Subgroups — AGL(1,ℤ/8)×C₁₁⋊C₈ #14723189

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067440	C₂	1	2	yes	maximal, complemented
4	SD₁₆⋊(C₁₁⋊C₈)	C₂	1	2	yes	maximal, complemented
5	SD₁₆×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
6	D₈×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
7	#13067368	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067007	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067003	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₂³×C₁₁⋊C₈	—	2	1	no	—
16	C₁₁×#442	C₄	1	2	yes	—
17	C₁₁×#440	C₄	1	2	yes	—
18	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
19	C₄×C₁₁×D₈	C₂²	1	2	yes	—
20	C₁₁×#428	C₄	1	1	yes	characteristic
21	C₁₁×#418	C₄	1	1	yes	characteristic
22	C₁₁×#417	C₄	1	1	yes	characteristic
23	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
25	Q₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	Q₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	D₄×C₁₁⋊C₈	—	2	1	no	—
28	D₄×C₁₁⋊C₈	—	2	1	no	—
29	D₄×C₁₁⋊C₈	—	2	1	no	—
30	D₄×C₁₁⋊C₈	—	2	1	no	—
31	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
32	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
33	D₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	D₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	#10622538	—	2	1	no	—
36	#10622538	C₂²	1	1	yes	characteristic
37	#10622538	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
40	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
42	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
43	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
44	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
45	#10622096	C₂²	1	2	yes	complemented
46	#10622095	C₂²	1	2	yes	complemented
47	#10622093	C₂²	1	2	yes	complemented
48	C₈×C₁₁⋊C₈	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₁	—	2	1	no	—
52	C₁₁×AGL(1,ℤ/8)	C₈	1	8	yes	complemented
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₄×D₄×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	—	2	1	no	—
61	C₄×D₄×C₁₁	—	2	1	no	—
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₁	C₂³	1	2	yes	—
66	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#117	—	2	1	no	—
68	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₁₁	—	2	1	no	—
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²×C₁₁⋊C₈	—	2	1	no	—
74	C₂²×C₁₁⋊C₈	—	2	1	no	—
75	C₂²×C₁₁⋊C₈	—	2	1	no	—
76	C₂²×C₁₁⋊C₈	—	2	2	no	—
77	C₂²×C₁₁⋊C₈	—	2	2	no	—
78	C₂²×C₁₁⋊C₈	—	4	4	no	—
79	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
80	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
81	C₁₁×#107	C₂×C₄	1	2	yes	—
82	C₁₁×#106	C₂×C₄	1	2	yes	—
83	C₁₁×#103	C₂×C₄	1	2	yes	—
84	C₁₁×#102	C₂×C₄	1	2	yes	—
85	C₁₁×#102	C₂×C₄	1	2	yes	—
86	C₁₁×#102	C₂×C₄	1	2	yes	—
87	C₁₁×#97	C₂×C₄	1	2	yes	—
88	C₄×C₈×C₁₁	C₂³	1	2	yes	—
89	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
