Finite Group Databasebeta

← #29456300

Subgroups — #29456300

Order 15104.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437500C211yesmaximal, characteristic, complemented
2#518×D59C211yesmaximal, characteristic
3#21433930C211yesmaximal, characteristic, complemented
4#21433929C211yesmaximal, characteristic, complemented
5#21433928C211yesmaximal, characteristic, complemented
6#21433927C211yesmaximal, characteristic, complemented
7#21433926C212yesmaximal, complemented
8#21433925C211yesmaximal, characteristic, complemented
9#21433924C212yesmaximal, complemented
10#21433923C211yesmaximal, characteristic, complemented
11#21433922C212yesmaximal, complemented
12#21433921C211yesmaximal, characteristic, complemented
13#21433920C212yesmaximal, complemented
14#21433894C212yesmaximal, complemented
15#21433891C212yesmaximal, complemented
16#21433891C212yesmaximal, complemented
17#21433888C212yesmaximal, complemented
18#21432684C211yesmaximal, characteristic, complemented
19#21432683C211yesmaximal, characteristic, complemented
20#21432657C211yesmaximal, characteristic, complemented
21C2×#16837405C211yesmaximal, characteristic
22#418×D59C211yesmaximal, characteristic
23C59×#3081C211yesmaximal, characteristic, complemented
24C22×D4×D59C2211yescharacteristic
25C22×#11745659C2211yescharacteristic
26C2×M16×D59C2211yescharacteristic
27#16838033C2211yescharacteristic, complemented
28#16838032—21no—
29#16838032C2212yescomplemented
30#16838030C2211yescharacteristic, complemented
31#16838030C2211yescharacteristic, complemented
32#16838029—21no—
33#16838029C2212yescomplemented
34#16838027—22no—
35#16837958—21no—
36#16837958C2212yescomplemented
37#16837957—21no—
38#16837957C2212yescomplemented
39#16837954—22no—
40#16837877C2211yescharacteristic
41#16837876C2211yescharacteristic
42#16837876C2211yescharacteristic
43#16837875—22no—
44#16837874—21no—
45#16837874—21no—
46#16837874C2212yes—
47#16837874C2212yes—
48C4×D4×D59—21no—
49C4×D4×D59—21no—
50C4×D4×D59C2212yes—
51C4×D4×D59C2212yes—
52C2×#14273685C2211yescharacteristic
53#117×D59C2211yescharacteristic
54#117×D59C2211yescharacteristic
55#117×D59C2211yescharacteristic
56C2×C22⋊C4×D59—22no—
57#16837705C2212yescomplemented
58#16837705C2212yescomplemented
59#16837704C2212yescomplemented
60#16837704C2212yescomplemented
61#16837703C2212yescomplemented
62#16837703C2212yescomplemented
63#16837702C2212yescomplemented
64#16837702C2212yescomplemented
65#16837701C2212yescomplemented
66#16837701C2212yescomplemented
67#16837700C2212yescomplemented
68#16837700C2212yescomplemented
69#16837699C2212yescomplemented
70#16837699C2212yescomplemented
71#16837693C2212yescomplemented
72#16837692C2212yescomplemented
73#16837691C2212yescomplemented
74#16837691C2212yescomplemented
75#16837690C2212yescomplemented
76#16837690C2212yescomplemented
77#16837689C2212yescomplemented
78#16837683C2212yescomplemented
79#16837682C2212yescomplemented
80#16837681C2212yescomplemented
81#16837681C2212yescomplemented
82#16837680C2212yescomplemented
83#16837680C2212yescomplemented
84#16837679C2212yescomplemented
85#16837445C2211yescharacteristic, complemented
86#16837444C2211yescharacteristic, complemented
87#16837443C2211yescharacteristic, complemented
88#16837443C2212yescomplemented
89#16837443C2211yescharacteristic, complemented
90#16837443C2211yescharacteristic, complemented
91#16837443C2211yescharacteristic, complemented
92#16837442C2211yescharacteristic, complemented
93#16837441C2211yescharacteristic, complemented
94#16837441C2212yescomplemented
95#16837441C2211yescharacteristic, complemented
96#16837441C2211yescharacteristic, complemented
97#16837441C2211yescharacteristic, complemented
98#16837440C2211yescharacteristic, complemented
99#16837439C2212yescomplemented
100#16837438C2211yescharacteristic, complemented
101#16837438C2211yescharacteristic, complemented
