Finite Group Databasebeta

← #28608947

Subgroups — #28608947

Order 15104.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837552C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C22×#14273647C211yesmaximal, characteristic
4C22⋊C4×D236C211yesmaximal, characteristic
5#21424980C211yesmaximal, characteristic, complemented
6#21424792C211yesmaximal, characteristic, complemented
7#21424716C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424342C211yesmaximal, characteristic, complemented
12#21424284C211yesmaximal, characteristic, complemented
13#21423924C211yesmaximal, characteristic, complemented
14#21423874C211yesmaximal, characteristic, complemented
15C59×#2360C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C22⋊C4×D59—21no—
23#16837552C418yescomplemented
24#16837500—24no—
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273660C2211yescharacteristic, complemented
27C2×#14273651C2211yescharacteristic, complemented
28C2×#14273651C2211yescharacteristic, complemented
29C2×#14273647—24no—
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic, complemented
38C2×#14273638C2211yescharacteristic, complemented
39#16837304C2211yescharacteristic
40#16837304C2211yescharacteristic
41#16837280—21no—
42#16837280—21no—
43#16837262C2211yescharacteristic
44#16837257—21no—
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50#16837157C2211yescharacteristic, complemented
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic, complemented
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic, complemented
55C59×#389—21no—
56C59×#389C2211yescharacteristic, complemented
57C59×#387—21no—
58C59×#385—21no—
59C4×C4⋊C4×C59C2211yescharacteristic, complemented
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C24×D59—21no—
63C22×D236—22no—
64C22×D236—22no—
65C22×D236—21no—
66C22×D236—22no—
67C22×D236—41no—
68C22×D236—41no—
69C22×D236C2×C414yes—
70C22×D236C2311yescharacteristic
71C22×D236C2311yescharacteristic
72C22×C4×D59—21no—
73C22×C4×D59—21no—
74C2×#11745671—22no—
75C2×#11745671—22no—
76C2×#11745671—41no—
77C2×#11745671—41no—
78C2×#11745671C2×C414yescomplemented
79C2×#11745671C2×C414yescomplemented
80C22×C59⋊C8—22no—
81C22×C59⋊C8—22no—
82C22×C59⋊C8—41no—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C4×D236—22no—
88C4×D236—22no—
89C4×D236—41no—
90C4×D236—41no—
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C22⋊Dic59—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C22⋊C4×D59—44no—
101#14273660—22no—
102#14273660—41no—
103#14273651—22no—
104#14273651—41no—
105#14273647—22no—
106#14273647—22no—
107#14273647—22no—
108#14273647C2×C414yescomplemented
109#14273647C2×C414yescomplemented
110#14273647D414yes—
111C22⋊(C59⋊C8)C2×C414yescomplemented
112#14273638—22no—
113#14273638—41no—
114C59⋊#95—21no—
115C22×Q8×C59C2311yescharacteristic
116C23×C4×C59—21no—
117C23×C4×C59C2311yescharacteristic
118C22⋊Q8×C59—22no—
119C22⋊Q8×C59C2×C414yescomplemented
120C4×Q8×C59—22no—
121C4×Q8×C59—41no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—22no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—41no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C42×C59—21no—
135C2×C42×C59—21no—
136C2×C42×C59C2311yescharacteristic
137C2×C42×C59C2311yescharacteristic
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59—21no—
142#95×C59D411yescharacteristic
143#95×C59D411yescharacteristic
144C24×C59C2×D411yescharacteristic
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—24no—
148C23×D59—42no—
149C23×D59—42no—
150C23×D59—42no—
151C23×D59—42no—
152C23×D59—81no—
153C23×D59—81no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59—21no—
158C2×Q8×C59—21no—
159C2×Q8×C59C22×C412yes—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—42no—
169C22×C4×C59—42no—
