Finite Group Databasebeta

← #28609122

Subgroups — #28609122

Order 15104.

1218 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837547C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×#16837403C211yesmaximal, characteristic, complemented
4#21427110C211yesmaximal, characteristic, complemented
5#21424953C211yesmaximal, characteristic, complemented
6#21424789C211yesmaximal, characteristic, complemented
7#21424727C211yesmaximal, characteristic, complemented
8#21424532C211yesmaximal, characteristic, complemented
9#21424444C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424357C211yesmaximal, characteristic, complemented
12#21424288C211yesmaximal, characteristic, complemented
13C4×#14273648C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2339C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×(C22⋊D59)⋊C4—21no—
22C22×C4⋊Dic59C2211yescharacteristic
23#16837547C418yescomplemented
24#16837512—24no—
25C2×#14273658C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27#16837403—24no—
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38C2×C4×C59⋊C8C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837294—21no—
42#16837279—21no—
43#16837276—21no—
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C22×#41×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#391C2211yescharacteristic
56C59×#386—21no—
57C59×#386—21no—
58C59×#381—21no—
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C2×#95×C59—21no—
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C23×Dic59—21no—
65C22×C4×D59—21no—
66C2×#11745671—41no—
67C2×#11745671—41no—
68C2×#11745671C2×C414yescomplemented
69C2×#11745669—22no—
70C2×#11745669—22no—
71C2×#11745669C2×C414yescomplemented
72C2×#11745664—22no—
73C2×#11745664—22no—
74C2×#11745664—41no—
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79#14273701—22no—
80#14273701C2×C414yescomplemented
81C4×D236—22no—
82C4×D236—41no—
83(C22⋊D59)⋊C4—44no—
84C2×C4⋊Dic59—22no—
85C2×C4⋊Dic59—21no—
86C2×C4⋊Dic59—41no—
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×Dic59⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×(C2×D59)⋊C4—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×C4×Dic59—21no—
96#14273658—22no—
97#14273658—41no—
98#14273651—22no—
99#14273651—22no—
100#14273651C2×C414yescomplemented
101#14273648—22no—
102#14273648C2×C414yescomplemented
103#14273648D414yescomplemented
104#14273647—22no—
105#14273647—41no—
106C22⋊(C59⋊C8)C2×C414yescomplemented
107#14273638—22no—
108C4×C59⋊C8—41no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—22no—
114C2×#41×C59—41no—
115C2×#41×C59—41no—
116C2×#41×C59C2×C414yescomplemented
117C22×Q8×C59C2311yescharacteristic
118C22×D4×C59—21no—
119C22×D4×C59C2311yescharacteristic
120C23×C4×C59—21no—
121C23×C4×C59—21no—
122C23×C4×C59—21no—
123C23×C4×C59C2311yescharacteristic
124C4×D4×C59—22no—
125C4×D4×C59—22no—
126C4×D4×C59—41no—
127C4×D4×C59—41no—
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C22⋊C4×C59D411yescharacteristic
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59—21no—
142#95×C59D411yescharacteristic
143#95×C59D411yescharacteristic
144C24×C59—21no—
145C24×C59C2×D411yescharacteristic
146C23×D59—21no—
147#41×C59—28no—
148#41×C59—44no—
149#41×C59—44no—
150#41×C59—44no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59C22×C412yes—
157C2×D4×C59—24no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59C22×C412yes—
164C2×D4×C59C2×D412yes—
165C2×D4×C59#4112yes—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—24no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—42no—
