Finite Group Databasebeta

← #29466406

Subgroups — #29466406

Order 15104.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437833C211yesmaximal, characteristic, complemented
2#21436423C212yesmaximal, complemented
3#21436349C212yesmaximal, complemented
4#21436282C212yesmaximal, complemented
5#21436102C212yesmaximal, complemented
6#21436102C212yesmaximal, complemented
7#21436087C212yesmaximal, complemented
8#21436046C212yesmaximal, complemented
9#21435998C212yesmaximal, complemented
10#21434450C211yesmaximal, characteristic, complemented
11#21434048C211yesmaximal, characteristic, complemented
12#21434005C211yesmaximal, characteristic, complemented
13#21433938C211yesmaximal, characteristic, complemented
14#21433741C211yesmaximal, characteristic, complemented
15#21433717C211yesmaximal, characteristic, complemented
16#21433595C211yesmaximal, characteristic, complemented
17#21433382C211yesmaximal, characteristic, complemented
18C2×#16837547C211yesmaximal, characteristic, complemented
19#21432955C211yesmaximal, characteristic, complemented
20#21432823C211yesmaximal, characteristic, complemented
21#21432629C211yesmaximal, characteristic, complemented
22#21432615C211yesmaximal, characteristic, complemented
23C59×#3487C211yesmaximal, characteristic, complemented
24C2×#14273752C2211yescharacteristic
25C22×#11745671C2211yescharacteristic
26C22×#11745669C2211yescharacteristic
27C2×#14273734C2211yescharacteristic
28C22×#11745664C2211yescharacteristic
29#16838117C2212yescomplemented
30#16838098C2212yescomplemented
31#16838098C2212yescomplemented
32#16838075—22no—
33#16838056C2212yescomplemented
34#16838039—22no—
35#16838030C2211yescharacteristic
36#16838025—21no—
37#16838005—21no—
38#16837966C2211yescharacteristic
39#16837947—21no—
40#16837938—21no—
41C2×#14273701C2211yescharacteristic
42#16837885C2211yescharacteristic
43#16837876C2211yescharacteristic
44C2×#14273686C2211yescharacteristic
45#16837766C2212yescomplemented
46#16837761C2212yescomplemented
47#16837756C2212yescomplemented
48#16837748C2212yescomplemented
49#16837740C2211yescharacteristic, complemented
50#16837740C2211yescharacteristic, complemented
51#16837735C2211yescharacteristic, complemented
52#16837730C2211yescharacteristic, complemented
53#16837723C2212yescomplemented
54#16837723C2211yescharacteristic, complemented
55#16837723C2212yescomplemented
56#16837723C2211yescharacteristic, complemented
57#16837718C2211yescharacteristic, complemented
58#16837718C2212yescomplemented
59#16837713C2211yescharacteristic, complemented
60#16837713C2212yescomplemented
61#16837709C2212yescomplemented
62#16837709C2212yescomplemented
63#16837697C2212yescomplemented
64#16837687C2212yescomplemented
65#16837653C2212yescomplemented
66#16837653C2212yescomplemented
67#16837653C2212yescomplemented
68#16837650C2212yescomplemented
69#16837636C2212yescomplemented
70#16837636C2212yescomplemented
71#16837636C2212yescomplemented
72#16837633C2212yescomplemented
73#16837614C2212yescomplemented
74#16837614C2212yescomplemented
75#16837594C2212yescomplemented
76#16837594C2212yescomplemented
77#16837547C2212yes—
78#16837547C2212yes—
79#16837547C2212yes—
80#16837547C2212yes—
81#16837547C2212yescomplemented
82#16837547C2212yescomplemented
83#16837541C2212yescomplemented
84#16837541C2212yescomplemented
85#16837500C2212yescomplemented
86#16837500C2212yescomplemented
87C4×#11745671C2212yescomplemented
88C4×#11745671C2212yescomplemented
89#16837480C2212yescomplemented
90#16837474C2212yescomplemented
91#16837474C2212yescomplemented
92D4×C59⋊C8C2212yescomplemented
93#16837445C2211yescharacteristic
94#16837438C2211yescharacteristic
95#16837438C2211yescharacteristic
96#16837429C2211yescharacteristic
97#16837411C2211yescharacteristic
