Subgroups — Q₈×C₁₁×AGL(1,ℤ/8) #14638559

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3386	C₂	1	6	yes	maximal, complemented
4	C₁₁×#3384	C₂	1	6	yes	maximal, complemented
5	Q₈×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
6	Q₈×C₁₁×D₈	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3165	C₂	1	3	yes	maximal, complemented
8	C₁₁×#3079	C₂	1	3	yes	maximal, complemented
9	C₁₁×#3077	C₂	1	3	yes	maximal, complemented
10	Q₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	3	yes	maximal
12	C₂³×Q₈×C₁₁	—	2	1	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₁	C₂²	1	1	yes	characteristic, complemented
15	C₁₁×#557	C₂²	1	3	yes	complemented
16	C₁₁×#554	—	2	3	no	—
17	C₁₁×#554	C₂²	1	3	yes	complemented
18	D₄×Q₈×C₁₁	—	2	1	no	—
19	D₄×Q₈×C₁₁	—	2	1	no	—
20	D₄×Q₈×C₁₁	—	2	3	no	—
21	D₄×Q₈×C₁₁	C₂²	1	2	yes	—
22	D₄×Q₈×C₁₁	C₂²	1	6	yes	—
23	D₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
24	C₁₁×#533	—	2	3	no	—
25	C₁₁×#533	C₂²	1	3	yes	—
26	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₂×C₁₁×C₂²⋊Q₈	—	2	3	no	—
28	C₄×C₁₁×#41	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₁	C₂²	1	3	yes	—
32	C₁₁×#501	C₂²	1	12	yes	complemented
33	C₁₁×#500	C₂²	1	6	yes	complemented
34	C₁₁×#498	C₂²	1	6	yes	complemented
35	C₁₁×#478	C₂²	1	12	yes	—
36	C₁₁×#477	C₂²	1	6	yes	complemented
37	C₁₁×#476	C₂²	1	6	yes	—
38	C₁₁×#476	C₂²	1	6	yes	complemented
39	C₁₁×#475	C₂²	1	6	yes	complemented
40	C₁₁×#474	C₂²	1	6	yes	—
41	C₁₁×#474	C₂²	1	6	yes	complemented
42	C₁₁×#446	C₂²	1	6	yes	complemented
43	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
44	C₁₁×#442	C₂²	1	6	yes	—
45	C₁₁×#440	C₂²	1	6	yes	—
46	C₄×C₁₁×SD₁₆	C₂²	1	6	yes	—
47	C₄×C₁₁×D₈	C₂²	1	6	yes	—
48	C₁₁×#428	C₂²	1	3	yes	—
49	C₁₁×#428	C₂²	1	6	yes	—
50	C₁₁×#423	C₂²	1	3	yes	—
51	C₁₁×#418	C₂²	1	3	yes	—
52	C₁₁×#417	C₂²	1	3	yes	—
53	C₄×C₁₁×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₁	—	2	1	no	—
56	C₂²×Q₈×C₁₁	—	2	6	no	—
57	C₂²×Q₈×C₁₁	—	2	2	no	—
58	C₂²×Q₈×C₁₁	—	2	3	no	—
59	C₂²×Q₈×C₁₁	—	4	8	no	—
60	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₁	—	2	3	no	—
63	C₁₁×AGL(1,ℤ/8)	Q₈	1	8	yes	direct product factor
64	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
65	C₂×C₁₁×D₈	C₂³	1	2	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
68	C₁₁×C₄⋊Q₈	—	2	3	no	—
69	C₁₁×C₄⋊Q₈	—	2	3	no	—
70	C₁₁×C₄⋊Q₈	—	2	3	no	—
71	C₁₁×C₄⋊Q₈	—	2	3	no	—
72	C₁₁×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₁×C₄⋊Q₈	C₂³	1	6	yes	—
74	C₁₁×C₄⋊Q₈	C₂³	1	3	yes	—
75	C₁₁×C₄⋊Q₈	C₂³	1	6	yes	—
76	C₁₁×#125	—	2	6	no	—
77	C₁₁×#125	C₂³	1	6	yes	—
78	C₁₁×C₂²⋊Q₈	—	2	3	no	—
79	C₁₁×C₂²⋊Q₈	—	2	3	no	—
