Finite Group Databasebeta

← C2×#21435981 #29465094

Subgroups — C2×#21435981 #29465094

Order 15104.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838087C211yesmaximal, characteristic, complemented
2C2×#16838058C211yesmaximal, characteristic
3#21435981C2116yesmaximal, direct product factor
4C2×#16837755C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837708C211yesmaximal, characteristic, complemented
7C2×#16837644C211yesmaximal, characteristic, complemented
8C2×#16837629C211yesmaximal, characteristic, complemented
9C2×#16837623C211yesmaximal, characteristic, complemented
10C2×#16837565C211yesmaximal, characteristic, complemented
11C2×#16837560C211yesmaximal, characteristic, complemented
12C2×#16837496C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
14C2×#16837395C211yesmaximal, characteristic, complemented
15C22×#14273650C211yesmaximal, characteristic, complemented
16C2×C59×#480C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C23×C59⋊C8C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16838087—24no—
25#16838087C2218yescomplemented
26#16838058—24no—
27#16838058C2218yes—
28C2×#14273722—21no—
29C2×#14273718C2211yescharacteristic
30C2×#14273717—21no—
31C2×#14273714C2211yescharacteristic
32C2×#14273713—21no—
33C2×#14273710—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273707C2211yescharacteristic
36C2×#14273706C2211yescharacteristic
37C2×#14273704—21no—
38C2×#14273699—21no—
39C2×#14273692C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×D4×Dic59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×#14273686—21no—
44C2×#14273685C2211yescharacteristic
45#16837755C2218yescomplemented
46#16837745C2218yescomplemented
47#16837708C2218yescomplemented
48#16837644C2218yescomplemented
49#16837629C2218yescomplemented
50#16837623C2218yescomplemented
51#16837565C2218yescomplemented
52#16837560C2218yescomplemented
53#16837496C2218yescomplemented
54(C22⋊D59)⋊C8C2218yescomplemented
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837395C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2218yescomplemented
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#480C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745687—22no—
78C2×#11745687—24no—
79C2×#11745687—42no—
80C2×#11745687C2314yes—
81C22×Dic118—24no—
82C22×Dic118—21no—
83C22×Dic118—22no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2314yes—
88C22×Dic118C2311yescharacteristic
89C22×C22⋊D59—21no—
90C22×C22⋊D59D411yescharacteristic
91C23×Dic59—21no—
92C23×Dic59—21no—
93C22×C4×D59C2311yescharacteristic
94C2×Dic236—24no—
95C2×Dic236—42no—
96C2×Dic236C2314yes—
97C2×Dic236C2314yes—
98C2×#11745670—42no—
99C2×#11745670C2314yes—
100C22×C59⋊C8—42no—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2314yes—
104C2×C8×D59—42no—
105C2×C8×D59C2314yes—
106#14273722—28no—
107#14273718—22no—
108#14273718C2314yes—
109#14273717—28no—
110#14273714—22no—
111#14273714C2314yes—
112#14273713—28no—
113#14273710—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707C2314yes—
117#14273707C2314yes—
118#14273706—22no—
119#14273706C2314yes—
120#14273704—28no—
121#14273699—28no—
122#14273692—22no—
123#14273692—22no—
124#14273692C2314yes—
125#14273692C2314yes—
126D4×Dic59—28no—
127C4×C22⋊D59D414yes—
128C4×C22⋊D59C2314yes—
129#14273686—28no—
130#14273685—22no—
131#14273685C2314yes—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59C2311yescharacteristic
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4D411yescharacteristic
141C2×C22⋊Dic59—21no—
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59D411yescharacteristic
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59C2311yescharacteristic
153#14273658C2314yes—
154Dic59⋊C8C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162#14273648C2314yes—
163(C2×D59)⋊C8C2314yes—
164C8×Dic59C2314yes—
165C22×D4×C59—21no—
166C22×D4×C59C2311yescharacteristic
167C23×C4×C59—21no—
168C23×C4×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171#121×C59—22no—