98#16837411C2211yescharacteristic
99#16837411C2212yescomplemented
100#16837407C2211yescharacteristic
101#16837407C2211yescharacteristic
102#16837406C2211yescharacteristic
103#16837403C2211yescharacteristic
104#16837403C2212yescomplemented
105#16837403C2212yescomplemented
106#16837403C2212yescomplemented
107#16837398C2211yescharacteristic
108#16837398C2211yescharacteristic
109#16837398C2212yescomplemented
110#16837398C2212yescomplemented
111#16837398C2212yescomplemented
112C2×#14273651C2211yescharacteristic
113C2×#14273651C2212yescomplemented
114C2×#14273648C2211yescharacteristic
115#16837369C2211yescharacteristic
116C2×C22⋊(C59⋊C8)C2211yescharacteristic
117#16837358C2211yescharacteristic
118C2×2−1+4×C59C2211yescharacteristic
119C22×#41×C59C2211yescharacteristic
120C59×#550—21no—
121C59×#550—21no—
122C59×#550C2212yescomplemented
123C59×#550C2212yescomplemented
124C59×#548—21no—
125C59×#548—21no—
126C59×#548C2212yescomplemented
127C59×#548C2212yescomplemented
128C59×#535—22no—
129C59×#535C2211yescharacteristic
130C59×#535C2211yescharacteristic
131C59×#525—22no—
132C59×#525C2211yescharacteristic
133C59×#525C2211yescharacteristic
134C59×#519C2211yescharacteristic
135C2×#11745687—22no—
136C22×D236C2311yescharacteristic
137C22×C22⋊D59—21no—
138#14273752—42no—
139C2×#11745671—24no—
140C2×#11745671C2312yes—
141C2×#11745671C2312yes—
142C2×#11745671C2312yes—
143C2×#11745669—42no—
144C2×#11745669C2312yes—
145C2×#11745669C2312yes—
146C2×#11745669C2312yes—
147#14273734—42no—
148C2×#11745664—42no—
149C2×#11745664C2311yescharacteristic
150C2×#11745664C2311yescharacteristic
151C2×#11745664C2312yes—
152C2×#11745664C2312yes—
153C22×C59⋊C8C2311yescharacteristic
154C22×C59⋊C8C2311yescharacteristic
155C22×C59⋊C8C2312yes—
156C22×C59⋊C8C2312yes—
157#14273727C2312yes—
158#14273726—21no—
159#14273723—21no—
160#14273722—22no—
161#14273722—22no—
162#14273719C2312yes—
163#14273718—21no—
164#14273716—21no—
165#14273713—22no—
166#14273713—22no—
167#14273711—22no—
168#14273711—22no—
169#14273709—22no—
170#14273709—22no—
171#14273707—22no—
172#14273704—22no—
173#14273701—21no—
174#14273701—21no—
175#14273701C2312yes—
176#14273701C2312yes—
177#14273701C2312yes—
178#14273701C2312yes—
179#14273699—22no—
180#14273699—22no—
181#14273698—22no—
182#14273695—22no—
183Q8×Dic59—21no—
184C4×D236C2312yes—
185C4×D236C2312yes—
186D4×Dic59—21no—
187D4×Dic59—22no—
188#14273689—21no—
189#14273689—21no—
190(C22⋊D59)⋊C4—22no—
191(C22⋊D59)⋊C4—22no—
192#14273686—21no—
193#14273686—21no—
194#14273686C2311yescharacteristic
195#14273686C2311yescharacteristic
196#14273686C2311yescharacteristic
197#14273686C2311yescharacteristic
198#14273686C2312yes—
199#14273685—22no—
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2312yes—
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×C22⋊Dic59—21no—
205C2×(C2×D59)⋊C4—21no—
206C22⋊C4×D59—22no—
207C2×C4×Dic59—21no—
208#14273660C2311yescharacteristic
209#14273660C2311yescharacteristic
210#14273660C2312yes—
211#14273660C2311yescharacteristic
212#14273660C2311yescharacteristic
213#14273658C2312yes—
214#14273658C2311yescharacteristic
215#14273658C2311yescharacteristic
216#14273658C2311yescharacteristic
217#14273658C2311yescharacteristic
218C4⋊(C59⋊C8)C2312yes—
219C4⋊(C59⋊C8)C2312yes—
220#14273651C2312yes—
221#14273651C2312yes—
222#14273651C2312yes—
223#14273651C2311yescharacteristic
224#14273651C2312yes—
225#14273651C2311yescharacteristic
226#14273651C2311yescharacteristic
227#14273651C2311yescharacteristic
228#14273651C2312yes—
229#14273651C2312yes—
230#14273651C2312yes—
231#14273648C2312yes—
232#14273648C2312yes—
233#14273648C2312yes—
234#14273648C2312yes—
235#14273648C2312yes—
236#14273648C2311yescharacteristic
237#14273648C2311yescharacteristic
