Finite Group Databasebeta

← #28494203

Subgroups — #28494203

Order 15104.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837882C211yesmaximal, characteristic
2C22×#14273655C211yesmaximal, characteristic
3C2×#16837404C211yesmaximal, characteristic
4C2×#16837170C211yesmaximal, characteristic, complemented
5#21423817C211yesmaximal, characteristic, complemented
6#21422326C211yesmaximal, characteristic, complemented
7C2×C59×#339C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10#16837882—22no—
11#16837882—22no—
12#16837882—22no—
13#16837882C414yescomplemented
14C2×C4×Dic118—21no—
15C2×C4×D236—21no—
16C2×(C22⋊D59)⋊C4—22no—
17C2×#14273685—21no—
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊C4×D59—21no—
21C2×#14273655—22no—
22C2×#14273655—22no—
23C2×#14273655C414yescomplemented
24#16837404—22no—
25#16837404C414yescomplemented
26C2×#14273652—21no—
27C2×#14273649—21no—
28C2×C59⋊#95—22no—
29#16837170—22no—
30#16837164—21no—
31#16837164—21no—
32C22×M16×C59C2211yescharacteristic
33C2×#117×C59C2211yescharacteristic
34C22×C42×C59C2211yescharacteristic
35C59×#339—22no—
36C2×#11745685—21no—
37C2×#11745685—21no—
38C2×#11745685—21no—
39C2×#11745685—21no—
40C2×#11745685—21no—
41C2×#11745685—21no—
42C2×#11745685C2×C412yes—
43C2×#11745685C2×C412yes—
44C2×#11745685C2×C412yes—
45C2×#11745685D412yes—
46C2×#11745685D412yes—
47C2×#11745685Q812yes—
48C22×Dic118D411yescharacteristic
49C22×D236D411yescharacteristic
50C22×C22⋊D59—21no—
51C23×Dic59—21no—
52C23×Dic59D412yes—
53C22×C4×D59—21no—
54C22×C4×D59—22no—
55C2×#11745664—21no—
56C2×#11745664—21no—
57C2×#11745664—21no—
58C2×#11745664—21no—
59C2×#11745664—21no—
60C2×#11745664C2×C412yescomplemented
61C22×C59⋊C8—21no—
62C4×Dic118—24no—
63C4×Dic118—24no—
64C4×D236—24no—
65C4×D236—24no—
66(C22⋊D59)⋊C4—28no—
67(C22⋊D59)⋊C4—28no—
68#14273685—24no—
69#14273685—24no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59—21no—
73C2×C4⋊Dic59—21no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59C2×C412yes—
80C2×C4⋊Dic59C2×C412yescomplemented
81C2×C4⋊Dic59D412yes—
82C2×Dic59⋊C4—22no—
83C4⋊C4×D59—24no—
84C4⋊C4×D59—24no—
85C2×(C2×D59)⋊C4—22no—
86C2×C4×Dic59—22no—
87#14273655—28no—
88#14273652—24no—
89#14273649—24no—
90C59⋊#95—44no—
91C23×C4×C59—21no—
92C23×C4×C59C2311yescharacteristic
93C2×M16×C59—21no—
94C2×M16×C59—21no—
95C2×M16×C59—21no—
96C2×M16×C59—21no—
97C2×M16×C59—21no—
98C2×M16×C59C2×C412yescomplemented
99C22×C8×C59—21no—
100#117×C59—21no—
101#117×C59—21no—
102#117×C59C2×C412yes—
103#117×C59D412yes—
104C2×C4⋊C4×C59D411yescharacteristic
105C2×C4⋊C4×C59D411yescharacteristic
106C2×C22⋊C4×C59—21no—
107C2×C42×C59—21no—
108C2×C42×C59—21no—
109C2×C42×C59—21no—
110C2×C42×C59—21no—
111C2×C42×C59—21no—
112C2×C42×C59—21no—
113C2×C42×C59C2×C412yescomplemented
114C24×C59C2×D411yescharacteristic
115C23×D59—21no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—41no—
122C22×C4×C59—41no—
123C22×C4×C59—41no—
124C22×C4×C59—41no—
125C22×C4×C59C22×C411yescharacteristic
126C22×C4×C59C22×C411yescharacteristic
127C22×C4×C59C22×C411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×Q811yescharacteristic
135C22×C4×C59#4111yescharacteristic
136C22×C4×C59#4111yescharacteristic
137C22×C4×C59#4111yescharacteristic
138C22×C4×C59#4111yescharacteristic
139C2×C22⋊D59—22no—
140C2×C22⋊D59—22no—
141C2×C22⋊D59—22no—
142C2×C22⋊D59—22no—
143C2×C22⋊D59—22no—
