Subgroups — #14725790

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079176	C₂	1	1	yes	maximal, characteristic
2	#13077682	C₂	1	1	yes	maximal, characteristic
3	#13067516	C₂	1	2	yes	maximal, complemented
4	#13067459	C₂	1	2	yes	maximal, complemented
5	#13067450	C₂	1	2	yes	maximal, complemented
6	#13067426	C₂	1	2	yes	maximal, complemented
7	#13067362	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067037	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067032	C₂	1	1	yes	maximal, characteristic
10	#13066906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	#10623008	C₂²	1	1	yes	characteristic
14	C₁₁×#446	—	2	1	no	—
15	C₁₁×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₁	—	2	1	no	—
17	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#433	—	2	2	no	—
19	C₁₁×#431	C₂²	1	1	yes	characteristic
20	C₁₁×#431	C₂²	1	1	yes	characteristic
21	#10622701	C₄	1	1	yes	characteristic
22	#10622698	C₄	1	1	yes	characteristic
23	#10622694	C₄	1	1	yes	characteristic
24	#10622692	C₄	1	1	yes	characteristic
25	#10622661	C₄	1	2	yes	—
26	#10622661	C₄	1	2	yes	—
27	C₄×#4325	C₂²	1	2	yes	—
28	C₄×#4325	C₂²	1	2	yes	—
29	#10622538	C₂²	1	1	yes	characteristic
30	C₄×#4318	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
32	#10622451	—	2	1	no	—
33	#10622447	—	2	1	no	—
34	#10622340	—	2	2	no	—
35	#10622301	C₂²	1	2	yes	—
36	C₈×D₄₄	C₂²	1	2	yes	—
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
39	#10622121	C₂²	1	2	yes	—
40	#10622121	C₂²	1	2	yes	—
41	#10622118	C₂²	1	1	yes	characteristic
42	#10622118	C₂²	1	1	yes	characteristic
43	#10622117	C₂²	1	1	yes	characteristic
44	#10622117	C₂²	1	1	yes	characteristic
45	#10622093	C₂²	1	2	yes	—
46	#10622092	C₂²	1	2	yes	—
47	C₂×#4339	—	2	1	no	—
48	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×#125	—	2	1	no	—
51	C₁₁×C₂²⋊Q₈	—	2	1	no	—
52	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
53	C₄×Q₈×C₁₁	—	2	1	no	—
54	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
55	C₁₁×#117	—	2	1	no	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×#4325	C₂×C₄	1	2	yes	—
58	C₂×#4325	C₂×C₄	1	2	yes	—
59	#66983	—	2	1	no	—
60	#66983	C₂×C₄	1	2	yes	—
61	C₂×#4318	—	2	1	no	—
62	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₂×#4313	—	2	2	no	—
65	C₂×C₈×D₁₁	—	2	2	no	—
66	#66928	—	2	1	no	—
67	#66927	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄₄	—	2	1	no	—
69	C₄×D₄₄	C₂³	1	2	yes	—
70	#66922	C₂×C₄	1	1	yes	characteristic
71	C₁₁×C₄⋊C₈	—	2	2	no	—
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
74	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
75	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₁×C₂²⋊C₈	—	2	1	no	—
78	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
79	C₁₁×#97	—	2	2	no	—
80	C₄×C₈×C₁₁	—	2	2	no	—
81	C₄×C₈×C₁₁	—	2	1	no	—
82	C₄×C₈×C₁₁	C₂³	1	2	yes	—
83	#66899	C₂×C₄	1	2	yes	—
84	#66899	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	(C₂×D₁₁)⋊C₈	—	2	2	no	—
88	#66873	C₂×C₄	1	2	yes	—
89	#66873	C₂×C₄	1	2	yes	—
90	#66872	C₂×C₄	1	2	yes	—
91	#66872	C₂×C₄	1	2	yes	—
92	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
93	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
94	#66867	—	2	1	no	—
95	C₄×C₁₁⋊C₈	—	2	1	no	—
96	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
99	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
101	#18089	—	11	1	no	maximal, Sylow
102	C₂×Q₈×C₁₁	—	2	1	no	—
103	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₁	—	2	2	no	—
108	#4339	—	8	1	no	—
109	#4339	—	8	1	no	—
110	C₂×D₄₄	—	2	1	no	—
111	C₂×D₄₄	—	2	1	no	—
112	C₂×D₄₄	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₁₁	—	2	2	no	—
114	C₂×Dic₂₂	—	2	1	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
119	C₁₁×C₄⋊C₄	—	2	1	no	—
120	C₁₁×C₄⋊C₄	—	2	1	no	—
121	C₁₁×C₄⋊C₄	—	2	1	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
