Finite Group Databasebeta

← #28555702

Subgroups — #28555702

Order 15104.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437706C211yesmaximal, characteristic
2#21433221C211yesmaximal, characteristic, complemented
3#21422566C211yesmaximal, characteristic, complemented
4#21422562C211yesmaximal, characteristic, complemented
5#21422557C211yesmaximal, characteristic, complemented
6#21422540C211yesmaximal, characteristic, complemented
7#21422531C211yesmaximal, characteristic, complemented
8#21422522C211yesmaximal, characteristic, complemented
9#21422510C211yesmaximal, characteristic, complemented
10#21422505C211yesmaximal, characteristic, complemented
11#21422496C211yesmaximal, characteristic, complemented
12#21422488C211yesmaximal, characteristic, complemented
13#21422484C211yesmaximal, characteristic, complemented
14C2×#16837131C211yesmaximal, characteristic, complemented
15C59×#2922C211yesmaximal, characteristic, complemented
16#16838137C411yescharacteristic
17#16838112C411yescharacteristic
18#16838109C411yescharacteristic
19#16838098C411yescharacteristic
20#16838098C411yescharacteristic
21#16838096—21no—
22#16838076—21no—
23#16838076—21no—
24#16838048C411yescharacteristic
25#16838048C411yescharacteristic
26#16838040—21no—
27D4×D236C411yescharacteristic
28#16837952C2211yescharacteristic
29#16837939—21no—
30#16837936C2211yescharacteristic
31#16837936C2211yescharacteristic
32#16837911—21no—
33#16837911—21no—
34C4×#11745685C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C4×D4×D59—21no—
38#16837533—21no—
39#16837474—21no—
40#16837474—21no—
41D4×C59⋊C8—21no—
42#16837459C2211yescharacteristic, complemented
43#16837459C2211yescharacteristic, complemented
44#16837455C2211yescharacteristic, complemented
45#16837426C2211yescharacteristic, complemented
46C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
47C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
48#16837134C2211yescharacteristic, complemented
49#16837134C2211yescharacteristic, complemented
50#16837134C2211yescharacteristic, complemented
51#16837134C2211yescharacteristic, complemented
52#16837131C2211yescharacteristic
53#16837131C2211yescharacteristic
54#16837131C2211yescharacteristic
55#16837131C2211yescharacteristic
56#16837131C2211yescharacteristic, complemented
57#16837131C2211yescharacteristic, complemented
58#16837131C2211yescharacteristic, complemented
59#16837131C2211yescharacteristic, complemented
60#16837131C2211yescharacteristic, complemented
61#16837131C2211yescharacteristic, complemented
62#16837131C2211yescharacteristic, complemented
63#16837131C2211yescharacteristic, complemented
64C4×#41×C59C2211yescharacteristic
65C59×#433—21no—
66C59×#433—21no—
67C59×#431C2211yescharacteristic, complemented
68C59×#431C2211yescharacteristic, complemented
69C59×#431C2211yescharacteristic, complemented
