	2	yes	—
353	C₁₁	#22268	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	2	4	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
362	Q₈	—	2	8	no	—
363	Q₈	—	4	4	no	—
364	D₄	—	2	8	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	8	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	8	no	—
388	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
389	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
390	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
391	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
392	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
393	C₂×C₄	C₁₁×#135	1	2	yes	—
394	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
395	C₂×C₄	C₁₁×#137	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
397	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
398	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
399	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
410	C₂²	C₁₁×#535	1	1	yes	characteristic
411	C₂²	C₁₁×#535	1	1	yes	characteristic
412	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
413	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
414	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂²	C₂×C₁₁×#137	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₄×C₁₁×SD₁₆	1	4	yes	—
424	C₄	C₁₁×#440	1	4	yes	—
425	C₄	C₁₁×#518	1	2	yes	—
426	C₄	C₁₁×#540	1	2	yes	—
427	C₂	—	8	4	no	—
428	C₂	C₁₁×#2328	1	1	yes	characteristic
429	C₂	C₂×C₄×C₁₁×SD₁₆	1	1	yes	characteristic
430	C₂	C₂×C₁₁×#440	1	1	yes	characteristic
431	C₂	C₁₁×#3206	1	1	yes	characteristic
432	C₂	C₁₁×#3207	1	1	yes	characteristic
433	C₂	C₁₁×#3208	1	1	yes	characteristic
434	C₂	C₁₁×#3210	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 ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
5. C₁₁×#1956	C₂	semidirect
6. C₁₁×#1880	C₂	semidirect
7. C₁₁×#1877	C₂	semidirect
8. C₁₁×#1834	C₂	semidirect
9. C₁₁×#1744	C₂	semidirect
17. C₁₁×#492	C₄	semidirect
43. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
47. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
77. C₄×C₈×C₁₁	C₂×C₄	semidirect
80. #22268	C₁₁	direct (N × H)
134. C₄²×C₁₁	SD₁₆	semidirect
138. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
141. #1956	C₂×C₁₁	semidirect
142. #1880	C₂×C₁₁	semidirect
143. #1877	C₂×C₁₁	semidirect
144. #1834	C₂×C₁₁	semidirect
145. #1744	C₂×C₁₁	semidirect
201. #492	C₄×C₁₁	semidirect
252. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
256. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
286. C₄×C₈	C₂×C₄×C₁₁	semidirect
350. C₄²	C₁₁×SD₁₆	semidirect
353. C₁₁	#22268	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×#492	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#127	2
C₁₁×#1957	2
C₁₁×#1956	2
C₁₁×#1880	2
C₁₁×#1877	2
C₁₁×#1834	2
C₁₁×#1744	2
#22268	11

Subgroups — C11×#22268 #14599461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22268 #14599461