Subgroups — #14724462

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077765	C₂	1	2	yes	maximal, complemented
2	#13067519	C₂	1	2	yes	maximal, complemented
3	#13067513	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067501	C₂	1	1	yes	maximal, characteristic, complemented
5	SD₁₆⋊(C₁₁⋊C₈)	C₂	1	2	yes	maximal, complemented
6	Q₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067375	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067081	C₂	1	2	yes	maximal, complemented
10	#13066899	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3168	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#529	C₂²	1	2	yes	—
13	C₁₁×#499	C₄	1	1	yes	characteristic
14	C₁₁×#495	C₄	1	1	yes	characteristic
15	C₁₁×#488	C₄	1	2	yes	—
16	C₁₁×#467	C₄	1	1	yes	characteristic
17	C₁₁×#466	C₄	1	1	yes	characteristic
18	C₁₁×#465	C₄	1	2	yes	—
19	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	#10622637	C₂²	1	2	yes	—
24	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
25	#10622625	—	2	2	no	—
26	#10622625	C₂²	1	2	yes	—
27	#10622624	—	2	2	no	—
28	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
29	#10622613	—	2	2	no	—
30	#10622612	—	2	2	no	—
31	#10622538	C₂²	1	1	yes	characteristic
32	#10622538	C₂²	1	1	yes	characteristic
33	#10622537	C₂²	1	2	yes	—
34	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
37	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	#10622096	C₂²	1	1	yes	characteristic
39	#10622096	C₂²	1	1	yes	characteristic
40	#10622096	C₂²	1	2	yes	—
41	#10622093	C₂²	1	1	yes	characteristic
42	#10622093	C₂²	1	1	yes	characteristic
43	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
44	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₁₁×#126	—	2	2	no	—
51	C₁₁×#125	C₂×C₄	1	2	yes	—
52	C₁₁×#124	C₂×C₄	1	2	yes	—
53	C₁₁×#123	—	2	2	no	—
54	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
55	C₁₁×#121	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
57	C₄×D₄×C₁₁	—	2	2	no	—
58	C₄×D₄×C₁₁	C₂³	1	2	yes	—
59	C₁₁×#117	—	2	2	no	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₂×#4318	—	2	2	no	—
62	C₂×#4318	—	2	2	no	—
63	C₂²×C₁₁⋊C₈	—	2	2	no	—
64	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
65	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
66	C₁₁×#106	C₂×C₄	1	2	yes	—
67	C₁₁×#103	C₂×C₄	1	2	yes	—
68	C₁₁×#103	C₂×C₄	1	2	yes	—
69	C₁₁×#102	C₂×C₄	1	2	yes	—
70	C₁₁×#102	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
79	C₂²⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
81	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
82	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
83	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
84	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
85	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
86	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
87	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
88	#66867	—	2	2	no	—
89	C₄×C₁₁⋊C₈	—	2	2	no	—
90	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	#17973	—	11	1	no	maximal, Sylow
95	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
102	C₁₁×Q₁₆	—	2	2	no	—
103	C₁₁×SD₁₆	—	2	4	no	—
104	C₁₁×D₈	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₁₁×C₄⋊C₄	—	2	2	no	—
112	C₁₁×C₄⋊C₄	—	2	2	no	—
113	C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₁₁×C₄⋊C₄	—	2	2	no	—
115	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
116	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
117	C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	2	no	—
119	C₁₁×C₂²⋊C₄	—	2	2	no	—
120	C₁₁×C₂²⋊C₄	—	2	2	no	—
