Subgroups — #28506858

Order 15104.

446 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432806	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16837187	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16837186	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16837185	C₂	1	1	yes	maximal, characteristic, complemented
6	M₃₂×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×#350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14273733	C₂²	1	1	yes	characteristic
9	#16837948	C₄	1	1	yes	characteristic
10	C₂×#14273667	C₂²	1	1	yes	characteristic
11	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	#16837478	—	2	1	no	—
13	#16837478	—	2	1	no	—
14	C₈×C₂²⋊D₅₉	—	2	1	no	—
15	C₈×C₂²⋊D₅₉	—	2	1	no	—
16	#16837425	C₄	1	1	yes	characteristic
17	#16837370	C₄	1	1	yes	characteristic
18	#16837369	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
20	Dic₅₉⋊C₁₆	—	2	1	no	—
21	Dic₅₉⋊C₁₆	—	2	1	no	—
22	#16837187	—	2	2	no	—
23	#16837186	—	2	2	no	—
24	#16837185	—	2	2	no	—
25	#16837177	—	2	1	no	—
26	C₁₆×Dic₅₉	—	2	1	no	—
27	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#350	—	2	2	no	—
31	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
32	#14273733	—	2	1	no	—
33	#14273733	—	2	1	no	—
34	#14273733	—	2	1	no	—
35	#14273733	—	2	1	no	—
36	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
37	C₂×#11745659	—	2	1	no	—
38	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×D₅₉	—	2	1	no	—
40	#14273725	C₈	1	1	yes	characteristic
41	#14273723	C₈	1	1	yes	characteristic
42	#14273716	C₈	1	1	yes	characteristic
43	#14273714	C₈	1	1	yes	characteristic
44	#14273699	—	2	1	no	—
45	#14273699	—	2	1	no	—
46	C₄×C₂²⋊D₅₉	—	2	1	no	—
47	C₄×C₂²⋊D₅₉	—	2	1	no	—
48	C₂×C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
49	#14273667	—	2	1	no	—
50	#14273667	D₄	1	2	yes	complemented
51	C₂×C₅₉⋊C₁₆	—	2	1	no	—
52	C₂×C₅₉⋊C₁₆	—	2	1	no	—
53	C₂×C₅₉⋊C₁₆	—	2	1	no	—
54	C₂×C₅₉⋊C₁₆	—	2	1	no	—
55	Dic₅₉⋊C₈	—	2	1	no	—
56	Dic₅₉⋊C₈	—	2	1	no	—
57	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
58	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
59	(C₂×D₅₉)⋊C₈	—	2	1	no	—
60	(C₂×D₅₉)⋊C₈	—	2	1	no	—
61	C₈×Dic₅₉	D₄	1	1	yes	characteristic
62	C₈×Dic₅₉	D₄	1	1	yes	characteristic
63	C₈×Dic₅₉	D₄	1	1	yes	characteristic
64	C₈×Dic₅₉	D₄	1	1	yes	characteristic
65	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
66	#131×C₅₉	—	2	1	no	—
67	#131×C₅₉	—	2	1	no	—
68	#131×C₅₉	—	2	1	no	—
69	#131×C₅₉	—	2	1	no	—
70	C₂×M₁₆×C₅₉	—	2	1	no	—
71	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	—	2	1	no	—
73	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
74	M₃₂×C₅₉	—	2	1	no	—
75	M₃₂×C₅₉	D₄	1	2	yes	complemented
76	C₂×C₁₆×C₅₉	—	2	1	no	—
77	C₂×C₁₆×C₅₉	—	2	1	no	—
78	C₂×C₁₆×C₅₉	—	2	1	no	—
79	C₂×C₁₆×C₅₉	—	2	1	no	—
80	#41×C₅₉	—	2	1	no	—
81	#41×C₅₉	—	2	1	no	—
82	#41×C₅₉	—	2	1	no	—
83	#41×C₅₉	—	2	1	no	—
84	C₂×Q₈×C₅₉	C₂×C₈	1	1	yes	characteristic
85	C₂×D₄×C₅₉	—	2	1	no	—
86	C₂×D₄×C₅₉	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	—	2	1	no	—
88	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊D₅₉	—	2	1	no	—
90	C₂×C₂²⋊D₅₉	—	2	1	no	—
91	C₂×C₂²⋊D₅₉	—	2	1	no	—
