Subgroups — C₁₁×#22165 #14599358

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3035	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1980	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1974	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1937	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	2	yes	—
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
16	C₁₁×#464	C₄	1	2	yes	complemented
17	C₁₁×#463	C₄	1	2	yes	complemented
18	C₁₁×#462	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#461	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#460	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#459	C₄	1	1	yes	characteristic, complemented
22	C₁₁×#436	—	2	1	no	—
23	C₁₁×#436	—	2	1	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	—	2	1	no	—
26	C₁₁×#433	—	2	1	no	—
27	C₁₁×#433	—	2	1	no	—
28	C₁₁×#431	—	2	1	no	—
29	C₁₁×#431	—	2	1	no	—
30	C₂×C₁₁×#108	C₂²	1	2	yes	—
31	C₁₁×#424	C₂²	1	1	yes	characteristic
32	C₁₁×#424	C₂²	1	1	yes	characteristic
33	C₁₁×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₂×C₁₁×#104	C₂²	1	2	yes	—
37	C₂×C₁₁×#104	C₂²	1	2	yes	—
38	C₁₁×#416	C₂²	1	2	yes	—
39	C₁₁×#408	C₂²	1	1	yes	characteristic
40	C₁₁×#408	C₂²	1	1	yes	characteristic
41	C₁₁×#408	C₂²	1	2	yes	—
42	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
45	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₁₁×#341	C₂²	1	2	yes	—
47	C₁₁×#339	C₂²	1	2	yes	—
48	C₁₁×#336	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂³	1	2	yes	—
51	C₁₁×#135	—	4	2	no	—
52	C₁₁×#135	—	4	2	no	—
53	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
57	C₁₁×#131	—	4	2	no	—
58	C₁₁×#131	—	4	2	no	—
59	C₂×C₁₁×M₁₆	—	2	2	no	—
60	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	—	2	2	no	—
64	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
68	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
69	C₁₁×#124	C₂×C₄	1	2	yes	—
70	C₁₁×#121	—	2	1	no	—
71	C₁₁×#121	—	2	1	no	—
72	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₁	—	2	1	no	—
75	C₄×D₄×C₁₁	—	2	1	no	—
76	C₄×D₄×C₁₁	—	2	1	no	—
77	C₄×D₄×C₁₁	—	2	1	no	—
78	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
80	C₁₁×#117	—	2	1	no	—
81	C₁₁×#117	C₂³	1	1	yes	characteristic
82	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₁₁	—	2	1	no	—
84	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×#108	—	4	2	no	—
87	C₁₁×C₄⋊C₈	—	2	1	no	—
88	C₁₁×C₄⋊C₈	—	2	1	no	—
89	C₁₁×C₄⋊C₈	—	2	1	no	—
90	C₁₁×C₄⋊C₈	—	2	1	no	—
91	C₁₁×C₄⋊C₈	—	2	1	no	—
92	C₁₁×C₄⋊C₈	—	2	1	no	—
93	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
96	C₁₁×#104	—	4	2	no	—
97	C₁₁×#104	—	4	2	no	—
98	C₁₁×#104	—	4	2	no	—
99	C₁₁×#103	C₂×C₄	1	2	yes	—
100	C₁₁×#103	C₂×C₄	1	2	yes	—
101	C₁₁×#102	C₂×C₄	1	2	yes	—
102	C₁₁×#102	C₂×C₄	1	2	yes	—
103	C₁₁×C₂²⋊C₈	—	2	1	no	—
104	C₁₁×C₂²⋊C₈	—	2	1	no	—
105	C₁₁×C₂²⋊C₈	—	2	1	no	—
106	C₁₁×C₂²⋊C₈	—	2	1	no	—
107	C₁₁×C₂²⋊C₈	—	2	2	no	—
108	C₁₁×C₂²⋊C₈	—	2	2	no	—
109	C₁₁×#97	—	2	1	no	—
110	C₄×C₈×C₁₁	—	2	1	no	—
111	C₄×C₈×C₁₁	—	4	2	no	—
112	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
113	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
115	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
116	C₁₁×#95	—	2	1	no	—
117	#22165	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₁₁×#41	—	2	1	no	—
119	C₁₁×#41	—	2	2	no	—
120	C₁₁×#41	—	2	2	no	—
121	C₁₁×#41	—	2	2	no	—
122	C₁₁×#41	—	2	1	no	—
123	C₁₁×#41	—	2	1	no	—
124	C₁₁×#41	—	2	1	no	—
125	C₁₁×#41	—	2	2	no	—
126	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₁₁	—	2	1	no	—
