Subgroups — C₁₁×#22235 #14599428

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3135	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1963	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1929	C₂	1	4	yes	maximal, complemented
7	C₁₁×#1866	C₂	1	4	yes	maximal, complemented
8	C₁₁×#1849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	C₂²	1	2	yes	—
11	C₁₁×#533	C₂²	1	1	yes	characteristic
12	C₁₁×#532	C₂²	1	1	yes	characteristic
13	C₁₁×#491	C₄	1	2	yes	complemented
14	C₁₁×#490	C₄	1	2	yes	complemented
15	C₁₁×#489	C₄	1	2	yes	complemented
16	C₁₁×#489	C₄	1	2	yes	complemented
17	C₁₁×#446	—	2	1	no	—
18	C₁₁×#446	—	2	1	no	—
19	C₈×Q₈×C₁₁	—	2	1	no	—
20	C₈×Q₈×C₁₁	—	2	1	no	—
21	C₁₁×#436	—	2	1	no	—
22	C₁₁×#436	—	2	1	no	—
23	C₈×D₄×C₁₁	—	2	1	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₂×C₁₁×#108	C₂²	1	4	yes	—
26	C₁₁×#424	C₂²	1	2	yes	—
27	C₁₁×#423	C₂²	1	1	yes	characteristic
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#104	C₂²	1	4	yes	—
30	C₁₁×#416	C₂²	1	4	yes	—
31	C₁₁×#408	C₂²	1	2	yes	—
32	C₁₁×#405	C₂²	1	2	yes	—
33	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#376	C₂²	1	1	yes	characteristic
36	C₁₁×#339	C₂²	1	4	yes	—
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₂×C₁₁×#41	C₂³	1	2	yes	—
40	C₁₁×#131	—	4	4	no	—
41	C₂×C₁₁×M₁₆	—	2	2	no	—
42	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
43	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	—	2	2	no	—
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
52	C₁₁×#125	C₂×C₄	1	2	yes	—
53	C₁₁×#124	C₂×C₄	1	2	yes	—
54	C₁₁×C₂²⋊Q₈	—	2	1	no	—
55	C₁₁×C₂²⋊Q₈	—	2	1	no	—
56	C₁₁×#121	—	2	1	no	—
57	C₁₁×#121	—	2	1	no	—
58	C₄×Q₈×C₁₁	—	2	1	no	—
59	C₄×Q₈×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	—	2	1	no	—
61	C₄×D₄×C₁₁	—	2	1	no	—
62	C₁₁×#117	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₁₁×#108	—	4	4	no	—
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	—	2	2	no	—
68	C₁₁×C₄⋊C₈	—	2	1	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	—	2	1	no	—
72	C₁₁×#104	—	4	4	no	—
73	C₁₁×#103	C₂×C₄	1	4	yes	—
74	C₁₁×#103	C₂×C₄	1	4	yes	—
75	C₁₁×#102	C₂×C₄	1	4	yes	—
76	C₁₁×#102	C₂×C₄	1	4	yes	—
77	C₁₁×C₂²⋊C₈	—	2	2	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×#97	—	2	2	no	—
80	C₁₁×#97	C₂×C₄	1	2	yes	—
81	C₁₁×#97	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
87	C₁₁×#95	—	2	1	no	—
88	C₁₁×#95	—	2	1	no	—
89	#22235	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₁×#41	—	2	4	no	—
91	C₁₁×#41	—	2	4	no	—
92	C₂×Q₈×C₁₁	—	2	1	no	—
93	C₂×Q₈×C₁₁	—	2	1	no	—
94	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	1	no	—
97	C₂×D₄×C₁₁	—	2	1	no	—
98	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
104	C₁₁×M₁₆	—	2	4	no	—
105	C₁₁×M₁₆	—	2	4	no	—
106	C₁₁×M₁₆	—	4	4	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	4	4	no	—
114	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₁₁×C₄⋊C₄	—	2	1	no	—
120	C₁₁×C₄⋊C₄	—	2	1	no	—
121	C₁₁×C₄⋊C₄	—	2	2	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	1	no	—
124	C₁₁×C₄⋊C₄	—	2	1	no	—
125	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
126	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
