Finite Group Databasebeta

← #29496848

Subgroups — #29496848

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#21438164C218yesmaximal, complemented
2#21438074C214yesmaximal, complemented
3#21438057C214yesmaximal, complemented
4#21437961C212yesmaximal, complemented
5#21437935C214yesmaximal, complemented
6#21437899C211yesmaximal, characteristic, complemented
7#21437860C211yesmaximal, characteristic, complemented
8#21437816C212yesmaximal, complemented
9#21437794C214yesmaximal, complemented
10#21437740C212yesmaximal, complemented
11#21437711C214yesmaximal, complemented
12#21437706C214yesmaximal, complemented
13#21437658C218yesmaximal, complemented
14#21437529C212yesmaximal, complemented
15#21437505C214yesmaximal, complemented
16#21437392C212yesmaximal, complemented
17C2×#16837936C214yesmaximal, complemented
18C4×#14273772C212yesmaximal, complemented
19C2×C4×#41×C59C211yesmaximal, characteristic, complemented
20C2×#14273772C2212yes—
21#16838137C2214yescomplemented
22#16838130C2214yescomplemented
23#16838125C2214yescomplemented
24#16838124C2218yescomplemented
25#16838120C2218yescomplemented
26#16838115C2218yescomplemented
27#16838112C2214yescomplemented
28#16838111C2218yescomplemented
29#16838109C2214yescomplemented
30#16838101C22116yescomplemented
31#16838098C2218yescomplemented
32#16838096C2218yescomplemented
33#16838093C2218yescomplemented
34#16838092C2218yescomplemented
35#16838091C2218yescomplemented
36#16838085C22116yescomplemented
37#16838085C22116yescomplemented
38#16838081C22116yescomplemented
39#16838076C22116yescomplemented
40#16838076C22116yescomplemented
41D4×Dic118C2214yescomplemented
42#16838061C2218yescomplemented
43#16838056C2214yescomplemented
44#16838051C2218yescomplemented
45#16838051C2218yescomplemented
46#16838048C2218yescomplemented
47#16838047C2218yescomplemented
48#16838040C2218yescomplemented
49#16838040C2218yescomplemented
50D4×D236C2214yescomplemented
51#16838033C2212yescomplemented
52#16838028C2214yescomplemented
53#16838024C2218yescomplemented
54#16838010C2218yescomplemented
55#16837999C2218yescomplemented
56#16837999C2218yescomplemented
57#16837994C22116yescomplemented
58#16837990C2218yescomplemented
59#16837985C22116yescomplemented
60#16837983C2212yes—
61#16837976C2214yescomplemented
62#16837964C2214yes—
63#16837961C2218yescomplemented
64#16837959C2212yescomplemented
65#16837959C2212yescomplemented
66#16837959C2212yescomplemented
67#16837956C2218yescomplemented
68#16837952C2212yes—
69#16837952C2212yescomplemented
70#16837952C2212yescomplemented
71#16837939C2218yescomplemented
72#16837936C2218yescomplemented
73#16837936C2218yescomplemented
74#16837936C2218yescomplemented
75#16837936C2214yescomplemented
76#16837936C2218yescomplemented
77#16837936C2218yescomplemented
78#16837936C2214yescomplemented
79#16837936C2214yescomplemented
80#16837936C2218yescomplemented
81#16837936C2218yescomplemented
82#16837936C2214yescomplemented
83#16837936C2214yescomplemented
84#16837936C2214yescomplemented
85#16837932C22116yescomplemented
86C2×#14273721C2218yescomplemented
87C2×#14273719C2214yescomplemented
88C2×#14273715C2214yescomplemented
89#16837913C2214yescomplemented
90#16837913C2214yescomplemented
91#16837913C2214yescomplemented
92#16837911C22116yescomplemented
93C2×#14273710C2218yescomplemented
94C2×#14273706C2214yescomplemented
95C2×#14273701C2214yes—
96#16837883C2214yescomplemented
97#16837881C2218yescomplemented
98#16837877C2212yes—
99#16837875C2218yescomplemented
100#16837874C2218yescomplemented
101C4×#11745685C2214yescomplemented
