Finite Group Databasebeta

← #29466383

Subgroups — #29466383

Order 15104.

2056 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437850C211yesmaximal, characteristic, complemented
2#21436412C212yesmaximal, complemented
3#21436312C212yesmaximal, complemented
4#21436192C212yesmaximal, complemented
5#21436192C212yesmaximal, complemented
6#21436177C212yesmaximal, complemented
7#21436132C212yesmaximal, complemented
8#21436013C212yesmaximal, complemented
9#21435931C212yesmaximal, complemented
10#21434461C211yesmaximal, characteristic, complemented
11#21434059C211yesmaximal, characteristic, complemented
12#21434005C211yesmaximal, characteristic, complemented
13#21433927C211yesmaximal, characteristic, complemented
14#21433748C211yesmaximal, characteristic, complemented
15#21433728C211yesmaximal, characteristic, complemented
16#21433622C211yesmaximal, characteristic, complemented
17#21433373C211yesmaximal, characteristic, complemented
18C2×#16837564C211yesmaximal, characteristic, complemented
19#21432953C211yesmaximal, characteristic, complemented
20#21432823C211yesmaximal, characteristic, complemented
21#21432622C211yesmaximal, characteristic, complemented
22#21432615C211yesmaximal, characteristic, complemented
23C59×#3485C211yesmaximal, characteristic
24C2×#14273757C2211yescharacteristic
25C22×#11745672C2211yescharacteristic, complemented
26C22×#11745670C2211yescharacteristic
27C2×#14273734C2211yescharacteristic
28C22×#11745664C2211yescharacteristic, complemented
29#16838122C2212yescomplemented
30#16838109C2212yescomplemented
31#16838092C2212yescomplemented
32#16838092C2212yescomplemented
33#16838089—22no—
34#16838083—22no—
35#16838030C2211yescharacteristic, complemented
36#16838019—21no—
37#16838012—21no—
38#16837973C2211yescharacteristic
39#16837954—21no—
40#16837933—21no—
41C2×#14273706C2211yescharacteristic, complemented
42#16837885C2211yescharacteristic
43#16837879C2211yescharacteristic, complemented
44C2×#14273686C2211yescharacteristic, complemented
45#16837770C2212yescomplemented
46#16837761C2212yescomplemented
47#16837756C2212yescomplemented
48#16837752C2212yescomplemented
49#16837740C2211yescharacteristic, complemented
50#16837740C2212yescomplemented
51#16837740C2211yescharacteristic, complemented
52#16837740C2212yescomplemented
53#16837735C2212yescomplemented
54#16837735C2211yescharacteristic, complemented
55#16837730C2212yescomplemented
56#16837730C2211yescharacteristic, complemented
57#16837723C2211yescharacteristic, complemented
58#16837723C2211yescharacteristic, complemented
59#16837718C2211yescharacteristic, complemented
60#16837713C2211yescharacteristic, complemented
61#16837702C2212yescomplemented
62#16837702C2212yescomplemented
63#16837692C2212yescomplemented
64#16837682C2212yescomplemented
65#16837658C2212yescomplemented
66#16837658C2212yescomplemented
67#16837658C2212yescomplemented
68#16837646C2212yescomplemented
69#16837641C2212yescomplemented
70#16837641C2212yescomplemented
71#16837641C2212yescomplemented
72#16837629C2212yescomplemented
73#16837621C2212yescomplemented
74#16837621C2212yescomplemented
75#16837609C2212yescomplemented
76#16837609C2212yescomplemented
77#16837564C2212yescomplemented
78#16837564C2212yescomplemented
79#16837564C2212yescomplemented
80#16837564C2212yescomplemented
81#16837564C2212yescomplemented
82#16837564C2212yescomplemented
83#16837553C2212yescomplemented
84#16837553C2212yescomplemented
85#16837502C2212yescomplemented
86#16837502C2212yescomplemented
87C4×#11745670C2212yescomplemented
88C4×#11745670C2212yescomplemented
89#16837480C2212yescomplemented
90#16837474C2212yescomplemented
91#16837474C2212yescomplemented
92D4×C59⋊C8C2212yescomplemented
