Subgroups — #28743764

Order 15104.

592 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434675	C₂	1	1	yes	maximal, characteristic, complemented
2	#21426287	C₂	1	2	yes	maximal, complemented
3	#21426238	C₂	1	1	yes	maximal, characteristic, complemented
4	#21426233	C₂	1	1	yes	maximal, characteristic, complemented
5	#21426136	C₂	1	1	yes	maximal, characteristic, complemented
6	#21426131	C₂	1	1	yes	maximal, characteristic, complemented
7	#21426019	C₂	1	2	yes	maximal, complemented
8	#21425970	C₂	1	2	yes	maximal, complemented
9	#21425958	C₂	1	2	yes	maximal, complemented
10	#21425899	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837952	—	2	1	no	—
13	C₂×#14273670	C₂²	1	2	yes	—
14	C₂×#14273668	C₂²	1	2	yes	—
15	#16837807	C₂²	1	1	yes	characteristic
16	#16837779	C₂²	1	1	yes	characteristic
17	#16837749	—	2	1	no	—
18	#16837638	—	2	1	no	—
19	#16837638	C₂²	1	2	yes	—
20	C₄×D₄₇₂	—	2	1	no	—
21	C₄×D₄₇₂	C₂²	1	2	yes	—
22	#16837229	C₂²	1	2	yes	—
23	#16837227	C₂²	1	2	yes	—
24	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
26	#16837206	C₂²	1	2	yes	—
27	#16837203	C₂²	1	2	yes	—
28	#16837202	C₂²	1	2	yes	—
29	#16837202	C₂²	1	2	yes	—
30	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	—
31	#16837178	C₂²	1	2	yes	—
32	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
33	C₄×#41×C₅₉	—	2	1	no	—
34	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
36	C₄×SD₁₆×C₅₉	—	2	1	no	—
37	C₄×SD₁₆×C₅₉	—	2	1	no	—
38	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#427	C₂²	1	1	yes	characteristic
41	C₅₉×#416	—	2	1	no	—
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#11745685	—	4	1	no	—
44	C₂×D₄₇₂	—	2	1	no	—
45	C₂×D₄₇₂	C₂³	1	2	yes	—
46	#14273727	—	2	1	no	—
47	#14273724	—	2	1	no	—
48	#14273715	—	4	1	no	—
49	#14273701	—	2	2	no	—
50	#14273701	—	4	1	no	—
51	C₄×D₂₃₆	—	2	2	no	—
52	C₄×D₂₃₆	—	4	1	no	—
53	#14273670	—	2	4	no	—
54	#14273668	—	2	4	no	—
55	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
56	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
57	#14273661	—	2	1	no	—
58	#14273661	C₂³	1	2	yes	—
59	#14273649	—	2	2	no	—
60	#14273649	—	2	2	no	—
61	C₂×#41×C₅₉	—	2	1	no	—
62	#135×C₅₉	—	2	2	no	—
63	#135×C₅₉	—	2	2	no	—
64	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₅₉	—	2	1	no	—
66	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₅₉	—	2	1	no	—
70	C₄×Q₈×C₅₉	—	2	1	no	—
71	C₄×D₄×C₅₉	—	2	1	no	—
72	C₄×D₄×C₅₉	—	2	1	no	—
73	C₄×D₄×C₅₉	—	4	1	no	—
74	C₄×D₄×C₅₉	—	4	1	no	—
75	#117×C₅₉	—	2	1	no	—
76	#117×C₅₉	—	4	1	no	—
77	C₂×C₄²×C₅₉	—	4	1	no	—
78	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
79	#107×C₅₉	C₂³	1	1	yes	characteristic
80	#107×C₅₉	C₂³	1	1	yes	characteristic
81	#106×C₅₉	—	2	1	no	—
82	#103×C₅₉	—	2	1	no	—
83	#103×C₅₉	—	2	1	no	—
84	#102×C₅₉	—	2	1	no	—
85	#102×C₅₉	—	2	1	no	—
86	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
88	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
90	#41×C₅₉	—	2	4	no	—