70C59×#431C2211yescharacteristic, complemented
71C59×#424—21no—
72C59×#408—21no—
73C4×M16×C59C2211yescharacteristic, complemented
74C2×C4×C8×C59C2211yescharacteristic, complemented
75C2×#11745685—21no—
76C2×#11745685C2×C411yescharacteristic
77C22×D236C2×C411yescharacteristic
78C22×D236C2×C411yescharacteristic
79C2×D4×D59—21no—
80C22×C4×D59—21no—
81C22×C4×D59—21no—
82C2×#11745664—21no—
83C22×C59⋊C8—21no—
84C22×C59⋊C8—21no—
85#14273727C2×C411yescharacteristic
86#14273724C2×C411yescharacteristic
87#14273722—21no—
88#14273722—21no—
89#14273721—21no—
90#14273721—21no—
91#14273719C2×C411yescharacteristic
92#14273719C2×C411yescharacteristic
93#14273718—21no—
94#14273716—21no—
95#14273715—21no—
96#14273715C2×C411yescharacteristic
97#14273715C2×C411yescharacteristic
98#14273712—21no—
99#14273712—21no—
100#14273712—21no—
101#14273712—21no—
102#14273710—21no—
103#14273710—21no—
104#14273709—21no—
105#14273709—21no—
106#14273706C2×C411yescharacteristic
107#14273706C2×C411yescharacteristic
108#14273705—21no—
109#14273705—21no—
110#14273704—21no—
111#14273704—21no—
112#14273703—21no—
113#14273702—21no—
114#14273701—21no—
115#14273701C2×C411yescharacteristic
116#14273701C2×C411yescharacteristic
117#14273701C2×C411yescharacteristic
118#14273701C2×C411yescharacteristic
119#14273700—21no—
120#14273700—21no—
121#14273699—21no—
122#14273699—21no—
123#14273697—21no—
124#14273697—21no—
125#14273695—21no—
126#14273695—21no—
127C4×Dic118C2×C411yescharacteristic
128C4×Dic118C2311yescharacteristic
129C4×D236—21no—
130C4×D236—21no—
131C4×D236—21no—
132C4×D236—21no—
133C4×D236—21no—
134C4×D236C2×C411yescharacteristic
135C4×D236C2×C411yescharacteristic
136C4×D236C2×C411yescharacteristic
137C4×D236C2×C411yescharacteristic
138C4×D236C2×C411yescharacteristic
139C4×D236C2311yescharacteristic
140C4×D236C2311yescharacteristic
141C4×D236C2311yescharacteristic
142D4×Dic59—21no—
143#14273689—21no—
144C4×C22⋊D59—21no—
145C4×C22⋊D59—21no—
146C4×C22⋊D59—21no—
147C4×C22⋊D59—21no—
148(C22⋊D59)⋊C4—21no—
149(C22⋊D59)⋊C4—21no—
150#14273686C2×C411yescharacteristic
151#14273684—21no—
152#14273684—21no—
153#14273684—21no—
154C2×C4⋊Dic59C2×C411yescharacteristic
155C2×C4⋊Dic59C2×C411yescharacteristic
156C4⋊C4×D59—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C22⋊C4×D59—21no—
160C22⋊C4×D59—21no—
161C42×D59—21no—
162C4⋊(C59⋊C8)—21no—
163C4⋊(C59⋊C8)—21no—
164C4⋊(C59⋊C8)—21no—
165C4⋊(C59⋊C8)C2311yescharacteristic
166C4⋊(C59⋊C8)C2311yescharacteristic
167C4⋊(C59⋊C8)C2311yescharacteristic
168C4⋊(C59⋊C8)C2311yescharacteristic
169C22⋊(C59⋊C8)—21no—
170C22⋊(C59⋊C8)—21no—
171C22⋊(C59⋊C8)—21no—
172#14273638—21no—
173#14273638—21no—
174C4×C59⋊C8—21no—
175C2×#41×C59D411yescharacteristic
176C2×M16×C59—21no—
177C22×C8×C59—21no—
178C4×Q8×C59C2×C411yescharacteristic
179C4×Q8×C59D411yescharacteristic
180C4×D4×C59C2×C411yescharacteristic
