Subgroups — #28558433

Order 15104.

682 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	#21433059	C₂	1	2	yes	maximal, complemented
2	C₄×#14273746	C₂	1	1	yes	maximal, characteristic
3	#21422994	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422992	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422989	C₂	1	2	yes	maximal, complemented
6	#21422984	C₂	1	2	yes	maximal, complemented
7	#21422981	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422843	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422475	C₂	1	2	yes	maximal, complemented
10	C₈²×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273746	C₄	1	1	yes	characteristic
13	C₄×#11745687	C₂²	1	2	yes	—
14	#16837532	C₂²	1	2	yes	—
15	#16837529	C₂²	1	2	yes	—
16	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
17	#16837496	C₄	1	1	yes	characteristic
18	#16837493	C₄	1	2	yes	—
19	C₄×#11745670	C₂²	1	2	yes	—
20	D₈×Dic₅₉	C₄	1	1	yes	characteristic
21	#16837480	C₂²	1	2	yes	—
22	#16837476	—	2	2	no	—
23	#16837471	—	2	2	no	—
24	#16837454	C₂²	1	2	yes	—
25	#16837452	—	2	2	no	—
26	#16837439	C₄	1	1	yes	characteristic
27	#16837395	C₄	1	2	yes	—
28	M₁₆×Dic₅₉	—	2	2	no	—
29	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
32	#16837155	C₂²	1	1	yes	characteristic
33	#16837152	C₂²	1	2	yes	—
34	#16837134	C₂²	1	2	yes	—
35	#16837132	C₂²	1	2	yes	—
36	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
37	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#436	C₂²	1	2	yes	—
42	C₅₉×#335	C₂²	1	1	yes	characteristic
43	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#11745687	C₂×C₄	1	2	yes	—
46	#14273746	—	2	4	no	—
47	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#11745670	C₂×C₄	1	2	yes	—
49	C₂×#11745664	—	2	2	no	—
50	C₂×C₈×D₅₉	—	2	1	no	—
51	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
55	C₄×Dic₁₁₈	C₂³	1	2	yes	—
56	#14273692	C₂×C₄	1	2	yes	—
57	D₄×Dic₅₉	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₅₉	—	2	2	no	—
59	(C₂²⋊D₅₉)⋊C₄	—	2	2	no	—
60	#14273685	C₂×C₄	1	2	yes	—
61	#14273683	—	2	2	no	—
62	C₂×C₄×Dic₅₉	—	2	2	no	—
63	C₄²×D₅₉	C₂³	1	1	yes	characteristic
64	#14273661	C₂×C₄	1	1	yes	characteristic
65	#14273658	C₂×C₄	1	2	yes	—
66	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₅₉⋊C₈	—	2	2	no	—
68	Dic₅₉⋊C₈	—	2	2	no	—
69	#14273652	C₂×C₄	1	2	yes	—
70	#14273650	C₂×C₄	1	2	yes	—
71	#14273648	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
73	(C₂×D₅₉)⋊C₈	—	2	2	no	—
74	#14273637	—	2	2	no	—
75	#14273637	—	2	2	no	—
76	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
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	C₈×Dic₅₉	—	2	1	no	—
81	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₉	D₄	1	1	yes	characteristic
84	C₈×Dic₅₉	D₄	1	1	yes	characteristic
85	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
86	C₂×M₁₆×C₅₉	—	2	2	no	—
87	C₄×D₄×C₅₉	C₂³	1	2	yes	—
88	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
