Subgroups — C₁₁×#22135 #14599328

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×#121	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1955	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1869	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1850	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₁	—	2	4	no	—
18	C₁₁×#431	—	2	4	no	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₁×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#390	C₄	1	1	yes	characteristic
34	C₁₁×#389	C₄	1	1	yes	characteristic
35	C₁₁×#388	C₄	1	2	yes	—
36	C₁₁×#386	C₄	1	2	yes	—
37	C₁₁×#380	C₄	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
44	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	—	2	4	no	—
50	C₂²×C₈×C₁₁	—	4	2	no	—
51	C₂²×C₈×C₁₁	—	4	2	no	—
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	2	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	C₁₁×#121	—	2	4	no	—
59	C₄×D₄×C₁₁	—	2	2	no	—
60	C₄×D₄×C₁₁	—	2	2	no	—
61	C₄×D₄×C₁₁	—	4	2	no	—
62	C₄×D₄×C₁₁	—	4	2	no	—
63	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₁	—	2	2	no	—
73	C₂×C₄²×C₁₁	—	2	2	no	—
74	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×C₄⋊C₈	—	2	2	no	—
82	C₁₁×C₄⋊C₈	—	2	2	no	—
83	C₁₁×C₄⋊C₈	—	4	2	no	—
84	C₁₁×C₂²⋊C₈	—	2	2	no	—
85	C₁₁×C₂²⋊C₈	—	2	2	no	—
86	C₁₁×C₂²⋊C₈	—	2	4	no	—
87	C₁₁×C₂²⋊C₈	—	4	2	no	—
88	C₁₁×C₂²⋊C₈	—	4	2	no	—
89	C₁₁×C₂²⋊C₈	—	4	2	no	—
90	C₁₁×#97	—	4	2	no	—
91	C₄×C₈×C₁₁	—	2	2	no	—
92	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
93	C₁₁×#95	C₂×C₄	1	2	yes	—
94	C₁₁×#95	C₂×C₄	1	2	yes	—
95	C₁₁×#95	C₂×C₄	1	2	yes	—
96	#22135	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×D₄×C₁₁	—	2	4	no	—
100	C₂×D₄×C₁₁	—	2	4	no	—
101	C₂×D₄×C₁₁	—	2	2	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	4	2	no	—
104	C₂×D₄×C₁₁	M₁₆	1	4	yes	—
105	C₂²×C₄×C₁₁	—	2	2	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
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	1	no	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	2	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	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	2	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	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	2	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	1	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	4	8	no	—
149	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
151	C₁₁×C₄⋊C₄	—	2	2	no	—
152	C₁₁×C₄⋊C₄	—	2	2	no	—
153	C₁₁×C₄⋊C₄	—	2	2	no	—
154	C₁₁×C₄⋊C₄	—	4	2	no	—
155	C₁₁×C₂²⋊C₄	—	2	4	no	—
156	C₁₁×C₂²⋊C₄	—	2	4	no	—
157	C₁₁×C₂²⋊C₄	—	2	4	no	—
158	C₁₁×C₂²⋊C₄	—	4	2	no	—
159	C₁₁×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₁₁	—	2	2	no	—
161	C₄²×C₁₁	—	2	2	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	C₂×D₄	1	2	yes	—
167	C₄²×C₁₁	#41	1	2	yes	—
168	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
169	C₂×#431	C₂×C₁₁	1	1	yes	characteristic, complemented
170	C₄×#121	C₂×C₁₁	1	1	yes	characteristic
171	#1955	C₂×C₁₁	1	2	yes	complemented
172	#1954	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1924	C₂×C₁₁	1	2	yes	complemented
175	#1869	C₂×C₁₁	1	2	yes	complemented
176	#1850	C₂×C₁₁	1	2	yes	complemented
177	#1797	C₂×C₁₁	1	1	yes	characteristic, complemented
178	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂³×C₁₁	—	2	2	no	—
180	C₂³×C₁₁	—	2	1	no	—
181	C₂³×C₁₁	—	2	1	no	—
182	C₂³×C₁₁	—	2	2	no	—
183	C₂³×C₁₁	—	2	2	no	—
184	C₂³×C₁₁	—	2	1	no	—
185	C₂³×C₁₁	—	2	1	no	—
186	C₂³×C₁₁	—	2	2	no	—
187	C₂³×C₁₁	—	2	1	no	—
188	C₂³×C₁₁	—	2	1	no	—
189	C₂³×C₁₁	—	2	2	no	—