80	C₁₁×C₂²⋊Q₈	—	2	3	no	—
81	C₁₁×C₂²⋊Q₈	—	2	6	no	—
82	C₁₁×C₂²⋊Q₈	—	2	12	no	—
83	C₁₁×C₂²⋊Q₈	—	2	6	no	—
84	C₁₁×C₂²⋊Q₈	—	2	3	no	—
85	C₁₁×C₂²⋊Q₈	—	2	6	no	—
86	C₄×Q₈×C₁₁	—	2	1	no	—
87	C₄×Q₈×C₁₁	—	2	3	no	—
88	C₄×Q₈×C₁₁	—	2	3	no	—
89	C₄×Q₈×C₁₁	—	2	3	no	—
90	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₁₁	D₄	1	3	yes	—
92	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
96	C₄×D₄×C₁₁	—	2	3	no	—
97	C₄×D₄×C₁₁	—	2	3	no	—
98	C₄×D₄×C₁₁	—	2	3	no	—
99	C₄×D₄×C₁₁	—	2	3	no	—
100	C₄×D₄×C₁₁	C₂³	1	6	yes	—
101	C₄×D₄×C₁₁	C₂³	1	6	yes	—
102	C₄×D₄×C₁₁	C₂³	1	3	yes	—
103	C₄×D₄×C₁₁	C₂³	1	3	yes	—
104	C₁₁×#117	—	2	3	no	—
105	C₁₁×#117	C₂³	1	3	yes	—
106	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₁×C₄⋊C₄	D₄	1	3	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
110	C₂×C₁₁×C₂²⋊C₄	—	2	3	no	—
111	C₂×C₄²×C₁₁	—	2	3	no	—
112	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
113	C₁₁×#107	C₂³	1	6	yes	—
114	C₁₁×#107	C₂³	1	12	yes	—
115	C₁₁×#106	C₂³	1	6	yes	—
116	C₁₁×#106	C₂³	1	12	yes	—
117	C₁₁×C₄⋊C₈	C₂³	1	6	yes	—
118	C₁₁×C₄⋊C₈	C₂³	1	6	yes	—
119	C₁₁×#103	C₂³	1	6	yes	—
120	C₁₁×#102	C₂³	1	6	yes	—
121	C₁₁×#102	C₂³	1	6	yes	—
122	C₁₁×#102	C₂³	1	6	yes	—
123	C₁₁×#97	C₂³	1	6	yes	—
124	C₄×C₈×C₁₁	C₂³	1	6	yes	—
125	Q₈×AGL(1,ℤ/8)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₁	—	2	1	no	—
127	C₁₁×#41	—	2	2	no	—
128	C₁₁×#41	C₂×Q₈	1	4	yes	complemented
129	C₂×Q₈×C₁₁	—	2	4	no	—
130	C₂×Q₈×C₁₁	—	2	3	no	—
131	C₂×Q₈×C₁₁	—	2	6	no	—
132	C₂×Q₈×C₁₁	—	2	6	no	—
133	C₂×Q₈×C₁₁	—	2	3	no	—
134	C₂×Q₈×C₁₁	—	4	12	no	—
135	C₂×Q₈×C₁₁	—	4	24	no	—
136	C₂×Q₈×C₁₁	—	4	4	no	—
137	C₂×Q₈×C₁₁	—	4	8	no	—
138	C₂×Q₈×C₁₁	C₂×D₄	1	3	yes	—
139	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₁	C₂⁴	1	1	yes	characteristic
141	C₂×D₄×C₁₁	—	2	1	no	—
142	C₂×D₄×C₁₁	—	2	1	no	—
143	C₂×D₄×C₁₁	—	2	2	no	—
144	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	complemented
145	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
146	C₂×D₄×C₁₁	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₁	—	2	1	no	—
148	C₂²×C₄×C₁₁	—	2	3	no	—
149	C₂²×C₄×C₁₁	—	2	3	no	—
150	C₂²×C₄×C₁₁	—	2	6	no	—
151	C₂²×C₄×C₁₁	—	2	6	no	—
152	C₂²×C₄×C₁₁	—	2	3	no	—
153	C₂²×C₄×C₁₁	—	4	12	no	—
154	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
157	C₁₁×SD₁₆	C₂×Q₈	1	8	yes	complemented
158	C₁₁×D₈	C₂×Q₈	1	8	yes	complemented
159	C₁₁×M₁₆	—	2	6	no	—
160	C₁₁×M₁₆	C₂×Q₈	1	4	yes	complemented
161	C₂×C₈×C₁₁	C₂⁴	1	6	yes	—
162	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
163	C₁₁×C₄⋊C₄	—	2	6	no	—
164	C₁₁×C₄⋊C₄	—	2	3	no	—
165	C₁₁×C₄⋊C₄	—	2	6	no	—
166	C₁₁×C₄⋊C₄	—	2	6	no	—
167	C₁₁×C₄⋊C₄	—	2	3	no	—
