Finite Group Databasebeta

← D59×#3509 #29497123

Subgroups — D59×#3509 #29497123

Order 15104.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437983C211yesmaximal, characteristic, complemented
2#21437982C211yesmaximal, characteristic, complemented
3#21437981C212yesmaximal, complemented
4#21437980C211yesmaximal, characteristic, complemented
5#21437979C214yesmaximal, complemented
6#21437978C214yesmaximal, complemented
7#21437977C212yesmaximal, complemented
8#21437976C214yesmaximal, complemented
9#21437975C214yesmaximal, complemented
10#21437974C218yesmaximal, complemented
11#557×D59C214yesmaximal, complemented
12#556×D59C214yesmaximal, complemented
13#552×D59C218yesmaximal, complemented
14#541×D59C214yesmaximal, complemented
15#536×D59C212yesmaximal
16#533×D59C214yesmaximal, complemented
17#533×D59C211yesmaximal, characteristic, complemented
18C2×C4⋊Q8×D59C211yesmaximal, characteristic, complemented
19#519×D59C212yesmaximal, complemented
20C4×#41×D59C211yesmaximal, characteristic
21C59×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D59C2211yescharacteristic
23C22×Q8×D59C2212yes—
24#16838131C2214yescomplemented
25#16838130C2218yescomplemented
26#16838130C2214yescomplemented
27#16838129C2218yescomplemented
28#16838129C22116yescomplemented
29#16838128C2218yescomplemented
30#16838127C2214yescomplemented
31#16838127C2218yescomplemented
32#16838126C2214yescomplemented
33#16838125C2214yescomplemented
34#16838124C2218yescomplemented
35#16838123C2218yescomplemented
36#16838122C2214yescomplemented
37#16838121C2218yescomplemented
38#16838120C2218yescomplemented
39#16838119C22116yescomplemented
40#16838094C2218yescomplemented
41#16838093C2218yescomplemented
42#16838092C2218yescomplemented
43#16838091C2218yescomplemented
44#16838090C2218yescomplemented
45#16838089C22116yescomplemented
46#16838088C22116yescomplemented
47#16838087C2218yescomplemented
48#16838086C2218yescomplemented
49#16838085C22116yescomplemented
50#16838084C22116yescomplemented
51#16838015C2214yescomplemented
52#16838014C2214yescomplemented
53#16838013C2214yescomplemented
54#16838012C2218yescomplemented
55#16838011C22116yescomplemented
56#16838010C2218yescomplemented
57#16838009C22116yescomplemented
58#16837978C2212yes—
59#16837977C2214yes—
60#16837976C2212yes—
61#16837975C2218yes—
62#16837974C2218yes—
63#16837973C2212yes—
64#16837972C2214yes—
65#16837959C2214yescomplemented
66#16837959C2211yescharacteristic, complemented
67#16837958C2218yescomplemented
68#16837958C2212yescomplemented
69#16837957C2212yescomplemented
70#16837957C2214yescomplemented
71#16837957C2214yescomplemented
72#16837956C2218yescomplemented
73#16837956C2214yescomplemented
74#16837956C2218yescomplemented
75#16837955C2218yescomplemented
76#16837955C2212yescomplemented
77#16837954C2214yescomplemented
78#16837954C2218yescomplemented
79#16837954C2218yescomplemented
80C2×#14273727C2211yescharacteristic, complemented
81C2×#14273726C2214yescomplemented
82C2×#14273725C2212yescomplemented
83C4⋊Q8×D59C2212yes—
84C4⋊Q8×D59C2212yes—
85C4⋊Q8×D59C2214yes—
86C4⋊Q8×D59C2212yes—
87C4⋊Q8×D59C2214yes—
88C4⋊Q8×D59C2212yescomplemented
89C4⋊Q8×D59C2214yescomplemented
90C4⋊Q8×D59C2212yescomplemented
91#126×D59C22116yes—
92#125×D59C2212yes—
93#125×D59C22116yes—
94#125×D59C2218yes—
95#124×D59C2214yes—
96#123×D59C2218yes—
97C22⋊Q8×D59C2218yes—
98C22⋊Q8×D59C2214yes—
99C22⋊Q8×D59C2218yes—
100#16837880C2212yescomplemented
101#16837879C2218yescomplemented
102#16837879C2212yescomplemented
103#16837879C2212yescomplemented
104#16837878C2218yescomplemented
105#16837878C2218yescomplemented
