Finite Group Databasebeta

← #29496849

Subgroups — #29496849

Order 15104.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438167C218yesmaximal, complemented
2#21438075C214yesmaximal, complemented
3#21438058C214yesmaximal, complemented
4#21437963C212yesmaximal, complemented
5#21437937C214yesmaximal, complemented
6#21437860C211yesmaximal, characteristic, complemented
7#21437817C212yesmaximal, complemented
8#21437795C214yesmaximal, complemented
9#21437741C212yesmaximal, complemented
10#21437717C214yesmaximal, complemented
11#21437707C214yesmaximal, complemented
12#21437662C218yesmaximal, complemented
13#21437530C212yesmaximal, complemented
14#21437508C214yesmaximal, complemented
15#21437393C212yesmaximal, complemented
16C2×#16837938C214yesmaximal, complemented
17#21437300C212yesmaximal, complemented
18C2×C4×#11745687C211yesmaximal, characteristic, complemented
19C59×#3501C211yesmaximal, characteristic, complemented
20C2×#14273772C2212yes—
21C22×#11745687C2211yescharacteristic
22#16838137C2214yescomplemented
23#16838131C2214yescomplemented
24#16838126C2214yescomplemented
25#16838126C2218yescomplemented
26#16838125C2218yescomplemented
27#16838118C2218yescomplemented
28#16838113C2214yescomplemented
29#16838105C2218yescomplemented
30#16838100C2218yescomplemented
31#16838100C22116yescomplemented
32#16838094C22116yescomplemented
33#16838094C2218yescomplemented
34#16838094C22116yescomplemented
35#16838090C2218yescomplemented
36#16838090C2218yescomplemented
37#16838079C22116yescomplemented
38#16838079C22116yescomplemented
39#16838079C22116yescomplemented
40#16838063C2218yescomplemented
41#16838056C2218yescomplemented
42#16838056C2214yescomplemented
43#16838056C2218yescomplemented
44#16838047C2218yescomplemented
45#16838047C2218yescomplemented
46#16838047C2218yescomplemented
47#16838043C2218yescomplemented
48D4×D236C2214yescomplemented
49#16838026C2218yescomplemented
50#16838015C2218yescomplemented
51#16838001C2218yescomplemented
52#16838001C22116yescomplemented
53#16838001C2218yescomplemented
54#16837992C22116yescomplemented
55#16837992C2218yescomplemented
56#16837983C2212yes—
57#16837978C2214yescomplemented
58#16837964C2214yes—
59#16837964C2218yescomplemented
60#16837957C2212yescomplemented
61#16837957C2218yescomplemented
62#16837957C2212yescomplemented
63#16837953C2212yescomplemented
64#16837953C2212yescomplemented
65#16837952C2212yes—
66#16837939C2214yescomplemented
67#16837939C2214yescomplemented
68#16837938C2218yescomplemented
69#16837938C2218yescomplemented
70#16837938C22116yescomplemented
71#16837938C2218yescomplemented
72#16837938C2214yescomplemented
73#16837938C2218yescomplemented
74#16837938C2218yescomplemented
75#16837938C2214yescomplemented
76#16837938C2218yescomplemented
77#16837938C2218yescomplemented
78#16837937C2218yescomplemented
79#16837937C2214yescomplemented
80#16837937C2214yescomplemented
81C2×#14273722C2218yescomplemented
82C2×#14273718C2214yescomplemented
83C2×#14273716C2214yescomplemented
84#16837915C22116yescomplemented
85#16837915C2214yescomplemented
86#16837915C2214yescomplemented
87#16837914C2214yescomplemented
88C2×#14273711C2218yescomplemented
89C2×#14273701C2214yes—
90#16837882C2214yescomplemented
91#16837881C2218yescomplemented
92#16837875C2218yescomplemented
93#16837874C2218yescomplemented
94C4×#11745689C2214yescomplemented
95C4×#11745689C2214yescomplemented
96#16837870C2214yescomplemented
97C4×#11745687C2214yescomplemented
98C4×#11745687C2218yescomplemented