127	C₁₁×C₂²⋊C₄	—	2	2	no	—
128	C₁₁×C₂²⋊C₄	—	2	2	no	—
129	C₁₁×C₂²⋊C₄	—	2	2	no	—
130	C₄²×C₁₁	—	2	2	no	—
131	C₄²×C₁₁	—	2	2	no	—
132	C₄²×C₁₁	—	2	2	no	—
133	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
137	#3135	C₂×C₁₁	1	1	yes	characteristic
138	#2960	C₂×C₁₁	1	1	yes	characteristic, complemented
139	#2931	C₂×C₁₁	1	1	yes	characteristic
140	#1995	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#1963	C₂×C₁₁	1	1	yes	characteristic
142	#1929	C₂×C₁₁	1	4	yes	complemented
143	#1866	C₂×C₁₁	1	4	yes	complemented
144	#1849	C₂×C₁₁	1	1	yes	characteristic, complemented
145	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂³×C₁₁	—	2	2	no	—
147	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
148	Q₈×C₁₁	—	2	4	no	—
149	Q₈×C₁₁	—	4	2	no	—
150	Q₈×C₁₁	—	4	2	no	—
151	D₄×C₁₁	—	2	4	no	—
152	D₄×C₁₁	—	4	2	no	—
153	D₄×C₁₁	—	4	2	no	—
154	D₄×C₁₁	—	4	4	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	4	1	no	—
159	C₂×C₄×C₁₁	—	4	1	no	—
160	C₂×C₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	—	4	2	no	—
162	C₂×C₄×C₁₁	—	4	2	no	—
163	C₂×C₄×C₁₁	—	4	2	no	—
164	C₂×C₄×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₁₁	—	2	4	no	—
174	C₈×C₁₁	—	2	1	no	—
175	C₈×C₁₁	—	2	1	no	—
176	C₈×C₁₁	—	2	1	no	—
177	C₈×C₁₁	—	2	1	no	—
178	C₈×C₁₁	—	4	2	no	—
179	C₈×C₁₁	—	4	2	no	—
180	C₂×#131	C₂²×C₁₁	1	2	yes	—
181	#533	C₂²×C₁₁	1	1	yes	characteristic
182	#532	C₂²×C₁₁	1	1	yes	characteristic
183	#491	C₄×C₁₁	1	2	yes	complemented
184	#490	C₄×C₁₁	1	2	yes	complemented
185	#489	C₄×C₁₁	1	2	yes	complemented
186	#489	C₄×C₁₁	1	2	yes	complemented
187	#446	—	2	1	no	—
188	#446	—	2	1	no	—
189	C₈×Q₈	—	2	1	no	—
190	C₈×Q₈	—	2	1	no	—
191	#436	—	2	1	no	—
192	#436	—	2	1	no	—
193	C₈×D₄	—	2	1	no	—
194	C₈×D₄	—	2	1	no	—
195	C₂×#108	C₂²×C₁₁	1	4	yes	—
196	#424	C₂²×C₁₁	1	2	yes	—
197	#423	C₂²×C₁₁	1	1	yes	characteristic
198	#423	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×#104	C₂²×C₁₁	1	4	yes	—
200	#416	C₂²×C₁₁	1	4	yes	—
201	#408	C₂²×C₁₁	1	2	yes	—
202	#405	C₂²×C₁₁	1	2	yes	—
203	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
205	#376	C₂²×C₁₁	1	1	yes	characteristic
206	#339	C₂²×C₁₁	1	4	yes	—
207	#336	C₂²×C₁₁	1	2	yes	—
208	#336	C₂²×C₁₁	1	2	yes	—
209	C₂²×C₁₁	—	2	1	no	—
210	C₂²×C₁₁	—	2	1	no	—
211	C₂²×C₁₁	—	4	2	no	—
212	C₂²×C₁₁	—	4	2	no	—
213	C₂²×C₁₁	—	4	2	no	—
214	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₁₁	#542	1	2	yes	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	—	2	1	no	—
218	C₄×C₁₁	—	2	1	no	—
219	C₄×C₁₁	—	2	1	no	—
220	C₄×C₁₁	—	4	2	no	—
221	C₄×C₁₁	—	4	2	no	—
222	C₄×C₁₁	—	4	2	no	—
223	C₄×C₁₁	—	8	2	no	—
224	C₄×C₁₁	#520	1	2	yes	—
225	C₄×C₁₁	#535	1	1	yes	characteristic
226	C₄×C₁₁	#536	1	1	yes	characteristic
227	C₂×#41	C₂³×C₁₁	1	2	yes	—
228	#131	—	4	4	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
231	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
236	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
237	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
238	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
239	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
240	#125	C₂×C₄×C₁₁	1	2	yes	—