106#41×Dic59C2211yescharacteristic
107C4×#11745689C2212yes—
108C4×#11745685C2212yes—
109C4×#11745685C2211yescharacteristic
110#16837870C2211yescharacteristic
111#16837870C2212yes—
112C4×#11745687C2214yes—
113C4×#11745687C2212yes—
114C4×Q8×D59C2218yes—
115C4×Q8×D59C2212yes—
116C4×Q8×D59C2218yes—
117C4×Q8×D59C2218yes—
118C4×Q8×D59C2214yes—
119C4×D4×D59C2214yes—
120C4×D4×D59C2212yes—
121#117×D59C2212yes—
122#117×D59C2211yescharacteristic
123#117×D59C2218yes—
124#117×D59C2212yes—
125#117×D59C2218yes—
126C2×C4⋊C4×D59C2214yes—
127C2×C42×D59C2211yescharacteristic
128C2×C42×D59C2212yes—
129C59×#557C2214yescomplemented
130C59×#556C2214yescomplemented
131C59×#552C2218yescomplemented
132C59×#541C2214yescomplemented
133C59×#536C2212yes—
134C59×#533C2214yescomplemented
135C59×#533C2211yescharacteristic, complemented
136C2×C4⋊Q8×C59C2211yescharacteristic, complemented
137C59×#519C2212yescomplemented
138C4×#41×C59C2211yescharacteristic
139C2×#11745689C2311yescharacteristic
140C2×#11745685C2312yes—
141C2×#11745685C2311yescharacteristic
142C2×#11745687C2311yescharacteristic
143C2×#11745687C2312yes—
144#41×D59—28no—
145C22×Dic118C2312yes—
146C22×Dic118C2314yes—
147C2×Q8×D59—216no—
148C2×Q8×D59C2314yes—
149C2×Q8×D59C2314yes—
150C2×Q8×D59C2314yes—
151C2×Q8×D59C2311yescharacteristic
152C2×Q8×D59C2314yes—
153C2×Q8×D59C2314yes—
154C2×D4×D59C2312yes—
155C2×D4×D59C2311yescharacteristic
156C22×C4×D59C2312yes—
157C22×C4×D59C2312yes—
158C22×C4×D59C2314yes—
159C22×C4×D59C2314yes—
160C22×C4×D59C2311yescharacteristic
161#14273727C2312yes—
162#14273727C2312yes—
163#14273727C2314yes—
164#14273727C2312yes—
165#14273727C2314yes—
166#14273726C2318yes—
167#14273726C2318yes—
168#14273726C2318yes—
169#14273726C2318yes—
170#14273726C2314yes—
171#14273726C2314yes—
172#14273726C23116yes—
173#14273725C2314yes—
174#14273725C2314yes—
175#14273725C2318yes—
176#14273725C2314yes—
177#14273725C2314yes—
178#14273725C2314yes—
179#14273722C23116yes—
180#14273722C23116yes—
181#14273722C23116yes—
182#14273721C23116yes—
183#14273720C23116yes—
184#14273720C23116yes—
185#14273720C23116yes—
186#14273719C2312yes—
187#14273719C2318yes—
188#14273719C23116yes—
189#14273718C2314yes—
190#14273718C2318yes—
191#14273718C2318yes—
192#14273718C23116yes—
193#14273718C23116yes—
194#14273717C2318yes—
195#14273717C23116yes—
196#14273717C23116yes—
197#14273717C23116yes—
198#14273717C23116yes—
199#14273717C23116yes—
200#14273717C23116yes—
201#14273716C2314yes—
202#14273715C2314yes—
203#14273714C2314yes—
204#14273713C23116yes—
205#14273712C23116yes—
206#14273711C2318yes—
207#14273710C2318yes—
208#14273709C23116yes—
209#14273708C2318yes—
210#14273707C2318yes—
211#14273707C2318yes—
212#14273707C2314yes—
213#14273706C2318yes—
214#14273706C2314yes—
215#14273706C2318yes—
216#14273705C23116yes—
217#14273705C2318yes—
218#14273705C23116yes—
219#14273704C23116yes—
220#14273704C2318yes—
221#14273704C23116yes—
222#14273703C2318yes—
223#14273703C2314yes—
224#14273703C2318yes—
225Q8×Dic59C2318yes—
226Q8×Dic59C2318yes—
227Q8×Dic59C2314yes—
228Q8×Dic59C2318yes—
229Q8×Dic59C2312yes—
230C4×Dic118C23116yes—
231C4×Dic118C23116yes—
232C4×Dic118C2318yes—
233C4×Dic118C2318yes—
234C4×Dic118C2318yes—
235C4×Dic118C2314yes—
236C4×Dic118C23116yes—
237C4×Dic118C2318yes—
238C4×Dic118C2312yes—
239C4×Dic118C2314yes—
240#14273692C2318yes—
241#14273692C2318yes—
242#14273692C2314yes—
243#14273692C23116yes—
244#14273692C23116yes—
245#14273692C2318yes—
246#14273692C23116yes—
247#14273692C2318yes—
248#14273692C2314yes—
249#14273692C2312yes—
250C4×D236C2314yes—
251C4×D236C2312yes—
252D4×Dic59C2314yes—
253D4×Dic59C2312yes—