170C22×C4×C59—81no—
171C22×C4×C59C22×C412yes—
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59#4112yes—
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236—28no—
189C2×D236—24no—
190C2×D236—21no—
191C2×D236—44no—
192C2×D236—44no—
193C2×D236—44no—
194C2×D236—42no—
195C2×D236—42no—
196C2×D236C22×C412yes—
197C2×D236C22×C412yes—
198C2×D236C2×D412yes—
199C2×D236#4112yes—
200C2×C4×D59—42no—
201C2×C4×D59—42no—
202C2×C4×D59—42no—
203C2×C4×D59—42no—
204C2×C4×D59—81no—
205C2×C4×D59—81no—
206C4⋊C4×C59—24no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—21no—
209C4⋊C4×C59—21no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—42no—
212C4⋊C4×C59—42no—
213C4⋊C4×C59—81no—
214C4⋊C4×C59C22×C412yes—
215C4⋊C4×C59C2×D412yes—
216C22⋊C4×C59—24no—
217C22⋊C4×C59—22no—
218C22⋊C4×C59—22no—
219C42×C59—21no—
220C42×C59—21no—
221C42×C59—21no—
222C42×C59—21no—
223C42×C59—42no—
224C42×C59—81no—
225C22⋊Dic59—42no—
226#11745671—28no—
227#11745671—44no—
228(C2×D59)⋊C4—42no—
229(C2×D59)⋊C4—42no—
230(C2×D59)⋊C4—42no—
231(C2×D59)⋊C4—42no—
232(C2×D59)⋊C4—81no—
233(C2×D59)⋊C4—81no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—44no—
248C2×C59⋊C8C22×C412yes—
249C2×C59⋊C8C22×C412yes—
250C2×C59⋊C8C2×D412yes—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59C4×D412yes—
256C23×C59AGL(1,ℤ/8)12yes—
257C23×C59#13712yes—
258C23×C59C22×D411yescharacteristic
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—48no—
264C22×D59—41no—
265C22×D59—41no—
266C22×D59—41no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273C22×D59—41no—
274C22×D59—48no—
275C22×D59—84no—
276C22×D59—84no—
277C22×D59—84no—
278C22×D59—84no—
279C22×D59—84no—
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—41no—
283Q8×C59—41no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—22no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—84no—
315C2×C4×C59C4×D412yes—
316C2×C4×C59C23×C411yescharacteristic
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C2×#4111yescharacteristic
319C2×C4×C59C2×#4111yescharacteristic
320C2×C4×C59H(5,𝔽2)11yescharacteristic
321C2×C4×C59H(5,𝔽2)11yescharacteristic
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328D236—22no—
329D236—22no—
330D236—22no—
331D236—22no—
332D236—22no—
333D236—48no—
334D236—41no—
335D236—41no—
336D236C4×D414yes—
337C4×D59—84no—
338C4×D59—84no—
339C59⋊C8—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C59⋊C8—41no—
343#22854—591nomaximal, Sylow
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59#44014yescomplemented
351C22×C59C2×C4×D411yescharacteristic
352C22×C59D4211yescharacteristic
353C22×C59#54611yescharacteristic
354C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C59C2×#13711yescharacteristic
356C22×C59#57611yescharacteristic
357C22×C59#57711yescharacteristic
358C2×D59—24no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—816no—
369C2×D59—81no—
370C2×D59—81no—
371C2×D59—81no—
372C2×D59—81no—
373C4×C59—22no—
374C4×C59—42no—
375C4×C59—42no—
376C4×C59—41no—
377C4×C59—42no—
378C4×C59—41no—
379C4×C59—41no—
380C4×C59—41no—
381C4×C59—81no—
382C4×C59C2×C4×D411yescharacteristic
383C4×C59#51811yescharacteristic
384C4×C59#54611yescharacteristic
385C4×C59#55111yescharacteristic
386Dic59—81no—
387Dic59—81no—
388C2×#450—591no—
389C2×#440—591no—
390C22×#102—591no—
391#2360D5911yescharacteristic, complemented
392D4×C22⋊C4—591no—
393#1973—591no—
394#1936—591no—
395#1925—591no—
396#1892—591no—
397#1880—591no—
398#1877—591no—
399#1862—591no—
400#1852—591no—
401#1762—591no—
402#1752—591no—
403C2×C59—24no—
404C2×C59#235811yescharacteristic
405C2×C59C2×#44011yescharacteristic
406C2×C59#294611yescharacteristic
407C2×C59#326411yescharacteristic
408C2×C59#326611yescharacteristic
409C2×C59#331011yescharacteristic
410C2×C59#331411yescharacteristic
