Finite Group Databasebeta

← #29496473

Subgroups — #29496473

Order 15104.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438764C218yesmaximal, complemented
2#21438724C214yesmaximal, complemented
3#21438652C214yesmaximal, complemented
4#21438549C214yesmaximal, complemented
5#21438448C214yesmaximal, complemented
6#21438299C214yesmaximal, complemented
7#21438280C214yesmaximal, complemented
8#21438243C212yesmaximal, complemented
9#21438232C212yesmaximal, complemented
10#21437698C214yesmaximal, complemented
11#21437658C218yesmaximal, complemented
12#21437525C214yesmaximal, complemented
13#21437506C214yesmaximal, complemented
14#21437481C214yesmaximal, complemented
15C2×#16837936C212yesmaximal, complemented
16C59×#3444C211yesmaximal, characteristic, complemented
17C59⋊#564C2212yescomplemented
18#16838156C2214yescomplemented
19#16838153C2218yescomplemented
20#16838152C2212yescomplemented
21#16838151C2214yescomplemented
22#16838151C2218yescomplemented
23#16838150C2212yescomplemented
24#16838148C2218yescomplemented
25#16838147C2218yescomplemented
26#16838146C2214yescomplemented
27#16838144C2212yescomplemented
28#16838140C2218yescomplemented
29#16838139C2214yescomplemented
30#16838136C2214yescomplemented
31#16838124C2218yescomplemented
32#16838115C2218yescomplemented
33#16838111C2218yescomplemented
34#16838106C2218yescomplemented
35#16838101C2218yescomplemented
36#16838101C2218yescomplemented
37#16838097C2218yescomplemented
38#16838095C2218yescomplemented
39#16838093C2218yescomplemented
40#16838091C2218yescomplemented
41#16838085C2218yescomplemented
42#16838085C2218yescomplemented
43#16838083C2214yescomplemented
44#16838081C2218yescomplemented
45#16838081C2218yescomplemented
46#16838080C2214yescomplemented
47#16838079C2218yescomplemented
48#16838076C2218yescomplemented
49#16838076C2218yescomplemented
50#16838051C2218yescomplemented
51#16838047C2218yescomplemented
52#16838041C2218yescomplemented
53#16838040C2218yescomplemented
54#16838039C2218yescomplemented
55#16838034C2214yescomplemented
56#16838031C2214yescomplemented
57#16838027C2214yescomplemented
58#16838024C2218yescomplemented
59#16838018C2218yescomplemented
60#16838017C2218yescomplemented
61#16838016C2218yescomplemented
62#16838011C2218yescomplemented
63#16838010C2218yescomplemented
64#16838009C2218yescomplemented
65#16838003C2218yescomplemented
66#16838001C2214yescomplemented
67#16838000C2218yescomplemented
68#16837997C2214yescomplemented
69#16837996C2218yescomplemented
70#16837996C2218yescomplemented
71#16837994C2218yescomplemented
72#16837994C2218yescomplemented
73#16837993C2218yescomplemented
74#16837992C2214yes—
75#16837991C2218yescomplemented
76#16837989C2214yescomplemented
77#16837986C2218yescomplemented
78#16837985C2218yescomplemented
79#16837985C2218yescomplemented
80#16837979C2214yes—
81#16837974C2218yescomplemented
82#16837963C2218yescomplemented
83#16837960C2214yescomplemented
84#16837956C2218yescomplemented
85#16837955C2214yescomplemented
86#16837948C2214yescomplemented
87#16837939C2218yescomplemented
88#16837936C2214yescomplemented
89#16837936C2214yescomplemented
90#16837936C2214yescomplemented
91#16837936C2218yescomplemented
92#16837936C2214yescomplemented
93#16837936C2214yescomplemented
94#16837936C2214yescomplemented
95#16837936C2214yescomplemented
96#16837936C2214yescomplemented
97#16837932C2218yescomplemented
98#16837932C2218yescomplemented
99#16837930C2218yescomplemented
100#16837930C2218yescomplemented
101C2×#14273721C2214yescomplemented
102C2×#14273719C2212yescomplemented
103C2×#14273715C2212yescomplemented
104#16837914C2214yescomplemented