181C4×D4×C59C2×C411yescharacteristic
182C4×D4×C59C2×C411yescharacteristic
183C4×D4×C59D411yescharacteristic
184C4×D4×C59D411yescharacteristic
185C4×D4×C59D411yescharacteristic
186#117×C59D411yescharacteristic
187#117×C59D411yescharacteristic
188#117×C59D411yescharacteristic
189C2×C42×C59C2311yescharacteristic
190C2×C42×C59C2311yescharacteristic
191C2×C42×C59C2311yescharacteristic
192C4⋊C8×C59—21no—
193C4⋊C8×C59—21no—
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199C22⋊C8×C59—21no—
200#97×C59—21no—
201C4×C8×C59—21no—
202C4×C8×C59C2311yescharacteristic
203C4×C8×C59C2311yescharacteristic
204C4×C8×C59C2311yescharacteristic
205C4×C8×C59C2311yescharacteristic
206C23×D59—21no—
207C23×D59—21no—
208#41×C59—42no—
209C2×Q8×C59C22⋊C411yescharacteristic
210C2×D4×C59C22⋊C411yescharacteristic
211C2×D4×C59C22⋊C411yescharacteristic
212C2×D4×C59C22⋊C411yescharacteristic
213C22×C4×C59C22×C411yescharacteristic
214C22×C4×C59C22×C411yescharacteristic
215C22×C4×C59C22×C411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C2×C22⋊D59—21no—
223C2×C22⋊D59—21no—
224C2×C22⋊D59—21no—
225C2×C22⋊D59—21no—
226C2×C22⋊D59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229D4×D59—44no—
230#11745685—22no—
231#11745685—41no—
232#11745685—81no—
233#11745685—81no—
234C2×D236—22no—
235C2×D236—22no—
236C2×D236—21no—
237C2×D236—21no—
238C2×D236—21no—
239C2×D236—21no—
240C2×D236—41no—
241C2×D236—41no—
242C2×D236C22×C411yescharacteristic
243C2×D236C22×C411yescharacteristic
244C2×D236C22×C411yescharacteristic
245C2×C4×D59—21no—
246C2×C4×D59—21no—
247C2×C4×D59—21no—
248C2×C4×D59—21no—
249C2×C4×D59—21no—
250C2×C4×D59—21no—
251C2×C4×D59—21no—
252C2×C4×D59—21no—
253C2×C4×D59—21no—
254C2×C4×D59—81no—
255C2×C4×D59—81no—
256C2×C4×D59—81no—
257C2×C4×D59—81no—
258C2×Dic118—21no—
259C2×Dic118C22×C411yescharacteristic
260M16×C59—42no—
261C2×C8×C59—21no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—42no—
266C4⋊C4×C59C22⋊C411yescharacteristic
267C4⋊C4×C59C22⋊C411yescharacteristic
268C4⋊C4×C59C22⋊C411yescharacteristic
269C4⋊C4×C59C22⋊C411yescharacteristic
270C4⋊C4×C59C22⋊C411yescharacteristic
271C4⋊C4×C59C22⋊C411yescharacteristic
272C22⋊C4×C59C22⋊C411yescharacteristic
273C22⋊C4×C59C22⋊C411yescharacteristic
274C22⋊C4×C59C22⋊C411yescharacteristic
275C22⋊C4×C59C22⋊C411yescharacteristic
276C22⋊C4×C59C22⋊C411yescharacteristic
277C22⋊C4×C59C22⋊C411yescharacteristic
278C42×C59C22×C411yescharacteristic
279C42×C59C22×C411yescharacteristic
280C42×C59C22×C411yescharacteristic
281C42×C59C2×D411yescharacteristic
282C42×C59C2×D411yescharacteristic
283C42×C59C2×D411yescharacteristic
284C42×C59C2×D411yescharacteristic
285C42×C59C2×D411yescharacteristic
286C42×C59C2×D411yescharacteristic
287C42×C59C2411yescharacteristic
288C22⋊Dic59—21no—
289C22⋊Dic59—21no—
290C22⋊Dic59—21no—
291(C2×D59)⋊C4—21no—
292(C2×D59)⋊C4—21no—
