Subgroups — #28484875

Order 15104.

590 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837602	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424901	C₂	1	1	yes	maximal, characteristic
4	C₂×#16837145	C₂	1	1	yes	maximal, characteristic
5	#21421979	C₂	1	1	yes	maximal, characteristic, complemented
6	#21421930	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11745671	—	2	1	no	—
9	C₂×#14273724	C₂²	1	1	yes	characteristic
10	#16837602	—	2	2	no	—
11	#16837602	C₄	1	4	yes	complemented
12	Q₈×C₅₉⋊C₈	—	2	2	no	—
13	Q₈×C₅₉⋊C₈	—	2	2	no	—
14	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#14273647	—	2	1	no	—
18	C₂×#14273647	—	2	1	no	—
19	C₂×#14273647	—	2	1	no	—
20	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
21	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
22	#16837145	—	2	2	no	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₅₉	—	2	1	no	—
26	C₅₉×#384	C₂²	1	1	yes	characteristic
27	C₅₉×#340	—	2	1	no	—
28	C₂²×D₂₃₆	—	2	1	no	—
29	C₂²×D₂₃₆	—	2	1	no	—
30	C₂²×D₂₃₆	—	2	1	no	—
31	C₂×#11745671	—	2	4	no	—
32	C₂×#11745671	—	4	2	no	—
33	C₂×#11745671	—	4	2	no	—
34	C₂²×C₅₉⋊C₈	—	2	1	no	—
35	C₂²×C₅₉⋊C₈	—	2	1	no	—
36	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
37	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
38	#14273724	—	2	1	no	—
39	#14273724	—	2	1	no	—
40	#14273724	—	2	1	no	—
41	#14273724	C₂×C₄	1	2	yes	—
42	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
43	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
46	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
47	#14273647	—	2	4	no	—
48	#14273647	—	4	2	no	—
49	#14273647	—	4	2	no	—
50	C₄×C₅₉⋊C₈	—	2	4	no	—
51	C₄×C₅₉⋊C₈	—	2	1	no	—
52	C₄×C₅₉⋊C₈	—	2	1	no	—
53	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₅₉	—	2	1	no	—
55	C₄×Q₈×C₅₉	—	2	1	no	—
56	C₄×Q₈×C₅₉	—	2	1	no	—
57	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₅₉	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₅₉	—	2	1	no	—
65	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₅₉	—	2	1	no	—
67	C₄⋊C₈×C₅₉	—	2	1	no	—
68	#103×C₅₉	—	4	2	no	—
69	C₂³×D₅₉	—	4	1	no	—
70	C₂×Q₈×C₅₉	—	2	1	no	—
71	C₂×Q₈×C₅₉	—	2	1	no	—
72	C₂×Q₈×C₅₉	—	2	1	no	—
73	C₂×Q₈×C₅₉	C₂²⋊C₄	1	2	yes	—
74	C₂×Q₈×C₅₉	D₈	1	2	yes	—
75	C₂×Q₈×C₅₉	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₅₉	—	2	1	no	—
77	C₂²×C₄×C₅₉	—	2	1	no	—
78	C₂²×C₄×C₅₉	—	4	1	no	—
79	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
82	C₂×D₂₃₆	—	2	2	no	—
83	C₂×D₂₃₆	—	2	2	no	—
84	C₂×D₂₃₆	—	2	2	no	—
85	C₂×D₂₃₆	—	4	1	no	—
86	C₂×D₂₃₆	—	4	1	no	—
87	C₂×D₂₃₆	—	4	1	no	—
88	C₂×D₂₃₆	—	4	1	no	—
89	C₂×D₂₃₆	—	4	1	no	—
90	C₂×D₂₃₆	—	4	1	no	—
91	C₂×D₂₃₆	—	4	1	no	—
92	C₂×D₂₃₆	—	4	1	no	—
93	C₂×D₂₃₆	—	4	1	no	—
94	C₂×D₂₃₆	—	4	1	no	—
95	C₂×D₂₃₆	—	4	1	no	—
96	C₂×D₂₃₆	—	8	1	no	—
97	C₂×D₂₃₆	—	8	1	no	—
98	C₂×C₈×C₅₉	—	4	1	no	—
99	C₂×C₈×C₅₉	—	4	1	no	—
100	C₂×C₈×C₅₉	—	4	1	no	—
101	C₄⋊C₄×C₅₉	—	2	2	no	—
102	C₄⋊C₄×C₅₉	—	2	1	no	—
103	C₄⋊C₄×C₅₉	—	2	2	no	—