93	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
94	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
95	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
96	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
97	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
98	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
99	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
100	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄×C₁₁⋊C₈	—	2	1	no	—
103	C₄×C₁₁⋊C₈	—	2	1	no	—
104	C₄×C₁₁⋊C₈	—	2	1	no	—
105	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
106	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
107	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
108	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
109	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₈×AGL(1,ℤ/8)	—	11	1	no	maximal, Sylow
111	C₂⁴×C₁₁	—	2	1	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₁₁×#41	C₂×C₈	1	4	yes	complemented
114	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	—	2	1	no	—
117	C₂×D₄×C₁₁	—	2	2	no	—
118	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	complemented
119	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	1	no	—
124	C₂²×C₄×C₁₁	—	2	2	no	—
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	4	2	no	—
128	C₂²×C₄×C₁₁	—	4	2	no	—
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
132	C₁₁×SD₁₆	C₂×C₈	1	8	yes	complemented
133	C₁₁×D₈	C₂×C₈	1	8	yes	complemented
134	C₁₁×M₁₆	—	2	2	no	—
135	C₁₁×M₁₆	C₂×C₈	1	4	yes	complemented
136	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₁₁×C₄⋊C₄	—	2	1	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
144	C₁₁×C₂²⋊C₄	—	2	1	no	—
145	C₁₁×C₂²⋊C₄	—	2	2	no	—
146	C₁₁×C₂²⋊C₄	—	2	1	no	—
147	C₁₁×C₂²⋊C₄	—	2	2	no	—
148	C₁₁×C₂²⋊C₄	—	2	1	no	—
149	C₄²×C₁₁	—	2	1	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₁	#41	1	1	yes	characteristic
155	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
156	C₂×C₁₁⋊C₈	—	2	2	no	—
157	C₂×C₁₁⋊C₈	—	2	1	no	—
158	C₂×C₁₁⋊C₈	—	2	1	no	—
159	C₂×C₁₁⋊C₈	—	2	2	no	—
160	C₂×C₁₁⋊C₈	—	2	2	no	—
161	C₂×C₁₁⋊C₈	—	4	1	no	—
162	C₂×C₁₁⋊C₈	—	4	2	no	—
163	C₂×C₁₁⋊C₈	—	4	2	no	—
164	C₂×C₁₁⋊C₈	—	4	4	no	—
165	C₂×C₁₁⋊C₈	—	4	2	no	—
166	C₂×C₁₁⋊C₈	—	4	4	no	—
167	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₈×#41	—	11	1	no	—
172	C₄×AGL(1,ℤ/8)	D₁₁	1	1	yes	characteristic
173	C₂×C₈×D₄	—	11	1	no	—
174	#1580	—	11	2	no	—
175	SD₁₆⋊C₈	—	11	2	no	—
176	C₈×SD₁₆	—	11	2	no	—
177	C₈×D₈	—	11	2	no	—
178	#1565	—	11	1	no	—
179	#1478	—	11	1	no	—
180	#1477	—	11	1	no	—
181	C₈×M₁₆	—	11	1	no	—
182	C₂³×C₁₁	—	2	1	no	—
183	C₂³×C₁₁	—	2	2	no	—
184	C₂³×C₁₁	—	2	4	no	—
185	C₂³×C₁₁	—	4	2	no	—
186	C₂³×C₁₁	—	4	2	no	—
187	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
188	Q₈×C₁₁	—	2	1	no	—
189	Q₈×C₁₁	C₂²×C₈	1	2	yes	complemented
190	D₄×C₁₁	—	2	4	no	—
