Subgroups — #28745479

Order 15104.

668 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21437234	C₂	1	1	yes	maximal, characteristic, complemented
2	#21435893	C₂	1	2	yes	maximal, complemented
3	#21426344	C₂	1	1	yes	maximal, characteristic, complemented
4	#21426216	C₂	1	1	yes	maximal, characteristic, complemented
5	#21426213	C₂	1	1	yes	maximal, characteristic, complemented
6	#21426170	C₂	1	2	yes	maximal, complemented
7	#21426053	C₂	1	2	yes	maximal, complemented
8	#21426050	C₂	1	2	yes	maximal, complemented
9	#21425977	C₂	1	1	yes	maximal, characteristic, complemented
10	#21425931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3415	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838205	—	2	2	no	—
13	#16838204	C₂²	1	2	yes	complemented
14	#16837839	—	2	2	no	—
15	#16837837	C₂²	1	2	yes	complemented
16	#16837835	—	2	1	no	—
17	C₂×D₉₄₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×#14273668	C₂²	1	2	yes	complemented
19	D₁₆×D₅₉	—	2	1	no	—
20	#16837818	C₂²	1	1	yes	characteristic, complemented
21	#16837777	C₂²	1	2	yes	complemented
22	#16837672	C₂²	1	2	yes	complemented
23	#16837670	—	2	2	no	—
24	#16837669	C₂²	1	2	yes	complemented
25	#16837570	—	2	2	no	—
26	#16837568	—	2	2	no	—
27	#16837519	C₂²	1	2	yes	complemented
28	#16837517	C₂²	1	1	yes	characteristic
29	#16837232	C₂²	1	1	yes	characteristic, complemented
30	#16837222	C₂²	1	1	yes	characteristic, complemented
31	#16837216	C₂²	1	2	yes	complemented
32	#16837215	C₂²	1	2	yes	complemented
33	#16837209	C₂²	1	2	yes	complemented
34	#16837187	C₂²	1	1	yes	characteristic, complemented
35	#16837186	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
37	C₅₉×#576	C₂²	1	2	yes	complemented
38	C₅₉×#509	—	2	2	no	—
39	C₅₉×#509	C₂²	1	2	yes	complemented
40	C₅₉×#508	—	2	1	no	—
41	C₅₉×#508	C₂²	1	1	yes	characteristic
42	C₂×D₁₆×C₅₉	—	2	1	no	—
43	C₂×D₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
44	C₅₉×#504	C₂²	1	1	yes	characteristic, complemented
45	#14273773	—	2	2	no	—
46	#14273754	—	4	2	no	—
47	#14273753	—	2	2	no	—
48	#14273753	—	4	2	no	—
49	#14273752	—	2	2	no	—
50	#14273752	—	2	2	no	—
51	#14273752	—	4	2	no	—
52	#14273750	—	2	2	no	—
53	#14273747	—	4	2	no	—
54	#14273747	D₄	1	1	yes	characteristic
55	C₂×D₄₇₂	C₂³	1	2	yes	—
56	C₂×#11745669	—	2	2	no	—
57	C₂×#11745669	—	4	2	no	—
58	D₈×D₅₉	—	2	2	no	—
59	#14273734	—	2	2	no	—
60	#14273733	C₂³	1	1	yes	characteristic
61	#14273723	—	2	2	no	—
62	#14273670	—	2	2	no	—
63	D₉₄₄	—	2	1	no	—
64	D₉₄₄	—	2	1	no	—
65	#14273668	—	2	2	no	—
66	#14273668	—	4	2	no	—
67	#14273667	C₂³	1	1	yes	characteristic
68	#14273666	—	2	1	no	—
69	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₁₆×D₅₉	—	2	1	no	—
71	#14273663	C₂³	1	2	yes	—
72	#14273662	D₄	1	1	yes	characteristic
73	#14273654	—	2	2	no	—
