Subgroups — #28571370

Order 15104.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434419	C₂	1	1	yes	maximal, characteristic
2	#21434135	C₂	1	1	yes	maximal, characteristic, complemented
3	#21434127	C₂	1	1	yes	maximal, characteristic
4	#21423678	C₂	1	2	yes	maximal, complemented
5	#21423664	C₂	1	2	yes	maximal, complemented
6	#21423650	C₂	1	2	yes	maximal, complemented
7	#21423636	C₂	1	2	yes	maximal, complemented
8	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422754	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422746	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837952	C₂²	1	1	yes	characteristic
14	#16837757	—	2	1	no	—
15	#16837757	—	2	1	no	—
16	#16837753	C₂²	1	1	yes	characteristic
17	#16837753	C₂²	1	1	yes	characteristic
18	#16837749	C₂²	1	1	yes	characteristic
19	#16837749	C₂²	1	1	yes	characteristic
20	#16837737	—	2	1	no	—
21	#16837720	—	2	1	no	—
22	#16837697	C₂²	1	2	yes	—
23	#16837687	C₂²	1	2	yes	—
24	#16837612	C₂²	1	2	yes	—
25	#16837602	C₂²	1	2	yes	—
26	#16837558	—	2	1	no	—
27	#16837541	—	2	1	no	—
28	C₄×#11745672	—	2	2	no	—
29	C₄×#11745671	—	2	2	no	—
30	#16837455	C₂²	1	1	yes	characteristic
31	#16837455	C₂²	1	1	yes	characteristic
32	#16837399	—	2	1	no	—
33	#16837399	—	2	1	no	—
34	#16837155	C₂²	1	2	yes	—
35	#16837153	C₂²	1	2	yes	—
36	#16837150	C₂²	1	2	yes	—
37	#16837149	C₂²	1	2	yes	—
38	#16837147	C₂²	1	2	yes	—
39	#16837145	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#446	—	2	1	no	—
42	C₅₉×#446	—	2	1	no	—
43	C₅₉×#446	C₂²	1	2	yes	—
44	C₅₉×#446	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
46	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#97×C₅₉	—	2	1	no	—
48	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#11745685	—	2	1	no	—
50	C₂×#11745672	—	2	2	no	—
51	C₂×#11745671	—	2	2	no	—
52	#14273727	C₂³	1	1	yes	characteristic
53	#14273727	C₂³	1	1	yes	characteristic
54	#14273727	C₂³	1	1	yes	characteristic
55	#14273724	C₂³	1	1	yes	characteristic
56	#14273719	—	2	1	no	—
57	#14273715	—	2	1	no	—
58	#14273706	—	2	1	no	—
59	#14273706	—	2	1	no	—
60	#14273701	—	2	1	no	—
61	#14273701	—	2	1	no	—
62	C₄×Dic₁₁₈	—	2	1	no	—
63	C₄×Dic₁₁₈	—	2	1	no	—
64	C₄×D₂₃₆	—	2	1	no	—
65	C₄×D₂₃₆	—	2	1	no	—
66	#14273686	—	2	1	no	—
67	#14273660	—	2	2	no	—
68	#14273658	—	2	2	no	—
69	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
70	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
71	#14273652	—	2	1	no	—
72	#14273652	—	2	1	no	—
73	#14273652	—	2	1	no	—
74	#14273652	—	2	1	no	—
75	#14273651	—	2	2	no	—
76	#14273651	—	2	2	no	—
77	#14273650	—	2	2	no	—
78	#14273649	—	2	1	no	—
79	#14273649	—	2	1	no	—
80	#14273649	—	2	1	no	—
81	#14273649	—	2	1	no	—
82	#14273647	—	2	2	no	—
83	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
84	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
85	C₄×C₅₉⋊C₈	—	2	1	no	—
86	C₄×C₅₉⋊C₈	—	2	1	no	—
87	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₅₉	—	2	1	no	—
89	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₅₉	—	2	1	no	—
92	C₄×Q₈×C₅₉	—	2	1	no	—
93	C₄×Q₈×C₅₉	D₄	1	2	yes	—
94	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅₉	—	2	1	no	—