102#16837437C2212yescomplemented
103#16837430C2211yescharacteristic, complemented
104#16837429C2211yescharacteristic, complemented
105#16837428C2211yescharacteristic, complemented
106#16837427C2212yescomplemented
107#16837427C2212yescomplemented
108#16837424C2212yescomplemented
109#16837424C2212yescomplemented
110#16837408C2211yescharacteristic
111#16837407C2211yescharacteristic
112#16837406C2211yescharacteristic
113#16837405C2212yes—
114#16837405C2212yes—
115#16837405C2212yes—
116#16837405C2212yes—
117#16837405C2212yes—
118#16837405C2212yes—
119C2×#14273649C2211yescharacteristic
120C2×#14273648C2211yescharacteristic
121C2×#14273647C2211yescharacteristic
122#102×D59C2212yes—
123#102×D59C2212yes—
124C59×#544C2211yescharacteristic, complemented
125C59×#518C2211yescharacteristic
126C59×#478C2212yescomplemented
127C59×#478C2212yescomplemented
128C59×#476C2212yescomplemented
129C59×#474C2212yescomplemented
130C59×#428C2211yescharacteristic, complemented
131C59×#427C2211yescharacteristic, complemented
132C59×#424C2211yescharacteristic, complemented
133C59×#418C2211yescharacteristic
134C2×#102×C59C2211yescharacteristic
135C24×D59—21no—
136C22×D236C2311yescharacteristic
137C22×C22⋊D59—21no—
138C2×D4×D59—21no—
139C2×D4×D59—21no—
140C2×D4×D59—24no—
141C2×D4×D59Q818yescomplemented
142C2×D4×D59C2312yes—
143C2×D4×D59C2312yes—
144C22×C4×D59—22no—
145C22×C4×D59—22no—
146C22×C4×D59C2311yescharacteristic
147C2×#11745664C2311yescharacteristic
148C2×#11745659—24no—
149C2×#11745659C2312yes—
150C2×#11745659C2311yescharacteristic
151C2×#11745659C2311yescharacteristic
152C2×#11745659C2311yescharacteristic
153C2×#11745659C2311yescharacteristic
154M16×D59—24no—
155C22×C59⋊C8C2311yescharacteristic
156C2×C8×D59C2312yes—
157#14273727—21no—
158#14273727C2312yescomplemented
159#14273726—21no—
160#14273726—21no—
161#14273726—22no—
162#14273726C2312yescomplemented
163#14273726C2312yescomplemented
164#14273725—22no—
165#14273719—21no—
166#14273719C2312yescomplemented
167#14273718—21no—
168#14273718—21no—
169#14273718C2312yescomplemented
170#14273718C2312yescomplemented
171#14273717—22no—
172#14273717—22no—
173#14273707—22no—
174#14273707—22no—
175#14273706—22no—
176#14273705—22no—
177#14273705—22no—
178#14273705—22no—
179#14273705—22no—
180#14273704—22no—
181#14273704—22no—
182#14273703—22no—
183#14273703—22no—
184Q8×Dic59—22no—
185#14273692—22no—
186#14273692—22no—
187#14273692—22no—
188C4×D236—21no—
189C4×D236—21no—
190C4×D236C2312yes—
191C4×D236C2312yes—
192D4×Dic59—21no—
193D4×Dic59—21no—
194D4×Dic59C2312yes—
195D4×Dic59C2312yes—
196#14273689—21no—
197#14273689—21no—
198#14273689C2312yes—
199#14273689C2312yes—
200C4×C22⋊D59—22no—
201C4×C22⋊D59—22no—
202C4×C22⋊D59—22no—
203C4×C22⋊D59—22no—
204(C22⋊D59)⋊C4—22no—
205(C22⋊D59)⋊C4—22no—
206(C22⋊D59)⋊C4—22no—
207(C22⋊D59)⋊C4—22no—
208#14273686C2311yescharacteristic
209#14273686C2311yescharacteristic
210#14273686C2311yescharacteristic
211#14273685—21no—
212#14273685—21no—
213#14273685D411yescharacteristic
214#14273685D411yescharacteristic
215#14273685C2312yes—
216#14273685C2311yescharacteristic
217#14273685C2312yes—
218#14273685C2311yescharacteristic
219#14273685C2311yescharacteristic
220#14273685C2311yescharacteristic
221#14273684—21no—
222#14273684—21no—
223#14273684C2312yes—
224#14273683—21no—
225#14273683—21no—
226#14273683D412yes—
227C2×C4⋊Dic59C2311yescharacteristic
228C4⋊C4×D59D411yescharacteristic
229C4⋊C4×D59D411yescharacteristic
230C4⋊C4×D59C2311yescharacteristic
231C4⋊C4×D59C2311yescharacteristic
232C4⋊C4×D59C2311yescharacteristic
233C4⋊C4×D59C2311yescharacteristic
234C2×C22⋊Dic59—22no—
235C2×(C2×D59)⋊C4—21no—
236C2×(C2×D59)⋊C4—22no—
237C2×(C2×D59)⋊C4—22no—
238C22⋊C4×D59—21no—
239C22⋊C4×D59—21no—
240C22⋊C4×D59—22no—
241C22⋊C4×D59—22no—
242C22⋊C4×D59—22no—
243C22⋊C4×D59—22no—
244C22⋊C4×D59—22no—
245C22⋊C4×D59—22no—
246C22⋊C4×D59D412yes—
247C2×C4×Dic59—21no—
