Subgroups — C₈×C₁₁×AGL(1,ℤ/8) #14595043

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	C₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1580	C₂	1	2	yes	maximal, complemented
5	C₁₁×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₈×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₁×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	—	2	1	no	—
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
17	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#442	C₄	1	2	yes	—
19	C₁₁×#440	C₄	1	2	yes	—
20	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₁×D₈	C₂²	1	2	yes	—
22	C₈×D₄×C₁₁	—	2	1	no	—
23	C₈×D₄×C₁₁	—	2	1	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	—	2	1	no	—
26	C₈×D₄×C₁₁	C₂²	1	2	yes	—
27	C₈×D₄×C₁₁	C₂²	1	2	yes	—
28	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#431	—	2	1	no	—
31	C₁₁×#431	C₂²	1	1	yes	characteristic
32	C₁₁×#431	C₂²	1	1	yes	characteristic
33	C₁₁×#428	C₄	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₁×#418	C₄	1	1	yes	characteristic
36	C₁₁×#417	C₄	1	1	yes	characteristic
37	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
38	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₁	—	2	1	no	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#335	C₂²	1	2	yes	complemented
42	C₁₁×#334	C₂²	1	2	yes	complemented
43	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₁×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₁₁×#322	C₂²	1	2	yes	complemented
48	C₈²×C₁₁	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	direct product factor
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	C₂²×C₈×C₁₁	—	2	1	no	—
58	C₂²×C₈×C₁₁	—	2	1	no	—
59	C₂²×C₈×C₁₁	—	2	2	no	—
60	C₂²×C₈×C₁₁	—	2	1	no	—
61	C₂²×C₈×C₁₁	—	2	2	no	—
62	C₂²×C₈×C₁₁	—	4	4	no	—
63	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₁	—	2	1	no	—
68	C₄×D₄×C₁₁	—	2	1	no	—
69	C₄×D₄×C₁₁	—	2	1	no	—
70	C₄×D₄×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
72	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₁	C₂³	1	2	yes	—
74	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×#117	—	2	1	no	—
76	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₁₁	—	2	1	no	—
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₁₁×#107	C₂×C₄	1	2	yes	—
82	C₁₁×#106	C₂×C₄	1	2	yes	—
83	C₁₁×C₄⋊C₈	—	2	1	no	—
84	C₁₁×C₄⋊C₈	—	2	1	no	—
85	C₁₁×C₄⋊C₈	—	2	1	no	—
86	C₁₁×C₄⋊C₈	—	2	1	no	—
87	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₁×#103	C₂×C₄	1	2	yes	—
91	C₁₁×#102	C₂×C₄	1	2	yes	—
92	C₁₁×#102	C₂×C₄	1	2	yes	—
93	C₁₁×#102	C₂×C₄	1	2	yes	—
94	C₁₁×C₂²⋊C₈	—	2	1	no	—
95	C₁₁×C₂²⋊C₈	—	2	1	no	—
96	C₁₁×C₂²⋊C₈	—	2	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×C₂²⋊C₈	—	2	1	no	—
99	C₁₁×C₂²⋊C₈	—	2	1	no	—
100	C₁₁×#97	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₁₁	—	2	1	no	—
102	C₄×C₈×C₁₁	—	2	1	no	—
103	C₄×C₈×C₁₁	—	2	1	no	—
104	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
106	C₄×C₈×C₁₁	C₂³	1	2	yes	—
107	C₄×C₈×C₁₁	C₂³	1	2	yes	—
108	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
110	C₈×AGL(1,ℤ/8)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, 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	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	4	1	no	—
142	C₂×C₈×C₁₁	—	4	2	no	—
143	C₂×C₈×C₁₁	—	4	2	no	—
144	C₂×C₈×C₁₁	—	4	4	no	—
145	C₂×C₈×C₁₁	—	4	2	no	—
146	C₂×C₈×C₁₁	—	4	4	no	—
147	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
153	C₁₁×C₄⋊C₄	—	2	1	no	—
154	C₁₁×C₄⋊C₄	—	2	1	no	—
155	C₁₁×C₄⋊C₄	—	2	1	no	—
156	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₁₁×C₂²⋊C₄	—	2	1	no	—
160	C₁₁×C₂²⋊C₄	—	2	2	no	—
161	C₁₁×C₂²⋊C₄	—	2	1	no	—
162	C₁₁×C₂²⋊C₄	—	2	2	no	—
163	C₁₁×C₂²⋊C₄	—	2	1	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₁	#41	1	1	yes	characteristic
170	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
171	C₈×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₄×AGL(1,ℤ/8)	C₂×C₁₁	1	1	yes	characteristic
173	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1580	C₂×C₁₁	1	2	yes	complemented
175	SD₁₆⋊C₈	C₂×C₁₁	1	2	yes	complemented
176	C₈×SD₁₆	C₂×C₁₁	1	2	yes	complemented
