Subgroups — #14723016

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077572	C₂	1	1	yes	maximal, characteristic
2	#13077284	C₂	1	1	yes	maximal, characteristic
3	#13077281	C₂	1	1	yes	maximal, characteristic
4	#13067393	C₂	1	2	yes	maximal, complemented
5	#13067393	C₂	1	2	yes	maximal, complemented
6	#13067387	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067376	C₂	1	2	yes	maximal, complemented
8	#13067374	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067361	C₂	1	2	yes	maximal, complemented
10	C₂×#10622117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4339	C₂²	1	1	yes	characteristic
13	C₁₁×#431	C₂²	1	1	yes	characteristic
14	C₁₁×#423	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	#10622742	—	2	1	no	—
17	#10622735	—	2	1	no	—
18	#10622723	—	2	1	no	—
19	#10622714	—	2	1	no	—
20	#10622537	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	#10622453	—	2	2	no	—
24	#10622453	—	2	2	no	—
25	#10622448	C₂²	1	2	yes	—
26	#10622448	C₂²	1	2	yes	—
27	#10622447	C₄	1	1	yes	characteristic
28	#10622447	C₄	1	1	yes	characteristic
29	#10622446	C₂²	1	2	yes	—
30	#10622446	C₂²	1	2	yes	—
31	#10622443	C₄	1	1	yes	characteristic
32	#10622443	C₄	1	1	yes	characteristic
33	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
34	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
35	#10622298	C₂²	1	2	yes	—
36	C₄×C₈×D₁₁	C₂²	1	2	yes	—
37	C₁₁×#334	C₂²	1	2	yes	—
38	C₁₁×#334	C₂²	1	2	yes	—
39	#10622117	C₂²	1	1	yes	characteristic
40	#10622117	C₂²	1	1	yes	characteristic
41	#10622117	C₂²	1	1	yes	characteristic
42	#10622117	C₂²	1	1	yes	characteristic
43	#10622117	C₂²	1	2	yes	—
44	#10622117	C₂²	1	2	yes	—
45	#10622095	C₂²	1	2	yes	—
46	#10622095	C₂²	1	2	yes	—
47	C₂×#4339	D₄	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
52	C₄×C₂²⋊D₁₁	Q₈	1	2	yes	—
53	#66979	D₄	1	1	yes	characteristic
54	C₂×#4318	—	2	1	no	—
55	C₂²×C₁₁⋊C₈	—	2	1	no	—
56	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
60	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄₄	Q₈	1	1	yes	characteristic
62	#66925	D₄	1	2	yes	—
63	C₄²×D₁₁	C₂³	1	2	yes	—
64	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₂₂	Q₈	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	—	2	1	no	—
67	C₁₁×C₄⋊C₈	—	2	1	no	—
68	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
71	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₁	C₂³	1	2	yes	—
75	(C₂×D₁₁)⋊C₈	—	2	2	no	—
76	(C₂×D₁₁)⋊C₈	—	2	2	no	—
77	(C₂×D₁₁)⋊C₈	—	2	2	no	—
78	(C₂×D₁₁)⋊C₈	—	2	2	no	—
79	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
81	#66879	—	2	2	no	—
82	#66879	—	2	2	no	—
83	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
84	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
85	C₈×Dic₁₁	—	2	2	no	—
86	C₈×Dic₁₁	—	2	2	no	—
87	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
88	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
89	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
90	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
91	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
92	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
93	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
94	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
98	#17829	—	11	1	no	maximal, Sylow
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	2	yes	—
103	#4339	—	2	2	no	—
104	#4339	—	2	2	no	—
105	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₁₁	C₂×Q₈	1	2	yes	—
109	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
110	C₁₁×M₁₆	—	4	2	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	4	2	no	—
115	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
117	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
121	C₂²⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
122	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
123	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
124	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
125	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
