Subgroups — #28554427

Order 15104.

798 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433063	C₂	1	1	yes	maximal, characteristic
2	#21433063	C₂	1	1	yes	maximal, characteristic
3	#21422399	C₂	1	2	yes	maximal, complemented
4	#21422393	C₂	1	2	yes	maximal, complemented
5	#21422388	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422385	C₂	1	2	yes	maximal, complemented
7	C₈×#11745664	C₂	1	2	yes	maximal, complemented
8	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16837124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#131×C₅₉	C₂	1	1	yes	maximal, characteristic
12	#16837533	C₄	1	2	yes	—
13	#16837533	C₄	1	2	yes	—
14	#16837480	C₄	1	2	yes	—
15	#16837480	C₄	1	2	yes	—
16	#16837474	C₄	1	4	yes	—
17	#16837474	C₄	1	4	yes	—
18	#16837455	C₂²	1	1	yes	characteristic
19	#16837455	C₂²	1	1	yes	characteristic
20	#16837455	C₂²	1	2	yes	—
21	#16837455	C₂²	1	2	yes	—
22	C₄×#11745664	C₂²	1	2	yes	—
23	C₄×#11745664	C₂²	1	2	yes	—
24	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
26	#16837124	C₂²	1	1	yes	characteristic
27	#16837124	C₂²	1	1	yes	characteristic
28	#16837124	C₂²	1	1	yes	characteristic
29	#16837124	C₂²	1	1	yes	characteristic
30	#16837124	C₂²	1	2	yes	—
31	#16837124	C₂²	1	2	yes	—
32	#16837123	C₂²	1	2	yes	—
33	#16837123	C₂²	1	2	yes	—
34	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
35	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
36	C₂×#131×C₅₉	C₄	1	2	yes	—
37	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#405	C₄	1	4	yes	—
39	C₅₉×#405	C₄	1	2	yes	—
40	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
44	C₂×#11745664	C₂×C₄	1	4	yes	—
45	C₂×#11745664	C₂×C₄	1	4	yes	—
46	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
49	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
50	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
51	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
52	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
53	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
54	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
55	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
56	#14273638	C₂×C₄	1	4	yes	—
57	#14273638	C₂×C₄	1	4	yes	—
58	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
59	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
63	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
64	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
67	#131×C₅₉	—	2	8	no	—
68	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
69	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
75	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
76	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
78	#117×C₅₉	C₂×C₄	1	2	yes	—
79	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
82	#97×C₅₉	C₂×C₄	1	4	yes	—
83	#97×C₅₉	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₅₉	C₂×C₄	1	4	yes	—
86	C₄×C₈×C₅₉	C₂³	1	2	yes	—
87	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	#41×C₅₉	—	2	4	no	—
90	C₂×Q₈×C₅₉	C₄²	1	1	yes	characteristic
91	C₂×D₄×C₅₉	C₄²	1	2	yes	—
92	C₂×D₄×C₅₉	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
99	M₁₆×C₅₉	—	2	8	no	—
100	M₁₆×C₅₉	M₁₆	1	8	yes	complemented
101	C₂×C₈×C₅₉	—	2	4	no	—
102	C₂×C₈×C₅₉	—	2	8	no	—
103	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
106	C₄⋊C₄×C₅₉	C₄²	1	2	yes	—
107	C₄⋊C₄×C₅₉	C₄²	1	2	yes	—
108	C₄⋊C₄×C₅₉	C₄²	1	1	yes	characteristic
109	C₄⋊C₄×C₅₉	C₄²	1	1	yes	characteristic
110	C₂²⋊C₄×C₅₉	C₄²	1	2	yes	—
111	C₂²⋊C₄×C₅₉	C₄²	1	2	yes	—
112	C₂²⋊C₄×C₅₉	C₄²	1	2	yes	—
113	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
116	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
117	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
119	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