105#16837911C2218yescomplemented
106#16837911C2218yescomplemented
107#16837909C2214yescomplemented
108C2×#14273710C2214yescomplemented
109C2×#14273706C2212yescomplemented
110C2×#14273701C2212yes—
111C4×#11745685C2214yescomplemented
112C4×#11745687C2218yescomplemented
113C2×C4×Dic118C2212yescomplemented
114C2×C4×D236C2212yescomplemented
115C2×C4×C22⋊D59C2214yescomplemented
116C4×D4×D59C2218yescomplemented
117C2×#14273684C2214yescomplemented
118C2×#14273684C2214yescomplemented
119C59×#533C2212yescomplemented
120C59×#533C2211yescharacteristic, complemented
121C59×#532C2211yescharacteristic, complemented
122C59×#532C2212yescomplemented
123C59×#529C2214yescomplemented
124C59×#529C2214yescomplemented
125C59×#529C2214yescomplemented
126C59×#525C2212yescomplemented
127C59×#525C2214yescomplemented
128C4×#41×C59C2212yescomplemented
129C4×#41×C59C2214yescomplemented
130C22×C42×C59C2211yescharacteristic, complemented
131C2×#11745685C2314yes—
132C2×#11745687C2318yes—
133C22×Dic118C2312yes—
134C22×D236C2312yes—
135C22×C22⋊D59C2314yes—
136C2×D4×D59C2318yes—
137C22×C4×D59C2314yes—
138C22×C4×D59C2314yes—
139#14273726C2318yes—
140#14273726C2318yes—
141#14273725C2314yes—
142#14273725C2318yes—
143#14273723C2314yes—
144#14273722C2318yes—
145#14273722C2318yes—
146#14273722C2318yes—
147#14273722C2318yes—
148#14273722C2318yes—
149#14273722C2318yes—
150#14273721C2318yes—
151#14273721C2318yes—
152#14273721C2318yes—
153#14273721C2318yes—
154#14273721C2318yes—
155#14273721C2318yes—
156#14273720C2318yes—
157#14273720C2318yes—
158#14273720C2318yes—
159#14273720C2318yes—
160#14273719C2314yes—
161#14273719C2314yes—
162#14273719C2314yes—
163#14273719C2314yes—
164#14273719C2318yes—
165#14273718C2318yes—
166#14273718C2318yes—
167#14273717C2318yes—
168#14273717C2318yes—
169#14273717C2318yes—
170#14273717C2318yes—
171#14273717C2318yes—
172#14273717C2318yes—
173#14273716C2314yes—
174#14273716C2318yes—
175#14273715C2314yes—
176#14273715C2314yes—
177#14273715C2314yes—
178#14273715C2314yes—
179#14273715C2318yes—
180#14273714C2314yes—
181#14273713C2318yes—
182#14273713C2318yes—
183#14273713C2318yes—
184#14273713C2318yes—
185#14273712C2318yes—
186#14273712C2318yes—
187#14273712C2318yes—
188#14273712C2318yes—
189#14273712C2318yes—
190#14273712C2318yes—
191#14273711C2318yes—
192#14273711C2318yes—
193#14273711C2318yes—
194#14273710C2318yes—
195#14273710C2318yes—
196#14273710C2318yes—
197#14273710C2318yes—
198#14273710C2318yes—
199#14273710C2318yes—
200#14273709C2318yes—
201#14273709C2318yes—
202#14273709C2318yes—
203#14273709C2318yes—
204#14273708C2314yes—
205#14273708C2318yes—
206#14273708C2314yes—
207#14273708C2318yes—
208#14273707C2318yes—
209#14273707C2318yes—
210#14273706C2314yes—
211#14273706C2314yes—
212#14273706C2314yes—
213#14273706C2314yes—
214#14273706C2318yes—
215#14273705C2318yes—
216#14273705C2318yes—
217#14273705C2318yes—
218#14273705C2318yes—
219#14273705C2318yes—
220#14273705C2318yes—
221#14273704C2318yes—
222#14273704C2318yes—
223#14273704C2318yes—
224#14273704C2318yes—
225#14273704C2318yes—
226#14273704C2318yes—
227#14273703C2318yes—
228#14273703C2318yes—
229#14273703C2318yes—
230#14273702C2318yes—
231#14273702C2318yes—
232#14273701C2314yes—
233#14273701C2314yes—
234#14273701C2314yes—
235#14273701C2314yes—
236#14273701C2318yes—
237#14273700C2318yes—
238#14273700C2318yes—
239#14273700C2318yes—
240#14273700C2318yes—
241#14273699C2318yes—
242#14273699C2318yes—
243#14273699C2318yes—
244#14273699C2318yes—
245#14273699C2318yes—
246#14273699C2318yes—
247#14273698C2318yes—
248#14273697C2318yes—
249#14273697C2318yes—
250#14273697C2318yes—
251#14273695C2314yes—
