Subgroups — #28741926

Order 15104.

646 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	C₂×#16837820	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16837819	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432997	C₂	1	1	yes	maximal, characteristic
4	#21425935	C₂	1	4	yes	maximal, complemented
5	#21425930	C₂	1	4	yes	maximal, complemented
6	#21425861	C₂	1	1	yes	maximal, characteristic, complemented
7	#21425723	C₂	1	1	yes	maximal, characteristic, complemented
8	#21425695	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838200	C₄	1	1	yes	characteristic
11	C₂×#14273733	C₂²	1	1	yes	characteristic
12	#16837820	—	2	1	no	—
13	#16837820	—	2	1	no	—
14	#16837820	C₂²	1	2	yes	complemented
15	#16837820	C₂²	1	2	yes	complemented
16	#16837819	—	2	1	no	—
17	#16837819	—	2	1	no	—
18	#16837819	C₂²	1	2	yes	complemented
19	#16837819	C₂²	1	2	yes	complemented
20	C₂×#14273667	—	2	1	no	—
21	C₂×#14273667	C₂²	1	1	yes	characteristic
22	C₂×#14273666	—	2	1	no	—
23	C₂²×C₅₉⋊C₁₆	—	2	1	no	—
24	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₅₉	—	2	1	no	—
26	#16837522	C₄	1	4	yes	—
27	#16837517	C₂²	1	4	yes	—
28	#16837450	C₄	1	1	yes	characteristic
29	#16837419	C₄	1	1	yes	characteristic
30	#16837418	C₄	1	1	yes	characteristic
31	#16837357	C₂²	1	1	yes	characteristic
32	#16837222	C₂²	1	4	yes	complemented
33	#16837185	C₂²	1	4	yes	complemented
34	#16837177	C₂²	1	2	yes	complemented
35	C₁₆×Dic₅₉	C₂²	1	2	yes	complemented
36	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#350	C₂²	1	4	yes	complemented
40	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
41	#14273758	C₈	1	2	yes	—
42	#14273757	C₈	1	2	yes	—
43	#14273753	C₈	1	2	yes	—
44	#14273752	C₈	1	2	yes	—
45	#14273747	C₂×C₄	1	4	yes	—
46	#14273733	—	2	1	no	—
47	#14273733	—	2	1	no	—
48	#14273733	C₂×C₄	1	2	yes	—
49	#14273733	C₂³	1	2	yes	—
50	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
51	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
52	C₂×#11745659	—	2	1	no	—
53	C₂×C₈×D₅₉	—	2	1	no	—
54	#14273686	C₂×C₄	1	1	yes	characteristic
55	#14273667	—	2	1	no	—
56	#14273667	—	2	2	no	—
57	#14273667	—	2	2	no	—
58	#14273667	C₂³	1	2	yes	—
59	#14273666	—	2	2	no	—
60	#14273666	—	2	2	no	—
61	C₂×C₅₉⋊C₁₆	—	2	1	no	—
62	C₂×C₅₉⋊C₁₆	—	2	2	no	—
63	C₂×C₅₉⋊C₁₆	—	2	2	no	—
64	C₂×C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
65	C₂×C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
66	C₂×C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
67	C₂×C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
68	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₁₆×D₅₉	—	2	2	no	—
71	C₁₆×D₅₉	—	2	2	no	—
72	#14273662	C₂×C₄	1	4	yes	—
73	#14273654	C₂×C₄	1	4	yes	—
74	#14273653	C₂×C₄	1	4	yes	—
75	#14273637	C₂×C₄	1	2	yes	—
76	C₈×Dic₅₉	C₂³	1	2	yes	—
77	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
78	#131×C₅₉	—	2	1	no	—
79	#131×C₅₉	—	2	1	no	—
80	#131×C₅₉	C₂×C₄	1	2	yes	—
81	#131×C₅₉	C₂³	1	2	yes	—
82	C₂×M₁₆×C₅₉	—	2	1	no	—
83	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₅₉	—	2	1	no	—
85	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
86	M₃₂×C₅₉	—	2	1	no	—
87	M₃₂×C₅₉	—	2	1	no	—
88	M₃₂×C₅₉	—	2	1	no	—
89	M₃₂×C₅₉	C₂³	1	2	yes	—
90	C₂×C₁₆×C₅₉	—	2	1	no	—