93#16837445C2211yescharacteristic, complemented
94#16837438C2211yescharacteristic, complemented
95#16837438C2211yescharacteristic, complemented
96#16837429C2211yescharacteristic, complemented
97#16837411C2211yescharacteristic, complemented
98#16837411C2211yescharacteristic, complemented
99#16837410C2211yescharacteristic, complemented
100#16837407C2211yescharacteristic
101#16837407C2211yescharacteristic
102#16837407C2212yescomplemented
103#16837403C2211yescharacteristic
104#16837403C2212yescomplemented
105#16837403C2212yescomplemented
106#16837403C2212yescomplemented
107#16837398C2211yescharacteristic
108#16837398C2211yescharacteristic
109#16837398C2212yescomplemented
110#16837398C2212yescomplemented
111#16837398C2212yescomplemented
112C2×#14273651C2211yescharacteristic, complemented
113C2×#14273648C2211yescharacteristic
114C2×#14273648C2212yescomplemented
115#16837369C2211yescharacteristic
116C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
117#16837358C2211yescharacteristic, complemented
118C2×H(5,𝔽2)×C59C2211yescharacteristic
119C22×#41×C59C2211yescharacteristic
120C59×#547—21no—
121C59×#547—21no—
122C59×#547C2212yes—
123C59×#547C2212yes—
124C59×#546—21no—
125C59×#546—21no—
126C59×#546C2212yes—
127C59×#546C2212yes—
128C59×#536C2211yescharacteristic
129C59×#536C2211yescharacteristic
130C59×#534—22no—
131C59×#525C2211yescharacteristic
132C59×#525C2211yescharacteristic
133C2×#123×C59—22no—
134C59×#518C2211yescharacteristic
135C22×Dic118C2311yescharacteristic
136#14273757—42no—
137C2×#11745672—42no—
138C2×#11745672C2312yes—
139C2×#11745672C2312yes—
140C2×#11745672C2312yes—
141C2×#11745670—24no—
142C2×#11745670C2312yes—
143C2×#11745670C2312yes—
144C2×#11745670C2312yes—
145#14273734—42no—
146C2×#11745664—42no—
147C2×#11745664C2311yescharacteristic
148C2×#11745664C2311yescharacteristic
149C2×#11745664C2312yes—
150C2×#11745664C2312yes—
151C22×C59⋊C8C2311yescharacteristic
152C22×C59⋊C8C2311yescharacteristic
153C22×C59⋊C8C2312yes—
154C22×C59⋊C8C2312yes—
155#14273727C2312yes—
156#14273726—21no—
157#14273725—21no—
158#14273720—22no—
159#14273720—22no—
160#14273720—22no—
161#14273720—22no—
162#14273719C2312yes—
163#14273718—21no—
164#14273718—22no—
165#14273717—22no—
166#14273717—22no—
167#14273714—21no—
168#14273714—22no—
169#14273708—22no—
170#14273708—22no—
171#14273708—22no—
172#14273706—21no—
173#14273706—21no—
174#14273706C2312yes—
175#14273706C2312yes—
176#14273706C2312yes—
177#14273706C2312yes—
178#14273704—22no—
179#14273704—22no—
180#14273704—22no—
181Q8×Dic59—21no—
182C4×Dic118C2312yes—
183C4×Dic118C2312yes—
184#14273692—21no—
185#14273692—21no—
186#14273692—22no—
187D4×Dic59—21no—
188D4×Dic59—22no—
189D4×Dic59—22no—
190#14273686—21no—
191#14273686—21no—
192#14273686C2311yescharacteristic
193#14273686C2311yescharacteristic
194#14273686C2311yescharacteristic
195#14273686C2311yescharacteristic
196#14273686C2312yes—
197#14273683—22no—
198#14273683—22no—
199#14273683—22no—
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2312yes—
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×Dic59⋊C4—21no—
205C2×C22⋊Dic59—21no—
206C2×C22⋊Dic59—21no—
207C2×C4×Dic59—21no—
208#14273660C2311yescharacteristic
209#14273660C2311yescharacteristic
210#14273660C2312yes—
211#14273660C2311yescharacteristic
212#14273660C2311yescharacteristic
213#14273658C2311yescharacteristic
214#14273658C2311yescharacteristic
215#14273658C2312yes—
216#14273658C2311yescharacteristic
217#14273658C2311yescharacteristic
218C4⋊(C59⋊C8)C2312yes—
219C4⋊(C59⋊C8)C2312yes—
220#14273651C2312yes—
221#14273651C2312yes—
222#14273651C2312yes—
223#14273651C2312yes—
224#14273651C2312yes—
225#14273651C2311yescharacteristic
226#14273651C2311yescharacteristic
227#14273651C2311yescharacteristic