98	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₅₉	—	2	2	no	—
100	C₄⋊C₈×C₅₉	—	2	2	no	—
101	C₄⋊C₈×C₅₉	—	2	1	no	—
102	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
103	#97×C₅₉	—	2	2	no	—
104	#97×C₅₉	—	2	2	no	—
105	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
106	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₅₉	—	2	1	no	—
110	C₂×Q₈×C₅₉	—	4	2	no	—
111	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₅₉	—	2	1	no	—
113	C₂²×C₄×C₅₉	—	2	1	no	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₅₉	—	4	1	no	—
118	#11745685	—	4	2	no	—
119	#11745685	—	4	2	no	—
120	C₂×D₂₃₆	—	2	1	no	—
121	C₂×D₂₃₆	—	2	1	no	—
122	C₂×D₂₃₆	—	2	1	no	—
123	C₂×C₄×D₅₉	—	4	1	no	—
124	C₂×Dic₁₁₈	—	2	1	no	—
125	C₂×Dic₁₁₈	—	2	1	no	—
126	C₂×Dic₁₁₈	—	2	1	no	—
127	C₂×C₈×C₅₉	—	2	2	no	—
128	C₂×C₈×C₅₉	—	2	2	no	—
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	4	2	no	—
131	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₅₉	—	2	2	no	—
136	C₄⋊C₄×C₅₉	—	2	1	no	—
137	C₄⋊C₄×C₅₉	—	2	2	no	—
138	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
139	C₄²×C₅₉	—	2	2	no	—
140	C₄²×C₅₉	—	2	2	no	—
141	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅₉	#41	1	1	yes	characteristic
144	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₅₉	—	4	1	no	—
146	#11745672	—	4	4	no	—
147	#11745671	—	4	4	no	—
148	(C₂×D₅₉)⋊C₄	—	4	1	no	—
149	(C₂×D₅₉)⋊C₄	—	4	1	no	—
150	C₄⋊Dic₅₉	—	2	1	no	—
151	C₄⋊Dic₅₉	—	2	1	no	—
152	C₄⋊Dic₅₉	—	2	1	no	—
153	C₄⋊Dic₅₉	—	2	1	no	—
154	C₄⋊Dic₅₉	—	2	1	no	—
155	C₄⋊Dic₅₉	—	2	1	no	—
156	Dic₅₉⋊C₄	—	4	1	no	—
157	Dic₅₉⋊C₄	—	4	1	no	—
158	C₄×Dic₅₉	—	4	1	no	—
159	C₂×C₅₉⋊C₈	—	2	2	no	—
160	C₂×C₅₉⋊C₈	—	2	2	no	—
161	C₂³×C₅₉	#121	1	1	yes	characteristic
162	C₂²×D₅₉	—	4	1	no	—
163	Q₈×C₅₉	—	2	2	no	—
164	Q₈×C₅₉	—	2	2	no	—
165	Q₈×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
167	C₂×C₄×C₅₉	—	2	2	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	4	1	no	—
170	C₂×C₄×C₅₉	—	4	2	no	—
171	C₂×C₄×C₅₉	—	4	2	no	—
172	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₅₉	#135	1	2	yes	—
176	C₂×C₄×C₅₉	#137	1	2	yes	—
177	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₅₉	—	8	2	no	—
181	C₂×Dic₅₉	—	4	1	no	—
182	C₂×Dic₅₉	—	4	1	no	—
183	C₂×Dic₅₉	—	4	1	no	—
184	D₂₃₆	—	4	1	no	—
185	D₂₃₆	—	4	1	no	—
186	D₂₃₆	—	4	2	no	—
187	D₂₃₆	—	8	1	no	—
188	C₄×D₅₉	—	8	2	no	—
189	Dic₁₁₈	—	4	1	no	—
190	Dic₁₁₈	—	4	1	no	—
191	Dic₁₁₈	—	4	2	no	—
192	Dic₁₁₈	—	8	1	no	—
193	C₈×C₅₉	—	2	1	no	—
194	C₈×C₅₉	—	2	1	no	—
195	C₈×C₅₉	—	2	1	no	—
196	C₈×C₅₉	—	2	1	no	—
197	C₈×C₅₉	—	4	2	no	—
198	C₅₉⋊C₈	—	4	2	no	—
199	C₅₉⋊C₈	—	4	2	no	—
200	#19155	—	59	1	no	maximal, Sylow
201	C₂²×C₅₉	—	2	1	no	—
202	C₂²×C₅₉	—	2	1	no	—
203	C₂²×C₅₉	#464	1	2	yes	—
204	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
205	C₂×D₅₉	—	8	1	no	—
206	C₂×D₅₉	—	8	1	no	—
207	C₂×D₅₉	—	8	1	no	—
208	C₄×C₅₉	—	2	1	no	—
209	C₄×C₅₉	—	2	1	no	—
210	C₄×C₅₉	—	2	1	no	—
211	C₄×C₅₉	—	4	2	no	—
212	C₄×C₅₉	—	4	2	no	—
213	C₄×C₅₉	#464	1	2	yes	—
214	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
215	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
216	C₄×C₅₉	#575	1	2	yes	—
217	Dic₅₉	—	8	1	no	—
218	Dic₅₉	—	8	1	no	—