99C4×#11745687C2214yescomplemented
100C4×#11745687C2214yescomplemented
101C4×#11745687C2214yescomplemented
102C2×Q8×Dic59C2214yescomplemented
103C2×C4×Dic118C2211yescharacteristic, complemented
104C2×#14273692C2211yescharacteristic, complemented
105C2×D4×Dic59C2211yescharacteristic
106C2×#14273689C2214yescomplemented
107C2×C4×C22⋊D59C2212yescomplemented
108C2×(C22⋊D59)⋊C4C2212yescomplemented
109C2×(C22⋊D59)⋊C4C2218yescomplemented
110C4×D4×D59C2218yescomplemented
111C2×#14273685C2211yescharacteristic, complemented
112C2×#14273685C2218yescomplemented
113C2×#14273683C2212yescomplemented
114C22×C4×Dic59C2212yescomplemented
115C2×C42×D59C2211yescharacteristic, complemented
116C59×#554C2214yescomplemented
117C59×#554C2218yescomplemented
118D4×Q8×C59C2214yescomplemented
119C59×#544C2212yescomplemented
120C59×#543C2214yescomplemented
121C59×#533C2212yescomplemented
122C2×C22⋊Q8×C59C2214yescomplemented
123C59×#518C2212yes—
124C2×C4×D4×C59C2211yescharacteristic
125#14273772—216no—
126C2×#11745689C2314yes—
127C2×#11745689C2314yes—
128C2×#11745685C2314yes—
129C2×#11745687—28no—
130C2×#11745687C2314yes—
131C2×#11745687C2314yes—
132C2×#11745687C2318yes—
133C22×Dic118C2311yescharacteristic
134C22×D236C2314yes—
135C22×C22⋊D59C2318yes—
136C22×C22⋊D59C2312yes—
137C2×D4×D59C2318yes—
138C23×Dic59C2312yes—
139C23×Dic59C2312yes—
140C22×C4×D59C2311yescharacteristic
141C22×C4×D59C2311yescharacteristic
142C22×C4×D59C2311yescharacteristic
143C22×C4×D59C2318yes—
144#14273727C2312yes—
145#14273727C2318yes—
146#14273724C2312yes—
147#14273722C2318yes—
148#14273722C23116yes—
149#14273722C23116yes—
150#14273722C23116yes—
151#14273722C2318yes—
152#14273722C23116yes—
153#14273722C23116yes—
154#14273722C23116yes—
155#14273718C2314yes—
156#14273718C2318yes—
157#14273718C2318yes—
158#14273718C2318yes—
159#14273718C2314yes—
160#14273718C23116yes—
161#14273718C23116yes—
162#14273716C2314yes—
163#14273716C2318yes—
164#14273716C2318yes—
165#14273716C2318yes—
166#14273716C2314yes—
167#14273716C23116yes—
168#14273715C2314yes—
169#14273715C2318yes—
170#14273712C2318yes—
171#14273712C2318yes—
172#14273712C23116yes—
173#14273712C23116yes—
174#14273712C23116yes—
175#14273711C2318yes—
176#14273711C23116yes—
177#14273711C23116yes—
178#14273711C23116yes—
179#14273711C23116yes—
180#14273711C23116yes—
181#14273707C2314yes—
182#14273707C2314yes—
183#14273707C2318yes—
184#14273707C2318yes—
185#14273707C2318yes—
186#14273703C2314yes—
187#14273703C2314yes—
188#14273703C23116yes—
189#14273703C23116yes—
190#14273702C2314yes—
191#14273702C2314yes—
192#14273702C2314yes—
193#14273702C2314yes—
194#14273702C23116yes—
195#14273702C2318yes—
196#14273701C2314yes—
197#14273701C2318yes—
198#14273701C2318yes—
199#14273701C2318yes—
200#14273701C2314yes—
201#14273701C23116yes—
202#14273701C23116yes—
203#14273697C2318yes—
204#14273697C23116yes—
205#14273697C23116yes—
206Q8×Dic59C2318yes—
207Q8×Dic59C2314yes—
208Q8×Dic59C2318yes—
209Q8×Dic59C2318yes—
210Q8×Dic59C2314yes—
211C4×Dic118C2314yes—
212C4×Dic118C2318yes—
213C4×Dic118C2314yes—
214#14273692C2314yes—
215#14273692C2314yes—
216#14273692C2314yes—
217#14273692C2314yes—
218C4×D236C2318yes—
219C4×D236C2318yes—
220C4×D236C2314yes—
221C4×D236C2314yes—
222C4×D236C2318yes—
223D4×Dic59C2314yes—
224D4×Dic59C2314yes—
225#14273689C2318yes—
226#14273689C2318yes—
227#14273689C2318yes—
228#14273689C2314yes—
229#14273689C2314yes—
230#14273689C2314yes—
231#14273689C2318yes—
232#14273689C2318yes—
233#14273689C2314yes—
234C4×C22⋊D59C2318yes—
