Subgroups — C₁₁×#22212 #14599405

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1924	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1850	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#124	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#446	—	2	4	no	—
15	C₈×D₄×C₁₁	—	2	4	no	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
22	C₂×C₁₁×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₁₁×#391	C₄	1	1	yes	characteristic
26	C₁₁×#390	C₄	1	1	yes	characteristic
27	C₁₁×#388	C₄	1	4	yes	—
28	C₁₁×#382	C₄	1	1	yes	characteristic
29	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₄³×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₁₁×#336	C₂²	1	4	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₁	—	2	4	no	—
38	C₂²×C₈×C₁₁	—	4	4	no	—
39	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×#124	—	2	4	no	—
45	C₄×Q₈×C₁₁	—	2	2	no	—
46	C₄×Q₈×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	—	2	2	no	—
48	C₄×D₄×C₁₁	—	2	2	no	—
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
53	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
54	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊C₈	—	2	4	no	—
62	C₁₁×C₄⋊C₈	—	2	2	no	—
63	C₁₁×C₄⋊C₈	—	2	2	no	—
64	C₁₁×C₄⋊C₈	—	4	4	no	—
65	C₁₁×C₂²⋊C₈	—	2	4	no	—
66	C₁₁×C₂²⋊C₈	—	4	4	no	—
67	C₁₁×#97	—	2	4	no	—
68	C₄×C₈×C₁₁	—	2	2	no	—
69	C₄×C₈×C₁₁	D₄	1	4	yes	—
70	C₁₁×#95	C₂×C₄	1	4	yes	—
71	C₁₁×#95	C₂×C₄	1	4	yes	—
72	#22212	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
74	C₂×Q₈×C₁₁	—	2	2	no	—
75	C₂×Q₈×C₁₁	—	2	2	no	—
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×D₄×C₁₁	—	2	2	no	—
78	C₂×D₄×C₁₁	—	2	2	no	—
79	C₂×D₄×C₁₁	M₁₆	1	4	yes	—
80	C₂²×C₄×C₁₁	—	2	2	no	—
81	C₂²×C₄×C₁₁	—	2	2	no	—
82	C₂²×C₄×C₁₁	—	2	4	no	—
83	C₂²×C₄×C₁₁	—	2	4	no	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	—	2	4	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	2	no	—
101	C₂×C₈×C₁₁	—	4	8	no	—
102	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
104	C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₁₁×C₄⋊C₄	—	2	2	no	—
106	C₁₁×C₄⋊C₄	—	2	4	no	—
107	C₁₁×C₂²⋊C₄	—	2	8	no	—
108	C₁₁×C₂²⋊C₄	—	2	4	no	—
109	C₁₁×C₂²⋊C₄	—	2	8	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	—	2	2	no	—
112	C₄²×C₁₁	—	2	4	no	—
113	C₄²×C₁₁	—	2	2	no	—
114	C₄²×C₁₁	—	2	2	no	—
115	C₄²×C₁₁	—	2	2	no	—
116	C₄²×C₁₁	—	2	2	no	—
117	C₄²×C₁₁	C₂×D₄	1	2	yes	—
118	C₄²×C₁₁	#41	1	2	yes	—
119	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
120	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
121	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
122	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
123	#1954	C₂×C₁₁	1	1	yes	characteristic
124	#1924	C₂×C₁₁	1	4	yes	complemented
125	#1850	C₂×C₁₁	1	4	yes	complemented
126	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
127	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
128	C₂³×C₁₁	—	2	2	no	—
129	C₂³×C₁₁	—	2	4	no	—
130	C₂³×C₁₁	—	2	4	no	—
131	C₂³×C₁₁	—	2	2	no	—
132	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
133	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
134	Q₈×C₁₁	—	4	4	no	—
135	D₄×C₁₁	—	2	8	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	2	4	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	4	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	4	2	no	—
150	C₂×C₄×C₁₁	—	4	2	no	—
151	C₂×C₄×C₁₁	—	4	4	no	—
152	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₁₁	#131	1	4	yes	—
156	C₂×C₄×C₁₁	#131	1	2	yes	—
157	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
160	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
161	C₈×C₁₁	—	2	2	no	—
162	C₈×C₁₁	—	2	2	no	—
163	C₈×C₁₁	—	4	2	no	—
164	C₈×C₁₁	—	4	2	no	—
165	C₈×C₁₁	—	4	2	no	—
166	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
167	C₂×#124	C₄×C₁₁	1	1	yes	characteristic
168	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
169	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
170	#446	—	2	4	no	—
171	C₈×D₄	—	2	4	no	—
172	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
178	C₂×#97	C₂²×C₁₁	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
180	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
181	#391	C₄×C₁₁	1	1	yes	characteristic
182	#390	C₄×C₁₁	1	1	yes	characteristic
183	#388	C₄×C₁₁	1	4	yes	—
184	#382	C₄×C₁₁	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
