Finite Group Databasebeta

← #28599565

Subgroups — #28599565

Order 15104.

744 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424895C211yesmaximal, characteristic
2#21424891C211yesmaximal, characteristic
3#21424820C211yesmaximal, characteristic, complemented
4#21424815C211yesmaximal, characteristic, complemented
5#21424711C211yesmaximal, characteristic, complemented
6#21424711C211yesmaximal, characteristic, complemented
7#21424704C211yesmaximal, characteristic, complemented
8#21424704C211yesmaximal, characteristic, complemented
9#21424167C211yesmaximal, characteristic, complemented
10#21424164C211yesmaximal, characteristic, complemented
11#21424080C211yesmaximal, characteristic, complemented
12#21424076C211yesmaximal, characteristic, complemented
13#21423953C211yesmaximal, characteristic, complemented
14#21423848C211yesmaximal, characteristic, complemented
15C59×#2290C211yesmaximal, characteristic
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17C2×C4⋊(C59⋊C8)C2211yescharacteristic
18C2×C4⋊(C59⋊C8)C2211yescharacteristic
19C2×C4⋊(C59⋊C8)C2211yescharacteristic
20C2×C4⋊(C59⋊C8)C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×C22⋊(C59⋊C8)C2211yescharacteristic
23C2×C22⋊(C59⋊C8)C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×#14273638C2211yescharacteristic
31C2×#14273638C2211yescharacteristic
32C2×C4×C59⋊C8C2211yescharacteristic
33C2×C4×C59⋊C8C2211yescharacteristic
34#16837157C2211yescharacteristic
35#16837157C2211yescharacteristic
36#16837157C2211yescharacteristic
37#16837157C2211yescharacteristic
38#16837157C2211yescharacteristic
39#16837157C2211yescharacteristic
40#16837157C2211yescharacteristic
41#16837157C2211yescharacteristic
42#16837157C2211yescharacteristic
43#16837157C2211yescharacteristic
44C2×C4×D4×C59C2211yescharacteristic
45C2×#117×C59C2211yescharacteristic
46C22×C42×C59C2211yescharacteristic
47C59×#388C411yescharacteristic
48C59×#388C411yescharacteristic
49C59×#387C411yescharacteristic
50C59×#387C411yescharacteristic
51C59×#386C411yescharacteristic
52C59×#386C411yescharacteristic
53C59×#385C411yescharacteristic
54C59×#385C411yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C4×C22⋊C4×C59C2211yescharacteristic
57C4×C22⋊C4×C59C2211yescharacteristic
58C59×#376C2211yescharacteristic
59C22×C59⋊C8C2311yescharacteristic
60C22×C59⋊C8C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C4⋊(C59⋊C8)—22no—
68C4⋊(C59⋊C8)—22no—
69C4⋊(C59⋊C8)—41no—
70C4⋊(C59⋊C8)—41no—
71C4⋊(C59⋊C8)—41no—
72C4⋊(C59⋊C8)—41no—
73C22⋊(C59⋊C8)—41no—
74C22⋊(C59⋊C8)—41no—
75C22⋊(C59⋊C8)—41no—
76C22⋊(C59⋊C8)—41no—
77C22⋊(C59⋊C8)—41no—
78C22⋊(C59⋊C8)—41no—
79C22⋊(C59⋊C8)—41no—
80C22⋊(C59⋊C8)—41no—
81#14273638—22no—
82#14273638—41no—
83C4×C59⋊C8—22no—
84C4×C59⋊C8—41no—
85C22×D4×C59C2×C411yescharacteristic
86C23×C4×C59C2×C411yescharacteristic
87C23×C4×C59C2×C411yescharacteristic
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C4×D4×C59—22no—
91C4×D4×C59—22no—
92#117×C59—41no—
93#117×C59—41no—
94C2×C4⋊C4×C59C2×C411yescharacteristic
95C2×C4⋊C4×C59C2×C411yescharacteristic
96C2×C4⋊C4×C59C2×C411yescharacteristic
97C2×C4⋊C4×C59C2×C411yescharacteristic
98C2×C4⋊C4×C59C2×C411yescharacteristic
99C2×C22⋊C4×C59C2×C411yescharacteristic
100C2×C22⋊C4×C59C2×C411yescharacteristic
101C2×C22⋊C4×C59C2×C411yescharacteristic
102C2×C22⋊C4×C59C2×C411yescharacteristic
103C2×C22⋊C4×C59C2×C411yescharacteristic
104C2×C22⋊C4×C59C2×C411yescharacteristic
105C2×C22⋊C4×C59C2×C411yescharacteristic