191	D₄×C₁₁	—	2	2	no	—
192	D₄×C₁₁	—	2	1	no	—
193	D₄×C₁₁	—	2	4	no	—
194	D₄×C₁₁	C₂²×C₈	1	4	yes	—
195	D₄×C₁₁	C₂²×C₈	1	2	yes	complemented
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	4	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	4	1	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	4	no	—
206	C₂×C₄×C₁₁	—	4	2	no	—
207	C₂×C₄×C₁₁	—	4	2	no	—
208	C₂×C₄×C₁₁	—	4	1	no	—
209	C₂×C₄×C₁₁	—	4	1	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
215	C₂×C₄×C₁₁	#131	1	2	yes	—
216	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
219	C₈×C₁₁	—	2	2	no	—
220	C₈×C₁₁	C₂²×C₈	1	4	yes	complemented
221	C₁₁⋊C₈	—	2	1	no	—
222	C₁₁⋊C₈	—	2	1	no	—
223	C₁₁⋊C₈	—	2	1	no	—
224	C₁₁⋊C₈	—	4	2	no	—
225	C₁₁⋊C₈	—	4	1	no	—
226	C₁₁⋊C₈	—	4	2	no	—
227	C₁₁⋊C₈	—	4	1	no	—
228	C₁₁⋊C₈	AGL(1,ℤ/8)	1	2	yes	direct product factor
229	C₂×AGL(1,ℤ/8)	Dic₁₁	1	1	yes	characteristic
230	C₂³×C₈	—	22	1	no	—
231	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
233	C₈×Q₈	—	11	1	no	—
234	C₈×Q₈	—	11	1	no	—
235	#442	Dic₁₁	1	2	yes	—
236	#440	Dic₁₁	1	2	yes	—
237	C₄×SD₁₆	C₂×D₁₁	1	2	yes	—
238	C₄×D₈	C₂×D₁₁	1	2	yes	—
239	C₈×D₄	—	11	1	no	—
240	C₈×D₄	—	11	2	no	—
241	C₈×D₄	—	11	2	no	—
242	C₈×D₄	—	11	1	no	—
243	C₈×D₄	—	22	1	no	—
244	C₈×D₄	—	22	1	no	—
245	C₈×D₄	—	22	1	no	—
246	C₈×D₄	—	22	1	no	—
247	#431	—	11	1	no	—
248	#431	—	11	1	no	—
249	#431	—	22	1	no	—
250	#428	Dic₁₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	—	11	1	no	—
252	#418	Dic₁₁	1	1	yes	characteristic
253	#417	Dic₁₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	—	22	1	no	—
255	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
256	C₂×C₄×C₈	—	11	1	no	—
257	C₂×C₄×C₈	—	22	1	no	—
258	#335	—	11	2	no	—
259	#334	—	11	2	no	—
260	Q₈⋊C₈	—	11	2	no	—
261	D₄⋊C₈	—	11	2	no	—
262	D₄⋊C₈	—	11	2	no	—
263	D₄⋊C₈	—	11	2	no	—
264	#322	—	11	2	no	—
265	C₈²	—	11	2	no	—
266	C₂²×C₁₁	—	2	1	no	—
267	C₂²×C₁₁	—	2	1	no	—
268	C₂²×C₁₁	—	2	2	no	—
269	C₂²×C₁₁	—	2	4	no	—
270	C₂²×C₁₁	—	4	8	no	—
271	C₂²×C₁₁	—	4	2	no	—
272	C₂²×C₁₁	—	4	1	no	—
273	C₂²×C₁₁	—	4	1	no	—
274	C₂²×C₁₁	—	4	2	no	—
275	C₂²×C₁₁	C₈×D₄	1	2	yes	—
276	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₁₁	—	2	2	no	—
278	C₄×C₁₁	—	2	1	no	—
279	C₄×C₁₁	—	2	1	no	—
280	C₄×C₁₁	—	2	1	no	—
281	C₄×C₁₁	—	4	1	no	—
282	C₄×C₁₁	—	4	2	no	—
283	C₄×C₁₁	—	4	1	no	—
284	C₄×C₁₁	C₈×D₄	1	2	yes	—
285	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
286	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
287	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₄×C₁₁	#575	1	1	yes	characteristic
289	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
290	C₂²×D₄	C₂×Dic₁₁	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	AGL(1,ℤ/8)	C₁₁⋊C₈	1	8	yes	direct product factor
293	C₂×SD₁₆	C₂×Dic₁₁	1	2	yes	—
294	C₂×D₈	C₂×Dic₁₁	1	2	yes	—
295	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
