Subgroups — #28559156

Order 15104.

606 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433191	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433137	C₂	1	1	yes	maximal, characteristic
3	#21422999	C₂	1	2	yes	maximal, complemented
4	#21422987	C₂	1	2	yes	maximal, complemented
5	#21422975	C₂	1	2	yes	maximal, complemented
6	#21422940	C₂	1	2	yes	maximal, complemented
7	#21422876	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422539	C₂	1	1	yes	maximal, characteristic
9	#21422517	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422391	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3101	C₂	1	1	yes	maximal, characteristic
12	#16837533	—	2	2	no	—
13	#16837533	C₂²	1	2	yes	complemented
14	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	complemented
15	#16837480	—	2	2	no	—
16	#16837480	C₂²	1	2	yes	—
17	#16837480	C₂²	1	2	yes	—
18	#16837463	—	2	2	no	—
19	#16837459	C₂²	1	1	yes	characteristic
20	#16837455	C₂²	1	1	yes	characteristic
21	#16837455	C₂²	1	1	yes	characteristic
22	#16837366	—	2	2	no	—
23	C₄×#11745664	C₂²	1	1	yes	characteristic
24	#16837155	C₂²	1	2	yes	complemented
25	#16837153	C₂²	1	2	yes	complemented
26	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	complemented
27	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	complemented
28	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
30	#16837124	C₂²	1	1	yes	characteristic, complemented
31	#16837124	C₂²	1	1	yes	characteristic, complemented
32	#16837123	C₂²	1	1	yes	characteristic, complemented
33	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₅₉×#533	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#483	C₄	1	2	yes	—
37	C₅₉×#476	C₄	1	2	yes	—
38	C₅₉×#461	C₄	1	2	yes	—
39	C₅₉×#450	C₄	1	2	yes	—
40	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
41	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
42	C₅₉×#431	C₂²	1	1	yes	characteristic
43	C₂×#11745664	—	2	1	no	—
44	C₂×#11745664	—	2	2	no	—
45	C₂×#11745664	—	2	2	no	—
46	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
49	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
50	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
51	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
52	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
53	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
56	#14273638	—	2	1	no	—
57	#14273638	—	2	1	no	—
58	#14273638	—	2	2	no	—
59	C₄×C₅₉⋊C₈	—	2	1	no	—
60	C₄×C₅₉⋊C₈	—	2	2	no	—
61	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅₉	—	2	1	no	—
67	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
68	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
69	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
71	#125×C₅₉	—	2	1	no	—
72	C₂²⋊Q₈×C₅₉	—	2	1	no	—
73	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
74	C₄×Q₈×C₅₉	—	2	1	no	—
75	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
76	C₄×D₄×C₅₉	—	2	1	no	—
77	C₄×D₄×C₅₉	—	2	1	no	—
78	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₅₉	C₂³	1	2	yes	—
80	#117×C₅₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
84	#106×C₅₉	C₂×C₄	1	2	yes	—
85	#106×C₅₉	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
87	#103×C₅₉	C₂×C₄	1	2	yes	—
88	#103×C₅₉	C₂×C₄	1	2	yes	—
89	#102×C₅₉	C₂×C₄	1	2	yes	—
90	#102×C₅₉	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
92	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₂⁴×C₅₉	—	2	1	no	—
95	C₂×Q₈×C₅₉	—	2	1	no	—
96	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₅₉	—	2	1	no	—
98	C₂×D₄×C₅₉	—	4	2	no	—
99	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅₉	—	2	1	no	—
