Subgroups — C₄×C₁₁×#467 #14598715

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₁₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1933	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1892	C₂	1	2	yes	maximal
9	C₁₁×#1808	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#467	C₄	1	8	yes	direct product factor
19	C₄×C₁₁×Q₁₆	—	2	4	no	—
20	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#103	C₂²	1	2	yes	—
24	C₂×C₁₁×#103	C₂²	1	2	yes	—
25	C₂×C₁₁×#103	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	—	2	4	no	—
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#391	C₂²	1	2	yes	—
32	C₁₁×#389	C₂²	1	2	yes	—
33	C₁₁×#387	—	2	2	no	—
34	C₁₁×#385	—	2	2	no	—
35	C₁₁×#380	C₂²	1	2	yes	—
36	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#340	C₂²	1	2	yes	—
41	C₁₁×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₁₁×Q₁₆	—	2	2	no	—
47	C₂×C₁₁×Q₁₆	—	2	2	no	—
48	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂²×C₈×C₁₁	—	2	2	no	—
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	2	2	no	—
52	C₂²×C₈×C₁₁	—	2	2	no	—
53	C₂²×C₈×C₁₁	—	2	2	no	—
54	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₂²⋊Q₈	—	2	4	no	—
60	C₁₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
61	C₄×Q₈×C₁₁	—	2	4	no	—
62	C₄×Q₈×C₁₁	—	2	4	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₁	—	2	2	no	—
72	C₂×C₄²×C₁₁	—	2	2	no	—
73	C₂×C₄²×C₁₁	—	2	2	no	—
74	C₂×C₄²×C₁₁	—	2	2	no	—
75	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#107	—	2	2	no	—
80	C₁₁×#107	—	2	2	no	—
81	C₁₁×#107	C₂×C₄	1	4	yes	complemented
82	C₁₁×#103	—	2	4	no	—
83	C₁₁×#103	—	2	4	no	—
84	C₁₁×#103	C₂×C₄	1	8	yes	complemented
85	C₄×C₈×C₁₁	—	2	2	no	—
86	C₄×C₈×C₁₁	—	2	2	no	—
87	C₄×C₈×C₁₁	—	2	2	no	—
88	C₄×C₈×C₁₁	D₄	1	4	yes	—
89	C₁₁×#95	—	2	2	no	—
90	C₁₁×#95	—	2	2	no	—
91	C₁₁×#95	—	2	2	no	—
92	C₁₁×#95	—	2	2	no	—
93	C₁₁×#95	—	2	2	no	—
94	C₄×#467	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	2	2	no	—
101	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	—	2	2	no	—
105	C₂²×C₄×C₁₁	—	2	2	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	2	no	—
115	C₂²×C₄×C₁₁	Q₁₆	1	4	yes	complemented
116	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	#41	1	2	yes	—
123	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
124	C₁₁×Q₁₆	—	2	8	no	—
125	C₂×C₈×C₁₁	—	2	8	no	—
126	C₂×C₈×C₁₁	—	2	8	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₁	#41	1	2	yes	—
138	C₂×C₈×C₁₁	#41	1	2	yes	—
139	C₁₁×C₄⋊C₄	—	2	8	no	—
140	C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₁₁×C₄⋊C₄	—	2	2	no	—
142	C₁₁×C₄⋊C₄	—	2	2	no	—
143	C₁₁×C₄⋊C₄	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₁₁×C₄⋊C₄	—	4	4	no	—
146	C₁₁×C₄⋊C₄	—	4	4	no	—
147	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
148	C₁₁×C₂²⋊C₄	—	2	8	no	—
149	C₁₁×C₂²⋊C₄	—	4	4	no	—
150	C₄²×C₁₁	—	2	2	no	—
151	C₄²×C₁₁	—	2	2	no	—
152	C₄²×C₁₁	—	2	1	no	—
153	C₄²×C₁₁	—	2	1	no	—
154	C₄²×C₁₁	—	4	4	no	—
155	C₄²×C₁₁	—	4	4	no	—
156	C₄²×C₁₁	C₂×D₄	1	2	yes	—
157	C₄²×C₁₁	#41	1	2	yes	—
158	C₂×#467	C₂×C₁₁	1	1	yes	characteristic
159	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
161	C₄×C₂²⋊Q₈	C₂×C₁₁	1	2	yes	—
162	#1969	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1942	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1933	C₂×C₁₁	1	2	yes	complemented
165	#1892	C₂×C₁₁	1	2	yes	—
166	#1808	C₂×C₁₁	1	1	yes	characteristic
167	C₄×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₄×#103	C₂×C₁₁	1	2	yes	complemented
169	C₂³×C₁₁	—	2	1	no	—
170	C₂³×C₁₁	—	2	1	no	—
171	C₂³×C₁₁	—	2	1	no	—
172	C₂³×C₁₁	—	2	1	no	—
