Subgroups — Q₈×C₁₁×#121 #14613734

Order 2816.

3016 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2857	C₂	1	3	yes	maximal, complemented
5	C₁₁×#2546	C₂	1	3	yes	maximal, complemented
6	C₁₁×#2538	C₂	1	3	yes	maximal, complemented
7	C₁₁×#2429	C₂	1	6	yes	maximal, complemented
8	C₁₁×#2417	C₂	1	6	yes	maximal, complemented
9	Q₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#121	C₂	1	3	yes	maximal
12	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₁₁	—	2	16	no	—
15	D₄×Q₈×C₁₁	—	2	8	no	—
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	6	yes	—
17	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
18	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	6	yes	—
19	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	6	yes	—
20	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	6	yes	—
21	C₂×C₁₁×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₁	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₁	C₂²	1	3	yes	—
24	C₂×C₄×Q₈×C₁₁	C₂²	1	3	yes	—
25	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₁	C₂²	1	6	yes	—
29	C₂×C₄×D₄×C₁₁	C₂²	1	3	yes	—
30	C₂²×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
31	C₂²×C₄²×C₁₁	C₂²	1	3	yes	—
32	C₁₁×#398	C₂²	1	12	yes	—
33	C₁₁×#396	C₂²	1	12	yes	—
34	C₁₁×#391	C₂²	1	6	yes	—
35	C₁₁×#391	C₂²	1	6	yes	—
36	C₁₁×#390	C₂²	1	3	yes	—
37	C₁₁×#389	C₂²	1	6	yes	—
38	C₁₁×#389	C₂²	1	6	yes	—
39	C₁₁×#389	C₂²	1	6	yes	—
40	C₁₁×#389	C₂²	1	3	yes	—
41	C₁₁×#388	C₂²	1	6	yes	—
42	C₁₁×#386	C₂²	1	6	yes	—
43	C₁₁×#384	C₂²	1	3	yes	—
44	C₁₁×#380	C₂²	1	6	yes	—
45	C₁₁×#380	C₂²	1	6	yes	—
46	C₁₁×#380	C₂²	1	3	yes	—
47	C₄×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
48	C₄×C₁₁×C₂²⋊C₄	C₂²	1	6	yes	—
49	C₂²×Q₈×C₁₁	—	2	4	no	—
50	C₂²×Q₈×C₁₁	—	2	4	no	—
51	C₂²×Q₈×C₁₁	—	2	8	no	—
52	C₂²×Q₈×C₁₁	—	2	8	no	—
53	C₂²×Q₈×C₁₁	—	2	8	no	—
54	C₂²×Q₈×C₁₁	D₄	1	8	yes	complemented
55	C₂²×Q₈×C₁₁	C₂³	1	6	yes	—
56	C₂²×Q₈×C₁₁	C₂³	1	3	yes	—
57	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
61	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
62	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×C₄⋊Q₈	—	2	24	no	—
65	C₁₁×C₄⋊Q₈	—	2	12	no	—
66	C₁₁×C₂²⋊Q₈	—	2	24	no	—
67	C₁₁×C₂²⋊Q₈	—	2	24	no	—
68	C₁₁×C₂²⋊Q₈	—	2	24	no	—
69	C₁₁×#121	Q₈	1	8	yes	direct product factor
70	C₄×Q₈×C₁₁	—	2	4	no	—
71	C₄×Q₈×C₁₁	—	2	8	no	—
72	C₄×Q₈×C₁₁	—	2	12	no	—
73	C₄×Q₈×C₁₁	—	2	12	no	—
74	C₄×Q₈×C₁₁	D₄	1	8	yes	complemented
75	C₄×D₄×C₁₁	—	2	24	no	—
76	C₄×D₄×C₁₁	—	2	12	no	—
77	C₂×C₁₁×C₄⋊C₄	—	2	12	no	—
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
79	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
80	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
81	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
82	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
83	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
84	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
85	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