126	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
127	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
128	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
129	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
130	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
131	#4318	—	4	2	no	—
132	C₂×C₁₁⋊C₈	—	2	2	no	—
133	C₂×C₁₁⋊C₈	—	2	1	no	—
134	C₂×C₁₁⋊C₈	—	2	2	no	—
135	C₂×C₁₁⋊C₈	—	2	1	no	—
136	C₂×C₁₁⋊C₈	—	4	1	no	—
137	C₂×C₁₁⋊C₈	—	4	2	no	—
138	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₁₁	—	2	4	no	—
143	C₈×D₁₁	—	4	2	no	—
144	C₈×#41	—	11	1	no	—
145	#2925	—	11	1	no	—
146	#2925	—	11	1	no	—
147	#1572	—	11	2	no	—
148	#1572	—	11	2	no	—
149	#1570	—	11	1	no	—
150	#1570	D₁₁	1	1	yes	characteristic, complemented
151	#1568	—	11	2	no	—
152	#1567	—	11	1	no	—
153	#1564	—	11	2	no	—
154	C₂×#335	—	11	1	no	—
155	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₁₁	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₁	—	2	1	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	4	1	no	—
160	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	#135	1	2	yes	—
164	C₂×C₄×C₁₁	#135	1	2	yes	—
165	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
168	C₂²⋊D₁₁	—	2	4	no	—
169	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
172	D₄₄	—	2	2	no	—
173	C₄×D₁₁	—	2	2	no	—
174	C₄×D₁₁	—	2	2	no	—
175	C₄×D₁₁	—	2	2	no	—
176	C₄×D₁₁	—	2	2	no	—
177	C₄×D₁₁	—	4	2	no	—
178	Dic₂₂	—	2	2	no	—
179	C₈×C₁₁	—	2	2	no	—
180	C₈×C₁₁	—	2	2	no	—
181	C₈×C₁₁	—	4	1	no	—
182	C₈×C₁₁	—	4	1	no	—
183	C₈×C₁₁	—	4	2	no	—
184	C₁₁⋊C₈	—	2	1	no	—
185	C₁₁⋊C₈	—	2	1	no	—
186	C₁₁⋊C₈	—	2	1	no	—
187	C₁₁⋊C₈	—	4	1	no	—
188	C₁₁⋊C₈	—	4	1	no	—
189	C₁₁⋊C₈	—	4	2	no	—
190	C₁₁⋊C₈	#131	1	2	yes	—
191	C₄×#41	—	11	1	no	—
192	C₈×Q₈	—	11	1	no	—
193	C₈×Q₈	—	11	1	no	—
194	C₈×D₄	—	11	1	no	—
195	C₈×D₄	—	11	1	no	—
196	C₈×D₄	—	11	2	no	—
197	C₈×D₄	—	11	2	no	—
198	#433	—	22	2	no	—
199	#433	—	22	2	no	—
200	#432	—	11	2	no	—
201	#432	—	11	2	no	—
202	#431	—	11	2	no	—
203	#431	—	11	2	no	—
204	#431	—	11	2	no	—
205	#431	C₂×D₁₁	1	1	yes	characteristic
206	#423	—	11	1	no	—
207	#423	C₂×D₁₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	11	1	no	—
209	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
210	#408	—	22	1	no	—
211	#408	—	22	1	no	—
212	#405	—	22	1	no	—
213	#405	—	22	1	no	—
214	C₂×C₄×C₈	—	11	1	no	—
215	C₂×C₄×C₈	—	11	2	no	—
216	#335	—	11	1	no	—
217	#335	—	11	1	no	—
218	#335	—	11	1	no	—
219	#335	—	11	1	no	—
220	#335	—	11	2	no	—
221	#335	—	11	2	no	—
222	#334	—	11	2	no	—
223	#334	—	11	2	no	—
224	#334	C₂×D₁₁	1	2	yes	—
225	#334	C₂×D₁₁	1	2	yes	—
226	C₂²×C₁₁	—	2	1	no	—
227	C₂²×C₁₁	—	2	1	no	—
228	C₂²×C₁₁	#427	1	2	yes	—
229	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
230	C₂×D₁₁	—	2	2	no	—
231	C₂×D₁₁	—	2	2	no	—
232	C₂×D₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	1	no	—
234	C₄×C₁₁	—	2	1	no	—
235	C₄×C₁₁	—	2	1	no	—
236	C₄×C₁₁	#427	1	2	yes	—
237	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
238	C₄×C₁₁	#568	1	1	yes	characteristic
239	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
240	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
241	Dic₁₁	—	2	2	no	—
242	Dic₁₁	—	2	2	no	—
243	Dic₁₁	—	2	2	no	—
244	C₂×#41	—	11	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	22	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	11	1	no	—
249	C₂²×C₈	—	11	1	no	—
250	C₂²×C₈	—	11	2	no	—
251	C₂²×C₈	—	11	2	no	—
252	C₂²×C₈	—	22	1	no	—
253	C₄×Q₈	—	11	1	no	—
254	C₄×Q₈	—	11	1	no	—
255	C₄×D₄	—	11	2	no	—
256	C₄×D₄	—	11	2	no	—
257	C₄×D₄	—	11	1	no	—
258	C₄×D₄	—	11	1	no	—
259	#117	—	11	1	no	—
260	#117	—	11	2	no	—
261	C₂×C₄²	—	11	2	no	—
262	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	11	2	no	—
266	C₄⋊C₈	—	11	2	no	—
267	C₄⋊C₈	—	11	1	no	—
268	C₄⋊C₈	—	11	1	no	—
269	C₄⋊C₈	—	11	2	no	—
270	C₄⋊C₈	—	22	1	no	—
271	C₄⋊C₈	—	22	1	no	—
272	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
273	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
