Finite Group Databasebeta

← #28556911

Subgroups — #28556911

Order 15104.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437992C211yesmaximal, characteristic
2#21433110C211yesmaximal, characteristic, complemented
3#21422728C211yesmaximal, characteristic, complemented
4#21422725C211yesmaximal, characteristic, complemented
5#21422719C211yesmaximal, characteristic, complemented
6#21422717C211yesmaximal, characteristic, complemented
7#21422714C211yesmaximal, characteristic, complemented
8#21422712C211yesmaximal, characteristic, complemented
9#21422710C211yesmaximal, characteristic, complemented
10#21422704C211yesmaximal, characteristic, complemented
11#21422701C211yesmaximal, characteristic, complemented
12#21422685C211yesmaximal, characteristic, complemented
13#21422682C211yesmaximal, characteristic, complemented
14C2×#16837141C211yesmaximal, characteristic, complemented
15C59×#2970C211yesmaximal, characteristic, complemented
16#16838135—21no—
17#16838135—21no—
18#16838124—21no—
19#16838124—21no—
20#16838081—21no—
21#16838081—21no—
22#16838081—21no—
23#16838081—21no—
24#16838023C411yescharacteristic
25#16838023C411yescharacteristic
26#16838023C411yescharacteristic
27#16838023C411yescharacteristic
28#16837973C411yescharacteristic
29#16837966C411yescharacteristic
30#16837959C2211yescharacteristic
31#16837936C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837936C2211yescharacteristic
34#16837936C2211yescharacteristic
35C2×#14273715C2211yescharacteristic
36#16837879C411yescharacteristic
37#16837876C411yescharacteristic
38#16837533—21no—
39#16837474—21no—
40#16837474—21no—
41D4×C59⋊C8—21no—
42#16837459C2211yescharacteristic
43#16837459C2211yescharacteristic, complemented
44#16837459C2211yescharacteristic, complemented
45C4×#11745664C2211yescharacteristic, complemented
46C2×#14273638C2211yescharacteristic
47C2×#14273638C2211yescharacteristic, complemented
48#16837143C2211yescharacteristic, complemented
49#16837143C2211yescharacteristic, complemented
50#16837143C2211yescharacteristic, complemented
51#16837143C2211yescharacteristic, complemented
52#16837143C2211yescharacteristic, complemented
53#16837143C2211yescharacteristic, complemented
54#16837143C2211yescharacteristic, complemented
55#16837143C2211yescharacteristic, complemented
56#16837141C2211yescharacteristic
57#16837141C2211yescharacteristic
58#16837141C2211yescharacteristic
59#16837141C2211yescharacteristic
60#16837141C2211yescharacteristic
61#16837141C2211yescharacteristic
62#16837141C2211yescharacteristic
63#16837141C2211yescharacteristic
64C4×#41×C59C2211yescharacteristic
65C59×#446—21no—
66C59×#435—21no—
67C59×#435—21no—
68C8×D4×C59—21no—
69C59×#432C2211yescharacteristic
70C59×#432C2211yescharacteristic, complemented
71C59×#432C2211yescharacteristic, complemented
72C4×M16×C59C2211yescharacteristic, complemented
73C2×#97×C59C2211yescharacteristic
74C2×#97×C59C2211yescharacteristic, complemented
75C22×Dic118C2×C411yescharacteristic
76C22×D236C2×C411yescharacteristic