144C2×C22⋊D59—22no—
145C22×Dic59—21no—
146C22×Dic59—22no—
147C22×Dic59—22no—
148C22×Dic59—22no—
149C22×Dic59—42no—
150C22×Dic59—42no—
151C22×Dic59—42no—
152C22×Dic59—42no—
153C22×Dic59—41no—
154C22×Dic59—41no—
155C22×Dic59C22⋊C414yes—
156#11745685—22no—
157#11745685—22no—
158#11745685—22no—
159#11745685—22no—
160#11745685—22no—
161#11745685—22no—
162#11745685—22no—
163#11745685—22no—
164#11745685—22no—
165#11745685—22no—
166#11745685—22no—
167#11745685—22no—
168#11745685C4214yes—
169#11745685C22⋊C414yes—
170#11745685C4⋊C414yes—
171#11745685C4⋊C414yes—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236C22⋊C412yes—
176C2×D236C22⋊C412yes—
177C2×D236C4⋊C412yes—
178C2×C4×D59—22no—
179C2×C4×D59—22no—
180C2×C4×D59—22no—
181C2×C4×D59—22no—
182C2×C4×D59—22no—
183C2×C4×D59—22no—
184C2×C4×D59—28no—
185C2×C4×D59—82no—
186C2×C4×D59—82no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C2×Dic118—21no—
190C2×Dic118C22⋊C412yes—
191C2×Dic118C22⋊C412yes—
192C2×Dic118C4⋊C412yes—
193M16×C59—22no—
194M16×C59—22no—
195M16×C59—41no—
196M16×C59—41no—
197C2×C8×C59—22no—
198C2×C8×C59—41no—
199C2×C8×C59—41no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59C22⋊C412yes—
203C4⋊C4×C59C22⋊C412yes—
204C22⋊C4×C59—22no—
205C22⋊C4×C59—22no—
206C42×C59—22no—
207C42×C59—22no—
208C42×C59—22no—
209C42×C59—22no—
210C42×C59—41no—
211C42×C59—41no—
212(C2×D59)⋊C4—28no—
213C4⋊Dic59—22no—
214C4⋊Dic59—22no—
215C4⋊Dic59—22no—
216C4⋊Dic59—22no—
217C4⋊Dic59—22no—
218C4⋊Dic59—22no—
219C4⋊Dic59—41no—
220C4⋊Dic59—41no—
221Dic59⋊C4—28no—
222C4×Dic59—28no—
223#11745664—22no—
224#11745664—22no—
225#11745664—41no—
226#11745664—41no—
227C2×C59⋊C8—22no—
228C2×C59⋊C8—41no—
229C2×C59⋊C8—41no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59C2×C22⋊C411yescharacteristic
235C23×C59C4×D411yescharacteristic
236C23×C59C4×D411yescharacteristic
237C23×C59#12011yescharacteristic
238C23×C59#12011yescharacteristic
239C23×C59#12111yescharacteristic
240C23×C59C22⋊Q811yescharacteristic
241C22×D59—22no—
242C22×D59—22no—
243C22×D59—22no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C2×C4×C59—24no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—42no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—42no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59C2×C4211yescharacteristic
262C2×C4×C59C2×C22⋊C411yescharacteristic
263C2×C4×C59C2×C22⋊C411yescharacteristic
264C2×C4×C59C2×C22⋊C411yescharacteristic
265C2×C4×C59C2×C22⋊C411yescharacteristic
266C2×C4×C59C2×C4⋊C411yescharacteristic
267C2×C4×C59C2×C4⋊C411yescharacteristic
268C2×C4×C59C2×C4⋊C411yescharacteristic
269C2×C4×C59#11711yescharacteristic
270C2×C4×C59#11711yescharacteristic
271C2×C4×C59C4×D411yescharacteristic
272C2×C4×C59C4×D411yescharacteristic
273C2×C4×C59C4×D411yescharacteristic
274C2×C4×C59C4×D411yescharacteristic
275C2×C4×C59C4×D411yescharacteristic
276C2×C4×C59C4×D411yescharacteristic
277C2×C4×C59#12011yescharacteristic
278C2×C4×C59#12011yescharacteristic
279C2×C4×C59#12111yescharacteristic
280C2×C4×C59#12111yescharacteristic
281C2×C4×C59#12111yescharacteristic
282C2×C4×C59C22⋊Q811yescharacteristic
283C2×C4×C59C22⋊Q811yescharacteristic
284C2×C4×C59C22⋊Q811yescharacteristic
285C2×C4×C59#12311yescharacteristic
286C2×C4×C59#12311yescharacteristic
287C2×C4×C59#12311yescharacteristic
288C2×C4×C59#12311yescharacteristic
289C22⋊D59—24no—
290C22⋊D59—24no—
291C22⋊D59—24no—