104	C₄⋊C₄×C₅₉	—	4	1	no	—
105	C₄⋊C₄×C₅₉	—	4	1	no	—
106	C₄⋊C₄×C₅₉	—	4	1	no	—
107	C₄⋊C₄×C₅₉	—	4	1	no	—
108	C₄⋊C₄×C₅₉	—	8	1	no	—
109	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
110	C₄²×C₅₉	—	2	2	no	—
111	C₄²×C₅₉	—	2	2	no	—
112	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₅₉	#41	1	1	yes	characteristic
116	#11745671	—	4	8	no	—
117	C₂×C₅₉⋊C₈	—	2	1	no	—
118	C₂×C₅₉⋊C₈	—	2	1	no	—
119	C₂×C₅₉⋊C₈	—	2	2	no	—
120	C₂×C₅₉⋊C₈	—	2	1	no	—
121	C₂×C₅₉⋊C₈	—	2	2	no	—
122	C₂×C₅₉⋊C₈	—	2	1	no	—
123	C₂×C₅₉⋊C₈	—	2	1	no	—
124	C₂×C₅₉⋊C₈	—	4	1	no	—
125	C₂×C₅₉⋊C₈	—	4	1	no	—
126	C₂×C₅₉⋊C₈	—	4	1	no	—
127	C₂×C₅₉⋊C₈	—	4	1	no	—
128	C₂×C₅₉⋊C₈	SD₁₆	1	2	yes	complemented
129	C₂³×C₅₉	#121	1	1	yes	characteristic
130	C₂²×D₅₉	—	4	2	no	—
131	C₂²×D₅₉	—	8	1	no	—
132	C₂²×D₅₉	—	8	1	no	—
133	C₂²×D₅₉	—	8	1	no	—
134	C₂²×D₅₉	—	8	1	no	—
135	C₂²×D₅₉	—	8	1	no	—
136	C₂²×D₅₉	—	8	1	no	—
137	Q₈×C₅₉	—	2	2	no	—
138	Q₈×C₅₉	—	2	2	no	—
139	Q₈×C₅₉	—	2	2	no	—
140	Q₈×C₅₉	#102	1	4	yes	complemented
141	C₂×C₄×C₅₉	—	2	2	no	—
142	C₂×C₄×C₅₉	—	2	2	no	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	1	no	—
145	C₂×C₄×C₅₉	—	2	1	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	4	1	no	—
148	C₂×C₄×C₅₉	—	4	1	no	—
149	C₂×C₄×C₅₉	—	8	1	no	—
150	C₂×C₄×C₅₉	—	8	1	no	—
151	C₂×C₄×C₅₉	—	8	1	no	—
152	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
164	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
166	D₂₃₆	—	4	2	no	—
167	D₂₃₆	—	4	2	no	—
168	D₂₃₆	—	4	2	no	—
169	D₂₃₆	—	4	2	no	—
170	D₂₃₆	—	8	2	no	—
171	D₂₃₆	—	8	2	no	—
172	D₂₃₆	—	8	1	no	—
173	D₂₃₆	—	8	1	no	—
174	D₂₃₆	—	8	1	no	—
175	D₂₃₆	—	8	1	no	—
176	C₈×C₅₉	—	8	1	no	—
177	C₅₉⋊C₈	—	2	2	no	—
178	C₅₉⋊C₈	—	4	2	no	—
179	C₅₉⋊C₈	—	4	1	no	—
180	C₅₉⋊C₈	—	4	2	no	—
181	#9222	—	59	1	no	maximal, Sylow
182	C₂²×C₅₉	#386	1	1	yes	characteristic
183	C₂²×C₅₉	#460	1	1	yes	characteristic
184	C₂²×C₅₉	#464	1	1	yes	characteristic
185	C₂²×C₅₉	#465	1	1	yes	characteristic
186	C₂²×C₅₉	#466	1	1	yes	characteristic
187	C₂²×C₅₉	#471	1	1	yes	characteristic
188	C₂²×C₅₉	#472	1	1	yes	characteristic
189	C₂×D₅₉	—	8	2	no	—
190	C₂×D₅₉	—	8	2	no	—
191	C₂×D₅₉	—	8	2	no	—
192	C₂×D₅₉	—	16	1	no	—
193	C₂×D₅₉	—	16	1	no	—
194	C₂×D₅₉	—	16	1	no	—
195	C₂×D₅₉	—	16	1	no	—
196	C₄×C₅₉	—	2	4	no	—
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	1	no	—
199	C₄×C₅₉	—	4	2	no	—
200	C₄×C₅₉	—	16	1	no	—
201	C₄×C₅₉	C₂×#102	1	1	yes	characteristic
202	C₄×C₅₉	#416	1	1	yes	characteristic
203	C₄×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
204	C₄×C₅₉	#440	1	1	yes	characteristic
205	C₄×C₅₉	#448	1	1	yes	characteristic
206	C₄×C₅₉	#449	1	1	yes	characteristic
207	C₄×C₅₉	#465	1	1	yes	characteristic
208	C₄×C₅₉	#466	1	1	yes	characteristic
209	C₂×#460	—	59	1	no	—
210	C₂×C₈×Q₈	—	59	1	no	—
211	#1957	—	59	1	no	—
212	#1803	D₅₉	1	1	yes	characteristic, complemented
213	C₂×#331	—	59	1	no	—
214	#1296	—	59	1	no	—
215	#1277	—	59	1	no	—
216	C₂×C₅₉	#1666	1	1	yes	characteristic