228#14273651C2311yescharacteristic
229#14273651C2312yes—
230#14273651C2312yes—
231#14273650C2312yes—
232#14273650C2312yes—
233#14273648C2312yes—
234#14273648C2312yes—
235#14273648C2311yescharacteristic
236#14273648C2312yes—
237#14273648C2312yes—
238#14273648C2311yescharacteristic
239#14273648C2311yescharacteristic
240#14273648C2311yescharacteristic
241#14273648C2312yes—
242#14273648C2312yes—
243#14273648C2312yes—
244C22⋊(C59⋊C8)C2311yescharacteristic
245C22⋊(C59⋊C8)C2311yescharacteristic
246C22⋊(C59⋊C8)C2311yescharacteristic
247C22⋊(C59⋊C8)C2311yescharacteristic
248C22⋊(C59⋊C8)C2312yes—
249C22⋊(C59⋊C8)C2312yes—
250#14273638C2312yes—
251C4×C59⋊C8C2312yes—
252H(5,𝔽2)×C59—24no—
253H(5,𝔽2)×C59—42no—
254C2×#41×C59—21no—
255C2×#41×C59—21no—
256C2×#41×C59—21no—
257C2×#41×C59—24no—
258C2×#41×C59—42no—
259C2×#41×C59C2311yescharacteristic
260C2×#41×C59C2312yes—
261C2×#41×C59C2312yes—
262C2×#41×C59C2312yes—
263C2×#41×C59C2311yescharacteristic
264C22×Q8×C59C2311yescharacteristic
265C22×D4×C59—21no—
266C22×D4×C59—22no—
267C22×D4×C59—21no—
268C22×D4×C59C2312yes—
269C22×D4×C59C2311yescharacteristic
270C23×C4×C59—21no—
271C23×C4×C59C2311yescharacteristic
272C4⋊Q8×C59—21no—
273C4⋊Q8×C59C2312yes—
274#124×C59—21no—
275#124×C59C2312yes—
276#123×C59—22no—
277#123×C59—21no—
278#123×C59—22no—
279#123×C59—22no—
280#123×C59—22no—
281#123×C59—22no—
282#123×C59—22no—
283#123×C59—22no—
284#123×C59—22no—
285#123×C59D412yes—
286C22⋊Q8×C59—21no—
287C22⋊Q8×C59—21no—
288C22⋊Q8×C59D411yescharacteristic
289C22⋊Q8×C59D411yescharacteristic
290C22⋊Q8×C59C2311yescharacteristic
291C22⋊Q8×C59C2312yes—
292C22⋊Q8×C59C2312yes—
293C22⋊Q8×C59C2311yescharacteristic
294#121×C59—22no—
295#121×C59—22no—
296#121×C59—22no—
297#121×C59—22no—
298#121×C59D411yescharacteristic
299#121×C59D411yescharacteristic
300#121×C59C2311yescharacteristic
301#121×C59C2311yescharacteristic
302#120×C59—21no—
303#120×C59—22no—
304#120×C59—22no—
305#120×C59D412yes—
306C4×D4×C59—21no—
307C4×D4×C59—21no—
308C4×D4×C59—21no—
309C4×D4×C59—21no—
310C4×D4×C59C2312yes—
311C4×D4×C59C2312yes—
312C4×D4×C59C2312yes—
313C4×D4×C59C2312yes—
314#117×C59C2311yescharacteristic
315#117×C59C2311yescharacteristic
316C2×C4⋊C4×C59—22no—
317C2×C4⋊C4×C59—22no—
318C2×C22⋊C4×C59—22no—
319C2×C22⋊C4×C59—22no—
320C2×C22⋊C4×C59—22no—
321C24×C59—21no—
322C24×C59—22no—
323C24×C59C2×D411yescharacteristic
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—44no—
335#41×C59—44no—
336#41×C59—44no—
337C2×Q8×C59—21no—
338C2×Q8×C59—22no—
339C2×Q8×C59—22no—
340C2×Q8×C59C2×D411yescharacteristic
341C2×Q8×C59C2412yes—
342C2×Q8×C59C2411yescharacteristic
343C2×D4×C59—24no—
344C2×D4×C59—22no—
345C2×D4×C59—22no—
346C2×D4×C59—21no—
347C2×D4×C59—22no—
348C2×D4×C59—21no—
349C2×D4×C59—21no—
350C2×D4×C59—21no—
351C2×D4×C59—22no—
352C2×D4×C59—22no—
353C2×D4×C59—42no—
354C2×D4×C59—44no—
355C2×D4×C59—48no—
356C2×D4×C59—44no—
357C2×D4×C59C2×D412yes—
358C2×D4×C59C2×D411yescharacteristic
359C2×D4×C59C2×D412yes—
360C2×D4×C59C2×D412yes—
361C2×D4×C59#4114yes—
362C2×D4×C59C2411yescharacteristic
363C2×D4×C59C2412yes—
364C22×C4×C59—22no—
365C22×C4×C59—22no—
366C22×C4×C59—21no—
367C22×C4×C59—22no—
368C22×C4×C59—22no—
369C22×C4×C59—22no—
370C22×C4×C59—21no—
371C22×C4×C59—22no—
372C22×C4×C59—22no—
373C22×C4×C59—44no—
374C22×C4×C59C2×D411yescharacteristic
375C22×C4×C59C2×D411yescharacteristic
376C22×C4×C59C2×D411yescharacteristic
377C22×C4×C59C2411yescharacteristic
378C22×C4×C59C2411yescharacteristic
379C22×C4×C59C2412yes—
380C22×C4×C59C2411yescharacteristic
381C22×Dic59—21no—
382C22×Dic59—21no—
383C22×Dic59—21no—
384C22×Dic59—21no—
385C22×Dic59—22no—
386C2×Dic118—22no—
387C2×Dic118—22no—
388C2×Dic118—21no—
389C2×Dic118—22no—