296	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
297	C₂²×C₈	—	11	1	no	—
298	C₂²×C₈	—	11	1	no	—
299	C₂²×C₈	—	22	2	no	—
300	C₂²×C₈	—	22	2	no	—
301	C₂²×C₈	—	22	1	no	—
302	C₂²×C₈	—	22	1	no	—
303	C₂²×C₈	—	22	1	no	—
304	C₂²×C₈	—	44	4	no	—
305	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
306	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
312	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
313	C₄×D₄	C₂²×D₁₁	1	2	yes	—
314	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₂×Dic₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×Dic₁₁	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
321	#107	C₂×Dic₁₁	1	2	yes	—
322	#106	C₂×Dic₁₁	1	2	yes	—
323	C₄⋊C₈	—	11	1	no	—
324	C₄⋊C₈	—	11	1	no	—
325	C₄⋊C₈	—	11	2	no	—
326	C₄⋊C₈	—	22	1	no	—
327	C₄⋊C₈	—	22	1	no	—
328	C₄⋊C₈	—	22	1	no	—
329	C₄⋊C₈	—	22	1	no	—
330	#103	C₂×Dic₁₁	1	2	yes	—
331	#102	C₂×Dic₁₁	1	2	yes	—
332	#102	C₂×Dic₁₁	1	2	yes	—
333	#102	C₂×Dic₁₁	1	2	yes	—
334	C₂²⋊C₈	—	22	2	no	—
335	C₂²⋊C₈	—	22	2	no	—
336	C₂²⋊C₈	—	22	1	no	—
337	C₂²⋊C₈	—	22	1	no	—
338	C₂²⋊C₈	—	22	1	no	—
339	C₂²⋊C₈	—	22	1	no	—
340	#97	C₂×Dic₁₁	1	2	yes	—
341	C₄×C₈	—	11	1	no	—
342	C₄×C₈	—	11	1	no	—
343	C₄×C₈	—	11	1	no	—
344	C₄×C₈	—	11	1	no	—
345	C₄×C₈	—	11	2	no	—
346	C₄×C₈	—	22	1	no	—
347	C₄×C₈	—	22	1	no	—
348	C₄×C₈	—	22	1	no	—
349	C₄×C₈	C₂²×D₁₁	1	2	yes	—
350	C₂×C₁₁	—	2	2	no	—
351	C₂×C₁₁	—	4	2	no	—
352	C₂×C₁₁	—	4	4	no	—
353	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
354	C₂×C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₂×C₁₁	#2955	1	1	yes	characteristic
356	C₂⁴	—	2	1	no	—
357	#41	—	2	2	no	—
358	#41	C₂×C₁₁⋊C₈	1	4	yes	complemented
359	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	C₂×C₁₁⋊C₈	1	4	yes	complemented
364	C₂×D₄	C₂²×Dic₁₁	1	2	yes	—
365	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
375	C₂²×C₄	#4341	1	1	yes	characteristic
376	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
377	SD₁₆	C₂×C₁₁⋊C₈	1	8	yes	complemented
378	D₈	C₂×C₁₁⋊C₈	1	8	yes	complemented
379	M₁₆	—	2	2	no	—
380	M₁₆	C₂×C₁₁⋊C₈	1	4	yes	complemented
381	C₂×C₈	—	11	1	no	—
382	C₂×C₈	—	11	1	no	—
383	C₂×C₈	—	11	1	no	—
384	C₂×C₈	—	11	1	no	—
385	C₂×C₈	—	22	2	no	—
386	C₂×C₈	—	22	1	no	—
387	C₂×C₈	—	22	1	no	—
388	C₂×C₈	—	22	2	no	—
389	C₂×C₈	—	22	2	no	—
390	C₂×C₈	—	44	4	no	—
391	C₂×C₈	—	44	2	no	—
392	C₂×C₈	—	44	1	no	—
393	C₂×C₈	—	44	4	no	—
394	C₂×C₈	—	44	2	no	—
395	C₂×C₈	—	44	2	no	—
396	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
397	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	D₄×D₁₁	1	1	yes	characteristic
413	C₄²	#4341	1	1	yes	characteristic
414	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
415	C₄²	C₂³×D₁₁	1	1	yes	characteristic
416	C₁₁	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂²×C₁₁⋊C₈	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	1	no	—
428	D₄	—	2	4	no	—