219	Dic₅₉	—	8	1	no	—
220	#3131	—	59	1	no	—
221	#3104	—	59	1	no	—
222	#3103	—	59	1	no	—
223	C₂×#446	D₅₉	1	1	yes	characteristic, complemented
224	#1704	—	59	2	no	—
225	#1702	—	59	2	no	—
226	#1700	—	59	2	no	—
227	#1698	—	59	2	no	—
228	#1564	—	59	1	no	—
229	#1542	—	59	1	no	—
230	#1540	—	59	1	no	—
231	C₂×C₅₉	—	2	2	no	—
232	C₂×C₅₉	C₂×#464	1	1	yes	characteristic
233	C₂×C₅₉	#3054	1	1	yes	characteristic
234	C₂×C₅₉	#3067	1	1	yes	characteristic
235	D₅₉	—	16	1	no	—
236	#533	—	59	1	no	—
237	#532	—	59	1	no	—
238	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
239	#488	—	118	1	no	—
240	#488	—	118	1	no	—
241	#487	—	59	1	no	—
242	#487	—	59	1	no	—
243	#486	—	59	1	no	—
244	#486	—	59	1	no	—
245	#484	—	118	1	no	—
246	#481	—	118	1	no	—
247	#477	—	59	2	no	—
248	#475	—	59	2	no	—
249	#462	—	59	2	no	—
250	#460	—	59	2	no	—
251	#451	—	118	1	no	—
252	#448	—	118	1	no	—
253	#446	—	2	1	no	—
254	#446	—	2	1	no	—
255	#446	C₂×D₅₉	1	2	yes	—
256	#446	C₂×D₅₉	1	2	yes	—
257	C₄×Q₁₆	—	118	2	no	—
258	C₄×SD₁₆	—	118	2	no	—
259	#431	—	59	1	no	—
260	#431	—	59	1	no	—
261	C₂×C₄⋊C₈	—	2	1	no	—
262	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
263	#416	—	118	1	no	—
264	#416	—	118	1	no	—
265	C₂×#97	—	2	1	no	—
266	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
267	#335	—	59	2	no	—
268	#334	—	59	2	no	—
269	#333	—	59	2	no	—
270	#332	—	59	2	no	—
271	#332	—	59	2	no	—
272	#331	—	59	2	no	—
273	C₅₉	#19155	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	118	1	no	—
275	C₂²×Q₈	D₂₃₆	1	1	yes	characteristic
276	C₂×Q₁₆	—	118	2	no	—
277	C₂×SD₁₆	—	118	2	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
280	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
281	C₄⋊Q₈	—	59	1	no	—
282	C₄⋊Q₈	—	59	1	no	—
283	C₄⋊Q₈	—	59	1	no	—
284	#127	—	59	1	no	—
285	#125	—	118	1	no	—
286	#124	—	118	1	no	—
287	C₂²⋊Q₈	—	118	1	no	—
288	C₂²⋊Q₈	—	118	1	no	—
289	#121	—	118	1	no	—
290	#121	—	118	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	118	1	no	—
294	C₄×Q₈	—	118	1	no	—
295	C₄×Q₈	D₂₃₆	1	2	yes	—
296	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
297	C₄×D₄	—	118	1	no	—
298	C₄×D₄	—	118	1	no	—
299	#117	—	118	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
304	#107	—	118	2	no	—
305	#106	—	118	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	59	2	no	—
310	C₄⋊C₈	—	59	2	no	—
311	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
312	#103	—	118	2	no	—
313	#103	—	118	2	no	—
314	#103	—	118	1	no	—
315	#103	—	118	1	no	—
316	#103	—	118	1	no	—
317	#103	—	118	1	no	—
318	#103	—	118	2	no	—
319	#102	—	118	1	no	—
320	#102	—	118	1	no	—
321	#102	—	118	1	no	—
322	#102	—	118	1	no	—
323	#102	—	118	2	no	—
324	C₂²⋊C₈	—	118	1	no	—
325	C₂²⋊C₈	—	118	1	no	—
326	#97	—	2	2	no	—
327	#97	—	2	2	no	—
328	C₄×C₈	—	118	1	no	—
329	C₄×C₈	—	118	1	no	—
330	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
331	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
334	#41	—	236	2	no	—
335	#41	—	236	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	118	1	no	—
339	C₂×Q₈	—	118	1	no	—
340	C₂×Q₈	—	118	1	no	—
341	C₂×Q₈	C₂×D₂₃₆	1	2	yes	—
342	C₂×D₄	—	118	1	no	—
343	C₂×D₄	—	118	1	no	—