91	#41×C₅₉	—	4	2	no	—
92	C₂×Q₈×C₅₉	—	2	1	no	—
93	C₂×D₄×C₅₉	—	2	1	no	—
94	C₂×D₄×C₅₉	—	4	1	no	—
95	C₂²×C₄×C₅₉	—	4	1	no	—
96	C₂²×C₄×C₅₉	—	4	1	no	—
97	C₂²×C₄×C₅₉	—	4	1	no	—
98	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₅₉	—	4	2	no	—
102	#11745685	—	8	4	no	—
103	C₂×D₂₃₆	—	2	2	no	—
104	C₂×D₂₃₆	—	4	1	no	—
105	C₂×D₂₃₆	—	4	1	no	—
106	C₂×C₄×D₅₉	—	4	2	no	—
107	C₂×Dic₁₁₈	—	4	1	no	—
108	Q₁₆×C₅₉	—	2	1	no	—
109	Q₁₆×C₅₉	#41	1	2	yes	complemented
110	SD₁₆×C₅₉	—	2	4	no	—
111	D₈×C₅₉	—	2	1	no	—
112	D₈×C₅₉	#41	1	2	yes	complemented
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
115	C₂×C₈×C₅₉	—	4	1	no	—
116	C₂×C₈×C₅₉	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₅₉	—	2	1	no	—
121	C₄⋊C₄×C₅₉	—	2	1	no	—
122	C₄⋊C₄×C₅₉	—	4	1	no	—
123	C₄⋊C₄×C₅₉	—	4	1	no	—
124	C₂²⋊C₄×C₅₉	—	4	1	no	—
125	C₂²⋊C₄×C₅₉	—	4	1	no	—
126	C₂²⋊C₄×C₅₉	—	4	1	no	—
127	C₄²×C₅₉	—	4	1	no	—
128	C₄²×C₅₉	—	4	1	no	—
129	C₄²×C₅₉	—	4	1	no	—
130	C₄²×C₅₉	D₈	1	1	yes	characteristic
131	C₄²×C₅₉	D₈	1	1	yes	characteristic
132	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
134	(C₂×D₅₉)⋊C₄	—	4	2	no	—
135	(C₂×D₅₉)⋊C₄	—	4	2	no	—
136	C₄⋊Dic₅₉	—	2	2	no	—
137	C₄⋊Dic₅₉	—	4	1	no	—
138	D₄₇₂	—	2	2	no	—
139	D₄₇₂	—	2	2	no	—
140	D₄₇₂	—	4	2	no	—
141	C₅₉⋊C₁₆	—	2	2	no	—
142	C₅₉⋊C₁₆	—	2	2	no	—
143	C₂³×C₅₉	—	4	1	no	—
144	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
145	C₂²×D₅₉	—	4	2	no	—
146	Q₈×C₅₉	—	2	2	no	—
147	Q₈×C₅₉	—	4	1	no	—
148	D₄×C₅₉	—	2	2	no	—
149	D₄×C₅₉	—	4	4	no	—
150	D₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	—	4	4	no	—
156	C₂×C₄×C₅₉	—	4	1	no	—
157	C₂×C₄×C₅₉	—	4	1	no	—
158	C₂×C₄×C₅₉	—	4	1	no	—
159	C₂×C₄×C₅₉	—	8	2	no	—
160	C₂×C₄×C₅₉	—	8	2	no	—
161	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
167	C₂²⋊D₅₉	—	8	4	no	—
168	C₂×Dic₅₉	—	4	2	no	—
169	D₂₃₆	—	4	2	no	—
170	D₂₃₆	—	4	2	no	—
171	D₂₃₆	—	8	2	no	—
172	D₂₃₆	—	8	2	no	—
173	C₄×D₅₉	—	8	4	no	—
174	Dic₁₁₈	—	8	2	no	—
175	C₈×C₅₉	—	2	1	no	—
176	C₈×C₅₉	—	2	1	no	—
177	C₈×C₅₉	—	2	1	no	—
178	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
179	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
180	#33675	—	59	1	no	maximal, Sylow
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	4	2	no	—
185	C₂²×C₅₉	—	8	1	no	—
186	C₂²×C₅₉	—	8	1	no	—
187	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
188	C₂×D₅₉	—	8	2	no	—
189	C₂×D₅₉	—	8	2	no	—
190	C₂×D₅₉	—	8	2	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	2	1	no	—
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	4	2	no	—
196	C₄×C₅₉	—	8	1	no	—
197	C₄×C₅₉	—	8	1	no	—
198	C₄×C₅₉	#509	1	2	yes	—
199	C₄×C₅₉	#525	1	1	yes	characteristic
200	C₄×C₅₉	#575	1	1	yes	characteristic
201	Dic₅₉	—	8	2	no	—
202	#3169	—	59	1	no	—
203	C₄×#135	D₅₉	1	1	yes	characteristic, complemented
204	#2234	—	59	2	no	—
205	#2225	—	59	1	no	—
206	#2224	—	59	1	no	—
207	#2207	—	59	1	no	—
208	#2206	—	59	1	no	—
209	#2186	—	59	2	no	—
210	#2177	—	59	2	no	—
211	#2175	—	59	2	no	—
212	#2163	—	59	1	no	—