77C2×#11745664—21no—
78C22×C59⋊C8—21no—
79C22×C59⋊C8—21no—
80#14273727C2×C411yescharacteristic
81#14273727C2×C411yescharacteristic
82#14273725—21no—
83#14273723—21no—
84#14273722—21no—
85#14273722—21no—
86#14273722—21no—
87#14273722—21no—
88#14273721—21no—
89#14273721—21no—
90#14273721—21no—
91#14273721—21no—
92#14273719C2311yescharacteristic
93#14273719C2311yescharacteristic
94#14273716—21no—
95#14273715—21no—
96#14273715—21no—
97#14273715C2×C411yescharacteristic
98#14273715C2×C411yescharacteristic
99#14273715C2311yescharacteristic
100#14273715C2311yescharacteristic
101#14273714—21no—
102#14273713—21no—
103#14273713—21no—
104#14273713—21no—
105#14273713—21no—
106#14273710—21no—
107#14273710—21no—
108#14273710—21no—
109#14273710—21no—
110#14273709—21no—
111#14273709—21no—
112#14273709—21no—
113#14273709—21no—
114#14273708—21no—
115#14273708—21no—
116#14273706—21no—
117#14273706—21no—
118#14273706C2×C411yescharacteristic
119#14273706C2×C411yescharacteristic
120#14273706C2×C411yescharacteristic
121#14273706C2×C411yescharacteristic
122#14273705—21no—
123#14273705—21no—
124#14273705—21no—
125#14273705—21no—
126#14273701C2×C411yescharacteristic
127#14273701C2×C411yescharacteristic
128#14273701C2×C411yescharacteristic
129#14273701C2×C411yescharacteristic
130#14273695—21no—
131#14273695—21no—
132C4×Dic118—21no—
133C4×Dic118—21no—
134C4×Dic118C2×C411yescharacteristic
135C4×Dic118C2×C411yescharacteristic
136C4×Dic118C2×C411yescharacteristic
137C4×Dic118C2×C411yescharacteristic
138#14273692—21no—
139#14273692—21no—
140C4×D236C2×C411yescharacteristic
141C4×D236C2×C411yescharacteristic
142C4×D236C2×C411yescharacteristic
143C4×D236C2×C411yescharacteristic
144#14273689—21no—
145#14273689—21no—
146C4×C22⋊D59—21no—
147C4×C22⋊D59—21no—
148C4×C22⋊D59—21no—
149C4×C22⋊D59—21no—
150#14273686C2×C411yescharacteristic
151#14273686C2×C411yescharacteristic
152#14273684—21no—
153#14273684—21no—
154#14273684—21no—
155#14273684—21no—
156#14273683—21no—
157#14273683—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C22⋊C4×D59—21no—
161C22⋊C4×D59—21no—
162C4⋊(C59⋊C8)—21no—
163C4⋊(C59⋊C8)—21no—
164C4⋊(C59⋊C8)—21no—
165C22⋊(C59⋊C8)—21no—
166C22⋊(C59⋊C8)—21no—
167C22⋊(C59⋊C8)—21no—
168#14273638—21no—
169#14273638—21no—
170#14273638C2311yescharacteristic
171#14273638C2311yescharacteristic
172#14273638C2311yescharacteristic
173#14273638C2311yescharacteristic
174C4×C59⋊C8—21no—
175C2×#41×C59C2×C411yescharacteristic
176C2×M16×C59—21no—
177C22×C8×C59—21no—
178C22×C8×C59—21no—
179C4×Q8×C59D411yescharacteristic
180C4×Q8×C59D411yescharacteristic
181C4×D4×C59D411yescharacteristic
182C4×D4×C59D411yescharacteristic
183C4×D4×C59D411yescharacteristic
184C4×D4×C59D411yescharacteristic
185C4×D4×C59D411yescharacteristic
186C4×D4×C59D411yescharacteristic
187#117×C59C2×C411yescharacteristic
188#117×C59C2×C411yescharacteristic
189#117×C59C2×C411yescharacteristic
190C2×C42×C59C2311yescharacteristic
191C2×C42×C59C2311yescharacteristic