248C42×D59—21no—
249C42×D59—21no—
250C42×D59C2312yes—
251#14273661C2311yescharacteristic, complemented
252#14273661C2312yescomplemented
253#14273661C2311yescharacteristic, complemented
254#14273660C2311yescharacteristic, complemented
255#14273660C2312yescomplemented
256#14273660C2311yescharacteristic, complemented
257#14273660C2311yescharacteristic, complemented
258#14273660C2312yescomplemented
259#14273660C2311yescharacteristic, complemented
260#14273659C2311yescharacteristic, complemented
261#14273659C2312yescomplemented
262#14273659C2311yescharacteristic, complemented
263#14273658C2311yescharacteristic, complemented
264#14273658C2312yescomplemented
265#14273658C2311yescharacteristic, complemented
266#14273658C2311yescharacteristic, complemented
267#14273658C2312yescomplemented
268#14273658C2311yescharacteristic, complemented
269C4⋊(C59⋊C8)C2312yescomplemented
270C4⋊(C59⋊C8)C2312yescomplemented
271Dic59⋊C8C2312yescomplemented
272Dic59⋊C8C2312yescomplemented
273Dic59⋊C8C2312yescomplemented
274Dic59⋊C8C2312yescomplemented
275#14273649C2312yes—
276#14273649C2312yes—
277#14273649C2312yes—
278#14273649C2312yes—
279#14273648C2312yes—
280#14273648C2312yes—
281#14273648C2312yes—
282#14273648C2312yes—
283#14273647C2312yes—
284#14273647C2312yes—
285#14273647C2312yes—
286#14273647C2312yes—
287C22×D4×C59C2311yescharacteristic
288C2×M16×C59C2311yescharacteristic
289C22×C8×C59C2311yescharacteristic
290C4⋊Q8×C59—21no—
291C4⋊Q8×C59C2312yescomplemented
292#125×C59—21no—
293#125×C59C2312yescomplemented
294C22⋊Q8×C59—22no—
295C4×D4×C59—21no—
296C4×D4×C59—21no—
297C4×D4×C59C2312yes—
298C4×D4×C59C2312yes—
299#117×C59C2311yescharacteristic
300#117×C59C2311yescharacteristic
301#117×C59C2311yescharacteristic
302C2×C4⋊C4×C59C2311yescharacteristic
303C2×C22⋊C4×C59—22no—
304#107×C59C2311yescharacteristic, complemented
305#107×C59C2312yescomplemented
306#107×C59C2311yescharacteristic, complemented
307#106×C59C2311yescharacteristic, complemented
308#106×C59C2312yescomplemented
309#106×C59C2311yescharacteristic, complemented
310C4⋊C8×C59C2312yescomplemented
311C4⋊C8×C59C2312yescomplemented
312#102×C59C2312yes—
313#102×C59C2312yes—
314#102×C59C2312yes—
315#102×C59C2312yes—
316C24×C59—21no—
317C23×D59—21no—
318C23×D59—22no—
319C23×D59—28no—
320C23×D59—22no—
321C23×D59—82no—
322C23×D59—82no—
323C23×D59C2×D411yescharacteristic
324C2×Q8×C59—22no—
325C2×D4×C59—21no—
326C2×D4×C59—22no—
327C2×D4×C59C2×Q814yes—
328C2×D4×C59C2412yes—
329C22×C4×C59—21no—
330C22×C4×C59—22no—
331C22×C4×C59—22no—
332C22×C4×C59C2411yescharacteristic
333C2×C22⋊D59—28no—
334C2×C22⋊D59—22no—
335C2×C22⋊D59—22no—
336C22×Dic59—21no—
337C22×Dic59—22no—
338C22×Dic59—22no—
339C22×Dic59C2×D411yescharacteristic
340D4×D59—28no—
341D4×D59—28no—
342D4×D59—24no—
343D4×D59—24no—
344D4×D59C2×Q818yes—
345D4×D59C2×Q818yes—
346C2×D236—21no—
347C2×D236—22no—
348C2×D236C2×Q814yes—
349C2×D236C2412yes—
350C2×C4×D59—21no—
351C2×C4×D59—21no—
352C2×C4×D59—21no—
353C2×C4×D59—21no—
354C2×C4×D59—22no—
355C2×C4×D59—22no—
356C2×C4×D59—22no—
357C2×C4×D59—22no—
358C2×C4×D59—84no—
359C2×C4×D59—84no—
360C2×C4×D59C2×D412yes—
361C2×C4×D59C2×D412yes—
362C2×C4×D59C2×D411yescharacteristic
363C2×C4×D59C2×D411yescharacteristic
364C2×C4×D59C2×Q814yes—
365C2×C4×D59#4114yes—
366C2×C4×D59C2411yescharacteristic
367C2×C4×D59C2411yescharacteristic
368C2×Dic118—22no—
369C2×Dic118—22no—
370C2×Dic118—22no—
371M16×C59—22no—
372C2×C8×C59—22no—
373C2×C8×C59C2411yescharacteristic
374C2×C8×C59C2412yes—
375C2×C8×C59C2411yescharacteristic
376C4⋊C4×C59—21no—
377C4⋊C4×C59—22no—
378C4⋊C4×C59—22no—
379C4⋊C4×C59—22no—
380C4⋊C4×C59C2×D411yescharacteristic
381C4⋊C4×C59C2×D411yescharacteristic
382C4⋊C4×C59C2412yes—
383C4⋊C4×C59C2411yescharacteristic
384C4⋊C4×C59C2411yescharacteristic
385C4⋊C4×C59C2411yescharacteristic
386C4⋊C4×C59C2411yescharacteristic
387C22⋊C4×C59—21no—
