Subgroups — C₁₁×#18057 #14595250

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1587	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1586	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1489	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₁₁×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
18	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
21	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
24	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
25	C₁₁×#436	—	2	2	no	—
26	C₁₁×#436	C₂²	1	2	yes	—
27	C₁₁×#435	—	2	2	no	—
28	C₈×D₄×C₁₁	C₂²	1	2	yes	—
29	C₁₁×#432	—	2	1	no	—
30	C₁₁×#431	—	2	1	no	—
31	C₁₁×#431	C₂²	1	1	yes	characteristic
32	C₁₁×#427	C₄	1	1	yes	characteristic
33	C₁₁×#423	—	2	1	no	—
34	C₁₁×#423	C₂²	1	1	yes	characteristic
35	C₁₁×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
37	C₁₁×#416	C₄	1	1	yes	characteristic
38	C₁₁×#416	C₄	1	1	yes	characteristic
39	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#334	C₂²	1	2	yes	—
42	C₁₁×#334	C₂²	1	2	yes	—
43	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₁×#322	C₂²	1	2	yes	—
48	C₈²×C₁₁	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#135	—	2	4	no	—
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×M₁₆	—	2	1	no	—
57	C₂×C₁₁×M₁₆	—	2	1	no	—
58	C₂×C₁₁×M₁₆	—	2	1	no	—
59	C₂×C₁₁×M₁₆	—	2	2	no	—
60	C₂²×C₈×C₁₁	—	2	2	no	—
61	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	C₂³	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	1	yes	characteristic
72	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×#117	—	2	1	no	—
76	C₁₁×#117	—	2	1	no	—
77	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
78	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₁	—	2	1	no	—
80	C₂×C₄²×C₁₁	—	2	1	no	—
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
84	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	—	2	2	no	—
87	C₁₁×C₄⋊C₈	—	2	2	no	—
88	C₁₁×C₄⋊C₈	—	2	1	no	—
89	C₁₁×C₄⋊C₈	—	2	1	no	—
90	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
91	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
93	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
94	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
96	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
97	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
98	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
99	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
100	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
101	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
102	C₁₁×C₂²⋊C₈	—	2	2	no	—
103	C₁₁×C₂²⋊C₈	—	2	2	no	—
104	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
105	C₁₁×#97	—	2	2	no	—
106	C₁₁×#97	—	2	1	no	—
107	C₄×C₈×C₁₁	—	2	2	no	—
108	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₁₁	C₂³	1	2	yes	—
111	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₁	C₂³	1	2	yes	—
114	#18057	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₁₁×#41	—	4	1	no	—
118	C₁₁×#41	—	4	1	no	—
119	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₁	—	2	1	no	—
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
134	C₁₁×Q₁₆	—	2	2	no	—
135	C₁₁×SD₁₆	—	2	2	no	—
136	C₁₁×SD₁₆	M₁₆	1	4	yes	complemented
137	C₁₁×D₈	—	2	2	no	—
138	C₁₁×M₁₆	—	2	4	no	—
139	C₁₁×M₁₆	—	8	1	no	—
140	C₁₁×M₁₆	—	8	1	no	—
141	C₁₁×M₁₆	—	8	2	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	4	1	no	—
147	C₂×C₈×C₁₁	—	8	2	no	—
148	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
154	C₁₁×C₄⋊C₄	—	2	1	no	—
155	C₁₁×C₄⋊C₄	—	2	1	no	—
156	C₁₁×C₄⋊C₄	—	2	1	no	—
157	C₁₁×C₄⋊C₄	—	2	1	no	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
160	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
161	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
162	C₁₁×C₂²⋊C₄	—	2	1	no	—
163	C₁₁×C₂²⋊C₄	—	2	1	no	—
164	C₁₁×C₂²⋊C₄	—	2	1	no	—
165	C₁₁×C₂²⋊C₄	—	2	1	no	—
166	C₁₁×C₂²⋊C₄	—	2	1	no	—
167	C₁₁×C₂²⋊C₄	—	2	1	no	—
168	C₄²×C₁₁	—	2	1	no	—
169	C₄²×C₁₁	—	2	1	no	—
170	C₄²×C₁₁	—	2	1	no	—
171	C₄²×C₁₁	—	2	1	no	—
172	C₄²×C₁₁	—	2	1	no	—
173	C₄²×C₁₁	—	2	1	no	—
174	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₁	#41	1	1	yes	characteristic
177	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
178	#2991	C₂×C₁₁	1	1	yes	characteristic, complemented
179	#2990	C₂×C₁₁	1	1	yes	characteristic, complemented
180	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