192C2×C42×C59C2311yescharacteristic
193C4⋊C8×C59—21no—
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199#97×C59—21no—
200#97×C59—21no—
201#97×C59C2311yescharacteristic
202#97×C59C2311yescharacteristic
203#97×C59C2311yescharacteristic
204#97×C59C2311yescharacteristic
205C4×C8×C59—21no—
206C23×D59—21no—
207#41×C59—42no—
208C2×Q8×C59C22⋊C411yescharacteristic
209C2×D4×C59C22⋊C411yescharacteristic
210C2×D4×C59C22⋊C411yescharacteristic
211C2×D4×C59C22⋊C411yescharacteristic
212C22×C4×C59C22×C411yescharacteristic
213C22×C4×C59C22×C411yescharacteristic
214C22×C4×C59C22×C411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D411yescharacteristic
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D411yescharacteristic
221C2×C22⋊D59—21no—
222C2×C22⋊D59—21no—
223C2×C22⋊D59—21no—
224C2×C22⋊D59—21no—
225C22×Dic59—21no—
226C2×D236—21no—
227C2×D236—42no—
228C2×D236C22×C411yescharacteristic
229C2×D236C22×C411yescharacteristic
230C2×C4×D59—21no—
231C2×C4×D59—21no—
232C2×C4×D59—21no—
233C2×C4×D59—21no—
234C2×Dic118—21no—
235C2×Dic118—21no—
236C2×Dic118—21no—
237C2×Dic118—42no—
238C2×Dic118C22×C411yescharacteristic
239C2×Dic118C22×C411yescharacteristic
240M16×C59—42no—
241C2×C8×C59—21no—
242C2×C8×C59—21no—
243C2×C8×C59—21no—
244C2×C8×C59—21no—
245C2×C8×C59—42no—
246C2×C8×C59—42no—
247C4⋊C4×C59C22⋊C411yescharacteristic
248C4⋊C4×C59C22⋊C411yescharacteristic
249C4⋊C4×C59C22⋊C411yescharacteristic
250C4⋊C4×C59C22⋊C411yescharacteristic
251C4⋊C4×C59C22⋊C411yescharacteristic
252C4⋊C4×C59C22⋊C411yescharacteristic
253C22⋊C4×C59C22⋊C411yescharacteristic
254C22⋊C4×C59C22⋊C411yescharacteristic
255C22⋊C4×C59C22⋊C411yescharacteristic
256C22⋊C4×C59C22⋊C411yescharacteristic
257C22⋊C4×C59C22⋊C411yescharacteristic
258C22⋊C4×C59C22⋊C411yescharacteristic
259C42×C59C22×C411yescharacteristic
260C42×C59C22×C411yescharacteristic
261C42×C59C22×C411yescharacteristic
262C42×C59C2×D411yescharacteristic
263C42×C59C2×D411yescharacteristic
264C42×C59C2×D411yescharacteristic
265C42×C59C2×D411yescharacteristic
266C42×C59C2×D411yescharacteristic
267C42×C59C2×D411yescharacteristic
268C42×C59C2411yescharacteristic
269C22⋊Dic59—21no—
270C22⋊Dic59—21no—
271C22⋊Dic59—21no—
272C22⋊Dic59—21no—
273C22⋊Dic59—21no—
274C22⋊Dic59—21no—
275(C2×D59)⋊C4—21no—
276(C2×D59)⋊C4—21no—
277(C2×D59)⋊C4—21no—
278(C2×D59)⋊C4—21no—
279(C2×D59)⋊C4—21no—
280(C2×D59)⋊C4—21no—
281(C2×D59)⋊C4—21no—
282(C2×D59)⋊C4—21no—
283(C2×D59)⋊C4—21no—
284(C2×D59)⋊C4—21no—
285(C2×D59)⋊C4—21no—
286(C2×D59)⋊C4—21no—
287(C2×D59)⋊C4—21no—
288(C2×D59)⋊C4—21no—
289(C2×D59)⋊C4—21no—
290(C2×D59)⋊C4—21no—
291C4⋊Dic59—21no—
292C4⋊Dic59—21no—
293C4⋊Dic59C22×C411yescharacteristic
294C4⋊Dic59C22×C411yescharacteristic
295C4⋊Dic59C22×C411yescharacteristic
296C4⋊Dic59C22×C411yescharacteristic
297Dic59⋊C4—21no—
298Dic59⋊C4—21no—
299Dic59⋊C4—21no—
300Dic59⋊C4—21no—
301Dic59⋊C4—21no—
302Dic59⋊C4—21no—
303Dic59⋊C4—21no—
304Dic59⋊C4—21no—
305Dic59⋊C4—21no—
306Dic59⋊C4—21no—
307Dic59⋊C4—21no—
308Dic59⋊C4—21no—
309C4×Dic59—21no—
310C4×Dic59—21no—