102C4×#11745685C2214yescomplemented
103C4×#11745685C2214yescomplemented
104C4×#11745687C2218yescomplemented
105C2×C4×Dic118C2214yescomplemented
106C2×C4×D236C2214yescomplemented
107C2×C4×C22⋊D59C2218yescomplemented
108C4×D4×D59C2218yescomplemented
109C2×#14273684C2218yescomplemented
110C22×#41×C59C2211yescharacteristic
111C4×#41×C59C2214yescomplemented
112C4×#41×C59C2214yescomplemented
113C4×#41×C59C2214yescomplemented
114C4×#41×C59C2214yescomplemented
115C2×C4×Q8×C59C2211yescharacteristic, complemented
116C2×C4×Q8×C59C2211yescharacteristic, complemented
117C2×C4×D4×C59C2211yescharacteristic
118C2×C4×D4×C59C2211yescharacteristic
119C2×C4×D4×C59C2212yescomplemented
120C2×C4×D4×C59C2212yescomplemented
121C2×#117×C59C2212yescomplemented
122C2×#117×C59C2211yescharacteristic, complemented
123C22×C42×C59C2212yescomplemented
124C22×C42×C59C2211yescharacteristic, complemented
125#14273772—216no—
126C2×#11745685C2314yes—
127C2×#11745685C2314yes—
128C2×#11745685C2314yes—
129C2×#11745687C2318yes—
130C22×Dic118C2314yes—
131C22×D236C2314yes—
132C22×C22⋊D59C2318yes—
133C2×D4×D59C2318yes—
134C22×C4×D59C2318yes—
135#14273727C2312yes—
136#14273727C2312yes—
137#14273727C2312yes—
138#14273726C2318yes—
139#14273725C2318yes—
140#14273724C2312yes—
141#14273722C23116yes—
142#14273722C23116yes—
143#14273721C2318yes—
144#14273721C23116yes—
145#14273721C23116yes—
146#14273721C23116yes—
147#14273721C2318yes—
148#14273720C23116yes—
149#14273719C2314yes—
150#14273719C2318yes—
151#14273719C2318yes—
152#14273719C2318yes—
153#14273719C2314yes—
154#14273719C2314yes—
155#14273718C2318yes—
156#14273717C23116yes—
157#14273717C23116yes—
158#14273716C2318yes—
159#14273715C2314yes—
160#14273715C2318yes—
161#14273715C2318yes—
162#14273715C2318yes—
163#14273715C2314yes—
164#14273715C2314yes—
165#14273713C23116yes—
166#14273712C23116yes—
167#14273712C23116yes—
168#14273711C23116yes—
169#14273710C2318yes—
170#14273710C23116yes—
171#14273710C23116yes—
172#14273710C23116yes—
173#14273710C2318yes—
174#14273710C2318yes—
175#14273709C23116yes—
176#14273708C23116yes—
177#14273707C2318yes—
178#14273706C2314yes—
179#14273706C2318yes—
180#14273706C2318yes—
181#14273706C2318yes—
182#14273706C2314yes—
183#14273706C2314yes—
184#14273706C2314yes—
185#14273706C2314yes—
186#14273706C2314yes—
187#14273705C23116yes—
188#14273705C23116yes—
189#14273704C23116yes—
190#14273704C23116yes—
191#14273703C2318yes—
192#14273703C2318yes—
193#14273702C2318yes—
194#14273701C2314yes—
195#14273701C2318yes—
196#14273701C2318yes—
197#14273701C2318yes—
198#14273701C2314yes—
199#14273701C2314yes—
200#14273701C2314yes—
201#14273701C2314yes—
202#14273701C2314yes—
203#14273700C23116yes—
204#14273699C23116yes—
205#14273699C23116yes—
206#14273697C23116yes—
207#14273696C2318yes—
208#14273695C23116yes—
209C4×Dic118C2318yes—
210C4×Dic118C2314yes—
211C4×Dic118C2318yes—
212C4×Dic118C2318yes—
213C4×Dic118C2314yes—
214C4×Dic118C2314yes—
215C4×Dic118C2314yes—
216C4×Dic118C2314yes—
217C4×Dic118C2314yes—
218#14273692C2318yes—
219C4×D236C2318yes—
220C4×D236C2314yes—
221C4×D236C2318yes—
222C4×D236C2318yes—
223C4×D236C2314yes—
224C4×D236C2314yes—
225C4×D236C2314yes—
226C4×D236C2314yes—
227C4×D236C2314yes—
228D4×Dic59C2318yes—
229D4×Dic59C2318yes—
230#14273689C2318yes—
231C4×C22⋊D59C2318yes—
232C4×C22⋊D59C23116yes—
233C4×C22⋊D59C2318yes—
234C4×C22⋊D59C2318yes—
235C4×C22⋊D59C2318yes—
236C4×C22⋊D59C2318yes—
237C4×C22⋊D59C2318yes—
238C4×C22⋊D59C23116yes—
239C4×C22⋊D59C23116yes—
240(C22⋊D59)⋊C4C23116yes—
241(C22⋊D59)⋊C4C23116yes—