101	C₂²×C₄×C₅₉	—	2	2	no	—
102	C₂²×C₄×C₅₉	—	2	2	no	—
103	C₂²×C₄×C₅₉	—	8	2	no	—
104	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
107	SD₁₆×C₅₉	—	4	2	no	—
108	SD₁₆×C₅₉	—	4	2	no	—
109	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
111	C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₄⋊C₄×C₅₉	—	2	1	no	—
114	C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₄⋊C₄×C₅₉	—	2	2	no	—
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₅₉	—	2	2	no	—
120	C₂²⋊C₄×C₅₉	—	2	2	no	—
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	#11745664	—	4	2	no	—
128	#11745664	—	8	2	no	—
129	#11745664	—	8	2	no	—
130	C₂×C₅₉⋊C₈	—	2	1	no	—
131	C₂×C₅₉⋊C₈	—	2	2	no	—
132	C₂×C₅₉⋊C₈	—	2	2	no	—
133	C₂×C₅₉⋊C₈	—	2	1	no	—
134	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
135	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
136	C₂³×C₅₉	—	2	2	no	—
137	C₂³×C₅₉	—	4	2	no	—
138	C₂³×C₅₉	—	8	1	no	—
139	C₂³×C₅₉	—	8	1	no	—
140	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₅₉	—	2	2	no	—
142	Q₈×C₅₉	—	2	2	no	—
143	Q₈×C₅₉	—	8	1	no	—
144	D₄×C₅₉	—	2	2	no	—
145	D₄×C₅₉	—	2	2	no	—
146	D₄×C₅₉	—	4	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	4	1	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	—	4	2	no	—
155	C₂×C₄×C₅₉	—	8	2	no	—
156	C₂×C₄×C₅₉	—	8	1	no	—
157	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
163	C₈×C₅₉	—	2	2	no	—
164	C₈×C₅₉	—	2	2	no	—
165	C₅₉⋊C₈	—	2	2	no	—
166	C₅₉⋊C₈	—	2	2	no	—
167	C₅₉⋊C₈	—	2	2	no	—
168	C₅₉⋊C₈	—	4	1	no	—
169	C₅₉⋊C₈	—	4	2	no	—
170	C₅₉⋊C₈	—	4	2	no	—
171	#17952	—	59	1	no	maximal, Sylow
172	C₂²×C₅₉	—	2	1	no	—
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	—	4	2	no	—
176	C₂²×C₅₉	—	4	2	no	—
177	C₂²×C₅₉	—	4	2	no	—
178	C₂²×C₅₉	—	8	4	no	—
179	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₅₉	—	2	1	no	—
181	C₄×C₅₉	—	2	1	no	—
182	C₄×C₅₉	—	2	1	no	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	4	2	no	—
185	C₄×C₅₉	—	4	2	no	—
186	C₄×C₅₉	—	4	2	no	—
187	C₄×C₅₉	#568	1	2	yes	—
188	C₄×C₅₉	#577	1	2	yes	—
189	#3101	D₅₉	1	1	yes	characteristic
190	#2985	—	59	1	no	—
191	#2975	—	59	1	no	—
192	#1592	—	59	2	no	—
193	#1590	—	59	2	no	—
194	#1588	—	59	2	no	—
195	#1583	—	59	2	no	—
196	#1572	—	59	1	no	—
197	#1490	—	59	1	no	—
198	#1485	—	59	1	no	—
199	#1453	—	59	1	no	—
200	C₂×C₅₉	—	4	1	no	—
201	C₂×C₅₉	—	8	2	no	—
202	C₂×C₅₉	#2930	1	1	yes	characteristic
203	C₂×C₅₉	#2949	1	1	yes	characteristic
204	C₂×C₅₉	#2956	1	1	yes	characteristic
205	#533	C₂×D₅₉	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
207	#483	Dic₅₉	1	2	yes	—
208	#476	Dic₅₉	1	2	yes	—
209	#461	Dic₅₉	1	2	yes	—
210	#450	Dic₅₉	1	2	yes	—
211	#446	—	59	2	no	—
212	#446	—	118	2	no	—
213	C₈×Q₈	—	59	2	no	—
214	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
215	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
216	#436	—	59	2	no	—
217	#436	—	59	2	no	—
218	#436	—	118	2	no	—
219	#433	—	118	2	no	—
220	#432	—	59	1	no	—
221	#431	—	59	1	no	—
222	#431	—	59	1	no	—
223	#431	C₂×D₅₉	1	1	yes	characteristic
224	#407	—	118	2	no	—
225	C₄×M₁₆	—	59	1	no	—
226	#335	—	59	2	no	—
227	#334	—	59	2	no	—
228	Q₈⋊C₈	—	59	2	no	—
229	Q₈⋊C₈	—	59	2	no	—
230	D₄⋊C₈	—	59	2	no	—
231	D₄⋊C₈	—	59	2	no	—
232	#322	—	59	1	no	—
233	#322	—	59	1	no	—
234	#322	—	59	1	no	—
235	C₈²	—	59	1	no	—
236	C₅₉	#17952	1	1	yes	characteristic, complemented, Sylow
237	C₂²×D₄	C₂×Dic₅₉	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
240	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
241	C₂×M₁₆	—	118	2	no	—
242	C₂×M₁₆	—	118	2	no	—
243	C₂×M₁₆	—	118	1	no	—
244	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