86	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
87	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
88	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
90	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
91	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
92	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
93	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₁	—	2	12	no	—
95	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
96	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
97	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
98	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
99	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
100	C₁₁×#95	C₂³	1	6	yes	—
101	C₁₁×#95	C₂³	1	6	yes	—
102	C₁₁×#95	C₂³	1	6	yes	—
103	C₁₁×#95	C₂³	1	12	yes	—
104	Q₈×#121	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
106	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
107	C₂×Q₈×C₁₁	—	2	32	no	—
108	C₂×Q₈×C₁₁	—	2	6	no	—
109	C₂×Q₈×C₁₁	—	2	12	no	—
110	C₂×Q₈×C₁₁	—	2	12	no	—
111	C₂×Q₈×C₁₁	—	2	6	no	—
112	C₂×Q₈×C₁₁	—	2	12	no	—
113	C₂×Q₈×C₁₁	—	4	32	no	—
114	C₂×Q₈×C₁₁	C₂×D₄	1	12	yes	—
115	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
116	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
117	C₂×Q₈×C₁₁	#41	1	4	yes	—
118	C₂×D₄×C₁₁	—	2	4	no	—
119	C₂×D₄×C₁₁	—	2	4	no	—
120	C₂×D₄×C₁₁	—	2	2	no	—
121	C₂×D₄×C₁₁	—	2	2	no	—
122	C₂×D₄×C₁₁	C₂×Q₈	1	8	yes	complemented
123	C₂×D₄×C₁₁	C₂×Q₈	1	4	yes	complemented
124	C₂²×C₄×C₁₁	—	2	2	no	—
125	C₂²×C₄×C₁₁	—	2	6	no	—
126	C₂²×C₄×C₁₁	—	2	6	no	—
127	C₂²×C₄×C₁₁	—	2	2	no	—
128	C₂²×C₄×C₁₁	—	2	6	no	—
129	C₂²×C₄×C₁₁	—	2	6	no	—
130	C₂²×C₄×C₁₁	—	2	12	no	—
131	C₂²×C₄×C₁₁	—	2	12	no	—
132	C₂²×C₄×C₁₁	—	2	12	no	—
133	C₂²×C₄×C₁₁	—	4	3	no	—
134	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
135	C₂²×C₄×C₁₁	C₂×Q₈	1	4	yes	complemented
136	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
137	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
138	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
139	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
140	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
144	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
145	C₁₁×C₄⋊C₄	—	2	12	no	—
146	C₁₁×C₄⋊C₄	—	2	6	no	—
147	C₁₁×C₄⋊C₄	—	2	12	no	—
148	C₁₁×C₄⋊C₄	—	2	6	no	—
149	C₁₁×C₄⋊C₄	—	2	12	no	—
150	C₁₁×C₄⋊C₄	—	2	24	no	—
151	C₁₁×C₄⋊C₄	—	2	12	no	—
152	C₁₁×C₄⋊C₄	—	2	6	no	—
153	C₁₁×C₄⋊C₄	—	4	6	no	—
154	C₁₁×C₄⋊C₄	C₂×D₄	1	12	yes	—
155	C₁₁×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
156	C₁₁×C₂²⋊C₄	—	2	12	no	—
157	C₁₁×C₂²⋊C₄	—	2	12	no	—
158	C₁₁×C₂²⋊C₄	—	2	12	no	—
159	C₁₁×C₂²⋊C₄	—	4	6	no	—
160	C₁₁×C₂²⋊C₄	C₂×Q₈	1	8	yes	complemented
161	C₄²×C₁₁	—	2	6	no	—
162	C₄²×C₁₁	—	2	6	no	—
163	C₄²×C₁₁	—	2	6	no	—
164	C₄²×C₁₁	—	2	12	no	—
165	C₄²×C₁₁	C₂×D₄	1	12	yes	—
166	C₂×D₄×Q₈	C₂×C₁₁	1	2	yes	complemented
167	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₂²×C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