175C22×C4×C59—42no—
176C22×C4×C59—42no—
177C22×C4×C59—42no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59—81no—
181C22×C4×C59—81no—
182C22×C4×C59C22×C412yes—
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59#4112yes—
189C22×C4×C59C2411yescharacteristic
190C2×C22⋊D59—24no—
191C2×C22⋊D59—42no—
192C2×C22⋊D59—42no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—42no—
197C22×Dic59—42no—
198C22×Dic59—81no—
199C2×D236—21no—
200C2×D236—21no—
201C2×D236—21no—
202C2×D236—21no—
203C2×D236—21no—
204C2×D236C22×C412yes—
205C2×C4×D59—42no—
206C2×C4×D59—42no—
207C2×C4×D59—81no—
208C4⋊C4×C59—21no—
209C4⋊C4×C59—21no—
210C4⋊C4×C59—21no—
211C4⋊C4×C59—21no—
212C22⋊C4×C59—22no—
213C22⋊C4×C59—41no—
214C22⋊C4×C59—42no—
215C22⋊C4×C59—42no—
216C22⋊C4×C59—81no—
217C42×C59—21no—
218C42×C59—21no—
219C42×C59—21no—
220C42×C59—21no—
221#11745671—44no—
222#11745669—28no—
223(C2×D59)⋊C4—24no—
224(C2×D59)⋊C4—42no—
225(C2×D59)⋊C4—42no—
226(C2×D59)⋊C4—81no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—21no—
231C4⋊Dic59—42no—
232C4⋊Dic59C22×C412yes—
233C4⋊Dic59C2×D412yes—
234Dic59⋊C4—42no—
235C4×Dic59—42no—
236#11745664—44no—
237C2×C59⋊C8—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⋊C8C22×C412yes—
247C2×C59⋊C8C22×C412yes—
248C2×C59⋊C8C2×D412yes—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—21no—
252C23×C59—22no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59C4×D412yes—
263C23×C59C22×D411yescharacteristic
264C22×D59—22no—
265C22×D59—41no—
266C22×D59—41no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271Q8×C59—22no—
272Q8×C59—22no—
273Q8×C59—41no—
274Q8×C59—41no—
275D4×C59—22no—
276D4×C59—22no—
277D4×C59—22no—
278D4×C59—48no—
279D4×C59C4×D414yescomplemented
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—48no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—84no—
308C2×C4×C59—84no—
309C2×C4×C59C4×D412yes—
310C2×C4×C59AGL(1,ℤ/8)12yes—
311C2×C4×C59C23×C411yescharacteristic
312C2×C4×C59C22×D411yescharacteristic
313C2×C4×C59C2×#4111yescharacteristic
314C2×C4×C59C2×#4111yescharacteristic
315C2×C4×C59H(5,𝔽2)11yescharacteristic
316C2×C4×C59H(5,𝔽2)11yescharacteristic
317C22⋊D59—48no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—84no—
328D236—22no—
329D236—22no—
330D236—41no—
331D236—41no—
332C4×D59—84no—
333C59⋊C8—22no—
334C59⋊C8—22no—
335C59⋊C8—22no—
336C59⋊C8—41no—
337#22866—591nomaximal, Sylow
338C22×C59—22no—
339C22×C59—24no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—41no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—41no—
348C22×C59—42no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—42no—
352C22×C59C2×C4×D411yescharacteristic
353C22×C59D4211yescharacteristic
354C22×C59#54611yescharacteristic
355C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C59#57511yescharacteristic
357C22×C59#57711yescharacteristic
358C22×C59#57711yescharacteristic
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—81no—
363C2×D59—81no—
364C2×D59—81no—
365C2×D59—81no—
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—42no—
369C4×C59—41no—
370C4×C59—41no—
371C4×C59—41no—
372C4×C59—81no—
373C4×C59—81no—
374C4×C59C2×C4×D411yescharacteristic
375C4×C59#51811yescharacteristic
376C4×C59#54611yescharacteristic
377C4×C59#55111yescharacteristic
378Dic59—42no—
379Dic59—42no—
380Dic59—81no—
381C2×#449—591no—
382C2×#442—591no—
383C2×#417—591no—
384#2361—591no—
385#2339D5911yescharacteristic, complemented
386#1968—591no—
387#1935—591no—
388#1927—591no—
389#1895—591no—
390#1879—591no—