388C22⋊C4×C59—21no—
389C22⋊C4×C59—22no—
390C22⋊C4×C59—22no—
391C22⋊C4×C59C2×D412yes—
392C42×C59—21no—
393C42×C59—21no—
394C42×C59C2412yes—
395C22⋊Dic59—21no—
396C22⋊Dic59—21no—
397C22⋊Dic59—22no—
398C22⋊Dic59—22no—
399C22⋊Dic59C2×D412yes—
400(C2×D59)⋊C4—21no—
401(C2×D59)⋊C4—21no—
402(C2×D59)⋊C4—21no—
403(C2×D59)⋊C4—21no—
404(C2×D59)⋊C4—22no—
405(C2×D59)⋊C4—22no—
406(C2×D59)⋊C4—22no—
407(C2×D59)⋊C4—22no—
408(C2×D59)⋊C4—22no—
409(C2×D59)⋊C4—22no—
410(C2×D59)⋊C4C2×D412yes—
411(C2×D59)⋊C4C2×D412yes—
412C4⋊Dic59—21no—
413C4⋊Dic59—22no—
414C4⋊Dic59—22no—
415C4⋊Dic59—22no—
416C4⋊Dic59C2×D411yescharacteristic
417C4⋊Dic59C2×D411yescharacteristic
418C4⋊Dic59C2411yescharacteristic
419C4⋊Dic59C2411yescharacteristic
420C4⋊Dic59C2412yes—
421C4⋊Dic59C2411yescharacteristic
422C4⋊Dic59C2411yescharacteristic
423Dic59⋊C4—22no—
424Dic59⋊C4—22no—
425Dic59⋊C4—21no—
426Dic59⋊C4—21no—
427Dic59⋊C4—21no—
428Dic59⋊C4—21no—
429Dic59⋊C4—22no—
430Dic59⋊C4—22no—
431Dic59⋊C4—22no—
432Dic59⋊C4—22no—
433Dic59⋊C4C2×D412yes—
434Dic59⋊C4C2×D412yes—
435C4×Dic59—21no—
436C4×Dic59—21no—
437C4×Dic59—21no—
438C4×Dic59—21no—
439C4×Dic59—21no—
440C4×Dic59—21no—
441C4×Dic59—22no—
442C4×Dic59—22no—
443C4×Dic59C2×D412yes—
444C4×Dic59C2×D412yes—
445C4×Dic59C2412yes—
446#11745664—22no—
447C2×C59⋊C8—22no—
448C2×C59⋊C8C2412yes—
449C2×C59⋊C8C2411yescharacteristic
450C2×C59⋊C8C2411yescharacteristic
451#11745659—24no—
452#11745659—22no—
453#11745659—22no—
454#11745659—22no—
455#11745659—22no—
456C8×D59—24no—
457C23×C59—22no—
458C23×C59—24no—
459C23×C59—81no—
460C23×C59—81no—
461C23×C59C22×D411yescharacteristic
462C22×D59—22no—
463C22×D59—24no—
464C22×D59—28no—
465C22×D59—28no—
466C22×D59—41no—
467C22×D59—41no—
468C22×D59—44no—
469C22×D59—44no—
470C22×D59—82no—
471C22×D59—82no—
472C22×D59—816no—
473C22×D59—81no—
474C22×D59—81no—
475C22×D59C22⋊Q814yes—
476C22×D59C22×D411yescharacteristic
477C22×D59C22×D411yescharacteristic
478Q8×C59—82no—
479D4×C59—24no—
480D4×C59—22no—
481D4×C59C22×Q814yes—
482C2×C4×C59—22no—
483C2×C4×C59—21no—
484C2×C4×C59—21no—
485C2×C4×C59—21no—
486C2×C4×C59—21no—
487C2×C4×C59—82no—
488C2×C4×C59—82no—
489C2×C4×C59—81no—
490C2×C4×C59C22×D412yes—
491C2×C4×C59C22×D412yes—
492C2×C4×C59C22×D411yescharacteristic
493C2×C4×C59C22×Q812yes—
494C2×C4×C59C2×#4112yes—
495C2×C4×C59C2511yescharacteristic
496C22⋊D59—28no—
497C22⋊D59—28no—
498C2×Dic59—21no—
499C2×Dic59—22no—
500C2×Dic59—21no—
501C2×Dic59—21no—
502C2×Dic59—21no—
503C2×Dic59—82no—
504C2×Dic59—82no—
505C2×Dic59—81no—
506C2×Dic59C22⋊Q814yes—
507C2×Dic59C22×D412yes—
508C2×Dic59C22×D412yes—
509C2×Dic59C22×D411yescharacteristic
510C2×Dic59C22×D411yescharacteristic
511D236—24no—
512D236—22no—
513D236C22×Q814yes—
514C4×D59—42no—
515C4×D59—42no—
516C4×D59—42no—
517C4×D59—42no—
518C4×D59—82no—
519C4×D59—82no—
520C4×D59—82no—
521C4×D59—82no—
522C4×D59—81no—
523C4×D59—81no—
524C4×D59C22⋊Q814yes—
525C4×D59C22⋊Q814yes—
526C4×D59C22×Q812yes—
527C4×D59C22×Q812yes—
528C4×D59C2×#4112yes—
529C4×D59C2×#4112yes—
530Dic118—82no—
531Dic118—82no—
532Dic118—82no—
533C8×C59—22no—
534C8×C59—21no—
535C8×C59—21no—
536C59⋊C8—22no—
537C59⋊C8—21no—
538C59⋊C8—21no—
539#60490—591nomaximal, Sylow
540C22×C59—21no—
541C22×C59—21no—
542C22×C59—24no—
543C22×C59—42no—
544C22×C59—42no—
545C22×C59—84no—
546C22×C59C2×C22⋊Q812yes—
547C22×C59C23×D411yescharacteristic
548C2×D59—21no—
549C2×D59—21no—
550C2×D59—21no—
551C2×D59—21no—
552C2×D59—24no—
553C2×D59—44no—
554C2×D59—416no—
555C2×D59—42no—
556C2×D59—42no—
557C2×D59—88no—
558C2×D59—84no—
559C2×D59C2×C22⋊Q812yes—
560C2×D59C2×C22⋊Q812yes—
561C4×C59—22no—
562C4×C59—22no—
563C4×C59—41no—
564C4×C59—42no—
565C4×C59—41no—
566C4×C59—41no—
567C4×C59—41no—
568C4×C59C2×C22⋊Q812yes—
569C4×C59C23×Q811yescharacteristic
570C4×C59C22×#4111yescharacteristic
571Dic59—22no—
572Dic59—22no—
573Dic59—41no—
574Dic59—41no—
575Dic59—42no—
576Dic59—41no—
577Dic59—41no—