169	#2857	C₂×C₁₁	1	3	yes	complemented
170	#2546	C₂×C₁₁	1	3	yes	complemented
171	#2538	C₂×C₁₁	1	3	yes	complemented
172	#2429	C₂×C₁₁	1	6	yes	complemented
173	#2417	C₂×C₁₁	1	6	yes	complemented
174	Q₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
175	Q₈×C₂²⋊C₄	C₂×C₁₁	1	2	yes	complemented
176	C₄×#121	C₂×C₁₁	1	3	yes	—
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	1	no	—
181	C₂³×C₁₁	—	2	2	no	—
182	C₂³×C₁₁	—	2	2	no	—
183	C₂³×C₁₁	—	2	2	no	—
184	C₂³×C₁₁	—	2	2	no	—
185	C₂³×C₁₁	—	2	2	no	—
186	C₂³×C₁₁	—	2	2	no	—
187	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
188	C₂³×C₁₁	C₂²×Q₈	1	4	yes	—
189	C₂³×C₁₁	C₂²×Q₈	1	2	yes	—
190	C₂³×C₁₁	2₋¹⁺⁴	1	2	yes	—
191	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
192	Q₈×C₁₁	—	2	24	no	—
193	Q₈×C₁₁	—	4	24	no	—
194	Q₈×C₁₁	#121	1	16	yes	direct product factor
195	D₄×C₁₁	—	2	16	no	—
196	D₄×C₁₁	—	2	8	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	2	no	—
199	C₂×C₄×C₁₁	—	2	3	no	—
200	C₂×C₄×C₁₁	—	2	3	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	3	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	2	3	no	—
205	C₂×C₄×C₁₁	—	2	24	no	—
206	C₂×C₄×C₁₁	—	2	8	no	—
207	C₂×C₄×C₁₁	—	2	3	no	—
208	C₂×C₄×C₁₁	—	2	6	no	—
209	C₂×C₄×C₁₁	—	2	6	no	—
210	C₂×C₄×C₁₁	—	2	6	no	—
211	C₂×C₄×C₁₁	—	2	6	no	—
212	C₂×C₄×C₁₁	—	2	6	no	—
213	C₂×C₄×C₁₁	—	2	3	no	—
214	C₂×C₄×C₁₁	—	2	3	no	—
215	C₂×C₄×C₁₁	—	2	6	no	—
216	C₂×C₄×C₁₁	—	4	12	no	—
217	C₂×C₄×C₁₁	—	4	24	no	—
218	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
219	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
220	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
221	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
222	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
224	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
225	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
226	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
227	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
228	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
229	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
230	D₄×Q₈	—	2	16	no	—
231	D₄×Q₈	—	2	8	no	—
232	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
233	C₂×C₄⋊Q₈	C₂²×C₁₁	1	6	yes	—
234	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	6	yes	—
235	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	6	yes	—
236	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	6	yes	—
237	C₂×#121	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	2	8	no	—
239	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₁₁	1	3	yes	—
242	C₂×C₄×Q₈	C₂²×C₁₁	1	3	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₁₁	1	6	yes	—
245	C₂×C₄×D₄	C₂²×C₁₁	1	3	yes	—
246	C₂²×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
247	C₂²×C₄²	C₂²×C₁₁	1	3	yes	—
248	#398	C₂²×C₁₁	1	12	yes	—
249	#396	C₂²×C₁₁	1	12	yes	—
250	#391	C₂²×C₁₁	1	6	yes	—
251	#391	C₂²×C₁₁	1	6	yes	—
252	#390	C₂²×C₁₁	1	3	yes	—