129	C₂×D₄×C₁₁	—	2	2	no	—
130	C₂×D₄×C₁₁	—	2	1	no	—
131	C₂×D₄×C₁₁	—	2	1	no	—
132	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁	—	2	2	no	—
135	C₂²×C₄×C₁₁	—	2	1	no	—
136	C₂²×C₄×C₁₁	—	2	1	no	—
137	C₂²×C₄×C₁₁	—	2	1	no	—
138	C₂²×C₄×C₁₁	—	2	2	no	—
139	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
142	C₁₁×Q₁₆	—	4	2	no	—
143	C₁₁×SD₁₆	—	4	2	no	—
144	C₁₁×SD₁₆	—	4	2	no	—
145	C₁₁×D₈	—	4	2	no	—
146	C₁₁×M₁₆	—	2	1	no	—
147	C₁₁×M₁₆	—	2	1	no	—
148	C₁₁×M₁₆	—	2	2	no	—
149	C₁₁×M₁₆	—	2	1	no	—
150	C₁₁×M₁₆	—	2	2	no	—
151	C₁₁×M₁₆	—	2	1	no	—
152	C₁₁×M₁₆	—	4	4	no	—
153	C₂×C₈×C₁₁	—	2	1	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	2	no	—
156	C₂×C₈×C₁₁	—	2	1	no	—
157	C₂×C₈×C₁₁	—	2	2	no	—
158	C₂×C₈×C₁₁	—	2	2	no	—
159	C₂×C₈×C₁₁	—	2	1	no	—
160	C₂×C₈×C₁₁	—	2	1	no	—
161	C₂×C₈×C₁₁	—	2	1	no	—
162	C₂×C₈×C₁₁	—	4	4	no	—
163	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₁₁×C₄⋊C₄	—	2	4	no	—
170	C₁₁×C₄⋊C₄	—	2	1	no	—
171	C₁₁×C₄⋊C₄	—	2	1	no	—
172	C₁₁×C₄⋊C₄	—	2	1	no	—
173	C₁₁×C₄⋊C₄	—	2	1	no	—
174	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
175	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₁₁×C₂²⋊C₄	—	2	1	no	—
177	C₁₁×C₂²⋊C₄	—	2	1	no	—
178	C₁₁×C₂²⋊C₄	—	2	1	no	—
179	C₁₁×C₂²⋊C₄	—	2	2	no	—
180	C₁₁×C₂²⋊C₄	—	2	2	no	—
181	C₄²×C₁₁	—	2	1	no	—
182	C₄²×C₁₁	—	2	1	no	—
183	C₄²×C₁₁	—	2	1	no	—
184	C₄²×C₁₁	—	2	2	no	—
185	C₄²×C₁₁	—	2	2	no	—
186	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
190	#3035	C₂×C₁₁	1	1	yes	characteristic
191	#2931	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#2922	C₂×C₁₁	1	1	yes	characteristic, complemented
193	#1980	C₂×C₁₁	1	1	yes	characteristic, complemented
194	#1974	C₂×C₁₁	1	2	yes	complemented
195	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
196	#1937	C₂×C₁₁	1	2	yes	complemented
197	#1876	C₂×C₁₁	1	2	yes	complemented
198	#1866	C₂×C₁₁	1	2	yes	complemented
199	#1806	C₂×C₁₁	1	1	yes	characteristic, complemented
200	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
201	C₂³×C₁₁	—	2	1	no	—
202	C₂³×C₁₁	—	2	2	no	—
203	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₁	—	2	1	no	—
205	Q₈×C₁₁	—	2	2	no	—
206	Q₈×C₁₁	—	2	2	no	—
207	Q₈×C₁₁	—	2	1	no	—
208	D₄×C₁₁	—	2	1	no	—
209	D₄×C₁₁	—	2	2	no	—
210	D₄×C₁₁	—	2	2	no	—
211	D₄×C₁₁	—	2	1	no	—
212	D₄×C₁₁	—	4	2	no	—
213	D₄×C₁₁	—	4	1	no	—
214	D₄×C₁₁	—	4	2	no	—
215	D₄×C₁₁	—	4	1	no	—
216	D₄×C₁₁	—	4	2	no	—
217	D₄×C₁₁	—	4	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	2	4	no	—
220	C₂×C₄×C₁₁	—	2	1	no	—
221	C₂×C₄×C₁₁	—	2	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	4	1	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	—	4	2	no	—
227	C₂×C₄×C₁₁	—	4	2	no	—
228	C₂×C₄×C₁₁	—	4	2	no	—
229	C₂×C₄×C₁₁	—	4	1	no	—
230	C₂×C₄×C₁₁	—	4	1	no	—
231	C₂×C₄×C₁₁	—	4	2	no	—
232	C₂×C₄×C₁₁	—	4	2	no	—
233	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
243	C₈×C₁₁	—	2	2	no	—
244	C₈×C₁₁	—	2	2	no	—
245	C₈×C₁₁	—	2	1	no	—
246	C₈×C₁₁	—	2	1	no	—
247	C₈×C₁₁	—	2	1	no	—
248	C₈×C₁₁	—	2	1	no	—
249	C₈×C₁₁	—	4	2	no	—
250	C₈×C₁₁	—	4	1	no	—
251	C₈×C₁₁	—	4	1	no	—
252	C₂×#135	C₂²×C₁₁	1	2	yes	—
253	C₂×#131	C₂²×C₁₁	1	2	yes	—
254	#532	C₂²×C₁₁	1	1	yes	characteristic
255	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
256	#464	C₄×C₁₁	1	2	yes	complemented
257	#463	C₄×C₁₁	1	2	yes	complemented
258	#462	C₄×C₁₁	1	1	yes	characteristic, complemented
259	#461	C₄×C₁₁	1	1	yes	characteristic, complemented
260	#460	C₄×C₁₁	1	1	yes	characteristic, complemented