238#14273648C2311yescharacteristic
239#14273648C2311yescharacteristic
240#14273648C2312yes—
241#14273648C2312yes—
242#14273647C2312yes—
243#14273647C2312yes—
244C22⋊(C59⋊C8)C2312yes—
245C22⋊(C59⋊C8)C2311yescharacteristic
246C22⋊(C59⋊C8)C2312yes—
247C22⋊(C59⋊C8)C2311yescharacteristic
248C22⋊(C59⋊C8)C2311yescharacteristic
249C22⋊(C59⋊C8)C2311yescharacteristic
250#14273638C2312yes—
251C4×C59⋊C8C2312yes—
2522−1+4×C59—24no—
2532−1+4×C59—42no—
254C2×#41×C59—22no—
255C2×#41×C59—21no—
256C2×#41×C59—21no—
257C2×#41×C59—21no—
258C2×#41×C59—24no—
259C2×#41×C59—42no—
260C2×#41×C59C2311yescharacteristic
261C2×#41×C59C2312yes—
262C2×#41×C59C2312yes—
263C2×#41×C59C2312yes—
264C2×#41×C59C2311yescharacteristic
265C22×Q8×C59—21no—
266C22×Q8×C59C2312yes—
267C22×Q8×C59C2311yescharacteristic
268C22×D4×C59—21no—
269C22×D4×C59C2311yescharacteristic
270C23×C4×C59—21no—
271C23×C4×C59C2311yescharacteristic
272#127×C59—22no—
273#127×C59—22no—
274#127×C59—21no—
275#127×C59C2312yes—
276#124×C59—21no—
277#124×C59—22no—
278#124×C59—22no—
279#124×C59C2312yes—
280#123×C59—21no—
281#123×C59D412yes—
282C22⋊Q8×C59—22no—
283C22⋊Q8×C59—22no—
284C22⋊Q8×C59D411yescharacteristic
285C22⋊Q8×C59D411yescharacteristic
286C22⋊Q8×C59C2311yescharacteristic
287C22⋊Q8×C59C2311yescharacteristic
288#121×C59—22no—
289#121×C59—22no—
290#121×C59—21no—
291#121×C59—21no—
292#121×C59—22no—
293#121×C59—22no—
294#121×C59—22no—
295#121×C59—22no—
296#121×C59D411yescharacteristic
297#121×C59D411yescharacteristic
298#121×C59C2311yescharacteristic
299#121×C59C2312yes—
300#121×C59C2312yes—
301#121×C59C2311yescharacteristic
302#120×C59—21no—
303#120×C59—22no—
304#120×C59—22no—
305#120×C59D412yes—
306C4×Q8×C59—21no—
307C4×Q8×C59—21no—
308C4×Q8×C59C2312yes—
309C4×Q8×C59C2312yes—
310C4×D4×C59—21no—
311C4×D4×C59—21no—
312C4×D4×C59—22no—
313C4×D4×C59—22no—
314C4×D4×C59—22no—
315C4×D4×C59—22no—
316C4×D4×C59C2312yes—
317C4×D4×C59C2312yes—
318#117×C59—22no—
319#117×C59C2311yescharacteristic
320#117×C59C2311yescharacteristic
321C24×C59—21no—
322C24×C59C2×D411yescharacteristic
323C23×D59—21no—
324#41×C59—22no—
325#41×C59—22no—
326#41×C59—24no—
327#41×C59—24no—
328#41×C59—24no—
329#41×C59—22no—
330#41×C59—22no—
331#41×C59—42no—
332#41×C59—42no—
333#41×C59—42no—
334#41×C59—48no—
335#41×C59—44no—
336#41×C59—44no—
337#41×C59—44no—
338C2×Q8×C59—21no—
339C2×Q8×C59—22no—
340C2×Q8×C59—22no—
341C2×Q8×C59—24no—
342C2×Q8×C59—42no—
343C2×Q8×C59—44no—
344C2×Q8×C59C2×D411yescharacteristic
345C2×Q8×C59#4114yescomplemented
346C2×Q8×C59C2411yescharacteristic
347C2×Q8×C59C2412yes—
348C2×D4×C59—21no—
349C2×D4×C59—22no—
350C2×D4×C59—22no—
351C2×D4×C59—22no—
352C2×D4×C59—22no—
353C2×D4×C59—22no—
354C2×D4×C59—21no—
355C2×D4×C59—21no—
356C2×D4×C59—21no—
357C2×D4×C59—22no—
358C2×D4×C59—22no—
359C2×D4×C59—22no—
360C2×D4×C59—22no—
361C2×D4×C59—44no—
362C2×D4×C59C2×D412yes—
363C2×D4×C59C2×D411yescharacteristic
364C2×D4×C59C2×D412yes—
365C2×D4×C59C2×D412yes—
366C2×D4×C59C2412yes—
367C2×D4×C59C2411yescharacteristic
368C22×C4×C59—21no—
369C22×C4×C59—22no—
370C22×C4×C59—22no—
371C22×C4×C59—22no—
372C22×C4×C59—22no—
373C22×C4×C59—21no—
374C22×C4×C59—22no—
375C22×C4×C59—22no—
376C22×C4×C59—44no—
377C22×C4×C59C2×D411yescharacteristic
378C22×C4×C59C2×D411yescharacteristic
379C22×C4×C59C2×D411yescharacteristic
380C22×C4×C59C2412yes—
381C22×C4×C59C2411yescharacteristic
382C22×C4×C59C2411yescharacteristic
383C22×C4×C59C2411yescharacteristic
384C2×C22⋊D59—22no—
385C2×C22⋊D59—22no—
386C2×C22⋊D59—22no—
387C2×C22⋊D59—22no—
388C2×C22⋊D59—82no—
389C22×Dic59—21no—
390C22×Dic59—21no—
391C22×Dic59—21no—
392C22×Dic59—22no—
393#11745687—84no—
394C2×D236—22no—
395C2×D236—22no—
396C2×D236—21no—
397C2×D236C2412yes—
398C2×C4×D59—22no—
399C2×C4×D59—22no—