213	C₂×C₅₉	—	4	1	no	—
214	C₂×C₅₉	—	8	2	no	—
215	C₂×C₅₉	#3100	1	1	yes	characteristic
216	C₂×C₅₉	C₂×#509	1	1	yes	characteristic
217	C₂×C₅₉	#3414	1	1	yes	characteristic
218	D₅₉	—	16	2	no	—
219	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
220	#532	—	118	1	no	—
221	C₄×#41	—	2	1	no	—
222	C₂×SD₃₂	—	59	2	no	—
223	C₂×D₁₆	—	59	2	no	—
224	#500	—	59	1	no	—
225	#493	—	59	1	no	—
226	#486	—	118	1	no	—
227	#466	—	59	2	no	—
228	#466	—	118	1	no	—
229	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
230	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
231	C₄×SD₁₆	—	2	1	no	—
232	C₄×SD₁₆	—	2	1	no	—
233	C₄×D₈	—	59	2	no	—
234	C₄×D₈	—	118	1	no	—
235	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
236	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
237	#427	C₂×D₅₉	1	1	yes	characteristic
238	#416	—	2	1	no	—
239	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
240	#367	—	59	2	no	—
241	#366	—	59	2	no	—
242	C₄⋊C₁₆	—	59	1	no	—
243	C₄⋊C₁₆	—	59	1	no	—
244	#358	—	59	2	no	—
245	#357	—	59	2	no	—
246	#357	—	59	2	no	—
247	#357	—	59	2	no	—
248	C₂²⋊C₁₆	—	59	2	no	—
249	#346	—	59	2	no	—
250	C₅₉	#33675	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	2	1	no	—
252	C₂×#41	—	236	1	no	—
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	C₂×Q₁₆	C₂²×D₅₉	1	1	yes	characteristic
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×D₈	—	59	2	no	—
258	C₂×D₈	—	118	1	no	—
259	C₂×D₈	C₂²×D₅₉	1	1	yes	characteristic
260	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
262	C₄⋊Q₈	—	118	1	no	—
263	#127	—	118	1	no	—
264	#124	—	236	1	no	—
265	#121	—	118	2	no	—
266	#121	—	236	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	4	1	no	—
272	C₄×D₄	—	4	1	no	—
273	C₄×D₄	—	118	2	no	—
274	C₄×D₄	—	236	1	no	—
275	#117	—	2	1	no	—
276	#117	—	4	1	no	—
277	C₂×C₄²	—	4	1	no	—
278	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
279	SD₃₂	—	118	4	no	—
280	D₁₆	—	118	4	no	—
281	C₂×C₁₆	—	59	2	no	—
282	C₂×C₁₆	—	59	2	no	—
283	#107	—	59	2	no	—
284	#107	—	118	1	no	—
285	#107	C₂²×D₅₉	1	1	yes	characteristic
286	#107	C₂²×D₅₉	1	1	yes	characteristic
287	#106	—	2	1	no	—
288	#103	—	2	1	no	—
289	#103	—	2	1	no	—
290	#102	—	2	1	no	—
291	#102	—	2	1	no	—
292	#102	—	118	2	no	—
293	#102	—	118	2	no	—
294	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
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	—	2	4	no	—
299	#41	—	4	2	no	—
300	#41	—	472	4	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	236	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	118	2	no	—
306	C₂×D₄	—	236	2	no	—
307	C₂×D₄	—	236	1	no	—
308	C₂×D₄	—	236	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	236	2	no	—
313	C₂²×C₄	#11745669	1	1	yes	characteristic
314	C₂²×C₄	#11745669	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
316	Q₁₆	—	2	1	no	—
317	Q₁₆	#11745685	1	2	yes	complemented
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	1	no	—
320	D₈	—	118	2	no	—