91	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
92	#41×C₅₉	—	2	1	no	—
93	#41×C₅₉	—	2	1	no	—
94	#41×C₅₉	C₂×C₈	1	2	yes	—
95	#41×C₅₉	C₂²×C₄	1	2	yes	—
96	C₂×Q₈×C₅₉	C₂×C₈	1	1	yes	characteristic
97	C₂×D₄×C₅₉	—	2	1	no	—
98	C₂×D₄×C₅₉	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	—	2	1	no	—
100	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₅₉	—	2	1	no	—
102	#11745685	—	2	1	no	—
103	#11745685	—	2	1	no	—
104	#11745685	C₂×C₈	1	2	yes	—
105	#11745685	C₂²×C₄	1	2	yes	—
106	C₂×D₂₃₆	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₅₉	—	2	1	no	—
108	C₂×Dic₁₁₈	C₂×C₈	1	1	yes	characteristic
109	M₁₆×C₅₉	—	2	1	no	—
110	M₁₆×C₅₉	—	2	2	no	—
111	M₁₆×C₅₉	—	2	2	no	—
112	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	2	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
120	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
122	C₂²⋊Dic₅₉	—	2	1	no	—
123	#11745672	C₂×C₈	1	4	yes	—
124	#11745671	C₂×C₈	1	4	yes	—
125	#11745670	C₂×C₈	1	4	yes	—
126	#11745669	C₂×C₈	1	4	yes	—
127	C₄⋊Dic₅₉	—	2	1	no	—
128	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
129	#11745664	—	2	1	no	—
130	#11745664	C₂×C₈	1	2	yes	—
131	#11745664	C₂×C₈	1	2	yes	—
132	#11745664	C₂²×C₄	1	2	yes	—
133	C₂×C₅₉⋊C₈	—	2	1	no	—
134	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
135	#11745659	—	2	2	no	—
136	#11745659	—	2	2	no	—
137	C₈×D₅₉	—	2	2	no	—
138	C₈×D₅₉	—	2	2	no	—
139	C₁₆×C₅₉	—	2	2	no	—
140	C₁₆×C₅₉	—	2	2	no	—
141	C₅₉⋊C₁₆	—	2	2	no	—
142	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
143	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
144	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
145	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₅₉	—	2	1	no	—
147	C₂³×C₅₉	#131	1	1	yes	characteristic
148	C₂²×D₅₉	—	2	1	no	—
149	Q₈×C₅₉	—	2	1	no	—
150	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
151	D₄×C₅₉	—	2	2	no	—
152	D₄×C₅₉	—	2	2	no	—
153	D₄×C₅₉	—	2	1	no	—
154	D₄×C₅₉	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₅₉	—	2	1	no	—
156	C₂×C₄×C₅₉	—	2	2	no	—
157	C₂×C₄×C₅₉	—	2	2	no	—
158	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
164	C₂²⋊D₅₉	—	2	2	no	—
165	C₂²⋊D₅₉	—	2	2	no	—
166	C₂×Dic₅₉	—	2	1	no	—
167	C₂×Dic₅₉	—	2	2	no	—
168	D₂₃₆	—	2	1	no	—
169	D₂₃₆	C₂²×C₈	1	2	yes	—
170	C₄×D₅₉	—	2	2	no	—
171	C₄×D₅₉	—	2	2	no	—
172	Dic₁₁₈	—	2	1	no	—
173	Dic₁₁₈	C₂²×C₈	1	2	yes	—
174	C₈×C₅₉	—	2	2	no	—
175	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
176	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
177	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
179	C₅₉⋊C₈	—	2	2	no	—
180	C₅₉⋊C₈	C₂²×C₈	1	4	yes	—
181	#33441	—	59	1	no	maximal, Sylow
182	C₂²×C₅₉	—	2	2	no	—
183	C₂²×C₅₉	—	4	1	no	—
184	C₂²×C₅₉	—	4	2	no	—
185	C₂²×C₅₉	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₅₉	C₈×D₄	1	1	yes	characteristic
187	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
188	C₂×D₅₉	—	2	2	no	—
189	C₂×D₅₉	—	4	2	no	—
190	C₄×C₅₉	—	2	2	no	—
191	C₄×C₅₉	C₈×D₄	1	1	yes	characteristic
192	C₄×C₅₉	C₈×D₄	1	1	yes	characteristic
193	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
195	Dic₅₉	—	2	2	no	—
196	Dic₅₉	—	4	2	no	—
197	C₂×#504	—	59	1	no	—
198	C₂×#504	—	59	1	no	—
199	#2955	—	59	1	no	—