400C2×Dic118—22no—
401C4⋊C4×C59—22no—
402C4⋊C4×C59—22no—
403C4⋊C4×C59—21no—
404C4⋊C4×C59—21no—
405C4⋊C4×C59C2×D411yescharacteristic
406C4⋊C4×C59C2×D411yescharacteristic
407C4⋊C4×C59C2×D412yes—
408C4⋊C4×C59C2×D412yes—
409C4⋊C4×C59C2411yescharacteristic
410C4⋊C4×C59C2411yescharacteristic
411C22⋊C4×C59—21no—
412C22⋊C4×C59—21no—
413C22⋊C4×C59—21no—
414C22⋊C4×C59—21no—
415C22⋊C4×C59—21no—
416C22⋊C4×C59—22no—
417C22⋊C4×C59—22no—
418C22⋊C4×C59—22no—
419C22⋊C4×C59—22no—
420C22⋊C4×C59C2×D412yes—
421C22⋊C4×C59C2×D412yes—
422C22⋊C4×C59C2×D412yes—
423C22⋊C4×C59C2×D412yes—
424C22⋊C4×C59C2×D412yes—
425C42×C59—22no—
426C42×C59—22no—
427C42×C59—21no—
428C42×C59C2412yes—
429C22⋊Dic59—21no—
430C22⋊Dic59—21no—
431C22⋊Dic59—21no—
432C22⋊Dic59—21no—
433C22⋊Dic59—22no—
434#11745671—24no—
435#11745671—24no—
436#11745671—42no—
437#11745669—42no—
438#11745669—42no—
439#11745669—42no—
440(C2×D59)⋊C4—22no—
441(C2×D59)⋊C4—22no—
442(C2×D59)⋊C4—22no—
443(C2×D59)⋊C4—22no—
444(C2×D59)⋊C4—22no—
445(C2×D59)⋊C4—22no—
446C4⋊Dic59—21no—
447C4⋊Dic59—21no—
448C4⋊Dic59—21no—
449C4⋊Dic59—22no—
450C4⋊Dic59—22no—
451C4⋊Dic59C2411yescharacteristic
452C4⋊Dic59C2412yes—
453C4⋊Dic59C2411yescharacteristic
454C4⋊Dic59C2411yescharacteristic
455C4⋊Dic59C2411yescharacteristic
456Dic59⋊C4—22no—
457Dic59⋊C4—22no—
458C4×Dic59—21no—
459C4×Dic59—21no—
460C4×Dic59—21no—
461C4×Dic59—21no—
462C4×Dic59—22no—
463#11745664—22no—
464#11745664—22no—
465#11745664—42no—
466#11745664—42no—
467C2×C59⋊C8—22no—
468C2×C59⋊C8—22no—
469C2×C59⋊C8—42no—
470C2×C59⋊C8—42no—
471C2×C59⋊C8C2411yescharacteristic
472C2×C59⋊C8C2412yes—
473C2×C59⋊C8C2411yescharacteristic
474C2×C59⋊C8C2412yes—
475C2×C59⋊C8C2411yescharacteristic
476C2×C59⋊C8C2411yescharacteristic
477C23×C59—22no—
478C23×C59—22no—
479C23×C59—21no—
480C23×C59—41no—
481C23×C59—41no—
482C23×C59—42no—
483C23×C59—81no—
484C23×C59—81no—
485C23×C59C22×D411yescharacteristic
486C23×C59C22×D412yes—
487C23×C59C22×D411yescharacteristic
488C23×C59C22×D411yescharacteristic
489C22×D59—22no—
490C22×D59—42no—
491C22×D59—81no—
492C22×D59—81no—
493Q8×C59—24no—
494Q8×C59—22no—
495Q8×C59—22no—
496Q8×C59—21no—
497Q8×C59—21no—
498Q8×C59—44no—
499Q8×C59C2×#4114yes—
500D4×C59—24no—
501D4×C59—22no—
502D4×C59—22no—
503D4×C59—21no—
504D4×C59—22no—
505D4×C59—21no—
506D4×C59—42no—
507D4×C59—42no—
508D4×C59—44no—
509D4×C59—44no—
510D4×C59—44no—
511D4×C59—42no—
512D4×C59—42no—
513D4×C59—82no—
514D4×C59—82no—
515D4×C59—81no—
516D4×C59—82no—
517D4×C59—82no—
518D4×C59—81no—
519C2×C4×C59—22no—
520C2×C4×C59—24no—
521C2×C4×C59—22no—
522C2×C4×C59—22no—
523C2×C4×C59—22no—
524C2×C4×C59—21no—
525C2×C4×C59—21no—
526C2×C4×C59—22no—
527C2×C4×C59—21no—
528C2×C4×C59—22no—
529C2×C4×C59—21no—
530C2×C4×C59—21no—
531C2×C4×C59—21no—
532C2×C4×C59—21no—
533C2×C4×C59—44no—
534C2×C4×C59—44no—
535C2×C4×C59—44no—
536C2×C4×C59—44no—
537C2×C4×C59—42no—
538C2×C4×C59C22×D411yescharacteristic
539C2×C4×C59C22×D412yes—
540C2×C4×C59C22×D412yes—
541C2×C4×C59C22×D412yes—
542C2×C4×C59C22×D411yescharacteristic
543C2×C4×C59C22×D411yescharacteristic
544C2×C4×C59C2×#4112yes—
545C2×C4×C59H(5,𝔽2)12yes—
546C2×C4×C59C2511yescharacteristic
547C22⋊D59—44no—
548C22⋊D59—82no—
549C22⋊D59—82no—
550C22⋊D59—82no—
551C2×Dic59—21no—
552C2×Dic59—21no—
553C2×Dic59—21no—
554C2×Dic59—21no—
555C2×Dic59—22no—
556C2×Dic59—42no—
557C2×Dic59—82no—
558C2×Dic59—81no—
559C2×Dic59—81no—
560D236—22no—
561D236—22no—
562D236—42no—
563C4×D59—82no—
564C4×D59—82no—
565Dic118—82no—
566C59⋊C8—21no—
567C59⋊C8—21no—
568C59⋊C8—21no—
569C59⋊C8—21no—
570C59⋊C8—22no—
571C59⋊C8—22no—
572#61189—591nomaximal, Sylow
573C22×C59—21no—
574C22×C59—21no—
575C22×C59—21no—
576C22×C59—22no—
577C22×C59—21no—
578C22×C59—21no—
579C22×C59—22no—
580C22×C59—21no—
581C22×C59—21no—