578Dic59C2×C22⋊Q812yes—
579Dic59C2×C22⋊Q812yes—
580#3458—591no—
581C2×#518—591no—
582#3081—592no—
583#3081—592no—
584#3081—592no—
585#3081—592no—
586#3081—591no—
587#3081—591no—
588#3081—591no—
589#3081—591no—
590#3081—591no—
591#3081—591no—
592#3081—591no—
593#3081D5911yescharacteristic, complemented
594#3077—592no—
595#3077—592no—
596#3077—592no—
597#3077—592no—
598#2911—591no—
599#2911—591no—
600#2905—591no—
601C2×#418—591no—
602C2×#418—591no—
603C2×C59—22no—
604C2×C59—44no—
605C2×C59C22×C22⋊Q811yescharacteristic
606C2×C59#358511yescharacteristic
607C2×C59#358511yescharacteristic
608D59—22no—
609D59—22no—
610D59—44no—
611C23×D4—591no—
612C22×M16—591no—
613C22×M16—591no—
614#544—592no—
615#544—592no—
616#544—591no—
617#544—591no—
618#544—591no—
619#544—1181no—
620#544—1181no—
621#544C2×D5911yescharacteristic, complemented
622#543—1182no—
623#533—592no—
624#533—592no—
625#533—1182no—
626#533—1181no—
627#533—1181no—
628#518—591no—
629#518—592no—
630#518—592no—
631#518—591no—
632#518—591no—
633#518—1182no—
634#518—1181no—
635#518—1181no—
636#518C2×D5911yescharacteristic
637C2×C4×D4—592no—
638C2×C4×D4—592no—
639C2×C4×D4—1181no—
640C2×C4×D4—1181no—
641C2×#117—591no—
642C2×#117—591no—
643C2×#117—591no—
644C2×#117—591no—
645C22×C22⋊C4—1182no—
646#478—592no—
647#478—592no—
648#478—592no—
649#478—592no—
650#478—592no—
651#478—592no—
652#478—592no—
653#478—592no—
654#478—592no—
655#478—592no—
656#478—592no—
657#478—592no—
658#478—592no—
659#478—592no—
660#478C2×D5912yescomplemented
661#478C2×D5912yescomplemented
662#476—592no—
663#476—592no—
664#476—592no—
665#476—592no—
666#476—592no—
667#476—592no—
668#476—592no—
669#476C2×D5912yescomplemented
670#474—592no—
671#474—592no—
672#474—592no—
673#474—592no—
674#474—592no—
675#474—592no—
676#474—592no—
677#474C2×D5912yescomplemented
678#428—591no—
679#428—591no—
680#428—591no—
681#428—592no—
682#428—591no—
683#428—591no—
684#428—591no—
685#428—591no—
686#428—592no—
687#428—591no—
688#428—591no—
689#428—591no—
690#428—591no—
691#428C2×D5911yescharacteristic, complemented
692#427—591no—
693#427—591no—
694#427—591no—
695#427—592no—
696#427—592no—
697#427C2×D5911yescharacteristic, complemented
698#424—591no—
699#424—591no—
700#424—591no—
701#424—592no—
702#424—592no—
703#424C2×D5911yescharacteristic, complemented
704#423—592no—
705#423—592no—
706#418—591no—
707#418—591no—
708#418—591no—
709#418—592no—
710#418—592no—
711#418—592no—
712#418—592no—
713#418—592no—
714#418—592no—
715#418C2×D5911yescharacteristic
716C2×#102—591no—
717C2×#102—591no—
718C2×#102—591no—
719C2×#102—592no—
720C2×#102—592no—
721C2×#102C2×D5911yescharacteristic
722C59#6049011yescharacteristic, complemented, Sylow
723C25—1181no—
724C22×D4—598no—
725C22×D4—592no—
726C22×D4—592no—
727C22×D4—591no—
728C22×D4—1181no—
729C22×D4—1181no—
730C22×D4—1184no—
731C22×D4—1181no—
732C22×D4C22×D5911yescharacteristic
733C23×C4—591no—
734C23×C4—1182no—
735C23×C4—1182no—
736C2×M16—591no—
737C2×M16—591no—
738C2×M16—592no—
739C2×M16—591no—
740C2×M16—591no—
741C2×M16—591no—
742C2×M16—1184no—
743C2×M16—1184no—
744C2×M16C22×D5911yescharacteristic
745C22×C8—591no—
746C22×C8—592no—
747C22×C8C22×D5911yescharacteristic
748C4⋊Q8—21no—
749C4⋊Q8—592no—
750C4⋊Q8—592no—
751C4⋊Q8—592no—
752C4⋊Q8—1181no—
753C4⋊Q8—1182no—
754C4⋊Q8—1181no—
755C4⋊Q8—1182no—
756C4⋊Q8—1181no—
757C4⋊Q8C22×D5912yescomplemented
758#125—21no—
759#125—592no—
760#125—592no—
761#125—592no—
762#125—1181no—
763#125—1182no—
764#125—1182no—
765#125—1181no—
766#125—1181no—
767#125C22×D5912yescomplemented
768C22⋊Q8—22no—
769C22⋊Q8—1182no—
770C22⋊Q8—1182no—
771C22⋊Q8—1182no—
772C22⋊Q8—1182no—
773C22⋊Q8—1182no—
774C22⋊Q8—1182no—
775C22⋊Q8—1182no—
776C22⋊Q8—1182no—
777C22⋊Q8—1182no—
778C22⋊Q8—1182no—
779C22⋊Q8—1182no—
780C4×Q8—1182no—
781C4×Q8—1182no—
782C4×Q8—1182no—
783C4×Q8—1182no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4—592no—
