Finite Group Databasebeta

← #28605117

Subgroups — #28605117

Order 15104.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838098C211yesmaximal, characteristic
2C2×#16837480C211yesmaximal, characteristic, complemented
3#21425060C211yesmaximal, characteristic, complemented
4#21425053C211yesmaximal, characteristic, complemented
5#21424532C211yesmaximal, characteristic, complemented
6#21424532C211yesmaximal, characteristic, complemented
7#21424418C211yesmaximal, characteristic, complemented
8#21424413C211yesmaximal, characteristic, complemented
9#21424188C211yesmaximal, characteristic, complemented
10#21424180C211yesmaximal, characteristic, complemented
11#21424103C211yesmaximal, characteristic, complemented
12C4×#14273647C211yesmaximal, characteristic, complemented
13#21423817C211yesmaximal, characteristic, complemented
14#21423815C211yesmaximal, characteristic, complemented
15C59×#2352C211yesmaximal, characteristic, complemented
16C22×#11745664C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18#16838098—24no—
19#16838098C418yescomplemented
20C2×#14273722—21no—
21C2×#14273719C2211yescharacteristic
22C2×#14273709—21no—
23C2×#14273701C2211yescharacteristic
24C2×#14273701C2211yescharacteristic
25C2×#14273699—21no—
26C2×C4×D236C2211yescharacteristic
27C2×(C22⋊D59)⋊C4—21no—
28C2×#14273686C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30#16837480—24no—
31C2×C4⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×C4×D4×C59C2211yescharacteristic
52C2×#117×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#388—21no—
55C59×#387—21no—
56C59×#386—21no—
57C59×#382C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59—21no—
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C22⋊D59—21no—
65C23×Dic59—21no—
66C22×C4×D59—21no—
67C2×#11745664—22no—
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664—22no—
71C2×#11745664—41no—
72C2×#11745664—41no—
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77#14273722—28no—
78#14273719—22no—
79#14273719C2×C414yescomplemented
80#14273709—28no—
81#14273701—22no—
82#14273701—22no—
83#14273701C2×C414yes—
84#14273701C2×C414yescomplemented
85#14273699—28no—
86C4×D236—22no—
87C4×D236C2×C414yescomplemented
88(C22⋊D59)⋊C4—28no—
89#14273686—22no—
90#14273686C2×C414yes—
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59C2×C414yescomplemented
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C4⋊Dic59C2311yescharacteristic
96C2×C4⋊Dic59C2311yescharacteristic
97C2×Dic59⋊C4—21no—
98C2×Dic59⋊C4—21no—
99C2×C22⋊Dic59—21no—
100C2×(C2×D59)⋊C4—21no—
101C2×(C2×D59)⋊C4—21no—
102C2×(C2×D59)⋊C4—21no—
103C2×C4×Dic59—21no—
104C4⋊(C59⋊C8)—22no—
105#14273647—22no—
106#14273647—22no—
107#14273647—41no—
108#14273647—41no—
109C22⋊(C59⋊C8)—22no—
110C22⋊(C59⋊C8)—22no—
111C4×C59⋊C8—22no—
112C22×D4×C59D411yescharacteristic
113C23×C4×C59—21no—
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C4×D4×C59C2×C414yes—
117C4×D4×C59D414yes—
118#117×C59—22no—
119#117×C59—41no—
120C2×C4⋊C4×C59—22no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—41no—
123C2×C4⋊C4×C59D411yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C23×D59—21no—
144C2×D4×C59—41no—
145C2×D4×C59—41no—
146C2×D4×C59C22⋊C414yes—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—81no—
162C22×C4×C59C22×C412yes—
163C22×C4×C59C22×C412yes—