120	#11745664	—	2	8	no	—
121	#11745664	—	4	4	no	—
122	C₂×C₅₉⋊C₈	—	2	4	no	—
123	C₂×C₅₉⋊C₈	—	4	2	no	—
124	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
128	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
129	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂³×C₅₉	C₂×C₄²	1	2	yes	—
131	C₂³×C₅₉	C₂×C₄²	1	1	yes	characteristic
132	Q₈×C₅₉	—	2	2	no	—
133	D₄×C₅₉	—	2	4	no	—
134	D₄×C₅₉	—	2	2	no	—
135	C₂×C₄×C₅₉	—	2	4	no	—
136	C₂×C₄×C₅₉	—	2	2	no	—
137	C₂×C₄×C₅₉	—	2	4	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	—	2	4	no	—
140	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
145	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₂×M₁₆	1	4	yes	—
147	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
150	C₈×C₅₉	—	2	2	no	—
151	C₈×C₅₉	—	2	2	no	—
152	C₈×C₅₉	C₂×M₁₆	1	8	yes	—
153	C₅₉⋊C₈	—	2	2	no	—
154	C₅₉⋊C₈	—	2	4	no	—
155	C₅₉⋊C₈	—	2	2	no	—
156	C₅₉⋊C₈	—	2	2	no	—
157	C₅₉⋊C₈	—	2	4	no	—
158	C₅₉⋊C₈	#131	1	4	yes	complemented
159	#17337	—	59	1	no	maximal, Sylow
160	C₂²×C₅₉	—	2	1	no	—
161	C₂²×C₅₉	—	2	1	no	—
162	C₂²×C₅₉	—	2	2	no	—
163	C₂²×C₅₉	—	2	2	no	—
164	C₂²×C₅₉	—	2	2	no	—
165	C₂²×C₅₉	C₄×M₁₆	1	2	yes	—
166	C₂²×C₅₉	C₂²×C₄²	1	1	yes	characteristic
167	C₄×C₅₉	—	2	2	no	—
168	C₄×C₅₉	—	2	1	no	—
169	C₄×C₅₉	—	2	2	no	—
170	C₄×C₅₉	—	2	1	no	—
171	C₄×C₅₉	—	2	2	no	—
172	C₄×C₅₉	C₄×M₁₆	1	2	yes	—
173	C₄×C₅₉	C₂²×M₁₆	1	2	yes	—
174	C₄×C₅₉	C₂×#131	1	2	yes	—
175	C₄×C₅₉	#568	1	2	yes	—
176	#2965	—	59	1	no	—
177	#2965	—	59	1	no	—
178	C₄×#131	D₅₉	1	1	yes	characteristic
179	#1455	—	59	2	no	—
180	#1453	—	59	2	no	—
181	#1452	—	59	1	no	—
182	#1451	—	59	2	no	—
183	C₈×M₁₆	—	59	1	no	—
184	C₈×M₁₆	—	59	1	no	—
185	C₈×M₁₆	—	59	2	no	—
186	C₂×#322	—	59	1	no	—
187	C₂×C₅₉	—	2	2	no	—
188	C₂×C₅₉	—	4	2	no	—
189	C₂×C₅₉	C₂×C₄×M₁₆	1	1	yes	characteristic
190	C₂×C₅₉	C₄×#131	1	1	yes	characteristic
191	C₂×C₅₉	#2875	1	1	yes	characteristic
192	C₂×#131	Dic₅₉	1	2	yes	—
193	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
194	#446	—	59	2	no	—
195	#446	—	59	2	no	—
196	#436	—	59	2	no	—
197	#436	—	59	2	no	—
198	#435	—	59	4	no	—
199	#435	—	59	4	no	—
200	#431	—	59	1	no	—
201	#431	—	59	1	no	—
202	#431	—	59	2	no	—
203	#431	—	59	2	no	—
204	#405	Dic₅₉	1	4	yes	—
205	#405	Dic₅₉	1	2	yes	—
206	C₄×M₁₆	—	59	2	no	—
207	C₄×M₁₆	—	59	2	no	—
208	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
209	C₄×M₁₆	C₂×D₅₉	1	2	yes	—
210	C₂×C₄×C₈	—	59	1	no	—
211	C₂×C₄×C₈	—	59	1	no	—
212	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂×D₅₉	1	2	yes	—
214	#322	—	59	2	no	—
215	#322	—	59	2	no	—
216	#322	—	59	1	no	—
217	#322	—	59	1	no	—
218	#322	—	59	1	no	—
219	#322	—	59	1	no	—
220	#322	—	59	2	no	—
221	#322	—	59	2	no	—
222	C₈²	—	59	2	no	—
223	C₈²	—	59	2	no	—
224	C₅₉	#17337	1	1	yes	characteristic, complemented, Sylow
225	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
226	#131	—	2	8	no	—
227	C₂×M₁₆	—	59	4	no	—
228	C₂×M₁₆	—	59	4	no	—
229	C₂×M₁₆	C₂×Dic₅₉	1	4	yes	—
230	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
231	C₂²×C₈	—	59	2	no	—
232	C₂²×C₈	—	59	2	no	—
233	C₂²×C₈	C₂×Dic₅₉	1	2	yes	—
234	C₂²×C₈	C₂×Dic₅₉	1	4	yes	—
235	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
236	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
237	C₄×D₄	C₄×D₅₉	1	2	yes	—
238	C₄×D₄	C₄×D₅₉	1	2	yes	—
239	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
240	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
241	#117	C₂×Dic₅₉	1	2	yes	—
242	#117	C₂×Dic₅₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
245	C₄⋊C₈	—	59	4	no	—
246	C₄⋊C₈	—	59	4	no	—
247	C₄⋊C₈	—	59	2	no	—
248	C₄⋊C₈	—	59	2	no	—
249	C₂²⋊C₈	—	59	2	no	—
250	C₂²⋊C₈	—	59	2	no	—
251	C₂²⋊C₈	—	59	4	no	—
252	C₂²⋊C₈	—	59	4	no	—
253	#97	—	59	4	no	—
254	#97	—	59	4	no	—
255	#97	C₂×Dic₅₉	1	4	yes	—