242#14273686C2314yes—
243#14273686C2314yes—
244#14273686C2314yes—
245#14273685C2318yes—
246#14273684C23116yes—
247#14273684C2318yes—
248#14273684C2318yes—
249#14273684C2318yes—
250#14273684C23116yes—
251#14273684C23116yes—
252#14273683C23116yes—
253C2×C4⋊Dic59C2314yes—
254C2×C4⋊Dic59C2314yes—
255C2×Dic59⋊C4C2318yes—
256C2×Dic59⋊C4C2318yes—
257C2×Dic59⋊C4C2318yes—
258C2×Dic59⋊C4C2318yes—
259C4⋊C4×D59C2318yes—
260C2×C22⋊Dic59C2318yes—
261C2×(C2×D59)⋊C4C2318yes—
262C2×(C2×D59)⋊C4C2318yes—
263C2×(C2×D59)⋊C4C2318yes—
264C2×(C2×D59)⋊C4C2318yes—
265C22⋊C4×D59C23116yes—
266C2×C4×Dic59C2318yes—
267C42×D59C2318yes—
268C2×#41×C59—28no—
269C2×#41×C59C2314yes—
270C2×#41×C59C2314yes—
271C22×Q8×C59C2311yescharacteristic
272C22×D4×C59C2312yes—
273C22×D4×C59C2311yescharacteristic
274C23×C4×C59C2312yes—
275C23×C4×C59C2311yescharacteristic
276C23×C4×C59C2312yes—
277C23×C4×C59C2311yescharacteristic
278C23×C4×C59C2311yescharacteristic
279C23×C4×C59C2312yes—
280C4×Q8×C59C2314yes—
281C4×Q8×C59C2314yes—
282C4×Q8×C59C2314yes—
283C4×Q8×C59C2314yes—
284C4×D4×C59C2318yes—
285C4×D4×C59C2318yes—
286C4×D4×C59C2314yes—
287C4×D4×C59C2314yes—
288C4×D4×C59C2318yes—
289C4×D4×C59C2314yes—
290C4×D4×C59C2314yes—
291C4×D4×C59C2318yes—
292#117×C59C2318yes—
293#117×C59C2318yes—
294#117×C59C2314yes—
295#117×C59C2314yes—
296C2×C4⋊C4×C59C2311yescharacteristic
297C2×C4⋊C4×C59C2312yes—
298C2×C4⋊C4×C59C2312yes—
299C2×C4⋊C4×C59C2311yescharacteristic
300C2×C22⋊C4×C59C2312yes—
301C2×C22⋊C4×C59C2312yes—
302C2×C22⋊C4×C59C2312yes—
303C2×C42×C59C2314yes—
304C2×C42×C59C2314yes—
305C2×C42×C59C2311yescharacteristic
306C2×C42×C59C2311yescharacteristic
307C2×C42×C59C2312yes—
308C2×C42×C59C2312yes—
309C2×C42×C59C2312yes—
310C2×C42×C59C2312yes—
311C2×C42×C59C2312yes—
312C2×C42×C59C2314yes—
313C2×C42×C59C2314yes—
314C2×C42×C59C2312yes—
315C2×C42×C59C2311yescharacteristic
316C2×C42×C59C2312yes—
317C2×C42×C59C2311yescharacteristic
318C24×C59C2411yescharacteristic
319C24×C59C2412yes—
320C23×D59C2418yes—
321#41×C59—216no—
322#41×C59—216no—
323C2×Q8×C59—24no—
324C2×Q8×C59C2414yes—
325C2×D4×C59—28no—
326C2×D4×C59#4118yescomplemented
327C2×D4×C59C2418yes—
328C2×D4×C59C2414yes—
329C22×C4×C59—28no—
330C22×C4×C59—24no—
331C22×C4×C59—44no—
332C22×C4×C59—44no—
333C22×C4×C59—42no—
334C22×C4×C59—42no—
335C22×C4×C59C2411yescharacteristic
336C22×C4×C59C2411yescharacteristic
337C22×C4×C59C2411yescharacteristic
338C22×C4×C59C2412yes—
339C22×C4×C59C2414yes—
340C22×C4×C59C2414yes—
341C22×C4×C59C2412yes—
342C22×C4×C59C2412yes—
343C22×C4×C59C2414yes—
344C22×C4×C59C2414yes—
345C22×C4×C59C2412yes—
346C22×C4×C59C2412yes—
347C22×C4×C59C2412yes—
348C22×C4×C59C2411yescharacteristic
349C22×C4×C59C2412yes—
350C22×C4×C59C2411yescharacteristic
351C22×C4×C59C2414yes—
352C22×C4×C59C2414yes—
353C22×C4×C59C2412yes—
354C22×C4×C59C2412yes—
355C22×C4×C59C2411yescharacteristic
356C2×C22⋊D59—232no—
357C2×C22⋊D59C24116yes—
358C2×C22⋊D59C2418yes—
359C2×C22⋊D59C2418yes—
360C2×C22⋊D59C2418yes—
361C22×Dic59C2418yes—
362C22×Dic59C2418yes—
363C22×Dic59C2418yes—
364#11745687—232no—
365D4×D59—232no—
366#11745685—216no—
367#11745685—48no—
368#11745685—48no—
369C2×D236—48no—
370C2×D236C2414yes—
371C2×D236C2414yes—
372C2×D236C2414yes—
373C2×D236C2418yes—
374C2×C4×D59—416no—
375C2×C4×D59C2418yes—
376C2×C4×D59C2418yes—
377C2×C4×D59C2418yes—
378C2×C4×D59C24116yes—
379C2×Dic118—48no—
380C2×Dic118C2414yes—
381C2×Dic118C2414yes—
382C2×Dic118C2414yes—
383C2×Dic118C2418yes—
384C4⋊C4×C59C2414yes—
385C4⋊C4×C59C2414yes—
386C4⋊C4×C59C2418yes—
387C4⋊C4×C59C2418yes—
388C22⋊C4×C59C2418yes—