254#14273689C2314yes—
255#14273689C2312yes—
256C4×C22⋊D59C2314yes—
257C4×C22⋊D59C2314yes—
258C4×C22⋊D59C2314yes—
259(C22⋊D59)⋊C4C2314yes—
260(C22⋊D59)⋊C4C2314yes—
261(C22⋊D59)⋊C4C2314yes—
262#14273686C2312yes—
263#14273686C2318yes—
264#14273686C2312yes—
265#14273686C2318yes—
266#14273686C2311yescharacteristic
267#14273685C2314yes—
268#14273685C2318yes—
269#14273685C2318yes—
270#14273685C2314yes—
271#14273685C23116yes—
272#14273685C2312yes—
273#14273684C2314yes—
274#14273684C23116yes—
275#14273684C2312yes—
276#14273684C2312yes—
277#14273684C23116yes—
278#14273684C2312yes—
279#14273683C2314yes—
280#14273683C23116yes—
281#14273683C2314yes—
282#14273683C2318yes—
283#14273683C2318yes—
284#14273683C2312yes—
285C2×C4⋊Dic59C2314yes—
286C2×Dic59⋊C4C2318yes—
287C4⋊C4×D59C2314yes—
288C4⋊C4×D59C23116yes—
289C4⋊C4×D59C2318yes—
290C4⋊C4×D59C23116yes—
291C4⋊C4×D59C2314yes—
292C4⋊C4×D59C2318yes—
293C4⋊C4×D59C2314yes—
294C4⋊C4×D59C2318yes—
295C4⋊C4×D59C2318yes—
296C4⋊C4×D59C2318yes—
297C4⋊C4×D59C2312yes—
298C22⋊C4×D59C2314yes—
299C22⋊C4×D59C23116yes—
300C22⋊C4×D59C2314yes—
301C22⋊C4×D59C2312yes—
302C2×C4×Dic59C2311yescharacteristic
303C2×C4×Dic59C2312yes—
304C2×C4×Dic59C2312yes—
305C2×C4×Dic59C2314yes—
306C42×D59C2314yes—
307C42×D59C2311yescharacteristic
308C42×D59C2314yes—
309C42×D59C23116yes—
310C42×D59C2311yescharacteristic
311C42×D59C2312yes—
312C42×D59C2312yes—
313C42×D59C2311yescharacteristic
314C42×D59C2311yescharacteristic
315C42×D59C2312yes—
316C42×D59C2314yes—
317C42×D59C2312yes—
318C42×D59C2312yes—
319C2×#41×C59C2311yescharacteristic
320C22×Q8×C59C2312yes—
321C4⋊Q8×C59C2312yes—
322C4⋊Q8×C59C2312yes—
323C4⋊Q8×C59C2314yes—
324C4⋊Q8×C59C2312yes—
325C4⋊Q8×C59C2314yes—
326#126×C59C23116yes—
327#125×C59C2312yes—
328#125×C59C2318yes—
329#125×C59C23116yes—
330#124×C59C2314yes—
331#123×C59C2318yes—
332C22⋊Q8×C59C2318yes—
333C22⋊Q8×C59C2318yes—
334C22⋊Q8×C59C2314yes—
335C4×Q8×C59C2318yes—
336C4×Q8×C59C2318yes—
337C4×Q8×C59C2314yes—
338C4×Q8×C59C2312yes—
339C4×Q8×C59C2318yes—
340C4×D4×C59C2314yes—
341C4×D4×C59C2312yes—
342#117×C59C2312yes—
343#117×C59C2318yes—
344#117×C59C2312yes—
345#117×C59C2311yescharacteristic
346#117×C59C2318yes—
347C2×C4⋊C4×C59C2314yes—
348C2×C42×C59C2311yescharacteristic
349C2×C42×C59C2312yes—
350C23×D59C2412yes—
351C23×D59C2411yescharacteristic
352#41×C59—24no—
353C2×Q8×C59—28no—
354C2×Q8×C59C2414yes—
355C2×Q8×C59C2414yes—
356C2×Q8×C59C2414yes—
357C2×Q8×C59C2411yescharacteristic
358C2×D4×C59C2412yes—
359C2×D4×C59C2411yescharacteristic
360C22×C4×C59C2412yes—
361C22×C4×C59C2414yes—
362C22×C4×C59C2412yes—
363C22×C4×C59C2414yes—
364C22×C4×C59C2411yescharacteristic
365C2×C22⋊D59C2412yes—
366C2×C22⋊D59C2412yes—
367C2×C22⋊D59C2412yes—
368C22×Dic59C2412yes—
369C22×Dic59C2414yes—
370C22×Dic59C2412yes—
371C22×Dic59C2414yes—
372C22×Dic59C2411yescharacteristic
373#11745689—24no—
374Q8×D59—216no—
375Q8×D59—216no—
376Q8×D59—216no—
377Q8×D59—216no—
378Q8×D59—24no—
379Q8×D59—216no—
380#11745687—28no—
381#11745687—24no—
382D4×D59—28no—
383D4×D59—24no—
384#11745685—24no—
385#11745685—28no—
386C2×D236C2412yes—
387C2×D236C2411yescharacteristic
388C2×C4×D59—216no—
389C2×C4×D59—28no—
390C2×C4×D59—28no—
391C2×C4×D59—216no—
392C2×C4×D59#4118yes—
393C2×C4×D59C2414yes—
394C2×C4×D59C2418yes—
395C2×C4×D59C2412yes—
396C2×C4×D59C2418yes—
397C2×C4×D59C2412yes—
398C2×C4×D59C2412yes—
399C2×C4×D59C2412yes—
400C2×C4×D59C2414yes—
401C2×C4×D59C2412yes—
402C2×C4×D59C2414yes—
403C2×C4×D59C2412yes—
404C2×C4×D59C2418yes—
405C2×C4×D59C2411yescharacteristic
406C2×C4×D59C2411yescharacteristic
407C2×C4×D59C2411yescharacteristic