235C4×C22⋊D59C23116yes—
236C4×C22⋊D59C2318yes—
237C4×C22⋊D59C23116yes—
238(C22⋊D59)⋊C4C2318yes—
239(C22⋊D59)⋊C4C23116yes—
240(C22⋊D59)⋊C4C2318yes—
241(C22⋊D59)⋊C4C2318yes—
242(C22⋊D59)⋊C4C23116yes—
243(C22⋊D59)⋊C4C23116yes—
244(C22⋊D59)⋊C4C2318yes—
245#14273685C23116yes—
246#14273685C2314yes—
247#14273685C2314yes—
248#14273685C2318yes—
249#14273685C2318yes—
250#14273685C23116yes—
251#14273685C23116yes—
252#14273685C2314yes—
253#14273685C2318yes—
254#14273685C2314yes—
255#14273684C2318yes—
256#14273683C2318yes—
257#14273683C2318yes—
258#14273683C23116yes—
259C2×C4⋊Dic59C2314yes—
260C2×C4⋊Dic59C2318yes—
261C2×C4⋊Dic59C2318yes—
262C2×C4⋊Dic59C2311yescharacteristic
263C2×Dic59⋊C4C2318yes—
264C2×Dic59⋊C4C2312yes—
265C2×Dic59⋊C4C2312yes—
266C4⋊C4×D59C2318yes—
267C2×C22⋊Dic59C2312yes—
268C2×(C2×D59)⋊C4C2318yes—
269C2×(C2×D59)⋊C4C2318yes—
270C2×(C2×D59)⋊C4C2318yes—
271C2×(C2×D59)⋊C4C2318yes—
272C2×(C2×D59)⋊C4C2312yes—
273C22⋊C4×D59C23116yes—
274C2×C4×Dic59C2314yes—
275C2×C4×Dic59C2314yes—
276C2×C4×Dic59C2311yescharacteristic
277C2×C4×Dic59C2311yescharacteristic
278C2×C4×Dic59C2312yes—
279C2×C4×Dic59C2312yes—
280C2×C4×Dic59C2312yes—
281C2×C4×Dic59C2314yes—
282C2×C4×Dic59C2314yes—
283C2×C4×Dic59C2318yes—
284C2×C4×Dic59C2311yescharacteristic
285C42×D59C2312yes—
286C42×D59C2312yes—
287C42×D59C2318yes—
288C42×D59C2312yes—
289C42×D59C2312yes—
290C22×Q8×C59C2314yes—
291C22×D4×C59C2311yescharacteristic
292C23×C4×C59C2312yes—
293C4⋊Q8×C59C2312yes—
294C4⋊Q8×C59C2312yes—
295C4⋊Q8×C59C2318yes—
296#125×C59C2314yes—
297#125×C59C2318yes—
298C22⋊Q8×C59C2314yes—
299C22⋊Q8×C59C2314yes—
300C22⋊Q8×C59C23116yes—
301C22⋊Q8×C59C2318yes—
302C22⋊Q8×C59C2318yes—
303C22⋊Q8×C59C2318yes—
304C22⋊Q8×C59C23116yes—
305C4×Q8×C59C2314yes—
306C4×Q8×C59C2314yes—
307C4×D4×C59C2314yes—
308C4×D4×C59C2314yes—
309C4×D4×C59C2318yes—
310C4×D4×C59C2318yes—
311#117×C59C2314yes—
312C2×C4⋊C4×C59C2314yes—
313C2×C4⋊C4×C59C2318yes—
314C2×C4⋊C4×C59C2311yescharacteristic
315C2×C22⋊C4×C59C2318yes—
316C2×C22⋊C4×C59C2312yes—
317C2×C42×C59C2311yescharacteristic
318C24×C59C2412yes—
319C23×D59C2418yes—
320C23×D59C2411yescharacteristic
321C2×Q8×C59—48no—
322C2×Q8×C59C2414yes—
323C2×Q8×C59C2414yes—
324C2×Q8×C59C2418yes—
325C2×D4×C59#4118yescomplemented
326C2×D4×C59C2414yes—
327C22×C4×C59—44no—
328C22×C4×C59C2411yescharacteristic
329C22×C4×C59C2414yes—
330C22×C4×C59C2411yescharacteristic
331C22×C4×C59C2418yes—
332C22×C4×C59C2418yes—
333C22×C4×C59C2412yes—
334C22×C4×C59C2414yes—
335C22×C4×C59C2411yescharacteristic
336C2×C22⋊D59—28no—
337C2×C22⋊D59—232no—
338C2×C22⋊D59C2418yes—
339C2×C22⋊D59C2418yes—
340C2×C22⋊D59C24116yes—
341C22×Dic59—28no—
342C22×Dic59—44no—
343C22×Dic59C2411yescharacteristic
344C22×Dic59C2414yes—
345C22×Dic59C2411yescharacteristic
346C22×Dic59C2414yes—
347C22×Dic59C2414yes—
348C22×Dic59C2412yes—
349C22×Dic59C2418yes—
350C22×Dic59C2414yes—
351C22×Dic59C2412yes—
352C22×Dic59C2411yescharacteristic
353#11745689—48no—
354#11745689—48no—
355#11745687—216no—
356#11745687—216no—
357#11745687—232no—
358D4×D59—232no—
359#11745685—216no—
360C2×D236—48no—
361C2×D236C2414yes—
362C2×D236C2414yes—
363C2×D236C2418yes—
364C2×D236C2414yes—
365C2×D236C2418yes—
366C2×D236C2418yes—
367C2×C4×D59—24no—
368C2×C4×D59—416no—
369C2×C4×D59—42no—
370C2×C4×D59—42no—
371C2×C4×D59C2412yes—
372C2×C4×D59C2412yes—
373C2×C4×D59C2412yes—
374C2×C4×D59C2412yes—
375C2×C4×D59C2418yes—
376C2×C4×D59C2418yes—
377C2×C4×D59C2412yes—
378C2×C4×D59C2412yes—
379C2×C4×D59C2418yes—
380C2×C4×D59C24116yes—