389C22⋊C4×C59C2418yes—
390C22⋊C4×C59C2418yes—
391C42×C59C2411yescharacteristic
392C42×C59C2411yescharacteristic
393C42×C59C2411yescharacteristic
394C42×C59C2411yescharacteristic
395C42×C59C2414yes—
396C42×C59C2412yes—
397C42×C59C2414yes—
398C42×C59C2412yes—
399C42×C59C2412yes—
400C42×C59C2412yes—
401C42×C59C2414yes—
402C42×C59C2414yes—
403C42×C59C2414yes—
404C42×C59C2412yes—
405C42×C59C2412yes—
406C42×C59C2414yes—
407C22⋊Dic59C24116yes—
408C22⋊Dic59C2418yes—
409C22⋊Dic59C2418yes—
410C22⋊Dic59C2418yes—
411(C2×D59)⋊C4C2418yes—
412(C2×D59)⋊C4C24116yes—
413(C2×D59)⋊C4C2418yes—
414(C2×D59)⋊C4C2418yes—
415(C2×D59)⋊C4C2418yes—
416(C2×D59)⋊C4C2418yes—
417(C2×D59)⋊C4C24116yes—
418(C2×D59)⋊C4C24116yes—
419(C2×D59)⋊C4C24116yes—
420(C2×D59)⋊C4C2418yes—
421C4⋊Dic59C2414yes—
422C4⋊Dic59C2414yes—
423C4⋊Dic59C2414yes—
424C4⋊Dic59C2418yes—
425C4⋊Dic59C2418yes—
426C4⋊Dic59C2414yes—
427C4⋊Dic59C2414yes—
428C4⋊Dic59C2414yes—
429Dic59⋊C4C24116yes—
430Dic59⋊C4C2418yes—
431Dic59⋊C4C2418yes—
432Dic59⋊C4C2418yes—
433Dic59⋊C4C2418yes—
434Dic59⋊C4C24116yes—
435Dic59⋊C4C24116yes—
436Dic59⋊C4C24116yes—
437Dic59⋊C4C2418yes—
438Dic59⋊C4C2418yes—
439C4×Dic59C2418yes—
440C4×Dic59C2418yes—
441C4×Dic59C2418yes—
442C4×Dic59C24116yes—
443C23×C59—22no—
444C23×C59—42no—
445C23×C59—42no—
446C23×C59—41no—
447C23×C59—41no—
448C23×C59C2×#4118yes—
449C23×C59C2512yes—
450C23×C59C2511yescharacteristic
451C23×C59C2514yes—
452C22×D59—216no—
453C22×D59—48no—
454C22×D59—48no—
455C22×D59C2518yes—
456Q8×C59—28no—
457D4×C59—216no—
458D4×C59C2×#41116yes—
459C2×C4×C59—22no—
460C2×C4×C59—24no—
461C2×C4×C59—28no—
462C2×C4×C59—28no—
463C2×C4×C59—24no—
464C2×C4×C59—24no—
465C2×C4×C59—28no—
466C2×C4×C59—28no—
467C2×C4×C59—24no—
468C2×C4×C59—24no—
469C2×C4×C59—22no—
470C2×C4×C59—22no—
471C2×C4×C59—42no—
472C2×C4×C59—41no—
473C2×C4×C59—44no—
474C2×C4×C59—42no—
475C2×C4×C59—42no—
476C2×C4×C59—41no—
477C2×C4×C59—44no—
478C2×C4×C59—42no—
479C2×C4×C59C2×#4114yes—
480C2×C4×C59C2512yes—
481C2×C4×C59C2514yes—
482C2×C4×C59C2511yescharacteristic
483C2×C4×C59C2511yescharacteristic
484C2×C4×C59C2511yescharacteristic
485C2×C4×C59C2511yescharacteristic
486C2×C4×C59C2514yes—
487C2×C4×C59C2514yes—
488C2×C4×C59C2512yes—
489C2×C4×C59C2512yes—
490C2×C4×C59C2511yescharacteristic
491C2×C4×C59C2511yescharacteristic
492C22⋊D59—216no—
493C22⋊D59—232no—
494C22⋊D59—48no—
495C22⋊D59—48no—
496C2×Dic59—216no—
497C2×Dic59—48no—
498C2×Dic59—48no—
499C2×Dic59C2518yes—
500C2×Dic59C2518yes—
501C2×Dic59C2518yes—
502D236—28no—
503D236—28no—
504D236—48no—
505D236—44no—
506C4×D59—216no—
507C4×D59—216no—
508C4×D59—416no—
509C4×D59—48no—
510Dic118—28no—
511Dic118—28no—
512Dic118—48no—
513Dic118—44no—
514#62781—591nomaximal, Sylow
515C22×C59—24no—
516C22×C59—24no—
517C22×C59—21no—
518C22×C59—21no—
519C22×C59—22no—
520C22×C59—22no—
521C22×C59—22no—
522C22×C59—48no—
523C22×C59—44no—
524C22×C59C22×#4118yes—
525C22×C59C22×#4112yes—
526C22×C59C2611yescharacteristic
527C2×D59—28no—
528C2×D59—28no—
529C2×D59—28no—
530C2×D59—816no—
531C4×C59—21no—
532C4×C59—21no—
533C4×C59—24no—
534C4×C59—24no—
535C4×C59—22no—
536C4×C59—24no—
537C4×C59—22no—
538C4×C59—21no—
539C4×C59—21no—
540C4×C59C22×#4114yes—
541C4×C59#58512yes—
542C4×C59#58512yes—
543Dic59—28no—
544Dic59—28no—
545Dic59—28no—
546#3521—598no—
547#3515—594no—
548#3514—594no—
549#3507—592no—
550#3505—594no—
551#3501—591no—
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×#41D5911yescharacteristic, complemented
565C2×C59—28no—
566C2×C59—22no—
567C2×C59—42no—
568C2×C59C23×#4111yescharacteristic