408C2×C4×D59C2411yescharacteristic
409C2×C4×D59C2412yes—
410C2×Dic118—28no—
411C2×Dic118—216no—
412C2×Dic118C2418yes—
413C2×Dic118C2414yes—
414C2×Dic118C2418yes—
415C2×Dic118C2414yes—
416C2×Dic118C2418yes—
417C2×Dic118C2414yes—
418C2×Dic118C2411yescharacteristic
419C2×Dic118C2412yes—
420C4⋊C4×C59C2418yes—
421C4⋊C4×C59C2418yes—
422C4⋊C4×C59C2414yes—
423C4⋊C4×C59C2412yes—
424C4⋊C4×C59C2414yes—
425C4⋊C4×C59C2414yes—
426C4⋊C4×C59C24116yes—
427C4⋊C4×C59C24116yes—
428C4⋊C4×C59C2418yes—
429C22⋊C4×C59C2412yes—
430C22⋊C4×C59C2414yes—
431C22⋊C4×C59C2414yes—
432C22⋊C4×C59C24116yes—
433C42×C59C2411yescharacteristic
434C42×C59C2412yes—
435C42×C59C2411yescharacteristic
436C42×C59C2414yes—
437C42×C59C2412yes—
438C42×C59C24116yes—
439C42×C59C2414yes—
440C22⋊Dic59C2412yes—
441C22⋊Dic59C2414yes—
442C22⋊Dic59C2414yes—
443C22⋊Dic59C24116yes—
444(C2×D59)⋊C4C2414yes—
445(C2×D59)⋊C4C2418yes—
446(C2×D59)⋊C4C2414yes—
447(C2×D59)⋊C4C2414yes—
448(C2×D59)⋊C4C24116yes—
449(C2×D59)⋊C4C24116yes—
450C4⋊Dic59C2418yes—
451C4⋊Dic59C2418yes—
452C4⋊Dic59C2414yes—
453C4⋊Dic59C2412yes—
454C4⋊Dic59C2414yes—
455C4⋊Dic59C2414yes—
456C4⋊Dic59C24116yes—
457C4⋊Dic59C24116yes—
458C4⋊Dic59C2418yes—
459Dic59⋊C4C24116yes—
460Dic59⋊C4C24116yes—
461Dic59⋊C4C2418yes—
462Dic59⋊C4C2414yes—
463Dic59⋊C4C2414yes—
464Dic59⋊C4C2414yes—
465Dic59⋊C4C24116yes—
466Dic59⋊C4C2418yes—
467Dic59⋊C4C24116yes—
468Dic59⋊C4C24116yes—
469Dic59⋊C4C2418yes—
470Dic59⋊C4C24116yes—
471Dic59⋊C4C2418yes—
472C4×Dic59C2411yescharacteristic
473C4×Dic59C2412yes—
474C4×Dic59C2414yes—
475C4×Dic59C2412yes—
476C4×Dic59C2412yes—
477C4×Dic59C2411yescharacteristic
478C4×Dic59C2412yes—
479C4×Dic59C2414yes—
480C4×Dic59C2414yes—
481C4×Dic59C2412yes—
482C4×Dic59C2414yes—
483C4×Dic59C2412yes—
484C4×Dic59C24116yes—
485C4×Dic59C24116yes—
486C4×Dic59C24116yes—
487C4×Dic59C2418yes—
488C4×Dic59C2414yes—
489C23×C59C2512yes—
490C23×C59C2511yescharacteristic
491C22×D59—24no—
492C22×D59—24no—
493C22×D59—28no—
494C22×D59C2×#4114yes—
495C22×D59C2512yes—
496C22×D59C2511yescharacteristic
497C22×D59C2511yescharacteristic
498Q8×C59—28no—
499Q8×C59—28no—
500Q8×C59—22no—
501Q8×C59—28no—
502D4×C59—24no—
503D4×C59—22no—
504C2×C4×C59—28no—
505C2×C4×C59—24no—
506C2×C4×C59—24no—
507C2×C4×C59—28no—
508C2×C4×C59C2×#4114yes—
509C2×C4×C59C2514yes—
510C2×C4×C59C2518yes—
511C2×C4×C59C2512yes—
512C2×C4×C59C2512yes—
513C2×C4×C59C2518yes—
514C2×C4×C59C2511yescharacteristic
515C2×C4×C59C2511yescharacteristic
516C2×C4×C59C2512yes—
517C22⋊D59—24no—
518C22⋊D59—24no—
519C22⋊D59—24no—
520C2×Dic59—28no—
521C2×Dic59—24no—
522C2×Dic59—24no—
523C2×Dic59—28no—
524C2×Dic59C2×#4114yes—
525C2×Dic59C2514yes—
526C2×Dic59C2518yes—
527C2×Dic59C2512yes—
528C2×Dic59C2512yes—
529C2×Dic59C2518yes—
530C2×Dic59C2511yescharacteristic
531C2×Dic59C2511yescharacteristic
532C2×Dic59C2512yes—
533D236—24no—
534D236—22no—
535C4×D59—24no—
536C4×D59—216no—
537C4×D59—216no—
538C4×D59—28no—
539C4×D59—24no—
540C4×D59—216no—
541C4×D59—24no—
542C4×D59—24no—
543C4×D59—28no—
544C4×D59—24no—
545C4×D59—24no—
546C4×D59—28no—
547C4×D59C2×#4114yes—
548C4×D59C2×#4114yes—
549C4×D59C2×#4114yes—
550C4×D59C2×#4114yes—
551C4×D592−1+418yes—
552Dic118—28no—
553Dic118—28no—
554Dic118—22no—
555Dic118—28no—
556Dic118—216no—
557Dic118—216no—
558Dic118—24no—
559Dic118—216no—
560C2×#3509—591nomaximal, Sylow
561C22×C59—22no—
562C22×C59—22no—
563C22×C59—24no—
564C22×C59C22×#4112yes—
565C22×C59C2611yescharacteristic
566C2×D59—22no—
567C2×D59—28no—
568C2×D59—22no—
569C2×D59—24no—
570C2×D59—48no—
571C2×D59C22×#4112yes—
572C2×D59C22×#4112yes—
573C2×D59C2×2−1+414yes—
574C4×C59—28no—
575C4×C59—22no—