381C2×Dic118—24no—
382C2×Dic118C2414yes—
383C2×Dic118C2414yes—
384C4⋊C4×C59C2418yes—
385C4⋊C4×C59C2414yes—
386C4⋊C4×C59C2414yes—
387C4⋊C4×C59C2418yes—
388C4⋊C4×C59C24116yes—
389C4⋊C4×C59C2414yes—
390C4⋊C4×C59C2414yes—
391C4⋊C4×C59C2418yes—
392C4⋊C4×C59C2414yes—
393C22⋊C4×C59C2418yes—
394C22⋊C4×C59C24116yes—
395C22⋊C4×C59C2418yes—
396C42×C59C2412yes—
397C42×C59C2412yes—
398C42×C59C2418yes—
399C22⋊Dic59C2418yes—
400(C2×D59)⋊C4C2418yes—
401(C2×D59)⋊C4C24116yes—
402(C2×D59)⋊C4C2418yes—
403(C2×D59)⋊C4C2418yes—
404(C2×D59)⋊C4C2418yes—
405(C2×D59)⋊C4C2418yes—
406(C2×D59)⋊C4C2418yes—
407(C2×D59)⋊C4C24116yes—
408(C2×D59)⋊C4C24116yes—
409(C2×D59)⋊C4C24116yes—
410(C2×D59)⋊C4C2418yes—
411(C2×D59)⋊C4C2418yes—
412(C2×D59)⋊C4C2418yes—
413C4⋊Dic59C2414yes—
414C4⋊Dic59C2418yes—
415C4⋊Dic59C2414yes—
416C4⋊Dic59C2418yes—
417C4⋊Dic59C24116yes—
418C4⋊Dic59C2418yes—
419C4⋊Dic59C24116yes—
420C4⋊Dic59C2414yes—
421Dic59⋊C4C24116yes—
422Dic59⋊C4C2418yes—
423Dic59⋊C4C2418yes—
424Dic59⋊C4C2418yes—
425Dic59⋊C4C2418yes—
426C4×Dic59C2412yes—
427C4×Dic59C2411yescharacteristic
428C4×Dic59C2411yescharacteristic
429C4×Dic59C2411yescharacteristic
430C4×Dic59C2411yescharacteristic
431C4×Dic59C2412yes—
432C4×Dic59C2412yes—
433C4×Dic59C2412yes—
434C4×Dic59C2418yes—
435C4×Dic59C2418yes—
436C4×Dic59C2414yes—
437C4×Dic59C2414yes—
438C4×Dic59C2414yes—
439C4×Dic59C2414yes—
440C4×Dic59C2414yes—
441C4×Dic59C2414yes—
442C4×Dic59C24116yes—
443C23×C59—42no—
444C23×C59—42no—
445C23×C59C2×#4118yes—
446C23×C59C2514yes—
447C23×C59C2511yescharacteristic
448C22×D59—22no—
449C22×D59—216no—
450C22×D59—41no—
451C22×D59—41no—
452C22×D59—48no—
453C22×D59—48no—
454C22×D59C2518yes—
455C22×D59C2512yes—
456Q8×C59—28no—
457Q8×C59—44no—
458Q8×C59—48no—
459D4×C59C2×#41116yes—
460C2×C4×C59—22no—
461C2×C4×C59—28no—
462C2×C4×C59—48no—
463C2×C4×C59—41no—
464C2×C4×C59—44no—
465C2×C4×C59—42no—
466C2×C4×C59—48no—
467C2×C4×C59C2×#4114yes—
468C2×C4×C59C2511yescharacteristic
469C2×C4×C59C2514yes—
470C2×C4×C59C2518yes—
471C2×C4×C59C2512yes—
472C2×C4×C59C2518yes—
473C2×C4×C59C2512yes—
474C2×C4×C59C2511yescharacteristic
475C22⋊D59—216no—
476C22⋊D59—232no—
477C22⋊D59—216no—
478C2×Dic59—24no—
479C2×Dic59—22no—
480C2×Dic59—28no—
481C2×Dic59—28no—
482C2×Dic59—216no—
483C2×Dic59—28no—
484C2×Dic59—22no—
485C2×Dic59—41no—
486C2×Dic59—42no—
487C2×Dic59—44no—
488C2×Dic59C2511yescharacteristic
489C2×Dic59C2512yes—
490C2×Dic59C2514yes—
491C2×Dic59C2511yescharacteristic
492C2×Dic59C2511yescharacteristic
493C2×Dic59C2518yes—
494C2×Dic59C2514yes—
495C2×Dic59C2511yescharacteristic
496D236—28no—
497D236—28no—
498D236—48no—
499D236—48no—
500D236—44no—
501D236—48no—
502C4×D59—24no—
503C4×D59—24no—
504C4×D59—216no—
505C4×D59—24no—
506C4×D59—216no—
507C4×D59—24no—
508C4×D59—42no—
509C4×D59—416no—
510C4×D59—42no—
511C4×D59—48no—
512Dic118—28no—
513Dic118—28no—
514#62781—591nomaximal, Sylow
515C22×C59—21no—
516C22×C59—24no—
517C22×C59—21no—
518C22×C59—24no—
519C22×C59—48no—
520C22×C59C22×#4118yes—
521C22×C59C22×#4112yes—
522C22×C59C2611yescharacteristic
523C2×D59—22no—
524C2×D59—28no—
525C2×D59—28no—
526C2×D59—22no—
527C2×D59—22no—
528C2×D59—28no—
529C2×D59—44no—
530C2×D59—816no—
531C4×C59—28no—
532C4×C59—22no—
533C4×C59—21no—
534C4×C59—28no—
535C4×C59—24no—
536C4×C59C22×#4114yes—
537C4×C59#58512yes—
538Dic59—24no—
539Dic59—28no—
540Dic59—21no—
541Dic59—21no—
542Dic59—22no—
543Dic59—24no—
544Dic59—21no—
545Dic59#58512yes—
546#3521—598no—
547#3515—594no—
548#3514—594no—
549#3507—592no—
550#3505—594no—