569C2×C59C2×#58511yescharacteristic
570C2×C59C2×#58511yescharacteristic
571D59—48no—
572C2×H(5,𝔽2)—592no—
573C22×#41C2×D5911yescharacteristic
574#559—594no—
575#557—594no—
576#556—598no—
577#556—594no—
578#556—598no—
579#555—598no—
580#554—594no—
581#554—598no—
582#554—594no—
583#553—5916no—
584#553—598no—
585#553—598no—
586#552—598no—
587#552—598no—
588#552—5916no—
589#552—598no—
590#552—5916no—
591#551—5916no—
592#551—5916no—
593#551—5916no—
594D4×Q8—594no—
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#544—592no—
605#543—594no—
606#542—598no—
607#541—598no—
608#539—5916no—
609#539—598no—
610#539—598no—
611#538—5916no—
612#538—598no—
613#537—592no—
614#536—594no—
615#534—598no—
616#534—594no—
617#533—598no—
618#533—592no—
619#533—592no—
620#533—592no—
621#532—592no—
622#532—592no—
623#532—592no—
624#529—598no—
625#529—5916no—
626#529—594no—
627#529—598no—
628#529—598no—
629#529—598no—
630#529—598no—
631#529—598no—
632#529—598no—
633#529—598no—
634#529—594no—
635#529—594no—
636#529—594no—
637#529—594no—
638#529—594no—
639C2×#126—598no—
640C2×#125—594no—
641C2×#124—594no—
642#525—594no—
643#525—594no—
644#525—594no—
645#525—5916no—
646C2×#123—598no—
647C2×C22⋊Q8—594no—
648C2×#121—594no—
649#520—598no—
650#520—594no—
651#518—592no—
652#518—598no—
653#518—598no—
654C4×#41—598no—
655C4×#41—594no—
656C4×#41—594no—
657C4×#41—594no—
658C4×#41C2×D5914yescomplemented
659C4×#41C2×D5914yescomplemented
660C4×#41C2×D5914yescomplemented
661C4×#41C2×D5914yescomplemented
662C2×C4×Q8—594no—
663C2×C4×Q8C2×D5911yescharacteristic, complemented
664C2×C4×Q8C2×D5911yescharacteristic, complemented
665C2×C4×D4—598no—
666C2×C4×D4—598no—
667C2×C4×D4—594no—
668C2×C4×D4C2×D5911yescharacteristic
669C2×C4×D4C2×D5911yescharacteristic
670C2×C4×D4C2×D5912yescomplemented
671C2×C4×D4C2×D5912yescomplemented
672C2×#117—598no—
673C2×#117C2×D5912yescomplemented
674C2×#117C2×D5911yescharacteristic, complemented
675C22×C42C2×D5912yescomplemented
676C22×C42C2×D5911yescharacteristic, complemented
677C59#6278111yescharacteristic, complemented, Sylow
678H(5,𝔽2)—11816no—
679C2×#41—28no—
680C2×#41—598no—
681C2×#41—594no—
682C2×#41—594no—
683C2×#41—594no—
684C2×#41C22×D5914yes—
685C2×#41C22×D5914yes—
686C22×Q8—594no—
687C22×Q8C22×D5911yescharacteristic
688C22×D4—598no—
689C22×D4—598no—
690C22×D4—594no—
691C22×D4C22×D5912yes—
692C22×D4C22×D5911yescharacteristic
693C23×C4—598no—
694C23×C4C22×D5912yes—
695C23×C4C22×D5911yescharacteristic
696C23×C4C22×D5912yes—
697C23×C4C22×D5912yes—
698C23×C4C22×D5911yescharacteristic
699C23×C4C22×D5911yescharacteristic
700C4⋊Q8—598no—
701C4⋊Q8—598no—
702C4⋊Q8—592no—
703C4⋊Q8—592no—
704C4⋊Q8—592no—
705#127—592no—
706#126—5916no—
707#126—5916no—
708#126—5916no—
709#126—598no—
710#126—5916no—
711#126—5916no—
712#126—5916no—
713#126—598no—
714#125—5916no—
715#125—598no—
716#125—5916no—
717#125—594no—
718#125—598no—
719#125—598no—
720#125—598no—
721#125—594no—
722#125—594no—
723#124—598no—
724#124—5916no—
725#124—594no—
726#124—598no—
727#124—598no—
728#124—598no—
729#124—594no—
730#124—594no—
731#123—5916no—
732#123—598no—
733#123—5916no—
734#123—5916no—
735#123—5916no—
736#123—598no—
737#123—598no—
738#123—5916no—
739#123—5916no—
740#123—5916no—
741#123—5916no—
742C22⋊Q8—598no—
743C22⋊Q8—598no—
744C22⋊Q8—594no—
745C22⋊Q8—598no—
746C22⋊Q8—598no—
747C22⋊Q8—598no—
748C22⋊Q8—594no—
749C22⋊Q8—594no—
750C22⋊Q8—594no—
751C22⋊Q8—594no—
752C22⋊Q8—594no—
753C22⋊Q8—5916no—
754C22⋊Q8—598no—
755C22⋊Q8—5916no—
756C22⋊Q8—5916no—
757C22⋊Q8—5916no—
758#121—5916no—