217	C₂×C₅₉	#1668	1	1	yes	characteristic
218	C₂×C₅₉	#1678	1	1	yes	characteristic
219	C₂×C₅₉	#1682	1	1	yes	characteristic
220	C₂×C₅₉	#1880	1	1	yes	characteristic
221	C₂×C₅₉	#1893	1	1	yes	characteristic
222	C₂×C₅₉	#1907	1	1	yes	characteristic
223	D₅₉	—	16	2	no	—
224	C₂²×SD₁₆	—	118	1	no	—
225	C₂×#127	—	59	1	no	—
226	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
227	#460	—	59	4	no	—
228	#460	—	118	2	no	—
229	C₈×Q₈	—	118	2	no	—
230	C₈×Q₈	—	118	2	no	—
231	C₂×C₄⋊C₈	—	59	1	no	—
232	C₂×C₄⋊C₈	—	59	1	no	—
233	C₂×C₄⋊C₈	—	118	1	no	—
234	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
235	C₂×#103	—	2	1	no	—
236	C₂×#102	—	118	1	no	—
237	C₂×#102	—	118	1	no	—
238	C₂×#102	—	118	1	no	—
239	C₂×C₄×C₈	—	59	1	no	—
240	C₂×C₄×C₈	—	118	1	no	—
241	#384	C₂×D₅₉	1	1	yes	characteristic
242	#340	—	2	1	no	—
243	#331	—	118	2	no	—
244	C₅₉	#9222	1	1	yes	characteristic, complemented, Sylow
245	C₂²×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
246	C₂²×D₄	—	118	1	no	—
247	C₂²×D₄	—	118	1	no	—
248	C₂²×D₄	—	118	1	no	—
249	C₂×SD₁₆	—	118	4	no	—
250	C₂×SD₁₆	—	236	2	no	—
251	C₂×SD₁₆	—	236	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	59	1	no	—
254	C₂²×C₈	—	59	1	no	—
255	C₂²×C₈	—	118	1	no	—
256	C₂²×C₈	—	118	1	no	—
257	#127	—	59	2	no	—
258	#127	—	118	1	no	—
259	#127	—	118	1	no	—
260	#127	—	118	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	C₄×D₅₉	1	2	yes	—
264	C₄×Q₈	D₂₃₆	1	2	yes	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	59	2	no	—
275	C₄⋊C₈	—	59	2	no	—
276	C₄⋊C₈	—	118	4	no	—
277	C₄⋊C₈	—	118	1	no	—
278	C₄⋊C₈	—	118	1	no	—
279	#103	—	4	2	no	—
280	#102	—	118	4	no	—
281	#102	—	236	2	no	—
282	#102	—	236	2	no	—
283	C₄×C₈	—	118	4	no	—
284	C₄×C₈	—	118	1	no	—
285	C₄×C₈	—	118	1	no	—
286	C₂⁴	—	236	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
291	C₂×Q₈	#11745669	1	2	yes	—
292	C₂×Q₈	#11745671	1	2	yes	—
293	C₂×D₄	—	118	2	no	—
294	C₂×D₄	—	118	2	no	—
295	C₂×D₄	—	118	2	no	—
296	C₂×D₄	—	472	1	no	—
297	C₂×D₄	—	472	1	no	—
298	C₂×D₄	—	236	1	no	—
299	C₂×D₄	—	236	1	no	—
300	C₂×D₄	—	236	1	no	—
301	C₂×D₄	—	236	1	no	—
302	C₂×D₄	—	236	1	no	—
303	C₂×D₄	—	236	1	no	—
304	C₂×D₄	—	236	1	no	—
305	C₂×D₄	—	236	1	no	—
306	C₂×D₄	—	236	1	no	—
307	C₂×D₄	—	236	1	no	—
308	C₂×D₄	—	236	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
313	C₂²×C₄	#11745687	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
315	SD₁₆	—	236	8	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	59	2	no	—
320	C₂×C₈	—	118	1	no	—
321	C₂×C₈	—	118	1	no	—
322	C₂×C₈	—	118	2	no	—
323	C₂×C₈	—	118	2	no	—
324	C₂×C₈	—	118	1	no	—
325	C₂×C₈	—	118	1	no	—
326	C₂×C₈	—	118	1	no	—
327	C₂×C₈	—	236	1	no	—
328	C₂×C₈	—	236	1	no	—
329	C₂×C₈	—	236	1	no	—
330	C₂×C₈	—	236	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
343	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
344	C₄²	D₄×D₅₉	1	1	yes	characteristic
345	C₄²	#11745687	1	1	yes	characteristic
346	C₂³	—	472	1	no	—
347	C₂³	—	472	1	no	—
