Subgroups — #28743747

Order 15104.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#21426291	C₂	1	1	yes	maximal, characteristic, complemented
3	#21426274	C₂	1	1	yes	maximal, characteristic, complemented
4	#21426250	C₂	1	2	yes	maximal, complemented
5	#21426148	C₂	1	2	yes	maximal, complemented
6	#21426024	C₂	1	1	yes	maximal, characteristic, complemented
7	#21426007	C₂	1	1	yes	maximal, characteristic
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	C₅₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄₇₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₂₃₆	—	2	1	no	—
14	C₂×#14273670	C₂²	1	2	yes	—
15	C₂×#14273668	C₂²	1	2	yes	—
16	C₄×D₄₇₂	—	2	1	no	—
17	C₄×D₄₇₂	—	2	1	no	—
18	C₄×D₄₇₂	C₂²	1	2	yes	—
19	C₄×D₄₇₂	C₂²	1	2	yes	—
20	C₂×#14273661	C₂²	1	1	yes	characteristic
21	C₂×#14273649	—	2	1	no	—
22	#16837229	C₂²	1	2	yes	complemented
23	#16837227	C₂²	1	2	yes	complemented
24	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	complemented
25	#16837206	C₂²	1	2	yes	complemented
26	#16837203	C₂²	1	2	yes	complemented
27	#16837202	C₂²	1	2	yes	—
28	#16837202	C₂²	1	2	yes	—
29	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
30	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
31	#16837178	C₂²	1	2	yes	complemented
32	C₅₉×#529	—	2	1	no	—
33	C₅₉×#499	C₂²	1	1	yes	characteristic, complemented
34	C₅₉×#495	C₂²	1	1	yes	characteristic, complemented
35	C₅₉×#488	—	2	1	no	—
36	C₅₉×#467	C₂²	1	1	yes	characteristic
37	C₅₉×#466	C₂²	1	1	yes	characteristic
38	C₅₉×#465	—	2	1	no	—
39	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×SD₁₆×C₅₉	—	2	1	no	—
41	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₂²×D₂₃₆	—	2	1	no	—
44	C₂²×C₄×D₅₉	—	4	1	no	—
45	C₂×D₄₇₂	—	2	1	no	—
46	C₂×D₄₇₂	—	2	4	no	—
47	C₂×D₄₇₂	C₂³	1	2	yes	—
48	C₄×D₂₃₆	—	2	2	no	—
49	C₄×D₂₃₆	—	2	2	no	—
50	C₄×D₂₃₆	—	4	1	no	—
51	C₄×D₂₃₆	—	4	1	no	—
52	C₂×C₄⋊Dic₅₉	—	2	1	no	—
53	C₂×(C₂×D₅₉)⋊C₄	—	4	1	no	—
54	#14273670	—	2	4	no	—
55	#14273668	—	2	4	no	—
56	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
57	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
58	#14273661	—	2	1	no	—
59	#14273661	C₂³	1	2	yes	—
60	#14273649	—	2	2	no	—
61	#14273649	—	2	2	no	—
62	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₅₉	—	2	1	no	—
64	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
67	#126×C₅₉	—	4	1	no	—
68	#125×C₅₉	—	2	1	no	—
69	#124×C₅₉	—	2	1	no	—
70	#123×C₅₉	—	4	1	no	—
71	C₂²⋊Q₈×C₅₉	—	2	1	no	—
72	#121×C₅₉	—	2	1	no	—
73	C₄×Q₈×C₅₉	—	2	1	no	—
74	C₄×D₄×C₅₉	—	2	1	no	—
75	C₄×D₄×C₅₉	—	4	1	no	—
76	#117×C₅₉	—	4	1	no	—
77	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
78	#107×C₅₉	C₂³	1	1	yes	characteristic
79	#107×C₅₉	C₂³	1	1	yes	characteristic
80	#106×C₅₉	—	2	1	no	—
81	#103×C₅₉	—	2	1	no	—
82	#103×C₅₉	—	2	1	no	—
83	#102×C₅₉	—	2	1	no	—
84	#102×C₅₉	—	2	1	no	—
85	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