172#121×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—22no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2314yes—
179C2×C22⋊C4×C59—21no—
180#107×C59C2314yes—
181#107×C59C2314yes—
182#102×C59C2314yes—
183#102×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188C2×D4×C59—24no—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—44no—
193C2×D4×C59C2412yes—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—24no—
200C22×C4×C59—44no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2411yescharacteristic
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—44no—
208C2×C22⋊D59C2×D414yes—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—24no—
214C22×Dic59—24no—
215C22×Dic59—44no—
216C22×Dic59—44no—
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220#11745687—28no—
221#11745687—44no—
222#11745687—48no—
223C2×C4×D59—22no—
224C2×C4×D59—22no—
225C2×C4×D59C2×D412yes—
226C2×C4×D59C2412yes—
227C2×Dic118—21no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—22no—
233C2×Dic118—28no—
234C2×Dic118—21no—
235C2×Dic118—24no—
236C2×Dic118—21no—
237C2×Dic118—44no—
238C2×Dic118—48no—
239C2×Dic118—44no—
240C2×Dic118#4114yes—
241C2×Dic118C2412yes—
242C2×Dic118C2412yes—
243C2×Dic118C2412yes—
244C2×C8×C59—22no—
245C2×C8×C59—22no—
246C2×C8×C59C2412yes—
247C2×C8×C59C2412yes—
248C4⋊C4×C59—21no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—24no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59C2412yes—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C22⋊C4×C59—24no—
256C22⋊Dic59—24no—
257C22⋊Dic59—24no—
258C22⋊Dic59—24no—
259C22⋊Dic59C2×D414yes—
260#11745670—44no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4C2×D414yes—
265C4⋊Dic59—21no—
266C4⋊Dic59—24no—
267C4⋊Dic59—24no—
268C4⋊Dic59—24no—
269C4⋊Dic59C2412yes—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4C2×D414yes—
275C4×Dic59—24no—
276C4×Dic59—24no—
277C4×Dic59—24no—
278C4×Dic59C2×D412yes—
279C4×Dic59C2412yes—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—44no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285Dic236—28no—
286Dic236—44no—
287C8×D59—44no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—42no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59#13514yes—
295C23×C59C22×D412yes—
296C23×C59C22×D411yescharacteristic
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59C22×D412yes—
301D4×C59—22no—
302D4×C59—22no—
303D4×C59—48no—
304D4×C59—42no—
305C2×C4×C59—22no—
306C2×C4×C59—24no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—48no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C2×#4112yes—
319C2×C4×C59H(5,𝔽2)12yes—
320C2×C4×C59C2511yescharacteristic
321C22⋊D59—28no—
322C22⋊D59—48no—
323C2×Dic59—24no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—48no—
332C2×Dic59—48no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59C22×D412yes—
337C2×Dic59C22×D412yes—
338C2×Dic59C22×D412yes—
339C4×D59—24no—
340C4×D59—22no—
341C4×D59—22no—
342Dic118—24no—
343Dic118—22no—
344Dic118—22no—
345Dic118—22no—
346Dic118—22no—
347Dic118—22no—
348Dic118—48no—
349Dic118—42no—
350Dic118—42no—
351Dic118C2×#4114yes—
352C8×C59—22no—
353C8×C59—22no—
354C59⋊C8—22no—
355C59⋊C8—22no—
356C2×#3300—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—28no—
359C22×C59—22no—
360C22×C59—42no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—84no—
364C22×C59#54612yes—
365C22×C59C2×#13514yes—
366C22×C59C2×#13512yes—
367C22×C59#57812yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—44no—
373C4×C59—22no—
374C4×C59—42no—
375C4×C59—42no—
376C4×C59—42no—
377C4×C59#54612yes—
378C4×C59C22×#4111yescharacteristic
379C4×C59C2×H(5,𝔽2)11yescharacteristic
380Dic59—24no—
381Dic59—22no—
382Dic59—22no—
383Dic59—22no—
384Dic59—42no—
385Dic59—42no—
386Dic59—42no—
387C2×#552—591no—
388C2×#548—591no—
389#3300—5916no—
390C2×#488—591no—
391C2×#485—591no—
392C2×#480D5911yescharacteristic, complemented
393C2×#479—591no—
394C2×#467—591no—
395C2×#465—591no—
396C2×#464—591no—
397C2×#452—591no—