261	#459	C₄×C₁₁	1	1	yes	characteristic, complemented
262	#436	—	2	1	no	—
263	#436	—	2	1	no	—
264	C₈×D₄	—	2	1	no	—
265	C₈×D₄	—	2	1	no	—
266	#433	—	2	1	no	—
267	#433	—	2	1	no	—
268	#431	—	2	1	no	—
269	#431	—	2	1	no	—
270	C₂×#108	C₂²×C₁₁	1	2	yes	—
271	#424	C₂²×C₁₁	1	1	yes	characteristic
272	#424	C₂²×C₁₁	1	1	yes	characteristic
273	#423	C₂²×C₁₁	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
275	C₂×#104	C₂²×C₁₁	1	2	yes	—
276	C₂×#104	C₂²×C₁₁	1	2	yes	—
277	C₂×#104	C₂²×C₁₁	1	2	yes	—
278	#416	C₂²×C₁₁	1	2	yes	—
279	#408	C₂²×C₁₁	1	1	yes	characteristic
280	#408	C₂²×C₁₁	1	1	yes	characteristic
281	#408	C₂²×C₁₁	1	2	yes	—
282	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
284	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
286	#341	C₂²×C₁₁	1	2	yes	—
287	#339	C₂²×C₁₁	1	2	yes	—
288	#336	C₂²×C₁₁	1	2	yes	—
289	C₂²×C₁₁	—	2	1	no	—
290	C₂²×C₁₁	—	2	1	no	—
291	C₂²×C₁₁	—	4	2	no	—
292	C₂²×C₁₁	—	4	1	no	—
293	C₂²×C₁₁	—	4	1	no	—
294	C₂²×C₁₁	—	4	2	no	—
295	C₂²×C₁₁	—	4	1	no	—
296	C₂²×C₁₁	—	4	2	no	—
297	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂²×C₁₁	#540	1	1	yes	characteristic
299	C₂²×C₁₁	#542	1	1	yes	characteristic
300	C₄×C₁₁	—	2	1	no	—
301	C₄×C₁₁	—	2	1	no	—
302	C₄×C₁₁	—	2	1	no	—
303	C₄×C₁₁	—	4	4	no	—
304	C₄×C₁₁	—	4	1	no	—
305	C₄×C₁₁	—	4	2	no	—
306	C₄×C₁₁	—	4	1	no	—
307	C₄×C₁₁	—	4	1	no	—
308	C₄×C₁₁	#443	1	2	yes	—
309	C₄×C₁₁	#518	1	1	yes	characteristic
310	C₄×C₁₁	#520	1	1	yes	characteristic
311	C₄×C₁₁	#535	1	1	yes	characteristic
312	C₄×C₁₁	#537	1	1	yes	characteristic
313	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
314	C₂×#41	C₂³×C₁₁	1	2	yes	—
315	#135	—	4	2	no	—
316	#135	—	4	2	no	—
317	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
318	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
319	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
320	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
321	#131	—	4	2	no	—
322	#131	—	4	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
325	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
326	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
331	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
332	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
333	#124	C₂×C₄×C₁₁	1	2	yes	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
337	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
343	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
344	#117	—	2	1	no	—
345	#117	C₂³×C₁₁	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
349	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
350	#108	—	4	2	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	2	1	no	—
357	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
358	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
359	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
360	#104	—	4	2	no	—
361	#104	—	4	2	no	—
362	#104	—	4	2	no	—
363	#103	C₂×C₄×C₁₁	1	2	yes	—
364	#103	C₂×C₄×C₁₁	1	2	yes	—
365	#102	C₂×C₄×C₁₁	1	2	yes	—
366	#102	C₂×C₄×C₁₁	1	2	yes	—
367	C₂²⋊C₈	—	2	1	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₂²⋊C₈	—	2	1	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	#97	—	2	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	4	2	no	—
376	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
377	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
378	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
379	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
380	#95	—	2	1	no	—