292C22⋊D59—24no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—24no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59—44no—
300C2×Dic59—44no—
301C2×Dic59—42no—
302C2×Dic59—82no—
303C2×Dic59—82no—
304C2×Dic59—81no—
305C2×Dic59—81no—
306D236—22no—
307D236—22no—
308D236—22no—
309D236#9514yescomplemented
310C4×D59—24no—
311C4×D59—24no—
312C4×D59—24no—
313C4×D59—24no—
314C4×D59—88no—
315Dic118—22no—
316Dic118—22no—
317Dic118—22no—
318Dic118#9514yescomplemented
319C8×C59—42no—
320C59⋊C8—42no—
321#10781—591nomaximal, Sylow
322C22×C59—21no—
323C22×C59—21no—
324C22×C59—21no—
325C22×C59—21no—
326C22×C59—21no—
327C22×C59—21no—
328C22×C59—21no—
329C22×C59—21no—
330C22×C59—21no—
331C22×C59—21no—
332C22×C59—21no—
333C22×C59—21no—
334C22×C59C4×C22⋊C411yescharacteristic
335C22×C59#37911yescharacteristic
336C22×C59#38011yescharacteristic
337C22×C59#38511yescharacteristic
338C22×C59#38511yescharacteristic
339C22×C59#38611yescharacteristic
340C22×C59#38611yescharacteristic
341C22×C59#45311yescharacteristic
342C22×C59#45411yescharacteristic
343C22×C59#45511yescharacteristic
344C22×C59#45611yescharacteristic
345C2×D59—24no—
346C2×D59—42no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C4×C59—44no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59C2×#9511yescharacteristic
356C4×C59C4×C22⋊C411yescharacteristic
357C4×C59#38011yescharacteristic
358C4×C59#38111yescharacteristic
359C4×C59#38511yescharacteristic
360C4×C59#38511yescharacteristic
361C4×C59#38611yescharacteristic
362C4×C59#38611yescharacteristic
363Dic59—24no—
364Dic59—44no—
365Dic59—82no—
366C2×#520—591no—
367C22×#104—591no—
368C2×#417—591no—
369C2×#343—591no—
370#1736—591no—
371C2×#339D5911yescharacteristic, complemented
372C4⋊#95—591no—
373C2×C59—21no—
374C2×C59—21no—
375C2×C59—21no—
376C2×C59—21no—
377C2×C59C22⋊#9511yescharacteristic
378C2×C59#179211yescharacteristic
379C2×C59#179311yescharacteristic
380C2×C59#185911yescharacteristic
381C2×C59#186011yescharacteristic
382C2×C59#188211yescharacteristic
383C2×C59#188311yescharacteristic
384D59—44no—
385C22×#41—591no—
386C22×M16—591no—
387C22×M16C2×D5911yescharacteristic
388#520—594no—
389#520—1182no—
390#520—1182no—
391#520—1182no—
392C2×C4×Q8—1181no—
393C2×C4×D4—1181no—
394C2×C4×D4—1182no—
395C2×#117—1181no—
396C2×#117C2×D5911yescharacteristic
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—1181no—
400C22×C42C2×D5911yescharacteristic
401C2×#104—594no—
402C2×#104—1182no—
403C2×#104—1182no—
404#417—594no—
405#417—1182no—
406C2×#103—1181no—
407C2×#102—1181no—
408C2×#95—1182no—
409#343—1182no—
410#340—1181no—
411#340—1181no—
412#339—22no—
413C59#1078111yescharacteristic, complemented, Sylow
414C2×#41—592no—
415C2×#41—592no—
416C2×#41—592no—
417C2×#41—592no—
418C2×#41—592no—
419C2×#41—592no—
420C2×#41—1181no—
421C2×#41—1181no—
422C2×#41—1181no—
423C2×#41—1181no—
424C2×#41—1181no—
425C2×#41—1181no—
426C22×Q8—591no—
427C22×D4—591no—
428C22×D4—1181no—
429C23×C4—21no—
430C23×C4—592no—
431C23×C4—1182no—
432C23×C4—1181no—
433C23×C4—1181no—
434C23×C4C22×D5911yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—592no—
441C2×M16—1181no—
442C2×M16—1181no—
443C2×M16—1181no—
444C2×M16—1181no—
445C2×M16—1181no—
446C2×M16C4×D5912yescomplemented
447C22×C8—21no—
448C22×C8—1181no—
449C4×Q8—1184no—
450C4×Q8—1184no—
451C4×D4—1184no—
452C4×D4—1184no—
453C4×D4—1188no—
454C4×D4—1188no—
