Subgroups — C₁₁×#22147 #14599340

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#460	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1982	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1968	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1934	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1877	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1864	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	—	2	1	no	—
16	C₂×C₄×D₄×C₁₁	—	2	1	no	—
17	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#460	C₄	1	8	yes	complemented
19	C₂×C₁₁×#106	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#103	C₂²	1	2	yes	—
23	C₂×C₁₁×#102	C₂²	1	2	yes	—
24	C₂×C₁₁×#102	C₂²	1	2	yes	—
25	C₂×C₁₁×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
27	C₁₁×#391	C₂²	1	1	yes	characteristic
28	C₁₁×#391	C₂²	1	1	yes	characteristic
29	C₁₁×#390	—	2	1	no	—
30	C₁₁×#390	—	2	1	no	—
31	C₁₁×#390	C₂²	1	2	yes	—
32	C₁₁×#389	C₂²	1	1	yes	characteristic
33	C₁₁×#389	C₂²	1	1	yes	characteristic
34	C₁₁×#387	—	2	1	no	—
35	C₁₁×#387	—	2	1	no	—
36	C₁₁×#384	C₂²	1	1	yes	characteristic
37	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₁×#376	—	2	1	no	—
40	C₄³×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#340	C₂²	1	2	yes	—
42	C₁₁×#340	C₂²	1	2	yes	—
43	C₁₁×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₁	—	2	1	no	—
46	C₂²×D₄×C₁₁	—	2	1	no	—
47	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₁	—	2	2	no	—
49	C₂×C₁₁×SD₁₆	—	4	2	no	—
50	C₂×C₁₁×SD₁₆	—	4	2	no	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
54	C₁₁×#127	—	2	2	no	—
55	C₁₁×#127	C₂×C₄	1	4	yes	—
56	C₄×Q₈×C₁₁	—	2	2	no	—
57	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	complemented
58	C₄×D₄×C₁₁	—	4	2	no	—
59	C₄×D₄×C₁₁	—	4	2	no	—
60	C₄×D₄×C₁₁	—	4	4	no	—
61	C₄×D₄×C₁₁	—	4	4	no	—
62	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	—	2	1	no	—
76	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
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	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₁₁×#106	—	4	2	no	—
84	C₁₁×C₄⋊C₈	—	2	2	no	—
85	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
86	C₁₁×#103	—	4	2	no	—
87	C₁₁×#102	—	4	2	no	—
88	C₁₁×#102	—	4	2	no	—
89	C₁₁×#102	C₂×C₄	1	8	yes	complemented
90	C₄×C₈×C₁₁	—	4	2	no	—
91	C₁₁×#95	—	2	1	no	—
92	C₁₁×#95	—	2	1	no	—
93	C₁₁×#95	—	2	1	no	—
94	C₁₁×#95	—	2	1	no	—
95	C₁₁×#95	—	2	1	no	—
96	C₁₁×#95	—	2	1	no	—
97	C₁₁×#95	—	2	1	no	—
98	#22147	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	2	1	no	—
101	C₂×Q₈×C₁₁	—	2	1	no	—
102	C₂×Q₈×C₁₁	—	2	1	no	—
103	C₂×Q₈×C₁₁	—	2	1	no	—
104	C₂×Q₈×C₁₁	—	2	1	no	—
105	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	—	2	4	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	4	2	no	—
115	C₂×D₄×C₁₁	—	4	2	no	—
116	C₂×D₄×C₁₁	—	4	2	no	—
117	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	2	no	—
123	C₂²×C₄×C₁₁	—	4	4	no	—
124	C₂²×C₄×C₁₁	—	4	4	no	—
125	C₂²×C₄×C₁₁	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₁₁×SD₁₆	—	4	8	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
140	C₁₁×C₄⋊C₄	—	2	4	no	—
141	C₁₁×C₄⋊C₄	—	2	1	no	—
142	C₁₁×C₄⋊C₄	—	2	1	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	2	no	—
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	—	4	2	no	—
149	C₁₁×C₄⋊C₄	—	4	2	no	—
150	C₁₁×C₄⋊C₄	—	4	2	no	—
151	C₁₁×C₄⋊C₄	—	4	2	no	—
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₁₁×C₂²⋊C₄	—	4	4	no	—
154	C₁₁×C₂²⋊C₄	—	4	4	no	—
155	C₁₁×C₂²⋊C₄	—	4	4	no	—
156	C₄²×C₁₁	—	2	4	no	—
157	C₄²×C₁₁	—	2	2	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	4	1	no	—
164	C₄²×C₁₁	—	4	2	no	—
165	C₄²×C₁₁	SD₁₆	1	4	yes	complemented
166	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
167	C₄²×C₁₁	#41	1	2	yes	—
168	C₂×#460	C₂×C₁₁	1	1	yes	characteristic
169	C₄×#127	C₂×C₁₁	1	1	yes	characteristic
170	#2295	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#1982	C₂×C₁₁	1	1	yes	characteristic