186	C₄³	C₂²×C₁₁	1	1	yes	characteristic
187	#336	C₂²×C₁₁	1	2	yes	—
188	#336	C₂²×C₁₁	1	4	yes	—
189	#336	C₂²×C₁₁	1	2	yes	—
190	C₂²×C₁₁	—	2	4	no	—
191	C₂²×C₁₁	—	2	8	no	—
192	C₂²×C₁₁	—	4	2	no	—
193	C₂²×C₁₁	—	4	2	no	—
194	C₂²×C₁₁	—	4	4	no	—
195	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₁₁	#520	1	2	yes	—
197	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
198	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
199	C₂²×C₁₁	C₂×#131	1	2	yes	—
200	C₄×C₁₁	—	2	2	no	—
201	C₄×C₁₁	—	2	4	no	—
202	C₄×C₁₁	—	4	2	no	—
203	C₄×C₁₁	—	4	2	no	—
204	C₄×C₁₁	—	4	2	no	—
205	C₄×C₁₁	—	4	2	no	—
206	C₄×C₁₁	#435	1	4	yes	—
207	C₄×C₁₁	#535	1	1	yes	characteristic
208	C₄×C₁₁	#536	1	1	yes	characteristic
209	C₄×C₁₁	#542	1	2	yes	—
210	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
211	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	—	4	4	no	—
215	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
216	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
220	#124	—	2	4	no	—
221	C₄×Q₈	—	2	2	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
231	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
233	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
235	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
236	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
237	C₄⋊C₈	—	2	4	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	4	4	no	—
241	C₂²⋊C₈	—	2	4	no	—
242	C₂²⋊C₈	—	4	4	no	—
243	#97	—	2	4	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	D₄×C₁₁	1	4	yes	—
246	#95	C₂×C₄×C₁₁	1	4	yes	—
247	#95	C₂×C₄×C₁₁	1	4	yes	—
248	C₂×C₁₁	—	4	4	no	—
249	C₂×C₁₁	#2326	1	1	yes	characteristic
250	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
251	C₂×C₁₁	#2931	1	1	yes	characteristic
252	C₂×C₁₁	#2990	1	2	yes	—
253	C₂×C₁₁	#2994	1	2	yes	—
254	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	C₁₁×M₁₆	1	4	yes	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	4	8	no	—
283	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	—	2	4	no	—
290	C₂²⋊C₄	—	2	8	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₂×D₄×C₁₁	1	2	yes	—
299	C₄²	C₁₁×#41	1	2	yes	—
300	C₁₁	#22212	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	—	2	2	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
306	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
307	Q₈	—	4	4	no	—
308	D₄	—	2	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
326	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
327	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
328	C₂×C₄	C₁₁×#131	1	4	yes	—
329	C₂×C₄	C₁₁×#131	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
332	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
333	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
334	C₈	—	2	2	no	—
335	C₈	—	2	2	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	8	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	2	no	—
344	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
345	C₂²	C₁₁×#520	1	2	yes	—
346	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
347	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
348	C₂²	C₂×C₁₁×#131	1	2	yes	—
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	C₁₁×#435	1	4	yes	—
356	C₄	C₁₁×#535	1	1	yes	characteristic
357	C₄	C₁₁×#536	1	1	yes	characteristic
358	C₄	C₁₁×#542	1	2	yes	—
359	C₂	—	4	4	no	—
360	C₂	C₁₁×#2326	1	1	yes	characteristic
361	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
362	C₂	C₁₁×#2931	1	1	yes	characteristic
363	C₂	C₁₁×#2990	1	2	yes	—
364	C₂	C₁₁×#2994	1	2	yes	—

	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	C₂²×D₄×C₁₁	C₂×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×C₁₁×#446	C₂	semidirect
4. C₁₁×#1984	C₂	semidirect
6. C₁₁×#1924	C₂	semidirect
7. C₁₁×#1850	C₂	semidirect
8. C₁₁×#1842	C₂	semidirect
9. C₁₁×#1744	C₂	semidirect
72. #22212	C₁₁	direct (N × H)
119. C₂×#446	C₂×C₁₁	semidirect
122. #1984	C₂×C₁₁	semidirect
124. #1924	C₂×C₁₁	semidirect
125. #1850	C₂×C₁₁	semidirect
126. #1842	C₂×C₁₁	semidirect
127. #1744	C₂×C₁₁	semidirect
300. C₁₁	#22212	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×#446	2
C₂×C₈×D₄×C₁₁	2
C₄×C₁₁×#124	2
C₁₁×#1984	2
C₁₁×#1954	2
C₁₁×#1924	2
C₁₁×#1850	2
C₁₁×#1842	2
C₁₁×#1744	2
#22212	11

Subgroups — C11×#22212 #14599405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22212 #14599405