576C4×C59—28no—
577C4×C59—24no—
578C4×C59—22no—
579C4×C59C22×#4112yes—
580C4×C59C22×#4112yes—
581C4×C59C2×2−1+414yes—
582Dic59—28no—
583Dic59—22no—
584Dic59—28no—
585Dic59—24no—
586Dic59—22no—
587Dic59C22×#4112yes—
588Dic59C22×#4112yes—
589Dic59C2×2−1+414yes—
590#3509—594no—
591#3509—594no—
592#3509—598no—
593#3509—594no—
594#3509—592no—
595#3509—594no—
596#3509—591no—
597#3509—591no—
598#3509—592no—
599#3509—591no—
600#3509D5911yescharacteristic, direct product factor
601C2×#557—594no—
602C2×#556—594no—
603C2×#552—598no—
604C2×#541—594no—
605C2×#536—592no—
606C2×#533—591no—
607C2×#533—594no—
608C22×C4⋊Q8—591no—
609C2×#519—592no—
610C2×C4×#41—591no—
611C2×C59—22no—
612C2×C59—42no—
613C2×C59C23×#4111yescharacteristic
614C2×C59C22×2−1+412yes—
615D59—22no—
616D59—42no—
617D59#350914yesdirect product factor
618C22×#41—591no—
619C23×Q8—592no—
620#557—598no—
621#557—594no—
622#557—5916no—
623#557—598no—
624#557—598no—
625#557—598no—
626#557—594no—
627#557—594no—
628#557C2×D5914yescomplemented
629#556—594no—
630#556—5916no—
631#556—598no—
632#556—598no—
633#556—598no—
634#556—594no—
635#556—594no—
636#556—598no—
637#556C2×D5914yescomplemented
638#552—5916no—
639#552—5916no—
640#552—598no—
641#552—5916no—
642#552—598no—
643#552—598no—
644#552—598no—
645#552—598no—
646#552—5916no—
647#552—598no—
648#552—598no—
649#552C2×D5918yescomplemented
650#541—594no—
651#541—5916no—
652#541—5916no—
653#541—594no—
654#541—598no—
655#541—598no—
656#541—594no—
657#541C2×D5914yescomplemented
658#536—592no—
659#536—592no—
660#536—594no—
661#536—594no—
662#536—598no—
663#536—598no—
664#536—592no—
665#536C2×D5912yes—
666#533—592no—
667#533—594no—
668#533—594no—
669#533—592no—
670#533—598no—
671#533—594no—
672#533—598no—
673#533—598no—
674#533—594no—
675#533—598no—
676#533—598no—
677#533—592no—
678#533—598no—
679#533—591no—
680#533—594no—
681#533C2×D5911yescharacteristic, complemented
682#533C2×D5914yescomplemented
683C2×C4⋊Q8—592no—
684C2×C4⋊Q8—592no—
685C2×C4⋊Q8—592no—
686C2×C4⋊Q8—594no—
687C2×C4⋊Q8—592no—
688C2×C4⋊Q8—594no—
689C2×C4⋊Q8—592no—
690C2×C4⋊Q8—592no—
691C2×C4⋊Q8—594no—
692C2×C4⋊Q8—594no—
693C2×C4⋊Q8—591no—
694C2×C4⋊Q8C2×D5911yescharacteristic, complemented
695C2×#126—5916no—
696C2×#125—592no—
697C2×#125—598no—
698C2×#125—5916no—
699C2×#124—594no—
700C2×#123—598no—
701C2×C22⋊Q8—598no—
702C2×C22⋊Q8—594no—
703C2×C22⋊Q8—598no—
704#519—592no—
705#519—598no—
706#519—598no—
707#519—592no—
708#519—592no—
709#519—598no—
710#519C2×D5912yescomplemented
711C4×#41—591no—
712C4×#41—592no—
713C4×#41—594no—
714C4×#41—592no—
715C4×#41—591no—
716C4×#41—592no—
717C4×#41—592no—
718C4×#41—591no—
719C4×#41C2×D5911yescharacteristic
720C2×C4×Q8—592no—
721C2×C4×Q8—598no—
722C2×C4×Q8—598no—
723C2×C4×Q8—598no—
724C2×C4×Q8—594no—
725C2×C4×D4—594no—
726C2×C4×D4—592no—
727C2×#117—591no—
728C2×#117—592no—
729C2×#117—592no—
730C2×#117—598no—
731C2×#117—598no—
732C22×C4⋊C4—594no—
733C22×C42—591no—
734C22×C42—592no—
735C59C2×#350911yescharacteristic, complemented, Sylow
736C2×#41—591no—
737C2×#41—592no—
738C2×#41—591no—
739C2×#41—592no—
740C2×#41—591no—
741C2×#41—1188no—
742C2×#41C22×D5911yescharacteristic
743C22×Q8—594no—
744C22×Q8—594no—
745C22×Q8—594no—
746C22×Q8—591no—
747C22×Q8—594no—
748C22×Q8—594no—
749C22×Q8—594no—
750C22×Q8—592no—
751C22×Q8—11816no—
752C22×Q8C22×D5912yes—
753C22×D4—592no—
754C22×D4—591no—
755C23×C4—591no—
756C23×C4—594no—
757C23×C4—592no—
758C23×C4—594no—
759C23×C4—592no—
760C4⋊Q8—594no—
761C4⋊Q8—594no—
762C4⋊Q8—598no—
763C4⋊Q8—594no—
764C4⋊Q8—594no—
765C4⋊Q8—594no—
766C4⋊Q8—598no—
767C4⋊Q8—598no—
768C4⋊Q8—598no—
769C4⋊Q8—598no—