256	#97	C₂×Dic₅₉	1	2	yes	—
257	C₄×C₈	—	59	2	no	—
258	C₄×C₈	—	59	2	no	—
259	C₄×C₈	—	59	1	no	—
260	C₄×C₈	—	59	1	no	—
261	C₄×C₈	—	59	2	no	—
262	C₄×C₈	—	59	2	no	—
263	C₄×C₈	—	59	1	no	—
264	C₄×C₈	—	59	1	no	—
265	C₄×C₈	C₂×Dic₅₉	1	2	yes	—
266	C₄×C₈	C₂×Dic₅₉	1	4	yes	—
267	C₄×C₈	C₂²×D₅₉	1	2	yes	—
268	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
269	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
270	#41	—	2	4	no	—
271	C₂×Q₈	C₄×Dic₅₉	1	1	yes	characteristic
272	C₂×D₄	C₄×Dic₅₉	1	2	yes	—
273	C₂×D₄	C₄×Dic₅₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅₉	1	2	yes	—
277	C₂²×C₄	C₂×C₄×D₅₉	1	2	yes	—
278	C₂²×C₄	C₂²×Dic₅₉	1	2	yes	—
279	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
280	M₁₆	—	2	8	no	—
281	M₁₆	—	118	8	no	—
282	M₁₆	—	236	4	no	—
283	M₁₆	#11745664	1	8	yes	complemented
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	—	59	2	no	—
287	C₂×C₈	—	59	2	no	—
288	C₂×C₈	—	59	2	no	—
289	C₂×C₈	—	59	2	no	—
290	C₂×C₈	—	59	4	no	—
291	C₂×C₈	—	59	4	no	—
292	C₂×C₈	—	118	4	no	—
293	C₂×C₈	—	236	2	no	—
294	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
295	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
296	C₂×C₈	C₂²×Dic₅₉	1	4	yes	—
297	C₄⋊C₄	C₄×Dic₅₉	1	2	yes	—
298	C₄⋊C₄	C₄×Dic₅₉	1	2	yes	—
299	C₄⋊C₄	C₄×Dic₅₉	1	1	yes	characteristic
300	C₄⋊C₄	C₄×Dic₅₉	1	1	yes	characteristic
301	C₂²⋊C₄	C₄×Dic₅₉	1	2	yes	—
302	C₂²⋊C₄	C₄×Dic₅₉	1	2	yes	—
303	C₂²⋊C₄	C₄×Dic₅₉	1	2	yes	—
304	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
305	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₅₉	1	2	yes	—
307	C₄²	C₂×C₄×D₅₉	1	2	yes	—
308	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
309	C₄²	C₂²×Dic₅₉	1	2	yes	—
310	C₄²	C₂³×D₅₉	1	1	yes	characteristic
311	C₂³	C₂×C₄×Dic₅₉	1	2	yes	—
312	C₂³	C₂×C₄×Dic₅₉	1	1	yes	characteristic
313	Q₈	—	2	2	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
322	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
323	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
324	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
326	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
327	C₂×C₄	C₂×#11745664	1	4	yes	—
328	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
330	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
331	C₈	—	2	2	no	—
332	C₈	—	2	2	no	—
333	C₈	—	59	4	no	—
334	C₈	—	118	2	no	—
335	C₈	—	118	4	no	—
336	C₈	—	118	2	no	—
337	C₈	—	118	2	no	—
338	C₈	—	118	4	no	—
339	C₈	C₂×#11745664	1	8	yes	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	C₄×#11745664	1	2	yes	—
346	C₂²	C₂²×C₄×Dic₅₉	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	2	no	—
352	C₄	C₄×#11745664	1	2	yes	—
353	C₄	C₂²×#11745664	1	2	yes	—
354	C₄	#131×D₅₉	1	2	yes	—
355	C₄	#16838167	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	4	2	no	—
358	C₂	C₂×C₄×#11745664	1	1	yes	characteristic
359	C₂	#131×Dic₅₉	1	1	yes	characteristic
360	C₂	#21432522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂²×C₄²
Fitting	C₄×#131×C₅₉	C₂
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₄×#131	D₅₉
hypocenter	C₅₉	#17337
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄² ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
3. #21422399	C₂	semidirect
4. #21422393	C₂	semidirect
5. #21422388	C₂	semidirect
6. #21422385	C₂	semidirect
7. C₈×#11745664	C₂	semidirect
8. M₁₆×C₅₉⋊C₈	C₂	semidirect
9. M₁₆×C₅₉⋊C₈	C₂	semidirect
10. C₂×#16837124	C₂	semidirect
100. M₁₆×C₅₉	M₁₆	semidirect
158. C₅₉⋊C₈	#131	semidirect
224. C₅₉	#17337	semidirect
283. M₁₆	#11745664	semidirect

Maximal subgroups

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

subgroup	index
#21433063	2
#21422399	2
#21422393	2
#21422388	2
#21422385	2
C₈×#11745664	2
M₁₆×C₅₉⋊C₈	2
C₂×#16837124	2
C₄×#131×C₅₉	2
#17337	59