Finite Group Databasebeta

← C2×#21438630 #29496056

Subgroups — C2×#21438630 #29496056

Order 15104.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438630C2132yesmaximal, direct product factor
2C2×#16838156C212yesmaximal, complemented
3C2×#16838150C212yesmaximal, complemented
4C2×#16838108C212yesmaximal, complemented
5C2×#16838105C212yesmaximal, complemented
6C2×#16838100C212yesmaximal, complemented
7C2×#16838053C212yesmaximal, complemented
8C2×#16838053C214yesmaximal, complemented
9C2×#16838032C212yesmaximal, complemented
10C2×#16838008C212yesmaximal, complemented
11C2×#16838000C214yesmaximal, complemented
12C2×#16837999C212yesmaximal, complemented
13C2×#16837983C212yesmaximal, complemented
14C2×#16837952C211yesmaximal, characteristic, complemented
15C2×#16837936C211yesmaximal, characteristic, complemented
16C22×#125×C59C211yesmaximal, characteristic, complemented
17C22×#11745685C2212yes—
18C22×#11745685C2214yes—
19#16838156C22132yescomplemented
20#16838150C22132yescomplemented
21#16838108C22132yescomplemented
22#16838105C22132yescomplemented
23#16838100C22132yescomplemented
24#16838053C22164yescomplemented
25#16838053C22132yescomplemented
26#16838032C22132yescomplemented
27#16838008C22132yescomplemented
28#16838000C22164yescomplemented
29#16837999C22132yescomplemented
30#16837983C22132yescomplemented
31#16837952C22116yescomplemented
32C2×#14273727C2211yescharacteristic
33C2×#14273726C2214yes—
34C2×#14273726C2212yes—
35C2×#14273724C2211yescharacteristic
36#16837936C22116yescomplemented
37C2×#14273722C2214yes—
38C2×#14273722C2214yes—
39C2×#14273721C2212yes—
40C2×#14273719C2211yescharacteristic
41C2×#14273718C2212yes—
42C2×#14273717C2214yes—
43C2×#14273715C2211yescharacteristic
44C2×#14273715C2212yes—
45C2×#14273712C2214yes—
46C2×#14273712C2214yes—
47C2×#14273712C2214yes—
48C2×#14273712C2214yes—
49C2×#14273712C2214yes—
50C2×#14273710C2214yes—
51C2×#14273710C2212yes—
52C2×#14273707C2214yes—
53C2×#14273707C2214yes—
54C2×#14273706C2211yescharacteristic
55C2×#14273705C2214yes—
56C2×#14273705C2214yes—
57C2×#14273705C2214yes—
58C2×#14273705C2214yes—
59C2×#14273702C2214yes—
60C2×#14273702C2214yes—
61C2×#14273702C2214yes—
62C2×#14273702C2212yes—
63C2×#14273702C2212yes—
64C2×#14273701C2212yes—
65C2×#14273701C2212yes—
66C2×#14273701C2214yes—
67C2×#14273701C2211yescharacteristic
68C2×C4×Dic118C2211yescharacteristic
69C2×C4×D236C2212yes—
70C2×C4×D236C2211yescharacteristic
71C2×C4×D236C2212yes—
72C2×#14273689C2214yes—
73C2×#14273689C2212yes—
74C2×#14273689C2212yes—
75C2×C4×C22⋊D59C2214yes—
76C2×C4×C22⋊D59C2212yes—
77C2×#14273685C2212yes—
78C2×#14273684C2212yes—
79C2×C4⋊C4×D59C2214yes—
80C2×C4⋊C4×D59C2212yes—
81C2×#125×C59C2212yes—