172	#1968	C₂×C₁₁	1	2	yes	complemented
173	#1948	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1934	C₂×C₁₁	1	2	yes	complemented
175	#1877	C₂×C₁₁	1	2	yes	complemented
176	#1864	C₂×C₁₁	1	2	yes	complemented
177	#1803	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂³×C₁₁	—	2	4	no	—
180	C₂³×C₁₁	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₁	—	2	2	no	—
188	Q₈×C₁₁	—	2	2	no	—
189	Q₈×C₁₁	—	4	1	no	—
190	Q₈×C₁₁	—	4	1	no	—
191	D₄×C₁₁	—	2	4	no	—
192	D₄×C₁₁	—	2	4	no	—
193	D₄×C₁₁	—	4	8	no	—
194	D₄×C₁₁	—	4	2	no	—
195	D₄×C₁₁	—	4	2	no	—
196	D₄×C₁₁	—	4	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	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	4	1	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	—	4	1	no	—
213	C₂×C₄×C₁₁	—	4	1	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	2	no	—
218	C₂×C₄×C₁₁	—	4	1	no	—
219	C₂×C₄×C₁₁	—	4	1	no	—
220	C₂×C₄×C₁₁	—	4	2	no	—
221	C₂×C₄×C₁₁	—	4	1	no	—
222	C₂×C₄×C₁₁	—	4	1	no	—
223	C₂×C₄×C₁₁	—	8	8	no	—
224	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
227	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
228	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
229	C₂×C₄×C₁₁	#135	1	2	yes	—
230	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
231	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
237	C₈×C₁₁	—	2	4	no	—
238	C₈×C₁₁	—	4	2	no	—
239	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
240	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
245	#460	C₄×C₁₁	1	8	yes	complemented
246	C₂×#106	C₂²×C₁₁	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×#103	C₂²×C₁₁	1	2	yes	—
250	C₂×#102	C₂²×C₁₁	1	2	yes	—
251	C₂×#102	C₂²×C₁₁	1	2	yes	—
252	C₂×#102	C₂²×C₁₁	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
254	#391	C₂²×C₁₁	1	1	yes	characteristic
255	#391	C₂²×C₁₁	1	1	yes	characteristic
256	#390	—	2	1	no	—
257	#390	—	2	1	no	—
258	#390	C₂²×C₁₁	1	2	yes	—
259	#389	C₂²×C₁₁	1	1	yes	characteristic
260	#389	C₂²×C₁₁	1	1	yes	characteristic
261	#387	—	2	1	no	—
262	#387	—	2	1	no	—
263	#384	C₂²×C₁₁	1	1	yes	characteristic
264	C₄×C₄⋊C₄	—	2	1	no	—
265	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
266	#376	—	2	1	no	—
267	C₄³	C₂²×C₁₁	1	1	yes	characteristic
268	#340	C₂²×C₁₁	1	2	yes	—
269	#340	C₂²×C₁₁	1	2	yes	—
270	#336	C₂²×C₁₁	1	2	yes	—
271	C₂²×C₁₁	—	4	4	no	—
272	C₂²×C₁₁	—	4	4	no	—
273	C₂²×C₁₁	—	4	4	no	—
274	C₂²×C₁₁	—	8	2	no	—
275	C₂²×C₁₁	—	8	2	no	—
276	C₂²×C₁₁	—	8	2	no	—
277	C₂²×C₁₁	—	8	2	no	—
278	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₁₁	#535	1	1	yes	characteristic
280	C₂²×C₁₁	#537	1	1	yes	characteristic
281	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
282	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
283	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂²×C₁₁	#575	1	1	yes	characteristic
285	C₄×C₁₁	—	2	2	no	—
286	C₄×C₁₁	—	2	2	no	—
287	C₄×C₁₁	—	2	2	no	—
288	C₄×C₁₁	—	2	2	no	—
289	C₄×C₁₁	—	4	2	no	—
290	C₄×C₁₁	—	4	2	no	—
291	C₄×C₁₁	—	4	1	no	—
292	C₄×C₁₁	—	8	2	no	—
293	C₄×C₁₁	—	8	1	no	—
294	C₄×C₁₁	—	8	1	no	—
295	C₄×C₁₁	C₄×SD₁₆	1	4	yes	—
296	C₄×C₁₁	#518	1	1	yes	characteristic
297	C₄×C₁₁	#520	1	1	yes	characteristic
298	C₄×C₁₁	#540	1	1	yes	characteristic
299	C₄×C₁₁	#542	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂×SD₁₆	—	4	2	no	—
306	C₂×SD₁₆	—	4	2	no	—
307	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
308	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
310	#127	—	2	2	no	—
311	#127	C₂×C₄×C₁₁	1	4	yes	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
314	C₄×D₄	—	4	2	no	—
315	C₄×D₄	—	4	2	no	—
316	C₄×D₄	—	4	4	no	—
317	C₄×D₄	—	4	4	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
334	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
335	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
339	#106	—	4	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	complemented