381	C₂×C₁₁	—	2	1	no	—
382	C₂×C₁₁	—	2	1	no	—
383	C₂×C₁₁	—	8	1	no	—
384	C₂×C₁₁	—	8	2	no	—
385	C₂×C₁₁	#2324	1	1	yes	characteristic
386	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
387	C₂×C₁₁	#2955	1	1	yes	characteristic
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	2	2	no	—
396	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
397	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
403	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
410	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
412	Q₁₆	—	4	2	no	—
413	SD₁₆	—	4	2	no	—
414	SD₁₆	—	4	2	no	—
415	D₈	—	4	2	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	1	no	—
422	M₁₆	—	4	4	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	4	4	no	—
433	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
434	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
436	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
437	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
438	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
457	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
460	C₁₁	#22165	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
494	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
495	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
496	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
497	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
499	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
503	C₈	—	2	2	no	—
504	C₈	—	2	2	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	1	no	—
520	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
521	C₂²	C₁₁×#540	1	1	yes	characteristic
522	C₂²	C₁₁×#542	1	1	yes	characteristic
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	C₁₁×#443	1	2	yes	—
532	C₄	C₁₁×#518	1	1	yes	characteristic
533	C₄	C₁₁×#520	1	1	yes	characteristic
534	C₄	C₁₁×#535	1	1	yes	characteristic
535	C₄	C₁₁×#537	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	2	1	no	—
538	C₂	—	8	1	no	—
539	C₂	—	8	2	no	—
540	C₂	C₁₁×#2324	1	1	yes	characteristic
541	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
542	C₂	C₁₁×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2931	C₂	semidirect
3. C₁₁×#2922	C₂	semidirect
4. C₁₁×#1980	C₂	semidirect
5. C₁₁×#1974	C₂	semidirect
6. C₁₁×#1950	C₂	semidirect
7. C₁₁×#1937	C₂	semidirect
8. C₁₁×#1876	C₂	semidirect
9. C₁₁×#1866	C₂	semidirect
10. C₁₁×#1806	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
16. C₁₁×#464	C₄	semidirect
17. C₁₁×#463	C₄	semidirect
18. C₁₁×#462	C₄	semidirect
19. C₁₁×#461	C₄	semidirect
20. C₁₁×#460	C₄	semidirect
21. C₁₁×#459	C₄	semidirect
117. #22165	C₁₁	direct (N × H)
191. #2931	C₂×C₁₁	semidirect
192. #2922	C₂×C₁₁	semidirect
193. #1980	C₂×C₁₁	semidirect
194. #1974	C₂×C₁₁	semidirect
195. #1950	C₂×C₁₁	semidirect
196. #1937	C₂×C₁₁	semidirect
197. #1876	C₂×C₁₁	semidirect
198. #1866	C₂×C₁₁	semidirect
199. #1806	C₂×C₁₁	semidirect
200. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
256. #464	C₄×C₁₁	semidirect
257. #463	C₄×C₁₁	semidirect
258. #462	C₄×C₁₁	semidirect
259. #461	C₄×C₁₁	semidirect
260. #460	C₄×C₁₁	semidirect
261. #459	C₄×C₁₁	semidirect
460. C₁₁	#22165	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×#3035	2
C₁₁×#2931	2
C₁₁×#2922	2
C₁₁×#1980	2
C₁₁×#1974	2
C₁₁×#1950	2
C₁₁×#1937	2
C₁₁×#1876	2
C₁₁×#1866	2
C₁₁×#1806	2
C₈×C₁₁×C₄⋊C₄	2
#22165	11

Subgroups — C11×#22165 #14599358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22165 #14599358