106C2×C22⋊C4×C59C2×C411yescharacteristic
107C2×C42×C59—41no—
108C2×C42×C59—41no—
109C2×C42×C59C2×C411yescharacteristic
110C2×C42×C59C2×C411yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113C2×C42×C59C2311yescharacteristic
114C2×C42×C59C2311yescharacteristic
115C2×C42×C59C2311yescharacteristic
116#95×C59C2×C411yescharacteristic
117#95×C59C2×C411yescharacteristic
118#95×C59C2×C411yescharacteristic
119#95×C59C2×C411yescharacteristic
120#95×C59C2×C411yescharacteristic
121#95×C59C2×C411yescharacteristic
122#95×C59C2×C411yescharacteristic
123#95×C59C2×C411yescharacteristic
124#95×C59C2×C411yescharacteristic
125#95×C59C2×C411yescharacteristic
126C24×C59C22×C411yescharacteristic
127C24×C59C22×C411yescharacteristic
128C2×D4×C59—22no—
129C2×D4×C59—22no—
130C2×D4×C59—41no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—41no—
146C22×C4×C59—41no—
147C22×C4×C59—41no—
148C22×C4×C59—41no—
149C22×C4×C59C22×C411yescharacteristic
150C22×C4×C59C22×C411yescharacteristic
151C22×C4×C59C22×C411yescharacteristic
152C22×C4×C59C22×C411yescharacteristic
153C22×C4×C59C22×C411yescharacteristic
154C22×C4×C59C22×C411yescharacteristic
155C22×C4×C59C22×C411yescharacteristic
156C22×C4×C59C22×C411yescharacteristic
157C22×C4×C59C22×C411yescharacteristic
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C2411yescharacteristic
162C4⋊C4×C59—22no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—41no—
165C4⋊C4×C59—41no—
166C4⋊C4×C59—41no—
167C22⋊C4×C59—22no—
168C22⋊C4×C59—22no—
169C22⋊C4×C59—22no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—41no—
172C22⋊C4×C59—41no—
173C22⋊C4×C59—41no—
174C22⋊C4×C59—41no—
175C42×C59—21no—
176C42×C59—21no—
177C42×C59—21no—
178C42×C59—21no—
179C42×C59—21no—
180C42×C59—21no—
181C42×C59—21no—
182C42×C59—21no—
183C42×C59—41no—
184C42×C59—41no—
185C42×C59#4112yes—
186C42×C59#4112yes—
187C2×C59⋊C8—21no—
188C2×C59⋊C8—21no—
189C2×C59⋊C8—21no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—21no—
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—21no—
206C2×C59⋊C8—21no—
207C2×C59⋊C8—21no—
208C2×C59⋊C8—21no—
209C2×C59⋊C8—21no—
210C2×C59⋊C8—21no—
211C23×C59—21no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59—21no—
218C23×C59—21no—
219C23×C59—21no—
220C23×C59—21no—
221C23×C59—21no—
222C23×C59—21no—
223C23×C59—21no—
224C23×C59#13112yes—
225C23×C59C23×C411yescharacteristic
226D4×C59—44no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—44no—
261C2×C4×C59—44no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59#11712yes—
271C2×C4×C59#11712yes—
272C2×C4×C59#13112yes—
273C2×C4×C59C2×#4111yescharacteristic
274C2×C4×C59C2×#4111yescharacteristic
275C2×C4×C59H(5,𝔽2)11yescharacteristic
276C2×C4×C59H(5,𝔽2)11yescharacteristic
277C2×C4×C59H(5,𝔽2)11yescharacteristic
278C2×C4×C592−1+411yescharacteristic
279C59⋊C8—41no—
280C59⋊C8—41no—
281C59⋊C8—41no—
282C59⋊C8—41no—
283C59⋊C8—41no—
284C59⋊C8—41no—
285C59⋊C8—41no—
286C59⋊C8—41no—
287#22017—591nomaximal, Sylow
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59—41no—
292C22×C59—41no—
293C22×C59—41no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59—41no—
298C22×C59—41no—
299C22×C59—41no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59C2×#11711yescharacteristic
303C22×C59#51811yescharacteristic
304C22×C59#52011yescharacteristic
305C22×C59C2×#13111yescharacteristic
306C22×C59C2×#13111yescharacteristic
307C22×C59#56811yescharacteristic
308C22×C59#56811yescharacteristic
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—22no—