759#121—5916no—
760#121—594no—
761#121—598no—
762#121—598no—
763#121—598no—
764#121—594no—
765#121—594no—
766#121—594no—
767#121—594no—
768#121—594no—
769#121—598no—
770#121—5916no—
771#120—598no—
772#120—5916no—
773#120—5916no—
774C4×Q8—598no—
775C4×Q8—594no—
776C4×Q8—598no—
777C4×Q8—598no—
778C4×Q8—598no—
779C4×Q8—594no—
780C4×Q8—594no—
781C4×Q8—594no—
782C4×Q8—594no—
783C4×Q8—594no—
784C4×Q8C22×D5914yes—
785C4×Q8C22×D5914yes—
786C4×Q8C22×D5914yes—
787C4×Q8C22×D5914yes—
788C4×D4—598no—
789C4×D4—598no—
790C4×D4—5916no—
791C4×D4—598no—
792C4×D4—5916no—
793C4×D4—5916no—
794C4×D4—598no—
795C4×D4—598no—
796C4×D4—598no—
797C4×D4—598no—
798C4×D4—598no—
799C4×D4—598no—
800C4×D4—5916no—
801C4×D4—5916no—
802C4×D4—594no—
803C4×D4—594no—
804C4×D4—598no—
805C4×D4—598no—
806C4×D4—598no—
807C4×D4—594no—
808C4×D4—594no—
809C4×D4—594no—
810C4×D4—594no—
811C4×D4C22×D5914yes—
812C4×D4C22×D5914yes—
813C4×D4C22×D5914yes—
814C4×D4C22×D5914yes—
815C4×D4C22×D5918yes—
816C4×D4C22×D5918yes—
817C4×D4C22×D5918yes—
818C4×D4C22×D5918yes—
819#117—594no—
820#117—594no—
821#117—594no—
822#117—598no—
823#117—5916no—
824#117—598no—
825#117—5916no—
826#117—5916no—
827#117—5916no—
828#117—598no—
829#117—598no—
830#117C22×D5918yes—
831#117C22×D5918yes—
832#117C22×D5914yes—
833#117C22×D5914yes—
834C2×C4⋊C4—598no—
835C2×C4⋊C4—598no—
836C2×C4⋊C4—598no—
837C2×C4⋊C4—594no—
838C2×C4⋊C4—594no—
839C2×C4⋊C4—598no—
840C2×C4⋊C4—598no—
841C2×C4⋊C4C22×D5911yescharacteristic
842C2×C4⋊C4C22×D5911yescharacteristic
843C2×C4⋊C4C22×D5912yes—
844C2×C4⋊C4C22×D5912yes—
845C2×C22⋊C4—598no—
846C2×C22⋊C4—598no—
847C2×C22⋊C4—598no—
848C2×C22⋊C4—598no—
849C2×C22⋊C4—598no—
850C2×C22⋊C4—5916no—
851C2×C22⋊C4C22×D5912yes—
852C2×C22⋊C4C22×D5912yes—
853C2×C22⋊C4C22×D5912yes—
854C2×C42—598no—
855C2×C42—598no—
856C2×C42C22×D5914yes—
857C2×C42C22×D5911yescharacteristic
858C2×C42C22×D5912yes—
859C2×C42C22×D5914yes—
860C2×C42C22×D5911yescharacteristic
861C2×C42C22×D5911yescharacteristic
862C2×C42C22×D5912yes—
863C2×C42C22×D5912yes—
864C2×C42C22×D5912yes—
865C2×C42C22×D5912yes—
866C2×C42C22×D5914yes—
867C2×C42C22×D5914yes—
868C2×C42C22×D5912yes—
869C2×C42C22×D5912yes—
870C2×C42C22×D5911yescharacteristic
871C24—598no—
872C24C23×D5911yescharacteristic
873C24C23×D5912yes—
874#41—216no—
875#41—216no—
876#41—11832no—
877#41—11816no—
878#41—2368no—
879#41—2368no—
880C2×Q8—24no—
881C2×Q8—594no—
882C2×Q8—594no—
883C2×Q8—594no—
884C2×Q8—598no—
885C2×Q8—2368no—
886C2×Q8C23×D5914yes—
887C2×D4—28no—
888C2×D4—598no—
889C2×D4—5916no—
890C2×D4—598no—
891C2×D4—598no—
892C2×D4—594no—
893C2×D4—594no—
894C2×D4—594no—
895C2×D4—598no—
896C2×D4—11832no—
897C2×D4—11832no—
898C2×D4—2368no—
899C2×D4#1174568518yescomplemented
900C2×D4C23×D5918yes—
901C2×D4C23×D5914yes—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—598no—
909C22×C4—598no—
910C22×C4—598no—
911C22×C4—598no—
912C22×C4—598no—
913C22×C4—598no—
914C22×C4—5916no—
915C22×C4—23616no—
916C22×C4C23×D5911yescharacteristic
917C22×C4C23×D5911yescharacteristic
918C22×C4C23×D5914yes—
919C22×C4C23×D5914yes—
920C22×C4C23×D5914yes—
921C22×C4C23×D5912yes—
922C22×C4C23×D5912yes—
923C22×C4C23×D5912yes—
924C22×C4C23×D5912yes—
925C22×C4C23×D5914yes—
926C22×C4C23×D5911yescharacteristic
927C22×C4C23×D5912yes—
928C22×C4C23×D5914yes—
929C22×C4C23×D5914yes—
930C22×C4C23×D5911yescharacteristic
931C22×C4C23×D5912yes—
932C22×C4C23×D5911yescharacteristic
933C22×C4C23×D5912yes—
934C22×C4C23×D5912yes—
935C22×C4C23×D5912yes—
936C22×C4C23×D5911yescharacteristic
937C4⋊C4—598no—
938C4⋊C4—598no—
939C4⋊C4—594no—