173	C₂³×C₁₁	C₄×D₄	1	2	yes	—
174	C₂³×C₁₁	C₂×Q₁₆	1	2	yes	—
175	C₂³×C₁₁	#135	1	2	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₁	—	2	4	no	—
178	Q₈×C₁₁	—	2	4	no	—
179	Q₈×C₁₁	—	4	2	no	—
180	Q₈×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	—	2	8	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	2	2	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	8	no	—
195	C₂×C₄×C₁₁	—	2	4	no	—
196	C₂×C₄×C₁₁	—	2	4	no	—
197	C₂×C₄×C₁₁	—	4	2	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	2	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	—	4	2	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	2	no	—
206	C₂×C₄×C₁₁	—	4	2	no	—
207	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₁₁	#121	1	2	yes	—
209	C₂×C₄×C₁₁	#121	1	2	yes	—
210	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
211	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
212	C₂×C₄×C₁₁	#135	1	2	yes	—
213	C₂×C₄×C₁₁	#135	1	2	yes	—
214	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	2	no	—
223	C₈×C₁₁	C₄×D₄	1	4	yes	—
224	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
225	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
229	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
230	#467	C₄×C₁₁	1	8	yes	direct product factor
231	C₄×Q₁₆	—	2	4	no	—
232	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
233	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₁	1	2	yes	—
236	C₂×#103	C₂²×C₁₁	1	2	yes	—
237	C₂×#103	C₂²×C₁₁	1	2	yes	—
238	C₂×C₄×C₈	—	2	4	no	—
239	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
243	#391	C₂²×C₁₁	1	2	yes	—
244	#389	C₂²×C₁₁	1	2	yes	—
245	#387	—	2	2	no	—
246	#385	—	2	2	no	—
247	#380	C₂²×C₁₁	1	2	yes	—
248	C₄×C₄⋊C₄	—	2	2	no	—
249	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
250	C₄×C₂²⋊C₄	—	2	2	no	—
251	#340	C₂²×C₁₁	1	2	yes	—
252	#340	C₂²×C₁₁	1	2	yes	—
253	#340	C₂²×C₁₁	1	2	yes	—
254	C₂²×C₁₁	—	2	2	no	—
255	C₂²×C₁₁	—	2	2	no	—
256	C₂²×C₁₁	—	2	2	no	—
257	C₂²×C₁₁	—	2	2	no	—
258	C₂²×C₁₁	—	2	2	no	—
259	C₂²×C₁₁	—	2	2	no	—
260	C₂²×C₁₁	C₄×Q₁₆	1	4	yes	complemented
261	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
263	C₂²×C₁₁	#532	1	1	yes	characteristic
264	C₂²×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
265	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
266	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
267	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
268	C₄×C₁₁	—	2	2	no	—
269	C₄×C₁₁	—	2	2	no	—
270	C₄×C₁₁	—	2	2	no	—
271	C₄×C₁₁	—	2	2	no	—
272	C₄×C₁₁	—	4	4	no	—
273	C₄×C₁₁	—	4	4	no	—
274	C₄×C₁₁	—	8	2	no	—
275	C₄×C₁₁	—	8	2	no	—
276	C₄×C₁₁	#467	1	4	yes	direct product factor
277	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
279	C₄×C₁₁	#525	1	1	yes	characteristic
280	C₄×C₁₁	#529	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
282	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
294	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
315	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#107	—	2	2	no	—
320	#107	C₂×C₄×C₁₁	1	4	yes	complemented
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	C₂×C₄×C₁₁	1	8	yes	complemented
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	D₄×C₁₁	1	4	yes	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	C₂×C₁₁	—	2	4	no	—
334	C₂×C₁₁	C₄×#121	1	1	yes	characteristic
335	C₂×C₁₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
336	C₂×C₁₁	C₄×#135	1	1	yes	characteristic
337	C₂×C₁₁	C₂×#467	1	1	yes	characteristic
338	C₂×C₁₁	#3050	1	1	yes	characteristic
339	C₂×C₁₁	#3168	1	1	yes	characteristic