293(C2×D59)⋊C4—21no—
294(C2×D59)⋊C4—21no—
295(C2×D59)⋊C4—21no—
296(C2×D59)⋊C4—21no—
297(C2×D59)⋊C4—21no—
298(C2×D59)⋊C4—21no—
299(C2×D59)⋊C4—21no—
300(C2×D59)⋊C4—21no—
301(C2×D59)⋊C4—21no—
302(C2×D59)⋊C4—21no—
303(C2×D59)⋊C4—21no—
304(C2×D59)⋊C4—21no—
305(C2×D59)⋊C4—21no—
306(C2×D59)⋊C4—21no—
307C4⋊Dic59—21no—
308C4⋊Dic59—21no—
309C4⋊Dic59—21no—
310C4⋊Dic59C22×C411yescharacteristic
311C4⋊Dic59C22×C411yescharacteristic
312C4⋊Dic59C22×C411yescharacteristic
313C4⋊Dic59C22×C411yescharacteristic
314Dic59⋊C4—21no—
315Dic59⋊C4—21no—
316Dic59⋊C4—21no—
317Dic59⋊C4—21no—
318Dic59⋊C4—21no—
319Dic59⋊C4—21no—
320Dic59⋊C4—21no—
321Dic59⋊C4—21no—
322C4×Dic59—21no—
323C4×Dic59—21no—
324C4×Dic59—21no—
325#11745664—81no—
326C2×C59⋊C8—21no—
327C2×C59⋊C8—21no—
328C2×C59⋊C8—21no—
329C2×C59⋊C8—21no—
330C2×C59⋊C8—81no—
331C2×C59⋊C8—81no—
332C23×C59C2×C22⋊C411yescharacteristic
333C23×C59C2×C22⋊C411yescharacteristic
334C23×C59C2×C22⋊C411yescharacteristic
335C22×D59—21no—
336C22×D59—21no—
337C22×D59—21no—
338C22×D59—42no—
339C22×D59—42no—
340C22×D59—42no—
341C22×D59—42no—
342C22×D59—81no—
343C22×D59—81no—
344Q8×C59—41no—
345D4×C59—22no—
346D4×C59—22no—
347D4×C59—41no—
348C2×C4×C59—22no—
349C2×C4×C59—21no—
350C2×C4×C59—21no—
351C2×C4×C59—21no—
352C2×C4×C59—21no—
353C2×C4×C59—21no—
354C2×C4×C59—21no—
355C2×C4×C59—21no—
356C2×C4×C59—21no—
357C2×C4×C59—21no—
358C2×C4×C59—21no—
359C2×C4×C59—21no—
360C2×C4×C59—21no—
361C2×C4×C59—41no—
362C2×C4×C59—41no—
363C2×C4×C59C2×C22⋊C411yescharacteristic
364C2×C4×C59C2×C22⋊C411yescharacteristic
365C2×C4×C59C2×C22⋊C411yescharacteristic
366C2×C4×C59C2×C22⋊C411yescharacteristic
367C2×C4×C59C2×C22⋊C411yescharacteristic
368C2×C4×C59C2×C22⋊C411yescharacteristic
369C2×C4×C59C2×C22⋊C411yescharacteristic
370C2×C4×C59C2×C22⋊C411yescharacteristic
371C2×C4×C59C2×C22⋊C411yescharacteristic
372C2×C4×C59C23×C411yescharacteristic
373C2×C4×C59C22×D411yescharacteristic
374C2×C4×C59C22×D411yescharacteristic
375C22⋊D59—42no—
376C22⋊D59—42no—
377C22⋊D59—42no—
378C22⋊D59—81no—
379C22⋊D59—81no—
380C2×Dic59—21no—
381C2×Dic59—21no—
382C2×Dic59—21no—
383C2×Dic59—21no—
384C2×Dic59—21no—
385C2×Dic59—81no—
386C2×Dic59—81no—
387D236—21no—
388D236—21no—
389D236—21no—
390D236—21no—
391D236—21no—
392D236—42no—
393D236—42no—
394D236—42no—
395D236—81no—
396D236#13112yes—
397C4×D59—42no—
398C4×D59—42no—
399C4×D59—41no—
400C4×D59—41no—
401C4×D59—41no—
402C4×D59—41no—
403C4×D59—41no—
404C4×D59—41no—
405C4×D59—81no—
406C4×D59—81no—
407C4×D59—81no—
408C4×D59—81no—
409Dic118—21no—
410Dic118—21no—
411Dic118—81no—
412C8×C59—41no—
413C8×C59—41no—
414C8×C59—41no—
415C8×C59—41no—
416C59⋊C8—41no—
417C59⋊C8—41no—
418C59⋊C8—41no—
419C59⋊C8—41no—
420#17521—591nomaximal, Sylow
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—21no—
429C22×C59#42112yes—
430C22×C59C22×C22⋊C411yescharacteristic