82C2×#125×C59C2212yes—
83C2×#125×C59C2212yes—
84C2×#125×C59C2212yes—
85C2×#125×C59C22116yescomplemented
86C22×C4⋊C4×C59C2212yes—
87C22×C4⋊C4×C59C2212yes—
88C22×C4⋊C4×C59C2211yescharacteristic
89C22×C4⋊C4×C59C2211yescharacteristic
90C22×C42×C59C2211yescharacteristic
91C2×#11745685—48no—
92C2×#11745685—416no—
93C2×#11745685C23116yes—
94C2×#11745685C23132yes—
95C22×Dic118C2311yescharacteristic
96C22×Dic118C2314yes—
97C22×Dic118C2312yes—
98C22×D236C2312yes—
99C22×D236C2314yes—
100C22×D236C2311yescharacteristic
101C22×D236C2312yes—
102C22×D236C2314yes—
103C22×D236C2312yes—
104C22×C22⋊D59C2314yes—
105C22×C22⋊D59C2312yes—
106C22×C4×D59C2312yes—
107C22×C4×D59C2314yes—
108C22×C4×D59C2314yes—
109C22×C4×D59C2314yes—
110C22×C4×D59C2314yes—
111#14273727C2318yes—
112#14273726C23132yes—
113#14273726C23116yes—
114#14273724C2318yes—
115#14273722C23132yes—
116#14273722C23132yes—
117#14273721C23116yes—
118#14273719C2318yes—
119#14273718C23116yes—
120#14273717C23132yes—
121#14273715C2318yes—
122#14273715C23116yes—
123#14273712C23132yes—
124#14273712C23132yes—
125#14273712C23132yes—
126#14273712C23132yes—
127#14273712C23132yes—
128#14273710C23116yes—
129#14273710C23132yes—
130#14273707C23132yes—
131#14273707C23132yes—
132#14273706C2318yes—
133#14273705C23132yes—
134#14273705C23132yes—
135#14273705C23132yes—
136#14273705C23132yes—
137#14273702C23132yes—
138#14273702C23132yes—
139#14273702C23132yes—
140#14273702C23116yes—
141#14273702C23116yes—
142#14273701C2318yes—
143#14273701C23116yes—
144#14273701C23116yes—
145#14273701C23132yes—
146C4×Dic118C2318yes—
147C4×D236C2318yes—
148C4×D236C23116yes—
149C4×D236C23116yes—
150#14273689C23132yes—
151#14273689C23116yes—
152#14273689C23116yes—
153C4×C22⋊D59C23116yes—
154C4×C22⋊D59C23132yes—
155#14273685C23116yes—
156#14273684C23116yes—
157C2×C4⋊Dic59C2311yescharacteristic
158C2×C4⋊Dic59C2312yes—
159C2×C4⋊Dic59C2314yes—
160C2×C4⋊Dic59C2312yes—
161C2×C4⋊Dic59C2311yescharacteristic
162C2×Dic59⋊C4C2314yes—
163C2×Dic59⋊C4C2314yes—
164C2×Dic59⋊C4C2312yes—
165C2×Dic59⋊C4C2312yes—
166C2×Dic59⋊C4C2314yes—
167C2×Dic59⋊C4C2312yes—
168C2×Dic59⋊C4C2312yes—
169C4⋊C4×D59C23132yes—
170C4⋊C4×D59C23116yes—
171C2×C22⋊Dic59C2312yes—
172C2×(C2×D59)⋊C4C2312yes—
173C2×(C2×D59)⋊C4C2314yes—
174C2×(C2×D59)⋊C4C2314yes—
175C2×(C2×D59)⋊C4C2314yes—
176C2×(C2×D59)⋊C4C2314yes—
177C2×(C2×D59)⋊C4C2312yes—
178C2×(C2×D59)⋊C4C2314yes—
179C2×(C2×D59)⋊C4C2314yes—
180C2×(C2×D59)⋊C4C2314yes—
181C2×(C2×D59)⋊C4C2312yes—
182C2×(C2×D59)⋊C4C2312yes—
183C2×C4×Dic59C2314yes—
184C2×C4×Dic59C2312yes—
185C23×C4×C59C2311yescharacteristic
186C23×C4×C59C2311yescharacteristic
187C23×C4×C59C2312yes—
188C23×C4×C59C2311yescharacteristic
189C23×C4×C59C2312yes—
190#125×C59C23116yes—