390C2×Dic118C2412yes—
391C4⋊C4×C59—21no—
392C4⋊C4×C59—21no—
393C4⋊C4×C59—22no—
394C4⋊C4×C59—22no—
395C4⋊C4×C59—22no—
396C4⋊C4×C59—22no—
397C4⋊C4×C59C2×D412yes—
398C4⋊C4×C59C2×D412yes—
399C4⋊C4×C59C2×D411yescharacteristic
400C4⋊C4×C59C2×D411yescharacteristic
401C4⋊C4×C59C2411yescharacteristic
402C4⋊C4×C59C2411yescharacteristic
403C22⋊C4×C59—21no—
404C22⋊C4×C59—22no—
405C22⋊C4×C59—22no—
406C22⋊C4×C59—21no—
407C22⋊C4×C59—21no—
408C22⋊C4×C59—21no—
409C22⋊C4×C59—21no—
410C22⋊C4×C59—22no—
411C22⋊C4×C59—22no—
412C22⋊C4×C59—22no—
413C22⋊C4×C59—22no—
414C22⋊C4×C59C2×D412yes—
415C22⋊C4×C59C2×D412yes—
416C22⋊C4×C59C2×D412yes—
417C22⋊C4×C59C2×D412yes—
418C22⋊C4×C59C2×D412yes—
419C42×C59—21no—
420C42×C59C2412yes—
421C22⋊Dic59—21no—
422C22⋊Dic59—22no—
423C22⋊Dic59—21no—
424C22⋊Dic59—21no—
425C22⋊Dic59—21no—
426C22⋊Dic59—22no—
427C22⋊Dic59—22no—
428C22⋊Dic59—22no—
429C22⋊Dic59—22no—
430#11745672—42no—
431#11745672—42no—
432#11745672—42no—
433#11745670—24no—
434#11745670—24no—
435#11745670—42no—
436C4⋊Dic59—21no—
437C4⋊Dic59—21no—
438C4⋊Dic59—22no—
439C4⋊Dic59—21no—
440C4⋊Dic59—22no—
441C4⋊Dic59C2411yescharacteristic
442C4⋊Dic59C2412yes—
443C4⋊Dic59C2411yescharacteristic
444C4⋊Dic59C2411yescharacteristic
445C4⋊Dic59C2411yescharacteristic
446Dic59⋊C4—22no—
447Dic59⋊C4—22no—
448Dic59⋊C4—22no—
449Dic59⋊C4—22no—
450Dic59⋊C4—22no—
451Dic59⋊C4—22no—
452Dic59⋊C4—22no—
453Dic59⋊C4—22no—
454C4×Dic59—21no—
455C4×Dic59—21no—
456C4×Dic59—21no—
457C4×Dic59—21no—
458C4×Dic59—22no—
459C4×Dic59—22no—
460C4×Dic59—22no—
461#11745664—22no—
462#11745664—22no—
463#11745664—42no—
464#11745664—42no—
465C2×C59⋊C8—22no—
466C2×C59⋊C8—22no—
467C2×C59⋊C8—42no—
468C2×C59⋊C8—42no—
469C2×C59⋊C8C2411yescharacteristic
470C2×C59⋊C8C2412yes—
471C2×C59⋊C8C2411yescharacteristic
472C2×C59⋊C8C2411yescharacteristic
473C2×C59⋊C8C2411yescharacteristic
474C2×C59⋊C8C2412yes—
475C23×C59—22no—
476C23×C59—22no—
477C23×C59—24no—
478C23×C59—21no—
479C23×C59—41no—
480C23×C59—41no—
481C23×C59—44no—
482C23×C59—81no—
483C23×C59—81no—
484C23×C59—82no—
485C23×C59—82no—
486C23×C59C22×D411yescharacteristic
487C23×C59C22×D412yes—
488C23×C59C22×D411yescharacteristic
489C23×C59C22×D411yescharacteristic
490Q8×C59—22no—
491Q8×C59—22no—
492Q8×C59—21no—
493Q8×C59—22no—
494Q8×C59—21no—
495Q8×C59—42no—
496D4×C59—24no—
497D4×C59—24no—
498D4×C59—22no—
499D4×C59—21no—
500D4×C59—22no—
501D4×C59—21no—
502D4×C59—42no—
503D4×C59—42no—
504D4×C59—44no—
505D4×C59—44no—
506D4×C59—44no—
507D4×C59—44no—
508D4×C59—42no—
509D4×C59—81no—
510D4×C59—81no—
511D4×C59C2×#4114yes—
512C2×C4×C59—22no—
513C2×C4×C59—22no—
514C2×C4×C59—22no—
515C2×C4×C59—21no—
516C2×C4×C59—21no—
517C2×C4×C59—22no—
518C2×C4×C59—21no—
519C2×C4×C59—22no—
520C2×C4×C59—21no—
521C2×C4×C59—21no—
522C2×C4×C59—21no—
523C2×C4×C59—22no—
524C2×C4×C59—21no—
525C2×C4×C59—44no—
526C2×C4×C59—44no—
527C2×C4×C59—44no—
528C2×C4×C59—42no—
529C2×C4×C59—42no—
530C2×C4×C59—82no—
531C2×C4×C59—82no—
532C2×C4×C59C22×D411yescharacteristic
533C2×C4×C59C22×D412yes—
534C2×C4×C59C22×D412yes—
535C2×C4×C59C22×D412yes—
536C2×C4×C59C22×D411yescharacteristic
537C2×C4×C59C22×D411yescharacteristic
538C2×C4×C59C2×#4112yes—
539C2×C4×C59H(5,𝔽2)12yes—
540C2×C4×C59C2511yescharacteristic
541C2×Dic59—21no—
542C2×Dic59—21no—
543C2×Dic59—21no—
544C2×Dic59—22no—
545C2×Dic59—21no—
546C2×Dic59—22no—
547C2×Dic59—42no—
548C2×Dic59—42no—
549C2×Dic59—81no—
550C2×Dic59—81no—
551C2×Dic59—82no—
552Dic118—22no—
553Dic118—22no—
554Dic118—42no—
555Dic118—82no—
556C59⋊C8—21no—
557C59⋊C8—21no—
558C59⋊C8—21no—
559C59⋊C8—21no—
560C59⋊C8—22no—
561C59⋊C8—22no—
562#61188—591nomaximal, Sylow
563C22×C59—21no—
564C22×C59—21no—
565C22×C59—22no—
566C22×C59—21no—
567C22×C59—21no—
568C22×C59—21no—
569C22×C59—22no—