253	#389	C₂²×C₁₁	1	6	yes	—
254	#389	C₂²×C₁₁	1	6	yes	—
255	#389	C₂²×C₁₁	1	6	yes	—
256	#389	C₂²×C₁₁	1	3	yes	—
257	#388	C₂²×C₁₁	1	6	yes	—
258	#386	C₂²×C₁₁	1	6	yes	—
259	#384	C₂²×C₁₁	1	3	yes	—
260	#380	C₂²×C₁₁	1	6	yes	—
261	#380	C₂²×C₁₁	1	3	yes	—
262	#380	C₂²×C₁₁	1	6	yes	—
263	C₄×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₁₁	1	6	yes	—
265	C₂²×C₁₁	—	2	2	no	—
266	C₂²×C₁₁	—	2	2	no	—
267	C₂²×C₁₁	—	2	2	no	—
268	C₂²×C₁₁	—	2	2	no	—
269	C₂²×C₁₁	—	2	2	no	—
270	C₂²×C₁₁	—	2	2	no	—
271	C₂²×C₁₁	—	2	4	no	—
272	C₂²×C₁₁	—	2	4	no	—
273	C₂²×C₁₁	—	2	4	no	—
274	C₂²×C₁₁	—	4	2	no	—
275	C₂²×C₁₁	—	4	2	no	—
276	C₂²×C₁₁	—	4	2	no	—
277	C₂²×C₁₁	—	4	2	no	—
278	C₂²×C₁₁	D₄×Q₈	1	4	yes	complemented
279	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
280	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
281	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
282	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
283	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
284	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
285	C₂²×C₁₁	#585	1	1	yes	characteristic
286	C₄×C₁₁	—	2	6	no	—
287	C₄×C₁₁	—	2	2	no	—
288	C₄×C₁₁	—	2	4	no	—
289	C₄×C₁₁	—	2	6	no	—
290	C₄×C₁₁	—	4	6	no	—
291	C₄×C₁₁	—	4	3	no	—
292	C₄×C₁₁	—	4	6	no	—
293	C₄×C₁₁	C₂×#121	1	12	yes	—
294	C₄×C₁₁	D₄×Q₈	1	4	yes	complemented
295	C₂²×Q₈	—	2	4	no	—
296	C₂²×Q₈	—	2	4	no	—
297	C₂²×Q₈	—	2	8	no	—
298	C₂²×Q₈	—	2	8	no	—
299	C₂²×Q₈	—	2	8	no	—
300	C₂²×Q₈	D₄×C₁₁	1	8	yes	complemented
301	C₂²×Q₈	C₂³×C₁₁	1	6	yes	—
302	C₂²×Q₈	C₂³×C₁₁	1	3	yes	—
303	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
305	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
307	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
308	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
309	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
310	C₄⋊Q₈	—	2	24	no	—
311	C₄⋊Q₈	—	2	12	no	—
312	C₂²⋊Q₈	—	2	24	no	—
313	C₂²⋊Q₈	—	2	24	no	—
314	C₂²⋊Q₈	—	2	24	no	—
315	#121	Q₈×C₁₁	1	8	yes	direct product factor
316	C₄×Q₈	—	2	4	no	—
317	C₄×Q₈	—	2	8	no	—
318	C₄×Q₈	—	2	12	no	—
319	C₄×Q₈	—	2	12	no	—
320	C₄×Q₈	D₄×C₁₁	1	8	yes	complemented
321	C₄×D₄	—	2	24	no	—
322	C₄×D₄	—	2	12	no	—
323	C₂×C₄⋊C₄	—	2	12	no	—
324	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
340	C₂×C₄²	—	2	12	no	—
341	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
342	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
343	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
344	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
345	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
346	#95	C₂³×C₁₁	1	6	yes	—
347	#95	C₂³×C₁₁	1	6	yes	—
348	#95	C₂³×C₁₁	1	6	yes	—
349	#95	C₂³×C₁₁	1	12	yes	—
350	C₂×C₁₁	—	2	4	no	—
351	C₂×C₁₁	—	4	4	no	—
352	C₂×C₁₁	C₂²×#121	1	1	yes	characteristic
353	C₂×C₁₁	C₂×D₄×Q₈	1	1	yes	characteristic
354	C₂×C₁₁	C₂×D₄×Q₈	1	1	yes	characteristic
355	C₂×C₁₁	Q₈×#41	1	1	yes	characteristic
356	C₂×C₁₁	#3489	1	1	yes	characteristic
357	C₂×C₁₁	#3497	1	1	yes	characteristic