391#1877—591no—
392#1864—591no—
393#1853—591no—
394C4×#102—591no—
395#1753—591no—
396C2×C59—42no—
397C2×C59—44no—
398C2×C59#235811yescharacteristic
399C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
400C2×C59#295211yescharacteristic
401C2×C59#327211yescharacteristic
402C2×C59#327511yescharacteristic
403C2×C59#330611yescharacteristic
404C2×C59#330711yescharacteristic
405D59—82no—
406C22×#41C2×D5911yescharacteristic
407C22×SD16—591no—
408C22×D8—591no—
409C22×M16—591no—
410C2×#121—591no—
411C2×C4×D4—591no—
412C2×C4×D4—1181no—
413C2×C4×D4C2×D5911yescharacteristic
414C2×C4×D4C2×D5911yescharacteristic
415C22×C4⋊C4—591no—
416#449—598no—
417#442—1184no—
418C2×#106—591no—
419C2×#106—591no—
420#417—1184no—
421C2×#103—591no—
422C2×#103—591no—
423C2×#103—591no—
424C2×#102—591no—
425C2×#102—591no—
426C2×#102—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×C22⋊C8—591no—
430C2×#97—591no—
431C2×C4×C8—591no—
432#391C2×D5911yescharacteristic
433#391C2×D5911yescharacteristic
434#390—591no—
435#389—591no—
436#388—1181no—
437#386—21no—
438#386—21no—
439#386—1181no—
440#385—1181no—
441#381—21no—
442#380C2×D5911yescharacteristic
443C4×C4⋊C4—591no—
444C4×C22⋊C4C2×D5911yescharacteristic
445C2×#95—21no—
446#340—591no—
447#340—591no—
448#340—591no—
449#340—591no—
450#336—591no—
451#336—591no—
452C59#2286611yescharacteristic, complemented, Sylow
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41C4×D5914yescomplemented
459C22×Q8C22×D5911yescharacteristic
460C22×D4—21no—
461C22×D4—591no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4C22×D5911yescharacteristic
470C2×SD16—594no—
471C2×SD16—2361no—
472C2×SD16—2361no—
473C2×D8—594no—
474C2×D8—1182no—
475C2×D8—1182no—
476C2×M16—1182no—
477C2×M16—1182no—
478C2×M16—2361no—
479C22×C8—591no—
480C22×C8—591no—
481C22×C8—591no—
482C22×C8—591no—
483#121—594no—
484#121—1182no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—41no—
488C4×D4—41no—
489C4×D4—1182no—
490C4×D4—2361no—
491C4×D4—2364no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—1182no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—2361no—
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4C22⋊D5911yescharacteristic
509C2×C22⋊C4C22⋊D5911yescharacteristic
510C2×C42—1181no—
511C2×C42C22×D5911yescharacteristic
512C2×C42C22×D5911yescharacteristic
513#106—1182no—
514#106—2361no—
515#103—594no—
516#103—1182no—
517#103—1182no—
518#102—594no—
519#102—594no—
520#102—1182no—
521#102—1182no—
522#102—2361no—
523C22⋊C8—594no—
524#97—1182no—
525C4×C8—2361no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—1181no—
532#95—1181no—
533#95C22⋊D5911yescharacteristic
534#95C22⋊D5911yescharacteristic
535C24—21no—
536C24—1181no—
537C24C2×C22⋊D5911yescharacteristic
538#41—28no—
539#41—44no—
540#41—44no—
541#41—44no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×C4×D5912yes—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—592no—
555C2×D4—1184no—
556C2×D4—1181no—
557C2×D4—1181no—
558C2×D4—1181no—
559C2×D4—1181no—
560C2×D4—1181no—
561C2×D4—2362no—
562C2×D4—2362no—
563C2×D4C2×C4×D5912yes—
564C2×D4D4×D5912yes—
565C2×D4#1174568712yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—4721no—
586C22×C4—4721no—
587C22×C4—2362no—
588C22×C4—2362no—
589C22×C4—2362no—
590C22×C4—2362no—
591C22×C4C2×C4×D5912yes—
592C22×C4#1174568512yes—
593C22×C4C2×C22⋊D5911yescharacteristic
594C22×C4C2×C22⋊D5911yescharacteristic
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C2×C22⋊D5911yescharacteristic
598C22×C4C23×D5911yescharacteristic
599SD16—2364no—