168	C₁₁×C₄⋊C₄	—	2	3	no	—
169	C₁₁×C₄⋊C₄	—	2	3	no	—
170	C₁₁×C₄⋊C₄	—	2	3	no	—
171	C₁₁×C₄⋊C₄	—	2	6	no	—
172	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
173	C₁₁×C₄⋊C₄	C₂×D₄	1	6	yes	—
174	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
175	C₁₁×C₄⋊C₄	C₂⁴	1	3	yes	—
176	C₁₁×C₄⋊C₄	C₂⁴	1	3	yes	—
177	C₁₁×C₄⋊C₄	C₂⁴	1	6	yes	—
178	C₁₁×C₂²⋊C₄	—	2	3	no	—
179	C₁₁×C₂²⋊C₄	—	2	6	no	—
180	C₁₁×C₂²⋊C₄	—	2	6	no	—
181	C₁₁×C₂²⋊C₄	—	2	3	no	—
182	C₁₁×C₂²⋊C₄	—	2	3	no	—
183	C₄²×C₁₁	—	2	3	no	—
184	C₄²×C₁₁	—	2	3	no	—
185	C₄²×C₁₁	—	2	3	no	—
186	C₄²×C₁₁	C₂×D₄	1	3	yes	—
187	C₄²×C₁₁	C₂×D₄	1	3	yes	—
188	C₄²×C₁₁	C₂⁴	1	3	yes	—
189	C₄²×C₁₁	C₂⁴	1	3	yes	—
190	Q₈×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
191	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#3386	C₂×C₁₁	1	6	yes	complemented
193	#3384	C₂×C₁₁	1	6	yes	complemented
194	Q₈×SD₁₆	C₂×C₁₁	1	2	yes	complemented
195	Q₈×D₈	C₂×C₁₁	1	2	yes	complemented
196	#3165	C₂×C₁₁	1	3	yes	complemented
197	#3079	C₂×C₁₁	1	3	yes	complemented
198	#3077	C₂×C₁₁	1	3	yes	complemented
199	Q₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
200	C₄×AGL(1,ℤ/8)	C₂×C₁₁	1	3	yes	—
201	C₂³×C₁₁	—	2	4	no	—
202	C₂³×C₁₁	—	2	1	no	—
203	C₂³×C₁₁	—	2	2	no	—
204	C₂³×C₁₁	—	4	2	no	—
205	C₂³×C₁₁	—	4	2	no	—
206	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₁	—	2	6	no	—
208	Q₈×C₁₁	—	2	1	no	—
209	Q₈×C₁₁	—	4	12	no	—
210	Q₈×C₁₁	—	4	6	no	—
211	Q₈×C₁₁	—	4	12	no	—
212	Q₈×C₁₁	—	8	3	no	—
213	Q₈×C₁₁	AGL(1,ℤ/8)	1	4	yes	direct product factor
214	Q₈×C₁₁	C₂²×Q₈	1	2	yes	complemented
215	D₄×C₁₁	—	2	4	no	—
216	D₄×C₁₁	—	2	4	no	—
217	D₄×C₁₁	—	2	2	no	—
218	D₄×C₁₁	—	2	1	no	—
219	D₄×C₁₁	C₂²×Q₈	1	4	yes	—
220	D₄×C₁₁	C₂²×Q₈	1	2	yes	complemented
221	C₂×C₄×C₁₁	—	2	1	no	—
222	C₂×C₄×C₁₁	—	2	4	no	—
223	C₂×C₄×C₁₁	—	2	6	no	—
224	C₂×C₄×C₁₁	—	2	3	no	—
225	C₂×C₄×C₁₁	—	2	3	no	—
226	C₂×C₄×C₁₁	—	2	6	no	—
227	C₂×C₄×C₁₁	—	4	3	no	—
228	C₂×C₄×C₁₁	—	4	12	no	—
229	C₂×C₄×C₁₁	—	4	6	no	—
230	C₂×C₄×C₁₁	—	4	12	no	—
231	C₂×C₄×C₁₁	—	4	6	no	—
232	C₂×C₄×C₁₁	—	8	3	no	—
233	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
234	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
235	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
236	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
238	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
239	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
240	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
241	C₈×C₁₁	—	2	6	no	—
242	C₈×C₁₁	C₂²×Q₈	1	4	yes	complemented
243	C₂³×Q₈	—	2	1	no	—
244	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	1	yes	characteristic