252#14273695C2314yes—
253#14273695C2318yes—
254#14273695C2318yes—
255C4×Dic118C2314yes—
256C4×Dic118C2318yes—
257C4×Dic118C2314yes—
258C4×Dic118C2314yes—
259C4×Dic118C2314yes—
260C4×Dic118C2318yes—
261#14273692C2318yes—
262C4×D236C2314yes—
263C4×D236C2318yes—
264C4×D236C2314yes—
265C4×D236C2314yes—
266C4×D236C2314yes—
267C4×D236C2318yes—
268D4×Dic59C2318yes—
269D4×Dic59C2318yes—
270#14273689C2318yes—
271C4×C22⋊D59C2318yes—
272C4×C22⋊D59C2318yes—
273C4×C22⋊D59C2318yes—
274C4×C22⋊D59C2318yes—
275C4×C22⋊D59C2318yes—
276C4×C22⋊D59C2318yes—
277C4×C22⋊D59C2318yes—
278C4×C22⋊D59C2318yes—
279(C22⋊D59)⋊C4C2318yes—
280(C22⋊D59)⋊C4C2318yes—
281(C22⋊D59)⋊C4C2318yes—
282(C22⋊D59)⋊C4C2318yes—
283#14273686C2314yes—
284#14273685C2318yes—
285#14273684C2318yes—
286#14273684C2318yes—
287#14273684C2318yes—
288#14273684C2318yes—
289#14273684C2318yes—
290#14273684C2318yes—
291#14273684C2318yes—
292#14273683C2318yes—
293#14273683C2318yes—
294C2×C4⋊Dic59C2312yes—
295C2×C4⋊Dic59C2312yes—
296C2×Dic59⋊C4C2314yes—
297C2×Dic59⋊C4C2314yes—
298C2×Dic59⋊C4C2314yes—
299C2×Dic59⋊C4C2314yes—
300C2×Dic59⋊C4C2318yes—
301C4⋊C4×D59C2318yes—
302C2×C22⋊Dic59C2314yes—
303C2×(C2×D59)⋊C4C2314yes—
304C2×(C2×D59)⋊C4C2314yes—
305C2×(C2×D59)⋊C4C2314yes—
306C2×(C2×D59)⋊C4C2314yes—
307C2×(C2×D59)⋊C4C2318yes—
308C22⋊C4×D59C2318yes—
309C22⋊C4×D59C2318yes—
310C2×C4×Dic59C2314yes—
311C2×C4×Dic59C2314yes—
312C42×D59C2318yes—
313C2×#41×C59C2312yes—
314C2×#41×C59C2314yes—
315C23×C4×C59C2312yes—
316C23×C4×C59C2311yescharacteristic
317C4⋊Q8×C59C2311yescharacteristic
318C4⋊Q8×C59C2312yes—
319#127×C59C2311yescharacteristic
320#126×C59C2318yes—
321#125×C59C2312yes—
322#125×C59C2314yes—
323#124×C59C2312yes—
324#124×C59C2314yes—
325#123×C59C2318yes—
326#123×C59C2314yes—
327C22⋊Q8×C59C2314yes—
328C22⋊Q8×C59C2314yes—
329C22⋊Q8×C59C2314yes—
330#121×C59C2314yes—
331#121×C59C2314yes—
332#121×C59C2314yes—
333#120×C59C2314yes—
334C4×Q8×C59C2314yes—
335C4×Q8×C59C2314yes—
336C4×Q8×C59C2314yes—
337C4×D4×C59C2314yes—
338C4×D4×C59C2318yes—
339C4×D4×C59C2314yes—
340C4×D4×C59C2318yes—
341C4×D4×C59C2318yes—
342C4×D4×C59C2314yes—
343#117×C59C2314yes—
344#117×C59C2312yes—
345#117×C59C2314yes—
346#117×C59C2318yes—
347C2×C42×C59C2312yes—
348C2×C42×C59C2312yes—
349C2×C42×C59C2311yescharacteristic
350C2×C42×C59C2312yes—
351C2×C42×C59C2311yescharacteristic
352C2×C42×C59C2312yes—
353C2×C42×C59C2312yes—
354C2×C42×C59C2314yes—
355C24×C59C2411yescharacteristic
356C23×D59C2414yes—
357C23×D59C2414yes—
358#41×C59—44no—
359#41×C59—48no—
360C2×Q8×C59C2414yes—
361C2×Q8×C59C2412yes—
362C2×D4×C59C2418yes—
363C2×D4×C59C2414yes—
364C2×D4×C59C2414yes—
365C2×D4×C59C2412yes—
366C22×C4×C59—42no—
367C22×C4×C59—44no—
368C22×C4×C59C2412yes—
369C22×C4×C59C2411yescharacteristic
370C22×C4×C59C2412yes—
371C22×C4×C59C2412yes—
372C22×C4×C59C2414yes—
373C22×C4×C59C2412yes—
374C22×C4×C59C2412yes—
375C22×C4×C59C2412yes—
376C22×C4×C59C2412yes—
377C22×C4×C59C2412yes—
378C22×C4×C59C2411yescharacteristic
379C22×C4×C59C2418yes—
380C2×C22⋊D59—48no—
381C2×C22⋊D59C2418yes—
382C2×C22⋊D59C2418yes—
383C2×C22⋊D59C2418yes—
384C2×C22⋊D59C2418yes—
385C2×C22⋊D59C2418yes—
386C22×Dic59C2414yes—
387C22×Dic59C2414yes—
388C22×Dic59C2418yes—
389C22×Dic59C2414yes—
390C22×Dic59C2414yes—
391#11745687—416no—
392D4×D59—416no—
393#11745685—48no—
394C2×D236—44no—
395C2×D236C2418yes—
396C2×D236C2414yes—
397C2×D236C2414yes—
398C2×D236C2414yes—
399C2×C4×D59—48no—
400C2×C4×D59—48no—
401C2×C4×D59C2418yes—
402C2×C4×D59C2418yes—
403C2×C4×D59C2418yes—
404C2×C4×D59C2418yes—
405C2×C4×D59C2418yes—
406C2×Dic118—44no—
407C2×Dic118C2418yes—
408C2×Dic118C2414yes—
409C2×Dic118C2414yes—