582C22×C59—21no—
583C22×C59—22no—
584C22×C59—41no—
585C22×C59—42no—
586C22×C59—41no—
587C22×C59—42no—
588C22×C59—41no—
589C22×C59—42no—
590C22×C59—82no—
591C22×C59—84no—
592C22×C59#54612yes—
593C22×C59C23×D411yescharacteristic
594C2×D59—42no—
595C2×D59—42no—
596C2×D59—42no—
597C2×D59—162no—
598C4×C59—22no—
599C4×C59—22no—
600C4×C59—21no—
601C4×C59—21no—
602C4×C59—24no—
603C4×C59—22no—
604C4×C59—41no—
605C4×C59—41no—
606C4×C59—41no—
607C4×C59#54612yes—
608C4×C59C22×#4111yescharacteristic
609C4×C59C2×H(5,𝔽2)11yescharacteristic
610Dic59—41no—
611Dic59—41no—
612Dic59—41no—
613Dic59—42no—
614Dic59—41no—
615#3494—591no—
616#3487D5911yescharacteristic, complemented
617#3332—592no—
618#3326—592no—
619#3321—592no—
620#3309—592no—
621#3309—592no—
622#3308—592no—
623#3305—592no—
624#3301—592no—
625#3136—591no—
626#3096—591no—
627#3091—591no—
628#3082—591no—
629#3058—591no—
630#3055—591no—
631#3041—591no—
632#3010—591no—
633C2×#449—591no—
634#2949—591no—
635#2933—591no—
636#2898—591no—
637#2896—591no—
638C2×C59—22no—
639C2×C59—42no—
640C2×C59—41no—
641C2×C59—41no—
642C2×C59—81no—
643C2×C59—82no—
644C2×C59C2×#54611yescharacteristic
645C2×C59#358411yescharacteristic
646C2×C59#358511yescharacteristic
647D59—82no—
648C2×2−1+4C2×D5911yescharacteristic
649C22×#41C2×D5911yescharacteristic
650C2×AGL(1,ℤ/8)—591no—
651C22×SD16—591no—
652C22×D8—591no—
653C2×#131—591no—
654C22×M16—591no—
655#555—592no—
656#553—592no—
657#553—592no—
658#551—1182no—
659#550—21no—
660#550—21no—
661#550C2×D5912yescomplemented
662#550C2×D5912yescomplemented
663#548—21no—
664#548—21no—
665#548C2×D5912yescomplemented
666#548C2×D5912yescomplemented
667#547—592no—
668#546—1182no—
669#544—591no—
670#542—1181no—
671#540—1181no—
672#535—22no—
673#535—591no—
674#535C2×D5911yescharacteristic
675#535C2×D5911yescharacteristic
676#532—1181no—
677#529—1181no—
678#525—22no—
679#525C2×D5911yescharacteristic
680#525C2×D5911yescharacteristic
681C2×#121—591no—
682#520—591no—
683#519C2×D5911yescharacteristic
684#518—591no—
685C2×#117—591no—
686#490—592no—
687#489—592no—
688#488—592no—
689#486—592no—
690#485—591no—
691#485—591no—
692#484—591no—
693#483—591no—
694#482—591no—
695#482—591no—
696#482—592no—
697#482—592no—
698#481—591no—
699#481—592no—
700#480—591no—
701#480—592no—
702#479—592no—
703#479—592no—
704#477—592no—
705#475—592no—
706#469—592no—
707#469—592no—
708#469—592no—
709#468—592no—
710#466—592no—
711#466—592no—
712#466—592no—
713#465—592no—
714#463—592no—
715#463—592no—
716#459—592no—
717#459—592no—
718#449—592no—
719#449—592no—
720#449—592no—
721#449—592no—
722#449—592no—
723#449—592no—
724#448—592no—
725#448—592no—
726#440—592no—
727#440—592no—
728C4×SD16—592no—
729C4×SD16—592no—
730#436—592no—
731#435—592no—
732#435—592no—
733C8×D4—592no—
734#428—591no—
735#427—591no—
736#427—591no—
737#424—591no—
738#419—591no—
739#419—591no—
740#419—592no—
741#418—591no—
742#418—591no—
743#418—591no—
744#417—592no—
745#417—592no—
746#417—591no—
747#417—592no—
748#416—591no—
749#416—591no—
750#416—592no—
751#416—592no—
752#416—592no—
753C2×#103—591no—
754C2×#103—592no—
755C2×#102—591no—
756#408—591no—
757C2×C22⋊C8—591no—
758#405—591no—
759C59#6118911yescharacteristic, complemented, Sylow
7602−1+4—24no—
7612−1+4—42no—
762C2×#41—22no—
763C2×#41—21no—
764C2×#41—21no—
765C2×#41—21no—
766C2×#41—24no—
767C2×#41—42no—
768C2×#41—1182no—
769C2×#41C22×D5911yescharacteristic
770C2×#41C22×D5912yes—
771C2×#41C22×D5912yes—
772C2×#41C22×D5912yes—
773C2×#41C22×D5911yescharacteristic
774C22×Q8—21no—
775C22×Q8C22×D5912yes—
776C22×Q8C22×D5911yescharacteristic
777C22×D4—21no—
778C22×D4—591no—
779C22×D4—1181no—
780C22×D4C22×D5911yescharacteristic
781C23×C4—21no—
782C23×C4C22×D5911yescharacteristic
783AGL(1,ℤ/8)—2362no—