344	C₂×D₄	—	118	1	no	—
345	C₂×D₄	—	236	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	236	1	no	—
349	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
350	C₂²×C₄	#11745685	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
352	Q₁₆	—	236	4	no	—
353	SD₁₆	—	236	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	118	2	no	—
359	C₂×C₈	—	118	2	no	—
360	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
362	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	118	1	no	—
368	C₄⋊C₄	—	118	1	no	—
369	C₄⋊C₄	—	118	1	no	—
370	C₄⋊C₄	—	118	1	no	—
371	C₄⋊C₄	—	118	1	no	—
372	C₄⋊C₄	—	118	1	no	—
373	C₄⋊C₄	—	236	1	no	—
374	C₄⋊C₄	—	236	1	no	—
375	C₄⋊C₄	C₂×D₂₃₆	1	2	yes	—
376	C₂²⋊C₄	—	236	1	no	—
377	C₂²⋊C₄	—	236	1	no	—
378	C₂²⋊C₄	—	236	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	236	1	no	—
382	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
383	C₄²	#11745685	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
385	C₄²	C₂³×D₅₉	1	1	yes	characteristic
386	C₂³	—	236	1	no	—
387	C₂³	#14273701	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	472	1	no	—
392	Q₈	—	236	1	no	—
393	Q₈	—	236	1	no	—
394	Q₈	—	236	2	no	—
395	D₄	—	472	1	no	—
396	D₄	—	472	2	no	—
397	D₄	—	236	1	no	—
398	D₄	—	236	1	no	—
399	D₄	—	236	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	472	2	no	—
407	C₂×C₄	—	236	1	no	—
408	C₂×C₄	—	236	1	no	—
409	C₂×C₄	—	236	1	no	—
410	C₂×C₄	#14273701	1	1	yes	characteristic
411	C₂×C₄	#14273701	1	1	yes	characteristic
412	C₂×C₄	#14273701	1	1	yes	characteristic
413	C₂×C₄	#14273747	1	2	yes	—
414	C₂×C₄	#14273758	1	2	yes	—
415	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
417	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	236	2	no	—
424	C₈	—	236	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	472	1	no	—
428	C₂²	—	472	1	no	—
429	C₂²	—	472	1	no	—
430	C₂²	#16837624	1	2	yes	—
431	C₂²	C₂×#14273701	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	472	1	no	—
438	C₄	—	472	1	no	—
439	C₄	—	472	1	no	—
440	C₄	#16837624	1	2	yes	—
441	C₄	C₂×#14273747	1	1	yes	characteristic
442	C₄	C₂×#14273758	1	1	yes	characteristic
443	C₄	#16838202	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	944	1	no	—
446	C₂	C₂×#16837624	1	1	yes	characteristic
447	C₂	#21433705	1	1	yes	characteristic
448	C₂	#21433816	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14273701
commutator, cosocle	C₄²×C₅₉	C₂⁴
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₅₉×#446	C₂
socle	C₂²×C₅₉	C₂×#121
prime radical	#16837952	C₂²
hypercenter	C₂×#446	D₅₉
hypocenter	C₅₉	#19155
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
2. #21434135	C₂	semidirect
4. #21423678	C₂	semidirect
5. #21423664	C₂	semidirect
6. #21423650	C₂	semidirect
7. #21423636	C₂	semidirect
8. #21422844	C₂	semidirect
9. #21422754	C₂	semidirect
11. C₂×C₅₉×#446	C₂	semidirect
223. C₂×#446	D₅₉	semidirect
273. C₅₉	#19155	semidirect

Maximal subgroups

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

subgroup	index
#21434419	2
#21434135	2
#21434127	2
#21423678	2
#21423664	2
#21423650	2
#21423636	2
#21422844	2
#21422754	2
#21422746	2
C₂×C₅₉×#446	2
#19155	59