410C2×Dic118C2414yes—
411C4⋊C4×C59C2414yes—
412C4⋊C4×C59C2414yes—
413C4⋊C4×C59C2414yes—
414C4⋊C4×C59C2418yes—
415C4⋊C4×C59C2418yes—
416C4⋊C4×C59C2418yes—
417C22⋊C4×C59C2418yes—
418C22⋊C4×C59C2414yes—
419C22⋊C4×C59C2418yes—
420C22⋊C4×C59C2418yes—
421C22⋊C4×C59C2418yes—
422C42×C59C2411yescharacteristic
423C42×C59C2412yes—
424C42×C59C2411yescharacteristic
425C42×C59C2412yes—
426C42×C59C2412yes—
427C42×C59C2412yes—
428C42×C59C2412yes—
429C42×C59C2411yescharacteristic
430C42×C59C2412yes—
431C42×C59C2411yescharacteristic
432C42×C59C2414yes—
433C42×C59C2418yes—
434C22⋊Dic59C2418yes—
435C22⋊Dic59C2418yes—
436C22⋊Dic59C2418yes—
437C22⋊Dic59C2418yes—
438C22⋊Dic59C2414yes—
439C22⋊Dic59C2414yes—
440(C2×D59)⋊C4C2418yes—
441(C2×D59)⋊C4C2418yes—
442(C2×D59)⋊C4C2418yes—
443(C2×D59)⋊C4C2418yes—
444(C2×D59)⋊C4C2418yes—
445(C2×D59)⋊C4C2418yes—
446(C2×D59)⋊C4C2418yes—
447(C2×D59)⋊C4C2418yes—
448(C2×D59)⋊C4C2418yes—
449(C2×D59)⋊C4C2418yes—
450(C2×D59)⋊C4C2418yes—
451(C2×D59)⋊C4C2418yes—
452(C2×D59)⋊C4C2418yes—
453(C2×D59)⋊C4C2418yes—
454C4⋊Dic59C2418yes—
455C4⋊Dic59C2414yes—
456C4⋊Dic59C2414yes—
457C4⋊Dic59C2414yes—
458C4⋊Dic59C2414yes—
459C4⋊Dic59C2418yes—
460C4⋊Dic59C2418yes—
461Dic59⋊C4C2418yes—
462Dic59⋊C4C2418yes—
463Dic59⋊C4C2418yes—
464Dic59⋊C4C2418yes—
465Dic59⋊C4C2418yes—
466Dic59⋊C4C2418yes—
467Dic59⋊C4C2418yes—
468Dic59⋊C4C2418yes—
469Dic59⋊C4C2418yes—
470Dic59⋊C4C2418yes—
471Dic59⋊C4C2418yes—
472Dic59⋊C4C2418yes—
473Dic59⋊C4C2418yes—
474Dic59⋊C4C2418yes—
475C4×Dic59C2418yes—
476C4×Dic59C2418yes—
477C4×Dic59C2418yes—
478C4×Dic59C2414yes—
479C4×Dic59C2418yes—
480C4×Dic59C2414yes—
481C23×C59—24no—
482C23×C59—41no—
483C23×C59C2511yescharacteristic
484C23×C59C2514yes—
485C23×C59C2512yes—
486C22×D59—28no—
487C22×D59—44no—
488C22×D59—44no—
489C22×D59—48no—
490C22×D59—44no—
491C22×D59C2518yes—
492Q8×C59—42no—
493Q8×C59—44no—
494D4×C59—216no—
495D4×C59—44no—
496D4×C59—42no—
497D4×C59—44no—
498C2×C4×C59—24no—
499C2×C4×C59—24no—
500C2×C4×C59—24no—
501C2×C4×C59—28no—
502C2×C4×C59—22no—
503C2×C4×C59—42no—
504C2×C4×C59—42no—
505C2×C4×C59—42no—
506C2×C4×C59—42no—
507C2×C4×C59—41no—
508C2×C4×C59—42no—
509C2×C4×C59—48no—
510C2×C4×C59C2512yes—
511C2×C4×C59C2514yes—
512C2×C4×C59C2518yes—
513C2×C4×C59C2512yes—
514C2×C4×C59C2512yes—
515C2×C4×C59C2511yescharacteristic
516C2×C4×C59C2512yes—
517C2×C4×C59C2512yes—
518C2×C4×C59C2511yescharacteristic
519C22⋊D59—216no—
520C22⋊D59—48no—
521C22⋊D59—48no—
522C22⋊D59—48no—
523C22⋊D59—48no—
524C2×Dic59—28no—
525C2×Dic59—44no—
526C2×Dic59—44no—
527C2×Dic59—48no—
528C2×Dic59—44no—
529C2×Dic59C2518yes—
530C2×Dic59C2518yes—
531C2×Dic59C2518yes—
532D236—44no—
533D236—44no—
534D236—44no—
535D236—48no—
536C4×D59—216no—
537C4×D59—48no—
538C4×D59—48no—
539C4×D59—48no—
540C4×D59—48no—
541Dic118—44no—
542Dic118—44no—
543Dic118—44no—
544Dic118—48no—
545#62755—591nomaximal, Sylow
546C22×C59—22no—
547C22×C59—22no—
548C22×C59—24no—
549C22×C59—28no—
550C22×C59—22no—
551C22×C59—21no—
552C22×C59—44no—
553C22×C59#58514yes—
554C22×C59C2611yescharacteristic
555C2×D59—28no—
556C2×D59—28no—
557C2×D59—28no—
558C2×D59—88no—
559C2×D59—88no—
560C4×C59—22no—
561C4×C59—22no—
562C4×C59—24no—
563C4×C59—28no—
564C4×C59—22no—
565C4×C59—22no—
566C4×C59—22no—
567C4×C59—21no—
568C4×C59#58512yes—
569Dic59—28no—
570Dic59—28no—
571Dic59—28no—
572#3566—598no—
573#3564—594no—
574#3560—594no—
575#3553—594no—
576#3545—594no—
577#3535—594no—
578#3534—594no—
579#3531—592no—
580#3529—592no—
581#3481—594no—
582#3475—598no—
583#3461—594no—
584#3459—594no—
585#3455—594no—
586#3444D5911yescharacteristic, complemented
587C2×#529—592no—
588C2×C59—24no—
589C2×C59—44no—