125	C₁₁×C₂²⋊C₄	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₁	#41	1	1	yes	characteristic
130	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
131	#4325	—	2	4	no	—
132	#4325	—	4	2	no	—
133	(C₂×D₁₁)⋊C₄	—	2	2	no	—
134	(C₂×D₁₁)⋊C₄	—	2	2	no	—
135	C₄⋊Dic₁₁	—	2	1	no	—
136	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
137	#4318	—	4	2	no	—
138	C₂×C₁₁⋊C₈	—	2	2	no	—
139	C₂×C₁₁⋊C₈	—	2	1	no	—
140	C₂×C₁₁⋊C₈	—	2	1	no	—
141	C₂×C₁₁⋊C₈	—	2	2	no	—
142	C₂×C₁₁⋊C₈	—	4	1	no	—
143	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	#4313	—	8	2	no	—
148	C₈×D₁₁	—	8	2	no	—
149	#3167	—	11	1	no	—
150	#2986	D₁₁	1	1	yes	characteristic, complemented
151	#2979	—	11	1	no	—
152	#1592	—	11	2	no	—
153	#1583	—	11	2	no	—
154	#1582	—	11	2	no	—
155	SD₁₆⋊C₈	—	11	2	no	—
156	#1564	—	11	1	no	—
157	#1485	—	11	1	no	—
158	#1484	—	11	1	no	—
159	#1451	—	11	1	no	—
160	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₁₁	—	2	2	no	—
162	Q₈×C₁₁	—	2	2	no	—
163	Q₈×C₁₁	—	2	2	no	—
164	Q₈×C₁₁	—	4	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₁₁	—	8	2	no	—
179	C₂×Dic₁₁	—	2	2	no	—
180	D₄₄	—	2	2	no	—
181	D₄₄	—	2	2	no	—
182	D₄₄	—	4	2	no	—
183	D₄₄	—	8	1	no	—
184	C₄×D₁₁	—	4	2	no	—
185	C₄×D₁₁	—	4	2	no	—
186	Dic₂₂	—	8	1	no	—
187	C₈×C₁₁	—	2	2	no	—
188	C₈×C₁₁	—	2	2	no	—
189	C₈×C₁₁	—	4	1	no	—
190	C₈×C₁₁	—	4	1	no	—
191	C₁₁⋊C₈	—	2	1	no	—
192	C₁₁⋊C₈	—	2	1	no	—
193	C₁₁⋊C₈	—	2	1	no	—
194	C₁₁⋊C₈	—	4	2	no	—
195	C₁₁⋊C₈	—	4	1	no	—
196	C₁₁⋊C₈	—	4	1	no	—
197	C₁₁⋊C₈	#131	1	2	yes	—
198	#533	C₂×D₁₁	1	1	yes	characteristic
199	#532	—	11	1	no	—
200	#498	—	11	1	no	—
201	#492	—	11	1	no	—
202	#487	—	11	1	no	—
203	#486	—	11	1	no	—
204	#465	—	11	2	no	—
205	#465	—	11	2	no	—
206	#446	—	2	1	no	—
207	#446	C₂×D₁₁	1	2	yes	—
208	C₈×Q₈	—	2	1	no	—
209	C₈×Q₈	C₂×D₁₁	1	2	yes	—
210	C₄×SD₁₆	—	11	2	no	—
211	C₄×SD₁₆	—	11	2	no	—
212	#436	—	11	2	no	—
213	#436	—	22	1	no	—
214	C₈×D₄	—	11	2	no	—
215	C₈×D₄	—	22	1	no	—
216	#433	—	2	2	no	—
217	#431	—	11	1	no	—
218	#431	C₂×D₁₁	1	1	yes	characteristic
219	#431	C₂×D₁₁	1	1	yes	characteristic
220	#408	—	22	2	no	—
221	C₄×M₁₆	—	11	1	no	—
222	C₂×C₄×C₈	—	11	1	no	—
223	#335	—	11	1	no	—
224	#335	—	11	1	no	—
225	#334	—	11	1	no	—
226	#334	—	11	1	no	—
227	Q₈⋊C₈	—	11	2	no	—
228	Q₈⋊C₈	—	11	2	no	—
229	D₄⋊C₈	—	11	2	no	—
230	D₄⋊C₈	—	11	2	no	—
231	#322	—	11	2	no	—
232	#322	—	11	2	no	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂×D₁₁	—	4	2	no	—
238	C₂×D₁₁	—	4	2	no	—
239	C₂×D₁₁	—	4	2	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	—	2	1	no	—
243	C₄×C₁₁	—	4	2	no	—
244	C₄×C₁₁	—	4	2	no	—
245	C₄×C₁₁	#444	1	2	yes	—
246	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
247	C₄×C₁₁	#568	1	1	yes	characteristic
248	C₄×C₁₁	#577	1	1	yes	characteristic
249	C₄×C₁₁	#577	1	1	yes	characteristic
250	Dic₁₁	—	4	2	no	—
251	C₂×#41	—	22	1	no	—
252	C₂×SD₁₆	—	11	2	no	—
253	C₂×SD₁₆	—	11	2	no	—
254	C₂×M₁₆	—	22	1	no	—
255	C₂×M₁₆	—	22	2	no	—
256	C₂²×C₈	—	11	1	no	—
257	C₂²×C₈	—	11	1	no	—
258	C₂²×C₈	—	22	2	no	—
259	C₄⋊Q₈	—	11	1	no	—
260	C₄⋊Q₈	C₄×D₁₁	1	1	yes	characteristic
261	C₄⋊Q₈	C₄×D₁₁	1	1	yes	characteristic
262	#127	—	11	1	no	—
263	#125	—	2	1	no	—
264	#124	—	22	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₄×D₁₁	1	2	yes	—
267	#121	—	11	2	no	—
268	#121	—	22	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
271	C₄×D₄	—	11	2	no	—
272	C₄×D₄	—	22	1	no	—
273	#117	—	2	1	no	—
274	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
275	#106	—	11	2	no	—
276	#106	—	11	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	11	1	no	—
280	C₄⋊C₈	—	11	1	no	—
281	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
282	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
283	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
284	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