92	C₂²×Dic₅₉	M₁₆	1	1	yes	characteristic
93	C₂²×Dic₅₉	M₁₆	1	1	yes	characteristic
94	#11745685	—	2	1	no	—
95	#11745685	—	2	1	no	—
96	#11745685	—	2	1	no	—
97	#11745685	—	2	1	no	—
98	C₂×D₂₃₆	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₅₉	—	2	1	no	—
100	C₂×Dic₁₁₈	C₂×C₈	1	1	yes	characteristic
101	M₁₆×C₅₉	—	2	1	no	—
102	M₁₆×C₅₉	—	2	1	no	—
103	M₁₆×C₅₉	—	4	1	no	—
104	M₁₆×C₅₉	—	4	1	no	—
105	C₂×C₈×C₅₉	—	2	1	no	—
106	C₂×C₈×C₅₉	—	4	1	no	—
107	C₂×C₈×C₅₉	—	4	1	no	—
108	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
113	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
114	C₂²⋊Dic₅₉	—	2	1	no	—
115	C₂²⋊Dic₅₉	—	2	1	no	—
116	(C₂×D₅₉)⋊C₄	—	2	1	no	—
117	(C₂×D₅₉)⋊C₄	—	2	1	no	—
118	Dic₅₉⋊C₄	—	2	1	no	—
119	Dic₅₉⋊C₄	—	2	1	no	—
120	C₄×Dic₅₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₅₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
124	#11745664	—	2	1	no	—
125	#11745664	—	2	1	no	—
126	C₂×C₅₉⋊C₈	—	2	1	no	—
127	C₂×C₅₉⋊C₈	—	2	1	no	—
128	C₂×C₅₉⋊C₈	—	2	1	no	—
129	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
131	#11745659	—	4	1	no	—
132	#11745659	—	4	1	no	—
133	C₈×D₅₉	—	4	1	no	—
134	C₈×D₅₉	—	4	1	no	—
135	C₁₆×C₅₉	—	2	2	no	—
136	C₁₆×C₅₉	—	4	1	no	—
137	C₅₉⋊C₁₆	—	2	2	no	—
138	C₅₉⋊C₁₆	—	4	1	no	—
139	C₂³×C₅₉	—	2	1	no	—
140	C₂³×C₅₉	C₂×M₁₆	1	1	yes	characteristic
141	C₂²×D₅₉	—	2	1	no	—
142	Q₈×C₅₉	—	2	1	no	—
143	Q₈×C₅₉	—	2	1	no	—
144	D₄×C₅₉	—	2	1	no	—
145	D₄×C₅₉	—	2	1	no	—
146	D₄×C₅₉	—	4	1	no	—
147	D₄×C₅₉	—	4	1	no	—
148	C₂×C₄×C₅₉	—	2	1	no	—
149	C₂×C₄×C₅₉	—	4	1	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
156	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
157	C₂²⋊D₅₉	—	4	2	no	—
158	C₂²⋊D₅₉	—	4	1	no	—
159	C₂²⋊D₅₉	—	4	1	no	—
160	C₂²⋊D₅₉	—	4	2	no	—
161	C₂×Dic₅₉	—	2	2	no	—
162	C₂×Dic₅₉	—	2	1	no	—
163	C₂×Dic₅₉	—	4	1	no	—
164	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
165	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
166	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
167	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
168	D₂₃₆	—	2	1	no	—
169	D₂₃₆	—	2	1	no	—
170	C₄×D₅₉	—	4	1	no	—
171	C₄×D₅₉	—	4	1	no	—
172	Dic₁₁₈	—	2	1	no	—
173	Dic₁₁₈	—	2	1	no	—
174	C₈×C₅₉	—	4	1	no	—
175	C₈×C₅₉	#121	1	1	yes	characteristic
176	C₈×C₅₉	#121	1	1	yes	characteristic
177	C₈×C₅₉	#124	1	1	yes	characteristic
178	C₈×C₅₉	#127	1	1	yes	characteristic
179	C₅₉⋊C₈	—	2	1	no	—
180	C₅₉⋊C₈	—	2	1	no	—
181	C₅₉⋊C₈	—	4	1	no	—
182	#13193	—	59	1	no	maximal, Sylow
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	2	1	no	—
185	C₂²×C₅₉	—	4	1	no	—
186	C₂²×C₅₉	—	4	1	no	—
187	C₂²×C₅₉	—	4	1	no	—
188	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
189	C₂²×C₅₉	#436	1	1	yes	characteristic
190	C₂²×C₅₉	#436	1	1	yes	characteristic
191	C₂×D₅₉	—	4	1	no	—
192	C₂×D₅₉	—	4	1	no	—
193	C₂×D₅₉	—	4	1	no	—
194	C₄×C₅₉	—	4	1	no	—
195	C₄×C₅₉	#390	1	1	yes	characteristic
196	C₄×C₅₉	#408	1	1	yes	characteristic
197	C₄×C₅₉	C₈×D₄	1	1	yes	characteristic
198	C₄×C₅₉	C₈×D₄	1	1	yes	characteristic
199	Dic₅₉	—	2	1	no	—
200	Dic₅₉	—	2	1	no	—
201	Dic₅₉	—	2	1	no	—
202	Dic₅₉	—	4	1	no	—
203	Dic₅₉	#350	1	2	yes	complemented
204	#2931	—	59	1	no	—
205	C₂×C₄⋊C₁₆	—	59	1	no	—