358	C₂×C₁₁	#3523	1	1	yes	characteristic
359	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
360	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
361	C₂×Q₈	—	2	32	no	—
362	C₂×Q₈	—	2	6	no	—
363	C₂×Q₈	—	2	12	no	—
364	C₂×Q₈	—	2	12	no	—
365	C₂×Q₈	—	2	6	no	—
366	C₂×Q₈	—	2	12	no	—
367	C₂×Q₈	—	4	32	no	—
368	C₂×Q₈	C₂×D₄×C₁₁	1	12	yes	—
369	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
370	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
371	C₂×Q₈	C₁₁×#41	1	4	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂×Q₈×C₁₁	1	8	yes	complemented
377	C₂×D₄	C₂×Q₈×C₁₁	1	4	yes	complemented
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	6	no	—
380	C₂²×C₄	—	2	6	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	6	no	—
383	C₂²×C₄	—	2	6	no	—
384	C₂²×C₄	—	2	12	no	—
385	C₂²×C₄	—	2	12	no	—
386	C₂²×C₄	—	2	12	no	—
387	C₂²×C₄	—	4	3	no	—
388	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
389	C₂²×C₄	C₂×Q₈×C₁₁	1	4	yes	complemented
390	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
391	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
392	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
393	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
394	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
395	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
398	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
399	C₄⋊C₄	—	2	12	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	12	no	—
402	C₄⋊C₄	—	2	6	no	—
403	C₄⋊C₄	—	2	12	no	—
404	C₄⋊C₄	—	2	24	no	—
405	C₄⋊C₄	—	2	12	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	4	6	no	—
408	C₄⋊C₄	C₂×D₄×C₁₁	1	12	yes	—
409	C₄⋊C₄	C₂×Q₈×C₁₁	1	4	yes	complemented
410	C₂²⋊C₄	—	2	12	no	—
411	C₂²⋊C₄	—	2	12	no	—
412	C₂²⋊C₄	—	2	12	no	—
413	C₂²⋊C₄	—	4	6	no	—
414	C₂²⋊C₄	C₂×Q₈×C₁₁	1	8	yes	complemented
415	C₄²	—	2	6	no	—
416	C₄²	—	2	6	no	—
417	C₄²	—	2	6	no	—
418	C₄²	—	2	12	no	—
419	C₄²	C₂×D₄×C₁₁	1	12	yes	—
420	C₁₁	Q₈×#121	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
432	C₂³	C₂²×Q₈×C₁₁	1	4	yes	—
433	C₂³	C₂²×Q₈×C₁₁	1	2	yes	—
434	C₂³	C₁₁×2₋¹⁺⁴	1	2	yes	—
435	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
436	Q₈	—	2	24	no	—
437	Q₈	—	4	24	no	—
438	Q₈	C₁₁×#121	1	16	yes	direct product factor
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	3	no	—
444	C₂×C₄	—	2	3	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	3	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	3	no	—
449	C₂×C₄	—	2	24	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	6	no	—
453	C₂×C₄	—	2	6	no	—
454	C₂×C₄	—	2	6	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	2	6	no	—
457	C₂×C₄	—	2	3	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	4	12	no	—
461	C₂×C₄	—	4	24	no	—
462	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
463	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
464	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
465	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