411D59—44no—
412D59—82no—
413C23×D4—591no—
414C22×SD16—591no—
415C22×SD16—591no—
416C23×C8—591no—
417C2×C22⋊Q8C2×D5911yescharacteristic
418C2×C4×Q8C2×D5911yescharacteristic, complemented
419C2×C4×D4—591no—
420C2×C4×D4—591no—
421C22×C4⋊C4C2×D5911yescharacteristic
422C22×C22⋊C4—1181no—
423#450—598no—
424#440—1184no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#102—1184no—
436C2×C22⋊C8—591no—
437C2×#97—591no—
438C2×#97—591no—
439#391C2×D5911yescharacteristic, complemented
440#390—591no—
441#390—591no—
442#389—21no—
443#389C2×D5911yescharacteristic, complemented
444#387—21no—
445#386—1181no—
446#386—1181no—
447#385—21no—
448#380—591no—
449#379—1181no—
450C4×C4⋊C4C2×D5911yescharacteristic, complemented
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2×D5911yescharacteristic
453#340—591no—
454#340—591no—
455#340—591no—
456#340—591no—
457#336—591no—
458#336—591no—
459C59#2285411yescharacteristic, complemented, Sylow
460C25—1181no—
461C22×Q8C22×D5911yescharacteristic
462C22×D4—594no—
463C22×D4—591no—
464C22×D4—591no—
465C22×D4—1182no—
466C22×D4—1182no—
467C22×D4—1182no—
468C22×D4—1181no—
469C22×D4—2361no—
470C22×D4—2361no—
471C23×C4—21no—
472C23×C4—1181no—
473C23×C4—1181no—
474C23×C4C22×D5911yescharacteristic
475C2×SD16—594no—
476C2×SD16—594no—
477C2×SD16—1182no—
478C2×SD16—1182no—
479C2×SD16—2361no—
480C2×SD16—2361no—
481C22×C8—591no—
482C22×C8—591no—
483C22×C8—591no—
484C22×C8—591no—
485C22×C8—1182no—
486C22×C8—1182no—
487C22×C8—2361no—
488C22⋊Q8—22no—
489C22⋊Q8C4×D5914yescomplemented
490C4×Q8—22no—
491C4×Q8—41no—
492C4×D4—1182no—
493C4×D4—1182no—
494C4×D4—2361no—
495C4×D4—2361no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—2364no—
516C2×C22⋊C4C22⋊D5911yescharacteristic
517C2×C22⋊C4C22⋊D5911yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C22×D5911yescharacteristic
521C2×C42C22×D5911yescharacteristic
522#107—1182no—
523#107—2361no—
524#103—1182no—
525#103—2361no—
526#102—594no—
527#102—594no—
528#102—594no—
529#102—1182no—
530#102—1182no—
531#102—1182no—
532C22⋊C8—594no—
533#97—1182no—
534#97—2361no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—1181no—
540#95C22⋊D5911yescharacteristic
541#95C22⋊D5911yescharacteristic
542C24—1181no—
543C24—1184no—
544C24—1181no—
545C24—4721no—
546C24—4721no—
547C24—2362no—
548C24—2362no—
549C24—2362no—
550C24—2362no—
551C24C2×C22⋊D5911yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×C4×D5912yes—
558C2×D4—592no—
559C2×D4—592no—
560C2×D4—592no—
561C2×D4—592no—
562C2×D4—1188no—
563C2×D4—1184no—
564C2×D4—1181no—
565C2×D4—1181no—
566C2×D4—1181no—
567C2×D4—1181no—
568C2×D4—1181no—
569C2×D4—1181no—
570C2×D4—1181no—
571C2×D4—1181no—
572C2×D4—2364no—
573C2×D4—2364no—
574C2×D4—2364no—
575C2×D4—2362no—
576C2×D4—2362no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—4721no—
591C22×C4—4721no—
592C22×C4—2362no—
593C22×C4—2362no—
594C22×C4—2362no—
595C22×C4—2362no—
596C22×C4C2×C4×D5912yes—
597C22×C4#1174568512yes—
598C22×C4C2×C22⋊D5911yescharacteristic
599C22×C4C2×C22⋊D5911yescharacteristic
600C22×C4C2×C22⋊D5911yescharacteristic
601C22×C4C2×C22⋊D5911yescharacteristic
602C22×C4C2×C22⋊D5911yescharacteristic
603C22×C4C23×D5911yescharacteristic
604SD16—1188no—
605SD16—2364no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—592no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C2×C8—1181no—
614C2×C8—1181no—
615C2×C8—1181no—
616C2×C8—1181no—
617C2×C8—1181no—
618C2×C8—2364no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—81no—
627C4⋊C4—1181no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4C2×C4×D5912yes—
632C4⋊C4D4×D5912yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—4721no—
637C22⋊C4—4721no—
638C22⋊C4—2362no—
639C22⋊C4—2362no—
640C22⋊C4—2362no—
641C22⋊C4—2362no—