342	#103	—	4	2	no	—
343	#102	—	4	2	no	—
344	#102	—	4	2	no	—
345	#102	C₂×C₄×C₁₁	1	8	yes	complemented
346	C₄×C₈	—	4	2	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	C₂×C₁₁	—	8	4	no	—
355	C₂×C₁₁	#2324	1	1	yes	characteristic
356	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
357	C₂×C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
358	C₂×C₁₁	#3208	1	1	yes	characteristic
359	C₂×C₁₁	#3212	1	1	yes	characteristic
360	C₂×C₁₁	#3246	1	1	yes	characteristic
361	C₂×C₁₁	#3247	1	1	yes	characteristic
362	C₂⁴	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
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	C₂⁴×C₁₁	1	1	yes	characteristic
396	SD₁₆	—	4	8	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	4	1	no	—
427	C₄²	—	4	2	no	—
428	C₄²	C₁₁×SD₁₆	1	4	yes	complemented
429	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
430	C₄²	C₁₁×#41	1	2	yes	—
431	C₁₁	#22147	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	4	1	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	8	no	—
450	C₂×C₄	—	2	1	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	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	8	no	—
477	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
478	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
479	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
480	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
481	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
482	C₂×C₄	C₁₁×#135	1	2	yes	—
483	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
484	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
486	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	4	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
500	C₂²	C₁₁×#535	1	1	yes	characteristic
501	C₂²	C₁₁×#537	1	1	yes	characteristic
502	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
503	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
504	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
505	C₂²	C₁₁×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₄×C₁₁×SD₁₆	1	4	yes	—
517	C₄	C₁₁×#518	1	1	yes	characteristic
518	C₄	C₁₁×#520	1	1	yes	characteristic
519	C₄	C₁₁×#540	1	1	yes	characteristic
520	C₄	C₁₁×#542	1	1	yes	characteristic
521	C₂	—	8	4	no	—
522	C₂	C₁₁×#2324	1	1	yes	characteristic
523	C₂	C₂×C₄×C₁₁×SD₁₆	1	1	yes	characteristic
524	C₂	C₄×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
525	C₂	C₁₁×#3208	1	1	yes	characteristic
526	C₂	C₁₁×#3212	1	1	yes	characteristic
527	C₂	C₁₁×#3246	1	1	yes	characteristic
528	C₂	C₁₁×#3247	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2295	C₂	semidirect
5. C₁₁×#1968	C₂	semidirect
6. C₁₁×#1948	C₂	semidirect
7. C₁₁×#1934	C₂	semidirect
8. C₁₁×#1877	C₂	semidirect
9. C₁₁×#1864	C₂	semidirect
10. C₁₁×#1803	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
18. C₁₁×#460	C₄	semidirect
51. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
57. C₄×Q₈×C₁₁	C₂×C₄	semidirect
85. C₁₁×C₄⋊C₈	C₂×C₄	semidirect
89. C₁₁×#102	C₂×C₄	semidirect
98. #22147	C₁₁	direct (N × H)
165. C₄²×C₁₁	SD₁₆	semidirect
170. #2295	C₂×C₁₁	semidirect
172. #1968	C₂×C₁₁	semidirect
173. #1948	C₂×C₁₁	semidirect
174. #1934	C₂×C₁₁	semidirect
175. #1877	C₂×C₁₁	semidirect
176. #1864	C₂×C₁₁	semidirect
177. #1803	C₂×C₁₁	semidirect
178. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
245. #460	C₄×C₁₁	semidirect
307. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
313. C₄×Q₈	C₂×C₄×C₁₁	semidirect
341. C₄⋊C₈	C₂×C₄×C₁₁	semidirect
345. #102	C₂×C₄×C₁₁	semidirect
428. C₄²	C₁₁×SD₁₆	semidirect
431. C₁₁	#22147	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×#460	2
C₄×C₁₁×#127	2
C₁₁×#2295	2
C₁₁×#1982	2
C₁₁×#1968	2
C₁₁×#1948	2
C₁₁×#1934	2
C₁₁×#1877	2
C₁₁×#1864	2
C₁₁×#1803	2
C₄×C₁₁×C₄⋊C₈	2
#22147	11

Subgroups — C11×#22147 #14599340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22147 #14599340