787C4×D4—592no—
788C4×D4—592no—
789C4×D4—592no—
790C4×D4—592no—
791C4×D4—592no—
792C4×D4—1181no—
793C4×D4—1181no—
794C4×D4—1182no—
795C4×D4—1182no—
796C4×D4—1182no—
797C4×D4—1182no—
798C4×D4—1182no—
799C4×D4—1182no—
800C4×D4—1182no—
801C4×D4—1182no—
802C4×D4—1181no—
803C4×D4—1181no—
804C4×D4—1181no—
805C4×D4—1181no—
806C4×D4C22×D5912yes—
807C4×D4C22×D5912yes—
808#117—591no—
809#117—591no—
810#117—591no—
811#117—592no—
812#117—592no—
813#117—591no—
814#117—591no—
815#117—591no—
816#117—591no—
817#117—591no—
818#117—591no—
819#117—592no—
820#117—592no—
821#117—1181no—
822#117—1181no—
823#117—1181no—
824#117—1181no—
825#117—1181no—
826#117—1181no—
827#117C22×D5911yescharacteristic
828#117C22×D5911yescharacteristic
829#117C22×D5911yescharacteristic
830C2×C4⋊C4—591no—
831C2×C4⋊C4—591no—
832C2×C4⋊C4—591no—
833C2×C4⋊C4—591no—
834C2×C4⋊C4—591no—
835C2×C4⋊C4—591no—
836C2×C4⋊C4—591no—
837C2×C4⋊C4C22×D5911yescharacteristic
838C2×C22⋊C4—22no—
839C2×C22⋊C4—592no—
840C2×C22⋊C4—1182no—
841C2×C22⋊C4—1182no—
842C2×C22⋊C4—1182no—
843C2×C22⋊C4—1182no—
844C2×C22⋊C4—1182no—
845C2×C22⋊C4—1181no—
846C2×C22⋊C4—1181no—
847C2×C22⋊C4—1182no—
848C2×C22⋊C4—1182no—
849C2×C22⋊C4—1182no—
850C2×C22⋊C4—1181no—
851C2×C22⋊C4—1182no—
852C2×C42—592no—
853C2×C42—1181no—
854C2×C42—1181no—
855C2×C42—1181no—
856#107—592no—
857#107—591no—
858#107—591no—
859#107—591no—
860#107—592no—
861#107—591no—
862#107—591no—
863#107—591no—
864#107—592no—
865#107C22×D5912yescomplemented
866#107C22×D5911yescharacteristic, complemented
867#107C22×D5911yescharacteristic, complemented
868#106—591no—
869#106—591no—
870#106—592no—
871#106—592no—
872#106—591no—
873#106—591no—
874#106—591no—
875#106—591no—
876#106—592no—
877#106C22×D5912yescomplemented
878#106C22×D5911yescharacteristic, complemented
879#106C22×D5911yescharacteristic, complemented
880C4⋊C8—592no—
881C4⋊C8—592no—
882C4⋊C8—592no—
883C4⋊C8—592no—
884C4⋊C8—592no—
885C4⋊C8—592no—
886C4⋊C8C22×D5912yescomplemented
887C4⋊C8C22×D5912yescomplemented
888#102—592no—
889#102—592no—
890#102—592no—
891#102—592no—
892#102—592no—
893#102—592no—
894#102—592no—
895#102—592no—
896#102—592no—
897#102—592no—
898#102—592no—
899#102—592no—
900#102C22×D5912yes—
901#102C22×D5912yes—
902#102C22×D5912yes—
903#102C22×D5912yes—
904C24—21no—
905C24—591no—
906C24—1182no—
907C24—1188no—
908C24—1182no—
909C24—1181no—
910C24—4722no—
911C24—4722no—
912C2×Q8—22no—
913C2×Q8—1182no—
914C2×Q8—1182no—
915C2×Q8—1182no—
916C2×D4—21no—
917C2×D4—22no—
918C2×D4—598no—
919C2×D4—598no—
920C2×D4—594no—
921C2×D4—592no—
922C2×D4—1188no—
923C2×D4—1188no—
924C2×D4—1184no—
925C2×D4—1184no—
926C2×D4—1182no—
927C2×D4—1182no—
928C2×D4—1188no—
929C2×D4—1181no—
930C2×D4—1182no—
931C2×D4Q8×D5914yes—
932C2×D4C23×D5912yes—
933C22×C4—21no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—591no—
937C22×C4—591no—
938C22×C4—591no—
939C22×C4—594no—
940C22×C4—594no—
941C22×C4—591no—
942C22×C4—591no—
943C22×C4—592no—
944C22×C4—592no—
945C22×C4—1182no—
946C22×C4—1182no—
947C22×C4—1181no—
948C22×C4—1181no—
949C22×C4—1181no—
950C22×C4—1181no—
951C22×C4—1182no—
952C22×C4—1182no—
953C22×C4—1181no—
954C22×C4—1182no—
955C22×C4—1182no—
956C22×C4—4724no—
957C22×C4—4724no—
958C22×C4C23×D5911yescharacteristic
959M16—22no—
960M16—1182no—
961M16—1182no—
962M16—1182no—
963M16—1182no—
964M16—1184no—
965M16—1182no—
966C2×C8—22no—
967C2×C8—592no—
968C2×C8—591no—
969C2×C8—591no—
970C2×C8—1184no—
971C2×C8—1182no—
972C2×C8C23×D5911yescharacteristic
973C2×C8C23×D5912yes—
974C2×C8C23×D5911yescharacteristic
975C4⋊C4—21no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—592no—
980C4⋊C4—592no—
981C4⋊C4—591no—
982C4⋊C4—591no—
983C4⋊C4—592no—
984C4⋊C4—591no—
985C4⋊C4—591no—
986C4⋊C4—591no—
987C4⋊C4—591no—
988C4⋊C4—1181no—
989C4⋊C4—1181no—
990C4⋊C4—1181no—
991C4⋊C4—1181no—
992C4⋊C4—1182no—
993C4⋊C4—1182no—
994C4⋊C4—1182no—
995C4⋊C4—1182no—