590C2×C59—41no—
591C2×C59C2×#58512yes—
592C2×C59C2×#58511yescharacteristic
593D59—48no—
594#564—592no—
595#563—594no—
596#563—598no—
597#563—594no—
598#563—592no—
599#563—598no—
600#562—592no—
601#562—594no—
602#562—598no—
603#562—598no—
604H(3,𝔽4)—592no—
605#560—594no—
606#560—598no—
607#559—594no—
608#556—598no—
609#555—598no—
610#554—598no—
611#554—598no—
612#553—598no—
613#553—598no—
614#553—598no—
615#553—598no—
616#552—598no—
617#552—598no—
618#552—598no—
619#552—598no—
620#551—594no—
621#551—598no—
622#551—594no—
623#551—598no—
624#551—598no—
625#551—598no—
626#551—598no—
627#547—598no—
628#546—598no—
629#546—598no—
630#546—598no—
631#546—598no—
632D42—594no—
633#544—594no—
634#543—594no—
635#542—598no—
636#542—598no—
637#542—598no—
638#542—598no—
639#541—598no—
640#541—598no—
641#541—598no—
642#540—598no—
643#539—598no—
644#539—598no—
645#539—598no—
646#539—598no—
647#539—594no—
648#539—594no—
649#539—598no—
650#539—598no—
651#538—598no—
652#538—598no—
653#538—594no—
654#538—594no—
655#538—598no—
656#538—598no—
657#537—594no—
658#536—598no—
659#534—598no—
660#534—594no—
661#533—598no—
662#533—594no—
663#533C2×D5911yescharacteristic, complemented
664#533C2×D5912yescomplemented
665#532—594no—
666#532C2×D5911yescharacteristic, complemented
667#532C2×D5912yescomplemented
668#529—598no—
669#529—598no—
670#529—598no—
671#529—598no—
672#529—598no—
673#529—594no—
674#529—594no—
675#529—594no—
676#529—594no—
677#529—594no—
678#529—594no—
679#529—594no—
680#529—594no—
681#529—598no—
682#529C2×D5914yescomplemented
683#529C2×D5914yescomplemented
684#529C2×D5914yescomplemented
685C2×#126—594no—
686C2×#125—592no—
687C2×#124—592no—
688#525—594no—
689#525—598no—
690#525—598no—
691#525—594no—
692#525C2×D5912yescomplemented
693#525C2×D5914yescomplemented
694C2×#123—594no—
695C2×C22⋊Q8—592no—
696C2×#121—592no—
697C4×#41—598no—
698C4×#41—594no—
699C4×#41C2×D5912yescomplemented
700C4×#41C2×D5914yescomplemented
701C2×C4×Q8—592no—
702C2×C4×D4—594no—
703C2×C4×D4—598no—
704C2×C4×D4—592no—
705C2×#117—594no—
706C2×#117—594no—
707C22×C42C2×D5911yescharacteristic, complemented
708C59#6275511yescharacteristic, complemented, Sylow
709C2×#41—598no—
710C2×#41—594no—
711C2×#41C22×D5912yes—
712C2×#41C22×D5914yes—
713C22×Q8—592no—
714C22×D4—594no—
715C22×D4—598no—
716C22×D4—592no—
717C23×C4—594no—
718C23×C4—594no—
719C23×C4C22×D5911yescharacteristic
720C23×C4C22×D5912yes—
721C4⋊Q8—594no—
722C4⋊Q8—598no—
723C4⋊Q8—598no—
724C4⋊Q8—598no—
725C4⋊Q8C22×D5911yescharacteristic
726C4⋊Q8C22×D5912yes—
727#127—594no—
728#127C22×D5911yescharacteristic
729#126—598no—
730#126—598no—
731#126—598no—
732#126—598no—
733#126—598no—
734#126—598no—
735#126—598no—
736#126—598no—
737#126—598no—
738#126—598no—
739#126—598no—
740#126—598no—
741#126—598no—
742#126—598no—
743#126—598no—
744#126—598no—
745#126C22×D5918yes—
746#125—598no—
747#125—598no—
748#125—598no—
749#125—598no—
750#125—598no—
751#125—598no—
752#125—598no—
753#125—598no—
754#125—594no—
755#125—594no—
756#125—594no—
757#125—594no—
758#125—598no—
759#125C22×D5914yes—
760#125C22×D5912yes—
761#124—598no—
762#124—594no—
763#124—594no—
764#124—598no—
765#124—598no—
766#124—598no—
767#124—598no—
768#124—594no—
769#124—594no—
770#124—594no—
771#124—594no—
772#124—598no—
773#124C22×D5914yes—
774#124C22×D5912yes—
775#123—594no—
776#123—594no—
777#123—598no—
778#123—598no—
779#123—598no—
780#123—598no—
781#123—598no—
782#123—598no—
783#123—598no—
784#123—598no—
785#123—598no—
786#123—598no—
787#123—598no—
788#123—598no—
789#123—598no—
790#123—598no—
791#123—598no—
792#123—598no—
793#123—598no—
794#123—598no—
795#123—598no—