181	#1590	C₂×C₁₁	1	2	yes	complemented
182	#1587	C₂×C₁₁	1	2	yes	complemented
183	#1586	C₂×C₁₁	1	2	yes	complemented
184	C₈×SD₁₆	C₂×C₁₁	1	2	yes	complemented
185	#1566	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#1489	C₂×C₁₁	1	1	yes	characteristic, complemented
187	#1489	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
189	C₂³×C₁₁	—	2	1	no	—
190	C₂³×C₁₁	—	2	1	no	—
191	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
192	Q₈×C₁₁	—	2	1	no	—
193	Q₈×C₁₁	—	2	1	no	—
194	Q₈×C₁₁	—	2	1	no	—
195	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
196	D₄×C₁₁	—	2	1	no	—
197	D₄×C₁₁	—	2	1	no	—
198	D₄×C₁₁	—	2	1	no	—
199	D₄×C₁₁	—	4	2	no	—
200	D₄×C₁₁	—	4	2	no	—
201	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
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	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	2	1	no	—
211	C₂×C₄×C₁₁	—	2	1	no	—
212	C₂×C₄×C₁₁	—	2	1	no	—
213	C₂×C₄×C₁₁	—	4	2	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	—	4	1	no	—
216	C₂×C₄×C₁₁	—	4	1	no	—
217	C₂×C₄×C₁₁	—	4	1	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	2	no	—
220	C₂×C₄×C₁₁	—	4	2	no	—
221	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₁	—	2	4	no	—
228	C₈×C₁₁	—	2	1	no	—
229	C₈×C₁₁	—	2	1	no	—
230	C₈×C₁₁	—	2	1	no	—
231	C₈×C₁₁	—	2	2	no	—
232	C₈×C₁₁	—	2	2	no	—
233	C₈×C₁₁	—	4	2	no	—
234	C₈×C₁₁	—	4	2	no	—
235	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
236	C₂×#135	C₄×C₁₁	1	1	yes	characteristic
237	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
238	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
239	#446	C₂²×C₁₁	1	2	yes	—
240	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
241	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic
242	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
243	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
244	C₄×SD₁₆	C₄×C₁₁	1	1	yes	characteristic
245	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
246	C₄×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
247	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic
248	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic
249	#436	—	2	2	no	—
250	#436	C₂²×C₁₁	1	2	yes	—
251	#435	—	2	2	no	—
252	C₈×D₄	C₂²×C₁₁	1	2	yes	—
253	#432	—	2	1	no	—
254	#431	—	2	1	no	—
255	#431	C₂²×C₁₁	1	1	yes	characteristic
256	#427	C₄×C₁₁	1	1	yes	characteristic
257	#423	—	2	1	no	—
258	#423	C₂²×C₁₁	1	1	yes	characteristic
259	#423	C₂²×C₁₁	1	1	yes	characteristic
260	C₂×C₄⋊C₈	—	2	1	no	—
261	#416	C₄×C₁₁	1	1	yes	characteristic
262	#416	C₄×C₁₁	1	1	yes	characteristic
263	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
265	#334	C₂²×C₁₁	1	2	yes	—
266	#334	C₂²×C₁₁	1	2	yes	—
267	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
268	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
269	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
270	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
271	#322	C₂²×C₁₁	1	2	yes	—
272	C₈²	C₂²×C₁₁	1	2	yes	—
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	—	2	2	no	—
275	C₂²×C₁₁	—	2	1	no	—
276	C₂²×C₁₁	—	2	1	no	—
277	C₂²×C₁₁	—	4	1	no	—
278	C₂²×C₁₁	—	4	1	no	—
279	C₂²×C₁₁	—	4	1	no	—
280	C₂²×C₁₁	—	4	1	no	—
281	C₂²×C₁₁	—	4	1	no	—
282	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₁₁	—	2	1	no	—
284	C₄×C₁₁	—	2	2	no	—
285	C₄×C₁₁	—	2	1	no	—
286	C₄×C₁₁	—	2	1	no	—
287	C₄×C₁₁	—	4	1	no	—
288	C₄×C₁₁	—	4	1	no	—
289	C₄×C₁₁	—	4	1	no	—
290	C₄×C₁₁	—	4	1	no	—
291	C₄×C₁₁	—	4	1	no	—
292	C₄×C₁₁	#443	1	2	yes	—
293	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
294	C₄×C₁₁	#568	1	1	yes	characteristic
295	C₄×C₁₁	#577	1	1	yes	characteristic
296	C₄×C₁₁	#577	1	1	yes	characteristic
297	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
298	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
299	#135	—	2	4	no	—
300	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
311	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
312	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
314	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
320	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
321	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
322	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
326	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
330	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
331	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