455#117—21no—
456#117—21no—
457#117—1184no—
458#117—1184no—
459#117C4×D5912yes—
460#117C22⋊D5912yes—
461C2×C4⋊C4—592no—
462C2×C4⋊C4—592no—
463C2×C4⋊C4—592no—
464C2×C4⋊C4—1184no—
465C2×C4⋊C4—1182no—
466C2×C4⋊C4—1181no—
467C2×C4⋊C4—1181no—
468C2×C4⋊C4—1181no—
469C2×C4⋊C4—1181no—
470C2×C4⋊C4—1184no—
471C2×C4⋊C4—1181no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4D23611yescharacteristic
477C2×C4⋊C4D23611yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1182no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—1182no—
487C2×C42C4×D5912yescomplemented
488#104—1188no—
489#103—1184no—
490#102—1184no—
491#95—2364no—
492C24—1181no—
493C24D4×D5911yescharacteristic
494#41—594no—
495#41—594no—
496#41—594no—
497#41—594no—
498#41—1182no—
499#41—1182no—
500#41—1182no—
501#41—1182no—
502#41—1182no—
503#41—1182no—
504#41—1182no—
505#41—1182no—
506#41—1182no—
507#41—1182no—
508#41—1182no—
509#41—1182no—
510C2×Q8—592no—
511C2×Q8—592no—
512C2×Q8—592no—
513C2×Q8—1181no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×D4—592no—
517C2×D4—592no—
518C2×D4—592no—
519C2×D4—1182no—
520C2×D4—1182no—
521C2×D4—1182no—
522C2×D4—1182no—
523C2×D4—1182no—
524C2×D4—1182no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—1181no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—594no—
538C22×C4—1188no—
539C22×C4—1181no—
540C22×C4—1182no—
541C22×C4—1182no—
542C22×C4—1182no—
543C22×C4—1182no—
544C22×C4—1182no—
545C22×C4—1182no—
546C22×C4—1182no—
547C22×C4—1182no—
548C22×C4—1182no—
549C22×C4—4722no—
550C22×C4—4722no—
551C22×C4—2362no—
552C22×C4—2362no—
553C22×C4—2361no—
554C22×C4—2361no—
555C22×C4—2362no—
556C22×C4—2362no—
557C22×C4C2×C4×D5911yescharacteristic
558C22×C4C2×C4×D5911yescharacteristic
559C22×C4C2×C4×D5911yescharacteristic
560C22×C4C2×D23611yescharacteristic
561C22×C4#1174568511yescharacteristic
562C22×C4#1174568511yescharacteristic
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4D4×D5911yescharacteristic
566C22×C4D4×D5911yescharacteristic
567C22×C4#1174568711yescharacteristic
568C22×C4Q8×D5911yescharacteristic
569C22×C4#1174568911yescharacteristic
570C22×C4C2×C22⋊D5911yescharacteristic
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—1182no—
576M16—1182no—
577M16—2361no—
578M16—2361no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—1182no—
583C2×C8—2361no—
584C2×C8—2361no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—1188no—
588C4⋊C4—1182no—
589C4⋊C4—1182no—
590C4⋊C4—1182no—
591C4⋊C4—1182no—
592C4⋊C4—1182no—
593C4⋊C4—1182no—
594C4⋊C4—2361no—
595C4⋊C4—2361no—
596C4⋊C4(C2×D59)⋊C412yes—
597C4⋊C4(C2×D59)⋊C412yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—1188no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—41no—
606C42—41no—
607C42—1188no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—1182no—
613C23—1182no—
614C23—1182no—
615C23—2361no—
616C23—2361no—
617C23—2361no—
618C23—2361no—
619C23C22⋊C4×D5911yescharacteristic
620C23(C22⋊D59)⋊C411yescharacteristic
621C23#1427368911yescharacteristic
622C23#1427369511yescharacteristic
623C23#1427369711yescharacteristic
624C23#1427370011yescharacteristic
625C23#1427370511yescharacteristic
626Q8—594no—
627Q8—1182no—
628Q8—1182no—
629Q8—1182no—
630D4—594no—
631D4—1184no—
632D4—1184no—
633D4—1184no—
634D4—1184no—
635D4—1182no—
636D4—1182no—
637D4—1182no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1184no—