121	C₁₁×C₂²⋊C₄	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₁	#41	1	1	yes	characteristic
126	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
127	#4318	—	8	2	no	—
128	#4318	—	8	2	no	—
129	C₂×C₁₁⋊C₈	—	2	2	no	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	—	2	1	no	—
132	C₂×C₁₁⋊C₈	—	2	1	no	—
133	C₂×C₁₁⋊C₈	—	8	2	no	—
134	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
138	#3168	D₁₁	1	1	yes	characteristic
139	#2993	—	11	2	no	—
140	#1592	—	11	2	no	—
141	#1591	—	11	1	no	—
142	#1589	—	11	1	no	—
143	SD₁₆⋊C₈	—	11	2	no	—
144	C₈×Q₁₆	—	11	1	no	—
145	C₈×D₈	—	11	1	no	—
146	#1567	—	11	1	no	—
147	#1495	—	11	2	no	—
148	#1450	—	11	1	no	—
149	C₂³×C₁₁	—	2	2	no	—
150	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
151	Q₈×C₁₁	—	2	2	no	—
152	Q₈×C₁₁	—	2	2	no	—
153	D₄×C₁₁	—	2	2	no	—
154	D₄×C₁₁	—	2	2	no	—
155	D₄×C₁₁	—	8	2	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	1	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	4	1	no	—
164	C₂×C₄×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	—	4	2	no	—
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	C₂×#41	1	1	yes	characteristic
172	C₈×C₁₁	—	2	1	no	—
173	C₈×C₁₁	—	2	1	no	—
174	C₈×C₁₁	#131	1	2	yes	—
175	C₈×C₁₁	#131	1	2	yes	—
176	C₁₁⋊C₈	—	2	1	no	—
177	C₁₁⋊C₈	—	2	1	no	—
178	C₁₁⋊C₈	—	2	1	no	—
179	C₁₁⋊C₈	—	2	1	no	—
180	C₁₁⋊C₈	—	4	1	no	—
181	C₁₁⋊C₈	—	4	1	no	—
182	C₁₁⋊C₈	—	4	2	no	—
183	C₁₁⋊C₈	—	4	2	no	—
184	#529	C₂×D₁₁	1	2	yes	—
185	#499	Dic₁₁	1	1	yes	characteristic
186	#495	Dic₁₁	1	1	yes	characteristic
187	#488	Dic₁₁	1	2	yes	—
188	#467	Dic₁₁	1	1	yes	characteristic
189	#466	Dic₁₁	1	1	yes	characteristic
190	#465	Dic₁₁	1	2	yes	—
191	#446	—	11	2	no	—
192	C₈×Q₈	—	11	2	no	—
193	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
194	C₄×SD₁₆	C₂×D₁₁	1	2	yes	—
195	C₄×D₈	C₂×D₁₁	1	1	yes	characteristic
196	#436	—	11	2	no	—
197	#436	—	22	2	no	—
198	#435	—	22	2	no	—
199	C₈×D₄	—	11	2	no	—
200	#433	—	22	2	no	—
201	#431	—	11	1	no	—
202	#431	—	11	1	no	—
203	#424	—	22	2	no	—
204	#423	—	11	2	no	—
205	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
206	#335	—	11	1	no	—
207	#335	—	11	1	no	—
208	#335	—	11	2	no	—
209	Q₈⋊C₈	—	11	2	no	—
210	Q₈⋊C₈	—	11	2	no	—
211	D₄⋊C₈	—	11	2	no	—
212	D₄⋊C₈	—	11	2	no	—
213	#322	—	11	1	no	—
214	#322	—	11	1	no	—
215	C₈²	—	11	1	no	—
216	C₈²	—	11	1	no	—
217	C₂²×C₁₁	—	2	1	no	—
218	C₂²×C₁₁	—	2	1	no	—
219	C₂²×C₁₁	—	2	1	no	—
220	C₂²×C₁₁	—	4	2	no	—
221	C₂²×C₁₁	—	4	2	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₁₁	—	2	1	no	—
225	C₄×C₁₁	—	2	1	no	—
226	C₄×C₁₁	—	2	1	no	—
227	C₄×C₁₁	—	2	1	no	—
228	C₄×C₁₁	—	4	2	no	—
229	C₄×C₁₁	—	4	2	no	—
230	C₄×C₁₁	—	4	2	no	—
231	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
232	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
233	C₄×C₁₁	#576	1	1	yes	characteristic
234	C₄×C₁₁	#578	1	1	yes	characteristic
235	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
236	C₂×SD₁₆	C₂×Dic₁₁	1	2	yes	—
237	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
238	C₂×M₁₆	—	22	2	no	—
239	C₂×M₁₆	—	22	2	no	—
240	C₂²×C₈	—	22	2	no	—
241	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
242	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
243	#126	—	2	2	no	—
244	#125	C₂×Dic₁₁	1	2	yes	—
245	#124	C₂×Dic₁₁	1	2	yes	—
246	#123	—	2	2	no	—
247	C₂²⋊Q₈	C₂×Dic₁₁	1	2	yes	—
248	#121	C₂×Dic₁₁	1	2	yes	—
249	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	C₂²×D₁₁	1	2	yes	—
252	#117	—	2	2	no	—
253	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
254	#107	C₂×Dic₁₁	1	1	yes	characteristic
255	#107	C₂×Dic₁₁	1	1	yes	characteristic
256	#106	C₂×Dic₁₁	1	2	yes	—