206	C₂×#350	—	59	1	no	—
207	C₂×#350	—	59	1	no	—
208	C₂×#350	—	59	1	no	—
209	C₂×#350	D₅₉	1	1	yes	characteristic, complemented
210	C₄×M₃₂	—	59	1	no	—
211	C₂×C₅₉	—	2	1	no	—
212	C₂×C₅₉	—	2	1	no	—
213	C₂×C₅₉	—	8	1	no	—
214	C₂×C₅₉	#1954	1	1	yes	characteristic
215	C₂×C₅₉	C₂×#350	1	1	yes	characteristic
216	C₂×C₅₉	#2117	1	1	yes	characteristic
217	D₅₉	—	8	1	no	—
218	C₂×#131	—	59	1	no	—
219	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
220	#532	—	59	1	no	—
221	C₂×M₃₂	—	59	1	no	—
222	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
223	C₂²×C₁₆	—	59	1	no	—
224	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
225	#436	—	118	1	no	—
226	#436	—	118	1	no	—
227	C₈×D₄	—	118	1	no	—
228	C₈×D₄	—	118	1	no	—
229	#423	—	59	1	no	—
230	#408	—	59	1	no	—
231	#408	—	59	1	no	—
232	C₂×C₄×C₈	—	59	1	no	—
233	C₄⋊C₁₆	—	118	1	no	—
234	C₄⋊C₁₆	—	118	1	no	—
235	#350	—	2	2	no	—
236	#350	—	118	2	no	—
237	#350	—	118	2	no	—
238	#350	—	118	2	no	—
239	#346	—	118	1	no	—
240	C₄×C₁₆	—	118	1	no	—
241	C₅₉	#13193	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	59	1	no	—
243	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
244	#131	—	2	1	no	—
245	#131	—	2	1	no	—
246	#131	—	2	1	no	—
247	#131	—	2	1	no	—
248	#131	—	118	1	no	—
249	#131	—	118	1	no	—
250	#131	—	118	1	no	—
251	#131	—	118	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	59	1	no	—
254	C₂×M₁₆	—	118	1	no	—
255	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	59	1	no	—
258	C₂²×C₈	—	118	1	no	—
259	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
260	C₄⋊Q₈	—	59	1	no	—
261	#127	—	59	1	no	—
262	#124	—	59	1	no	—
263	#124	—	59	1	no	—
264	#121	—	118	1	no	—
265	#121	—	118	1	no	—
266	C₄×D₄	—	118	1	no	—
267	C₄×D₄	—	118	1	no	—
268	C₂×C₄²	—	59	1	no	—
269	M₃₂	—	2	1	no	—
270	M₃₂	—	59	2	no	—
271	M₃₂	—	118	1	no	—
272	M₃₂	C₂²⋊D₅₉	1	2	yes	complemented
273	C₂×C₁₆	—	2	1	no	—
274	C₂×C₁₆	—	2	1	no	—
275	C₂×C₁₆	—	2	1	no	—
276	C₂×C₁₆	—	2	1	no	—
277	C₂×C₁₆	—	118	1	no	—
278	C₂×C₁₆	—	118	1	no	—
279	C₂×C₁₆	—	118	1	no	—
280	C₂×C₁₆	—	118	1	no	—
281	C₄⋊C₈	—	118	1	no	—
282	C₄⋊C₈	—	118	1	no	—
283	C₂²⋊C₈	—	118	1	no	—
284	C₂²⋊C₈	—	118	1	no	—
285	C₂²⋊C₈	—	118	1	no	—
286	C₂²⋊C₈	—	118	1	no	—
287	C₄×C₈	—	59	1	no	—
288	C₄×C₈	—	59	1	no	—
289	C₄×C₈	—	59	1	no	—
290	C₄×C₈	—	59	1	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	#41	—	118	1	no	—
296	#41	—	118	1	no	—
297	#41	—	118	1	no	—
298	#41	—	118	1	no	—
299	C₂×Q₈	—	59	1	no	—
300	C₂×Q₈	C₈×D₅₉	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	59	1	no	—
303	C₂×D₄	—	118	1	no	—
304	C₂×D₄	—	118	1	no	—
305	C₂×D₄	—	118	1	no	—
306	C₂×D₄	C₈×D₅₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	59	1	no	—
309	C₂²×C₄	—	59	1	no	—
310	C₂²×C₄	—	118	1	no	—
311	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
312	M₁₆	—	2	1	no	—
313	M₁₆	—	2	1	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	118	1	no	—
317	M₁₆	—	118	1	no	—
318	M₁₆	—	236	1	no	—
319	M₁₆	—	236	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	59	1	no	—
324	C₂×C₈	—	59	1	no	—
325	C₂×C₈	—	118	1	no	—
326	C₂×C₈	—	118	1	no	—
327	C₂×C₈	—	118	1	no	—
328	C₂×C₈	—	236	1	no	—
329	C₂×C₈	—	236	1	no	—
330	C₂×C₈	#11745685	1	1	yes	characteristic