311C4×Dic59—21no—
312C4×Dic59—21no—
313C4×Dic59—21no—
314C4×Dic59—21no—
315#11745664—42no—
316C2×C59⋊C8—21no—
317C2×C59⋊C8—21no—
318C2×C59⋊C8—21no—
319C2×C59⋊C8—21no—
320C2×C59⋊C8—42no—
321C2×C59⋊C8—42no—
322C23×C59C2×C22⋊C411yescharacteristic
323C23×C59C2×C22⋊C411yescharacteristic
324C23×C59C2×C22⋊C411yescharacteristic
325C22×D59—21no—
326C22×D59—21no—
327C22×D59—42no—
328C22×D59—81no—
329C22×D59—81no—
330Q8×C59—41no—
331D4×C59—22no—
332D4×C59—22no—
333D4×C59—41no—
334C2×C4×C59—22no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59C2×C22⋊C411yescharacteristic
344C2×C4×C59C2×C22⋊C411yescharacteristic
345C2×C4×C59C2×C22⋊C411yescharacteristic
346C2×C4×C59C2×C22⋊C411yescharacteristic
347C2×C4×C59C2×C22⋊C411yescharacteristic
348C2×C4×C59C2×C22⋊C411yescharacteristic
349C2×C4×C59C2×C22⋊C411yescharacteristic
350C2×C4×C59C2×C22⋊C411yescharacteristic
351C2×C4×C59C2×C22⋊C411yescharacteristic
352C2×C4×C59C23×C411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59C22×D411yescharacteristic
355C22⋊D59—81no—
356C22⋊D59—81no—
357C22⋊D59—81no—
358C22⋊D59—81no—
359C2×Dic59—21no—
360C2×Dic59—21no—
361C2×Dic59—21no—
362C2×Dic59—21no—
363C2×Dic59—21no—
364C2×Dic59—21no—
365C2×Dic59—42no—
366D236—41no—
367D236—41no—
368D236—42no—
369C4×D59—81no—
370C4×D59—81no—
371C4×D59—81no—
372C4×D59—81no—
373Dic118—42no—
374Dic118—41no—
375Dic118—41no—
376Dic118—81no—
377Dic118—81no—
378C8×C59—22no—
379C8×C59—41no—
380C8×C59—41no—
381C8×C59—41no—
382C59⋊C8—22no—
383C59⋊C8—41no—
384C59⋊C8—41no—
385C59⋊C8—41no—
386#17686—591nomaximal, Sylow
387C22×C59—21no—
388C22×C59—21no—
389C22×C59—21no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—21no—
394C22×C59—21no—
395C22×C59#41312yes—
396C22×C59C22×C22⋊C411yescharacteristic
397C2×D59—41no—
398C2×D59—41no—
399C2×D59—41no—
400C2×D59—41no—
401C2×D59—41no—
402C2×D59—41no—
403C2×D59—162no—
404C4×C59—21no—
405C4×C59—21no—
406C4×C59—21no—
407C4×C59—21no—
408C4×C59—21no—
409C4×C59—21no—
410C4×C59—21no—
411C4×C59—21no—
412C4×C59—21no—
413C4×C59—21no—
414C4×C59—21no—
415C4×C59—21no—
416Dic59—41no—
417Dic59—41no—
418Dic59—41no—
419Dic59—41no—
420Dic59—41no—
421Dic59—41no—
422#3510—591no—
423#2970—591no—
424#2970D5911yescharacteristic, complemented
425#1535—591no—
426#1535—591no—
427#1533—591no—
428#1532—591no—
429#1532—591no—
430#1531—591no—
431#1531—591no—
432#1529—591no—
433#1529—591no—
434#1524—591no—
435#1524—591no—
436C2×#329—591no—
437C2×C59—22no—
438C2×C59—41no—
439C2×C59—41no—
440C2×C59C2×#41311yescharacteristic
441C2×C59#290111yescharacteristic
442C2×C59#290111yescharacteristic
443D59—81no—
444D59—81no—
445#559—1181no—
446#559—1181no—
447#556—1181no—
448#556—1181no—
449#551—1181no—
450#551—1181no—
451#551—1181no—
452#551—1181no—
453#542—591no—
454#542—591no—
455#542—591no—
456#542—591no—
457#536—591no—
458#535—591no—
459#533—591no—
460#529—591no—
461#529—591no—
462#529—591no—
463#529—591no—
464C2×#124—591no—
465#519—591no—
466#518—591no—
467C4×#41C2×D5911yescharacteristic
468#446—21no—