940C4⋊C4—594no—
941C4⋊C4—5916no—
942C4⋊C4—598no—
943C4⋊C4—594no—
944C4⋊C4—598no—
945C4⋊C4—5916no—
946C4⋊C4—5916no—
947C4⋊C4—598no—
948C4⋊C4—598no—
949C4⋊C4—5916no—
950C4⋊C4—594no—
951C4⋊C4—598no—
952C4⋊C4—594no—
953C4⋊C4—594no—
954C4⋊C4—598no—
955C4⋊C4C23×D5914yes—
956C4⋊C4C23×D5914yes—
957C4⋊C4C23×D5918yes—
958C4⋊C4C23×D5918yes—
959C22⋊C4—598no—
960C22⋊C4—5916no—
961C22⋊C4—598no—
962C22⋊C4—598no—
963C22⋊C4—598no—
964C22⋊C4—598no—
965C22⋊C4—598no—
966C22⋊C4—598no—
967C22⋊C4—5916no—
968C22⋊C4—598no—
969C22⋊C4—5916no—
970C22⋊C4—5916no—
971C22⋊C4—5916no—
972C22⋊C4—598no—
973C22⋊C4C23×D5918yes—
974C22⋊C4C23×D5918yes—
975C22⋊C4C23×D5918yes—
976C42—598no—
977C42—5916no—
978C42—598no—
979C42—598no—
980C42C23×D5911yescharacteristic
981C42C23×D5911yescharacteristic
982C42C23×D5914yes—
983C42C23×D5912yes—
984C42C23×D5912yes—
985C42C23×D5914yes—
986C42C23×D5914yes—
987C42C23×D5912yes—
988C42C23×D5914yes—
989C42C23×D5912yes—
990C42C23×D5912yes—
991C42C23×D5914yes—
992C42C23×D5912yes—
993C42C23×D5911yescharacteristic
994C42C23×D5911yescharacteristic
995C42C23×D5914yes—
996C23—22no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—598no—
1002C23—11816no—
1003C23—2368no—
1004C23—2368no—
1005C23C2×#1174568518yes—
1006C23C24×D5912yes—
1007C23C24×D5911yescharacteristic
1008C23C24×D5914yes—
1009Q8—28no—
1010Q8—1188no—
1011Q8—1188no—
1012Q8—2368no—
1013Q8—2364no—
1014D4—216no—
1015D4—11816no—
1016D4—11832no—
1017D4—1188no—
1018D4—1188no—
1019D4—2368no—
1020D4—2364no—
1021D4—2368no—
1022D4—2368no—
1023D4C2×#11745685116yes—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—41no—
1042C2×C4—42no—
1043C2×C4—41no—
1044C2×C4—598no—
1045C2×C4—598no—
1046C2×C4—598no—
1047C2×C4—11816no—
1048C2×C4—11816no—
1049C2×C4—11816no—
1050C2×C4—23616no—
1051C2×C4—2368no—
1052C2×C4—2368no—
1053C2×C4—2368no—
1054C2×C4C2×#1174568514yes—
1055C2×C4C24×D5912yes—
1056C2×C4C24×D5914yes—
1057C2×C4C24×D5911yescharacteristic
1058C2×C4C24×D5911yescharacteristic
1059C2×C4C24×D5911yescharacteristic
1060C2×C4C24×D5911yescharacteristic
1061C2×C4C24×D5914yes—
1062C2×C4C24×D5912yes—
1063C2×C4C24×D5914yes—
1064C2×C4C24×D5912yes—
1065C2×C4C24×D5911yescharacteristic
1066C2×C4C24×D5911yescharacteristic
1067C22—21no—
1068C22—21no—
1069C22—24no—
1070C22—24no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—48no—
1075C22—44no—
1076C22—1188no—
1077C22—1188no—
1078C22—1188no—
1079C22—47216no—
1080C22C22×#1174568512yes—
1081C22C22×#1174568518yes—
1082C22C25×D5911yescharacteristic
1083C4—21no—
1084C4—21no—
1085C4—24no—
1086C4—21no—
1087C4—21no—
1088C4—24no—
1089C4—22no—
1090C4—24no—
1091C4—22no—
1092C4—1188no—
1093C4—1188no—
1094C4—1188no—
1095C4C22×#1174568514yes—
1096C4#1683823812yes—
1097C4#1683823812yes—
1098C2—22no—
1099C2—28no—
1100C2—42no—
1101C2—2368no—
1102C2C23×#1174568511yescharacteristic
1103C2C2×#1683823811yescharacteristic
1104C2C2×#1683823811yescharacteristic
subgroupG/H
centerC2×C4C24×D59
commutator, socle, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C4×#41×C59C2
hypercenterC2×C4×#41D59
hypocenterC59#62781
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21438164C2semidirect
2. #21438074C2semidirect
3. #21438057C2semidirect
4. #21437961C2semidirect
5. #21437935C2semidirect
6. #21437899C2semidirect
7. #21437860C2semidirect
8. #21437816C2semidirect
9. #21437794C2semidirect
10. #21437740C2semidirect
11. #21437711C2semidirect
12. #21437706C2semidirect
13. #21437658C2semidirect
14. #21437529C2semidirect
15. #21437505C2semidirect
16. #21437392C2semidirect
17. C2×#16837936C2semidirect