570C22×C59—21no—
571C22×C59—21no—
572C22×C59—21no—
573C22×C59—22no—
574C22×C59—24no—
575C22×C59—42no—
576C22×C59—42no—
577C22×C59—41no—
578C22×C59—41no—
579C22×C59—41no—
580C22×C59—82no—
581C22×C59—84no—
582C22×C59—164no—
583C22×C59#54612yes—
584C22×C59C23×D411yescharacteristic
585C4×C59—22no—
586C4×C59—22no—
587C4×C59—21no—
588C4×C59—21no—
589C4×C59—22no—
590C4×C59—41no—
591C4×C59—41no—
592C4×C59—41no—
593C4×C59—42no—
594C4×C59#54612yes—
595C4×C59C22×#4111yescharacteristic
596C4×C59C2×H(5,𝔽2)11yescharacteristic
597Dic59—41no—
598Dic59—42no—
599Dic59—41no—
600Dic59—41no—
601Dic59—41no—
602Dic59—42no—
603#3495—591no—
604#3485D5911yescharacteristic
605#3331—592no—
606#3323—592no—
607#3315—592no—
608#3315—592no—
609#3314—592no—
610#3311—592no—
611#3302—592no—
612#3296—592no—
613#3137—591no—
614#3097—591no—
615#3091—591no—
616#3081—591no—
617#3059—591no—
618#3056—591no—
619#3044—591no—
620#3009—591no—
621C2×#452—591no—
622#2949—591no—
623#2933—591no—
624#2897—591no—
625#2896—591no—
626C2×C59—22no—
627C2×C59—41no—
628C2×C59—41no—
629C2×C59—42no—
630C2×C59—44no—
631C2×C59—81no—
632C2×C59C2×#54611yescharacteristic
633C2×C59#358411yescharacteristic
634C2×C59#358611yescharacteristic
635C2×H(5,𝔽2)C2×D5911yescharacteristic
636C22×#41C2×D5911yescharacteristic
637C2×#137—591no—
638C22×Q16—591no—
639C22×SD16—591no—
640C2×#131—591no—
641C22×M16—591no—
642#556—592no—
643#554—592no—
644#552—592no—
645#552—592no—
646#552—1182no—
647#551—1182no—
648#547—21no—
649#547—21no—
650#547C2×D5912yes—
651#547C2×D5912yes—
652#546—21no—
653#546—21no—
654#546C2×D5912yes—
655#546C2×D5912yes—
656#544—591no—
657#542—1181no—
658#541—1181no—
659#536—591no—
660#536C2×D5911yescharacteristic
661#536C2×D5911yescharacteristic
662#534—22no—
663#533—1181no—
664#529—1181no—
665#525C2×D5911yescharacteristic
666#525C2×D5911yescharacteristic
667C2×#123—22no—
668C2×C22⋊Q8—591no—
669#520—591no—
670#519—591no—
671#518C2×D5911yescharacteristic
672C2×#117—591no—
673#491—592no—
674#489—592no—
675#488—592no—
676#487—592no—
677#485—591no—
678#485—591no—
679#485—592no—
680#485—592no—
681#484—591no—
682#484—592no—
683#483—591no—
684#483—592no—
685#482—591no—
686#482—591no—
687#481—591no—
688#480—591no—
689#478—592no—
690#478—592no—
691#476—592no—
692#474—592no—
693#470—592no—
694#470—592no—
695#470—592no—
696#468—592no—
697#467—592no—
698#467—592no—
699#467—592no—
700#465—592no—
701#464—592no—
702#464—592no—
703#462—592no—
704#462—592no—
705#452—592no—
706#452—592no—
707#452—592no—
708#452—592no—
709#452—592no—
710#452—592no—
711#450—592no—
712#450—592no—
713#440—592no—
714#440—592no—
715C4×SD16—592no—
716C4×SD16—592no—
717#436—592no—
718#435—592no—
719#435—592no—
720C8×D4—592no—
721#428—591no—
722#427—591no—
723#427—591no—
724#424—591no—
725#419—591no—
726#419—591no—
727#419—591no—
728#418—591no—
729#418—591no—
730#418—592no—
731#417—592no—
732#417—592no—
733#417—591no—
734#417—592no—
735#416—591no—
736#416—591no—
737#416—592no—
738#416—592no—
739#416—592no—
740C2×#103—591no—
741C2×#102—591no—
742C2×#102—592no—
743#408—591no—
744C2×C22⋊C8—591no—
745#405—591no—
746C59#6118811yescharacteristic, complemented, Sylow
747H(5,𝔽2)—24no—
748H(5,𝔽2)—42no—
749C2×#41—21no—
750C2×#41—21no—
751C2×#41—21no—
752C2×#41—24no—
753C2×#41—42no—
754C2×#41C22×D5911yescharacteristic
755C2×#41C22×D5912yes—
756C2×#41C22×D5912yes—
757C2×#41C22×D5912yes—
758C2×#41C22×D5911yescharacteristic
759C22×Q8—591no—
760C22×Q8C22×D5911yescharacteristic
761C22×D4—21no—
762C22×D4—22no—
763C22×D4—21no—
764C22×D4C22×D5912yes—
765C22×D4C22×D5911yescharacteristic
766C23×C4—21no—
767C23×C4C22×D5911yescharacteristic
768#137—2362no—
769C2×Q16—592no—
770C2×Q16—592no—
771C2×Q16—592no—
772C2×Q16—2362no—