190	C₂³×C₁₁	—	2	2	no	—
191	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
192	C₂³×C₁₁	#131	1	2	yes	—
193	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
194	D₄×C₁₁	—	2	8	no	—
195	D₄×C₁₁	—	4	8	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	2	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	2	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	2	no	—
210	C₂×C₄×C₁₁	—	2	1	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	2	no	—
216	C₂×C₄×C₁₁	—	4	2	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	1	no	—
221	C₂×C₄×C₁₁	—	4	2	no	—
222	C₂×C₄×C₁₁	—	4	1	no	—
223	C₂×C₄×C₁₁	—	4	2	no	—
224	C₂×C₄×C₁₁	—	4	4	no	—
225	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
228	C₂×C₄×C₁₁	#131	1	2	yes	—
229	C₂×C₄×C₁₁	#131	1	2	yes	—
230	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₁	H(5,𝔽₂)	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	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₁	—	2	2	no	—
237	C₈×C₁₁	—	2	2	no	—
238	C₈×C₁₁	—	4	1	no	—
239	C₈×C₁₁	—	4	2	no	—
240	C₈×C₁₁	—	4	1	no	—
241	C₈×C₁₁	—	4	2	no	—
242	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
243	C₂×#121	C₄×C₁₁	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
246	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
247	C₈×D₄	—	2	4	no	—
248	#431	—	2	4	no	—
249	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
260	C₂×#97	C₂²×C₁₁	1	2	yes	—
261	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
263	#390	C₄×C₁₁	1	1	yes	characteristic
264	#389	C₄×C₁₁	1	1	yes	characteristic
265	#388	C₄×C₁₁	1	2	yes	—
266	#386	C₄×C₁₁	1	2	yes	—
267	#380	C₄×C₁₁	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
269	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
270	#336	C₂²×C₁₁	1	2	yes	—
271	#336	C₂²×C₁₁	1	2	yes	—
272	#336	C₂²×C₁₁	1	2	yes	—
273	C₂²×C₁₁	—	2	4	no	—
274	C₂²×C₁₁	—	2	2	no	—
275	C₂²×C₁₁	—	2	2	no	—
276	C₂²×C₁₁	—	2	4	no	—
277	C₂²×C₁₁	—	2	4	no	—
278	C₂²×C₁₁	—	2	2	no	—
279	C₂²×C₁₁	—	4	2	no	—
280	C₂²×C₁₁	—	4	1	no	—
281	C₂²×C₁₁	—	4	1	no	—
282	C₂²×C₁₁	—	4	2	no	—
283	C₂²×C₁₁	—	4	1	no	—
284	C₂²×C₁₁	—	4	2	no	—
285	C₂²×C₁₁	—	4	1	no	—
286	C₂²×C₁₁	—	4	2	no	—
287	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₁₁	#518	1	1	yes	characteristic
289	C₂²×C₁₁	#520	1	1	yes	characteristic
290	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
291	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
292	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
293	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
294	C₄×C₁₁	—	2	2	no	—
295	C₄×C₁₁	—	2	2	no	—
296	C₄×C₁₁	—	4	1	no	—
297	C₄×C₁₁	—	4	2	no	—
298	C₄×C₁₁	—	4	1	no	—
299	C₄×C₁₁	—	4	2	no	—
300	C₄×C₁₁	—	4	2	no	—
301	C₄×C₁₁	#435	1	4	yes	—
302	C₄×C₁₁	#535	1	1	yes	characteristic
303	C₄×C₁₁	#537	1	1	yes	characteristic
304	C₄×C₁₁	#540	1	1	yes	characteristic
305	C₄×C₁₁	#542	1	1	yes	characteristic
306	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
307	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
308	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
312	C₂²×C₈	—	2	4	no	—
313	C₂²×C₈	—	4	2	no	—
314	C₂²×C₈	—	4	2	no	—
315	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
321	#121	—	2	4	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	4	2	no	—
325	C₄×D₄	—	4	2	no	—
326	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	—	2	2	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	—	4	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	4	no	—
350	C₂²⋊C₈	—	4	2	no	—
351	C₂²⋊C₈	—	4	2	no	—
352	C₂²⋊C₈	—	4	2	no	—
353	#97	—	4	2	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