431C2×D59—22no—
432C2×D59—41no—
433C2×D59—41no—
434C2×D59—41no—
435C2×D59—41no—
436C2×D59—41no—
437C2×D59—41no—
438C2×D59—41no—
439C2×D59—41no—
440C2×D59—84no—
441C2×D59—84no—
442C4×C59—21no—
443C4×C59—21no—
444C4×C59—21no—
445C4×C59—21no—
446C4×C59—21no—
447C4×C59—21no—
448C4×C59—21no—
449C4×C59—21no—
450C4×C59—21no—
451C4×C59—21no—
452C4×C59C2×#13111yescharacteristic
453C4×C59#56811yescharacteristic
454C4×C59#57611yescharacteristic
455C4×C59#57711yescharacteristic
456Dic59—41no—
457Dic59—41no—
458Dic59—41no—
459Dic59—41no—
460Dic59—41no—
461#3481—591no—
462#2990—591no—
463#2922D5911yescharacteristic, complemented
464#1496—591no—
465#1495—591no—
466#1494—591no—
467#1490—591no—
468#1488—591no—
469#1486—591no—
470#1483—591no—
471#1482—591no—
472#1480—591no—
473#1478—591no—
474#1477—591no—
475C2×D4⋊C8—591no—
476C2×C59—22no—
477C2×C59—41no—
478C2×C59—41no—
479C2×C59#288011yescharacteristic
480C2×C59#289711yescharacteristic
481C2×C59C2×#42111yescharacteristic
482D59—42no—
483D59—81no—
484D59—81no—
485#559—591no—
486#554—591no—
487#554—591no—
488#553—591no—
489#553—591no—
490#553—1181no—
491#551—1181no—
492#551—1181no—
493#546—591no—
494#546—591no—
495#546—1181no—
496D42—591no—
497#532—591no—
498#529—591no—
499#529—591no—
500#529—1181no—
501#525—1181no—
502#525—1181no—
503C4×#41—591no—
504C4×#41C2×D5911yescharacteristic
505C2×C4×D4—591no—
506C2×C4×D4—591no—
507C2×C4×D4—1181no—
508#446—1181no—
509#435—1181no—
510#435—1181no—
511C8×D4—1181no—
512#433—21no—
513#433—21no—
514#432—591no—
515#432—591no—
516#431—591no—
517#431C2×D5911yescharacteristic, complemented
518#431C2×D5911yescharacteristic, complemented
519#431C2×D5911yescharacteristic, complemented
520#431C2×D5911yescharacteristic, complemented
521#424—21no—
522#423—591no—
523C2×C4⋊C8—591no—
524C2×C4⋊C8—591no—
525#408—21no—
526C4×M16C2×D5911yescharacteristic, complemented
527C2×C4×C8C2×D5911yescharacteristic, complemented
528Q8⋊C8—591no—
529Q8⋊C8—591no—
530Q8⋊C8—591no—
531Q8⋊C8—591no—
532D4⋊C8—591no—
533D4⋊C8—591no—
534D4⋊C8—591no—
535D4⋊C8—591no—
536D4⋊C8—591no—
537D4⋊C8—591no—
538D4⋊C8—591no—
539D4⋊C8—591no—
540D4⋊C8—591no—
541D4⋊C8—591no—
542D4⋊C8—591no—
543D4⋊C8—591no—
544C59#1752111yescharacteristic, complemented, Sylow
545C2×#41—591no—
546C2×#41—1181no—
547C2×#41C22⋊D5911yescharacteristic
548C22×D4—591no—
549C22×D4—591no—
550C22×D4—1181no—
551C23×C4—1181no—
552C23×C4—1181no—
553C2×M16—21no—
554C2×M16—1181no—
555C22×C8—21no—
556C22×C8—1181no—
557C22×C8—1181no—
558C4⋊Q8—591no—
559#127—591no—
560#126—1181no—
561#126—1181no—
562#126—1181no—
563#126—1181no—
564#125—591no—
565#125—591no—
566#125—1181no—
567#124—591no—
568#124—591no—
569#124—1181no—
570#124—1181no—
571#123—1181no—
572#123—1181no—
573#123—1181no—
574#123—1181no—
575#123—1181no—
576#123—1181no—
577#123—1181no—
578#123—1181no—
579C22⋊Q8—591no—
580C22⋊Q8—591no—