773C2×SD16—592no—
774C2×SD16—592no—
775C2×SD16—592no—
776C2×SD16—1184no—
777#131—2362no—
778C2×M16—591no—
779C2×M16—591no—
780C2×M16—592no—
781C2×M16—592no—
782C2×M16—2362no—
783C22×C8—591no—
784C22×C8—591no—
785C22×C8—592no—
786C22×C8—592no—
787C4⋊Q8—21no—
788C4⋊Q8—592no—
789C4⋊Q8—1181no—
790C4⋊Q8—1181no—
791C4⋊Q8C22×D5912yes—
792#126—1182no—
793#126—1182no—
794#126—1182no—
795#126—1182no—
796#125—592no—
797#125—1181no—
798#125—1182no—
799#125—1182no—
800#125—1182no—
801#124—21no—
802#124—1181no—
803#124—1182no—
804#124C22×D5912yes—
805#123—22no—
806#123—21no—
807#123—22no—
808#123—22no—
809#123—22no—
810#123—22no—
811#123—22no—
812#123—22no—
813#123—22no—
814#123—1182no—
815#123—1182no—
816#123—1182no—
817#123C22⋊D5912yes—
818C22⋊Q8—21no—
819C22⋊Q8—21no—
820C22⋊Q8—592no—
821C22⋊Q8—592no—
822C22⋊Q8—592no—
823C22⋊Q8—592no—
824C22⋊Q8—1181no—
825C22⋊Q8—1181no—
826C22⋊Q8—1182no—
827C22⋊Q8—1182no—
828C22⋊Q8—1182no—
829C22⋊Q8C22⋊D5911yescharacteristic
830C22⋊Q8C22⋊D5911yescharacteristic
831C22⋊Q8C22×D5911yescharacteristic
832C22⋊Q8C22×D5911yescharacteristic
833C22⋊Q8C22×D5912yes—
834C22⋊Q8C22×D5912yes—
835#121—22no—
836#121—22no—
837#121—22no—
838#121—22no—
839#121C22⋊D5911yescharacteristic
840#121C22⋊D5911yescharacteristic
841#121C22×D5911yescharacteristic
842#121C22×D5911yescharacteristic
843#120—21no—
844#120—22no—
845#120—22no—
846#120C22⋊D5912yes—
847C4×Q8—592no—
848C4×Q8—592no—
849C4×Q8—1181no—
850C4×Q8—1181no—
851C4×Q8—1181no—
852C4×Q8—1182no—
853C4×D4—21no—
854C4×D4—21no—
855C4×D4—21no—
856C4×D4—21no—
857C4×D4—1181no—
858C4×D4—1182no—
859C4×D4—1182no—
860C4×D4C22×D5912yes—
861C4×D4C22×D5912yes—
862C4×D4C22×D5912yes—
863C4×D4C22×D5912yes—
864#117—591no—
865#117—591no—
866#117—591no—
867#117—591no—
868#117—592no—
869#117—1181no—
870#117—1181no—
871#117—1182no—
872#117—1182no—
873#117—1182no—
874#117C22×D5911yescharacteristic
875#117C22×D5911yescharacteristic
876C2×C4⋊C4—22no—
877C2×C4⋊C4—22no—
878C2×C4⋊C4—591no—
879C2×C4⋊C4—591no—
880C2×C4⋊C4—591no—
881C2×C4⋊C4—592no—
882C2×C4⋊C4—1181no—
883C2×C22⋊C4—22no—
884C2×C22⋊C4—22no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—1181no—
887C2×C22⋊C4—1181no—
888C2×C42—1181no—
889#107—591no—
890#107—591no—
891#107—591no—
892#107—591no—
893#107—592no—
894#106—591no—
895#106—591no—
896#106—591no—
897#106—591no—
898#106—592no—
899C4⋊C8—592no—
900C4⋊C8—592no—
901#103—592no—
902#103—592no—
903#103—591no—
904#103—591no—
905#103—592no—
906#103—592no—
907#103—592no—
908#103—592no—
909#103—592no—
910#103—591no—
911#103—591no—
912#103—592no—
913#103—592no—
914#102—592no—
915#102—591no—
916#102—592no—
917#102—592no—
918#102—592no—
919#102—592no—
920#102—592no—
921#102—592no—
922#102—591no—
923#102—591no—
924#102—591no—
925C22⋊C8—591no—
926C22⋊C8—591no—
927C22⋊C8—591no—
928C22⋊C8—591no—
929C22⋊C8—592no—
930C22⋊C8—592no—
931#97—592no—
932C4×C8—592no—
933C24—21no—
934C24—22no—
935C24C2×C22⋊D5911yescharacteristic
936#41—22no—
937#41—22no—
938#41—24no—
939#41—24no—
940#41—24no—
941#41—22no—
942#41—22no—
943#41—42no—
944#41—42no—
945#41—42no—
946#41—44no—
947#41—44no—
948#41—44no—
949C2×Q8—21no—
950C2×Q8—22no—
951C2×Q8—22no—
952C2×Q8—592no—
953C2×Q8—1182no—
954C2×Q8—1181no—
955C2×Q8—1182no—
956C2×Q8—1182no—
957C2×Q8C2×C22⋊D5911yescharacteristic
958C2×Q8C23×D5912yes—
959C2×Q8C23×D5911yescharacteristic
960C2×D4—24no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—21no—
967C2×D4—21no—
968C2×D4—22no—
969C2×D4—22no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—48no—
973C2×D4—44no—
974C2×D4#1174568714yes—
975C2×D4C2×C22⋊D5912yes—
976C2×D4C2×C22⋊D5911yescharacteristic
977C2×D4C2×C22⋊D5912yes—
978C2×D4C2×C22⋊D5912yes—
979C2×D4C23×D5911yescharacteristic