321	D₈	—	118	2	no	—
322	D₈	—	236	2	no	—
323	D₈	#11745685	1	2	yes	complemented
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
329	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
330	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	118	2	no	—
336	C₄⋊C₄	—	236	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	236	2	no	—
341	C₂²⋊C₄	—	236	2	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	#11745669	1	1	yes	characteristic
346	C₄²	#11745669	1	1	yes	characteristic
347	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
348	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
349	C₁₆	—	118	2	no	—
350	C₁₆	—	118	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	236	2	no	—
353	C₂³	C₂×#11745669	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	472	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	1	no	—
360	D₄	—	472	2	no	—
361	D₄	—	472	4	no	—
362	D₄	—	472	2	no	—
363	D₄	—	236	2	no	—
364	D₄	—	236	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	472	4	no	—
376	C₂×C₄	—	236	2	no	—
377	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
378	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
379	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
380	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
381	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	C₂×#11745685	1	1	yes	characteristic
387	C₈	C₂×#11745685	1	1	yes	characteristic
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	472	2	no	—
395	C₂²	—	472	2	no	—
396	C₂²	—	472	2	no	—
397	C₂²	C₂²×#11745669	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	8	1	no	—
405	C₄	—	472	2	no	—
406	C₄	#16837837	1	2	yes	—
407	C₄	#16837913	1	1	yes	characteristic
408	C₄	#16838200	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	8	2	no	—
411	C₂	—	944	2	no	—
412	C₂	#21434096	1	1	yes	characteristic
413	C₂	C₂×#16837837	1	1	yes	characteristic
414	C₂	#21437230	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11745669
commutator, cosocle	C₂×C₈×C₅₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₄×#135×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×D₈
hypercenter	C₄×#135	D₅₉
hypocenter	C₅₉	#33675
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #21434675	C₂	semidirect
2. #21426287	C₂	semidirect
3. #21426238	C₂	semidirect
4. #21426233	C₂	semidirect
5. #21426136	C₂	semidirect
6. #21426131	C₂	semidirect
7. #21426019	C₂	semidirect
8. #21425970	C₂	semidirect
9. #21425958	C₂	semidirect
10. #21425899	C₂	semidirect
11. C₄×#135×C₅₉	C₂	semidirect
109. Q₁₆×C₅₉	#41	semidirect
112. D₈×C₅₉	#41	semidirect
203. C₄×#135	D₅₉	semidirect
250. C₅₉	#33675	semidirect
317. Q₁₆	#11745685	semidirect
323. D₈	#11745685	semidirect

Maximal subgroups

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

subgroup	index
#21434675	2
#21426287	2
#21426238	2
#21426233	2
#21426136	2
#21426131	2
#21426019	2
#21425970	2
#21425958	2
#21425899	2
C₄×#135×C₅₉	2
#33675	59