340	C₂×C₁₁	#3170	1	1	yes	characteristic
341	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₁₁×Q₁₆	1	4	yes	complemented
362	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
368	C₂²×C₄	C₁₁×#41	1	2	yes	—
369	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
370	Q₁₆	—	2	8	no	—
371	C₂×C₈	—	2	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
380	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
383	C₂×C₈	C₁₁×#41	1	2	yes	—
384	C₂×C₈	C₁₁×#41	1	2	yes	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	4	4	no	—
402	C₄²	C₂×D₄×C₁₁	1	2	yes	—
403	C₄²	C₁₁×#41	1	2	yes	—
404	C₁₁	C₄×#467	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	C₄×D₄×C₁₁	1	2	yes	—
410	C₂³	C₂×C₁₁×Q₁₆	1	2	yes	—
411	C₂³	C₁₁×#135	1	2	yes	—
412	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
444	C₂×C₄	C₁₁×#121	1	2	yes	—
445	C₂×C₄	C₁₁×#121	1	2	yes	—
446	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
447	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
448	C₂×C₄	C₁₁×#135	1	2	yes	—
449	C₂×C₄	C₁₁×#135	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
455	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	C₄×D₄×C₁₁	1	4	yes	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₄×C₁₁×Q₁₆	1	4	yes	complemented
467	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
468	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
469	C₂²	C₁₁×#532	1	1	yes	characteristic
470	C₂²	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
472	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
473	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	4	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	2	no	—
482	C₄	C₁₁×#467	1	4	yes	direct product factor
483	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
484	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
485	C₄	C₁₁×#525	1	1	yes	characteristic
486	C₄	C₁₁×#529	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×C₁₁×#121	1	1	yes	characteristic
489	C₂	C₂×C₄×C₁₁×Q₁₆	1	1	yes	characteristic
490	C₂	C₄×C₁₁×#135	1	1	yes	characteristic
491	C₂	C₂×C₁₁×#467	1	1	yes	characteristic
492	C₂	C₁₁×#3050	1	1	yes	characteristic
493	C₂	C₁₁×#3168	1	1	yes	characteristic
494	C₂	C₁₁×#3170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂²×D₄
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
5. C₁₁×#1969	C₂	semidirect
6. C₁₁×#1942	C₂	semidirect
7. C₁₁×#1933	C₂	semidirect
10. C₄×C₁₁×#107	C₂	semidirect
11. C₄×C₁₁×#103	C₂	semidirect
18. C₁₁×#467	C₄	direct (N × H)
48. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
81. C₁₁×#107	C₂×C₄	semidirect
84. C₁₁×#103	C₂×C₄	semidirect
94. C₄×#467	C₁₁	direct (N × H)
115. C₂²×C₄×C₁₁	Q₁₆	semidirect
159. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
162. #1969	C₂×C₁₁	semidirect
163. #1942	C₂×C₁₁	semidirect
164. #1933	C₂×C₁₁	semidirect
167. C₄×#107	C₂×C₁₁	semidirect
168. C₄×#103	C₂×C₁₁	semidirect
230. #467	C₄×C₁₁	direct (N × H)
260. C₂²×C₁₁	C₄×Q₁₆	semidirect
276. C₄×C₁₁	#467	direct (N × H)
287. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
320. #107	C₂×C₄×C₁₁	semidirect
323. #103	C₂×C₄×C₁₁	semidirect
361. C₂²×C₄	C₁₁×Q₁₆	semidirect
404. C₁₁	C₄×#467	direct (N × H)
466. C₂²	C₄×C₁₁×Q₁₆	semidirect
482. C₄	C₁₁×#467	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×#467	2
C₂×C₄×C₁₁×Q₁₆	2
C₂²×C₄×C₈×C₁₁	2
C₄×C₁₁×C₂²⋊Q₈	2
C₁₁×#1969	2
C₁₁×#1942	2
C₁₁×#1933	2
C₁₁×#1892	2
C₁₁×#1808	2
C₄×C₁₁×#107	2
C₄×C₁₁×#103	2
C₄×#467	11

Subgroups — C4×C11×#467 #14598715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×#467 #14598715