86	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₂³×D₅₉	—	4	1	no	—
90	C₂×Q₈×C₅₉	—	2	1	no	—
91	C₂×D₄×C₅₉	—	2	1	no	—
92	C₂×D₄×C₅₉	—	4	1	no	—
93	C₂²×C₄×C₅₉	—	4	1	no	—
94	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₅₉	—	4	1	no	—
98	C₂×D₂₃₆	—	2	4	no	—
99	C₂×D₂₃₆	—	2	2	no	—
100	C₂×D₂₃₆	—	4	2	no	—
101	C₂×D₂₃₆	—	4	1	no	—
102	C₂×C₄×D₅₉	—	4	2	no	—
103	C₂×C₄×D₅₉	—	4	2	no	—
104	C₂×C₄×D₅₉	—	8	4	no	—
105	Q₁₆×C₅₉	—	2	2	no	—
106	SD₁₆×C₅₉	—	4	2	no	—
107	D₈×C₅₉	—	2	2	no	—
108	C₂×C₈×C₅₉	—	2	2	no	—
109	C₂×C₈×C₅₉	—	4	1	no	—
110	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₄⋊C₄×C₅₉	—	2	1	no	—
116	C₄⋊C₄×C₅₉	—	4	1	no	—
117	C₄⋊C₄×C₅₉	—	4	1	no	—
118	C₄⋊C₄×C₅₉	—	4	1	no	—
119	C₄⋊C₄×C₅₉	—	4	1	no	—
120	C₂²⋊C₄×C₅₉	—	4	1	no	—
121	C₂²⋊C₄×C₅₉	—	4	1	no	—
122	C₂²⋊C₄×C₅₉	—	4	1	no	—
123	C₂²⋊C₄×C₅₉	—	4	1	no	—
124	C₂²⋊C₄×C₅₉	—	4	1	no	—
125	C₄²×C₅₉	—	4	1	no	—
126	C₄²×C₅₉	D₈	1	1	yes	characteristic
127	C₄²×C₅₉	D₈	1	1	yes	characteristic
128	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
130	(C₂×D₅₉)⋊C₄	—	4	2	no	—
131	(C₂×D₅₉)⋊C₄	—	4	2	no	—
132	C₄⋊Dic₅₉	—	2	2	no	—
133	C₄⋊Dic₅₉	—	4	1	no	—
134	D₄₇₂	—	2	4	no	—
135	D₄₇₂	—	2	2	no	—
136	D₄₇₂	#41	1	4	yes	—
137	C₅₉⋊C₁₆	—	2	2	no	—
138	C₅₉⋊C₁₆	—	2	2	no	—
139	C₂³×C₅₉	—	4	1	no	—
140	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
141	C₂²×D₅₉	—	4	4	no	—
142	C₂²×D₅₉	—	4	2	no	—
143	C₂²×D₅₉	—	8	2	no	—
144	C₂²×D₅₉	—	8	2	no	—
145	Q₈×C₅₉	—	4	1	no	—
146	Q₈×C₅₉	—	4	1	no	—
147	D₄×C₅₉	—	4	1	no	—
148	D₄×C₅₉	—	4	1	no	—
149	D₄×C₅₉	—	8	2	no	—
150	C₂×C₄×C₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	4	1	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	—	4	1	no	—
157	C₂×C₄×C₅₉	—	8	2	no	—
158	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×Dic₅₉	—	4	2	no	—
165	C₂×Dic₅₉	—	8	2	no	—
166	D₂₃₆	—	2	4	no	—
167	D₂₃₆	—	4	4	no	—
168	D₂₃₆	—	4	2	no	—
169	C₄×D₅₉	—	8	4	no	—
170	C₄×D₅₉	—	8	4	no	—
171	C₈×C₅₉	—	2	1	no	—
172	C₈×C₅₉	—	2	1	no	—
173	C₈×C₅₉	—	2	1	no	—
174	C₈×C₅₉	C₂×#41	1	2	yes	—
175	#33674	—	59	1	no	maximal, Sylow
176	C₂²×C₅₉	—	2	1	no	—
177	C₂²×C₅₉	—	2	1	no	—
178	C₂²×C₅₉	—	8	1	no	—
179	C₂²×C₅₉	—	8	1	no	—
180	C₂²×C₅₉	—	8	1	no	—
181	C₂²×C₅₉	#509	1	2	yes	—
182	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₅₉	—	4	4	no	—
184	C₂×D₅₉	—	8	8	no	—
185	C₂×D₅₉	—	8	2	no	—
186	C₂×D₅₉	—	8	2	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	8	1	no	—
193	C₄×C₅₉	—	8	1	no	—
194	C₄×C₅₉	—	8	1	no	—
195	C₄×C₅₉	#525	1	1	yes	characteristic
196	C₄×C₅₉	#575	1	1	yes	characteristic
197	Dic₅₉	—	8	2	no	—
198	#3168	D₅₉	1	1	yes	characteristic, complemented
199	C₂×C₄×D₈	—	59	1	no	—
200	#2235	—	59	1	no	—
201	#2232	—	59	1	no	—
202	#2228	—	59	2	no	—
203	#2210	—	59	2	no	—
204	#2187	—	59	1	no	—
205	#2184	—	59	1	no	—
206	#2177	—	59	2	no	—
207	#2175	—	59	2	no	—
208	#2163	—	59	1	no	—
209	C₂×C₅₉	—	2	2	no	—
210	C₂×C₅₉	—	16	1	no	—
211	C₂×C₅₉	#3100	1	1	yes	characteristic