74	#14273654	D₄	1	1	yes	characteristic
75	#14273653	D₄	1	1	yes	characteristic
76	#14273644	—	2	2	no	—
77	#14273643	—	2	2	no	—
78	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
79	H(5,𝔽₂)×C₅₉	—	2	2	no	—
80	AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
81	AGL(1,ℤ/8)×C₅₉	—	4	2	no	—
82	#135×C₅₉	—	2	2	no	—
83	#135×C₅₉	C₂³	1	2	yes	—
84	C₂×D₈×C₅₉	—	2	2	no	—
85	C₂×D₈×C₅₉	C₂³	1	2	yes	—
86	#131×C₅₉	C₂³	1	1	yes	characteristic
87	Q₃₂×C₅₉	D₄	1	1	yes	characteristic, complemented
88	SD₃₂×C₅₉	—	2	2	no	—
89	SD₃₂×C₅₉	D₄	1	2	yes	complemented
90	D₁₆×C₅₉	—	2	2	no	—
91	D₁₆×C₅₉	—	2	1	no	—
92	D₁₆×C₅₉	—	2	1	no	—
93	D₁₆×C₅₉	D₄	1	1	yes	characteristic, complemented
94	M₃₂×C₅₉	—	2	1	no	—
95	M₃₂×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₅₉	—	2	1	no	—
97	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
98	#41×C₅₉	—	2	2	no	—
99	#41×C₅₉	—	4	2	no	—
100	#41×C₅₉	—	4	2	no	—
101	#41×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₅₉	—	2	2	no	—
103	C₂×D₄×C₅₉	—	4	2	no	—
104	C₂×D₄×C₅₉	—	4	2	no	—
105	C₂×D₄×C₅₉	—	8	2	no	—
106	C₂×C₂²⋊D₅₉	—	8	2	no	—
107	#11745689	—	4	2	no	—
108	D₄×D₅₉	—	4	2	no	—
109	D₄×D₅₉	—	8	2	no	—
110	#11745685	—	4	2	no	—
111	#11745685	C₂×D₄	1	1	yes	characteristic
112	C₂×D₂₃₆	—	2	2	no	—
113	C₂×D₂₃₆	—	4	2	no	—
114	Q₁₆×C₅₉	C₂×D₄	1	2	yes	—
115	SD₁₆×C₅₉	—	2	2	no	—
116	SD₁₆×C₅₉	—	4	2	no	—
117	D₈×C₅₉	—	2	2	no	—
118	D₈×C₅₉	—	2	2	no	—
119	D₈×C₅₉	—	4	2	no	—
120	D₈×C₅₉	C₂×D₄	1	2	yes	—
121	M₁₆×C₅₉	—	2	1	no	—
122	M₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	—	2	1	no	—
124	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
125	#11745672	D₈	1	1	yes	characteristic
126	#11745671	—	4	2	no	—
127	#11745671	—	4	2	no	—
128	#11745671	D₈	1	1	yes	characteristic
129	#11745670	—	4	2	no	—
130	#11745670	D₈	1	1	yes	characteristic
131	#11745669	—	4	2	no	—
132	#11745669	—	4	2	no	—
133	#11745669	—	4	2	no	—
134	#11745669	—	4	2	no	—
135	#11745669	—	4	2	no	—
136	#11745669	D₈	1	1	yes	characteristic
137	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
138	#11745664	—	2	2	no	—
139	#11745664	—	4	2	no	—
140	#11745664	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅₉⋊C₈	—	4	2	no	—
142	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
143	D₄₇₂	—	2	2	no	—
144	D₄₇₂	—	2	2	no	—
145	#11745659	—	2	1	no	—
146	C₈×D₅₉	—	2	1	no	—
147	C₁₆×C₅₉	—	2	1	no	—
148	C₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
149	C₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₅₉⋊C₁₆	—	2	1	no	—
151	C₅₉⋊C₁₆	—	2	1	no	—
152	C₂³×C₅₉	—	4	2	no	—
153	C₂³×C₅₉	—	8	2	no	—
154	C₂²×D₅₉	—	4	2	no	—
155	C₂²×D₅₉	—	8	2	no	—
156	Q₈×C₅₉	—	2	2	no	—
157	Q₈×C₅₉	C₂×D₈	1	1	yes	characteristic
158	D₄×C₅₉	—	2	1	no	—
159	D₄×C₅₉	—	2	2	no	—
160	D₄×C₅₉	—	4	2	no	—
161	D₄×C₅₉	—	4	2	no	—
162	D₄×C₅₉	—	4	2	no	—
163	D₄×C₅₉	—	8	2	no	—