177	C₈×D₈	C₂×C₁₁	1	2	yes	complemented
178	#1565	C₂×C₁₁	1	1	yes	characteristic, complemented
179	#1478	C₂×C₁₁	1	1	yes	characteristic, complemented
180	#1477	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
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	—	2	1	no	—
221	C₈×C₁₁	—	2	1	no	—
222	C₈×C₁₁	—	2	1	no	—
223	C₈×C₁₁	—	4	2	no	—
224	C₈×C₁₁	—	4	1	no	—
225	C₈×C₁₁	—	4	2	no	—
226	C₈×C₁₁	—	4	1	no	—
227	C₈×C₁₁	C₂²×C₈	1	4	yes	complemented
228	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	direct product factor
229	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	1	yes	characteristic
230	C₂³×C₈	—	2	1	no	—
231	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
233	C₈×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
234	C₈×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
235	#442	C₄×C₁₁	1	2	yes	—
236	#440	C₄×C₁₁	1	2	yes	—
237	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
238	C₄×D₈	C₂²×C₁₁	1	2	yes	—
239	C₈×D₄	—	2	1	no	—
240	C₈×D₄	—	2	1	no	—
241	C₈×D₄	—	2	1	no	—
242	C₈×D₄	—	2	1	no	—
243	C₈×D₄	C₂²×C₁₁	1	2	yes	—
244	C₈×D₄	C₂²×C₁₁	1	2	yes	—
245	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
247	#431	—	2	1	no	—
248	#431	C₂²×C₁₁	1	1	yes	characteristic
249	#431	C₂²×C₁₁	1	1	yes	characteristic
250	#428	C₄×C₁₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
252	#418	C₄×C₁₁	1	1	yes	characteristic
253	#417	C₄×C₁₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	—	2	1	no	—
255	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₄×C₈	—	2	1	no	—
257	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
258	#335	C₂²×C₁₁	1	2	yes	complemented
259	#334	C₂²×C₁₁	1	2	yes	complemented
260	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	complemented
261	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
262	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
263	D₄⋊C₈	C₂²×C₁₁	1	2	yes	complemented
264	#322	C₂²×C₁₁	1	2	yes	complemented
265	C₈²	C₂²×C₁₁	1	2	yes	complemented
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×C₄×C₁₁	1	1	yes	characteristic
290	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	AGL(1,ℤ/8)	C₈×C₁₁	1	8	yes	direct product factor
293	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
294	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
295	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	4	4	no	—
303	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
304	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
305	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₄×Q₈	C₂³×C₁₁	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×C₄×C₁₁	1	2	yes	—
312	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₄×D₄	C₂³×C₁₁	1	2	yes	—
314	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
321	#107	C₂×C₄×C₁₁	1	2	yes	—
322	#106	C₂×C₄×C₁₁	1	2	yes	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
330	#103	C₂×C₄×C₁₁	1	2	yes	—
331	#102	C₂×C₄×C₁₁	1	2	yes	—
332	#102	C₂×C₄×C₁₁	1	2	yes	—
333	#102	C₂×C₄×C₁₁	1	2	yes	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	#97	C₂×C₄×C₁₁	1	2	yes	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
345	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
346	C₄×C₈	C₂³×C₁₁	1	2	yes	—
347	C₄×C₈	C₂³×C₁₁	1	2	yes	—
348	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
349	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
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×C₈×C₁₁	1	4	yes	complemented
359	C₂×Q₈	C₂²×C₄×C₁₁	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×C₈×C₁₁	1	4	yes	complemented
364	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
365	C₂×D₄	C₂²×C₄×C₁₁	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	C₂²×C₄×C₁₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
376	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
377	SD₁₆	C₂×C₈×C₁₁	1	8	yes	complemented
378	D₈	C₂×C₈×C₁₁	1	8	yes	complemented
379	M₁₆	—	2	2	no	—
380	M₁₆	C₂×C₈×C₁₁	1	4	yes	complemented
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	4	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	4	2	no	—