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D412yes—
169C22×C4×C59C2×D412yes—
170C22×C4×C59C2411yescharacteristic
171C2×C22⋊D59—24no—
172C2×C22⋊D59—24no—
173C2×C22⋊D59—42no—
174C2×C22⋊D59—42no—
175C2×C22⋊D59—81no—
176C2×C22⋊D59—81no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—24no—
181C22×Dic59—81no—
182C22×Dic59—81no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236C22×C412yes—
189C2×C4×D59—24no—
190C2×C4×D59—81no—
191C2×C4×D59—81no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—42no—
200C4⋊C4×C59C22⋊C414yes—
201C4⋊C4×C59#4112yes—
202C22⋊C4×C59—42no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—81no—
205C22⋊C4×C59C22⋊C414yes—
206C22⋊C4×C59C22⋊C414yes—
207C42×C59—42no—
208C42×C59—81no—
209C42×C59C22×C412yes—
210C42×C59C2×D412yes—
211C22⋊Dic59—24no—
212(C2×D59)⋊C4—24no—
213(C2×D59)⋊C4—24no—
214(C2×D59)⋊C4—24no—
215C4⋊Dic59—24no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59C22×C412yes—
220C4⋊Dic59C22×C412yes—
221C4⋊Dic59C22×C412yes—
222Dic59⋊C4—24no—
223Dic59⋊C4—24no—
224C4×Dic59—24no—
225#11745664—44no—
226#11745664—44no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8#4112yes—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59C2×C22⋊C412yes—
252C23×C59C2×C22⋊C412yes—
253C23×C59C22×D411yescharacteristic
254C22×D59—22no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—41no—
261D4×C59—44no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—84no—
291C2×C4×C59C2×C22⋊C412yes—
292C2×C4×C59C2×C22⋊C412yes—
293C2×C4×C59C2×C22⋊C412yes—
294C2×C4×C59C2×C22⋊C412yes—
295C2×C4×C59C23×C411yescharacteristic
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4111yescharacteristic
298C2×C4×C59C2×#4111yescharacteristic
299C2×C4×C59H(5,𝔽2)11yescharacteristic
300C2×C4×C592−1+411yescharacteristic
301C22⋊D59—48no—
302C22⋊D59—84no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—84no—
313D236—22no—
314D236—22no—
315D236—41no—
316D236—41no—
317C4×D59—84no—
318C59⋊C8—22no—
319C59⋊C8—41no—
320C59⋊C8—41no—
321C59⋊C8—41no—
322#22501—591nomaximal, Sylow
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—41no—
332C22×C59—41no—
333C22×C59—41no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59C22×C22⋊C411yescharacteristic
338C22×C59#54611yescharacteristic
339C22×C59#54711yescharacteristic
340C22×C59#57511yescharacteristic
341C22×C59#57511yescharacteristic
342C22×C59#57611yescharacteristic
343C22×C59#57711yescharacteristic
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C2×D59—81no—
348C2×D59—81no—
349C2×D59—81no—
350C2×D59—81no—
351C4×C59—22no—
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—42no—
356C4×C59—81no—
357C4×C59—81no—
358C4×C59—81no—
359C4×C59C4×#4111yescharacteristic
360C4×C59#52011yescharacteristic
361C4×C59#54611yescharacteristic
362C4×C59#54711yescharacteristic
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366C2×#553—591no—
367C2×#436—591no—
368#2352D5911yescharacteristic, complemented
369#1991—591no—
370#1989—591no—
371#1895—591no—
372#1895—591no—
373#1875—591no—
374#1874—591no—
375#1825—591no—
376#1823—591no—
377#1804—591no—
378C4×#102—591no—
379#1736—591no—
380#1736—591no—
381C2×C59—42no—
382C2×C59—42no—
383C2×C59#233911yescharacteristic
384C2×C59#289611yescharacteristic
385C2×C59#289711yescharacteristic
386C2×C59#332211yescharacteristic
387C2×C59#332611yescharacteristic