551#3501D5911yescharacteristic, complemented
552#3496—591no—
553#3493—592no—
554#3491—594no—
555#3485—592no—
556#3482—594no—
557#3481—594no—
558#3475—598no—
559#3461—592no—
560#3459—594no—
561#3444—592no—
562C2×#529—594no—
563C4×H(5,𝔽2)—592no—
564C2×C4×#41—591no—
565C2×C59—22no—
566C2×C59—28no—
567C2×C59C23×#4111yescharacteristic
568C2×C59C2×#58511yescharacteristic
569C2×C59C2×#58511yescharacteristic
570D59—42no—
571D59—48no—
572C2×H(5,𝔽2)—592no—
573C22×#41—591no—
574#559—594no—
575#557—594no—
576#556—598no—
577#556—594no—
578#556—598no—
579#555—598no—
580#554—594no—
581#554C2×D5918yescomplemented
582#554C2×D5914yescomplemented
583#553—598no—
584#553—5916no—
585#553—598no—
586#552—598no—
587#552—598no—
588#552—5916no—
589#552—5916no—
590#552—598no—
591#551—5916no—
592#551—5916no—
593#551—5916no—
594D4×Q8C2×D5914yescomplemented
595#548—598no—
596#547—598no—
597#547—598no—
598#547—594no—
599#546—598no—
600#546—598no—
601#546—598no—
602#546—598no—
603D42—594no—
604#544C2×D5912yescomplemented
605#543C2×D5914yescomplemented
606#542—598no—
607#541—598no—
608#539—598no—
609#539—5916no—
610#539—598no—
611#538—598no—
612#538—5916no—
613#537—592no—
614#536—594no—
615#534—594no—
616#534—598no—
617#533—592no—
618#533—592no—
619#533—598no—
620#533C2×D5912yescomplemented
621#532—592no—
622#532—592no—
623#532—592no—
624#529—594no—
625#529—594no—
626#529—598no—
627#529—594no—
628#529—598no—
629#529—598no—
630#529—598no—
631#529—598no—
632#529—598no—
633#529—598no—
634#529—598no—
635#529—594no—
636#529—5916no—
637#529—594no—
638#529—594no—
639C2×#126—598no—
640C2×#125—594no—
641C2×#124—594no—
642#525—594no—
643#525—594no—
644#525—5916no—
645#525—594no—
646C2×#123—598no—
647C2×C22⋊Q8C2×D5914yescomplemented
648C2×#121—594no—
649#520—598no—
650#520—594no—
651#518—598no—
652#518—598no—
653#518C2×D5912yes—
654C4×#41—594no—
655C4×#41—594no—
656C4×#41—594no—
657C4×#41—594no—
658C4×#41—594no—
659C4×#41—594no—
660C4×#41—598no—
661C4×#41—594no—
662C2×C4×Q8—594no—
663C2×C4×Q8—591no—
664C2×C4×Q8—591no—
665C2×C4×D4—591no—
666C2×C4×D4—592no—
667C2×C4×D4—598no—
668C2×C4×D4—594no—
669C2×C4×D4—592no—
670C2×C4×D4—598no—
671C2×C4×D4C2×D5911yescharacteristic
672C2×#117—591no—
673C2×#117—598no—
674C2×#117—592no—
675C22×C42—592no—
676C22×C42—591no—
677C59#6278111yescharacteristic, complemented, Sylow
678H(5,𝔽2)—11816no—
679C2×#41—594no—
680C2×#41—594no—
681C2×#41—594no—
682C2×#41—594no—
683C2×#41—598no—
684C2×#41—594no—
685C2×#41—1188no—
686C22×Q8—591no—
687C22×Q8C22×D5914yes—
688C22×D4—592no—
689C22×D4—598no—
690C22×D4—598no—
691C22×D4—594no—
692C22×D4C22×D5911yescharacteristic
693C23×C4—592no—
694C23×C4—592no—
695C23×C4—591no—
696C23×C4—598no—
697C23×C4—591no—
698C23×C4—591no—
699C23×C4C22×D5912yes—
700C4⋊Q8—592no—
701C4⋊Q8—598no—
702C4⋊Q8C22×D5912yes—
703C4⋊Q8C22×D5912yes—
704C4⋊Q8C22×D5918yes—
705#127—592no—
706#126—598no—
707#126—5916no—
708#126—5916no—
709#126—5916no—
710#126—598no—
711#126—5916no—
712#126—5916no—
713#126—5916no—
714#125—594no—
715#125—598no—
716#125—598no—
717#125—598no—
718#125—594no—
719#125—5916no—
720#125—5916no—
721#125C22×D5914yes—
722#125C22×D5918yes—
723#124—594no—
724#124—598no—
725#124—598no—
726#124—598no—
727#124—594no—
728#124—5916no—
729#124—594no—
730#124—598no—
731#123—598no—
732#123—598no—
733#123—5916no—
734#123—5916no—
735#123—5916no—
736#123—598no—
737#123—5916no—
738#123—5916no—
739#123—5916no—
740#123—5916no—
741#123—5916no—
742C22⋊Q8—594no—
743C22⋊Q8—594no—
744C22⋊Q8—5916no—
745C22⋊Q8—5916no—