770C4⋊Q8—594no—
771C4⋊Q8—594no—
772C4⋊Q8—5916no—
773C4⋊Q8—592no—
774C4⋊Q8—592no—
775C4⋊Q8—594no—
776C4⋊Q8—592no—
777C4⋊Q8—594no—
778C4⋊Q8C22×D5912yes—
779C4⋊Q8C22×D5912yes—
780C4⋊Q8C22×D5914yes—
781C4⋊Q8C22×D5912yes—
782C4⋊Q8C22×D5914yes—
783#126—5916no—
784#126—5916no—
785#126—5916no—
786#126—5916no—
787#126—5916no—
788#126—5916no—
789#126—5916no—
790#126C22×D59116yes—
791#125—598no—
792#125—594no—
793#125—5916no—
794#125—5916no—
795#125—598no—
796#125—598no—
797#125—5916no—
798#125—5916no—
799#125—5916no—
800#125—5916no—
801#125—5916no—
802#125—5916no—
803#125—592no—
804#125—598no—
805#125—5916no—
806#125C22×D5912yes—
807#125C22×D5918yes—
808#125C22×D59116yes—
809#124—594no—
810#124—594no—
811#124—5916no—
812#124—594no—
813#124C22×D5914yes—
814#123—598no—
815#123—598no—
816#123—5916no—
817#123—5916no—
818#123—598no—
819#123C22×D5918yes—
820C22⋊Q8—598no—
821C22⋊Q8—594no—
822C22⋊Q8—598no—
823C22⋊Q8—598no—
824C22⋊Q8—594no—
825C22⋊Q8—598no—
826C22⋊Q8—5916no—
827C22⋊Q8—598no—
828C22⋊Q8—598no—
829C22⋊Q8—594no—
830C22⋊Q8—5916no—
831C22⋊Q8—598no—
832C22⋊Q8—5916no—
833C22⋊Q8—598no—
834C22⋊Q8—5916no—
835C22⋊Q8C22×D5918yes—
836C22⋊Q8C22×D5914yes—
837C22⋊Q8C22×D5918yes—
838C4×Q8—592no—
839C4×Q8—598no—
840C4×Q8—598no—
841C4×Q8—598no—
842C4×Q8—594no—
843C4×Q8—594no—
844C4×Q8—592no—
845C4×Q8—5916no—
846C4×Q8—598no—
847C4×Q8—5916no—
848C4×Q8—598no—
849C4×Q8—5916no—
850C4×Q8—598no—
851C4×Q8—598no—
852C4×Q8—594no—
853C4×Q8—592no—
854C4×Q8—594no—
855C4×Q8—5916no—
856C4×Q8—598no—
857C4×Q8—598no—
858C4×Q8—5916no—
859C4×Q8—5916no—
860C4×Q8—598no—
861C4×Q8—598no—
862C4×Q8—594no—
863C4×Q8C22×D5912yes—
864C4×Q8C22×D5918yes—
865C4×Q8C22×D5918yes—
866C4×Q8C22×D5918yes—
867C4×Q8C22×D5914yes—
868C4×D4—594no—
869C4×D4—592no—
870C4×D4—594no—
871C4×D4—594no—
872C4×D4—594no—
873C4×D4—594no—
874C4×D4—592no—
875C4×D4—594no—
876C4×D4—594no—
877C4×D4—594no—
878C4×D4—594no—
879C4×D4—592no—
880C4×D4C22×D5914yes—
881C4×D4C22×D5912yes—
882#117—591no—
883#117—592no—
884#117—592no—
885#117—598no—
886#117—598no—
887#117—592no—
888#117—594no—
889#117—594no—
890#117—5916no—
891#117—598no—
892#117—598no—
893#117—592no—
894#117—594no—
895#117—594no—
896#117—598no—
897#117—598no—
898#117—5916no—
899#117—592no—
900#117—592no—
901#117—592no—
902#117—594no—
903#117—5916no—
904#117—5916no—
905#117C22×D5911yescharacteristic
906#117C22×D5912yes—
907#117C22×D5912yes—
908#117C22×D5918yes—
909#117C22×D5918yes—
910C2×C4⋊C4—598no—
911C2×C4⋊C4—594no—
912C2×C4⋊C4—598no—
913C2×C4⋊C4—598no—
914C2×C4⋊C4—598no—
915C2×C4⋊C4—598no—
916C2×C4⋊C4—594no—
917C2×C4⋊C4—592no—
918C2×C4⋊C4—594no—
919C2×C4⋊C4—594no—
920C2×C4⋊C4—5916no—
921C2×C4⋊C4—5916no—
922C2×C4⋊C4—598no—
923C2×C4⋊C4C22×D5914yes—
924C2×C22⋊C4—592no—
925C2×C22⋊C4—594no—
926C2×C22⋊C4—594no—
927C2×C22⋊C4—5916no—
928C2×C42—592no—
929C2×C42—591no—
930C2×C42—592no—
931C2×C42—594no—
932C2×C42—592no—
933C2×C42—5916no—
934C2×C42—591no—
935C2×C42—594no—
936C2×C42—594no—
937C2×C42—592no—
938C2×C42—592no—
939C2×C42—591no—
940C2×C42—591no—
941C2×C42—594no—
942C2×C42—592no—
943C2×C42—592no—
944C2×C42—591no—
945C2×C42C22×D5911yescharacteristic
946C2×C42C22×D5912yes—
947C24—591no—
948C24—592no—
949#41—24no—
950#41—1188no—
951#41—1188no—
952#41—1184no—
953#41—1184no—
954#41—1184no—
955C2×Q8—28no—
956C2×Q8—598no—
957C2×Q8—594no—
958C2×Q8—598no—
959C2×Q8—594no—
960C2×Q8—598no—
961C2×Q8—594no—
962C2×Q8—592no—
963C2×Q8—591no—
964C2×Q8—11816no—
965C2×Q8—11816no—
966C2×Q8—11816no—
967C2×Q8—11816no—
968C2×Q8—11816no—
969C2×Q8—1184no—
970C2×Q8—11816no—
971C2×Q8—1188no—
972C2×Q8C23×D5914yes—
973C2×Q8C23×D5914yes—
974C2×Q8C23×D5914yes—