312C4×C59—41no—
313C4×C59—41no—
314C4×C59—41no—
315C4×C59—41no—
316C4×C59—41no—
317C4×C59—41no—
318C4×C59—41no—
319C4×C59—41no—
320C4×C59—41no—
321C4×C59#54011yescharacteristic
322C4×C59#54011yescharacteristic
323C4×C59#54211yescharacteristic
324C4×C59#54211yescharacteristic
325#2290D5911yescharacteristic
326#1955—591no—
327#1954—591no—
328#1940—591no—
329#1939—591no—
330#1924—591no—
331#1924—591no—
332#1923—591no—
333#1923—591no—
334#1818—591no—
335#1817—591no—
336#1798—591no—
337#1797—591no—
338#1768—591no—
339#1746—591no—
340C2×C59—42no—
341C2×C59—81no—
342C2×C59#231911yescharacteristic
343C2×C59#292411yescharacteristic
344C2×C59#292511yescharacteristic
345C2×C59#297711yescharacteristic
346C2×C59#297811yescharacteristic
347C2×C59#299211yescharacteristic
348C2×C59#299311yescharacteristic
349C2×C4×D4C2×D5911yescharacteristic
350C2×#117C2×D5911yescharacteristic
351C22×C42C2×D5911yescharacteristic
352C2×C4⋊C8—591no—
353C2×C4⋊C8—591no—
354C2×C4⋊C8—591no—
355C2×C4⋊C8—591no—
356C2×C4⋊C8—591no—
357C2×C4⋊C8—591no—
358C2×C22⋊C8—591no—
359C2×C22⋊C8—591no—
360C2×C22⋊C8—591no—
361C2×C22⋊C8—591no—
362C2×C22⋊C8—591no—
363C2×C22⋊C8—591no—
364C2×C22⋊C8—591no—
365C2×C22⋊C8—591no—
366C2×#97—591no—
367C2×#97—591no—
368C2×C4×C8—591no—
369C2×C4×C8—591no—
370#388Dic5911yescharacteristic
371#388Dic5911yescharacteristic
372#387Dic5911yescharacteristic
373#387Dic5911yescharacteristic
374#386Dic5911yescharacteristic
375#386Dic5911yescharacteristic
376#385Dic5911yescharacteristic
377#385Dic5911yescharacteristic
378C4×C4⋊C4C2×D5911yescharacteristic
379C4×C22⋊C4C2×D5911yescharacteristic
380C4×C22⋊C4C2×D5911yescharacteristic
381#376C2×D5911yescharacteristic
382#336—591no—
383#336—591no—
384#336—591no—
385#336—591no—
386#336—591no—
387#336—591no—
388#336—591no—
389#336—591no—
390#336—591no—
391#336—591no—
392C59#2201711yescharacteristic, complemented, Sylow
393C22×D4C2×Dic5911yescharacteristic
394C23×C4C2×Dic5911yescharacteristic
395C23×C4C2×Dic5911yescharacteristic
396C23×C4C22×D5911yescharacteristic
397C23×C4C22×D5911yescharacteristic
398C22×C8—591no—
399C22×C8—591no—
400C22×C8—591no—
401C22×C8—591no—
402C22×C8—591no—
403C22×C8—591no—
404C22×C8—591no—
405C22×C8—591no—
406C4×D4—22no—
407C4×D4—22no—
408#117—41no—
409#117—41no—
410C2×C4⋊C4C2×Dic5911yescharacteristic
411C2×C4⋊C4C2×Dic5911yescharacteristic
412C2×C4⋊C4C2×Dic5911yescharacteristic
413C2×C4⋊C4C2×Dic5911yescharacteristic
414C2×C4⋊C4C2×Dic5911yescharacteristic
415C2×C22⋊C4C2×Dic5911yescharacteristic
416C2×C22⋊C4C2×Dic5911yescharacteristic
417C2×C22⋊C4C2×Dic5911yescharacteristic
418C2×C22⋊C4C2×Dic5911yescharacteristic
419C2×C22⋊C4C2×Dic5911yescharacteristic
420C2×C22⋊C4C2×Dic5911yescharacteristic
421C2×C22⋊C4C2×Dic5911yescharacteristic
422C2×C22⋊C4C2×Dic5911yescharacteristic
423C2×C42—41no—
424C2×C42—41no—
425C2×C42C2×Dic5911yescharacteristic
426C2×C42C2×Dic5911yescharacteristic
427C2×C42C22×D5911yescharacteristic
428C2×C42C22×D5911yescharacteristic
429C2×C42C22×D5911yescharacteristic
430C2×C42C22×D5911yescharacteristic
431C2×C42C22×D5911yescharacteristic
432C4⋊C8—1182no—
433C4⋊C8—1182no—
434C4⋊C8—2361no—
435C4⋊C8—2361no—
436C4⋊C8—2361no—
437C4⋊C8—2361no—
438C22⋊C8—2361no—
439C22⋊C8—2361no—
440C22⋊C8—2361no—
441C22⋊C8—2361no—
442C22⋊C8—2361no—
443C22⋊C8—2361no—
444C22⋊C8—2361no—
445C22⋊C8—2361no—
446#97—1182no—
447#97—2361no—
448C4×C8—1182no—
449C4×C8—2361no—
450#95C2×Dic5911yescharacteristic
451#95C2×Dic5911yescharacteristic