200	#2171	—	59	4	no	—
201	#2170	—	59	4	no	—
202	#2153	—	59	1	no	—
203	#2117	—	59	1	no	—
204	#2117	D₅₉	1	1	yes	characteristic, complemented
205	#2108	—	59	1	no	—
206	C₂×C₅₉	—	2	1	no	—
207	C₂×C₅₉	—	2	1	no	—
208	C₂×C₅₉	—	2	1	no	—
209	C₂×C₅₉	—	4	2	no	—
210	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
211	D₅₉	—	4	2	no	—
212	#575	—	59	1	no	—
213	C₂×#131	—	59	1	no	—
214	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
215	#504	—	59	2	no	—
216	#504	—	59	2	no	—
217	#504	—	59	2	no	—
218	#504	—	59	2	no	—
219	#504	—	118	1	no	—
220	#504	—	118	1	no	—
221	#504	—	118	1	no	—
222	#504	—	118	1	no	—
223	C₂×M₃₂	—	59	1	no	—
224	C₂×M₃₂	—	118	1	no	—
225	C₂×M₃₂	—	118	1	no	—
226	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
227	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
228	C₂²×C₁₆	—	59	1	no	—
229	C₂²×C₁₆	—	118	1	no	—
230	C₂²×C₁₆	—	118	1	no	—
231	#444	—	59	4	no	—
232	#443	—	59	4	no	—
233	#430	—	59	1	no	—
234	#421	—	59	1	no	—
235	#421	—	59	1	no	—
236	#405	—	59	1	no	—
237	#364	—	59	4	no	—
238	#350	—	59	4	no	—
239	#350	C₂×D₅₉	1	4	yes	complemented
240	#346	—	59	2	no	—
241	C₄×C₁₆	—	59	2	no	—
242	C₅₉	#33441	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	59	1	no	—
244	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
245	#137	—	59	2	no	—
246	#137	—	59	2	no	—
247	AGL(1,ℤ/8)	—	59	2	no	—
248	AGL(1,ℤ/8)	—	59	2	no	—
249	#135	—	59	4	no	—
250	#131	—	2	1	no	—
251	#131	—	2	1	no	—
252	#131	—	59	2	no	—
253	#131	—	59	2	no	—
254	#131	—	118	1	no	—
255	#131	—	118	1	no	—
256	#131	C₄×D₅₉	1	2	yes	—
257	#131	C₂²×D₅₉	1	2	yes	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	59	1	no	—
260	C₂×M₁₆	—	59	1	no	—
261	C₂×M₁₆	—	118	1	no	—
262	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	118	1	no	—
265	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
266	#117	—	59	1	no	—
267	M₃₂	—	2	1	no	—
268	M₃₂	—	2	1	no	—
269	M₃₂	—	2	1	no	—
270	M₃₂	—	59	2	no	—
271	M₃₂	—	118	2	no	—
272	M₃₂	—	118	2	no	—
273	M₃₂	—	118	2	no	—
274	M₃₂	—	118	2	no	—
275	M₃₂	—	118	1	no	—
276	M₃₂	C₂²×D₅₉	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	59	1	no	—
279	C₂×C₁₆	—	59	1	no	—
280	C₂×C₁₆	—	59	1	no	—
281	C₂×C₁₆	—	59	1	no	—
282	C₂×C₁₆	—	59	1	no	—
283	C₂×C₁₆	—	59	1	no	—
284	C₂×C₁₆	—	118	2	no	—
285	C₂×C₁₆	—	118	2	no	—
286	C₂×C₁₆	—	118	2	no	—
287	C₂×C₁₆	—	118	2	no	—
288	C₂×C₁₆	—	118	1	no	—
289	C₂×C₁₆	C₂²×D₅₉	1	2	yes	—
290	#108	—	59	4	no	—
291	#104	—	59	4	no	—
292	#104	—	59	4	no	—
293	#97	—	59	2	no	—
294	C₄×C₈	—	59	2	no	—
295	#41	—	2	1	no	—
296	#41	—	2	1	no	—
297	#41	—	59	2	no	—
298	#41	—	59	2	no	—
299	#41	—	118	1	no	—
300	#41	—	118	1	no	—
301	#41	C₈×D₅₉	1	2	yes	—
302	#41	C₂×C₄×D₅₉	1	2	yes	—
303	C₂×Q₈	—	59	1	no	—
304	C₂×Q₈	C₈×D₅₉	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	59	1	no	—
307	C₂×D₄	—	118	1	no	—
308	C₂×D₄	C₈×D₅₉	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	118	1	no	—
311	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
312	Q₁₆	—	59	4	no	—
313	SD₁₆	—	59	4	no	—
314	SD₁₆	—	59	4	no	—
315	D₈	—	59	4	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	59	2	no	—
320	M₁₆	—	59	2	no	—
321	M₁₆	—	59	2	no	—
322	M₁₆	—	118	1	no	—
323	M₁₆	—	118	2	no	—
324	M₁₆	—	118	2	no	—