388C2×C59#335111yescharacteristic
389C2×C59#335511yescharacteristic
390D59—82no—
391C22×M16—591no—
392C22×M16—591no—
393#553—598no—
394#553—1184no—
395C2×#126—1181no—
396C2×#125—591no—
397C2×#123—1181no—
398C2×#121—591no—
399C2×#121—591no—
400C2×#121—1181no—
401C2×C4×D4—591no—
402C2×C4×D4—1181no—
403C2×C4×D4C2×D5911yescharacteristic
404C2×#117—591no—
405C2×#117C2×D5911yescharacteristic
406C22×C4⋊C4—591no—
407C22×C4⋊C4C2×D5911yescharacteristic
408#436—1184no—
409C2×C4⋊C8—591no—
410C2×#102—591no—
411C2×#102—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×C22⋊C8—591no—
415C2×C22⋊C8—591no—
416C2×C4×C8—591no—
417#388—21no—
418#387—21no—
419#386—21no—
420#382C2×D5911yescharacteristic
421#380C2×D5911yescharacteristic
422#380C2×D5911yescharacteristic
423C4×C4⋊C4C2×D5911yescharacteristic
424C4×C22⋊C4—21no—
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#340—591no—
430#340—591no—
431#340—591no—
432#340—591no—
433#340—591no—
434#340—591no—
435#340—591no—
436#340—591no—
437C59#2250111yescharacteristic, complemented, Sylow
438C22×D4—591no—
439C22×D4—1181no—
440C22×D4—1181no—
441C22×D4C22⋊D5911yescharacteristic
442C23×C4—21no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C23×C4C22×D5911yescharacteristic
447C2×M16—1182no—
448C2×M16—1182no—
449C2×M16—1182no—
450C2×M16—1182no—
451C2×M16—2361no—
452C2×M16—2361no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8—591no—
456C22×C8—591no—
457#126—1188no—
458#125—594no—
459#125—1182no—
460#123—1188no—
461#121—594no—
462#121—594no—
463#121—1188no—
464#121—1182no—
465#121—1182no—
466C4×D4—594no—
467C4×D4—1188no—
468C4×D4—1182no—
469C4×D4C4×D5914yes—
470C4×D4D23614yes—
471#117—22no—
472#117—41no—
473#117—594no—
474#117—1182no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—1182no—
483C2×C4⋊C4—1181no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4C22⋊D5911yescharacteristic
487C2×C4⋊C4C22×D5911yescharacteristic
488C2×C4⋊C4C22×D5911yescharacteristic
489C2×C4⋊C4C22×D5911yescharacteristic
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1181no—
495C2×C22⋊C4—1181no—
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4C22⋊D5911yescharacteristic
499C2×C22⋊C4C22⋊D5911yescharacteristic
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—1181no—
503C2×C42C22×D5911yescharacteristic
504C4⋊C8—1182no—
505#102—1182no—
506#102—1182no—
507#102—2361no—
508#102—2361no—
509C22⋊C8—1182no—
510C22⋊C8—1182no—
511C4×C8—1182no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24—1181no—
518C24C2×C22⋊D5911yescharacteristic
519C24C2×C22⋊D5911yescharacteristic
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—592no—
523C2×D4—1184no—
524C2×D4—1184no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—1181no—
528C2×D4—1181no—
529C2×D4—1181no—
530C2×D4—4721no—
531C2×D4—4721no—
532C2×D4—2362no—
533C2×D4—2362no—
534C2×D4(C2×D59)⋊C414yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—81no—
550C22×C4—1184no—
551C22×C4—1181no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—1184no—
555C22×C4—4721no—
556C22×C4—4721no—
557C22×C4—4721no—
558C22×C4—4721no—
559C22×C4C2×C4×D5912yes—
560C22×C4C2×C4×D5912yes—
561C22×C4C2×D23612yes—
562C22×C4C2×D23612yes—
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C2×C22⋊D5911yescharacteristic
565C22×C4C2×C22⋊D5911yescharacteristic
566C22×C4C2×C22⋊D5911yescharacteristic