469#446—1181no—
470#435—21no—
471#435—21no—
472#435—1181no—
473#435—1181no—
474C8×D4—21no—
475C8×D4—1181no—
476#432—591no—
477#432—591no—
478#432—591no—
479#432C2×D5911yescharacteristic
480#432C2×D5911yescharacteristic, complemented
481#432C2×D5911yescharacteristic, complemented
482C4×M16—591no—
483C4×M16C2×D5911yescharacteristic, complemented
484C2×#97—591no—
485C2×#97—591no—
486C2×#97C2×D5911yescharacteristic
487C2×#97C2×D5911yescharacteristic, complemented
488#330—591no—
489#330—591no—
490#330—591no—
491#330—591no—
492#330—591no—
493#330—591no—
494#330—591no—
495#330—591no—
496#329—591no—
497#329—591no—
498#329—591no—
499#329—591no—
500#329—591no—
501#329—591no—
502#329—591no—
503#329—591no—
504C59#1768611yescharacteristic, complemented, Sylow
505C2×#41C4×D5911yescharacteristic
506C22×Q8—591no—
507C22×D4—591no—
508C2×M16—21no—
509C2×M16—1181no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—1181no—
513C22×C8—1181no—
514C4⋊Q8—591no—
515C4⋊Q8—591no—
516C4⋊Q8—1181no—
517#127—1181no—
518#126—1181no—
519#126—1181no—
520#126—1181no—
521#126—1181no—
522#126—1181no—
523#126—1181no—
524#126—1181no—
525#126—1181no—
526#125—591no—
527#125—591no—
528#124—591no—
529#124—591no—
530#124—591no—
531#124—591no—
532#124—1181no—
533#124—1181no—
534#124—1181no—
535#124—1181no—
536#124—1181no—
537#124—1181no—
538#124—1181no—
539#124—1181no—
540#123—1181no—
541#123—1181no—
542#123—1181no—
543#123—1181no—
544#123—1181no—
545#123—1181no—
546#123—1181no—
547#123—1181no—
548#123—1181no—
549#123—1181no—
550C22⋊Q8—591no—
551C22⋊Q8—591no—
552C22⋊Q8—591no—
553C22⋊Q8—591no—
554C22⋊Q8—1181no—
555C22⋊Q8—1181no—
556C22⋊Q8—1181no—
557C22⋊Q8—1181no—
558C22⋊Q8—1181no—
559C22⋊Q8—1181no—
560#121—591no—
561#121—591no—
562#121—591no—
563#121—591no—
564#120—1181no—
565#120—1181no—
566C4×Q8—591no—
567C4×Q8—591no—
568C4×Q8—591no—
569C4×Q8—591no—
570C4×Q8—1181no—
571C4×Q8—1181no—
572C4×Q8—1181no—
573C4×Q8—1181no—
574C4×Q8D23611yescharacteristic
575C4×Q8C22⋊D5911yescharacteristic
576C4×D4—591no—
577C4×D4—591no—
578C4×D4—591no—
579C4×D4—591no—
580C4×D4—1181no—
581C4×D4—1181no—
582C4×D4—1181no—
583C4×D4—1181no—
584C4×D4—1181no—
585C4×D4—1181no—
586C4×D4D23611yescharacteristic
587C4×D4D23611yescharacteristic
588C4×D4D23611yescharacteristic
589C4×D4C22⋊D5911yescharacteristic
590C4×D4C22⋊D5911yescharacteristic
591C4×D4C22⋊D5911yescharacteristic
592#117—591no—
593#117—591no—
594#117—1181no—
595#117—1181no—
596#117—1181no—
597#117—1181no—
598#117—1181no—
599#117—1181no—
600#117C4×D5911yescharacteristic
601#117C4×D5911yescharacteristic
602#117C4×D5911yescharacteristic
603C2×C22⋊C4—1181no—
604C2×C22⋊C4—1181no—
605C2×C22⋊C4—1181no—
606C2×C22⋊C4—1181no—
607C2×C42C22×D5911yescharacteristic
608C2×C42C22×D5911yescharacteristic
609C2×C42C22×D5911yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—21no—
613C4⋊C8—1181no—
614C4⋊C8—1181no—
615C4⋊C8—1181no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—1181no—
620C22⋊C8—1181no—
621C22⋊C8—1181no—
622#97—21no—