245	Q₈²	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	#557	C₂²×C₁₁	1	3	yes	complemented
247	#554	—	2	3	no	—
248	#554	C₂²×C₁₁	1	3	yes	complemented
249	D₄×Q₈	—	2	1	no	—
250	D₄×Q₈	—	2	1	no	—
251	D₄×Q₈	—	2	3	no	—
252	D₄×Q₈	C₂²×C₁₁	1	2	yes	—
253	D₄×Q₈	C₂²×C₁₁	1	6	yes	—
254	D₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
255	#533	—	2	3	no	—
256	#533	C₂²×C₁₁	1	3	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
258	C₂×C₂²⋊Q₈	—	2	3	no	—
259	C₄×#41	C₂²×C₁₁	1	3	yes	—
260	C₂×C₄×Q₈	—	2	1	no	—
261	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₁₁	1	3	yes	—
263	#501	C₂²×C₁₁	1	12	yes	complemented
264	#500	C₂²×C₁₁	1	6	yes	complemented
265	#498	C₂²×C₁₁	1	6	yes	complemented
266	#478	C₂²×C₁₁	1	12	yes	—
267	#477	C₂²×C₁₁	1	6	yes	complemented
268	#476	C₂²×C₁₁	1	6	yes	—
269	#476	C₂²×C₁₁	1	6	yes	complemented
270	#475	C₂²×C₁₁	1	6	yes	complemented
271	#474	C₂²×C₁₁	1	6	yes	—
272	#474	C₂²×C₁₁	1	6	yes	complemented
273	#446	C₂²×C₁₁	1	6	yes	complemented
274	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
275	#442	C₂²×C₁₁	1	6	yes	—
276	#440	C₂²×C₁₁	1	6	yes	—
277	C₄×SD₁₆	C₂²×C₁₁	1	6	yes	—
278	C₄×D₈	C₂²×C₁₁	1	6	yes	—
279	#428	C₂²×C₁₁	1	6	yes	—
280	#428	C₂²×C₁₁	1	3	yes	—
281	#423	C₂²×C₁₁	1	3	yes	—
282	#418	C₂²×C₁₁	1	3	yes	—
283	#417	C₂²×C₁₁	1	3	yes	—
284	C₄×M₁₆	C₂²×C₁₁	1	3	yes	—
285	C₂²×C₁₁	—	2	1	no	—
286	C₂²×C₁₁	—	2	1	no	—
287	C₂²×C₁₁	—	2	2	no	—
288	C₂²×C₁₁	—	2	4	no	—
289	C₂²×C₁₁	—	4	8	no	—
290	C₂²×C₁₁	—	4	1	no	—
291	C₂²×C₁₁	—	4	2	no	—
292	C₂²×C₁₁	—	4	2	no	—
293	C₂²×C₁₁	—	4	1	no	—
294	C₂²×C₁₁	D₄×Q₈	1	2	yes	—
295	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₁₁	—	2	3	no	—
297	C₄×C₁₁	—	2	3	no	—
298	C₄×C₁₁	—	2	2	no	—
299	C₄×C₁₁	—	2	3	no	—
300	C₄×C₁₁	—	4	3	no	—
301	C₄×C₁₁	—	4	6	no	—
302	C₄×C₁₁	—	4	3	no	—
303	C₄×C₁₁	D₄×Q₈	1	2	yes	—
304	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	6	yes	—
305	C₄×C₁₁	C₂³×Q₈	1	1	yes	characteristic
306	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	—	2	6	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	3	no	—
312	C₂²×Q₈	—	4	8	no	—
313	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
314	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
315	C₂³×C₄	—	2	3	no	—
316	AGL(1,ℤ/8)	Q₈×C₁₁	1	8	yes	direct product factor
317	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
318	C₂×D₈	C₂³×C₁₁	1	2	yes	—
319	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
320	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
321	C₄⋊Q₈	—	2	3	no	—
322	C₄⋊Q₈	—	2	3	no	—
323	C₄⋊Q₈	—	2	3	no	—
324	C₄⋊Q₈	—	2	3	no	—
325	C₄⋊Q₈	C₂³×C₁₁	1	6	yes	—
326	C₄⋊Q₈	C₂³×C₁₁	1	6	yes	—