285	#103	—	11	2	no	—
286	#103	—	11	2	no	—
287	#102	—	11	2	no	—
288	#102	—	11	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	22	1	no	—
291	C₂²⋊C₈	—	22	2	no	—
292	C₂²⋊C₈	—	22	2	no	—
293	C₂²⋊C₈	C₂²⋊D₁₁	1	2	yes	—
294	#97	—	2	2	no	—
295	#97	—	22	1	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	11	1	no	—
299	C₄×C₈	—	11	1	no	—
300	C₄×C₈	—	11	1	no	—
301	C₄×C₈	—	11	1	no	—
302	C₄×C₈	—	11	2	no	—
303	C₄×C₈	—	22	1	no	—
304	C₄×C₈	C₂²×D₁₁	1	2	yes	—
305	C₂×C₁₁	—	4	1	no	—
306	C₂×C₁₁	#2935	1	1	yes	characteristic
307	C₂×C₁₁	#2949	1	1	yes	characteristic
308	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
309	D₁₁	—	8	2	no	—
310	#41	—	88	1	no	—
311	#41	—	88	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	22	1	no	—
314	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
315	C₂×D₄	—	11	2	no	—
316	C₂×D₄	—	22	2	no	—
317	C₂×D₄	—	22	1	no	—
318	C₂×D₄	—	22	1	no	—
319	C₂²×C₄	—	22	2	no	—
320	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
321	C₂²×C₄	#4339	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
323	SD₁₆	—	22	4	no	—
324	SD₁₆	—	44	2	no	—
325	M₁₆	—	44	2	no	—
326	M₁₆	—	88	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	11	1	no	—
330	C₂×C₈	—	11	1	no	—
331	C₂×C₈	—	11	1	no	—
332	C₂×C₈	—	11	1	no	—
333	C₂×C₈	—	22	2	no	—
334	C₂×C₈	—	22	2	no	—
335	C₂×C₈	—	22	1	no	—
336	C₂×C₈	—	22	1	no	—
337	C₂×C₈	—	44	1	no	—
338	C₂×C₈	—	88	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	11	2	no	—
347	C₄⋊C₄	—	22	1	no	—
348	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	22	2	no	—
351	C₂²⋊C₄	—	22	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
354	C₄²	#4339	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
356	C₄²	C₂³×D₁₁	1	1	yes	characteristic
357	C₁₁	#18089	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	22	2	no	—
359	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	88	1	no	—
364	D₄	—	22	2	no	—
365	D₄	—	22	2	no	—
366	D₄	—	44	2	no	—
367	D₄	—	88	1	no	—
368	D₄	—	88	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	22	2	no	—
377	C₂×C₄	—	44	2	no	—
378	C₂×C₄	—	44	2	no	—
379	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
381	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂×#4339	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	11	2	no	—
390	C₈	—	22	1	no	—
391	C₈	—	22	1	no	—
392	C₈	—	22	1	no	—
393	C₈	—	44	2	no	—
394	C₈	—	44	1	no	—
395	C₈	—	44	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	44	2	no	—
400	C₂²	—	44	2	no	—
401	C₂²	—	44	2	no	—
402	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	44	2	no	—
409	C₄	#10622758	1	2	yes	—
410	C₄	D₁₁×#131	1	1	yes	characteristic
411	C₄	#10623281	1	1	yes	characteristic
412	C₄	#10623368	1	1	yes	characteristic
413	C₄	#10623368	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	88	2	no	—
416	C₂	#13077358	1	1	yes	characteristic
417	C₂	#13077475	1	1	yes	characteristic
418	C₂	C₂×#10622758	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2986	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#10623008	C₂²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2986	D₁₁
hypocenter	C₁₁	#18089
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2986

Complements

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

N	H ≅ G/N	type
3. #13067516	C₂	semidirect
4. #13067459	C₂	semidirect
5. #13067450	C₂	semidirect
6. #13067426	C₂	semidirect
7. #13067362	C₂	semidirect
8. #13067037	C₂	semidirect
10. #13066906	C₂	semidirect
11. C₁₁×#2986	C₂	semidirect
150. #2986	D₁₁	semidirect
357. C₁₁	#18089	semidirect

Maximal subgroups

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

subgroup	index
#13079176	2
#13077682	2
#13067516	2
#13067459	2
#13067450	2
#13067426	2
#13067362	2
#13067037	2
#13067032	2
#13066906	2
C₁₁×#2986	2
#18089	11