Subgroups — #28560464

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434678	C₂	1	1	yes	maximal, characteristic
2	#21433043	C₂	1	1	yes	maximal, characteristic
3	#21422991	C₂	1	2	yes	maximal, complemented
4	#21422946	C₂	1	2	yes	maximal, complemented
5	#21422944	C₂	1	2	yes	maximal, complemented
6	C₈×#11745672	C₂	1	2	yes	maximal, complemented
7	C₂×#16837154	C₂	1	1	yes	maximal, characteristic
8	#21422499	C₂	1	1	yes	maximal, characteristic
9	#21422498	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#2962	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837805	C₄	1	1	yes	characteristic
14	#16837781	C₄	1	1	yes	characteristic
15	#16837754	C₄	1	1	yes	characteristic
16	#16837752	C₄	1	1	yes	characteristic
17	#16837641	C₄	1	2	yes	—
18	#16837641	C₄	1	2	yes	—
19	#16837532	C₂²	1	2	yes	—
20	#16837530	—	2	2	no	—
21	C₈×Dic₁₁₈	C₂²	1	2	yes	—
22	C₄×#11745672	C₂²	1	2	yes	—
23	C₄×#11745672	C₂²	1	2	yes	—
24	#16837455	C₂²	1	1	yes	characteristic
25	#16837430	—	2	1	no	—
26	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#16837360	—	2	1	no	—
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	#16837154	C₂²	1	1	yes	characteristic
30	#16837154	C₂²	1	1	yes	characteristic
31	#16837154	C₂²	1	1	yes	characteristic
32	#16837154	C₂²	1	1	yes	characteristic
33	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
34	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
35	#16837132	C₂²	1	2	yes	—
36	#16837132	C₂²	1	2	yes	—
37	#16837123	C₂²	1	2	yes	—
38	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
39	C₅₉×#533	C₂²	1	1	yes	characteristic
40	C₅₉×#446	—	2	2	no	—
41	C₅₉×#446	C₂²	1	2	yes	—
42	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
43	C₅₉×#424	—	2	1	no	—
44	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#405	—	2	1	no	—
46	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#11745672	C₂×C₄	1	2	yes	—
48	C₂×#11745672	C₂×C₄	1	2	yes	—
49	C₂²×C₅₉⋊C₈	—	2	1	no	—
50	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	#14273727	C₂×C₄	1	1	yes	characteristic
53	#14273727	C₂×C₄	1	1	yes	characteristic
54	#14273719	—	2	1	no	—
55	#14273706	—	2	1	no	—
56	#14273706	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₁₈	—	2	1	no	—
58	C₄×Dic₁₁₈	C₂³	1	2	yes	—
59	#14273686	—	2	1	no	—
60	#14273660	C₂×C₄	1	2	yes	—
61	#14273660	C₂×C₄	1	2	yes	—
62	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
66	Dic₅₉⋊C₈	—	2	2	no	—
67	Dic₅₉⋊C₈	—	2	2	no	—
68	#14273651	C₂×C₄	1	2	yes	—
69	#14273651	C₂×C₄	1	2	yes	—
70	#14273650	C₂×C₄	1	2	yes	—
71	#14273650	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
73	#14273637	—	2	2	no	—
74	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
77	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₅₉	—	2	2	no	—
80	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₅₉	—	2	1	no	—
83	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
85	#125×C₅₉	—	2	1	no	—
86	C₂²⋊Q₈×C₅₉	—	2	1	no	—
87	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
88	C₄×Q₈×C₅₉	—	2	1	no	—
89	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
90	#117×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₉	—	2	2	no	—
93	C₄⋊C₈×C₅₉	—	2	2	no	—
94	C₄⋊C₈×C₅₉	—	2	1	no	—
95	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
97	#97×C₅₉	—	2	2	no	—
98	#97×C₅₉	D₄	1	2	yes	—
99	C₄×C₈×C₅₉	—	2	2	no	—
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	C₂×Q₈×C₅₉	—	2	1	no	—
102	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
106	C₂×Dic₁₁₈	—	2	1	no	—
107	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
108	M₁₆×C₅₉	—	2	2	no	—
109	M₁₆×C₅₉	Q₁₆	1	4	yes	complemented
110	C₂×C₈×C₅₉	—	2	1	no	—
111	C₂×C₈×C₅₉	—	2	1	no	—
112	C₂×C₈×C₅₉	—	4	2	no	—
113	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₅₉	—	2	1	no	—
116	C₄⋊C₄×C₅₉	—	2	1	no	—
117	C₄⋊C₄×C₅₉	—	2	1	no	—