257	C₄⋊C₈	—	11	1	no	—
258	C₄⋊C₈	—	11	1	no	—
259	C₄⋊C₈	—	11	2	no	—
260	C₄⋊C₈	—	11	2	no	—
261	C₄⋊C₈	—	22	2	no	—
262	C₄⋊C₈	—	22	2	no	—
263	C₄⋊C₈	—	22	2	no	—
264	C₄⋊C₈	—	22	1	no	—
265	#103	C₂×Dic₁₁	1	2	yes	—
266	#103	C₂×Dic₁₁	1	2	yes	—
267	#102	C₂×Dic₁₁	1	2	yes	—
268	#102	C₂×Dic₁₁	1	2	yes	—
269	C₂²⋊C₈	—	11	1	no	—
270	C₂²⋊C₈	—	11	1	no	—
271	C₂²⋊C₈	—	22	2	no	—
272	C₂²⋊C₈	—	22	2	no	—
273	C₂²⋊C₈	—	22	1	no	—
274	#97	—	22	2	no	—
275	C₄×C₈	—	11	1	no	—
276	C₄×C₈	—	11	1	no	—
277	C₄×C₈	—	11	1	no	—
278	C₄×C₈	—	11	1	no	—
279	C₄×C₈	—	22	2	no	—
280	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
281	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
282	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
284	C₂×C₁₁	—	4	1	no	—
285	C₂×C₁₁	—	8	2	no	—
286	C₂×C₁₁	#2931	1	1	yes	characteristic
287	C₂×C₁₁	#2951	1	1	yes	characteristic
288	C₂×C₁₁	#2957	1	1	yes	characteristic
289	C₂×Q₈	C₂²×Dic₁₁	1	2	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	C₂²×Dic₁₁	1	2	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
294	C₂²×C₄	#4341	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
296	Q₁₆	—	2	2	no	—
297	SD₁₆	—	2	4	no	—
298	D₈	—	2	2	no	—
299	M₁₆	—	88	2	no	—
300	M₁₆	—	88	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	11	1	no	—
304	C₂×C₈	—	11	1	no	—
305	C₂×C₈	—	11	1	no	—
306	C₂×C₈	—	11	1	no	—
307	C₂×C₈	—	22	2	no	—
308	C₂×C₈	—	22	2	no	—
309	C₂×C₈	—	22	1	no	—
310	C₂×C₈	—	22	1	no	—
311	C₂×C₈	—	88	2	no	—
312	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
313	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
314	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
315	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	D₄×D₁₁	1	1	yes	characteristic
329	C₄²	#4341	1	1	yes	characteristic
330	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
331	C₄²	C₂³×D₁₁	1	1	yes	characteristic
332	C₁₁	#17973	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	2	2	no	—
334	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
351	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
352	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
353	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
354	C₂×C₄	C₂×#4341	1	1	yes	characteristic
355	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	22	1	no	—
359	C₈	—	22	1	no	—
360	C₈	—	22	1	no	—
361	C₈	—	22	1	no	—
362	C₈	—	44	1	no	—
363	C₈	—	44	1	no	—
364	C₈	—	44	2	no	—
365	C₈	—	44	2	no	—
366	C₈	#67001	1	2	yes	—
367	C₈	#67001	1	2	yes	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	#10623300	1	1	yes	characteristic
383	C₄	#10623302	1	1	yes	characteristic
384	C₄	C₂×#67001	1	1	yes	characteristic
385	C₄	C₂×#67001	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	8	2	no	—
388	C₂	#13077328	1	1	yes	characteristic
389	C₂	#13077492	1	1	yes	characteristic
390	C₂	#13077533	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#3168	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#466	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#3168	D₁₁
hypocenter	C₁₁	#17973
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #13077765	C₂	semidirect
2. #13067519	C₂	semidirect
3. #13067513	C₂	semidirect
4. #13067501	C₂	semidirect
5. SD₁₆⋊(C₁₁⋊C₈)	C₂	semidirect
6. Q₁₆×C₁₁⋊C₈	C₂	semidirect
7. D₈×C₁₁⋊C₈	C₂	semidirect
8. #13067375	C₂	semidirect
9. #13067081	C₂	semidirect
10. #13066899	C₂	semidirect
332. C₁₁	#17973	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13077765	2
#13067519	2
#13067513	2
#13067501	2
SD₁₆⋊(C₁₁⋊C₈)	2
Q₁₆×C₁₁⋊C₈	2
D₈×C₁₁⋊C₈	2
#13067375	2
#13067081	2
#13066899	2
C₁₁×#3168	2
#17973	11