325	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	59	2	no	—
330	C₂×C₈	—	118	1	no	—
331	C₂×C₈	—	118	2	no	—
332	C₂×C₈	—	118	2	no	—
333	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
334	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
335	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
336	C₂×C₈	#11745687	1	1	yes	characteristic
337	C₂×C₈	#11745687	1	1	yes	characteristic
338	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
339	C₄⋊C₄	—	118	1	no	—
340	C₂²⋊C₄	—	118	1	no	—
341	C₄²	—	59	2	no	—
342	C₁₆	—	2	2	no	—
343	C₁₆	—	2	2	no	—
344	C₁₆	—	59	1	no	—
345	C₁₆	—	59	1	no	—
346	C₁₆	—	59	1	no	—
347	C₁₆	—	59	1	no	—
348	C₁₆	—	118	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	118	1	no	—
351	C₂³	#14273735	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	59	2	no	—
354	Q₈	—	118	1	no	—
355	Q₈	C₂×C₈×D₅₉	1	2	yes	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	1	no	—
359	D₄	—	59	2	no	—
360	D₄	—	118	2	no	—
361	D₄	—	118	2	no	—
362	D₄	—	118	1	no	—
363	D₄	C₂×C₈×D₅₉	1	2	yes	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	118	1	no	—
368	C₂×C₄	—	118	2	no	—
369	C₂×C₄	—	118	2	no	—
370	C₂×C₄	—	118	2	no	—
371	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
375	C₂×C₄	#14273735	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	59	4	no	—
379	C₈	—	118	2	no	—
380	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
381	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
382	C₈	C₂×D₄×D₅₉	1	1	yes	characteristic
383	C₈	C₂×#11745687	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	118	2	no	—
388	C₂²	—	236	2	no	—
389	C₂²	(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
390	C₂²	(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
391	C₂²	C₂×#14273735	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	118	2	no	—
394	C₄	—	236	2	no	—
395	C₄	(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
396	C₄	(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
397	C₄	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
398	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	2	no	—
403	C₂	—	236	2	no	—
404	C₂	C₂×(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2117	C₂
socle	C₂×C₅₉	C₂×C₈×D₄
prime radical	#16838200	C₄
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2117	D₅₉
hypocenter	C₅₉	#33441
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2117

Complements

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

N	H ≅ G/N	type
1. C₂×#16837820	C₂	semidirect
2. C₂×#16837819	C₂	semidirect
4. #21425935	C₂	semidirect
5. #21425930	C₂	semidirect
6. #21425861	C₂	semidirect
7. #21425723	C₂	semidirect
8. #21425695	C₂	semidirect
9. C₅₉×#2117	C₂	semidirect
14. #16837820	C₂²	semidirect
15. #16837820	C₂²	semidirect
18. #16837819	C₂²	semidirect
19. #16837819	C₂²	semidirect
32. #16837222	C₂²	semidirect
33. #16837185	C₂²	semidirect
34. #16837177	C₂²	semidirect
35. C₁₆×Dic₅₉	C₂²	semidirect
39. C₅₉×#350	C₂²	semidirect
204. #2117	D₅₉	semidirect
239. #350	C₂×D₅₉	semidirect
242. C₅₉	#33441	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837820	2
C₂×#16837819	2
#21432997	2
#21425935	2
#21425930	2
#21425861	2
#21425723	2
#21425695	2
C₅₉×#2117	2
#33441	59