164	D₄×C₅₉	—	8	2	no	—
165	D₄×C₅₉	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	—	8	2	no	—
169	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
170	C₂²⋊D₅₉	—	2	1	no	—
171	C₂²⋊D₅₉	—	8	2	no	—
172	C₂²⋊D₅₉	—	16	4	no	—
173	C₂×Dic₅₉	—	2	1	no	—
174	D₂₃₆	—	4	2	no	—
175	D₂₃₆	—	4	2	no	—
176	D₂₃₆	—	8	2	no	—
177	D₂₃₆	C₂×D₈	1	1	yes	characteristic
178	C₄×D₅₉	—	2	1	no	—
179	C₄×D₅₉	—	8	2	no	—
180	Dic₁₁₈	C₂×D₈	1	1	yes	characteristic
181	C₈×C₅₉	—	2	1	no	—
182	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₅₉⋊C₈	—	2	1	no	—
185	C₅₉⋊C₈	—	4	2	no	—
186	C₅₉⋊C₈	C₂×D₈	1	1	yes	characteristic
187	C₅₉⋊C₈	C₂×D₈	1	1	yes	characteristic
188	#33858	—	59	1	no	maximal, Sylow
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	—	4	2	no	—
191	C₂²×C₅₉	—	8	2	no	—
192	C₂²×C₅₉	—	16	2	no	—
193	C₂²×C₅₉	—	32	2	no	—
194	C₂²×C₅₉	#576	1	1	yes	characteristic
195	C₂×D₅₉	—	2	1	no	—
196	C₂×D₅₉	—	8	2	no	—
197	C₂×D₅₉	—	16	2	no	—
198	C₂×D₅₉	—	32	2	no	—
199	C₄×C₅₉	—	2	1	no	—
200	C₄×C₅₉	—	4	2	no	—
201	C₄×C₅₉	D₄²	1	1	yes	characteristic
202	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
203	Dic₅₉	—	2	2	no	—
204	Dic₅₉	—	2	1	no	—
205	#3415	—	59	1	no	—
206	#3415	D₅₉	1	1	yes	characteristic, complemented
207	#3292	—	59	2	no	—
208	#2246	—	59	1	no	—
209	#2221	—	59	1	no	—
210	#2221	—	59	1	no	—
211	#2213	—	59	2	no	—
212	#2192	—	59	2	no	—
213	#2192	—	59	2	no	—
214	#2178	—	59	1	no	—
215	#2170	—	59	1	no	—
216	C₂×C₅₉	—	2	1	no	—
217	C₂×C₅₉	—	4	1	no	—
218	C₂×C₅₉	—	8	2	no	—
219	C₂×C₅₉	—	16	2	no	—
220	C₂×C₅₉	D₄×D₈	1	1	yes	characteristic
221	D₅₉	—	4	1	no	—
222	D₅₉	—	16	2	no	—
223	#576	—	59	2	no	—
224	#576	—	118	2	no	—
225	#576	C₂×D₅₉	1	2	yes	complemented
226	#509	—	2	2	no	—
227	#509	—	59	2	no	—
228	#509	—	118	2	no	—
229	#509	C₂×D₅₉	1	2	yes	complemented
230	#508	—	2	1	no	—
231	#508	—	118	1	no	—
232	#508	C₂×D₅₉	1	1	yes	characteristic
233	C₂×D₁₆	—	2	1	no	—
234	C₂×D₁₆	—	59	2	no	—
235	C₂×D₁₆	—	59	1	no	—
236	C₂×D₁₆	—	118	1	no	—
237	C₂×D₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
238	#504	—	59	1	no	—
239	#504	C₂×D₅₉	1	1	yes	characteristic, complemented
240	#493	—	59	2	no	—
241	#472	—	59	2	no	—
242	#472	—	59	2	no	—
243	#472	—	118	2	no	—
244	#453	—	118	2	no	—
245	#453	—	118	2	no	—
246	#443	—	59	1	no	—
247	#443	—	59	2	no	—
248	#368	—	59	1	no	—
249	#364	—	59	1	no	—
250	#361	—	59	2	no	—
251	#361	—	59	2	no	—
252	#359	—	59	2	no	—
253	#350	—	59	1	no	—
254	#350	—	59	1	no	—
255	C₄×C₁₆	—	59	1	no	—
256	C₅₉	#33858	1	1	yes	characteristic, complemented, Sylow
257	H(5,𝔽₂)	—	2	2	no	—
258	H(5,𝔽₂)	—	118	2	no	—
259	AGL(1,ℤ/8)	—	2	2	no	—
260	AGL(1,ℤ/8)	—	4	2	no	—
261	AGL(1,ℤ/8)	—	118	2	no	—
262	AGL(1,ℤ/8)	—	118	2	no	—
263	AGL(1,ℤ/8)	—	118	2	no	—
264	AGL(1,ℤ/8)	—	236	2	no	—
265	AGL(1,ℤ/8)	—	236	2	no	—
266	AGL(1,ℤ/8)	—	236	2	no	—
267	#135	—	2	2	no	—