796#123—598no—
797#123—598no—
798#123C22×D5918yes—
799#123C22×D5914yes—
800C22⋊Q8—598no—
801C22⋊Q8—598no—
802C22⋊Q8—598no—
803C22⋊Q8—594no—
804C22⋊Q8—594no—
805C22⋊Q8—594no—
806C22⋊Q8—594no—
807C22⋊Q8—598no—
808C22⋊Q8—598no—
809C22⋊Q8—598no—
810C22⋊Q8—598no—
811C22⋊Q8—598no—
812C22⋊Q8—598no—
813C22⋊Q8—598no—
814C22⋊Q8—598no—
815C22⋊Q8—598no—
816C22⋊Q8—598no—
817C22⋊Q8—598no—
818C22⋊Q8—598no—
819C22⋊Q8—598no—
820C22⋊Q8—598no—
821C22⋊Q8—598no—
822C22⋊Q8C22×D5914yes—
823C22⋊Q8C22×D5914yes—
824C22⋊Q8C22×D5914yes—
825#121—598no—
826#121—598no—
827#121—598no—
828#121—598no—
829#121—598no—
830#121—598no—
831#121—598no—
832#121—594no—
833#121—594no—
834#121—594no—
835#121—594no—
836#121—598no—
837#121—598no—
838#121—598no—
839#121—598no—
840#121—598no—
841#121—598no—
842#121—598no—
843#121C22×D5914yes—
844#121C22×D5914yes—
845#121C22×D5914yes—
846#120—598no—
847#120—598no—
848#120—594no—
849#120—594no—
850#120—598no—
851#120—598no—
852#120—598no—
853#120C22×D5914yes—
854C4×Q8—598no—
855C4×Q8—594no—
856C4×Q8—594no—
857C4×Q8—594no—
858C4×Q8—594no—
859C4×Q8—598no—
860C4×Q8—598no—
861C4×Q8C22×D5914yes—
862C4×Q8C22×D5914yes—
863C4×Q8C22×D5914yes—
864C4×D4—598no—
865C4×D4—598no—
866C4×D4—598no—
867C4×D4—598no—
868C4×D4—598no—
869C4×D4—598no—
870C4×D4—598no—
871C4×D4—598no—
872C4×D4—598no—
873C4×D4—598no—
874C4×D4—598no—
875C4×D4—598no—
876C4×D4—598no—
877C4×D4—598no—
878C4×D4—598no—
879C4×D4—598no—
880C4×D4—594no—
881C4×D4—594no—
882C4×D4—594no—
883C4×D4—594no—
884C4×D4—598no—
885C4×D4C22×D5918yes—
886C4×D4C22×D5914yes—
887C4×D4C22×D5918yes—
888C4×D4C22×D5918yes—
889C4×D4C22×D5914yes—
890C4×D4C22×D5914yes—
891#117—594no—
892#117—598no—
893#117—598no—
894#117—598no—
895#117—598no—
896#117—598no—
897#117—598no—
898#117—598no—
899#117—598no—
900#117—598no—
901#117—598no—
902#117C22×D5914yes—
903#117C22×D5912yes—
904#117C22×D5914yes—
905#117C22×D5918yes—
906C2×C4⋊C4—594no—
907C2×C4⋊C4—594no—
908C2×C4⋊C4—598no—
909C2×C4⋊C4—592no—
910C2×C4⋊C4—594no—
911C2×C4⋊C4—592no—
912C2×C4⋊C4—594no—
913C2×C4⋊C4—598no—
914C2×C22⋊C4—594no—
915C2×C22⋊C4—594no—
916C2×C22⋊C4—594no—
917C2×C22⋊C4—598no—
918C2×C22⋊C4—594no—
919C2×C22⋊C4—594no—
920C2×C22⋊C4—598no—
921C2×C22⋊C4—598no—
922C2×C42—594no—
923C2×C42—594no—
924C2×C42—598no—
925C2×C42C22×D5912yes—
926C2×C42C22×D5914yes—
927C2×C42C22×D5912yes—
928C2×C42C22×D5911yescharacteristic
929C2×C42C22×D5912yes—
930C2×C42C22×D5912yes—
931C2×C42C22×D5912yes—
932C2×C42C22×D5911yescharacteristic
933C24—594no—
934C24—594no—
935C24C23×D5911yescharacteristic
936#41—44no—
937#41—48no—
938#41—2368no—
939#41—23616no—
940C2×Q8—594no—
941C2×Q8—594no—
942C2×Q8—594no—
943C2×Q8—598no—
944C2×Q8—2364no—
945C2×Q8C23×D5914yes—
946C2×Q8C23×D5912yes—
947C2×D4—598no—
948C2×D4—598no—
949C2×D4—598no—
950C2×D4—598no—
951C2×D4—598no—
952C2×D4—594no—
953C2×D4—598no—
954C2×D4—594no—
955C2×D4—594no—
956C2×D4—2364no—
957C2×D4—23616no—
958C2×D4—2368no—
959C2×D4C23×D5918yes—
960C2×D4C23×D5914yes—
961C2×D4C23×D5912yes—
962C2×D4C23×D5914yes—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—594no—
966C22×C4—594no—
967C22×C4—598no—
968C22×C4—594no—
969C22×C4—594no—
970C22×C4—598no—
971C22×C4—598no—
972C22×C4—598no—
973C22×C4—598no—
974C22×C4—598no—
975C22×C4—2368no—
976C22×C4—2368no—
977C22×C4C23×D5912yes—
978C22×C4C23×D5912yes—
979C22×C4C23×D5912yes—
980C22×C4C23×D5914yes—
981C22×C4C23×D5911yescharacteristic
982C22×C4C23×D5912yes—
983C22×C4C23×D5912yes—
984C22×C4C23×D5912yes—
985C22×C4C23×D5911yescharacteristic
986C22×C4C23×D5912yes—
987C22×C4C23×D5912yes—
988C22×C4C23×D5918yes—
989C4⋊C4—598no—
990C4⋊C4—598no—
991C4⋊C4—598no—
992C4⋊C4—598no—
993C4⋊C4—598no—