975C2×Q8C23×D5911yescharacteristic
976C2×D4—592no—
977C2×D4—592no—
978C2×D4—592no—
979C2×D4—592no—
980C2×D4—591no—
981C2×D4—1184no—
982C2×D4—1188no—
983C2×D4C23×D5912yes—
984C2×D4C23×D5911yescharacteristic
985C22×C4—591no—
986C22×C4—598no—
987C22×C4—591no—
988C22×C4—592no—
989C22×C4—591no—
990C22×C4—591no—
991C22×C4—591no—
992C22×C4—592no—
993C22×C4—594no—
994C22×C4—592no—
995C22×C4—594no—
996C22×C4—594no—
997C22×C4—598no—
998C22×C4—592no—
999C22×C4—598no—
1000C22×C4—592no—
1001C22×C4—592no—
1002C22×C4—592no—
1003C22×C4—594no—
1004C22×C4—594no—
1005C22×C4—592no—
1006C22×C4—592no—
1007C22×C4—598no—
1008C22×C4—1188no—
1009C22×C4—1188no—
1010C22×C4—11816no—
1011C22×C4—11816no—
1012C22×C4C23×D5912yes—
1013C22×C4C23×D5914yes—
1014C22×C4C23×D5912yes—
1015C22×C4C23×D5914yes—
1016C22×C4C23×D5911yescharacteristic
1017C4⋊C4—5916no—
1018C4⋊C4—598no—
1019C4⋊C4—5916no—
1020C4⋊C4—598no—
1021C4⋊C4—598no—
1022C4⋊C4—594no—
1023C4⋊C4—594no—
1024C4⋊C4—592no—
1025C4⋊C4—594no—
1026C4⋊C4—594no—
1027C4⋊C4—594no—
1028C4⋊C4—598no—
1029C4⋊C4—594no—
1030C4⋊C4—5916no—
1031C4⋊C4—5916no—
1032C4⋊C4—5916no—
1033C4⋊C4—5916no—
1034C4⋊C4—5916no—
1035C4⋊C4—5916no—
1036C4⋊C4—598no—
1037C4⋊C4—598no—
1038C4⋊C4—598no—
1039C4⋊C4C23×D5918yes—
1040C4⋊C4C23×D5918yes—
1041C4⋊C4C23×D5914yes—
1042C4⋊C4C23×D5912yes—
1043C4⋊C4C23×D5914yes—
1044C4⋊C4C23×D5914yes—
1045C4⋊C4C23×D59116yes—
1046C4⋊C4C23×D59116yes—
1047C4⋊C4C23×D5918yes—
1048C22⋊C4—592no—
1049C22⋊C4—594no—
1050C22⋊C4—594no—
1051C22⋊C4—5916no—
1052C22⋊C4—594no—
1053C22⋊C4—598no—
1054C22⋊C4—594no—
1055C22⋊C4—594no—
1056C22⋊C4—5916no—
1057C22⋊C4—5916no—
1058C22⋊C4C23×D5912yes—
1059C22⋊C4C23×D5914yes—
1060C22⋊C4C23×D5914yes—
1061C22⋊C4C23×D59116yes—
1062C42—591no—
1063C42—592no—
1064C42—594no—
1065C42—592no—
1066C42—592no—
1067C42—591no—
1068C42—594no—
1069C42—594no—
1070C42—594no—
1071C42—592no—
1072C42—592no—
1073C42—592no—
1074C42—5916no—
1075C42—5916no—
1076C42—5916no—
1077C42—598no—
1078C42—594no—
1079C42C23×D5911yescharacteristic
1080C42C23×D5912yes—
1081C42C23×D5911yescharacteristic
1082C42C23×D5914yes—
1083C42C23×D5912yes—
1084C42C23×D59116yes—
1085C42C23×D5914yes—
1086C23—591no—
1087C23—594no—
1088C23—591no—
1089C23—592no—
1090C23—1184no—
1091C23—1184no—
1092C23—1188no—
1093C23C24×D5912yes—
1094C23C24×D5911yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—22no—
1098Q8—28no—
1099Q8—11816no—
1100Q8—11816no—
1101Q8—11816no—
1102Q8—1184no—
1103Q8—1188no—
1104Q8—1188no—
1105Q8—1182no—
1106Q8—1188no—
1107D4—24no—
1108D4—22no—
1109D4—1184no—
1110D4—1184no—
1111D4—1184no—
1112D4—1184no—
1113D4—1182no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—594no—
1119C2×C4—591no—
1120C2×C4—592no—
1121C2×C4—591no—
1122C2×C4—594no—
1123C2×C4—594no—
1124C2×C4—594no—
1125C2×C4—594no—
1126C2×C4—598no—
1127C2×C4—594no—
1128C2×C4—598no—
1129C2×C4—592no—
1130C2×C4—598no—
1131C2×C4—592no—
1132C2×C4—1184no—
1133C2×C4—1188no—
1134C2×C4—1184no—
1135C2×C4—1188no—
1136C2×C4—1184no—
1137C2×C4—1184no—
1138C2×C4—11816no—
1139C2×C4—11816no—
1140C2×C4—11816no—
1141C2×C4—1184no—
1142C2×C4—1188no—
1143C2×C4—1184no—
1144C2×C4—1188no—
1145C2×C4—1184no—
1146C2×C4—1184no—
1147C2×C4—1188no—
1148C2×C4#41×D5914yes—
1149C2×C4C24×D5914yes—
1150C2×C4C24×D5918yes—
1151C2×C4C24×D5912yes—
1152C2×C4C24×D5918yes—
1153C2×C4C24×D5912yes—
1154C2×C4C24×D5911yescharacteristic
1155C2×C4C24×D5911yescharacteristic
1156C2×C4C24×D5912yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—592no—
1161C22—594no—
1162C22—592no—
1163C22—1188no—
1164C22—1182no—
1165C22—1182no—
1166C22—1184no—
1167C22—2368no—
1168C22C2×#41×D5912yes—