655C2×C4—1184no—
656C2×C4—1184no—
657C2×C4—1184no—
658C2×C4—1184no—
659C2×C4—4728no—
660C2×C4—4722no—
661C2×C4—4721no—
662C2×C4—4721no—
663C2×C4—4722no—
664C2×C4—2364no—
665C2×C4—2362no—
666C2×C4—2362no—
667C2×C4—2362no—
668C2×C4—2364no—
669C2×C4C42×D5911yescharacteristic
670C2×C4C22⋊C4×D5911yescharacteristic
671C2×C4C22⋊C4×D5911yescharacteristic
672C2×C4C22⋊C4×D5911yescharacteristic
673C2×C4C2×(C2×D59)⋊C411yescharacteristic
674C2×C4C4⋊C4×D5911yescharacteristic
675C2×C4C4⋊C4×D5911yescharacteristic
676C2×C4C4⋊C4×D5911yescharacteristic
677C2×C4#1427368411yescharacteristic
678C2×C4#1427368511yescharacteristic
679C2×C4(C22⋊D59)⋊C411yescharacteristic
680C2×C4C4×C22⋊D5911yescharacteristic
681C2×C4C4×C22⋊D5911yescharacteristic
682C2×C4#1427368911yescharacteristic
683C2×C4C4×D23611yescharacteristic
684C2×C4C4×D23611yescharacteristic
685C2×C4#1427369511yescharacteristic
686C2×C4#1427369711yescharacteristic
687C2×C4#1427369811yescharacteristic
688C2×C4#1427370011yescharacteristic
689C2×C4#1427370211yescharacteristic
690C2×C4#1427370311yescharacteristic
691C2×C4#1427370511yescharacteristic
692C2×C4#1427370711yescharacteristic
693C2×C4#1427370911yescharacteristic
694C2×C4#1427370911yescharacteristic
695C2×C4#1427371211yescharacteristic
696C2×C4#1427371211yescharacteristic
697C8—42no—
698C8—2362no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—1184no—
712C22—2362no—
713C22—2362no—
714C22—2362no—
715C22—2362no—
716C22—2362no—
717C22—2362no—
718C22#1683724911yescharacteristic
719C22#1683725711yescharacteristic
720C22#1683726111yescharacteristic
721C22#1683727311yescharacteristic
722C22#1683727611yescharacteristic
723C22#1683727811yescharacteristic
724C22#1683728011yescharacteristic
725C22#1683757111yescharacteristic
726C22#1683757611yescharacteristic
727C22#1683758111yescharacteristic
728C22#1683758611yescharacteristic
729C4—44no—
730C4—42no—
731C4—42no—
732C4—1184no—
733C4—4722no—
734C4—2364no—
735C4#95×D5911yescharacteristic
736C4C4×(C2×D59)⋊C411yescharacteristic
737C4#1683725911yescharacteristic
738C4#1683726411yescharacteristic
739C4#1683727311yescharacteristic
740C4#1683727611yescharacteristic
741C4#1683727811yescharacteristic
742C4#1683728011yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—2364no—
748C2(C2×D59)⋊#9511yescharacteristic
749C2#2142405111yescharacteristic
750C2#2142405611yescharacteristic
751C2#2142432311yescharacteristic
752C2#2142433011yescharacteristic
753C2#2142446611yescharacteristic
754C2#2142447311yescharacteristic
subgroupG/H
centerC23#14273697
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C59×#339C2
socleC23×C59#120
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×#339D59
hypocenterC59#10781
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#16837170C2semidirect
5. #21423817C2semidirect
6. #21422326C2semidirect
7. C2×C59×#339C2semidirect
13. #16837882C4semidirect
23. C2×#14273655C4semidirect
25. #16837404C4semidirect
60. C2×#11745664C2×C4semidirect
80. C2×C4⋊Dic59C2×C4semidirect
98. C2×M16×C59C2×C4semidirect
113. C2×C42×C59C2×C4semidirect
309. D236#95semidirect
318. Dic118#95semidirect
371. C2×#339D59semidirect
413. C59#10781semidirect
446. C2×M16C4×D59semidirect
487. C2×C42C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168378822
C22×#142736552
C2×#168374042
C2×#168371702
#214238172
#214223262
C2×C59×#3392
#1078159