268	#135	—	59	1	no	—
269	#135	—	118	2	no	—
270	#135	—	236	2	no	—
271	#135	C₂²×D₅₉	1	2	yes	—
272	C₂×D₈	—	2	2	no	—
273	C₂×D₈	—	59	2	no	—
274	C₂×D₈	—	118	2	no	—
275	C₂×D₈	—	118	2	no	—
276	C₂×D₈	—	236	2	no	—
277	C₂×D₈	C₂²×D₅₉	1	2	yes	—
278	#131	—	59	1	no	—
279	#131	—	118	2	no	—
280	#131	C₂²×D₅₉	1	1	yes	characteristic
281	#127	—	118	2	no	—
282	Q₃₂	C₂²⋊D₅₉	1	1	yes	characteristic, complemented
283	SD₃₂	—	2	2	no	—
284	SD₃₂	—	118	2	no	—
285	SD₃₂	C₂²⋊D₅₉	1	2	yes	complemented
286	D₁₆	—	2	2	no	—
287	D₁₆	—	2	1	no	—
288	D₁₆	—	2	1	no	—
289	D₁₆	—	118	2	no	—
290	D₁₆	—	118	1	no	—
291	D₁₆	—	118	1	no	—
292	D₁₆	—	236	2	no	—
293	D₁₆	C₂²⋊D₅₉	1	1	yes	characteristic, complemented
294	M₃₂	—	2	1	no	—
295	M₃₂	—	59	1	no	—
296	M₃₂	—	118	1	no	—
297	M₃₂	C₂²×D₅₉	1	1	yes	characteristic
298	C₂×C₁₆	—	2	1	no	—
299	C₂×C₁₆	—	59	1	no	—
300	C₂×C₁₆	—	118	1	no	—
301	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
302	#108	—	59	1	no	—
303	#108	—	59	2	no	—
304	#104	—	59	1	no	—
305	#104	—	59	1	no	—
306	#104	—	118	2	no	—
307	#100	—	118	2	no	—
308	#100	—	118	2	no	—
309	C₄×C₈	—	59	1	no	—
310	#41	—	2	2	no	—
311	#41	—	4	2	no	—
312	#41	—	4	2	no	—
313	#41	—	59	1	no	—
314	#41	—	236	2	no	—
315	#41	—	236	2	no	—
316	#41	D₄×D₅₉	1	1	yes	characteristic
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	118	2	no	—
322	C₂×D₄	—	472	2	no	—
323	C₂×D₄	—	472	2	no	—
324	C₂×D₄	—	236	2	no	—
325	C₂×D₄	—	236	2	no	—
326	Q₁₆	—	59	1	no	—
327	Q₁₆	C₂×C₂²⋊D₅₉	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	4	2	no	—
330	SD₁₆	—	59	1	no	—
331	SD₁₆	—	59	1	no	—
332	SD₁₆	—	236	2	no	—
333	SD₁₆	—	236	2	no	—
334	SD₁₆	—	236	2	no	—
335	D₈	—	2	2	no	—
336	D₈	—	2	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	59	1	no	—
339	D₈	—	118	2	no	—
340	D₈	—	118	2	no	—
341	D₈	—	236	2	no	—
342	D₈	—	236	2	no	—
343	D₈	—	236	2	no	—
344	D₈	—	236	2	no	—
345	D₈	—	236	2	no	—
346	D₈	C₂×C₂²⋊D₅₉	1	2	yes	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	59	1	no	—
349	M₁₆	—	118	1	no	—
350	M₁₆	—	118	2	no	—
351	M₁₆	—	236	2	no	—
352	M₁₆	D₄×D₅₉	1	1	yes	characteristic
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	59	1	no	—
355	C₂×C₈	—	118	1	no	—
356	C₂×C₈	—	236	2	no	—
357	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
358	C₄²	—	59	1	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	118	1	no	—
361	C₁₆	—	118	1	no	—
362	C₁₆	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
363	C₁₆	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₂³	—	4	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	472	2	no	—
367	C₂³	—	236	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	59	1	no	—
370	Q₈	D₈×D₅₉	1	1	yes	characteristic
371	D₄	—	2	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	2	no	—
378	D₄	—	59	1	no	—
379	D₄	—	118	1	no	—
380	D₄	—	944	4	no	—