1169C22C25×D5911yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—592no—
1176C4—592no—
1177C4—594no—
1178C4—1182no—
1179C4—1188no—
1180C4—1184no—
1181C4—1182no—
1182C4—1188no—
1183C4C2×#41×D5912yes—
1184C4C2×#41×D5912yes—
1185C42−1+4×D5914yes—
1186C2—22no—
1187C2—42no—
1188C2—594no—
1189C2—1182no—
1190C2—2362no—
1191C2C22×#41×D5911yescharacteristic
1192C2C2×2−1+4×D5912yes—
subgroupG/H
center, FrattiniC22C25×D59
commutator, socle, cosocleC22×C59C26
FittingC59×#3509C2
prime radicalC2×#41×D59C22
hypercenter#3509D59
hypocenterC59C2×#3509
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #21437983C2semidirect
2. #21437982C2semidirect
3. #21437981C2semidirect
4. #21437980C2semidirect
5. #21437979C2semidirect
6. #21437978C2semidirect
7. #21437977C2semidirect
8. #21437976C2semidirect
9. #21437975C2semidirect
10. #21437974C2semidirect
11. #557×D59C2semidirect
12. #556×D59C2semidirect
13. #552×D59C2semidirect
14. #541×D59C2semidirect
16. #533×D59C2semidirect
17. #533×D59C2semidirect
18. C2×C4⋊Q8×D59C2semidirect
19. #519×D59C2semidirect
21. C59×#3509C2semidirect
24. #16838131C22semidirect
25. #16838130C22semidirect
26. #16838130C22semidirect
27. #16838129C22semidirect
28. #16838129C22semidirect
29. #16838128C22semidirect
30. #16838127C22semidirect
31. #16838127C22semidirect
32. #16838126C22semidirect
33. #16838125C22semidirect
34. #16838124C22semidirect
35. #16838123C22semidirect
36. #16838122C22semidirect
37. #16838121C22semidirect
38. #16838120C22semidirect
39. #16838119C22semidirect
40. #16838094C22semidirect
41. #16838093C22semidirect
42. #16838092C22semidirect
43. #16838091C22semidirect
44. #16838090C22semidirect
45. #16838089C22semidirect
46. #16838088C22semidirect
47. #16838087C22semidirect
48. #16838086C22semidirect
49. #16838085C22semidirect
50. #16838084C22semidirect
51. #16838015C22semidirect
52. #16838014C22semidirect
53. #16838013C22semidirect
54. #16838012C22semidirect
55. #16838011C22semidirect
56. #16838010C22semidirect
57. #16838009C22semidirect
65. #16837959C22semidirect
66. #16837959C22semidirect
67. #16837958C22semidirect
68. #16837958C22semidirect
69. #16837957C22semidirect
70. #16837957C22semidirect
71. #16837957C22semidirect
72. #16837956C22semidirect
73. #16837956C22semidirect
74. #16837956C22semidirect
75. #16837955C22semidirect
76. #16837955C22semidirect
77. #16837954C22semidirect
78. #16837954C22semidirect
79. #16837954C22semidirect
80. C2×#14273727C22semidirect
81. C2×#14273726C22semidirect
82. C2×#14273725C22semidirect
88. C4⋊Q8×D59C22semidirect
89. C4⋊Q8×D59C22semidirect
90. C4⋊Q8×D59C22semidirect
100. #16837880C22semidirect
101. #16837879C22semidirect
102. #16837879C22semidirect
103. #16837879C22semidirect
104. #16837878C22semidirect
105. #16837878C22semidirect
129. C59×#557C22semidirect
130. C59×#556C22semidirect
131. C59×#552C22semidirect
132. C59×#541C22semidirect
134. C59×#533C22semidirect
135. C59×#533C22semidirect
136. C2×C4⋊Q8×C59C22semidirect
137. C59×#519C22semidirect
600. #3509D59direct (N × H)
617. D59#3509direct (N × H)
628. #557C2×D59semidirect
637. #556C2×D59semidirect
649. #552C2×D59semidirect
657. #541C2×D59semidirect
681. #533C2×D59semidirect
682. #533C2×D59semidirect
694. C2×C4⋊Q8C2×D59semidirect
710. #519C2×D59semidirect
735. C59C2×#3509semidirect

Maximal subgroups

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

subgroupindex
#214379832
#214379822
#214379812
#214379802
#214379792
#214379782
#214379772
#214379762
#214379752
#214379742
#557×D592
#556×D592
#552×D592
#541×D592
#536×D592
#533×D592
C2×C4⋊Q8×D592
#519×D592
C4×#41×D592
C59×#35092
C2×#350959