623#97—21no—
624#97—591no—
625#97—591no—
626#97—591no—
627#97—591no—
628#97—1181no—
629#97—1181no—
630#97C22×D5911yescharacteristic
631#97C22×D5911yescharacteristic
632#97C22×D5911yescharacteristic
633#97C22×D5911yescharacteristic
634C4×C8—21no—
635C4×C8—1181no—
636C24—1181no—
637#41—42no—
638C2×Q8—591no—
639C2×Q8—591no—
640C2×Q8—1181no—
641C2×Q8—1181no—
642C2×Q8—1181no—
643C2×Q8—2362no—
644C2×Q8(C2×D59)⋊C411yescharacteristic
645C2×D4—591no—
646C2×D4—591no—
647C2×D4—1181no—
648C2×D4—1181no—
649C2×D4—1181no—
650C2×D4—1181no—
651C2×D4—1181no—
652C2×D4—2362no—
653C2×D4(C2×D59)⋊C411yescharacteristic
654C2×D4(C2×D59)⋊C411yescharacteristic
655C2×D4(C2×D59)⋊C411yescharacteristic
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—1181no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4C2×C4×D5911yescharacteristic
662C22×C4C2×C4×D5911yescharacteristic
663C22×C4C2×C4×D5911yescharacteristic
664C22×C4C2×D23611yescharacteristic
665C22×C4C2×D23611yescharacteristic
666C22×C4C2×D23611yescharacteristic
667C22×C4C2×C22⋊D5911yescharacteristic
668C22×C4C2×C22⋊D5911yescharacteristic
669C22×C4C2×C22⋊D5911yescharacteristic
670M16—42no—
671M16—2362no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—1181no—
679C2×C8—1181no—
680C2×C8—1181no—
681C2×C8—1181no—
682C2×C8—2362no—
683C2×C8—2362no—
684C4⋊C4—591no—
685C4⋊C4—591no—
686C4⋊C4—591no—
687C4⋊C4—591no—
688C4⋊C4—1181no—
689C4⋊C4—1181no—
690C4⋊C4—1181no—
691C4⋊C4—1181no—
692C4⋊C4—1181no—
693C4⋊C4—1181no—
694C4⋊C4—1181no—
695C4⋊C4—1181no—
696C4⋊C4—1181no—
697C4⋊C4—1181no—
698C4⋊C4—1181no—
699C4⋊C4—1181no—
700C4⋊C4—1181no—
701C4⋊C4—1181no—
702C4⋊C4(C2×D59)⋊C411yescharacteristic
703C4⋊C4(C2×D59)⋊C411yescharacteristic
704C4⋊C4(C2×D59)⋊C411yescharacteristic
705C4⋊C4(C2×D59)⋊C411yescharacteristic
706C4⋊C4(C2×D59)⋊C411yescharacteristic
707C4⋊C4(C2×D59)⋊C411yescharacteristic
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—1181no—
718C22⋊C4—1181no—
719C22⋊C4—1181no—
720C22⋊C4—1181no—
721C22⋊C4—1181no—
722C22⋊C4—1181no—
723C22⋊C4—1181no—
724C22⋊C4—1181no—
725C22⋊C4—1181no—
726C22⋊C4—1181no—
727C22⋊C4—1181no—
728C22⋊C4—1181no—
729C22⋊C4—1181no—
730C22⋊C4(C2×D59)⋊C411yescharacteristic
731C22⋊C4(C2×D59)⋊C411yescharacteristic
732C22⋊C4(C2×D59)⋊C411yescharacteristic
733C22⋊C4(C2×D59)⋊C411yescharacteristic
734C22⋊C4(C2×D59)⋊C411yescharacteristic
735C22⋊C4(C2×D59)⋊C411yescharacteristic
736C42—1181no—
737C42—1181no—
738C42—1181no—
739C42—1181no—
740C42—1181no—
741C42—1181no—
742C42C2×C4×D5911yescharacteristic
743C42C2×C4×D5911yescharacteristic
744C42C2×C4×D5911yescharacteristic
745C42C2×D23611yescharacteristic
746C42C2×D23611yescharacteristic
747C42C2×D23611yescharacteristic
748C42C2×C22⋊D5911yescharacteristic
749C42C2×C22⋊D5911yescharacteristic
750C42C2×C22⋊D5911yescharacteristic
751C42C23×D5911yescharacteristic
752C23—1181no—
753C23—1181no—
754C23—4721no—
755C23—4721no—
756C23—2362no—
757C23C2×(C2×D59)⋊C411yescharacteristic
758C23C2×(C2×D59)⋊C411yescharacteristic
759C23C2×(C2×D59)⋊C411yescharacteristic