356	#95	C₂×C₄×C₁₁	1	2	yes	—
357	#95	C₂×C₄×C₁₁	1	2	yes	—
358	#95	C₂×C₄×C₁₁	1	2	yes	—
359	C₂×C₁₁	—	4	4	no	—
360	C₂×C₁₁	—	4	2	no	—
361	C₂×C₁₁	#2324	1	1	yes	characteristic
362	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
363	C₂×C₁₁	#2929	1	1	yes	characteristic
364	C₂×C₁₁	#2974	1	1	yes	characteristic
365	C₂×C₁₁	#2979	1	1	yes	characteristic
366	C₂×C₁₁	#2990	1	1	yes	characteristic
367	C₂×C₁₁	#2994	1	1	yes	characteristic
368	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
369	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	C₁₁×M₁₆	1	4	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
396	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
397	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	4	8	no	—
420	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
421	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	C₂×D₄×C₁₁	1	2	yes	—
438	C₄²	C₁₁×#41	1	2	yes	—
439	C₁₁	#22135	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
453	C₂³	C₁₁×#131	1	2	yes	—
454	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
455	D₄	—	2	8	no	—
456	D₄	—	4	8	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
487	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
488	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
489	C₂×C₄	C₁₁×#131	1	2	yes	—
490	C₂×C₄	C₁₁×#131	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
492	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
493	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	4	2	no	—
500	C₈	—	4	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	2	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
518	C₂²	C₁₁×#518	1	1	yes	characteristic
519	C₂²	C₁₁×#520	1	1	yes	characteristic
520	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
521	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
522	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
523	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	C₁₁×#435	1	4	yes	—
532	C₄	C₁₁×#535	1	1	yes	characteristic
533	C₄	C₁₁×#537	1	1	yes	characteristic
534	C₄	C₁₁×#540	1	1	yes	characteristic
535	C₄	C₁₁×#542	1	1	yes	characteristic
536	C₂	—	4	4	no	—
537	C₂	—	4	2	no	—
538	C₂	C₁₁×#2324	1	1	yes	characteristic
539	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
540	C₂	C₁₁×#2929	1	1	yes	characteristic
541	C₂	C₁₁×#2974	1	1	yes	characteristic
542	C₂	C₁₁×#2979	1	1	yes	characteristic
543	C₂	C₁₁×#2990	1	1	yes	characteristic
544	C₂	C₁₁×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂×C₁₁×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₁	C₂	semidirect
2. C₂×C₁₁×#431	C₂	semidirect
4. C₁₁×#1955	C₂	semidirect
5. C₁₁×#1954	C₂	semidirect
6. C₁₁×#1939	C₂	semidirect
7. C₁₁×#1924	C₂	semidirect
8. C₁₁×#1869	C₂	semidirect
9. C₁₁×#1850	C₂	semidirect
10. C₁₁×#1797	C₂	semidirect
11. C₁₁×#1770	C₂	semidirect
92. C₄×C₈×C₁₁	D₄	semidirect
96. #22135	C₁₁	direct (N × H)
168. C₂×C₈×D₄	C₂×C₁₁	semidirect
169. C₂×#431	C₂×C₁₁	semidirect
171. #1955	C₂×C₁₁	semidirect
172. #1954	C₂×C₁₁	semidirect
173. #1939	C₂×C₁₁	semidirect
174. #1924	C₂×C₁₁	semidirect
175. #1869	C₂×C₁₁	semidirect
176. #1850	C₂×C₁₁	semidirect
177. #1797	C₂×C₁₁	semidirect
178. #1770	C₂×C₁₁	semidirect
355. C₄×C₈	D₄×C₁₁	semidirect
439. C₁₁	#22135	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×C₈×D₄×C₁₁	2
C₂×C₁₁×#431	2
C₄×C₁₁×#121	2
C₁₁×#1955	2
C₁₁×#1954	2
C₁₁×#1939	2
C₁₁×#1924	2
C₁₁×#1869	2
C₁₁×#1850	2
C₁₁×#1797	2
C₁₁×#1770	2
#22135	11

Subgroups — C11×#22135 #14599328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22135 #14599328