Subgroups — C₄×C₁₁×#466 #14598714

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×#121	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1934	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1893	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₁×D₈	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×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₁	—	2	2	no	—
17	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#466	C₄	1	8	yes	direct product factor
20	C₄×C₁₁×D₈	—	2	4	no	—
21	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#102	C₂²	1	2	yes	—
25	C₂×C₁₁×#102	C₂²	1	2	yes	—
26	C₂×C₁₁×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₁	—	2	4	no	—
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	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#390	C₂²	1	2	yes	—
33	C₁₁×#389	C₂²	1	2	yes	—
34	C₁₁×#388	—	2	2	no	—
35	C₁₁×#386	—	2	2	no	—
36	C₁₁×#380	C₂²	1	2	yes	—
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×D₄×C₁₁	—	2	2	no	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	—	2	2	no	—
45	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×D₈	—	2	2	no	—
49	C₂×C₁₁×D₈	—	2	2	no	—
50	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
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	—	2	2	no	—
55	C₂²×C₈×C₁₁	—	2	2	no	—
56	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×#121	—	2	4	no	—
62	C₁₁×#121	C₂×C₄	1	8	yes	complemented
63	C₄×D₄×C₁₁	—	2	4	no	—
64	C₄×D₄×C₁₁	—	2	4	no	—
65	C₄×D₄×C₁₁	—	4	8	no	—
66	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₁₁	—	2	2	no	—
76	C₂×C₄²×C₁₁	—	2	2	no	—
77	C₂×C₄²×C₁₁	—	2	2	no	—
78	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₁₁×#107	—	2	2	no	—
83	C₁₁×#107	—	2	2	no	—
84	C₁₁×#107	C₂×C₄	1	4	yes	complemented
85	C₁₁×#102	—	2	4	no	—
86	C₁₁×#102	—	2	4	no	—
87	C₁₁×#102	C₂×C₄	1	8	yes	complemented
88	C₄×C₈×C₁₁	—	2	2	no	—
89	C₄×C₈×C₁₁	—	2	2	no	—
90	C₄×C₈×C₁₁	—	2	2	no	—
91	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
92	C₁₁×#95	—	2	2	no	—
93	C₁₁×#95	—	2	2	no	—
94	C₁₁×#95	—	2	2	no	—
95	C₄×#466	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₁	—	2	2	no	—
97	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₁	—	2	8	no	—
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	2	2	no	—
101	C₂×D₄×C₁₁	—	2	2	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	4	4	no	—
105	C₂×D₄×C₁₁	—	4	4	no	—
106	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	4	4	no	—
120	C₂²×C₄×C₁₁	—	4	4	no	—
121	C₂²×C₄×C₁₁	—	4	4	no	—
122	C₂²×C₄×C₁₁	D₈	1	4	yes	complemented
123	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	#41	1	2	yes	—
130	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₁₁×D₈	—	2	8	no	—
132	C₂×C₈×C₁₁	—	2	8	no	—
133	C₂×C₈×C₁₁	—	2	8	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₁	#41	1	2	yes	—
145	C₂×C₈×C₁₁	#41	1	2	yes	—
146	C₁₁×C₄⋊C₄	—	2	2	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	2	no	—
149	C₁₁×C₄⋊C₄	—	2	2	no	—
150	C₁₁×C₄⋊C₄	—	2	2	no	—
151	C₁₁×C₄⋊C₄	—	4	4	no	—
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
153	C₁₁×C₂²⋊C₄	—	2	8	no	—
154	C₁₁×C₂²⋊C₄	—	4	4	no	—
155	C₁₁×C₂²⋊C₄	—	4	4	no	—
156	C₁₁×C₂²⋊C₄	—	4	4	no	—
157	C₁₁×C₂²⋊C₄	—	4	4	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	—	2	2	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	4	4	no	—
163	C₄²×C₁₁	C₂×D₄	1	2	yes	—
164	C₄²×C₁₁	#41	1	2	yes	—
165	C₂×#466	C₂×C₁₁	1	1	yes	characteristic
166	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₄×#121	C₂×C₁₁	1	2	yes	complemented
169	#1970	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1942	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#1934	C₂×C₁₁	1	2	yes	complemented
172	#1893	C₂×C₁₁	1	2	yes	complemented
173	#1808	C₂×C₁₁	1	1	yes	characteristic, complemented
174	C₄×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₄×#102	C₂×C₁₁	1	2	yes	complemented
176	C₂³×C₁₁	—	2	1	no	—
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	4	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	—	4	2	no	—
183	C₂³×C₁₁	—	4	2	no	—