994C4⋊C4—598no—
995C4⋊C4—598no—
996C4⋊C4—598no—
997C4⋊C4—598no—
998C4⋊C4—598no—
999C4⋊C4—594no—
1000C4⋊C4—594no—
1001C4⋊C4—594no—
1002C4⋊C4—594no—
1003C4⋊C4—598no—
1004C4⋊C4—598no—
1005C4⋊C4—598no—
1006C4⋊C4—598no—
1007C4⋊C4—598no—
1008C4⋊C4—598no—
1009C4⋊C4—598no—
1010C4⋊C4C23×D5918yes—
1011C4⋊C4C23×D5918yes—
1012C4⋊C4C23×D5918yes—
1013C4⋊C4C23×D5914yes—
1014C4⋊C4C23×D5914yes—
1015C4⋊C4C23×D5914yes—
1016C22⋊C4—598no—
1017C22⋊C4—598no—
1018C22⋊C4—598no—
1019C22⋊C4—594no—
1020C22⋊C4—598no—
1021C22⋊C4—594no—
1022C22⋊C4—598no—
1023C22⋊C4—598no—
1024C22⋊C4—598no—
1025C22⋊C4—598no—
1026C22⋊C4—598no—
1027C22⋊C4—598no—
1028C22⋊C4—598no—
1029C22⋊C4—598no—
1030C22⋊C4—598no—
1031C22⋊C4—598no—
1032C22⋊C4—598no—
1033C22⋊C4—598no—
1034C22⋊C4—598no—
1035C22⋊C4—598no—
1036C22⋊C4C23×D5918yes—
1037C22⋊C4C23×D5918yes—
1038C22⋊C4C23×D5918yes—
1039C22⋊C4C23×D5918yes—
1040C22⋊C4C23×D5914yes—
1041C42—594no—
1042C42—598no—
1043C42—598no—
1044C42—594no—
1045C42—598no—
1046C42—598no—
1047C42C23×D5912yes—
1048C42C23×D5912yes—
1049C42C23×D5912yes—
1050C42C23×D5912yes—
1051C42C23×D5912yes—
1052C42C23×D5911yescharacteristic
1053C42C23×D5911yescharacteristic
1054C42C23×D5918yes—
1055C42C23×D5914yes—
1056C42C23×D5911yescharacteristic
1057C42C23×D5912yes—
1058C42C23×D5911yescharacteristic
1059C23—24no—
1060C23—41no—
1061C23—598no—
1062C23—1188no—
1063C23—2364no—
1064C23—2364no—
1065C23—2364no—
1066C23—2368no—
1067C23C24×D5911yescharacteristic
1068C23C24×D5914yes—
1069C23C24×D5912yes—
1070Q8—42no—
1071Q8—44no—
1072Q8—2364no—
1073Q8—2364no—
1074Q8—2364no—
1075Q8—2368no—
1076D4—216no—
1077D4—42no—
1078D4—44no—
1079D4—44no—
1080D4—11816no—
1081D4—2364no—
1082D4—2364no—
1083D4—2368no—
1084D4—2364no—
1085D4—2368no—
1086D4—2368no—
1087D4—2368no—
1088D4—2368no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—28no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—48no—
1101C2×C4—598no—
1102C2×C4—598no—
1103C2×C4—598no—
1104C2×C4—1188no—
1105C2×C4—11816no—
1106C2×C4—2368no—
1107C2×C4—2368no—
1108C2×C4—2368no—
1109C2×C4—2368no—
1110C2×C4—2364no—
1111C2×C4—2364no—
1112C2×C4—2364no—
1113C2×C4—2368no—
1114C2×C4C24×D5912yes—
1115C2×C4C24×D5914yes—
1116C2×C4C24×D5918yes—
1117C2×C4C24×D5912yes—
1118C2×C4C24×D5912yes—
1119C2×C4C24×D5911yescharacteristic
1120C2×C4C24×D5912yes—
1121C2×C4C24×D5912yes—
1122C2×C4C24×D5911yescharacteristic
1123C22—22no—
1124C22—22no—
1125C22—21no—
1126C22—24no—
1127C22—22no—
1128C22—28no—
1129C22—44no—
1130C22—1188no—
1131C22—1188no—
1132C22—1188no—
1133C22—4728no—
1134C22—4728no—
1135C22#1683823814yes—
1136C22C25×D5911yescharacteristic
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—21no—
1141C4—22no—
1142C4—22no—
1143C4—24no—
1144C4—28no—
1145C4—1188no—
1146C4—1188no—
1147C4—1188no—
1148C4#1683823812yes—
1149C2—24no—
1150C2—41no—
1151C2—44no—
1152C2—2368no—
1153C2C2×#1683823812yes—
1154C2C2×#1683823811yescharacteristic
subgroupG/H
centerC2×C4C24×D59
commutator, socle, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC59×#3444C2
hypercenter#3444D59
hypocenterC59#62755
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #21438764C2semidirect
2. #21438724C2semidirect
3. #21438652C2semidirect
4. #21438549C2semidirect
5. #21438448C2semidirect
6. #21438299C2semidirect
7. #21438280C2semidirect
8. #21438243C2semidirect
9. #21438232C2semidirect
10. #21437698C2semidirect
11. #21437658C2semidirect
12. #21437525C2semidirect
13. #21437506C2semidirect
14. #21437481C2semidirect
15. C2×#16837936C2semidirect
16. C59×#3444C2semidirect
17. C59⋊#564C22semidirect
18. #16838156C22semidirect
19. #16838153C22semidirect
20. #16838152C22semidirect