90	#102×C₅₉	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₅₉	—	2	2	no	—
92	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₉	—	2	2	no	—
97	C₂×C₂²⋊D₅₉	—	2	2	no	—
98	C₂²×Dic₅₉	—	2	2	no	—
99	C₂²×Dic₅₉	—	2	2	no	—
100	#11745687	—	2	4	no	—
101	#11745687	—	2	4	no	—
102	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
105	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
106	D₈×C₅₉	—	2	2	no	—
107	M₁₆×C₅₉	—	4	4	no	—
108	C₂×C₈×C₅₉	—	2	1	no	—
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
115	C₂²⋊C₄×C₅₉	—	2	2	no	—
116	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
117	C₂²⋊Dic₅₉	—	2	2	no	—
118	#11745670	—	2	4	no	—
119	(C₂×D₅₉)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
121	Dic₅₉⋊C₄	—	2	2	no	—
122	Dic₅₉⋊C₄	—	2	2	no	—
123	C₄×Dic₅₉	—	2	2	no	—
124	C₄×Dic₅₉	—	2	2	no	—
125	C₄×Dic₅₉	—	2	2	no	—
126	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₅₉	#41	1	1	yes	characteristic
129	#11745664	—	4	4	no	—
130	C₂×C₅₉⋊C₈	—	2	1	no	—
131	C₂×C₅₉⋊C₈	—	2	2	no	—
132	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
136	Dic₂₃₆	—	2	2	no	—
137	C₈×D₅₉	—	2	4	no	—
138	C₈×D₅₉	—	2	2	no	—
139	C₈×D₅₉	—	2	2	no	—
140	C₈×D₅₉	—	2	2	no	—
141	C₈×D₅₉	M₁₆	1	4	yes	complemented
142	C₂³×C₅₉	—	2	2	no	—
143	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
144	D₄×C₅₉	—	2	2	no	—
145	D₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	4	2	no	—
148	C₂×C₄×C₅₉	—	4	2	no	—
149	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
152	C₂²⋊D₅₉	—	4	4	no	—
153	C₂×Dic₅₉	—	2	2	no	—
154	C₂×Dic₅₉	—	2	2	no	—
155	C₂×Dic₅₉	—	4	4	no	—
156	C₂×Dic₅₉	—	4	4	no	—
157	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
160	C₄×D₅₉	—	2	1	no	—
161	C₄×D₅₉	—	2	1	no	—
162	C₄×D₅₉	—	2	2	no	—
163	C₄×D₅₉	C₂×M₁₆	1	2	yes	—
164	C₄×D₅₉	#131	1	2	yes	—
165	Dic₁₁₈	—	2	2	no	—
166	Dic₁₁₈	—	2	2	no	—
167	C₈×C₅₉	—	2	2	no	—
168	C₈×C₅₉	—	2	1	no	—
169	C₈×C₅₉	—	2	1	no	—
170	C₈×C₅₉	—	4	2	no	—
171	C₈×C₅₉	C₂×M₁₆	1	2	yes	—
172	C₈×C₅₉	#135	1	2	yes	complemented
173	C₅₉⋊C₈	—	2	2	no	—
174	C₅₉⋊C₈	—	2	1	no	—
175	C₅₉⋊C₈	—	2	1	no	—
176	C₅₉⋊C₈	—	4	2	no	—
177	C₅₉⋊C₈	C₂×M₁₆	1	2	yes	—
178	C₅₉⋊C₈	#135	1	2	yes	complemented
179	#17886	—	59	1	no	maximal, Sylow
180	C₂²×C₅₉	—	4	2	no	—
181	C₂²×C₅₉	—	4	2	no	—
182	C₂²×C₅₉	—	4	2	no	—
183	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×D₅₉	—	2	1	no	—
185	C₂×D₅₉	—	2	1	no	—
186	C₂×D₅₉	#436	1	2	yes	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	4	2	no	—
189	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
190	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
191	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
192	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
193	Dic₅₉	—	2	1	no	—
194	Dic₅₉	—	4	2	no	—
195	Dic₅₉	—	4	2	no	—
196	Dic₅₉	#436	1	2	yes	—
197	Dic₅₉	#443	1	2	yes	—
198	#2965	—	59	2	no	—
199	C₄×#135	—	59	1	no	—
200	#1591	—	59	1	no	—
201	#1591	—	59	1	no	—
202	#1590	—	59	2	no	—
203	#1590	—	59	2	no	—
204	#1589	—	59	1	no	—