429	D₄	C₂²×C₁₁⋊C₈	1	4	yes	—
430	D₄	C₂²×C₁₁⋊C₈	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
447	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
448	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
449	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
450	C₂×C₄	#67001	1	2	yes	—
451	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#4341	1	1	yes	characteristic
453	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	11	2	no	—
456	C₈	—	22	1	no	—
457	C₈	—	22	1	no	—
458	C₈	—	22	1	no	—
459	C₈	—	44	2	no	—
460	C₈	—	44	2	no	—
461	C₈	—	44	1	no	—
462	C₈	—	44	1	no	—
463	C₈	C₂²×C₁₁⋊C₈	1	4	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
474	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
483	C₄	D₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
484	C₄	#10623304	1	1	yes	characteristic
485	C₄	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
486	C₄	C₂×#67001	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
491	C₂	AGL(1,ℤ/8)×Dic₁₁	1	1	yes	characteristic
492	C₂	#13077519	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₄×C₁₁×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×AGL(1,ℤ/8)	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₁₁
hypocenter	C₁₁	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #41×C₁₁⋊C₈	C₂	semidirect
2. C₂×D₄×C₁₁⋊C₈	C₂	semidirect
3. #13067440	C₂	semidirect
4. SD₁₆⋊(C₁₁⋊C₈)	C₂	semidirect
5. SD₁₆×C₁₁⋊C₈	C₂	semidirect
6. D₈×C₁₁⋊C₈	C₂	semidirect
7. #13067368	C₂	semidirect
8. #13067007	C₂	semidirect
9. #13067003	C₂	semidirect
10. M₁₆×C₁₁⋊C₈	C₂	semidirect
25. Q₈×C₁₁⋊C₈	C₂²	semidirect
26. Q₈×C₁₁⋊C₈	C₂²	semidirect
33. D₄×C₁₁⋊C₈	C₂²	semidirect
34. D₄×C₁₁⋊C₈	C₂²	semidirect
41. Q₈⋊(C₁₁⋊C₈)	C₂²	semidirect
44. D₄⋊(C₁₁⋊C₈)	C₂²	semidirect
45. #10622096	C₂²	semidirect
46. #10622095	C₂²	semidirect
47. #10622093	C₂²	semidirect
48. C₈×C₁₁⋊C₈	C₂²	semidirect
52. C₁₁×AGL(1,ℤ/8)	C₈	semidirect
113. C₁₁×#41	C₂×C₈	semidirect
118. C₂×D₄×C₁₁	C₂×C₈	semidirect
132. C₁₁×SD₁₆	C₂×C₈	semidirect
133. C₁₁×D₈	C₂×C₈	semidirect
135. C₁₁×M₁₆	C₂×C₈	semidirect
189. Q₈×C₁₁	C₂²×C₈	semidirect
195. D₄×C₁₁	C₂²×C₈	semidirect
220. C₈×C₁₁	C₂²×C₈	semidirect
228. C₁₁⋊C₈	AGL(1,ℤ/8)	direct (N × H)
292. AGL(1,ℤ/8)	C₁₁⋊C₈	direct (N × H)
358. #41	C₂×C₁₁⋊C₈	semidirect
363. C₂×D₄	C₂×C₁₁⋊C₈	semidirect
377. SD₁₆	C₂×C₁₁⋊C₈	semidirect
378. D₈	C₂×C₁₁⋊C₈	semidirect
380. M₁₆	C₂×C₁₁⋊C₈	semidirect
416. C₁₁	C₈×AGL(1,ℤ/8)	semidirect
424. Q₈	C₂²×C₁₁⋊C₈	semidirect
430. D₄	C₂²×C₁₁⋊C₈	semidirect
463. C₈	C₂²×C₁₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#41×C₁₁⋊C₈	2
C₂×D₄×C₁₁⋊C₈	2
#13067440	2
SD₁₆⋊(C₁₁⋊C₈)	2
SD₁₆×C₁₁⋊C₈	2
D₈×C₁₁⋊C₈	2
#13067368	2
#13067007	2
#13067003	2
M₁₆×C₁₁⋊C₈	2
C₄×C₁₁×AGL(1,ℤ/8)	2
C₈×AGL(1,ℤ/8)	11

Subgroups — AGL(1,ℤ/8)×C11⋊C8 #14723189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,ℤ/8)×C₁₁⋊C₈ #14723189