746C22⋊Q8—594no—
747C22⋊Q8—594no—
748C22⋊Q8—598no—
749C22⋊Q8—598no—
750C22⋊Q8—598no—
751C22⋊Q8C22×D5914yes—
752C22⋊Q8C22×D5918yes—
753C22⋊Q8C22×D5918yes—
754C22⋊Q8C22×D5918yes—
755C22⋊Q8C22×D5914yes—
756C22⋊Q8C22×D59116yes—
757C22⋊Q8C22×D59116yes—
758#121—594no—
759#121—598no—
760#121—598no—
761#121—598no—
762#121—594no—
763#121—5916no—
764#121—5916no—
765#121—594no—
766#121—594no—
767#121—594no—
768#121—594no—
769#121—5916no—
770#121—598no—
771#120—598no—
772#120—5916no—
773#120—5916no—
774C4×Q8—594no—
775C4×Q8—598no—
776C4×Q8—598no—
777C4×Q8—598no—
778C4×Q8—594no—
779C4×Q8—594no—
780C4×Q8—594no—
781C4×Q8—594no—
782C4×Q8—594no—
783C4×Q8—594no—
784C4×Q8—594no—
785C4×Q8—598no—
786C4×Q8C22×D5914yes—
787C4×Q8C22×D5914yes—
788C4×D4—594no—
789C4×D4—594no—
790C4×D4—598no—
791C4×D4—598no—
792C4×D4—5916no—
793C4×D4—5916no—
794C4×D4—594no—
795C4×D4—594no—
796C4×D4—598no—
797C4×D4—598no—
798C4×D4—598no—
799C4×D4—594no—
800C4×D4—598no—
801C4×D4—598no—
802C4×D4—594no—
803C4×D4—5916no—
804C4×D4—598no—
805C4×D4—598no—
806C4×D4—598no—
807C4×D4—5916no—
808C4×D4—5916no—
809C4×D4—598no—
810C4×D4—598no—
811C4×D4—598no—
812C4×D4—598no—
813C4×D4—594no—
814C4×D4—594no—
815C4×D4C22×D5918yes—
816C4×D4C22×D5914yes—
817C4×D4C22×D5914yes—
818C4×D4C22×D5918yes—
819#117—598no—
820#117—594no—
821#117—594no—
822#117—5916no—
823#117—5916no—
824#117—5916no—
825#117—598no—
826#117—594no—
827#117—594no—
828#117—598no—
829#117—598no—
830#117—598no—
831#117—5916no—
832#117—598no—
833#117C22×D5914yes—
834C2×C4⋊C4—591no—
835C2×C4⋊C4—592no—
836C2×C4⋊C4—592no—
837C2×C4⋊C4—598no—
838C2×C4⋊C4—598no—
839C2×C4⋊C4—594no—
840C2×C4⋊C4—598no—
841C2×C4⋊C4—598no—
842C2×C4⋊C4C22×D5911yescharacteristic
843C2×C4⋊C4C22×D5918yes—
844C2×C4⋊C4C22×D5914yes—
845C2×C22⋊C4—592no—
846C2×C22⋊C4—592no—
847C2×C22⋊C4—598no—
848C2×C22⋊C4—598no—
849C2×C22⋊C4—598no—
850C2×C22⋊C4—598no—
851C2×C22⋊C4—5916no—
852C2×C22⋊C4C22×D5912yes—
853C2×C22⋊C4C22×D5918yes—
854C2×C42—594no—
855C2×C42—592no—
856C2×C42—591no—
857C2×C42—598no—
858C2×C42—591no—
859C2×C42—594no—
860C2×C42—592no—
861C2×C42—592no—
862C2×C42—594no—
863C2×C42—594no—
864C2×C42—591no—
865C2×C42—598no—
866C2×C42—592no—
867C2×C42—592no—
868C2×C42—592no—
869C2×C42—592no—
870C2×C42C22×D5911yescharacteristic
871C24—598no—
872C24—591no—
873C24C23×D5912yes—
874#41—11816no—
875#41—11816no—
876#41—11832no—
877#41—11816no—
878#41—2368no—
879#41—2368no—
880C2×Q8—48no—
881C2×Q8—594no—
882C2×Q8—594no—
883C2×Q8—1184no—
884C2×Q8C23×D5914yes—
885C2×Q8C23×D5918yes—
886C2×Q8C23×D5914yes—
887C2×D4—598no—
888C2×D4—5916no—
889C2×D4—598no—
890C2×D4—594no—
891C2×D4—594no—
892C2×D4—594no—
893C2×D4—598no—
894C2×D4—598no—
895C2×D4—598no—
896C2×D4—1188no—
897C2×D4—11832no—
898C2×D4—11832no—
899C2×D4—2368no—
900C2×D4#1174568918yescomplemented
901C2×D4C23×D5914yes—
902C22×C4—44no—
903C22×C4—594no—
904C22×C4—591no—
905C22×C4—591no—
906C22×C4—594no—
907C22×C4—594no—
908C22×C4—592no—
909C22×C4—598no—
910C22×C4—594no—
911C22×C4—591no—
912C22×C4—592no—
913C22×C4—592no—
914C22×C4—592no—
915C22×C4—592no—
916C22×C4—592no—
917C22×C4—598no—
918C22×C4—598no—
919C22×C4—592no—
920C22×C4—592no—
921C22×C4—598no—
922C22×C4—5916no—
923C22×C4—1188no—
924C22×C4—1184no—
925C22×C4—2362no—
926C22×C4—23616no—
927C22×C4—2362no—
928C22×C4—2364no—
929C22×C4C23×D5911yescharacteristic
930C22×C4C23×D5914yes—
931C22×C4C23×D5914yes—
932C22×C4C23×D5912yes—
933C22×C4C23×D5911yescharacteristic
934C22×C4C23×D5918yes—
935C22×C4C23×D5918yes—
936C22×C4C23×D5911yescharacteristic