600D8—1188no—
601M16—2364no—
602C2×C8—592no—
603C2×C8—592no—
604C2×C8—592no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C2×C8—1181no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—592no—
619C4⋊C4—592no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—2362no—
625C4⋊C4—2362no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—1184no—
632C22⋊C4—4721no—
633C22⋊C4—2362no—
634C22⋊C4—2362no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—2362no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—1182no—
654C23—2361no—
655C23—2361no—
656C23—2361no—
657C23—2361no—
658C23—2361no—
659C23—2361no—
660C23C4×C22⋊D5912yes—
661C23C22×C22⋊D5911yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—48no—
670D4—1182no—
671D4—1182no—
672D4—2368no—
673D4—2361no—
674D4—2361no—
675D4(C22⋊D59)⋊C414yescomplemented
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—4724no—
708C2×C4—4724no—
709C2×C4—2361no—
710C2×C4—2361no—
711C2×C4—2361no—
712C2×C4—2361no—
713C2×C4—2361no—
714C2×C4—2361no—
715C2×C4—2361no—
716C2×C4C4×C22⋊D5912yes—
717C2×C4#1427375212yes—
718C2×C4C22×C4×D5911yescharacteristic
719C2×C4C2×D4×D5911yescharacteristic
720C2×C4C2×#1174568711yescharacteristic
721C2×C4C2×#1174568511yescharacteristic
722C2×C4#1427377211yescharacteristic
723C2×C4#1427377211yescharacteristic
724C8—1182no—
725C8—1182no—
726C8—1182no—
727C8—2361no—
728C22—22no—
729C22—22no—
730C22—24no—
731C22—22no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—4721no—
743C22—4721no—
744C22—4721no—
745C22—4721no—
746C22—2362no—
747C22—2362no—
748C22—2362no—
749C22C2×C4×C22⋊D5911yescharacteristic
750C22D4×C22⋊D5911yescharacteristic
751C22#1683804611yescharacteristic
752C22C2×#1427375211yescharacteristic
753C22#1683820011yescharacteristic
754C22#1683821011yescharacteristic
755C22#1683821311yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—81no—
763C4—81no—
764C4—4721no—
765C4—2362no—
766C4—2362no—
767C4C2×(C22⋊D59)⋊C411yescharacteristic
768C4#1683787511yescharacteristic
769C4#1683804211yescharacteristic
770C4#1683807811yescharacteristic
771C2—42no—
772C2—44no—
773C2—4722no—
774C2#2142707511yescharacteristic
775C2C4×#1427375211yescharacteristic
776C2#2143297711yescharacteristic
777C2#2143569611yescharacteristic
778C2#2143572311yescharacteristic
779C2#2143605711yescharacteristic
780C2#2143607211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2339C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
cosocleC22×C4×C59C24
hypercenter#2339D59
hypocenterC59#22866
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×#16837403C2semidirect
4. #21427110C2semidirect
5. #21424953C2semidirect
6. #21424789C2semidirect
7. #21424727C2semidirect
8. #21424532C2semidirect
9. #21424444C2semidirect
10. #21424433C2semidirect
11. #21424357C2semidirect
12. #21424288C2semidirect
13. C4×#14273648C2semidirect
14. #21423880C2semidirect
15. C59×#2339C2semidirect
23. #16837547C4semidirect
68. C2×#11745671C2×C4semidirect
71. C2×#11745669C2×C4semidirect
80. #14273701C2×C4semidirect
100. #14273651C2×C4semidirect
102. #14273648C2×C4semidirect
103. #14273648D4semidirect
106. C22⋊(C59⋊C8)C2×C4semidirect
116. C2×#41×C59C2×C4semidirect
279. D4×C59C4×D4semidirect
385. #2339D59semidirect
452. C59#22866semidirect
458. C2×#41C4×D59semidirect
675. D4(C22⋊D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168375472
C2×#168375122
C2×#168374032
#214271102
#214249532
#214247892
#214247272
#214245322
#214244442
#214244332
#214243572
#214242882
C4×#142736482
#214238802
C59×#23392
#2286659