348	C₂³	—	472	1	no	—
349	C₂³	—	472	1	no	—
350	C₂³	—	472	1	no	—
351	C₂³	—	472	1	no	—
352	C₂³	—	236	2	no	—
353	C₂³	#14273699	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	#14273647	1	4	yes	complemented
358	D₄	—	472	2	no	—
359	D₄	—	472	2	no	—
360	D₄	—	472	1	no	—
361	D₄	—	472	1	no	—
362	D₄	—	472	1	no	—
363	D₄	—	472	1	no	—
364	D₄	—	236	2	no	—
365	D₄	—	236	2	no	—
366	D₄	—	236	2	no	—
367	D₄	—	236	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	#14273697	1	1	yes	characteristic
383	C₂×C₄	#14273699	1	1	yes	characteristic
384	C₂×C₄	#14273711	1	1	yes	characteristic
385	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
386	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
388	C₂×C₄	#14273747	1	1	yes	characteristic
389	C₂×C₄	#14273747	1	1	yes	characteristic
390	C₂×C₄	#14273750	1	1	yes	characteristic
391	C₂×C₄	#14273754	1	1	yes	characteristic
392	C₂×C₄	#14273759	1	1	yes	characteristic
393	C₈	—	8	1	no	—
394	C₈	—	118	2	no	—
395	C₈	—	236	2	no	—
396	C₈	—	236	1	no	—
397	C₈	—	236	2	no	—
398	C₂²	—	944	1	no	—
399	C₂²	—	944	1	no	—
400	C₂²	—	944	1	no	—
401	C₂²	—	944	1	no	—
402	C₂²	—	472	2	no	—
403	C₂²	—	472	2	no	—
404	C₂²	—	472	2	no	—
405	C₂²	#16837279	1	1	yes	characteristic
406	C₂²	#16837600	1	1	yes	characteristic
407	C₂²	#16837626	1	1	yes	characteristic
408	C₂²	#16837633	1	1	yes	characteristic
409	C₂²	#16837636	1	1	yes	characteristic
410	C₂²	#16837667	1	1	yes	characteristic
411	C₂²	#16837670	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	16	1	no	—
417	C₄	C₂×#14273647	1	1	yes	characteristic
418	C₄	#16837396	1	1	yes	characteristic
419	C₄	#16837487	1	1	yes	characteristic
420	C₄	#16837505	1	1	yes	characteristic
421	C₄	#16837542	1	1	yes	characteristic
422	C₄	#16837550	1	1	yes	characteristic
423	C₄	#16837633	1	1	yes	characteristic
424	C₄	#16837636	1	1	yes	characteristic
425	C₂	—	944	2	no	—
426	C₂	#21423446	1	1	yes	characteristic
427	C₂	#21423454	1	1	yes	characteristic
428	C₂	#21423514	1	1	yes	characteristic
429	C₂	#21423542	1	1	yes	characteristic
430	C₂	#21424449	1	1	yes	characteristic
431	C₂	#21424522	1	1	yes	characteristic
432	C₂	#21424602	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14273699
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1803	C₂
socle	C₂³×C₅₉	#121
prime radical	C₂×#14273724	C₂²
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1803	D₅₉
hypocenter	C₅₉	#9222
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1803

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₅₉⋊C₈	C₂	semidirect
5. #21421979	C₂	semidirect
6. #21421930	C₂	semidirect
7. C₅₉×#1803	C₂	semidirect
11. #16837602	C₄	semidirect
128. C₂×C₅₉⋊C₈	SD₁₆	semidirect
140. Q₈×C₅₉	#102	semidirect
212. #1803	D₅₉	semidirect
244. C₅₉	#9222	semidirect
357. Q₈	#14273647	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837602	2
C₂×Q₈×C₅₉⋊C₈	2
#21424901	2
C₂×#16837145	2
#21421979	2
#21421930	2
C₅₉×#1803	2
#9222	59