331	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
332	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
333	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
334	C₂×C₈	#11745687	1	1	yes	characteristic
335	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
336	C₄⋊C₄	—	118	1	no	—
337	C₄⋊C₄	—	118	1	no	—
338	C₂²⋊C₄	—	118	1	no	—
339	C₂²⋊C₄	—	118	1	no	—
340	C₂²⋊C₄	—	118	1	no	—
341	C₂²⋊C₄	—	118	1	no	—
342	C₄²	—	59	1	no	—
343	C₄²	—	59	1	no	—
344	C₄²	—	59	1	no	—
345	C₄²	—	59	1	no	—
346	C₁₆	—	2	2	no	—
347	C₁₆	—	4	1	no	—
348	C₁₆	—	118	2	no	—
349	C₁₆	—	236	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	118	1	no	—
352	C₂³	M₁₆×D₅₉	1	1	yes	characteristic
353	Q₈	—	2	1	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	118	1	no	—
356	Q₈	—	118	1	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	118	1	no	—
362	D₄	—	118	1	no	—
363	D₄	—	236	2	no	—
364	D₄	—	236	2	no	—
365	D₄	—	236	1	no	—
366	D₄	—	236	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	59	1	no	—
371	C₂×C₄	—	59	1	no	—
372	C₂×C₄	—	59	1	no	—
373	C₂×C₄	—	59	1	no	—
374	C₂×C₄	—	118	2	no	—
375	C₂×C₄	—	118	1	no	—
376	C₂×C₄	—	236	1	no	—
377	C₂×C₄	—	236	1	no	—
378	C₂×C₄	—	236	1	no	—
379	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
382	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
383	C₂×C₄	#14273733	1	1	yes	characteristic
384	C₂×C₄	#14273735	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	118	1	no	—
387	C₈	—	118	1	no	—
388	C₈	—	236	1	no	—
389	C₈	#14273699	1	1	yes	characteristic
390	C₈	#14273700	1	1	yes	characteristic
391	C₈	#14273713	1	1	yes	characteristic
392	C₈	#14273723	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	236	1	no	—
399	C₂²	—	236	1	no	—
400	C₂²	—	236	1	no	—
401	C₂²	C₂²⋊C₈×D₅₉	1	1	yes	characteristic
402	C₂²	#16837477	1	1	yes	characteristic
403	C₂²	#16837478	1	1	yes	characteristic
404	C₄	—	4	1	no	—
405	C₄	—	59	2	no	—
406	C₄	—	118	1	no	—
407	C₄	—	118	1	no	—
408	C₄	—	118	1	no	—
409	C₄	—	236	1	no	—
410	C₄	#16837302	1	1	yes	characteristic
411	C₄	#16837367	1	1	yes	characteristic
412	C₄	(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
413	C₄	C₈×C₂²⋊D₅₉	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	8	1	no	—
417	C₂	—	472	1	no	—
418	C₂	#21424888	1	1	yes	characteristic
419	C₂	#350×D₅₉	1	1	yes	characteristic
420	C₂	#21425722	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₂×C₅₉×#350	C₂
socle	C₂²×C₅₉	C₂×C₂²⋊C₈
prime radical	#16837948	C₄
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂×#350	D₅₉
hypocenter	C₅₉	#13193
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#350

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₉⋊C₁₆	C₂	semidirect
3. C₂×#16837187	C₂	semidirect
4. C₂×#16837186	C₂	semidirect
5. C₂×#16837185	C₂	semidirect
6. M₃₂×Dic₅₉	C₂	semidirect
7. C₂×C₅₉×#350	C₂	semidirect
50. #14273667	D₄	semidirect
75. M₃₂×C₅₉	D₄	semidirect
203. Dic₅₉	#350	semidirect
209. C₂×#350	D₅₉	semidirect
241. C₅₉	#13193	semidirect
272. M₃₂	C₂²⋊D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21432806	2
C₂×Dic₅₉⋊C₁₆	2
C₂×#16837187	2
C₂×#16837186	2
C₂×#16837185	2
M₃₂×Dic₅₉	2
C₂×C₅₉×#350	2
#13193	59