980C2×D4C23×D5912yes—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—21no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—44no—
991C22×C4—1181no—
992C22×C4—1181no—
993C22×C4—1182no—
994C22×C4—1181no—
995C22×C4—1181no—
996C22×C4C2×C22⋊D5911yescharacteristic
997C22×C4C2×C22⋊D5911yescharacteristic
998C22×C4C2×C22⋊D5911yescharacteristic
999C22×C4C23×D5911yescharacteristic
1000C22×C4C23×D5912yes—
1001C22×C4C23×D5911yescharacteristic
1002C22×C4C23×D5911yescharacteristic
1003Q16—2362no—
1004Q16—2362no—
1005Q16—2362no—
1006SD16—1184no—
1007SD16—1184no—
1008SD16—2362no—
1009M16—1182no—
1010M16—1182no—
1011M16—2362no—
1012M16—2362no—
1013C2×C8—591no—
1014C2×C8—592no—
1015C2×C8—591no—
1016C2×C8—591no—
1017C2×C8—591no—
1018C2×C8—592no—
1019C2×C8—1182no—
1020C2×C8—1182no—
1021C2×C8—2362no—
1022C2×C8—2362no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—591no—
1030C4⋊C4—592no—
1031C4⋊C4—591no—
1032C4⋊C4—591no—
1033C4⋊C4—591no—
1034C4⋊C4—1181no—
1035C4⋊C4—1181no—
1036C4⋊C4—1181no—
1037C4⋊C4—1182no—
1038C4⋊C4—1182no—
1039C4⋊C4—1182no—
1040C4⋊C4—1182no—
1041C4⋊C4—1182no—
1042C4⋊C4—1182no—
1043C4⋊C4—1182no—
1044C4⋊C4—1182no—
1045C4⋊C4—1182no—
1046C4⋊C4—1182no—
1047C4⋊C4C2×C22⋊D5912yes—
1048C4⋊C4C2×C22⋊D5912yes—
1049C4⋊C4C2×C22⋊D5911yescharacteristic
1050C4⋊C4C2×C22⋊D5911yescharacteristic
1051C4⋊C4C23×D5911yescharacteristic
1052C4⋊C4C23×D5911yescharacteristic
1053C22⋊C4—21no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—21no—
1057C22⋊C4—21no—
1058C22⋊C4—21no—
1059C22⋊C4—21no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—1181no—
1065C22⋊C4—1181no—
1066C22⋊C4—1181no—
1067C22⋊C4—1181no—
1068C22⋊C4—1182no—
1069C22⋊C4—1182no—
1070C22⋊C4—1182no—
1071C22⋊C4—1182no—
1072C22⋊C4—1182no—
1073C22⋊C4C2×C22⋊D5912yes—
1074C22⋊C4C2×C22⋊D5912yes—
1075C22⋊C4C2×C22⋊D5912yes—
1076C22⋊C4C2×C22⋊D5912yes—
1077C22⋊C4C2×C22⋊D5912yes—
1078C42—21no—
1079C42—1181no—
1080C42—1181no—
1081C42—1181no—
1082C42—1181no—
1083C42—1182no—
1084C42—1182no—
1085C42—1182no—
1086C42C23×D5912yes—
1087C23—22no—
1088C23—22no—
1089C23—24no—
1090C23—21no—
1091C23—41no—
1092C23—41no—
1093C23—44no—
1094C23—81no—
1095C23—81no—
1096C23—82no—
1097C23—82no—
1098C23C22×C22⋊D5912yes—
1099C23C22×C22⋊D5911yescharacteristic
1100C23C22×C22⋊D5911yescharacteristic
1101C23C22×C22⋊D5911yescharacteristic
1102Q8—22no—
1103Q8—22no—
1104Q8—21no—
1105Q8—22no—
1106Q8—21no—
1107Q8—42no—
1108Q8—1182no—
1109Q8—1182no—
1110Q8—4722no—
1111Q8—2362no—
1112D4—24no—
1113D4—21no—
1114D4—22no—
1115D4—21no—
1116D4—24no—
1117D4—22no—
1118D4—42no—
1119D4—42no—
1120D4—44no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—42no—
1125D4—81no—
1126D4—81no—
1127D4C2×#1174568714yes—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—82no—
1147C2×C4—82no—
1148C2×C4—1181no—
1149C2×C4—1181no—
1150C2×C4—1181no—
1151C2×C4—1181no—
1152C2×C4—1182no—
1153C2×C4—1182no—
1154C2×C4—4722no—
1155C2×C4—4721no—
1156C2×C4—4721no—
1157C2×C4—2362no—
1158C2×C4—2362no—
1159C2×C4C22×C22⋊D5911yescharacteristic
1160C2×C4C22×C22⋊D5912yes—
1161C2×C4C22×C22⋊D5912yes—
1162C2×C4C22×C22⋊D5912yes—
1163C2×C4C22×C22⋊D5911yescharacteristic
1164C2×C4C22×C22⋊D5911yescharacteristic
1165C2×C4C2×#1174568712yes—
1166C2×C4#1427377212yes—
1167C2×C4C24×D5911yescharacteristic
1168C8—1181no—
1169C8—1181no—
1170C8—1181no—
1171C8—1181no—
1172C8—1182no—
1173C8—1182no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—22no—
1179C22—24no—
1180C22—22no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—22no—
1185C22—21no—
1186C22—42no—
1187C22—42no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—82no—
1192C22—84no—
1193C22—164no—
1194C22#1683804612yes—
1195C22C23×C22⋊D5911yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—22no—
1199C4—22no—