246	#125	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	C₂×Dic₅₉	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
254	C₄×D₄	C₂²×D₅₉	1	2	yes	—
255	#117	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
259	#106	C₂×Dic₅₉	1	2	yes	—
260	#106	C₂×Dic₅₉	1	2	yes	—
261	C₄⋊C₈	—	59	2	no	—
262	C₄⋊C₈	—	59	2	no	—
263	C₄⋊C₈	—	59	2	no	—
264	C₄⋊C₈	—	118	2	no	—
265	C₄⋊C₈	—	118	2	no	—
266	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
267	#103	C₂×Dic₅₉	1	2	yes	—
268	#103	C₂×Dic₅₉	1	2	yes	—
269	#102	C₂×Dic₅₉	1	2	yes	—
270	#102	C₂×Dic₅₉	1	2	yes	—
271	C₂²⋊C₈	—	59	2	no	—
272	C₂²⋊C₈	—	118	2	no	—
273	C₂²⋊C₈	—	118	2	no	—
274	C₂²⋊C₈	—	118	1	no	—
275	C₂²⋊C₈	—	118	1	no	—
276	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
277	#97	—	118	2	no	—
278	#97	—	118	1	no	—
279	#97	—	118	1	no	—
280	C₄×C₈	—	59	1	no	—
281	C₄×C₈	—	59	1	no	—
282	C₄×C₈	—	59	1	no	—
283	C₄×C₈	—	59	1	no	—
284	C₄×C₈	—	118	2	no	—
285	C₄×C₈	—	118	1	no	—
286	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
287	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
299	C₂²×C₄	#11745687	1	1	yes	characteristic
300	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
301	SD₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	M₁₆	—	472	2	no	—
304	M₁₆	—	472	2	no	—
305	M₁₆	—	236	2	no	—
306	C₂×C₈	—	59	2	no	—
307	C₂×C₈	—	59	2	no	—
308	C₂×C₈	—	118	1	no	—
309	C₂×C₈	—	118	2	no	—
310	C₂×C₈	—	118	2	no	—
311	C₂×C₈	—	118	1	no	—
312	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
313	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	D₄×D₅₉	1	1	yes	characteristic
327	C₄²	#11745687	1	1	yes	characteristic
328	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
329	C₄²	C₂³×D₅₉	1	1	yes	characteristic
330	C₂³	—	2	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	—	8	1	no	—
334	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	1	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
352	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
353	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
354	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
356	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	118	2	no	—
360	C₈	—	118	2	no	—
361	C₈	—	118	2	no	—
362	C₈	—	236	1	no	—
363	C₈	—	236	2	no	—
364	C₈	—	236	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	#16838169	1	2	yes	—
381	C₄	#16838208	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	8	2	no	—
384	C₂	#21432800	1	1	yes	characteristic
385	C₂	#21432956	1	1	yes	characteristic
386	C₂	#21433006	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×#3101	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3101	D₅₉
hypocenter	C₅₉	#17952
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #21433191	C₂	semidirect
3. #21422999	C₂	semidirect
4. #21422987	C₂	semidirect
5. #21422975	C₂	semidirect
6. #21422940	C₂	semidirect
7. #21422876	C₂	semidirect
9. #21422517	C₂	semidirect
10. #21422391	C₂	semidirect
13. #16837533	C₂²	semidirect
14. Q₈×C₅₉⋊C₈	C₂²	semidirect
24. #16837155	C₂²	semidirect
25. #16837153	C₂²	semidirect
26. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
27. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
30. #16837124	C₂²	semidirect
31. #16837124	C₂²	semidirect
32. #16837123	C₂²	semidirect
33. C₈×C₅₉⋊C₈	C₂²	semidirect
236. C₅₉	#17952	semidirect

Maximal subgroups

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

subgroup	index
#21433191	2
#21433137	2
#21422999	2
#21422987	2
#21422975	2
#21422940	2
#21422876	2
#21422539	2
#21422517	2
#21422391	2
C₅₉×#3101	2
#17952	59