205	#1589	D₅₉	1	1	yes	characteristic, complemented
206	#1564	—	59	1	no	—
207	#1476	—	59	2	no	—
208	C₂×C₈²	—	59	1	no	—
209	C₂×C₅₉	—	8	2	no	—
210	C₂×C₅₉	C₂×#436	1	1	yes	characteristic
211	C₂×C₅₉	C₄×#135	1	1	yes	characteristic
212	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
213	D₅₉	—	2	2	no	—
214	C₂×#135	—	59	1	no	—
215	C₄×#41	—	59	2	no	—
216	#446	—	59	2	no	—
217	#446	—	59	2	no	—
218	C₄×Q₁₆	—	59	1	no	—
219	C₄×Q₁₆	—	59	1	no	—
220	C₄×SD₁₆	—	59	2	no	—
221	C₄×SD₁₆	—	59	2	no	—
222	C₄×D₈	—	59	1	no	—
223	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
224	#436	—	59	2	no	—
225	#436	C₂×D₅₉	1	2	yes	—
226	#435	—	118	2	no	—
227	#435	—	118	2	no	—
228	#431	—	59	2	no	—
229	#431	—	118	2	no	—
230	#427	—	59	1	no	—
231	#416	—	59	2	no	—
232	C₄×M₁₆	—	118	2	no	—
233	C₂×C₄×C₈	—	59	1	no	—
234	C₂×C₄×C₈	—	59	1	no	—
235	C₂×C₄×C₈	—	59	1	no	—
236	#335	—	59	1	no	—
237	#335	C₂×D₅₉	1	1	yes	characteristic
238	#334	—	59	2	no	—
239	Q₈⋊C₈	—	59	2	no	—
240	Q₈⋊C₈	—	59	2	no	—
241	D₄⋊C₈	—	59	2	no	—
242	D₄⋊C₈	C₂×D₅₉	1	2	yes	—
243	C₈²	—	59	1	no	—
244	C₈²	—	59	1	no	—
245	C₈²	—	59	1	no	—
246	C₈²	C₂×D₅₉	1	1	yes	characteristic
247	C₅₉	#17886	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	59	2	no	—
249	#135	—	118	4	no	—
250	C₂×Q₁₆	—	59	1	no	—
251	C₂×SD₁₆	—	59	2	no	—
252	C₂×D₈	C₄×D₅₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	118	2	no	—
255	C₂²×C₈	—	59	1	no	—
256	C₂²×C₈	—	59	1	no	—
257	C₂²×C₈	—	59	1	no	—
258	C₂²×C₈	—	59	1	no	—
259	C₂²×C₈	—	118	1	no	—
260	C₄×Q₈	—	59	2	no	—
261	C₄×Q₈	—	59	2	no	—
262	C₄×D₄	—	59	2	no	—
263	C₄×D₄	—	118	2	no	—
264	C₄×D₄	—	118	2	no	—
265	C₄×D₄	C₂²×D₅₉	1	2	yes	—
266	#117	—	59	2	no	—
267	#117	—	118	2	no	—
268	C₂×C₄²	—	59	1	no	—
269	C₂×C₄²	—	118	2	no	—
270	#107	—	59	1	no	—
271	#107	C₄×D₅₉	1	1	yes	characteristic
272	#106	—	59	2	no	—
273	C₄⋊C₈	—	59	2	no	—
274	C₄⋊C₈	—	118	2	no	—
275	C₄⋊C₈	—	118	2	no	—
276	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
277	#103	—	59	2	no	—
278	#103	—	59	2	no	—
279	#102	—	59	2	no	—
280	#102	C₄×D₅₉	1	2	yes	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	118	2	no	—
283	C₂²⋊C₈	—	118	2	no	—
284	#97	—	118	2	no	—
285	#97	—	118	2	no	—
286	C₄×C₈	—	59	1	no	—
287	C₄×C₈	—	59	1	no	—
288	C₄×C₈	—	59	1	no	—
289	C₄×C₈	—	59	1	no	—
290	C₄×C₈	—	59	1	no	—
291	C₄×C₈	—	59	1	no	—
292	C₄×C₈	—	59	1	no	—
293	C₄×C₈	—	118	1	no	—
294	C₄×C₈	—	118	2	no	—
295	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
298	#41	—	118	4	no	—
299	#41	—	118	4	no	—
300	C₂×Q₈	—	59	2	no	—
301	C₂×D₄	—	118	2	no	—
302	C₂×D₄	C₂×C₄×D₅₉	1	2	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	59	1	no	—
305	C₂²×C₄	—	59	1	no	—
306	C₂²×C₄	—	59	1	no	—
307	C₂²×C₄	—	118	2	no	—
308	C₂²×C₄	—	118	2	no	—
309	Q₁₆	—	118	2	no	—
310	SD₁₆	—	118	4	no	—
311	D₈	—	2	2	no	—
312	M₁₆	—	4	4	no	—
313	M₁₆	—	236	4	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	59	1	no	—
317	C₂×C₈	—	59	1	no	—
318	C₂×C₈	—	59	4	no	—
319	C₂×C₈	—	59	1	no	—