1200C4—22no—
1201C4—41no—
1202C4—42no—
1203C4—41no—
1204C4—41no—
1205C4—2362no—
1206C4—2361no—
1207C4—2362no—
1208C4—2361no—
1209C4—2361no—
1210C4—2361no—
1211C4#1683804612yes—
1212C4C22×#1174568711yescharacteristic
1213C4C2×#1427377211yescharacteristic
1214C2—22no—
1215C2—41no—
1216C2—41no—
1217C2—42no—
1218C2—44no—
1219C2—81no—
1220C2C2×#1683804611yescharacteristic
1221C2#2143886711yescharacteristic
1222C2#2143888211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC59×#3485C2
socleC22×C59C23×D4
hypercenter#3485D59
hypocenterC59#61188
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #525 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #21437850C2semidirect
2. #21436412C2semidirect
3. #21436312C2semidirect
4. #21436192C2semidirect
5. #21436192C2semidirect
6. #21436177C2semidirect
7. #21436132C2semidirect
8. #21436013C2semidirect
9. #21435931C2semidirect
10. #21434461C2semidirect
11. #21434059C2semidirect
12. #21434005C2semidirect
13. #21433927C2semidirect
14. #21433748C2semidirect
15. #21433728C2semidirect
16. #21433622C2semidirect
17. #21433373C2semidirect
18. C2×#16837564C2semidirect
19. #21432953C2semidirect
20. #21432823C2semidirect
21. #21432622C2semidirect
22. #21432615C2semidirect
25. C22×#11745672C22semidirect
28. C22×#11745664C22semidirect
29. #16838122C22semidirect
30. #16838109C22semidirect
31. #16838092C22semidirect
32. #16838092C22semidirect
35. #16838030C22semidirect
41. C2×#14273706C22semidirect
43. #16837879C22semidirect
44. C2×#14273686C22semidirect
45. #16837770C22semidirect
46. #16837761C22semidirect
47. #16837756C22semidirect
48. #16837752C22semidirect
49. #16837740C22semidirect
50. #16837740C22semidirect
51. #16837740C22semidirect
52. #16837740C22semidirect
53. #16837735C22semidirect
54. #16837735C22semidirect
55. #16837730C22semidirect
56. #16837730C22semidirect
57. #16837723C22semidirect
58. #16837723C22semidirect
59. #16837718C22semidirect
60. #16837713C22semidirect
61. #16837702C22semidirect
62. #16837702C22semidirect
63. #16837692C22semidirect
64. #16837682C22semidirect
65. #16837658C22semidirect
66. #16837658C22semidirect
67. #16837658C22semidirect
68. #16837646C22semidirect
69. #16837641C22semidirect
70. #16837641C22semidirect
71. #16837641C22semidirect
72. #16837629C22semidirect
73. #16837621C22semidirect
74. #16837621C22semidirect
75. #16837609C22semidirect
76. #16837609C22semidirect
77. #16837564C22semidirect
78. #16837564C22semidirect
79. #16837564C22semidirect
80. #16837564C22semidirect
81. #16837564C22semidirect
82. #16837564C22semidirect
83. #16837553C22semidirect
84. #16837553C22semidirect
85. #16837502C22semidirect
86. #16837502C22semidirect
87. C4×#11745670C22semidirect
88. C4×#11745670C22semidirect
89. #16837480C22semidirect
90. #16837474C22semidirect
91. #16837474C22semidirect
92. D4×C59⋊C8C22semidirect
93. #16837445C22semidirect
94. #16837438C22semidirect
95. #16837438C22semidirect
96. #16837429C22semidirect
97. #16837411C22semidirect
98. #16837411C22semidirect
99. #16837410C22semidirect
102. #16837407C22semidirect
104. #16837403C22semidirect
105. #16837403C22semidirect
106. #16837403C22semidirect
109. #16837398C22semidirect
110. #16837398C22semidirect
111. #16837398C22semidirect
112. C2×#14273651C22semidirect
114. C2×#14273648C22semidirect
116. C2×C22⋊(C59⋊C8)C22semidirect
117. #16837358C22semidirect
746. C59#61188semidirect

Maximal subgroups

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

subgroupindex
#214378502
#214364122
#214363122
#214361922
#214361772
#214361322
#214360132
#214359312
#214344612
#214340592
#214340052
#214339272
#214337482
#214337282
#214336222
#214333732
C2×#168375642
#214329532
#214328232
#214326222
#214326152
C59×#34852
#6118859