581C22⋊Q8—1181no—
582C22⋊Q8—1181no—
583C22⋊Q8—1181no—
584C22⋊Q8—1181no—
585C22⋊Q8—1181no—
586#121—591no—
587#121—591no—
588#121—591no—
589#121—591no—
590#121—1181no—
591#121—1181no—
592#121—1181no—
593#121—1181no—
594#121—1181no—
595#121—1181no—
596#120—1181no—
597#120—1181no—
598#120—1181no—
599#120—1181no—
600C4×Q8—591no—
601C4×Q8—591no—
602C4×Q8C4×D5911yescharacteristic
603C4×Q8D23611yescharacteristic
604C4×D4—591no—
605C4×D4—591no—
606C4×D4—591no—
607C4×D4—591no—
608C4×D4—591no—
609C4×D4—591no—
610C4×D4—591no—
611C4×D4—591no—
612C4×D4—1181no—
613C4×D4—1181no—
614C4×D4—1181no—
615C4×D4—1181no—
616C4×D4—1181no—
617C4×D4—1181no—
618C4×D4—1181no—
619C4×D4—1181no—
620C4×D4—1181no—
621C4×D4—1181no—
622C4×D4—1181no—
623C4×D4—1181no—
624C4×D4—1181no—
625C4×D4C4×D5911yescharacteristic
626C4×D4C4×D5911yescharacteristic
627C4×D4C4×D5911yescharacteristic
628C4×D4D23611yescharacteristic
629C4×D4D23611yescharacteristic
630C4×D4D23611yescharacteristic
631#117—591no—
632#117—1181no—
633#117—1181no—
634#117—1181no—
635#117C22⋊D5911yescharacteristic
636#117C22⋊D5911yescharacteristic
637#117C22⋊D5911yescharacteristic
638C2×C4⋊C4—591no—
639C2×C4⋊C4—591no—
640C2×C4⋊C4—1181no—
641C2×C22⋊C4—1181no—
642C2×C22⋊C4—1181no—
643C2×C22⋊C4—1181no—
644C2×C22⋊C4—1181no—
645C2×C42—1181no—
646C2×C42C22×D5911yescharacteristic
647C2×C42C22×D5911yescharacteristic
648C2×C42C22×D5911yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—21no—
653C4⋊C8—591no—
654C4⋊C8—591no—
655C4⋊C8—591no—
656C4⋊C8—591no—
657C4⋊C8—1181no—
658C4⋊C8—1181no—
659C4⋊C8—1181no—
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—1181no—
665C22⋊C8—1181no—
666C22⋊C8—1181no—
667#97—21no—
668#97—1181no—
669#97—1181no—
670C4×C8—21no—
671C4×C8—1181no—
672C4×C8C22×D5911yescharacteristic
673C4×C8C22×D5911yescharacteristic
674C4×C8C22×D5911yescharacteristic
675C4×C8C22×D5911yescharacteristic
676C24—1181no—
677C24—1181no—
678#41—42no—
679#41—1182no—
680#41—4721no—
681#41—4721no—
682#41—2361no—
683C2×Q8—591no—
684C2×Q8—1181no—
685C2×Q8(C2×D59)⋊C411yescharacteristic
686C2×D4—591no—
687C2×D4—591no—
688C2×D4—591no—
689C2×D4—1182no—
690C2×D4—1182no—
691C2×D4—1181no—
692C2×D4—1181no—
693C2×D4—1181no—
694C2×D4—1181no—
695C2×D4—1181no—
696C2×D4—1181no—
697C2×D4—1181no—
698C2×D4—1181no—
699C2×D4—1181no—
700C2×D4—2361no—
701C2×D4—2361no—
702C2×D4—2364no—
703C2×D4(C2×D59)⋊C411yescharacteristic
704C2×D4(C2×D59)⋊C411yescharacteristic
705C2×D4(C2×D59)⋊C411yescharacteristic
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—4721no—
718C22×C4—4721no—
719C22×C4—4721no—
720C22×C4—4721no—
721C22×C4C2×C4×D5911yescharacteristic
722C22×C4C2×C4×D5911yescharacteristic
723C22×C4C2×C4×D5911yescharacteristic
724C22×C4C2×D23611yescharacteristic
725C22×C4C2×D23611yescharacteristic
726C22×C4C2×D23611yescharacteristic
727C22×C4C2×C22⋊D5911yescharacteristic