937C4⋊C4—594no—
938C4⋊C4—598no—
939C4⋊C4—598no—
940C4⋊C4—5916no—
941C4⋊C4—594no—
942C4⋊C4—598no—
943C4⋊C4—598no—
944C4⋊C4—598no—
945C4⋊C4—5916no—
946C4⋊C4—598no—
947C4⋊C4—5916no—
948C4⋊C4—598no—
949C4⋊C4—594no—
950C4⋊C4C23×D5914yes—
951C4⋊C4C23×D5918yes—
952C4⋊C4C23×D5914yes—
953C4⋊C4C23×D5914yes—
954C4⋊C4C23×D59116yes—
955C4⋊C4C23×D5918yes—
956C4⋊C4C23×D5914yes—
957C4⋊C4C23×D5914yes—
958C4⋊C4C23×D5918yes—
959C22⋊C4—598no—
960C22⋊C4—598no—
961C22⋊C4—598no—
962C22⋊C4—598no—
963C22⋊C4—598no—
964C22⋊C4—598no—
965C22⋊C4—5916no—
966C22⋊C4—598no—
967C22⋊C4—5916no—
968C22⋊C4—5916no—
969C22⋊C4—5916no—
970C22⋊C4—598no—
971C22⋊C4—598no—
972C22⋊C4—598no—
973C22⋊C4C23×D59116yes—
974C22⋊C4C23×D5918yes—
975C22⋊C4C23×D5918yes—
976C42—591no—
977C42—592no—
978C42—591no—
979C42—591no—
980C42—591no—
981C42—594no—
982C42—592no—
983C42—594no—
984C42—598no—
985C42—592no—
986C42—594no—
987C42—592no—
988C42—594no—
989C42—594no—
990C42—594no—
991C42—598no—
992C42—5916no—
993C42C23×D5912yes—
994C42C23×D5912yes—
995C42C23×D5918yes—
996C23—42no—
997C23—42no—
998C23—598no—
999C23—592no—
1000C23—11816no—
1001C23—1182no—
1002C23—2368no—
1003C23—2368no—
1004C23—2361no—
1005C23—2361no—
1006C23C2×#1174568918yes—
1007C23C24×D5914yes—
1008C23C24×D5911yescharacteristic
1009Q8—28no—
1010Q8—48no—
1011Q8—44no—
1012Q8—1188no—
1013Q8—1188no—
1014D4—11832no—
1015D4—11816no—
1016D4—11816no—
1017D4—1188no—
1018D4—1188no—
1019D4—2368no—
1020D4—2368no—
1021D4—2364no—
1022D4—2368no—
1023D4C2×#11745689116yes—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—48no—
1029C2×C4—41no—
1030C2×C4—48no—
1031C2×C4—591no—
1032C2×C4—591no—
1033C2×C4—591no—
1034C2×C4—591no—
1035C2×C4—594no—
1036C2×C4—592no—
1037C2×C4—594no—
1038C2×C4—598no—
1039C2×C4—11816no—
1040C2×C4—1184no—
1041C2×C4—1188no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1184no—
1045C2×C4—1188no—
1046C2×C4—1188no—
1047C2×C4—11816no—
1048C2×C4—1184no—
1049C2×C4—1184no—
1050C2×C4—11816no—
1051C2×C4—1184no—
1052C2×C4—23616no—
1053C2×C4—2362no—
1054C2×C4—2362no—
1055C2×C4—2368no—
1056C2×C4—2364no—
1057C2×C4—2362no—
1058C2×C4—2361no—
1059C2×C4C2×#1174568914yes—
1060C2×C4C24×D5911yescharacteristic
1061C2×C4C24×D5914yes—
1062C2×C4C24×D5918yes—
1063C2×C4C24×D5912yes—
1064C2×C4C24×D5918yes—
1065C2×C4C24×D5912yes—
1066C2×C4C24×D5911yescharacteristic
1067C22—24no—
1068C22—21no—
1069C22—24no—
1070C22—21no—
1071C22—48no—
1072C22—1182no—
1073C22—1188no—
1074C22—1188no—
1075C22—1182no—
1076C22—1182no—
1077C22—1188no—
1078C22—47216no—
1079C22—2364no—
1080C22C22×#1174568918yes—
1081C22C22×#1174568912yes—
1082C22C25×D5911yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—28no—
1088C4—592no—
1089C4—1181no—
1090C4—1181no—
1091C4—1188no—
1092C4—1184no—
1093C4—1184no—
1094C4—1181no—
1095C4—1182no—
1096C4C22×#1174568914yes—
1097C4#1683823712yes—
1098C2—22no—
1099C2—28no—
1100C2—2368no—
1101C2—2362no—
1102C2C23×#1174568911yescharacteristic
1103C2#585×D5911yescharacteristic
1104C2C2×#1683823711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D59
commutator, socle, cosocleC22×C59C26
FittingC59×#3501C2
hypercenter#3501D59
hypocenterC59#62781
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #21438167C2semidirect
2. #21438075C2semidirect
3. #21438058C2semidirect
4. #21437963C2semidirect
5. #21437937C2semidirect
6. #21437860C2semidirect
7. #21437817C2semidirect
8. #21437795C2semidirect
9. #21437741C2semidirect
10. #21437717C2semidirect
11. #21437707C2semidirect
12. #21437662C2semidirect
13. #21437530C2semidirect