212	C₂×C₅₉	C₂×#509	1	1	yes	characteristic
213	C₂×C₅₉	#3414	1	1	yes	characteristic
214	D₅₉	—	8	4	no	—
215	C₂²×D₈	—	59	1	no	—
216	#529	—	2	1	no	—
217	C₂×C₄×D₄	—	118	1	no	—
218	C₂×SD₃₂	—	59	2	no	—
219	C₂×D₁₆	—	59	2	no	—
220	#499	C₂×D₅₉	1	1	yes	characteristic, complemented
221	#495	C₂×D₅₉	1	1	yes	characteristic, complemented
222	#488	—	2	1	no	—
223	#467	C₂×D₅₉	1	1	yes	characteristic
224	#466	C₂×D₅₉	1	1	yes	characteristic
225	#465	—	2	1	no	—
226	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
227	C₄×SD₁₆	—	2	1	no	—
228	C₄×D₈	—	59	2	no	—
229	C₄×D₈	—	59	2	no	—
230	C₄×D₈	—	118	1	no	—
231	C₄×D₈	—	118	1	no	—
232	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic, complemented
233	C₂×#107	—	59	1	no	—
234	C₂×#102	—	118	1	no	—
235	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
236	#367	—	59	2	no	—
237	#366	—	59	2	no	—
238	C₄⋊C₁₆	—	59	2	no	—
239	#358	—	59	2	no	—
240	#357	—	59	2	no	—
241	#357	—	59	2	no	—
242	#357	—	59	2	no	—
243	C₂²⋊C₁₆	—	59	1	no	—
244	C₂²⋊C₁₆	—	59	1	no	—
245	#346	—	59	2	no	—
246	C₅₉	#33674	1	1	yes	characteristic, complemented, Sylow
247	C₂²×D₄	—	118	1	no	—
248	C₂³×C₄	—	236	1	no	—
249	C₂×Q₁₆	C₂²×D₅₉	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	—	59	2	no	—
252	C₂×D₈	—	118	4	no	—
253	C₂×D₈	—	118	1	no	—
254	C₂×D₈	C₂²×D₅₉	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
257	#126	—	4	1	no	—
258	#125	—	2	1	no	—
259	#124	—	2	1	no	—
260	#123	—	4	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	#121	—	2	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	118	2	no	—
267	C₄×D₄	—	118	2	no	—
268	C₄×D₄	—	236	1	no	—
269	C₄×D₄	—	236	1	no	—
270	#117	—	4	1	no	—
271	C₂×C₄⋊C₄	—	118	1	no	—
272	C₂×C₂²⋊C₄	—	236	1	no	—
273	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
274	SD₃₂	—	118	4	no	—
275	D₁₆	—	118	4	no	—
276	C₂×C₁₆	—	59	2	no	—
277	C₂×C₁₆	—	59	2	no	—
278	#107	—	59	2	no	—
279	#107	—	118	1	no	—
280	#107	C₂²×D₅₉	1	1	yes	characteristic
281	#107	C₂²×D₅₉	1	1	yes	characteristic
282	#106	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#102	—	2	1	no	—
286	#102	—	2	1	no	—
287	#102	—	118	2	no	—
288	#102	—	118	2	no	—
289	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
290	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
292	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
293	C₂⁴	—	236	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	118	4	no	—
298	C₂×D₄	—	118	2	no	—
299	C₂×D₄	—	236	2	no	—
300	C₂×D₄	—	236	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	472	4	no	—
303	C₂²×C₄	—	236	1	no	—
304	C₂²×C₄	—	236	2	no	—
305	C₂²×C₄	—	236	2	no	—
306	C₂²×C₄	#11745669	1	1	yes	characteristic
307	C₂²×C₄	#11745669	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
309	Q₁₆	—	2	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	59	4	no	—
313	D₈	—	118	4	no	—
314	D₈	—	118	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