728C22×C4C2×C22⋊D5911yescharacteristic
729C22×C4C2×C22⋊D5911yescharacteristic
730M16—42no—
731M16—4721no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—42no—
737C2×C8—1181no—
738C2×C8—1181no—
739C2×C8—1181no—
740C2×C8—1181no—
741C2×C8—4721no—
742C2×C8—4721no—
743C4⋊C4—591no—
744C4⋊C4—591no—
745C4⋊C4—591no—
746C4⋊C4—591no—
747C4⋊C4—1181no—
748C4⋊C4—1181no—
749C4⋊C4—1181no—
750C4⋊C4—1181no—
751C4⋊C4—1181no—
752C4⋊C4—1181no—
753C4⋊C4—1181no—
754C4⋊C4—1181no—
755C4⋊C4—1181no—
756C4⋊C4—1181no—
757C4⋊C4—1181no—
758C4⋊C4(C2×D59)⋊C411yescharacteristic
759C4⋊C4(C2×D59)⋊C411yescharacteristic
760C4⋊C4(C2×D59)⋊C411yescharacteristic
761C4⋊C4(C2×D59)⋊C411yescharacteristic
762C4⋊C4(C2×D59)⋊C411yescharacteristic
763C4⋊C4(C2×D59)⋊C411yescharacteristic
764C22⋊C4—1181no—
765C22⋊C4—1181no—
766C22⋊C4—1181no—
767C22⋊C4—1181no—
768C22⋊C4—1181no—
769C22⋊C4—1181no—
770C22⋊C4—1181no—
771C22⋊C4—1181no—
772C22⋊C4—1181no—
773C22⋊C4—1181no—
774C22⋊C4—1181no—
775C22⋊C4—1181no—
776C22⋊C4—1181no—
777C22⋊C4—1181no—
778C22⋊C4—1181no—
779C22⋊C4—1181no—
780C22⋊C4—1181no—
781C22⋊C4—1181no—
782C22⋊C4—1181no—
783C22⋊C4(C2×D59)⋊C411yescharacteristic
784C22⋊C4(C2×D59)⋊C411yescharacteristic
785C22⋊C4(C2×D59)⋊C411yescharacteristic
786C22⋊C4(C2×D59)⋊C411yescharacteristic
787C22⋊C4(C2×D59)⋊C411yescharacteristic
788C22⋊C4(C2×D59)⋊C411yescharacteristic
789C42—1181no—
790C42—1181no—
791C42—1181no—
792C42C2×C4×D5911yescharacteristic
793C42C2×C4×D5911yescharacteristic
794C42C2×C4×D5911yescharacteristic
795C42C2×D23611yescharacteristic
796C42C2×D23611yescharacteristic
797C42C2×D23611yescharacteristic
798C42C2×C22⋊D5911yescharacteristic
799C42C2×C22⋊D5911yescharacteristic
800C42C2×C22⋊D5911yescharacteristic
801C42C23×D5911yescharacteristic
802C23—1181no—
803C23—1181no—
804C23—1181no—
805C23—4721no—
806C23—4721no—
807C23—2362no—
808C23—2362no—
809C23—2362no—
810C23—2362no—
811C23C2×(C2×D59)⋊C411yescharacteristic
812C23C2×(C2×D59)⋊C411yescharacteristic
813C23C2×(C2×D59)⋊C411yescharacteristic
814Q8—41no—
815Q8—1181no—
816Q8—1181no—
817Q8—4721no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—592no—
822D4—1181no—
823D4—1181no—
824D4—1181no—
825D4—1181no—
826D4—1181no—
827D4—4721no—
828D4—4721no—
829D4—4721no—
830D4—2362no—
831D4—2362no—
832D4—2362no—
833D4—2362no—
834D4—2362no—
835D4—2362no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—1181no—
852C2×C4—1181no—
853C2×C4—1181no—
854C2×C4—1181no—
855C2×C4—1181no—
856C2×C4—4721no—
857C2×C4—4721no—
858C2×C4—4721no—
859C2×C4—4721no—
860C2×C4—4721no—
861C2×C4—4721no—
862C2×C4—2362no—
863C2×C4—2362no—
864C2×C4—2361no—
865C2×C4—2361no—
866C2×C4—2361no—
867C2×C4—2361no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4C2×(C2×D59)⋊C411yescharacteristic
871C2×C4C2×(C2×D59)⋊C411yescharacteristic
872C2×C4C2×(C2×D59)⋊C411yescharacteristic
873C2×C4C2×(C2×D59)⋊C411yescharacteristic