452#95C2×Dic5911yescharacteristic
453#95C2×Dic5911yescharacteristic
454#95C2×Dic5911yescharacteristic
455#95C2×Dic5911yescharacteristic
456#95C2×Dic5911yescharacteristic
457#95C2×Dic5911yescharacteristic
458#95C2×Dic5911yescharacteristic
459#95C2×Dic5911yescharacteristic
460C24C22×Dic5911yescharacteristic
461C24C22×Dic5911yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4C22×Dic5911yescharacteristic
484C22×C4C22×Dic5911yescharacteristic
485C22×C4C22×Dic5911yescharacteristic
486C22×C4C22×Dic5911yescharacteristic
487C22×C4C22×Dic5911yescharacteristic
488C22×C4C22×Dic5911yescharacteristic
489C22×C4C22×Dic5911yescharacteristic
490C22×C4C22×Dic5911yescharacteristic
491C22×C4C22×Dic5911yescharacteristic
492C22×C4C22×Dic5911yescharacteristic
493C22×C4C22×Dic5911yescharacteristic
494C22×C4C22×Dic5911yescharacteristic
495C22×C4C23×D5911yescharacteristic
496C2×C8—1181no—
497C2×C8—1181no—
498C2×C8—1181no—
499C2×C8—1181no—
500C2×C8—1181no—
501C2×C8—1181no—
502C2×C8—1181no—
503C2×C8—1181no—
504C2×C8—1181no—
505C2×C8—1181no—
506C2×C8—1181no—
507C2×C8—1181no—
508C2×C8—1181no—
509C2×C8—1181no—
510C2×C8—1181no—
511C2×C8—1181no—
512C2×C8—1181no—
513C2×C8—1181no—
514C2×C8—1181no—
515C2×C8—1181no—
516C2×C8—1181no—
517C2×C8—1181no—
518C2×C8—1181no—
519C2×C8—1181no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—41no—
542C42—41no—
543C42#1174568512yes—
544C42#1174568512yes—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23#1427373412yes—
559C23C23×Dic5911yescharacteristic
560D4—44no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4#1427368612yes—
605C2×C4#1427368612yes—
606C2×C4#1427373412yes—
607C2×C4C2×#1174568511yescharacteristic
608C2×C4C2×#1174568511yescharacteristic
609C2×C4#1427377211yescharacteristic
610C2×C4#1427377211yescharacteristic
611C2×C4#1427377311yescharacteristic
612C2×C4#1427377411yescharacteristic
613C8—2361no—
614C8—2361no—
615C8—2361no—
616C8—2361no—
617C8—2361no—
618C8—2361no—
619C8—2361no—
620C8—2361no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#1427368611yescharacteristic
636C22#1683787711yescharacteristic
637C22#1683788511yescharacteristic
638C22C2×#1427373411yescharacteristic
639C22C2×#1427373411yescharacteristic
640C22#1683816911yescharacteristic
641C22#1683816911yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4#1683800311yescharacteristic
655C4#1683800311yescharacteristic
656C4#1683801711yescharacteristic
657C4#1683801711yescharacteristic
658C2—42no—
659C2—81no—
660C2#2142673911yescharacteristic
661C2#2143275411yescharacteristic
662C2#2143276211yescharacteristic
663C2#2143315211yescharacteristic
664C2#2143315811yescharacteristic
665C2#2143323511yescharacteristic
666C2#2143324511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#2290C2
prime radicalC22×D4×C59C2×C4
cosocleC22×C4×C59C24
hypercenter#2290D59
hypocenterC59#22017
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
3. #21424820C2semidirect
4. #21424815C2semidirect
5. #21424711C2semidirect
6. #21424711C2semidirect
7. #21424704C2semidirect
8. #21424704C2semidirect
9. #21424167C2semidirect
10. #21424164C2semidirect
11. #21424080C2semidirect
12. #21424076C2semidirect
13. #21423953C2semidirect
14. #21423848C2semidirect
392. C59#22017semidirect

Maximal subgroups

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

subgroupindex
#214248952
#214248912
#214248202
#214248152
#214247112
#214247042
#214241672
#214241642
#214240802
#214240762
#214239532
#214238482
C59×#22902
#2201759