320	C₂×C₈	—	59	1	no	—
321	C₂×C₈	—	118	2	no	—
322	C₂×C₈	—	118	2	no	—
323	C₂×C₈	—	118	4	no	—
324	C₂×C₈	—	118	1	no	—
325	C₂×C₈	—	118	2	no	—
326	C₂×C₈	—	118	2	no	—
327	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
329	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
330	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
331	C₄⋊C₄	—	59	2	no	—
332	C₄⋊C₄	—	118	2	no	—
333	C₄⋊C₄	—	118	2	no	—
334	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	118	2	no	—
337	C₂²⋊C₄	—	118	2	no	—
338	C₄²	—	59	1	no	—
339	C₄²	—	59	1	no	—
340	C₄²	—	59	1	no	—
341	C₄²	—	118	2	no	—
342	C₄²	—	118	2	no	—
343	C₄²	—	118	2	no	—
344	C₄²	C₂³×D₅₉	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	59	1	no	—
347	Q₈	—	118	2	no	—
348	Q₈	—	118	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	236	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	59	1	no	—
356	C₂×C₄	—	59	1	no	—
357	C₂×C₄	—	59	2	no	—
358	C₂×C₄	—	59	2	no	—
359	C₂×C₄	—	59	1	no	—
360	C₂×C₄	—	118	2	no	—
361	C₂×C₄	—	118	1	no	—
362	C₂×C₄	—	118	1	no	—
363	C₂×C₄	—	118	2	no	—
364	C₂×C₄	—	118	2	no	—
365	C₂×C₄	—	236	4	no	—
366	C₂×C₄	—	236	4	no	—
367	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
369	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	59	2	no	—
375	C₈	—	59	2	no	—
376	C₈	—	118	2	no	—
377	C₈	—	118	1	no	—
378	C₈	—	118	1	no	—
379	C₈	—	236	2	no	—
380	C₈	M₁₆×D₅₉	1	2	yes	—
381	C₈	#14273746	1	2	yes	complemented
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	59	2	no	—
386	C₂²	—	118	1	no	—
387	C₂²	—	118	1	no	—
388	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	59	2	no	—
392	C₄	—	59	2	no	—
393	C₄	—	118	1	no	—
394	C₄	—	236	2	no	—
395	C₄	—	236	2	no	—
396	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
397	C₄	#131×D₅₉	1	1	yes	characteristic
398	C₄	#135×D₅₉	1	1	yes	characteristic
399	C₄	C₂×#14273746	1	1	yes	characteristic
400	C₂	—	8	2	no	—
401	C₂	—	118	2	no	—
402	C₂	#436×D₅₉	1	1	yes	characteristic
403	C₂	C₄×#14273746	1	1	yes	characteristic
404	C₂	#443×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1589	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273746	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1589	D₅₉
hypocenter	C₅₉	#17886
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
1. #21433059	C₂	semidirect
3. #21422994	C₂	semidirect
4. #21422992	C₂	semidirect
5. #21422989	C₂	semidirect
6. #21422984	C₂	semidirect
7. #21422981	C₂	semidirect
8. #21422843	C₂	semidirect
9. #21422475	C₂	semidirect
10. C₈²×D₅₉	C₂	semidirect
11. C₅₉×#1589	C₂	semidirect
141. C₈×D₅₉	M₁₆	semidirect
172. C₈×C₅₉	#135	semidirect
178. C₅₉⋊C₈	#135	semidirect
205. #1589	D₅₉	semidirect
247. C₅₉	#17886	semidirect
381. C₈	#14273746	semidirect

Maximal subgroups

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

subgroup	index
#21433059	2
C₄×#14273746	2
#21422994	2
#21422992	2
#21422989	2
#21422984	2
#21422981	2
#21422843	2
#21422475	2
C₈²×D₅₉	2
C₅₉×#1589	2
#17886	59