191#125×C59C23116yes—
192#125×C59C23116yes—
193#125×C59C23116yes—
194C2×C4⋊C4×C59C2314yes—
195C2×C4⋊C4×C59C2314yes—
196C2×C4⋊C4×C59C2314yes—
197C2×C4⋊C4×C59C2312yes—
198C2×C4⋊C4×C59C2312yes—
199C2×C4⋊C4×C59C2312yes—
200C2×C4⋊C4×C59C2314yes—
201C2×C4⋊C4×C59C2312yes—
202C2×C4⋊C4×C59C23116yes—
203C2×C4⋊C4×C59C2318yes—
204C2×C4⋊C4×C59C23116yes—
205C2×C4⋊C4×C59C2318yes—
206C2×C42×C59C2311yescharacteristic
207C2×C42×C59C2311yescharacteristic
208C2×C42×C59C2318yes—
209C2×C42×C59C2311yescharacteristic
210C2×C42×C59C2311yescharacteristic
211C24×C59C2411yescharacteristic
212C23×D59C2412yes—
213C23×D59C2414yes—
214C22×C4×C59—24no—
215C22×C4×C59—28no—
216C22×C4×C59—24no—
217C22×C4×C59—42no—
218C22×C4×C59—44no—
219C22×C4×C59C2411yescharacteristic
220C22×C4×C59C2411yescharacteristic
221C22×C4×C59C2411yescharacteristic
222C22×C4×C59C2411yescharacteristic
223C22×C4×C59C2411yescharacteristic
224C22×C4×C59C2414yes—
225C22×C4×C59C2414yes—
226C22×C4×C59C2414yes—
227C22×C4×C59C2414yes—
228C22×C4×C59C2418yes—
229C22×C4×C59C2414yes—
230C22×C4×C59C2418yes—
231C22×C4×C59C2411yescharacteristic
232C2×C22⋊D59—216no—
233C2×C22⋊D59—28no—
234C2×C22⋊D59C2418yes—
235C2×C22⋊D59C24116yes—
236C22×Dic59C2412yes—
237C22×Dic59C2412yes—
238C22×Dic59C2414yes—
239C22×Dic59C2412yes—
240#11745685—432no—
241#11745685—464no—
242C2×D236—28no—
243C2×D236—42no—
244C2×D236—48no—
245C2×D236—44no—
246C2×D236—44no—
247C2×D236—48no—
248C2×D236C2418yes—
249C2×D236C24116yes—
250C2×D236C2414yes—
251C2×D236C2418yes—
252C2×D236C24116yes—
253C2×D236C2418yes—
254C2×C4×D59—28no—
255C2×C4×D59—48no—
256C2×C4×D59—48no—
257C2×C4×D59—48no—
258C2×C4×D59—48no—
259C2×C4×D59C2418yes—
260C2×C4×D59C24116yes—
261C2×C4×D59C24116yes—
262C2×C4×D59C24116yes—
263C2×C4×D59C24116yes—
264C2×Dic118—42no—
265C2×Dic118—44no—
266C2×Dic118—48no—
267C2×Dic118C2414yes—
268C2×Dic118C24116yes—
269C2×Dic118C2418yes—
270C4⋊C4×C59C2418yes—
271C4⋊C4×C59C24116yes—
272C4⋊C4×C59C2418yes—
273C4⋊C4×C59C24116yes—
274C4⋊C4×C59C24116yes—
275C4⋊C4×C59C24116yes—
276C4⋊C4×C59C2418yes—
277C4⋊C4×C59C2418yes—
278C42×C59C2414yes—
279C42×C59C2414yes—
280C42×C59C2414yes—
281C42×C59C2414yes—
282C22⋊Dic59C2418yes—
283(C2×D59)⋊C4C2418yes—
284(C2×D59)⋊C4C2418yes—
285(C2×D59)⋊C4C24116yes—
286(C2×D59)⋊C4C24116yes—
287(C2×D59)⋊C4C2418yes—
288(C2×D59)⋊C4C2418yes—
289(C2×D59)⋊C4C24116yes—
290(C2×D59)⋊C4C24116yes—
291(C2×D59)⋊C4C24116yes—
292(C2×D59)⋊C4C24116yes—
293(C2×D59)⋊C4C24116yes—
294C4⋊Dic59C2418yes—
295C4⋊Dic59C24116yes—
296C4⋊Dic59C2418yes—
297C4⋊Dic59C2414yes—
298C4⋊Dic59C2414yes—
299Dic59⋊C4C2418yes—
300Dic59⋊C4C24116yes—
301Dic59⋊C4C24116yes—
302Dic59⋊C4C2418yes—
303Dic59⋊C4C2418yes—
304Dic59⋊C4C24116yes—
305Dic59⋊C4C2418yes—
306C4×Dic59C2418yes—