567C22×C4C23×D5911yescharacteristic
568M16—2364no—
569M16—2364no—
570C2×C8—592no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—592no—
591C4⋊C4—592no—
592C4⋊C4—592no—
593C4⋊C4—1184no—
594C4⋊C4—1184no—
595C4⋊C4—1184no—
596C4⋊C4—1181no—
597C4⋊C4—1181no—
598C4⋊C4—1181no—
599C4⋊C4(C2×D59)⋊C414yes—
600C4⋊C4#1174568712yes—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C22⋊C4—1184no—
605C22⋊C4—1184no—
606C22⋊C4—1184no—
607C22⋊C4—1184no—
608C22⋊C4(C2×D59)⋊C414yes—
609C22⋊C4(C2×D59)⋊C414yes—
610C42—42no—
611C42—81no—
612C42—1184no—
613C42C2×C4×D5912yes—
614C42C2×D23612yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—1182no—
628C23—2361no—
629C23—2361no—
630C23—2361no—
631C23—2361no—
632C23—2361no—
633C23—2361no—
634C23C2×(C2×D59)⋊C412yes—
635C23C2×(C2×D59)⋊C412yes—
636C23C22×C22⋊D5911yescharacteristic
637D4—44no—
638D4—1182no—
639D4—1182no—
640D4—4724no—
641D4—2368no—
642D4—2361no—
643D4—2361no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—84no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—4724no—
677C2×C4—4724no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4C2×(C2×D59)⋊C412yes—
685C2×C4C2×(C2×D59)⋊C412yes—
686C2×C4C2×(C2×D59)⋊C412yes—
687C2×C4C2×(C2×D59)⋊C412yes—
688C2×C4C22×C4×D5911yescharacteristic
689C2×C4C22×D23611yescharacteristic
690C2×C4#41×D5911yescharacteristic
691C2×C4C2×#1174568711yescharacteristic
692C2×C4#1427377211yescharacteristic
693C2×C4#1427377411yescharacteristic
694C8—1182no—
695C8—2361no—
696C8—2361no—
697C8—2361no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—4721no—
713C22—4721no—
714C22—4721no—
715C22—4721no—
716C22—2362no—
717C22—2362no—
718C22—2362no—
719C22C22×(C2×D59)⋊C411yescharacteristic
720C22#1683804611yescharacteristic
721C22#1683805111yescharacteristic
722C22#1683820011yescharacteristic
723C22#1683820011yescharacteristic
724C22#1683820511yescharacteristic
725C22#1683821011yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4C4×#1174568711yescharacteristic
738C4#1683788111yescharacteristic
739C4#1683804711yescharacteristic
740C4#1683805611yescharacteristic
741C2—42no—
742C2—42no—
743C2—4722no—
744C2#2142692111yescharacteristic
745C2#2143261311yescharacteristic
746C2#2143261911yescharacteristic
747C2#2143629711yescharacteristic
748C2#2143634911yescharacteristic
749C2#2143665611yescharacteristic
750C2#2143669611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2352C2
socleC23×C59C22×D4
prime radicalC2×#16838098C2
cosocleC22×C4×C59C24
hypercenter#2352D59
hypocenterC59#22501
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16837480C2semidirect
3. #21425060C2semidirect
4. #21425053C2semidirect
5. #21424532C2semidirect
6. #21424532C2semidirect
7. #21424418C2semidirect
8. #21424413C2semidirect
9. #21424188C2semidirect
10. #21424180C2semidirect
11. #21424103C2semidirect
12. C4×#14273647C2semidirect
13. #21423817C2semidirect
14. #21423815C2semidirect
15. C59×#2352C2semidirect
19. #16838098C4semidirect
79. #14273719C2×C4semidirect
84. #14273701C2×C4semidirect
87. C4×D236C2×C4semidirect
93. C2×C4⋊Dic59C2×C4semidirect
368. #2352D59semidirect
437. C59#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#168380982
C2×#168374802
#214250602
#214250532
#214245322
#214244182
#214244132
#214241882
#214241802
#214241032
C4×#142736472
#214238172
#214238152
C59×#23522
#2250159