14. #21437508C2semidirect
15. #21437393C2semidirect
16. C2×#16837938C2semidirect
17. #21437300C2semidirect
18. C2×C4×#11745687C2semidirect
19. C59×#3501C2semidirect
22. #16838137C22semidirect
23. #16838131C22semidirect
24. #16838126C22semidirect
25. #16838126C22semidirect
26. #16838125C22semidirect
27. #16838118C22semidirect
28. #16838113C22semidirect
29. #16838105C22semidirect
30. #16838100C22semidirect
31. #16838100C22semidirect
32. #16838094C22semidirect
33. #16838094C22semidirect
34. #16838094C22semidirect
35. #16838090C22semidirect
36. #16838090C22semidirect
37. #16838079C22semidirect
38. #16838079C22semidirect
39. #16838079C22semidirect
40. #16838063C22semidirect
41. #16838056C22semidirect
42. #16838056C22semidirect
43. #16838056C22semidirect
44. #16838047C22semidirect
45. #16838047C22semidirect
46. #16838047C22semidirect
47. #16838043C22semidirect
48. D4×D236C22semidirect
49. #16838026C22semidirect
50. #16838015C22semidirect
51. #16838001C22semidirect
52. #16838001C22semidirect
53. #16838001C22semidirect
54. #16837992C22semidirect
55. #16837992C22semidirect
57. #16837978C22semidirect
59. #16837964C22semidirect
60. #16837957C22semidirect
61. #16837957C22semidirect
62. #16837957C22semidirect
63. #16837953C22semidirect
64. #16837953C22semidirect
66. #16837939C22semidirect
67. #16837939C22semidirect
68. #16837938C22semidirect
69. #16837938C22semidirect
70. #16837938C22semidirect
71. #16837938C22semidirect
72. #16837938C22semidirect
73. #16837938C22semidirect
74. #16837938C22semidirect
75. #16837938C22semidirect
76. #16837938C22semidirect
77. #16837938C22semidirect
78. #16837937C22semidirect
79. #16837937C22semidirect
80. #16837937C22semidirect
81. C2×#14273722C22semidirect
82. C2×#14273718C22semidirect
83. C2×#14273716C22semidirect
84. #16837915C22semidirect
85. #16837915C22semidirect
86. #16837915C22semidirect
87. #16837914C22semidirect
88. C2×#14273711C22semidirect
90. #16837882C22semidirect
91. #16837881C22semidirect
92. #16837875C22semidirect
93. #16837874C22semidirect
94. C4×#11745689C22semidirect
95. C4×#11745689C22semidirect
96. #16837870C22semidirect
97. C4×#11745687C22semidirect
98. C4×#11745687C22semidirect
99. C4×#11745687C22semidirect
100. C4×#11745687C22semidirect
101. C4×#11745687C22semidirect
102. C2×Q8×Dic59C22semidirect
103. C2×C4×Dic118C22semidirect
104. C2×#14273692C22semidirect
106. C2×#14273689C22semidirect
107. C2×C4×C22⋊D59C22semidirect
108. C2×(C22⋊D59)⋊C4C22semidirect
109. C2×(C22⋊D59)⋊C4C22semidirect
110. C4×D4×D59C22semidirect
111. C2×#14273685C22semidirect
112. C2×#14273685C22semidirect
113. C2×#14273683C22semidirect
114. C22×C4×Dic59C22semidirect
115. C2×C42×D59C22semidirect
116. C59×#554C22semidirect
117. C59×#554C22semidirect
118. D4×Q8×C59C22semidirect
119. C59×#544C22semidirect
120. C59×#543C22semidirect
121. C59×#533C22semidirect
122. C2×C22⋊Q8×C59C22semidirect
325. C2×D4×C59#41semidirect
551. #3501D59semidirect
581. #554C2×D59semidirect
582. #554C2×D59semidirect
594. D4×Q8C2×D59semidirect
604. #544C2×D59semidirect
605. #543C2×D59semidirect
620. #533C2×D59semidirect
647. C2×C22⋊Q8C2×D59semidirect
677. C59#62781semidirect
900. C2×D4#11745689semidirect

Maximal subgroups

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

subgroupindex
#214381672
#214380752
#214380582
#214379632
#214379372
#214378602
#214378172
#214377952
#214377412
#214377172
#214377072
#214376622
#214375302
#214375082
#214373932
C2×#168379382
#214373002
C2×C4×#117456872
C59×#35012
#6278159