118	C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₄⋊C₄×C₅₉	—	2	2	no	—
120	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₅₉	—	2	2	no	—
122	C₄²×C₅₉	—	2	2	no	—
123	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅₉	#41	1	1	yes	characteristic
126	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
127	C₂²⋊Dic₅₉	—	2	2	no	—
128	#11745672	—	2	4	no	—
129	#11745672	—	4	2	no	—
130	C₄⋊Dic₅₉	—	2	1	no	—
131	C₄⋊Dic₅₉	—	2	1	no	—
132	C₄⋊Dic₅₉	—	2	1	no	—
133	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
134	Dic₅₉⋊C₄	—	2	2	no	—
135	Dic₅₉⋊C₄	—	2	2	no	—
136	C₄×Dic₅₉	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	2	no	—
138	C₂×C₅₉⋊C₈	—	2	1	no	—
139	C₂×C₅₉⋊C₈	—	2	1	no	—
140	C₂×C₅₉⋊C₈	—	2	2	no	—
141	C₂×C₅₉⋊C₈	—	4	1	no	—
142	C₂×C₅₉⋊C₈	—	4	2	no	—
143	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
148	Q₈×C₅₉	—	2	2	no	—
149	Q₈×C₅₉	—	2	2	no	—
150	Q₈×C₅₉	—	8	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₅₉	#135	1	2	yes	—
161	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₅₉	—	2	2	no	—
165	C₂×Dic₅₉	—	2	2	no	—
166	Dic₁₁₈	—	2	2	no	—
167	Dic₁₁₈	—	2	2	no	—
168	Dic₁₁₈	—	8	1	no	—
169	C₈×C₅₉	—	2	2	no	—
170	C₈×C₅₉	—	4	1	no	—
171	C₈×C₅₉	—	4	1	no	—
172	C₈×C₅₉	C₂×Q₁₆	1	4	yes	—
173	C₅₉⋊C₈	—	2	1	no	—
174	C₅₉⋊C₈	—	2	1	no	—
175	C₅₉⋊C₈	—	2	1	no	—
176	C₅₉⋊C₈	—	4	2	no	—
177	C₅₉⋊C₈	—	4	1	no	—
178	C₅₉⋊C₈	—	4	1	no	—
179	C₅₉⋊C₈	#131	1	2	yes	—
180	#18068	—	59	1	no	maximal, Sylow
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	C₄×Q₁₆	1	2	yes	—
184	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	4	2	no	—
189	C₄×C₅₉	—	4	2	no	—
190	C₄×C₅₉	C₄×Q₁₆	1	2	yes	—
191	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
192	C₄×C₅₉	#568	1	1	yes	characteristic
193	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
194	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
195	Dic₅₉	—	4	2	no	—
196	Dic₅₉	—	4	2	no	—
197	#3170	—	59	1	no	—
198	#2962	—	59	1	no	—
199	#2962	D₅₉	1	1	yes	characteristic
200	#1591	—	59	2	no	—
201	#1584	—	59	2	no	—
202	#1584	—	59	2	no	—
203	C₈×Q₁₆	—	59	2	no	—
204	C₂×#335	—	59	1	no	—
205	#1481	—	59	1	no	—
206	#1481	—	59	1	no	—
207	C₈×M₁₆	—	59	1	no	—
208	C₂×C₅₉	—	2	2	no	—
209	C₂×C₅₉	#2935	1	1	yes	characteristic
210	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
211	C₂×C₅₉	#2957	1	1	yes	characteristic
212	#533	—	59	1	no	—
213	#533	C₂×D₅₉	1	1	yes	characteristic
214	#500	—	59	1	no	—
215	#494	—	59	1	no	—
216	#487	—	59	1	no	—
217	#487	—	59	1	no	—
218	#467	—	59	2	no	—
219	#467	—	59	2	no	—
220	#446	—	2	2	no	—
221	#446	—	59	2	no	—
222	#446	—	118	2	no	—
223	#446	C₂×D₅₉	1	2	yes	—
224	C₈×Q₈	—	59	2	no	—
225	C₈×Q₈	C₂×D₅₉	1	2	yes	—
226	C₄×Q₁₆	—	59	2	no	—
227	C₄×Q₁₆	—	59	2	no	—
228	#431	—	59	1	no	—
229	#424	—	2	1	no	—
230	#424	—	118	1	no	—
231	C₂×C₄⋊C₈	—	59	1	no	—
232	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
233	#405	—	2	1	no	—
234	#405	—	118	1	no	—
235	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
236	C₂×C₄×C₈	—	59	1	no	—
237	#335	—	59	1	no	—
238	#335	—	59	1	no	—
239	#335	—	59	1	no	—
240	#335	—	59	1	no	—
241	Q₈⋊C₈	—	59	2	no	—
242	Q₈⋊C₈	—	59	2	no	—
243	Q₈⋊C₈	—	59	2	no	—
244	Q₈⋊C₈	—	59	2	no	—
245	#322	—	59	2	no	—
246	C₈²	—	59	2	no	—
247	C₅₉	#18068	1	1	yes	characteristic, complemented, Sylow
248	C₂×Q₁₆	—	59	2	no	—
249	C₂×Q₁₆	—	59	2	no	—
250	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
251	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	59	1	no	—
254	C₂²×C₈	—	59	1	no	—
255	C₂²×C₈	—	118	1	no	—
256	C₄⋊Q₈	—	59	1	no	—
257	C₄⋊Q₈	—	59	1	no	—
258	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
259	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#125	—	118	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	59	2	no	—
264	C₂²⋊Q₈	—	118	1	no	—
265	C₂²⋊Q₈	C₄×D₅₉	1	2	yes	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	59	2	no	—
268	C₄×Q₈	—	118	1	no	—