784C2×SD16—592no—
785C2×SD16—592no—
786C2×SD16—592no—
787C2×SD16—1184no—
788C2×D8—592no—
789C2×D8—592no—
790C2×D8—592no—
791C2×D8—2362no—
792#131—2362no—
793C2×M16—591no—
794C2×M16—591no—
795C2×M16—592no—
796C2×M16—592no—
797C2×M16—2362no—
798C22×C8—591no—
799C22×C8—591no—
800C22×C8—592no—
801C22×C8—592no—
802C4⋊Q8—592no—
803C4⋊Q8—1181no—
804#127—22no—
805#127—22no—
806#127—21no—
807#127—1181no—
808#127C22×D5912yes—
809#126—1182no—
810#126—1182no—
811#125—592no—
812#125—1181no—
813#124—21no—
814#124—22no—
815#124—22no—
816#124—1181no—
817#124—1182no—
818#124—1182no—
819#124C22×D5912yes—
820#123—21no—
821#123—1182no—
822#123—1182no—
823#123—1182no—
824#123—1182no—
825#123C22⋊D5912yes—
826C22⋊Q8—22no—
827C22⋊Q8—22no—
828C22⋊Q8—1182no—
829C22⋊Q8—1182no—
830C22⋊Q8C22⋊D5911yescharacteristic
831C22⋊Q8C22⋊D5911yescharacteristic
832C22⋊Q8C22×D5911yescharacteristic
833C22⋊Q8C22×D5911yescharacteristic
834#121—22no—
835#121—22no—
836#121—21no—
837#121—21no—
838#121—22no—
839#121—22no—
840#121—22no—
841#121—22no—
842#121—592no—
843#121—592no—
844#121—592no—
845#121—592no—
846#121—1182no—
847#121—1182no—
848#121—1182no—
849#121—1181no—
850#121—1181no—
851#121C22⋊D5911yescharacteristic
852#121C22⋊D5911yescharacteristic
853#121C22×D5911yescharacteristic
854#121C22×D5911yescharacteristic
855#121C22×D5912yes—
856#121C22×D5912yes—
857#120—21no—
858#120—22no—
859#120—22no—
860#120—1182no—
861#120C22⋊D5912yes—
862C4×Q8—21no—
863C4×Q8—21no—
864C4×Q8—1181no—
865C4×Q8C22×D5912yes—
866C4×Q8C22×D5912yes—
867C4×D4—21no—
868C4×D4—21no—
869C4×D4—22no—
870C4×D4—22no—
871C4×D4—22no—
872C4×D4—22no—
873C4×D4—592no—
874C4×D4—592no—
875C4×D4—1181no—
876C4×D4—1182no—
877C4×D4—1181no—
878C4×D4—1181no—
879C4×D4—1182no—
880C4×D4—1182no—
881C4×D4C22×D5912yes—
882C4×D4C22×D5912yes—
883#117—22no—
884#117—591no—
885#117—591no—
886#117—591no—
887#117—591no—
888#117—592no—
889#117—1181no—
890#117—1181no—
891#117—1182no—
892#117C22×D5911yescharacteristic
893#117C22×D5911yescharacteristic
894C2×C4⋊C4—591no—
895C2×C4⋊C4—591no—
896C2×C4⋊C4—591no—
897C2×C4⋊C4—592no—
898C2×C22⋊C4—1181no—
899C2×C22⋊C4—1181no—
900C2×C22⋊C4—1182no—
901C2×C42—1181no—
902#107—591no—
903#107—591no—
904#107—591no—
905#107—591no—
906#107—592no—
907#106—591no—
908#106—591no—
909#106—591no—
910#106—591no—
911#106—592no—
912C4⋊C8—592no—
913C4⋊C8—592no—
914#103—592no—
915#103—591no—
916#103—592no—
917#103—592no—
918#103—592no—
919#103—592no—
920#103—592no—
921#103—592no—
922#103—591no—
923#103—591no—
924#103—591no—
925#102—592no—
926#102—592no—
927#102—591no—
928#102—591no—
929#102—592no—
930#102—592no—
931#102—592no—
932#102—592no—
933#102—592no—
934#102—591no—
935#102—591no—
936#102—592no—
937#102—592no—
938C22⋊C8—591no—
939C22⋊C8—591no—
940C22⋊C8—591no—
941C22⋊C8—591no—
942C22⋊C8—592no—
943C22⋊C8—592no—
944#97—592no—
945C4×C8—592no—
946C24—21no—
947C24—1181no—
948C24C2×C22⋊D5911yescharacteristic
949#41—22no—
950#41—22no—
951#41—24no—
952#41—24no—
953#41—24no—
954#41—22no—
955#41—22no—
956#41—42no—
957#41—42no—
958#41—42no—
959#41—48no—
960#41—44no—
961#41—44no—
962#41—44no—
963#41—4724no—
964C2×Q8—21no—
965C2×Q8—22no—
966C2×Q8—22no—
967C2×Q8—24no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—1182no—
971C2×Q8#1174568714yescomplemented
972C2×Q8C2×C22⋊D5911yescharacteristic
973C2×Q8C23×D5911yescharacteristic
974C2×Q8C23×D5912yes—
975C2×D4—21no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—22no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—21no—
982C2×D4—21no—
983C2×D4—21no—
984C2×D4—22no—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—44no—
989C2×D4—592no—
990C2×D4—1182no—
991C2×D4—1182no—
992C2×D4—1182no—
993C2×D4—1182no—
994C2×D4—1181no—
995C2×D4—1182no—
996C2×D4—1182no—