184	C₂³×C₁₁	—	4	2	no	—
185	C₂³×C₁₁	—	4	2	no	—
186	C₂³×C₁₁	—	4	2	no	—
187	C₂³×C₁₁	C₄×D₄	1	2	yes	—
188	C₂³×C₁₁	C₂×D₈	1	2	yes	—
189	C₂³×C₁₁	#135	1	2	yes	—
190	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₁₁	—	2	4	no	—
192	D₄×C₁₁	—	2	4	no	—
193	D₄×C₁₁	—	4	16	no	—
194	D₄×C₁₁	—	4	2	no	—
195	D₄×C₁₁	—	4	2	no	—
196	C₂×C₄×C₁₁	—	2	8	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	8	no	—
210	C₂×C₄×C₁₁	—	2	4	no	—
211	C₂×C₄×C₁₁	—	4	2	no	—
212	C₂×C₄×C₁₁	—	4	2	no	—
213	C₂×C₄×C₁₁	—	4	2	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	2	no	—
216	C₂×C₄×C₁₁	—	4	2	no	—
217	C₂×C₄×C₁₁	—	4	2	no	—
218	C₂×C₄×C₁₁	—	4	2	no	—
219	C₂×C₄×C₁₁	—	8	8	no	—
220	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₁₁	#121	1	2	yes	—
222	C₂×C₄×C₁₁	#121	1	2	yes	—
223	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
224	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
225	C₂×C₄×C₁₁	#135	1	2	yes	—
226	C₂×C₄×C₁₁	#135	1	2	yes	—
227	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
233	C₈×C₁₁	—	2	2	no	—
234	C₈×C₁₁	—	2	2	no	—
235	C₈×C₁₁	—	2	2	no	—
236	C₈×C₁₁	C₄×D₄	1	4	yes	complemented
237	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×#121	C₂²×C₁₁	1	2	yes	—
241	C₂×C₄×D₄	—	2	2	no	—
242	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
243	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
244	#466	C₄×C₁₁	1	8	yes	direct product factor
245	C₄×D₈	—	2	4	no	—
246	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
248	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×#102	C₂²×C₁₁	1	2	yes	—
250	C₂×#102	C₂²×C₁₁	1	2	yes	—
251	C₂×#102	C₂²×C₁₁	1	2	yes	—
252	C₂×C₄×C₈	—	2	4	no	—
253	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
257	#390	C₂²×C₁₁	1	2	yes	—
258	#389	C₂²×C₁₁	1	2	yes	—
259	#388	—	2	2	no	—
260	#386	—	2	2	no	—
261	#380	C₂²×C₁₁	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
263	C₄×C₂²⋊C₄	—	2	2	no	—
264	#340	C₂²×C₁₁	1	2	yes	—
265	#340	C₂²×C₁₁	1	2	yes	—
266	#340	C₂²×C₁₁	1	2	yes	—
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	2	no	—
272	C₂²×C₁₁	—	2	2	no	—
273	C₂²×C₁₁	—	4	4	no	—
274	C₂²×C₁₁	—	4	4	no	—
275	C₂²×C₁₁	—	4	4	no	—
276	C₂²×C₁₁	—	8	2	no	—
277	C₂²×C₁₁	—	8	2	no	—
278	C₂²×C₁₁	—	8	2	no	—
279	C₂²×C₁₁	—	8	2	no	—
280	C₂²×C₁₁	C₄×D₈	1	4	yes	complemented
281	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
283	C₂²×C₁₁	#532	1	1	yes	characteristic
284	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
285	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
286	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
287	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
288	C₄×C₁₁	—	2	2	no	—
289	C₄×C₁₁	—	2	2	no	—
290	C₄×C₁₁	—	2	2	no	—
291	C₄×C₁₁	—	2	2	no	—
292	C₄×C₁₁	—	4	4	no	—
293	C₄×C₁₁	—	8	2	no	—
294	C₄×C₁₁	—	8	2	no	—
295	C₄×C₁₁	#466	1	4	yes	direct product factor
296	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
297	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
298	C₄×C₁₁	#525	1	1	yes	characteristic
299	C₄×C₁₁	#529	1	1	yes	characteristic
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
302	C₂³×C₄	—	2	2	no	—
303	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
306	C₂×D₈	—	2	2	no	—
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
315	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
319	#121	—	2	4	no	—
320	#121	C₂×C₄×C₁₁	1	8	yes	complemented
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	4	8	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	#107	—	2	2	no	—
342	#107	C₂×C₄×C₁₁	1	4	yes	complemented
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	#102	C₂×C₄×C₁₁	1	8	yes	complemented
346	C₄×C₈	—	2	2	no	—
347	C₄×C₈	—	2	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	C₂×C₁₁	—	2	4	no	—
354	C₂×C₁₁	—	8	4	no	—
355	C₂×C₁₁	C₄×#121	1	1	yes	characteristic
356	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
357	C₂×C₁₁	C₄×#135	1	1	yes	characteristic
358	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
359	C₂×C₁₁	#3050	1	1	yes	characteristic
360	C₂×C₁₁	#3168	1	1	yes	characteristic