466	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
467	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
468	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
469	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
470	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
471	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	D₄×Q₈×C₁₁	1	4	yes	complemented
486	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
487	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
488	C₂²	C₂³×Q₈×C₁₁	1	1	yes	characteristic
489	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
490	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
492	C₂²	C₁₁×#585	1	1	yes	characteristic
493	C₄	—	2	6	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	4	no	—
496	C₄	—	2	6	no	—
497	C₄	—	4	6	no	—
498	C₄	—	4	3	no	—
499	C₄	—	4	6	no	—
500	C₄	C₂×C₁₁×#121	1	12	yes	—
501	C₄	D₄×Q₈×C₁₁	1	4	yes	complemented
502	C₂	—	2	4	no	—
503	C₂	—	4	4	no	—
504	C₂	C₂²×C₁₁×#121	1	1	yes	characteristic
505	C₂	C₂×D₄×Q₈×C₁₁	1	1	yes	characteristic
506	C₂	C₂×D₄×Q₈×C₁₁	1	1	yes	characteristic
507	C₂	Q₈×C₁₁×#41	1	1	yes	characteristic
508	C₂	C₁₁×#3489	1	1	yes	characteristic
509	C₂	C₁₁×#3497	1	1	yes	characteristic
510	C₂	C₁₁×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₁₁	C₂	semidirect
2. C₂×D₄×Q₈×C₁₁	C₂	semidirect
3. C₂²×C₄×Q₈×C₁₁	C₂	semidirect
4. C₁₁×#2857	C₂	semidirect
5. C₁₁×#2546	C₂	semidirect
6. C₁₁×#2538	C₂	semidirect
7. C₁₁×#2429	C₂	semidirect
8. C₁₁×#2417	C₂	semidirect
9. Q₈×C₁₁×C₄⋊C₄	C₂	semidirect
10. Q₈×C₁₁×C₂²⋊C₄	C₂	semidirect
54. C₂²×Q₈×C₁₁	D₄	semidirect
69. C₁₁×#121	Q₈	direct (N × H)
74. C₄×Q₈×C₁₁	D₄	semidirect
104. Q₈×#121	C₁₁	direct (N × H)
122. C₂×D₄×C₁₁	C₂×Q₈	semidirect
123. C₂×D₄×C₁₁	C₂×Q₈	semidirect
135. C₂²×C₄×C₁₁	C₂×Q₈	semidirect
155. C₁₁×C₄⋊C₄	C₂×Q₈	semidirect
160. C₁₁×C₂²⋊C₄	C₂×Q₈	semidirect
166. C₂×D₄×Q₈	C₂×C₁₁	semidirect
167. C₂×D₄×Q₈	C₂×C₁₁	semidirect
168. C₂²×C₄×Q₈	C₂×C₁₁	semidirect
169. #2857	C₂×C₁₁	semidirect
170. #2546	C₂×C₁₁	semidirect
171. #2538	C₂×C₁₁	semidirect
172. #2429	C₂×C₁₁	semidirect
173. #2417	C₂×C₁₁	semidirect
174. Q₈×C₄⋊C₄	C₂×C₁₁	semidirect
175. Q₈×C₂²⋊C₄	C₂×C₁₁	semidirect
194. Q₈×C₁₁	#121	direct (N × H)
278. C₂²×C₁₁	D₄×Q₈	semidirect
294. C₄×C₁₁	D₄×Q₈	semidirect
300. C₂²×Q₈	D₄×C₁₁	semidirect
315. #121	Q₈×C₁₁	direct (N × H)
320. C₄×Q₈	D₄×C₁₁	semidirect
376. C₂×D₄	C₂×Q₈×C₁₁	semidirect
377. C₂×D₄	C₂×Q₈×C₁₁	semidirect
389. C₂²×C₄	C₂×Q₈×C₁₁	semidirect
409. C₄⋊C₄	C₂×Q₈×C₁₁	semidirect
414. C₂²⋊C₄	C₂×Q₈×C₁₁	semidirect
420. C₁₁	Q₈×#121	direct (N × H)
438. Q₈	C₁₁×#121	direct (N × H)
485. C₂²	D₄×Q₈×C₁₁	semidirect
501. C₄	D₄×Q₈×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₁	2
C₂²×C₄×Q₈×C₁₁	2
C₁₁×#2857	2
C₁₁×#2546	2
C₁₁×#2538	2
C₁₁×#2429	2
C₁₁×#2417	2
Q₈×C₁₁×C₄⋊C₄	2
Q₈×C₁₁×C₂²⋊C₄	2
C₄×C₁₁×#121	2
Q₈×#121	11

Subgroups — Q8×C11×#121 #14613734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×#121 #14613734