997C2×D4—4722no—
998C2×D4C2×C22⋊D5912yes—
999C2×D4C2×C22⋊D5911yescharacteristic
1000C2×D4C2×C22⋊D5912yes—
1001C2×D4C2×C22⋊D5912yes—
1002C2×D4C23×D5912yes—
1003C2×D4C23×D5911yescharacteristic
1004C22×C4—21no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—22no—
1009C22×C4—21no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—44no—
1013C22×C4—1181no—
1014C22×C4—1181no—
1015C22×C4—1182no—
1016C22×C4—1181no—
1017C22×C4—1182no—
1018C22×C4—1182no—
1019C22×C4C2×C22⋊D5911yescharacteristic
1020C22×C4C2×C22⋊D5911yescharacteristic
1021C22×C4C2×C22⋊D5911yescharacteristic
1022C22×C4C23×D5911yescharacteristic
1023C22×C4C23×D5912yes—
1024C22×C4C23×D5911yescharacteristic
1025C22×C4C23×D5911yescharacteristic
1026SD16—1184no—
1027SD16—1184no—
1028SD16—2362no—
1029D8—2362no—
1030D8—2362no—
1031D8—2362no—
1032M16—1182no—
1033M16—1182no—
1034M16—2362no—
1035M16—2362no—
1036C2×C8—591no—
1037C2×C8—592no—
1038C2×C8—591no—
1039C2×C8—592no—
1040C2×C8—591no—
1041C2×C8—591no—
1042C2×C8—1182no—
1043C2×C8—1182no—
1044C2×C8—2362no—
1045C2×C8—2362no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—591no—
1051C4⋊C4—592no—
1052C4⋊C4—591no—
1053C4⋊C4—591no—
1054C4⋊C4—591no—
1055C4⋊C4—1181no—
1056C4⋊C4—1181no—
1057C4⋊C4—1181no—
1058C4⋊C4—1182no—
1059C4⋊C4—1182no—
1060C4⋊C4—1182no—
1061C4⋊C4—1182no—
1062C4⋊C4C2×C22⋊D5912yes—
1063C4⋊C4C2×C22⋊D5911yescharacteristic
1064C4⋊C4C2×C22⋊D5911yescharacteristic
1065C4⋊C4C2×C22⋊D5912yes—
1066C4⋊C4C23×D5911yescharacteristic
1067C4⋊C4C23×D5911yescharacteristic
1068C22⋊C4—21no—
1069C22⋊C4—21no—
1070C22⋊C4—21no—
1071C22⋊C4—21no—
1072C22⋊C4—21no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—1181no—
1078C22⋊C4—1181no—
1079C22⋊C4—1181no—
1080C22⋊C4—1181no—
1081C22⋊C4—1182no—
1082C22⋊C4—1182no—
1083C22⋊C4—1182no—
1084C22⋊C4—1182no—
1085C22⋊C4—1182no—
1086C22⋊C4—1182no—
1087C22⋊C4—1182no—
1088C22⋊C4C2×C22⋊D5912yes—
1089C22⋊C4C2×C22⋊D5912yes—
1090C22⋊C4C2×C22⋊D5912yes—
1091C22⋊C4C2×C22⋊D5912yes—
1092C22⋊C4C2×C22⋊D5912yes—
1093C42—22no—
1094C42—22no—
1095C42—21no—
1096C42—1181no—
1097C42—1181no—
1098C42—1181no—
1099C42—1181no—
1100C42—1182no—
1101C42C23×D5912yes—
1102C23—22no—
1103C23—22no—
1104C23—21no—
1105C23—41no—
1106C23—41no—
1107C23—42no—
1108C23—81no—
1109C23—81no—
1110C23—1182no—
1111C23—4721no—
1112C23—4721no—
1113C23—2362no—
1114C23C22×C22⋊D5911yescharacteristic
1115C23C22×C22⋊D5911yescharacteristic
1116C23C22×C22⋊D5912yes—
1117C23C22×C22⋊D5911yescharacteristic
1118Q8—22no—
1119Q8—24no—
1120Q8—22no—
1121Q8—21no—
1122Q8—21no—
1123Q8—44no—
1124Q8—4722no—
1125Q8C2×#1174568714yes—
1126D4—24no—
1127D4—22no—
1128D4—21no—
1129D4—22no—
1130D4—21no—
1131D4—22no—
1132D4—42no—
1133D4—42no—
1134D4—44no—
1135D4—44no—
1136D4—44no—
1137D4—42no—
1138D4—42no—
1139D4—82no—
1140D4—82no—
1141D4—81no—
1142D4—82no—
1143D4—82no—
1144D4—81no—
1145D4—1182no—
1146D4—1182no—
1147D4—4722no—
1148D4—4722no—
1149D4—4722no—
1150D4—2364no—
1151D4—2362no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—42no—
1171C2×C4—1181no—
1172C2×C4—1181no—
1173C2×C4—1181no—
1174C2×C4—1181no—
1175C2×C4—1182no—
1176C2×C4—4722no—
1177C2×C4—4722no—
1178C2×C4—4721no—
1179C2×C4—4721no—
1180C2×C4—4722no—
1181C2×C4—2362no—
1182C2×C4C22×C22⋊D5912yes—
1183C2×C4C22×C22⋊D5912yes—
1184C2×C4C22×C22⋊D5911yescharacteristic
1185C2×C4C22×C22⋊D5912yes—
1186C2×C4C22×C22⋊D5911yescharacteristic
1187C2×C4C22×C22⋊D5911yescharacteristic
1188C2×C4C2×#1174568712yes—
1189C2×C4#1427377212yes—
1190C2×C4C24×D5911yescharacteristic
1191C8—1181no—
1192C8—1181no—
1193C8—1181no—
1194C8—1181no—
1195C8—1182no—
1196C8—1182no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—22no—
1202C22—21no—
1203C22—21no—
1204C22—22no—
1205C22—22no—
1206C22—21no—
1207C22—21no—
1208C22—41no—