398C2×#451—591no—
399C2×C4×Q16—591no—
400C2×C8×D4—591no—
401C2×#416—591no—
402C22×#103—591no—
403C2×C59—24no—
404C2×C59—82no—
405C2×C59#330014yescomplemented
406C2×C59C2×#54611yescharacteristic
407C2×C59C22×#13511yescharacteristic
408C2×C59C2×#57811yescharacteristic
409D59—42no—
410C22×#41—591no—
411C23×Q8—591no—
412C22×Q16—591no—
413C22×Q16—591no—
414C22×SD16—591no—
415C23×C8—591no—
416C23×C8—591no—
417#552—598no—
418#552—1184no—
419#548—598no—
420#548—1184no—
421C2×#126—1181no—
422C2×#125—591no—
423C2×#125—1181no—
424C2×#124—591no—
425C2×#124—1181no—
426C2×#123—1181no—
427C2×C22⋊Q8—591no—
428C2×C22⋊Q8—591no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—1181no—
431C2×#121—1181no—
432C2×#121C2×D5911yescharacteristic
433C2×C4×Q8—591no—
434C2×C4×Q8—591no—
435C2×C4×D4—591no—
436C2×C4×D4—1181no—
437C2×#117—591no—
438C2×#117—1181no—
439C22×C4⋊C4C2×D5911yescharacteristic
440#488—598no—
441#485—598no—
442#480C2×D5918yescomplemented
443#479—598no—
444#467—598no—
445#465—598no—
446#464—598no—
447#452—598no—
448#451—598no—
449C4×Q16—598no—
450C8×D4—598no—
451C2×#107C2×D5911yescharacteristic
452C2×#107C2×D5911yescharacteristic
453C2×#106—591no—
454C2×C4⋊C8—591no—
455#416—598no—
456C2×#103—591no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—598no—
464C2×#102—591no—
465C2×#102C2×D5911yescharacteristic
466C2×#102C2×D5911yescharacteristic
467C2×C22⋊C8—591no—
468C2×C22⋊C8C2×D5911yescharacteristic
469C2×C4×C8—591no—
470C59C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—594no—
472C2×#41—1182no—
473C2×#41—1184no—
474C2×#41—2362no—
475C22×Q8—591no—
476C22×Q8—591no—
477C22×Q8—591no—
478C22×Q8—594no—
479C22×Q8—1184no—
480C22×Q8—1181no—
481C22×Q8—1182no—
482C22×Q8—2362no—
483C22×D4—21no—
484C22×D4—591no—
485C22×D4—1181no—
486C22×D4C22×D5911yescharacteristic
487C23×C4—21no—
488C23×C4—591no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4C22×D5911yescharacteristic
492C2×Q16—594no—
493C2×Q16—594no—
494C2×Q16—1184no—
495C2×Q16—2362no—
496C2×SD16—594no—
497C2×SD16—2362no—
498C22×C8—591no—
499C22×C8—591no—
500C22×C8—594no—
501C22×C8—594no—
502C22×C8—2362no—
503C22×C8—2362no—
504C22×C8C22×D5911yescharacteristic
505C22×C8C22×D5911yescharacteristic
506#126—1188no—
507#125—594no—
508#125—1182no—
509#125—1188no—
510#124—594no—
511#124—1182no—
512#124—1188no—
513#123—1188no—
514C22⋊Q8—594no—
515C22⋊Q8—594no—
516C22⋊Q8—594no—
517C22⋊Q8—1188no—
518C22⋊Q8—1182no—
519C22⋊Q8—1182no—
520C22⋊Q8—1182no—
521#121—22no—
522#121—1188no—
523#121C22×D5914yes—
524C4×Q8—594no—
525C4×Q8—594no—
526C4×Q8—1182no—
527C4×Q8—1182no—
528C4×D4—594no—
529C4×D4—594no—
530C4×D4—1188no—
531#117—594no—
532#117—1188no—
533#117—1182no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4C22×D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C4⋊C4C22×D5914yes—
548C2×C4⋊C4C22×D5911yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—591no—
551C2×C22⋊C4—591no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C42—591no—
559C2×C42—1181no—
560C2×C42—1181no—
561C2×C42—1181no—
562#107C22×D5914yes—
563#107C22×D5914yes—
564#106—594no—
565C4⋊C8—594no—
566#103—594no—
567#103—594no—
568#103—594no—
569#103—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#102—594no—
574#102C22×D5914yes—
575#102C22×D5914yes—
576C22⋊C8—594no—
577C22⋊C8C22×D5914yes—
578C4×C8—594no—
579C24—21no—
580C24—591no—
581C24D4×D5911yescharacteristic
582#41—1188no—
583#41—2364no—
584#41—2368no—
585C2×Q8—594no—
586C2×Q8—592no—
587C2×Q8—592no—
588C2×Q8—592no—
589C2×Q8—1188no—
590C2×Q8—1181no—
591C2×Q8—1181no—
592C2×Q8—1184no—
593C2×Q8—1181no—
594C2×Q8—1182no—
595C2×Q8—1182no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8—2364no—
600C2×Q8—2364no—
601C2×Q8—2368no—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—594no—
608C2×D4—1184no—
609C2×D4—1184no—
610C2×D4—2364no—
611C2×D4C23×D5912yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—44no—
619C22×C4—591no—
620C22×C4—591no—
621C22×C4—591no—
622C22×C4—592no—
623C22×C4—592no—
624C22×C4—1184no—