361	C₂×C₁₁	#3169	1	1	yes	characteristic
362	C₂⁴	—	2	2	no	—
363	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	C₁₁×D₈	1	4	yes	complemented
389	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₁₁×#41	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
397	D₈	—	2	8	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	8	no	—
406	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
407	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
408	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
410	C₂×C₈	C₁₁×#41	1	2	yes	—
411	C₂×C₈	C₁₁×#41	1	2	yes	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	4	4	no	—
429	C₄²	C₂×D₄×C₁₁	1	2	yes	—
430	C₄²	C₁₁×#41	1	2	yes	—
431	C₁₁	C₄×#466	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	C₄×D₄×C₁₁	1	2	yes	—
444	C₂³	C₂×C₁₁×D₈	1	2	yes	—
445	C₂³	C₁₁×#135	1	2	yes	—
446	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
477	C₂×C₄	C₁₁×#121	1	2	yes	—
478	C₂×C₄	C₁₁×#121	1	2	yes	—
479	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
480	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
481	C₂×C₄	C₁₁×#135	1	2	yes	—
482	C₂×C₄	C₁₁×#135	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	C₄×D₄×C₁₁	1	4	yes	complemented
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₄×C₁₁×D₈	1	4	yes	complemented
507	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
508	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
509	C₂²	C₁₁×#532	1	1	yes	characteristic
510	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
511	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
512	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
513	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	2	no	—
521	C₄	C₁₁×#466	1	4	yes	direct product factor
522	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
523	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
524	C₄	C₁₁×#525	1	1	yes	characteristic
525	C₄	C₁₁×#529	1	1	yes	characteristic
526	C₂	—	2	4	no	—
527	C₂	—	8	4	no	—
528	C₂	C₄×C₁₁×#121	1	1	yes	characteristic
529	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
530	C₂	C₄×C₁₁×#135	1	1	yes	characteristic
531	C₂	C₂×C₁₁×#466	1	1	yes	characteristic
532	C₂	C₁₁×#3050	1	1	yes	characteristic
533	C₂	C₁₁×#3168	1	1	yes	characteristic
534	C₂	C₁₁×#3169	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	C₂×C₁₁×#466	C₂
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×D₈	C₂	semidirect
3. C₂²×C₄×C₈×C₁₁	C₂	semidirect
4. C₄×C₁₁×#121	C₂	semidirect
5. C₁₁×#1970	C₂	semidirect
6. C₁₁×#1942	C₂	semidirect
7. C₁₁×#1934	C₂	semidirect
8. C₁₁×#1893	C₂	semidirect
9. C₁₁×#1808	C₂	semidirect
10. C₄×C₁₁×#107	C₂	semidirect
11. C₄×C₁₁×#102	C₂	semidirect
19. C₁₁×#466	C₄	direct (N × H)
50. C₂×C₁₁×D₈	C₂×C₄	semidirect
56. C₂²×C₈×C₁₁	C₂×C₄	semidirect
62. C₁₁×#121	C₂×C₄	semidirect
84. C₁₁×#107	C₂×C₄	semidirect
87. C₁₁×#102	C₂×C₄	semidirect
91. C₄×C₈×C₁₁	D₄	semidirect
95. C₄×#466	C₁₁	direct (N × H)
122. C₂²×C₄×C₁₁	D₈	semidirect
166. C₂×C₄×D₈	C₂×C₁₁	semidirect
167. C₂²×C₄×C₈	C₂×C₁₁	semidirect
168. C₄×#121	C₂×C₁₁	semidirect
169. #1970	C₂×C₁₁	semidirect
170. #1942	C₂×C₁₁	semidirect
171. #1934	C₂×C₁₁	semidirect
172. #1893	C₂×C₁₁	semidirect
173. #1808	C₂×C₁₁	semidirect
174. C₄×#107	C₂×C₁₁	semidirect
175. C₄×#102	C₂×C₁₁	semidirect
236. C₈×C₁₁	C₄×D₄	semidirect
244. #466	C₄×C₁₁	direct (N × H)
280. C₂²×C₁₁	C₄×D₈	semidirect
295. C₄×C₁₁	#466	direct (N × H)
308. C₂×D₈	C₂×C₄×C₁₁	semidirect
314. C₂²×C₈	C₂×C₄×C₁₁	semidirect
320. #121	C₂×C₄×C₁₁	semidirect
342. #107	C₂×C₄×C₁₁	semidirect
345. #102	C₂×C₄×C₁₁	semidirect
349. C₄×C₈	D₄×C₁₁	semidirect
388. C₂²×C₄	C₁₁×D₈	semidirect
431. C₁₁	C₄×#466	direct (N × H)
492. C₈	C₄×D₄×C₁₁	semidirect
506. C₂²	C₄×C₁₁×D₈	semidirect
521. C₄	C₁₁×#466	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×#466	2
C₂×C₄×C₁₁×D₈	2
C₂²×C₄×C₈×C₁₁	2
C₄×C₁₁×#121	2
C₁₁×#1970	2
C₁₁×#1942	2
C₁₁×#1934	2
C₁₁×#1893	2
C₁₁×#1808	2
C₄×C₁₁×#107	2
C₄×C₁₁×#102	2
C₄×#466	11

Subgroups — C4×C11×#466 #14598714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×#466 #14598714