327	C₄⋊Q₈	C₂³×C₁₁	1	3	yes	—
328	C₄⋊Q₈	C₂³×C₁₁	1	3	yes	—
329	#125	—	2	6	no	—
330	#125	C₂³×C₁₁	1	6	yes	—
331	C₂²⋊Q₈	—	2	3	no	—
332	C₂²⋊Q₈	—	2	3	no	—
333	C₂²⋊Q₈	—	2	3	no	—
334	C₂²⋊Q₈	—	2	6	no	—
335	C₂²⋊Q₈	—	2	12	no	—
336	C₂²⋊Q₈	—	2	6	no	—
337	C₂²⋊Q₈	—	2	3	no	—
338	C₂²⋊Q₈	—	2	6	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	3	no	—
341	C₄×Q₈	—	2	3	no	—
342	C₄×Q₈	—	2	3	no	—
343	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
344	C₄×Q₈	D₄×C₁₁	1	3	yes	—
345	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
346	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
347	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
348	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
349	C₄×D₄	—	2	3	no	—
350	C₄×D₄	—	2	3	no	—
351	C₄×D₄	—	2	3	no	—
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	C₂³×C₁₁	1	6	yes	—
354	C₄×D₄	C₂³×C₁₁	1	6	yes	—
355	C₄×D₄	C₂³×C₁₁	1	3	yes	—
356	C₄×D₄	C₂³×C₁₁	1	3	yes	—
357	#117	—	2	3	no	—
358	#117	C₂³×C₁₁	1	3	yes	—
359	C₂×C₄⋊C₄	—	2	3	no	—
360	C₂×C₄⋊C₄	—	2	3	no	—
361	C₂×C₄⋊C₄	D₄×C₁₁	1	3	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
363	C₂×C₂²⋊C₄	—	2	3	no	—
364	C₂×C₄²	—	2	3	no	—
365	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
366	#107	C₂³×C₁₁	1	6	yes	—
367	#107	C₂³×C₁₁	1	12	yes	—
368	#106	C₂³×C₁₁	1	6	yes	—
369	#106	C₂³×C₁₁	1	12	yes	—
370	C₄⋊C₈	C₂³×C₁₁	1	6	yes	—
371	C₄⋊C₈	C₂³×C₁₁	1	6	yes	—
372	#103	C₂³×C₁₁	1	6	yes	—
373	#102	C₂³×C₁₁	1	6	yes	—
374	#102	C₂³×C₁₁	1	6	yes	—
375	#102	C₂³×C₁₁	1	6	yes	—
376	#97	C₂³×C₁₁	1	6	yes	—
377	C₄×C₈	C₂³×C₁₁	1	6	yes	—
378	C₂×C₁₁	—	2	2	no	—
379	C₂×C₁₁	—	4	2	no	—
380	C₂×C₁₁	—	4	4	no	—
381	C₂×C₁₁	C₂×D₄×Q₈	1	1	yes	characteristic
382	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂×C₁₁	#3586	1	1	yes	characteristic
384	C₂⁴	—	2	1	no	—
385	#41	—	2	2	no	—
386	#41	C₂×Q₈×C₁₁	1	4	yes	complemented
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	3	no	—
389	C₂×Q₈	—	2	6	no	—
390	C₂×Q₈	—	2	6	no	—
391	C₂×Q₈	—	2	3	no	—
392	C₂×Q₈	—	4	12	no	—
393	C₂×Q₈	—	4	24	no	—
394	C₂×Q₈	—	4	8	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	C₂×D₄×C₁₁	1	3	yes	—
397	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
398	C₂×Q₈	C₂⁴×C₁₁	1	1	yes	characteristic
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	complemented
403	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
404	C₂×D₄	C₂⁴×C₁₁	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	2	6	no	—
409	C₂²×C₄	—	2	6	no	—
410	C₂²×C₄	—	2	3	no	—
411	C₂²×C₄	—	4	12	no	—
412	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
413	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