307C4×Dic59C24116yes—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59H(5,𝔽2)14yes—
311C23×C59C2512yes—
312C23×C59C2511yescharacteristic
313C22×D59—24no—
314C22×D59—28no—
315C22×D59—24no—
316C22×D59—28no—
317C22×D59—28no—
318C22×D59—24no—
319C22×D59C2514yes—
320C22×D59C2518yes—
321C2×C4×C59—22no—
322C2×C4×C59—28no—
323C2×C4×C59—22no—
324C2×C4×C59—28no—
325C2×C4×C59—216no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—28no—
329C2×C4×C59—22no—
330C2×C4×C59—28no—
331C2×C4×C59—44no—
332C2×C4×C59—48no—
333C2×C4×C592−1+414yes—
334C2×C4×C59C2518yes—
335C2×C4×C59C2512yes—
336C2×C4×C59C2512yes—
337C2×C4×C59C2512yes—
338C2×C4×C59C2512yes—
339C2×C4×C59C2518yes—
340C2×C4×C59C2512yes—
341C2×C4×C59C2512yes—
342C22⋊D59—232no—
343C22⋊D59—216no—
344C2×Dic59—28no—
345C2×Dic59—24no—
346C2×Dic59—24no—
347C2×Dic59—24no—
348C2×Dic59C2514yes—
349C2×Dic59C2514yes—
350C2×Dic59C2514yes—
351C2×Dic59C2518yes—
352D236—216no—
353D236—44no—
354D236—416no—
355D236—48no—
356D236—48no—
357D236—416no—
358C4×D59—216no—
359C4×D59—416no—
360C4×D59—416no—
361C4×D59—416no—
362C4×D59—416no—
363Dic118—44no—
364Dic118—48no—
365Dic118—416no—
366C2×#3559—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—28no—
370C22×C59C2×H(5,𝔽2)14yes—
371C22×C59C2×H(5,𝔽2)12yes—
372C22×C59C2×2−1+412yes—
373C22×C59#58512yes—
374C22×C59C2611yescharacteristic
375C2×D59—24no—
376C2×D59—28no—
377C2×D59—24no—
378C2×D59—28no—
379C2×D59—28no—
380C2×D59—24no—
381C2×D59—48no—
382C2×D59—416no—
383C4×C59—22no—
384C4×C59—28no—
385C4×C59—22no—
386C4×C59—22no—
387C4×C59—22no—
388C4×C59—28no—
389C4×C59—22no—
390C4×C59C2×2−1+414yes—
391Dic59—28no—
392Dic59—24no—
393Dic59—24no—
394Dic59—24no—
395#3559—5932no—
396C2×#563—592no—
397C2×#562—592no—
398C2×#554—592no—
399C2×#553—592no—
400C2×#553—592no—
401C2×#547—594no—
402C2×#547—592no—
403C2×#544—592no—
404C2×#540—592no—
405C2×#539—594no—
406C2×#539—592no—
407C2×#537—592no—
408C2×#532—591no—
409C2×#529—591no—
410C22×#125D5911yescharacteristic, complemented
411C2×C59—24no—
412C2×C59#355914yescomplemented
413C2×C59C22×H(5,𝔽2)11yescharacteristic
414C2×C59C22×2−1+411yescharacteristic
415C2×C59C2×#58511yescharacteristic
416D59—44no—
417D59—48no—
418C22×#41—592no—
419C22×#41—594no—
420#563—5932no—
421#562—5932no—
422#554—5932no—
423#553—5932no—
424#553—5932no—
425#547—5964no—
426#547—5932no—
427#544—5932no—
428#540—5932no—
429#539—5964no—
430#539—5932no—
431#537—5932no—
432#532—5916no—
433C2×C4⋊Q8—592no—
434C2×C4⋊Q8—594no—
435C2×C4⋊Q8—591no—
436C2×#127—591no—
437#529—5916no—
438C2×#126—594no—
439C2×#126—594no—
440C2×#126—592no—
441C2×#125—594no—
442C2×#125—592no—
443C2×#125—591no—
444C2×#125C2×D5912yes—
445C2×#125C2×D5912yes—
446C2×#125C2×D5912yes—