996C4⋊C4—1182no—
997C4⋊C4—1182no—
998C4⋊C4—1181no—
999C4⋊C4—1182no—
1000C4⋊C4—1182no—
1001C4⋊C4—1182no—
1002C4⋊C4D4×D5911yescharacteristic
1003C4⋊C4D4×D5911yescharacteristic
1004C4⋊C4C23×D5911yescharacteristic
1005C4⋊C4C23×D5911yescharacteristic
1006C4⋊C4C23×D5912yes—
1007C4⋊C4C23×D5911yescharacteristic
1008C4⋊C4C23×D5911yescharacteristic
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—592no—
1014C22⋊C4—592no—
1015C22⋊C4—592no—
1016C22⋊C4—1182no—
1017C22⋊C4—1182no—
1018C22⋊C4—1181no—
1019C22⋊C4—1181no—
1020C22⋊C4—1181no—
1021C22⋊C4—1181no—
1022C22⋊C4—1182no—
1023C22⋊C4—1182no—
1024C22⋊C4—1182no—
1025C22⋊C4—1182no—
1026C22⋊C4—1181no—
1027C22⋊C4—1181no—
1028C22⋊C4—1182no—
1029C22⋊C4—1182no—
1030C22⋊C4D4×D5912yes—
1031C42—21no—
1032C42—21no—
1033C42—592no—
1034C42—592no—
1035C42—592no—
1036C42—1181no—
1037C42—1181no—
1038C42—1181no—
1039C42—1181no—
1040C42—1182no—
1041C42—1182no—
1042C42—1181no—
1043C42—1181no—
1044C42C23×D5912yes—
1045C23—22no—
1046C23—24no—
1047C23—81no—
1048C23—81no—
1049C23—591no—
1050C23—591no—
1051C23—594no—
1052C23—1188no—
1053C23—1188no—
1054C23—1184no—
1055C23—1182no—
1056C23—4721no—
1057C23—4721no—
1058C23—4722no—
1059C23—4722no—
1060C23—47216no—
1061C23—2361no—
1062C23—2361no—
1063C23—2364no—
1064C23—2364no—
1065C23C2×D4×D5911yescharacteristic
1066Q8—82no—
1067Q8—4722no—
1068Q8—4722no—
1069Q8—4722no—
1070D4—24no—
1071D4—22no—
1072D4—594no—
1073D4—1188no—
1074D4—1188no—
1075D4—1184no—
1076D4—1182no—
1077D4C2×Q8×D5914yes—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—81no—
1086C2×C4—594no—
1087C2×C4—591no—
1088C2×C4—591no—
1089C2×C4—594no—
1090C2×C4—594no—
1091C2×C4—592no—
1092C2×C4—592no—
1093C2×C4—592no—
1094C2×C4—592no—
1095C2×C4—592no—
1096C2×C4—592no—
1097C2×C4—1181no—
1098C2×C4—1181no—
1099C2×C4—1181no—
1100C2×C4—1182no—
1101C2×C4—1181no—
1102C2×C4—4722no—
1103C2×C4—4722no—
1104C2×C4—4722no—
1105C2×C4—4722no—
1106C2×C4—4721no—
1107C2×C4—4721no—
1108C2×C4—4722no—
1109C2×C4—4722no—
1110C2×C4—4721no—
1111C2×C4—2362no—
1112C2×C4—2362no—
1113C2×C4—2362no—
1114C2×C4—2362no—
1115C2×C4C2×D4×D5912yes—
1116C2×C4C2×D4×D5912yes—
1117C2×C4C2×D4×D5911yescharacteristic
1118C2×C4C2×Q8×D5912yes—
1119C2×C4#41×D5912yes—
1120C2×C4C24×D5911yescharacteristic
1121C8—21no—
1122C8—21no—
1123C8—22no—
1124C8—1182no—
1125C8—1181no—
1126C8—1181no—
1127C22—21no—
1128C22—21no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—84no—
1133C22—592no—
1134C22—592no—
1135C22—1181no—
1136C22—1181no—
1137C22—1181no—
1138C22—1181no—
1139C22—1184no—
1140C22—4724no—
1141C22—4728no—
1142C22—2364no—
1143C22—23616no—
1144C22—2362no—
1145C22—2362no—
1146C22C22⋊Q8×D5912yes—
1147C22C22×D4×D5911yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—592no—
1156C4—592no—
1157C4—1182no—
1158C4—1182no—
1159C4—2361no—
1160C4—2361no—
1161C4—2361no—
1162C4—2361no—
1163C4—2362no—
1164C4C22⋊Q8×D5912yes—
1165C4C22×Q8×D5911yescharacteristic
1166C4C2×#41×D5911yescharacteristic
1167C2—22no—
1168C2—44no—
1169C2—1182no—
1170C2—1182no—
1171C2—2364no—
1172C2C2×C22⋊Q8×D5911yescharacteristic
1173C2#2143887111yescharacteristic
1174C2#2143887411yescharacteristic
subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3081C2
socleC22×C59C23×D4
prime radicalC22×D4×D59C22
hypercenter#3081D59
hypocenterC59#60490
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #21437500C2semidirect
3. #21433930C2semidirect
4. #21433929C2semidirect
5. #21433928C2semidirect
6. #21433927C2semidirect
7. #21433926C2semidirect
8. #21433925C2semidirect
9. #21433924C2semidirect
10. #21433923C2semidirect
11. #21433922C2semidirect
12. #21433921C2semidirect
13. #21433920C2semidirect
14. #21433894C2semidirect
15. #21433891C2semidirect
16. #21433891C2semidirect
17. #21433888C2semidirect
18. #21432684C2semidirect
19. #21432683C2semidirect
20. #21432657C2semidirect
23. C59×#3081C2semidirect
27. #16838033C22semidirect