625C22×C4—1181no—
626C22×C4—1182no—
627C22×C4—1182no—
628C22×C4—1184no—
629C22×C4—1181no—
630C22×C4—1181no—
631C22×C4—1181no—
632C22×C4—2364no—
633C22×C4—2364no—
634C22×C4D4×D5912yes—
635C22×C4D4×D5911yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638Q16—1188no—
639Q16—2364no—
640SD16—2364no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—592no—
644C2×C8—592no—
645C2×C8—1182no—
646C2×C8—1182no—
647C2×C8—2364no—
648C2×C8—2364no—
649C2×C8C23×D5912yes—
650C2×C8C23×D5912yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—594no—
656C4⋊C4—592no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4—1184no—
662C4⋊C4—1184no—
663C4⋊C4—1181no—
664C4⋊C4—1184no—
665C4⋊C4C23×D5912yes—
666C4⋊C4C23×D5912yes—
667C4⋊C4C23×D5912yes—
668C22⋊C4—24no—
669C22⋊C4—594no—
670C22⋊C4—594no—
671C22⋊C4—1184no—
672C22⋊C4—1184no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C22⋊C4—1184no—
677C42—592no—
678C42—592no—
679C42—1184no—
680C42—1184no—
681C42—1184no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—592no—
689C23—1182no—
690C23—1182no—
691C23—1182no—
692C23#1427374614yes—
693C23C2×D4×D5912yes—
694C23C2×D4×D5911yescharacteristic
695Q8—594no—
696Q8—1182no—
697Q8—1184no—
698Q8—1182no—
699Q8—1182no—
700Q8—1182no—
701Q8—1182no—
702Q8—2368no—
703Q8—2362no—
704Q8—2362no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—42no—
709D4—1188no—
710D4—2368no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—592no—
723C2×C4—592no—
724C2×C4—592no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1184no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1184no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—2368no—
737C2×C4—2368no—
738C2×C4—2362no—
739C2×C4—2362no—
740C2×C4—2362no—
741C2×C4C2×D4×D5912yes—
742C2×C4C2×D4×D5911yescharacteristic
743C2×C4#41×D5912yes—
744C2×C4#1427377312yes—
745C2×C4C24×D5911yescharacteristic
746C8—22no—
747C8—22no—
748C8—1182no—
749C8—1182no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—84no—
757C22—1182no—
758C22—1182no—
759C22—1182no—
760C22—2364no—
761C22#1683804412yes—
762C22C2×#1427374614yes—
763C22C2×#1427374612yes—
764C22#1683821812yes—
765C22C22×D4×D5911yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—1182no—
771C4—1182no—
772C4—1184no—
773C4—1182no—
774C4—2362no—
775C4—2362no—
776C4—2362no—
777C4#1683804412yes—
778C4C2×#41×D5911yescharacteristic
779C4C2×#1427377311yescharacteristic
780C2—24no—
781C2—82no—
782C2—2362no—
783C2#2143598114yesdirect product factor
784C2C2×#1683804411yescharacteristic
785C2C22×#1427374611yescharacteristic
786C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#480C2
socleC23×C59C22×D4
prime radicalC2×#16838058C2
hypercenterC2×#480D59
hypocenterC59C2×#3300
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16838087C2semidirect
3. #21435981C2direct (N × H)
4. C2×#16837755C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837708C2semidirect
7. C2×#16837644C2semidirect
8. C2×#16837629C2semidirect
9. C2×#16837623C2semidirect
10. C2×#16837565C2semidirect
11. C2×#16837560C2semidirect
12. C2×#16837496C2semidirect
13. C2×(C22⋊D59)⋊C8C2semidirect
14. C2×#16837395C2semidirect
15. C22×#14273650C2semidirect
16. C2×C59×#480C2semidirect
25. #16838087C22semidirect
45. #16837755C22semidirect
46. #16837745C22semidirect
47. #16837708C22semidirect
48. #16837644C22semidirect
49. #16837629C22semidirect
50. #16837623C22semidirect
51. #16837565C22semidirect
52. #16837560C22semidirect
53. #16837496C22semidirect
54. (C22⋊D59)⋊C8C22semidirect
57. #16837395C22semidirect
65. C2×#14273650C22semidirect
71. C59×#480C22semidirect
392. C2×#480D59semidirect
405. C2×C59#3300semidirect
442. #480C2×D59semidirect
470. C59C2×#3300semidirect
783. C2#21435981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380872
C2×#168380582
#214359812
C2×#168377552
C2×#168377452
C2×#168377082
C2×#168376442
C2×#168376292
C2×#168376232
C2×#168375652
C2×#168375602
C2×#168374962
C2×(C22⋊D59)⋊C82
C2×#168373952
C22×#142736502
C2×C59×#4802
C2×#330059