241	#124	C₂×C₄×C₁₁	1	2	yes	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	#121	—	2	1	no	—
245	#121	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	#117	C₂³×C₁₁	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
252	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
253	#108	—	4	4	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	#104	—	4	4	no	—
261	#103	C₂×C₄×C₁₁	1	4	yes	—
262	#103	C₂×C₄×C₁₁	1	4	yes	—
263	#102	C₂×C₄×C₁₁	1	4	yes	—
264	#102	C₂×C₄×C₁₁	1	4	yes	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	#97	—	2	2	no	—
268	#97	C₂×C₄×C₁₁	1	2	yes	—
269	#97	C₂×C₄×C₁₁	1	2	yes	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
272	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
273	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
274	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	C₂×C₁₁	—	2	2	no	—
278	C₂×C₁₁	—	8	2	no	—
279	C₂×C₁₁	#2326	1	1	yes	characteristic
280	C₂×C₁₁	#2955	1	1	yes	characteristic
281	C₂×C₁₁	#2955	1	1	yes	characteristic
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
294	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
296	M₁₆	—	2	4	no	—
297	M₁₆	—	2	4	no	—
298	M₁₆	—	4	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
307	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
318	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
326	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
329	C₁₁	#22235	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	2	no	—
331	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
332	Q₈	—	2	4	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	D₄	—	2	4	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
355	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
356	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
357	C₈	—	2	4	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
370	C₂²	C₁₁×#542	1	2	yes	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₁₁×#520	1	2	yes	—
380	C₄	C₁₁×#535	1	1	yes	characteristic
381	C₄	C₁₁×#536	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	8	2	no	—
384	C₂	C₁₁×#2326	1	1	yes	characteristic
385	C₂	C₁₁×#2955	1	1	yes	characteristic
386	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×#532	C₂²
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×#2960	C₂	semidirect
4. C₁₁×#1995	C₂	semidirect
6. C₁₁×#1929	C₂	semidirect
7. C₁₁×#1866	C₂	semidirect
8. C₁₁×#1849	C₂	semidirect
9. C₁₁×#1746	C₂	semidirect
13. C₁₁×#491	C₄	semidirect
14. C₁₁×#490	C₄	semidirect
15. C₁₁×#489	C₄	semidirect
16. C₁₁×#489	C₄	semidirect
89. #22235	C₁₁	direct (N × H)
138. #2960	C₂×C₁₁	semidirect
140. #1995	C₂×C₁₁	semidirect
142. #1929	C₂×C₁₁	semidirect
143. #1866	C₂×C₁₁	semidirect
144. #1849	C₂×C₁₁	semidirect
145. #1746	C₂×C₁₁	semidirect
183. #491	C₄×C₁₁	semidirect
184. #490	C₄×C₁₁	semidirect
185. #489	C₄×C₁₁	semidirect
186. #489	C₄×C₁₁	semidirect
329. C₁₁	#22235	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×#3135	2
C₁₁×#2960	2
C₁₁×#2931	2
C₁₁×#1995	2
C₁₁×#1963	2
C₁₁×#1929	2
C₁₁×#1866	2
C₁₁×#1849	2
C₁₁×#1746	2
#22235	11

Subgroups — C11×#22235 #14599428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22235 #14599428