447C2×#125C2×D5912yes—
448C2×#125C2×D59116yescomplemented
449C2×#124—591no—
450C2×#124—592no—
451C2×#123—592no—
452C2×#123—594no—
453C2×#123—594no—
454C2×#123—594no—
455C2×#123—594no—
456C2×#123—594no—
457C2×#123—594no—
458C2×C22⋊Q8—591no—
459C2×C22⋊Q8—594no—
460C2×C22⋊Q8—594no—
461C2×C22⋊Q8—594no—
462C2×C22⋊Q8—594no—
463C2×C22⋊Q8—594no—
464C2×C22⋊Q8—594no—
465C2×#121—591no—
466C2×#121—592no—
467C2×#121—592no—
468C2×#121—594no—
469C2×#121—594no—
470C2×#121—594no—
471C2×#121—592no—
472C2×#121—594no—
473C2×#121—592no—
474C2×C4×Q8—591no—
475C2×C4×D4—592no—
476C2×C4×D4—594no—
477C2×C4×D4—594no—
478C2×C4×D4—592no—
479C2×C4×D4—592no—
480C2×C4×D4—591no—
481C2×C4×D4—592no—
482C2×C4×D4—592no—
483C2×#117—592no—
484C2×#117—592no—
485C22×C4⋊C4—594no—
486C22×C4⋊C4—592no—
487C22×C4⋊C4C2×D5912yes—
488C22×C4⋊C4C2×D5911yescharacteristic
489C22×C4⋊C4C2×D5912yes—
490C22×C4⋊C4C2×D5911yescharacteristic
491C22×C42C2×D5911yescharacteristic
492C59C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—5916no—
494C2×#41—5932no—
495C2×#41—2368no—
496C2×#41—23616no—
497C22×Q8—591no—
498C22×Q8—594no—
499C22×Q8—592no—
500C22×D4—592no—
501C22×D4—594no—
502C22×D4—592no—
503C22×D4—594no—
504C22×D4—591no—
505C22×D4—592no—
506C22×D4—594no—
507C22×D4—592no—
508C23×C4—592no—
509C23×C4—594no—
510C23×C4—594no—
511C23×C4—594no—
512C23×C4—594no—
513C23×C4C22×D5912yes—
514C23×C4C22×D5911yescharacteristic
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5912yes—
517C23×C4C22×D5911yescharacteristic
518C4⋊Q8—5916no—
519C4⋊Q8—5932no—
520C4⋊Q8—598no—
521#127—598no—
522#126—5932no—
523#126—5932no—
524#126—5916no—
525#125—5932no—
526#125—5916no—
527#125—598no—
528#125C22×D59116yes—
529#125C22×D59116yes—
530#125C22×D59116yes—
531#125C22×D59116yes—
532#124—598no—
533#124—5916no—
534#123—5916no—
535#123—5932no—
536#123—5932no—
537#123—5932no—
538#123—5932no—
539#123—5932no—
540#123—5932no—
541C22⋊Q8—598no—
542C22⋊Q8—5932no—
543C22⋊Q8—5932no—
544C22⋊Q8—5932no—
545C22⋊Q8—5932no—
546C22⋊Q8—5932no—
547C22⋊Q8—5932no—
548#121—598no—
549#121—5916no—
550#121—5916no—
551#121—5932no—
552#121—5932no—
553#121—5932no—
554#121—5916no—
555#121—5932no—
556#121—5916no—
557C4×Q8—598no—
558C4×D4—5916no—
559C4×D4—5932no—
560C4×D4—5932no—
561C4×D4—5916no—
562C4×D4—5916no—
563C4×D4—598no—
564C4×D4—5916no—
565C4×D4—5916no—
566#117—5916no—
567#117—5916no—
568C2×C4⋊C4—592no—
569C2×C4⋊C4—592no—
570C2×C4⋊C4—594no—
571C2×C4⋊C4—594no—
572C2×C4⋊C4—594no—
573C2×C4⋊C4—592no—
574C2×C4⋊C4—592no—
575C2×C4⋊C4—592no—
576C2×C4⋊C4—594no—
577C2×C4⋊C4—592no—
578C2×C4⋊C4—591no—
579C2×C4⋊C4—591no—
580C2×C4⋊C4—5932no—
581C2×C4⋊C4—5916no—
582C2×C4⋊C4C22×D5912yes—
583C2×C4⋊C4C22×D5914yes—
584C2×C4⋊C4C22×D5912yes—
585C2×C4⋊C4C22×D5914yes—