414	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
415	SD₁₆	C₂×Q₈×C₁₁	1	8	yes	complemented
416	D₈	C₂×Q₈×C₁₁	1	8	yes	complemented
417	M₁₆	—	2	6	no	—
418	M₁₆	C₂×Q₈×C₁₁	1	4	yes	complemented
419	C₂×C₈	C₂⁴×C₁₁	1	6	yes	—
420	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
421	C₄⋊C₄	—	2	6	no	—
422	C₄⋊C₄	—	2	3	no	—
423	C₄⋊C₄	—	2	6	no	—
424	C₄⋊C₄	—	2	6	no	—
425	C₄⋊C₄	—	2	3	no	—
426	C₄⋊C₄	—	2	3	no	—
427	C₄⋊C₄	—	2	3	no	—
428	C₄⋊C₄	—	2	3	no	—
429	C₄⋊C₄	—	2	6	no	—
430	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
431	C₄⋊C₄	C₂×D₄×C₁₁	1	6	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
433	C₄⋊C₄	C₂⁴×C₁₁	1	3	yes	—
434	C₄⋊C₄	C₂⁴×C₁₁	1	3	yes	—
435	C₄⋊C₄	C₂⁴×C₁₁	1	6	yes	—
436	C₂²⋊C₄	—	2	3	no	—
437	C₂²⋊C₄	—	2	6	no	—
438	C₂²⋊C₄	—	2	6	no	—
439	C₂²⋊C₄	—	2	3	no	—
440	C₂²⋊C₄	—	2	3	no	—
441	C₄²	—	2	3	no	—
442	C₄²	—	2	3	no	—
443	C₄²	—	2	3	no	—
444	C₄²	C₂×D₄×C₁₁	1	3	yes	—
445	C₄²	C₂×D₄×C₁₁	1	3	yes	—
446	C₄²	C₂⁴×C₁₁	1	3	yes	—
447	C₄²	C₂⁴×C₁₁	1	3	yes	—
448	C₁₁	Q₈×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
449	C₂³	—	2	4	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
455	Q₈	—	2	6	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	4	12	no	—
458	Q₈	—	4	6	no	—
459	Q₈	—	4	12	no	—
460	Q₈	—	8	3	no	—
461	Q₈	C₁₁×AGL(1,ℤ/8)	1	4	yes	direct product factor
462	Q₈	C₂²×Q₈×C₁₁	1	2	yes	complemented
463	D₄	—	2	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	C₂²×Q₈×C₁₁	1	4	yes	—
468	D₄	C₂²×Q₈×C₁₁	1	2	yes	complemented
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	6	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	2	6	no	—
475	C₂×C₄	—	4	3	no	—
476	C₂×C₄	—	4	12	no	—
477	C₂×C₄	—	4	6	no	—
478	C₂×C₄	—	4	12	no	—
479	C₂×C₄	—	4	6	no	—
480	C₂×C₄	—	8	3	no	—
481	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
482	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
483	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
484	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
486	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
487	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
489	C₈	—	2	6	no	—
490	C₈	C₂²×Q₈×C₁₁	1	4	yes	complemented
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	D₄×Q₈×C₁₁	1	2	yes	—
501	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	3	no	—
504	C₄	—	2	3	no	—
505	C₄	—	2	3	no	—
506	C₄	—	4	6	no	—
507	C₄	—	4	3	no	—
508	C₄	—	4	3	no	—
509	C₄	D₄×Q₈×C₁₁	1	2	yes	—
510	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	6	yes	—
511	C₄	C₂³×Q₈×C₁₁	1	1	yes	characteristic
512	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
513	C₂	—	2	2	no	—