332	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
333	#106	C₂×C₄×C₁₁	1	1	yes	characteristic
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	—	2	1	no	—
338	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
339	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
340	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
341	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
342	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
343	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
344	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
345	#103	C₂×C₄×C₁₁	1	1	yes	characteristic
346	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
347	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
348	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
349	#102	C₂×C₄×C₁₁	1	1	yes	characteristic
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
353	#97	—	2	2	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
357	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
358	C₄×C₈	C₂³×C₁₁	1	2	yes	—
359	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₁₁	1	2	yes	—
362	C₂×C₁₁	—	4	1	no	—
363	C₂×C₁₁	—	4	2	no	—
364	C₂×C₁₁	—	8	1	no	—
365	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
366	C₂×C₁₁	#2952	1	1	yes	characteristic
367	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	—	4	1	no	—
371	#41	—	4	1	no	—
372	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
373	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
377	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
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	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
386	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
387	Q₁₆	—	2	2	no	—
388	SD₁₆	—	2	2	no	—
389	SD₁₆	C₁₁×M₁₆	1	4	yes	complemented
390	D₈	—	2	2	no	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	8	2	no	—
393	M₁₆	—	8	1	no	—
394	M₁₆	—	8	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	8	2	no	—
401	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
405	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
406	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
412	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
413	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
414	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
429	C₄²	C₁₁×#41	1	1	yes	characteristic
430	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
431	C₁₁	#18057	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	C₂×C₁₁×M₁₆	1	2	yes	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	2	1	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	C₂×C₁₁×M₁₆	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
465	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
466	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
469	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
470	C₈	—	2	4	no	—
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	2	1	no	—
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	C₁₁×#443	1	2	yes	—
499	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
500	C₄	C₁₁×#568	1	1	yes	characteristic
501	C₄	C₁₁×#577	1	1	yes	characteristic
502	C₄	C₁₁×#577	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
507	C₂	C₁₁×#2952	1	1	yes	characteristic
508	C₂	C₂×C₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2991	C₂	semidirect
2. C₁₁×#2990	C₂	semidirect
4. C₁₁×#1590	C₂	semidirect
5. C₁₁×#1587	C₂	semidirect
6. C₁₁×#1586	C₂	semidirect
7. C₈×C₁₁×SD₁₆	C₂	semidirect
8. C₁₁×#1566	C₂	semidirect
9. C₁₁×#1489	C₂	semidirect
10. C₁₁×#1489	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
114. #18057	C₁₁	direct (N × H)
136. C₁₁×SD₁₆	M₁₆	semidirect
178. #2991	C₂×C₁₁	semidirect
179. #2990	C₂×C₁₁	semidirect
181. #1590	C₂×C₁₁	semidirect
182. #1587	C₂×C₁₁	semidirect
183. #1586	C₂×C₁₁	semidirect
184. C₈×SD₁₆	C₂×C₁₁	semidirect
185. #1566	C₂×C₁₁	semidirect
186. #1489	C₂×C₁₁	semidirect
187. #1489	C₂×C₁₁	semidirect
188. C₈×M₁₆	C₂×C₁₁	semidirect
389. SD₁₆	C₁₁×M₁₆	semidirect
431. C₁₁	#18057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2991	2
C₁₁×#2990	2
C₄×C₁₁×#135	2
C₁₁×#1590	2
C₁₁×#1587	2
C₁₁×#1586	2
C₈×C₁₁×SD₁₆	2
C₁₁×#1566	2
C₁₁×#1489	2
C₈×C₁₁×M₁₆	2
#18057	11

Subgroups — C11×#18057 #14595250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#18057 #14595250