586C2×C4⋊C4C22×D5914yes—
587C2×C4⋊C4C22×D5914yes—
588C2×C4⋊C4C22×D5912yes—
589C2×C4⋊C4C22×D5912yes—
590C2×C4⋊C4C22×D59116yes—
591C2×C4⋊C4C22×D5918yes—
592C2×C4⋊C4C22×D59116yes—
593C2×C4⋊C4C22×D5918yes—
594C2×C22⋊C4—592no—
595C2×C22⋊C4—592no—
596C2×C22⋊C4—594no—
597C2×C22⋊C4—592no—
598C2×C22⋊C4—592no—
599C2×C22⋊C4—594no—
600C2×C22⋊C4—594no—
601C2×C22⋊C4—594no—
602C2×C22⋊C4—594no—
603C2×C22⋊C4—594no—
604C2×C22⋊C4—594no—
605C2×C22⋊C4—592no—
606C2×C42—592no—
607C2×C42—594no—
608C2×C42C22×D5911yescharacteristic
609C2×C42C22×D5911yescharacteristic
610C2×C42C22×D5911yescharacteristic
611C2×C42C22×D5911yescharacteristic
612C2×C42C22×D5918yes—
613C24—592no—
614C24—594no—
615C24C23×D5911yescharacteristic
616#41—23632no—
617#41—23664no—
618C2×Q8—594no—
619C2×Q8—5916no—
620C2×Q8—598no—
621C2×Q8—2368no—
622C2×Q8—2364no—
623C2×Q8—2362no—
624C2×D4—598no—
625C2×D4—5916no—
626C2×D4—598no—
627C2×D4—5916no—
628C2×D4—594no—
629C2×D4—598no—
630C2×D4—5916no—
631C2×D4—598no—
632C2×D4—1188no—
633C2×D4—11816no—
634C2×D4—1188no—
635C2×D4—2368no—
636C2×D4—2364no—
637C2×D4—2368no—
638C2×D4—2364no—
639C2×D4—2362no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—592no—
646C22×C4—592no—
647C22×C4—592no—
648C22×C4—594no—
649C22×C4—598no—
650C22×C4—5916no—
651C22×C4—5916no—
652C22×C4—5916no—
653C22×C4—5916no—
654C22×C4—1188no—
655C22×C4—2368no—
656C22×C4—2368no—
657C22×C4—2368no—
658C22×C4—2368no—
659C22×C4C23×D5914yes—
660C22×C4C23×D5914yes—
661C22×C4C23×D5918yes—
662C22×C4C23×D5914yes—
663C22×C4C23×D5911yescharacteristic
664C22×C4C23×D5911yescharacteristic
665C22×C4C23×D5911yescharacteristic
666C22×C4C23×D5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668C22×C4C23×D5914yes—
669C22×C4C23×D5914yes—
670C22×C4C23×D5918yes—
671C22×C4C23×D5911yescharacteristic
672C4⋊C4—598no—
673C4⋊C4—598no—
674C4⋊C4—5916no—
675C4⋊C4—5916no—
676C4⋊C4—5916no—
677C4⋊C4—598no—
678C4⋊C4—598no—
679C4⋊C4—598no—
680C4⋊C4—5916no—
681C4⋊C4—598no—
682C4⋊C4—594no—
683C4⋊C4—594no—
684C4⋊C4C23×D5918yes—
685C4⋊C4C23×D59116yes—
686C4⋊C4C23×D5918yes—
687C4⋊C4C23×D59116yes—
688C4⋊C4C23×D59116yes—
689C4⋊C4C23×D59116yes—
690C4⋊C4C23×D5918yes—
691C4⋊C4C23×D5918yes—
692C22⋊C4—598no—
693C22⋊C4—598no—
694C22⋊C4—5916no—
695C22⋊C4—598no—
696C22⋊C4—598no—
697C22⋊C4—5916no—
698C22⋊C4—5916no—
699C22⋊C4—5916no—
700C22⋊C4—5916no—
701C22⋊C4—5916no—
702C22⋊C4—5916no—
703C22⋊C4—598no—
704C42—598no—
705C42—5916no—
706C42C23×D5914yes—
707C42C23×D5914yes—
708C42C23×D5914yes—
709C42C23×D5914yes—
710C23—22no—
711C23—22no—
712C23—594no—
713C23—598no—
714C23—1184no—
715C23—1188no—
716C23—1184no—
717C23—1188no—
718C23—1188no—
719C23—1184no—
720C23#1427377314yes—
721C23C24×D5912yes—
722C23C24×D5911yescharacteristic