392	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
393	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
395	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
396	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄×C₁₁	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	C₂²×C₄×C₁₁	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
414	C₄²	C₁₁×#41	1	1	yes	characteristic
415	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
416	C₁₁	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, 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	C₄×D₄×C₁₁	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂²×C₈×C₁₁	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×C₈×C₁₁	1	4	yes	—
430	D₄	C₂²×C₈×C₁₁	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	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	C₄×D₄×C₁₁	1	1	yes	characteristic
447	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
448	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
449	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
450	C₂×C₄	C₁₁×#131	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	C₂²×C₈×C₁₁	1	4	yes	complemented
463	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	direct product factor
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	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₈×D₄×C₁₁	1	2	yes	—
474	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	C₈×D₄×C₁₁	1	2	yes	—
483	C₄	C₂³×C₈×C₁₁	1	1	yes	characteristic
484	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
485	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	C₁₁×#575	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	4	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×C₈×D₄×C₁₁	1	1	yes	characteristic
491	C₂	C₄×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂	C₁₁×#2955	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈×C₁₁×#41	C₂	semidirect
3. C₂×C₈×D₄×C₁₁	C₂	semidirect
4. C₁₁×#1580	C₂	semidirect
5. C₁₁×SD₁₆⋊C₈	C₂	semidirect
6. C₈×C₁₁×SD₁₆	C₂	semidirect
7. C₈×C₁₁×D₈	C₂	semidirect
8. C₁₁×#1565	C₂	semidirect
9. C₁₁×#1478	C₂	semidirect
10. C₁₁×#1477	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
16. C₈×Q₈×C₁₁	C₂²	semidirect
17. C₈×Q₈×C₁₁	C₂²	semidirect
28. C₈×D₄×C₁₁	C₂²	semidirect
29. C₈×D₄×C₁₁	C₂²	semidirect
41. C₁₁×#335	C₂²	semidirect
42. C₁₁×#334	C₂²	semidirect
43. C₁₁×Q₈⋊C₈	C₂²	semidirect
46. C₁₁×D₄⋊C₈	C₂²	semidirect
47. C₁₁×#322	C₂²	semidirect
48. C₈²×C₁₁	C₂²	semidirect
52. C₁₁×AGL(1,ℤ/8)	C₈	direct (N × H)
110. C₈×AGL(1,ℤ/8)	C₁₁	direct (N × H)
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
171. C₈×#41	C₂×C₁₁	semidirect
173. C₂×C₈×D₄	C₂×C₁₁	semidirect
174. #1580	C₂×C₁₁	semidirect
175. SD₁₆⋊C₈	C₂×C₁₁	semidirect
176. C₈×SD₁₆	C₂×C₁₁	semidirect
177. C₈×D₈	C₂×C₁₁	semidirect
178. #1565	C₂×C₁₁	semidirect
179. #1478	C₂×C₁₁	semidirect
180. #1477	C₂×C₁₁	semidirect
181. C₈×M₁₆	C₂×C₁₁	semidirect
189. Q₈×C₁₁	C₂²×C₈	semidirect
195. D₄×C₁₁	C₂²×C₈	semidirect
227. C₈×C₁₁	C₂²×C₈	semidirect
228. C₈×C₁₁	AGL(1,ℤ/8)	direct (N × H)
233. C₈×Q₈	C₂²×C₁₁	semidirect
234. C₈×Q₈	C₂²×C₁₁	semidirect
245. C₈×D₄	C₂²×C₁₁	semidirect
246. C₈×D₄	C₂²×C₁₁	semidirect
258. #335	C₂²×C₁₁	semidirect
259. #334	C₂²×C₁₁	semidirect
260. Q₈⋊C₈	C₂²×C₁₁	semidirect
263. D₄⋊C₈	C₂²×C₁₁	semidirect
264. #322	C₂²×C₁₁	semidirect
265. C₈²	C₂²×C₁₁	semidirect
292. AGL(1,ℤ/8)	C₈×C₁₁	direct (N × H)
358. #41	C₂×C₈×C₁₁	semidirect
363. C₂×D₄	C₂×C₈×C₁₁	semidirect
377. SD₁₆	C₂×C₈×C₁₁	semidirect
378. D₈	C₂×C₈×C₁₁	semidirect
380. M₁₆	C₂×C₈×C₁₁	semidirect
416. C₁₁	C₈×AGL(1,ℤ/8)	direct (N × H)
424. Q₈	C₂²×C₈×C₁₁	semidirect
430. D₄	C₂²×C₈×C₁₁	semidirect
462. C₈	C₂²×C₈×C₁₁	semidirect
463. C₈	C₁₁×AGL(1,ℤ/8)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₁×#41	2
C₄×C₁₁×AGL(1,ℤ/8)	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#1580	2
C₁₁×SD₁₆⋊C₈	2
C₈×C₁₁×SD₁₆	2
C₈×C₁₁×D₈	2
C₁₁×#1565	2
C₁₁×#1478	2
C₁₁×#1477	2
C₈×C₁₁×M₁₆	2
C₈×AGL(1,ℤ/8)	11

Subgroups — C8×C11×AGL(1,ℤ/8) #14595043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₁×AGL(1,ℤ/8) #14595043