29. #16838032C22semidirect
30. #16838030C22semidirect
31. #16838030C22semidirect
33. #16838029C22semidirect
36. #16837958C22semidirect
38. #16837957C22semidirect
57. #16837705C22semidirect
58. #16837705C22semidirect
59. #16837704C22semidirect
60. #16837704C22semidirect
61. #16837703C22semidirect
62. #16837703C22semidirect
63. #16837702C22semidirect
64. #16837702C22semidirect
65. #16837701C22semidirect
66. #16837701C22semidirect
67. #16837700C22semidirect
68. #16837700C22semidirect
69. #16837699C22semidirect
70. #16837699C22semidirect
71. #16837693C22semidirect
72. #16837692C22semidirect
73. #16837691C22semidirect
74. #16837691C22semidirect
75. #16837690C22semidirect
76. #16837690C22semidirect
77. #16837689C22semidirect
78. #16837683C22semidirect
79. #16837682C22semidirect
80. #16837681C22semidirect
81. #16837681C22semidirect
82. #16837680C22semidirect
83. #16837680C22semidirect
84. #16837679C22semidirect
85. #16837445C22semidirect
86. #16837444C22semidirect
87. #16837443C22semidirect
88. #16837443C22semidirect
89. #16837443C22semidirect
90. #16837443C22semidirect
91. #16837443C22semidirect
92. #16837442C22semidirect
93. #16837441C22semidirect
94. #16837441C22semidirect
95. #16837441C22semidirect
96. #16837441C22semidirect
97. #16837441C22semidirect
98. #16837440C22semidirect
99. #16837439C22semidirect
100. #16837438C22semidirect
101. #16837438C22semidirect
102. #16837437C22semidirect
103. #16837430C22semidirect
104. #16837429C22semidirect
105. #16837428C22semidirect
106. #16837427C22semidirect
107. #16837427C22semidirect
108. #16837424C22semidirect
109. #16837424C22semidirect
124. C59×#544C22semidirect
126. C59×#478C22semidirect
127. C59×#478C22semidirect
128. C59×#476C22semidirect
129. C59×#474C22semidirect
130. C59×#428C22semidirect
131. C59×#427C22semidirect
132. C59×#424C22semidirect
141. C2×D4×D59Q8semidirect
158. #14273727C23semidirect
162. #14273726C23semidirect
163. #14273726C23semidirect
166. #14273719C23semidirect
169. #14273718C23semidirect
170. #14273718C23semidirect
251. #14273661C23semidirect
252. #14273661C23semidirect
253. #14273661C23semidirect
254. #14273660C23semidirect
255. #14273660C23semidirect
256. #14273660C23semidirect
257. #14273660C23semidirect
258. #14273660C23semidirect
259. #14273660C23semidirect
260. #14273659C23semidirect
261. #14273659C23semidirect
262. #14273659C23semidirect
263. #14273658C23semidirect
264. #14273658C23semidirect
265. #14273658C23semidirect
266. #14273658C23semidirect
267. #14273658C23semidirect
268. #14273658C23semidirect
269. C4⋊(C59⋊C8)C23semidirect
270. C4⋊(C59⋊C8)C23semidirect
271. Dic59⋊C8C23semidirect
272. Dic59⋊C8C23semidirect
273. Dic59⋊C8C23semidirect
274. Dic59⋊C8C23semidirect
291. C4⋊Q8×C59C23semidirect
293. #125×C59C23semidirect
304. #107×C59C23semidirect
305. #107×C59C23semidirect
306. #107×C59C23semidirect
307. #106×C59C23semidirect
308. #106×C59C23semidirect
309. #106×C59C23semidirect
310. C4⋊C8×C59C23semidirect
311. C4⋊C8×C59C23semidirect
593. #3081D59semidirect
621. #544C2×D59semidirect
660. #478C2×D59semidirect
661. #478C2×D59semidirect
669. #476C2×D59semidirect
677. #474C2×D59semidirect
691. #428C2×D59semidirect
697. #427C2×D59semidirect
703. #424C2×D59semidirect
722. C59#60490semidirect
757. C4⋊Q8C22×D59semidirect
767. #125C22×D59semidirect
865. #107C22×D59semidirect
866. #107C22×D59semidirect
867. #107C22×D59semidirect
877. #106C22×D59semidirect
878. #106C22×D59semidirect
879. #106C22×D59semidirect
886. C4⋊C8C22×D59semidirect
887. C4⋊C8C22×D59semidirect

Maximal subgroups

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

subgroupindex
#214375002
#518×D592
#214339302
#214339292
#214339282
#214339272
#214339262
#214339252
#214339242
#214339232
#214339222
#214339212
#214339202
#214338942
#214338912
#214338882
#214326842
#214326832
#214326572
C2×#168374052
#418×D592
C59×#30812
#6049059