318	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
319	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
320	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	118	2	no	—
328	C₄⋊C₄	—	236	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	236	2	no	—
335	C₂²⋊C₄	—	236	2	no	—
336	C₄²	—	4	1	no	—
337	C₄²	#11745669	1	1	yes	characteristic
338	C₄²	#11745669	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
341	C₁₆	—	118	2	no	—
342	C₁₆	—	118	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	472	2	no	—
345	C₂³	—	472	2	no	—
346	C₂³	—	236	4	no	—
347	C₂³	—	236	2	no	—
348	C₂³	C₂×#11745669	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	118	4	no	—
355	D₄	—	236	4	no	—
356	D₄	—	236	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	472	4	no	—
366	C₂×C₄	—	472	4	no	—
367	C₂×C₄	—	472	2	no	—
368	C₂×C₄	—	236	2	no	—
369	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
370	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
371	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
372	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
373	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	#41×D₅₉	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	472	8	no	—
385	C₂²	—	472	2	no	—
386	C₂²	—	472	2	no	—
387	C₂²	—	236	4	no	—
388	C₂²	#16837837	1	2	yes	—
389	C₂²	C₂²×#11745669	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	1	no	—
398	C₄	—	472	2	no	—
399	C₄	#16837909	1	1	yes	characteristic
400	C₄	#16838200	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	16	1	no	—
403	C₂	—	472	4	no	—
404	C₂	#21434092	1	1	yes	characteristic
405	C₂	C₂×#16837837	1	1	yes	characteristic
406	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	C₅₉×#3168	C₂
socle	C₂²×C₅₉	C₂²×D₈
prime radical	#21426007	C₂
hypercenter	#3168	D₅₉
hypocenter	C₅₉	#33674
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3168

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₄₇₂	C₂	semidirect
2. #21426291	C₂	semidirect
3. #21426274	C₂	semidirect
4. #21426250	C₂	semidirect
5. #21426148	C₂	semidirect
6. #21426024	C₂	semidirect
8. #21425970	C₂	semidirect
9. #21425958	C₂	semidirect
10. #21425899	C₂	semidirect
11. C₅₉×#3168	C₂	semidirect
22. #16837229	C₂²	semidirect
23. #16837227	C₂²	semidirect
24. C₄⋊(C₅₉⋊C₁₆)	C₂²	semidirect
25. #16837206	C₂²	semidirect
26. #16837203	C₂²	semidirect
31. #16837178	C₂²	semidirect
33. C₅₉×#499	C₂²	semidirect
34. C₅₉×#495	C₂²	semidirect
39. C₄×Q₁₆×C₅₉	C₂²	semidirect
41. C₄×D₈×C₅₉	C₂²	semidirect
198. #3168	D₅₉	semidirect
220. #499	C₂×D₅₉	semidirect
221. #495	C₂×D₅₉	semidirect
226. C₄×Q₁₆	C₂×D₅₉	semidirect
232. C₄×D₈	C₂×D₅₉	semidirect
246. C₅₉	#33674	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄₇₂	2
#21426291	2
#21426274	2
#21426250	2
#21426148	2
#21426024	2
#21426007	2
#21425970	2
#21425958	2
#21425899	2
C₅₉×#3168	2
#33674	59