874C2×C4C2×(C2×D59)⋊C411yescharacteristic
875C2×C4C2×(C2×D59)⋊C411yescharacteristic
876C2×C4C2×(C2×D59)⋊C411yescharacteristic
877C2×C4C2×(C2×D59)⋊C411yescharacteristic
878C2×C4C2×(C2×D59)⋊C411yescharacteristic
879C2×C4C22×C4×D5911yescharacteristic
880C2×C4C22×C22⋊D5911yescharacteristic
881C2×C4C22×D23611yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—2361no—
887C8—2361no—
888C8—2361no—
889C8—2361no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—1182no—
899C22—4724no—
900C22—4724no—
901C22—2361no—
902C22—2361no—
903C22—2361no—
904C22—2361no—
905C22—2361no—
906C22—2361no—
907C22—2361no—
908C22—2361no—
909C22#1683742012yes—
910C22C22×(C2×D59)⋊C411yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—2361no—
922C4—2361no—
923C4—2361no—
924C4—2361no—
925C4—2361no—
926C4#131×D5911yescharacteristic
927C4#1683816711yescharacteristic
928C4#1683820711yescharacteristic
929C4#1683821411yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—4721no—
934C2—4721no—
935C2—2362no—
936C2#2143254311yescharacteristic
937C2#2143262311yescharacteristic
938C2C2×#1683742011yescharacteristic
subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2922C2
socleC22×C59C22×C22⋊C4
prime radical#21437706C2
cosocleC42×C59C24
hypercenter#2922D59
hypocenterC59#17521
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #21433221C2semidirect
3. #21422566C2semidirect
4. #21422562C2semidirect
5. #21422557C2semidirect
6. #21422540C2semidirect
7. #21422531C2semidirect
8. #21422522C2semidirect
9. #21422510C2semidirect
10. #21422505C2semidirect
11. #21422496C2semidirect
12. #21422488C2semidirect
13. #21422484C2semidirect
14. C2×#16837131C2semidirect
15. C59×#2922C2semidirect
42. #16837459C22semidirect
43. #16837459C22semidirect
44. #16837455C22semidirect
45. #16837426C22semidirect
46. C2×C4⋊(C59⋊C8)C22semidirect
47. C2×C4⋊(C59⋊C8)C22semidirect
48. #16837134C22semidirect
49. #16837134C22semidirect
50. #16837134C22semidirect
51. #16837134C22semidirect
56. #16837131C22semidirect
57. #16837131C22semidirect
58. #16837131C22semidirect
59. #16837131C22semidirect
60. #16837131C22semidirect
61. #16837131C22semidirect
62. #16837131C22semidirect
63. #16837131C22semidirect
67. C59×#431C22semidirect
68. C59×#431C22semidirect
69. C59×#431C22semidirect
70. C59×#431C22semidirect
73. C4×M16×C59C22semidirect
74. C2×C4×C8×C59C22semidirect
463. #2922D59semidirect
517. #431C2×D59semidirect
518. #431C2×D59semidirect
519. #431C2×D59semidirect
520. #431C2×D59semidirect
526. C4×M16C2×D59semidirect
527. C2×C4×C8C2×D59semidirect
544. C59#17521semidirect

Maximal subgroups

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

subgroupindex
#214377062
#214332212
#214225662
#214225622
#214225572
#214225402
#214225312
#214225222
#214225102
#214225052
#214224962
#214224882
#214224842
C2×#168371312
C59×#29222
#1752159