723Q8—2364no—
724Q8—23616no—
725Q8—2368no—
726D4—11816no—
727D4—11832no—
728D4—11816no—
729D4—23616no—
730D4—2368no—
731D4—2364no—
732D4—23616no—
733D4—2368no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—594no—
747C2×C4—594no—
748C2×C4—594no—
749C2×C4—598no—
750C2×C4—1184no—
751C2×C4—1188no—
752C2×C4—1184no—
753C2×C4—1184no—
754C2×C4—11816no—
755C2×C4—23616no—
756C2×C4—23616no—
757C2×C4—23616no—
758C2×C4—23616no—
759C2×C4#1427377514yes—
760C2×C4C24×D5918yes—
761C2×C4C24×D5912yes—
762C2×C4C24×D5912yes—
763C2×C4C24×D5912yes—
764C2×C4C24×D5912yes—
765C2×C4C24×D5912yes—
766C2×C4C24×D5918yes—
767C2×C4C24×D5912yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—1184no—
772C22—1188no—
773C22—1184no—
774C22—1188no—
775C22—1188no—
776C22—1184no—
777C22—2368no—
778C22—23616no—
779C22C2×#1427377314yes—
780C22C2×#1427377312yes—
781C22C2×#1427377512yes—
782C22#1683823812yes—
783C22C25×D5911yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1184no—
792C4—1188no—
793C4—1184no—
794C4—1184no—
795C4C2×#1427377514yes—
796C2—24no—
797C2—2364no—
798C2—2368no—
799C2#2143863014yesdirect product factor
800C2C22×#1427377311yescharacteristic
801C2C22×#1427377511yescharacteristic
802C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×#125×C59C2
socleC23×C59C25
hypercenterC22×#125D59
hypocenterC59C2×#3559
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #21438630C2direct (N × H)
2. C2×#16838156C2semidirect
3. C2×#16838150C2semidirect
4. C2×#16838108C2semidirect
5. C2×#16838105C2semidirect
6. C2×#16838100C2semidirect
7. C2×#16838053C2semidirect
8. C2×#16838053C2semidirect
9. C2×#16838032C2semidirect
10. C2×#16838008C2semidirect
11. C2×#16838000C2semidirect
12. C2×#16837999C2semidirect
13. C2×#16837983C2semidirect
14. C2×#16837952C2semidirect
15. C2×#16837936C2semidirect
16. C22×#125×C59C2semidirect
19. #16838156C22semidirect
20. #16838150C22semidirect
21. #16838108C22semidirect
22. #16838105C22semidirect
23. #16838100C22semidirect
24. #16838053C22semidirect
25. #16838053C22semidirect
26. #16838032C22semidirect
27. #16838008C22semidirect
28. #16838000C22semidirect
29. #16837999C22semidirect
30. #16837983C22semidirect
31. #16837952C22semidirect
36. #16837936C22semidirect
85. C2×#125×C59C22semidirect
410. C22×#125D59semidirect
412. C2×C59#3559semidirect
448. C2×#125C2×D59semidirect
492. C59C2×#3559semidirect
799. C2#21438630direct (N × H)

Maximal subgroups

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

subgroupindex
#214386302
C2×#168381562
C2×#168381502
C2×#168381082
C2×#168381052
C2×#168381002
C2×#168380532
C2×#168380322
C2×#168380082
C2×#168380002
C2×#168379992
C2×#168379832
C2×#168379522
C2×#168379362
C22×#125×C592
C2×#355959