381	D₄	—	472	2	no	—
382	D₄	—	472	2	no	—
383	D₄	—	236	2	no	—
384	D₄	—	236	2	no	—
385	D₄	D₈×D₅₉	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	118	1	no	—
390	C₂×C₄	—	118	1	no	—
391	C₂×C₄	—	472	2	no	—
392	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	59	1	no	—
395	C₈	—	59	1	no	—
396	C₈	—	118	1	no	—
397	C₈	—	236	2	no	—
398	C₈	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
399	C₈	#14273772	1	1	yes	characteristic
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	16	2	no	—
404	C₂²	—	32	2	no	—
405	C₂²	—	1888	2	no	—
406	C₂²	—	118	1	no	—
407	C₂²	—	944	2	no	—
408	C₂²	—	472	2	no	—
409	C₂²	#16838203	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	118	2	no	—
413	C₄	—	118	1	no	—
414	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
415	C₄	C₂×D₈×D₅₉	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	4	1	no	—
418	C₂	—	8	2	no	—
419	C₂	—	16	2	no	—
420	C₂	—	944	2	no	—
421	C₂	—	236	1	no	—
422	C₂	D₈×C₂²⋊D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×C₂²⋊D₅₉
commutator, cosocle	C₂×C₈×C₅₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#3415	C₂
socle	C₂×C₅₉	D₄×D₈
hypercenter	#3415	D₅₉
hypocenter	C₅₉	#33858
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #3415

Complements

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

N	H ≅ G/N	type
1. #21437234	C₂	semidirect
2. #21435893	C₂	semidirect
3. #21426344	C₂	semidirect
4. #21426216	C₂	semidirect
5. #21426213	C₂	semidirect
6. #21426170	C₂	semidirect
7. #21426053	C₂	semidirect
8. #21426050	C₂	semidirect
9. #21425977	C₂	semidirect
10. #21425931	C₂	semidirect
11. C₅₉×#3415	C₂	semidirect
13. #16838204	C₂²	semidirect
15. #16837837	C₂²	semidirect
17. C₂×D₉₄₄	C₂²	semidirect
18. C₂×#14273668	C₂²	semidirect
20. #16837818	C₂²	semidirect
21. #16837777	C₂²	semidirect
22. #16837672	C₂²	semidirect
24. #16837669	C₂²	semidirect
27. #16837519	C₂²	semidirect
29. #16837232	C₂²	semidirect
30. #16837222	C₂²	semidirect
31. #16837216	C₂²	semidirect
32. #16837215	C₂²	semidirect
33. #16837209	C₂²	semidirect
34. #16837187	C₂²	semidirect
35. #16837186	C₂²	semidirect
36. C₁₆×Dic₅₉	C₂²	semidirect
37. C₅₉×#576	C₂²	semidirect
39. C₅₉×#509	C₂²	semidirect
43. C₂×D₁₆×C₅₉	C₂²	semidirect
44. C₅₉×#504	C₂²	semidirect
87. Q₃₂×C₅₉	D₄	semidirect
89. SD₃₂×C₅₉	D₄	semidirect
93. D₁₆×C₅₉	D₄	semidirect
206. #3415	D₅₉	semidirect
225. #576	C₂×D₅₉	semidirect
229. #509	C₂×D₅₉	semidirect
237. C₂×D₁₆	C₂×D₅₉	semidirect
239. #504	C₂×D₅₉	semidirect
256. C₅₉	#33858	semidirect
282. Q₃₂	C₂²⋊D₅₉	semidirect
285. SD₃₂	C₂²⋊D₅₉	semidirect
293. D₁₆	C₂²⋊D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21437234	2
#21435893	2
#21426344	2
#21426216	2
#21426213	2
#21426170	2
#21426053	2
#21426050	2
#21425977	2
#21425931	2
C₅₉×#3415	2
#33858	59