274	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
275	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
276	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
277	C₂²⋊C₈	—	11	2	no	—
278	C₂²⋊C₈	—	11	2	no	—
279	C₂²⋊C₈	—	22	2	no	—
280	C₂²⋊C₈	—	22	2	no	—
281	C₂²⋊C₈	—	22	2	no	—
282	C₂²⋊C₈	—	22	2	no	—
283	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
284	#97	—	22	2	no	—
285	#97	—	22	2	no	—
286	C₄×C₈	—	11	2	no	—
287	C₄×C₈	—	11	2	no	—
288	C₄×C₈	—	11	1	no	—
289	C₄×C₈	—	11	1	no	—
290	C₄×C₈	—	11	1	no	—
291	C₄×C₈	—	11	1	no	—
292	C₄×C₈	—	22	2	no	—
293	C₄×C₈	—	22	2	no	—
294	C₄×C₈	C₂²×D₁₁	1	2	yes	—
295	C₂×C₁₁	—	2	2	no	—
296	C₂×C₁₁	#2906	1	1	yes	characteristic
297	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
298	C₂×C₁₁	#2916	1	1	yes	characteristic
299	D₁₁	—	4	2	no	—
300	#41	—	22	2	no	—
301	#41	—	22	2	no	—
302	C₂×Q₈	—	11	1	no	—
303	C₂×D₄	—	11	2	no	—
304	C₂×D₄	—	11	1	no	—
305	C₂²×C₄	—	11	2	no	—
306	C₂²×C₄	—	11	2	no	—
307	C₂²×C₄	—	11	2	no	—
308	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
310	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
311	M₁₆	—	4	2	no	—
312	M₁₆	—	44	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	11	1	no	—
318	C₂×C₈	—	11	1	no	—
319	C₂×C₈	—	11	1	no	—
320	C₂×C₈	—	11	1	no	—
321	C₂×C₈	—	22	4	no	—
322	C₂×C₈	—	22	2	no	—
323	C₂×C₈	—	22	1	no	—
324	C₂×C₈	—	22	2	no	—
325	C₂×C₈	—	22	1	no	—
326	C₂×C₈	—	44	2	no	—
327	C₂×C₈	—	44	1	no	—
328	C₂×C₈	—	44	2	no	—
329	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
330	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
331	C₄⋊C₄	—	11	2	no	—
332	C₄⋊C₄	—	11	2	no	—
333	C₄⋊C₄	—	11	1	no	—
334	C₄⋊C₄	—	11	1	no	—
335	C₂²⋊C₄	—	11	2	no	—
336	C₂²⋊C₄	—	11	2	no	—
337	C₂²⋊C₄	—	11	2	no	—
338	C₄²	—	11	2	no	—
339	C₄²	—	11	2	no	—
340	C₄²	—	11	2	no	—
341	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
342	C₄²	D₄×D₁₁	1	1	yes	characteristic
343	C₄²	Q₈×D₁₁	1	1	yes	characteristic
344	C₄²	C₂³×D₁₁	1	1	yes	characteristic
345	C₁₁	#17829	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	11	2	no	—
347	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
348	Q₈	—	22	2	no	—
349	D₄	—	22	4	no	—
350	D₄	—	22	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	11	2	no	—
355	C₂×C₄	—	11	2	no	—
356	C₂×C₄	—	11	2	no	—
357	C₂×C₄	—	22	2	no	—
358	C₂×C₄	—	22	2	no	—
359	C₂×C₄	—	22	2	no	—
360	C₂×C₄	—	22	2	no	—
361	C₂×C₄	—	44	2	no	—
362	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
365	C₂×C₄	#66969	1	2	yes	—
366	C₂×C₄	#66969	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	11	2	no	—
376	C₈	—	22	1	no	—
377	C₈	—	22	1	no	—
378	C₈	—	22	1	no	—
379	C₈	—	44	1	no	—
380	C₈	—	44	1	no	—
381	C₈	—	44	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	22	2	no	—
385	C₂²	—	22	2	no	—
386	C₂²	—	22	2	no	—
387	C₂²	#10622473	1	2	yes	—
388	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	22	2	no	—
393	C₄	—	22	2	no	—
394	C₄	—	22	2	no	—
395	C₄	#10622473	1	2	yes	—
396	C₄	D₁₁×#131	1	1	yes	characteristic
397	C₄	#10623281	1	1	yes	characteristic
398	C₄	C₂×#66969	1	1	yes	characteristic
399	C₄	C₂×#66969	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	44	2	no	—
402	C₂	#13077183	1	1	yes	characteristic
403	C₂	C₂×#10622473	1	1	yes	characteristic
404	C₂	#13077226	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×#1570	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×#4339	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1570	D₁₁
hypocenter	C₁₁	#17829
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #13067393	C₂	semidirect
5. #13067393	C₂	semidirect
6. #13067387	C₂	semidirect
7. #13067376	C₂	semidirect
8. #13067374	C₂	semidirect
9. #13067361	C₂	semidirect
10. C₂×#10622117	C₂	semidirect
11. C₁₁×#1570	C₂	semidirect
150. #1570	D₁₁	semidirect
345. C₁₁	#17829	semidirect

Maximal subgroups

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

subgroup	index
#13077572	2
#13077284	2
#13077281	2
#13067393	2
#13067387	2
#13067376	2
#13067374	2
#13067361	2
C₂×#10622117	2
C₁₁×#1570	2
#17829	11