642C22⋊C4—2362no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—1182no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23—4724no—
658C23—4724no—
659C23—4724no—
660C23—4724no—
661C23—4724no—
662C23—2368no—
663C23—2361no—
664C23—2361no—
665C23—2361no—
666C23—2361no—
667C23—2368no—
668C23—2361no—
669C23—2361no—
670C23—2361no—
671C23—2361no—
672C23—2361no—
673C23—2361no—
674C23C4×C22⋊D5912yes—
675C23#1427375212yes—
676C23#1427375812yes—
677C23C22×C22⋊D5911yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—594no—
683D4—1182no—
684D4—1182no—
685D4—1182no—
686D4—1182no—
687D4—1182no—
688D4—2368no—
689D4—2361no—
690D4—2361no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—4724no—
723C2×C4—4724no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4C4×C22⋊D5912yes—
731C2×C4C22×C4×D5911yescharacteristic
732C2×C4C2×D4×D5911yescharacteristic
733C2×C4#41×D5911yescharacteristic
734C2×C4C2×#1174568511yescharacteristic
735C2×C4#1427377211yescharacteristic
736C2×C4#1427377311yescharacteristic
737C8—1182no—
738C8—1182no—
739C8—1182no—
740C8—2361no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—1184no—
748C22—47216no—
749C22—4721no—
750C22—4721no—
751C22—4721no—
752C22—4721no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22—2362no—
757C22—2362no—
758C22—2362no—
759C22—2362no—
760C22—2362no—
761C22—2362no—
762C22#1683750014yescomplemented
763C22C2×C4×C22⋊D5911yescharacteristic
764C22D4×C22⋊D5911yescharacteristic
765C22#1683804011yescharacteristic
766C22C2×#1427375211yescharacteristic
767C22C2×#1427375811yescharacteristic
768C22#1683820511yescharacteristic
769C22#1683821011yescharacteristic
770C4—22no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—81no—
779C4—4721no—
780C4—4721no—
781C4C4×D4×D5911yescharacteristic
782C4#1683787411yescharacteristic
783C4#1683804811yescharacteristic
784C4#1683808111yescharacteristic
785C2—24no—
786C2—4722no—
787C2—2364no—
788C2#2142707311yescharacteristic
789C2C2×#1683750011yescharacteristic
790C2#2143292411yescharacteristic
791C2#2143557711yescharacteristic
792C2#2143560711yescharacteristic
793C2#2143611111yescharacteristic
794C2#2143617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2360C2
socleC23×C59C22×D4
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenter#2360D59
hypocenterC59#22854
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
5. #21424980C2semidirect
6. #21424792C2semidirect
7. #21424716C2semidirect
8. #21424520C2semidirect
9. #21424451C2semidirect
10. #21424433C2semidirect
11. #21424342C2semidirect
12. #21424284C2semidirect
13. #21423924C2semidirect
14. #21423874C2semidirect
15. C59×#2360C2semidirect
23. #16837552C4semidirect
25. C2×#14273660C22semidirect
26. C2×#14273660C22semidirect
27. C2×#14273651C22semidirect
28. C2×#14273651C22semidirect
37. C2×#14273638C22semidirect
38. C2×#14273638C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837157C22semidirect
50. #16837157C22semidirect
52. C2×C4×Q8×C59C22semidirect
54. C59×#391C22semidirect
56. C59×#389C22semidirect
59. C4×C4⋊C4×C59C22semidirect
78. C2×#11745671C2×C4semidirect
79. C2×#11745671C2×C4semidirect
108. #14273647C2×C4semidirect
109. #14273647C2×C4semidirect
111. C22⋊(C59⋊C8)C2×C4semidirect
119. C22⋊Q8×C59C2×C4semidirect
350. C22×C59#440semidirect
391. #2360D59semidirect
418. C2×C4×Q8C2×D59semidirect
439. #391C2×D59semidirect
443. #389C2×D59semidirect
450. C4×C4⋊C4C2×D59semidirect
459. C59#22854semidirect
489. C22⋊Q8C4×D59semidirect
762. C22#16837500semidirect

Maximal subgroups

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

subgroupindex
C2×#168375522
C2×#168375002
C22×#142736472
C22⋊C4×D2362
#214249802
#214247922
#214247162
#214245202
#214244512
#214244332
#214243422
#214242842
#214239242
#214238742
C59×#23602
#2285459