760Q8—41no—
761Q8—4721no—
762Q8—4721no—
763Q8—2361no—
764Q8—2361no—
765Q8—2362no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—4721no—
770D4—4721no—
771D4—4721no—
772D4—4721no—
773D4—2361no—
774D4—2361no—
775D4—2362no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—1181no—
786C2×C4—1181no—
787C2×C4—1181no—
788C2×C4—1181no—
789C2×C4—1181no—
790C2×C4—1181no—
791C2×C4—4721no—
792C2×C4—4721no—
793C2×C4—4721no—
794C2×C4—4721no—
795C2×C4—2362no—
796C2×C4C2×(C2×D59)⋊C411yescharacteristic
797C2×C4C2×(C2×D59)⋊C411yescharacteristic
798C2×C4C2×(C2×D59)⋊C411yescharacteristic
799C2×C4C2×(C2×D59)⋊C411yescharacteristic
800C2×C4C2×(C2×D59)⋊C411yescharacteristic
801C2×C4C2×(C2×D59)⋊C411yescharacteristic
802C2×C4C2×(C2×D59)⋊C411yescharacteristic
803C2×C4C2×(C2×D59)⋊C411yescharacteristic
804C2×C4C2×(C2×D59)⋊C411yescharacteristic
805C2×C4C22×C4×D5911yescharacteristic
806C2×C4C22×C22⋊D5911yescharacteristic
807C2×C4C22×D23611yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—1182no—
813C8—2361no—
814C8—2361no—
815C8—2361no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—9442no—
825C22—2361no—
826C22—2361no—
827C22—2361no—
828C22—2361no—
829C22—2361no—
830C22—2361no—
831C22#1683738412yes—
832C22C22×(C2×D59)⋊C411yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—2361no—
846C4—2361no—
847C4—2361no—
848C4—2361no—
849C4—2361no—
850C4—2361no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—4721no—
855C2—4721no—
856C2C2×#1683738411yescharacteristic
857C2#2143264111yescharacteristic
858C2#2143264411yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2970C2
socleC22×C59C22×C22⋊C4
prime radical#16837966C4
cosocleC42×C59C24
hypercenter#2970D59
hypocenterC59#17686
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #21433110C2semidirect
3. #21422728C2semidirect
4. #21422725C2semidirect
5. #21422719C2semidirect
6. #21422717C2semidirect
7. #21422714C2semidirect
8. #21422712C2semidirect
9. #21422710C2semidirect
10. #21422704C2semidirect
11. #21422701C2semidirect
12. #21422685C2semidirect
13. #21422682C2semidirect
14. C2×#16837141C2semidirect
15. C59×#2970C2semidirect
43. #16837459C22semidirect
44. #16837459C22semidirect
45. C4×#11745664C22semidirect
47. C2×#14273638C22semidirect
48. #16837143C22semidirect
49. #16837143C22semidirect
50. #16837143C22semidirect
51. #16837143C22semidirect
52. #16837143C22semidirect
53. #16837143C22semidirect
54. #16837143C22semidirect
55. #16837143C22semidirect
70. C59×#432C22semidirect
71. C59×#432C22semidirect
72. C4×M16×C59C22semidirect
74. C2×#97×C59C22semidirect
424. #2970D59semidirect
480. #432C2×D59semidirect
481. #432C2×D59semidirect
483. C4×M16C2×D59semidirect
487. C2×#97C2×D59semidirect
504. C59#17686semidirect

Maximal subgroups

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

subgroupindex
#214379922
#214331102
#214227282
#214227252
#214227192
#214227172
#214227142
#214227122
#214227102
#214227042
#214227012
#214226852
#214226822
C2×#168371412
C59×#29702
#1768659