21. #16838151C22semidirect
22. #16838151C22semidirect
23. #16838150C22semidirect
24. #16838148C22semidirect
25. #16838147C22semidirect
26. #16838146C22semidirect
27. #16838144C22semidirect
28. #16838140C22semidirect
29. #16838139C22semidirect
30. #16838136C22semidirect
31. #16838124C22semidirect
32. #16838115C22semidirect
33. #16838111C22semidirect
34. #16838106C22semidirect
35. #16838101C22semidirect
36. #16838101C22semidirect
37. #16838097C22semidirect
38. #16838095C22semidirect
39. #16838093C22semidirect
40. #16838091C22semidirect
41. #16838085C22semidirect
42. #16838085C22semidirect
43. #16838083C22semidirect
44. #16838081C22semidirect
45. #16838081C22semidirect
46. #16838080C22semidirect
47. #16838079C22semidirect
48. #16838076C22semidirect
49. #16838076C22semidirect
50. #16838051C22semidirect
51. #16838047C22semidirect
52. #16838041C22semidirect
53. #16838040C22semidirect
54. #16838039C22semidirect
55. #16838034C22semidirect
56. #16838031C22semidirect
57. #16838027C22semidirect
58. #16838024C22semidirect
59. #16838018C22semidirect
60. #16838017C22semidirect
61. #16838016C22semidirect
62. #16838011C22semidirect
63. #16838010C22semidirect
64. #16838009C22semidirect
65. #16838003C22semidirect
66. #16838001C22semidirect
67. #16838000C22semidirect
68. #16837997C22semidirect
69. #16837996C22semidirect
70. #16837996C22semidirect
71. #16837994C22semidirect
72. #16837994C22semidirect
73. #16837993C22semidirect
75. #16837991C22semidirect
76. #16837989C22semidirect
77. #16837986C22semidirect
78. #16837985C22semidirect
79. #16837985C22semidirect
81. #16837974C22semidirect
82. #16837963C22semidirect
83. #16837960C22semidirect
84. #16837956C22semidirect
85. #16837955C22semidirect
86. #16837948C22semidirect
87. #16837939C22semidirect
88. #16837936C22semidirect
89. #16837936C22semidirect
90. #16837936C22semidirect
91. #16837936C22semidirect
92. #16837936C22semidirect
93. #16837936C22semidirect
94. #16837936C22semidirect
95. #16837936C22semidirect
96. #16837936C22semidirect
97. #16837932C22semidirect
98. #16837932C22semidirect
99. #16837930C22semidirect
100. #16837930C22semidirect
101. C2×#14273721C22semidirect
102. C2×#14273719C22semidirect
103. C2×#14273715C22semidirect
104. #16837914C22semidirect
105. #16837911C22semidirect
106. #16837911C22semidirect
107. #16837909C22semidirect
108. C2×#14273710C22semidirect
109. C2×#14273706C22semidirect
111. C4×#11745685C22semidirect
112. C4×#11745687C22semidirect
113. C2×C4×Dic118C22semidirect
114. C2×C4×D236C22semidirect
115. C2×C4×C22⋊D59C22semidirect
116. C4×D4×D59C22semidirect
117. C2×#14273684C22semidirect
118. C2×#14273684C22semidirect
119. C59×#533C22semidirect
120. C59×#533C22semidirect
121. C59×#532C22semidirect
122. C59×#532C22semidirect
123. C59×#529C22semidirect
124. C59×#529C22semidirect
125. C59×#529C22semidirect
126. C59×#525C22semidirect
127. C59×#525C22semidirect
128. C4×#41×C59C22semidirect
129. C4×#41×C59C22semidirect
130. C22×C42×C59C22semidirect
586. #3444D59semidirect
663. #533C2×D59semidirect
664. #533C2×D59semidirect
666. #532C2×D59semidirect
667. #532C2×D59semidirect
682. #529C2×D59semidirect
683. #529C2×D59semidirect
684. #529C2×D59semidirect
692. #525C2×D59semidirect
693. #525C2×D59semidirect
699. C4×#41C2×D59semidirect
700. C4×#41C2×D59semidirect
707. C22×C42C2×D59semidirect
708. C59#62755semidirect

Maximal subgroups

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

subgroupindex
#214387642
#214387242
#214386522
#214385492
#214384482
#214382992
#214382802
#214382432
#214382322
#214376982
#214376582
#214375252
#214375062
#214374812
C2×#168379362
C59×#34442
#6275559