18. C4×#14273772C2semidirect
19. C2×C4×#41×C59C2semidirect
21. #16838137C22semidirect
22. #16838130C22semidirect
23. #16838125C22semidirect
24. #16838124C22semidirect
25. #16838120C22semidirect
26. #16838115C22semidirect
27. #16838112C22semidirect
28. #16838111C22semidirect
29. #16838109C22semidirect
30. #16838101C22semidirect
31. #16838098C22semidirect
32. #16838096C22semidirect
33. #16838093C22semidirect
34. #16838092C22semidirect
35. #16838091C22semidirect
36. #16838085C22semidirect
37. #16838085C22semidirect
38. #16838081C22semidirect
39. #16838076C22semidirect
40. #16838076C22semidirect
41. D4×Dic118C22semidirect
42. #16838061C22semidirect
43. #16838056C22semidirect
44. #16838051C22semidirect
45. #16838051C22semidirect
46. #16838048C22semidirect
47. #16838047C22semidirect
48. #16838040C22semidirect
49. #16838040C22semidirect
50. D4×D236C22semidirect
51. #16838033C22semidirect
52. #16838028C22semidirect
53. #16838024C22semidirect
54. #16838010C22semidirect
55. #16837999C22semidirect
56. #16837999C22semidirect
57. #16837994C22semidirect
58. #16837990C22semidirect
59. #16837985C22semidirect
61. #16837976C22semidirect
63. #16837961C22semidirect
64. #16837959C22semidirect
65. #16837959C22semidirect
66. #16837959C22semidirect
67. #16837956C22semidirect
69. #16837952C22semidirect
70. #16837952C22semidirect
71. #16837939C22semidirect
72. #16837936C22semidirect
73. #16837936C22semidirect
74. #16837936C22semidirect
75. #16837936C22semidirect
76. #16837936C22semidirect
77. #16837936C22semidirect
78. #16837936C22semidirect
79. #16837936C22semidirect
80. #16837936C22semidirect
81. #16837936C22semidirect
82. #16837936C22semidirect
83. #16837936C22semidirect
84. #16837936C22semidirect
85. #16837932C22semidirect
86. C2×#14273721C22semidirect
87. C2×#14273719C22semidirect
88. C2×#14273715C22semidirect
89. #16837913C22semidirect
90. #16837913C22semidirect
91. #16837913C22semidirect
92. #16837911C22semidirect
93. C2×#14273710C22semidirect
94. C2×#14273706C22semidirect
96. #16837883C22semidirect
97. #16837881C22semidirect
99. #16837875C22semidirect
100. #16837874C22semidirect
101. C4×#11745685C22semidirect
102. C4×#11745685C22semidirect
103. C4×#11745685C22semidirect
104. C4×#11745687C22semidirect
105. C2×C4×Dic118C22semidirect
106. C2×C4×D236C22semidirect
107. C2×C4×C22⋊D59C22semidirect
108. C4×D4×D59C22semidirect
109. C2×#14273684C22semidirect
111. C4×#41×C59C22semidirect
112. C4×#41×C59C22semidirect
113. C4×#41×C59C22semidirect
114. C4×#41×C59C22semidirect
115. C2×C4×Q8×C59C22semidirect
116. C2×C4×Q8×C59C22semidirect
119. C2×C4×D4×C59C22semidirect
120. C2×C4×D4×C59C22semidirect
121. C2×#117×C59C22semidirect
122. C2×#117×C59C22semidirect
123. C22×C42×C59C22semidirect
124. C22×C42×C59C22semidirect
326. C2×D4×C59#41semidirect
564. C2×C4×#41D59semidirect
658. C4×#41C2×D59semidirect
659. C4×#41C2×D59semidirect
660. C4×#41C2×D59semidirect
661. C4×#41C2×D59semidirect
663. C2×C4×Q8C2×D59semidirect
664. C2×C4×Q8C2×D59semidirect
670. C2×C4×D4C2×D59semidirect
671. C2×C4×D4C2×D59semidirect
673. C2×#117C2×D59semidirect
674. C2×#117C2×D59semidirect
675. C22×C42C2×D59semidirect
676. C22×C42C2×D59semidirect
677. C59#62781semidirect
899. C2×D4#11745685semidirect

Maximal subgroups

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

subgroupindex
#214381642
#214380742
#214380572
#214379612
#214379352
#214378992
#214378602
#214378162
#214377942
#214377402
#214377112
#214377062
#214376582
#214375292
#214375052
#214373922
C2×#168379362
C4×#142737722
C2×C4×#41×C592
#6278159