1209C22—42no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—42no—
1214C22—82no—
1215C22—84no—
1216C22—9442no—
1217C22—2362no—
1218C22—2362no—
1219C22—2362no—
1220C22#1683804612yes—
1221C22C23×C22⋊D5911yescharacteristic
1222C4—21no—
1223C4—21no—
1224C4—24no—
1225C4—22no—
1226C4—22no—
1227C4—22no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—2361no—
1232C4—2361no—
1233C4—2361no—
1234C4—2362no—
1235C4—2361no—
1236C4#1683804612yes—
1237C4C22×#1174568711yescharacteristic
1238C4C2×#1427377211yescharacteristic
1239C2—22no—
1240C2—41no—
1241C2—41no—
1242C2—42no—
1243C2—82no—
1244C2—81no—
1245C2—4722no—
1246C2C2×#1683804611yescharacteristic
1247C2#2143886711yescharacteristic
1248C2#2143887511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3487C2
socleC22×C59C23×D4
hypercenter#3487D59
hypocenterC59#61189
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #525 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #21437833C2semidirect
2. #21436423C2semidirect
3. #21436349C2semidirect
4. #21436282C2semidirect
5. #21436102C2semidirect
6. #21436102C2semidirect
7. #21436087C2semidirect
8. #21436046C2semidirect
9. #21435998C2semidirect
10. #21434450C2semidirect
11. #21434048C2semidirect
12. #21434005C2semidirect
13. #21433938C2semidirect
14. #21433741C2semidirect
15. #21433717C2semidirect
16. #21433595C2semidirect
17. #21433382C2semidirect
18. C2×#16837547C2semidirect
19. #21432955C2semidirect
20. #21432823C2semidirect
21. #21432629C2semidirect
22. #21432615C2semidirect
23. C59×#3487C2semidirect
29. #16838117C22semidirect
30. #16838098C22semidirect
31. #16838098C22semidirect
33. #16838056C22semidirect
45. #16837766C22semidirect
46. #16837761C22semidirect
47. #16837756C22semidirect
48. #16837748C22semidirect
49. #16837740C22semidirect
50. #16837740C22semidirect
51. #16837735C22semidirect
52. #16837730C22semidirect
53. #16837723C22semidirect
54. #16837723C22semidirect
55. #16837723C22semidirect
56. #16837723C22semidirect
57. #16837718C22semidirect
58. #16837718C22semidirect
59. #16837713C22semidirect
60. #16837713C22semidirect
61. #16837709C22semidirect
62. #16837709C22semidirect
63. #16837697C22semidirect
64. #16837687C22semidirect
65. #16837653C22semidirect
66. #16837653C22semidirect
67. #16837653C22semidirect
68. #16837650C22semidirect
69. #16837636C22semidirect
70. #16837636C22semidirect
71. #16837636C22semidirect
72. #16837633C22semidirect
73. #16837614C22semidirect
74. #16837614C22semidirect
75. #16837594C22semidirect
76. #16837594C22semidirect
81. #16837547C22semidirect
82. #16837547C22semidirect
83. #16837541C22semidirect
84. #16837541C22semidirect
85. #16837500C22semidirect
86. #16837500C22semidirect
87. C4×#11745671C22semidirect
88. C4×#11745671C22semidirect
89. #16837480C22semidirect
90. #16837474C22semidirect
91. #16837474C22semidirect
92. D4×C59⋊C8C22semidirect
99. #16837411C22semidirect
104. #16837403C22semidirect
105. #16837403C22semidirect
106. #16837403C22semidirect
109. #16837398C22semidirect
110. #16837398C22semidirect
111. #16837398C22semidirect
113. C2×#14273651C22semidirect
122. C59×#550C22semidirect
123. C59×#550C22semidirect
126. C59×#548C22semidirect
127. C59×#548C22semidirect
345. C2×Q8×C59#41semidirect
616. #3487D59semidirect
661. #550C2×D59semidirect
662. #550C2×D59semidirect
665. #548C2×D59semidirect
666. #548C2×D59semidirect
759. C59#61189semidirect
971. C2×Q8#11745687semidirect

Maximal subgroups

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

subgroupindex
#214378332
#214364232
#214363492
#214362822
#214361022
#214360872
#214360462
#214359982
#214344502
#214340482
#214340052
#214339382
#214337412
#214337172
#214335952
#214333822
C2×#168375472
#214329552
#214328232
#214326292
#214326152
C59×#34872
#6118959