269	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
270	#117	—	2	1	no	—
271	#117	—	118	1	no	—
272	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
273	#107	—	59	2	no	—
274	#107	—	59	2	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	59	1	no	—
279	C₄⋊C₈	—	59	1	no	—
280	C₄⋊C₈	—	118	2	no	—
281	C₄⋊C₈	—	118	2	no	—
282	C₄⋊C₈	—	118	1	no	—
283	C₄⋊C₈	—	118	1	no	—
284	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
285	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
286	#103	—	59	2	no	—
287	#103	—	59	2	no	—
288	#103	—	59	2	no	—
289	#103	—	59	2	no	—
290	C₂²⋊C₈	—	118	1	no	—
291	#97	—	2	2	no	—
292	#97	—	118	2	no	—
293	#97	C₂²⋊D₅₉	1	2	yes	—
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	—	59	1	no	—
296	C₄×C₈	—	59	1	no	—
297	C₄×C₈	—	59	1	no	—
298	C₄×C₈	—	59	1	no	—
299	C₄×C₈	—	59	2	no	—
300	C₄×C₈	—	118	2	no	—
301	C₄×C₈	C₂²×D₅₉	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	59	2	no	—
304	C₂×Q₈	—	118	1	no	—
305	C₂×Q₈	C₂×C₄×D₅₉	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
307	C₂²×C₄	#11745685	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
309	Q₁₆	—	118	4	no	—
310	Q₁₆	—	236	2	no	—
311	M₁₆	—	2	2	no	—
312	M₁₆	#11745672	1	4	yes	complemented
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	59	1	no	—
317	C₂×C₈	—	59	1	no	—
318	C₂×C₈	—	59	1	no	—
319	C₂×C₈	—	59	1	no	—
320	C₂×C₈	—	118	2	no	—
321	C₂×C₈	—	118	1	no	—
322	C₂×C₈	—	118	1	no	—
323	C₂×C₈	—	118	2	no	—
324	C₂×C₈	—	236	1	no	—
325	C₂×C₈	—	236	2	no	—
326	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
327	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	59	2	no	—
334	C₄⋊C₄	—	118	1	no	—
335	C₄⋊C₄	—	118	1	no	—
336	C₄⋊C₄	—	118	2	no	—
337	C₄⋊C₄	—	118	1	no	—
338	C₄⋊C₄	—	118	2	no	—
339	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	118	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	118	2	no	—
344	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
345	C₄²	#11745685	1	1	yes	characteristic
346	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
347	C₄²	C₂³×D₅₉	1	1	yes	characteristic
348	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	8	1	no	—
352	Q₈	—	118	2	no	—
353	Q₈	—	118	2	no	—
354	Q₈	—	472	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	118	2	no	—
361	C₂×C₄	—	118	2	no	—
362	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
363	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#11745672	1	2	yes	—
366	C₂×C₄	#14273747	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	59	2	no	—
374	C₈	—	118	1	no	—
375	C₈	—	118	1	no	—
376	C₈	—	118	1	no	—
377	C₈	—	236	2	no	—
378	C₈	—	236	1	no	—
379	C₈	—	236	1	no	—
380	C₈	C₂×#11745672	1	4	yes	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	C₄×#11745672	1	2	yes	—
384	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	236	2	no	—
391	C₄	—	236	2	no	—
392	C₄	C₄×#11745672	1	2	yes	—
393	C₄	#131×D₅₉	1	1	yes	characteristic
394	C₄	#16838167	1	1	yes	characteristic
395	C₄	C₂²×#11745672	1	1	yes	characteristic
396	C₄	C₂×#14273747	1	1	yes	characteristic
397	C₂	—	2	2	no	—
398	C₂	#21432838	1	1	yes	characteristic
399	C₂	C₂×C₄×#11745672	1	1	yes	characteristic
400	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2962	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂³×C₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2962	D₅₉
hypocenter	C₅₉	#18068
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #21422991	C₂	semidirect
4. #21422946	C₂	semidirect
5. #21422944	C₂	semidirect
6. C₈×#11745672	C₂	semidirect
109. M₁₆×C₅₉	Q₁₆	semidirect
247. C₅₉	#18068	semidirect
312. M₁₆	#11745672	semidirect

Maximal subgroups

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

subgroup	index
#21434678	2
#21433043	2
#21422991	2
#21422946	2
#21422944	2
C₈×#11745672	2
C₂×#16837154	2
#21422499	2
#21422498	2
M₁₆×C₅₉⋊C₈	2
C₅₉×#2962	2
#18068	59