514	C₂	—	4	4	no	—
515	C₂	—	4	2	no	—
516	C₂	C₂×D₄×Q₈×C₁₁	1	1	yes	characteristic
517	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂	C₁₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₁×#41	C₂	semidirect
2. C₂×D₄×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#3386	C₂	semidirect
4. C₁₁×#3384	C₂	semidirect
5. Q₈×C₁₁×SD₁₆	C₂	semidirect
6. Q₈×C₁₁×D₈	C₂	semidirect
7. C₁₁×#3165	C₂	semidirect
8. C₁₁×#3079	C₂	semidirect
9. C₁₁×#3077	C₂	semidirect
10. Q₈×C₁₁×M₁₆	C₂	semidirect
14. Q₈²×C₁₁	C₂²	semidirect
15. C₁₁×#557	C₂²	semidirect
17. C₁₁×#554	C₂²	semidirect
23. D₄×Q₈×C₁₁	C₂²	semidirect
32. C₁₁×#501	C₂²	semidirect
33. C₁₁×#500	C₂²	semidirect
34. C₁₁×#498	C₂²	semidirect
36. C₁₁×#477	C₂²	semidirect
38. C₁₁×#476	C₂²	semidirect
39. C₁₁×#475	C₂²	semidirect
41. C₁₁×#474	C₂²	semidirect
42. C₁₁×#446	C₂²	semidirect
43. C₈×Q₈×C₁₁	C₂²	semidirect
63. C₁₁×AGL(1,ℤ/8)	Q₈	direct (N × H)
125. Q₈×AGL(1,ℤ/8)	C₁₁	direct (N × H)
128. C₁₁×#41	C₂×Q₈	semidirect
144. C₂×D₄×C₁₁	C₂×Q₈	semidirect
157. C₁₁×SD₁₆	C₂×Q₈	semidirect
158. C₁₁×D₈	C₂×Q₈	semidirect
160. C₁₁×M₁₆	C₂×Q₈	semidirect
190. Q₈×#41	C₂×C₁₁	semidirect
191. C₂×D₄×Q₈	C₂×C₁₁	semidirect
192. #3386	C₂×C₁₁	semidirect
193. #3384	C₂×C₁₁	semidirect
194. Q₈×SD₁₆	C₂×C₁₁	semidirect
195. Q₈×D₈	C₂×C₁₁	semidirect
196. #3165	C₂×C₁₁	semidirect
197. #3079	C₂×C₁₁	semidirect
198. #3077	C₂×C₁₁	semidirect
199. Q₈×M₁₆	C₂×C₁₁	semidirect
213. Q₈×C₁₁	AGL(1,ℤ/8)	direct (N × H)
214. Q₈×C₁₁	C₂²×Q₈	semidirect
220. D₄×C₁₁	C₂²×Q₈	semidirect
242. C₈×C₁₁	C₂²×Q₈	semidirect
245. Q₈²	C₂²×C₁₁	semidirect
246. #557	C₂²×C₁₁	semidirect
248. #554	C₂²×C₁₁	semidirect
254. D₄×Q₈	C₂²×C₁₁	semidirect
263. #501	C₂²×C₁₁	semidirect
264. #500	C₂²×C₁₁	semidirect
265. #498	C₂²×C₁₁	semidirect
267. #477	C₂²×C₁₁	semidirect
269. #476	C₂²×C₁₁	semidirect
270. #475	C₂²×C₁₁	semidirect
272. #474	C₂²×C₁₁	semidirect
273. #446	C₂²×C₁₁	semidirect
274. C₈×Q₈	C₂²×C₁₁	semidirect
316. AGL(1,ℤ/8)	Q₈×C₁₁	direct (N × H)
386. #41	C₂×Q₈×C₁₁	semidirect
402. C₂×D₄	C₂×Q₈×C₁₁	semidirect
415. SD₁₆	C₂×Q₈×C₁₁	semidirect
416. D₈	C₂×Q₈×C₁₁	semidirect
418. M₁₆	C₂×Q₈×C₁₁	semidirect
448. C₁₁	Q₈×AGL(1,ℤ/8)	direct (N × H)
461. Q₈	C₁₁×AGL(1,ℤ/8)	direct (N × H)
462. Q₈	C₂²×Q₈×C₁₁	semidirect
468. D₄	C₂²×Q₈×C₁₁	semidirect
490. C₈	C₂²×Q₈×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×#41	2
C₂×D₄×Q₈×C₁₁	2
C₁₁×#3386	2
C₁₁×#3384	2
Q₈×C₁₁×SD₁₆	2
Q₈×C₁₁×D₈	2
C₁₁×#3165	2
C₁₁×#3079	2
C₁₁×#3077	2
Q₈×C₁₁×M₁₆	2
C₄×C₁₁×AGL(1,ℤ/8)	2
Q₈×AGL(1,ℤ/8)	11

Subgroups — Q8×C11×AGL(1,ℤ/8) #14638559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×AGL(1,ℤ/8) #14638559