Finite Group Databasebeta

← #28591200

Subgroups — #28591200

Order 15104.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837449C211yesmaximal, characteristic, complemented
2C2×#104×D59C211yesmaximal, characteristic
3#21432611C211yesmaximal, characteristic
4#21432538C211yesmaximal, characteristic
5#21432512C211yesmaximal, characteristic, complemented
6#21424747C211yesmaximal, characteristic, complemented
7#21424746C211yesmaximal, characteristic, complemented
8#21424745C211yesmaximal, characteristic, complemented
9#21424744C211yesmaximal, characteristic, complemented
10#21424743C211yesmaximal, characteristic, complemented
11#21424742C211yesmaximal, characteristic, complemented
12#21424741C211yesmaximal, characteristic, complemented
13#339×D59C211yesmaximal, characteristic, complemented
14#21423788C211yesmaximal, characteristic, complemented
15C59×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D59C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C2×M16×D59C2211yescharacteristic
20C2×M16×D59C2211yescharacteristic
21#117×D59C2211yescharacteristic
22C2×C42×D59C2211yescharacteristic
23#16837449—24no—
24C2×#14273663C2211yescharacteristic, complemented
25C2×#14273662C2211yescharacteristic, complemented
26C2×#14273662C2211yescharacteristic, complemented
27C2×#14273655C2211yescharacteristic
28C2×#14273654C2211yescharacteristic
29C2×#14273653C2211yescharacteristic
30#104×D59—24no—
31#16837409C411yescharacteristic, complemented
32#16837409C411yescharacteristic, complemented
33#16837405C411yescharacteristic, complemented
34#16837405C411yescharacteristic, complemented
35#16837402C411yescharacteristic, complemented
36#16837402C411yescharacteristic, complemented
37#16837400C411yescharacteristic, complemented
38#16837400C411yescharacteristic, complemented
39#16837399C2211yescharacteristic
40#16837398C2211yescharacteristic
41#16837396C2211yescharacteristic
42#16837370C2211yescharacteristic
43#16837369C2211yescharacteristic
44#16837368C2211yescharacteristic
45#16837367—21no—
46#16837367—21no—
47#16837364—21no—
48#16837364—21no—
49#16837360C2211yescharacteristic, complemented
50#16837359—21no—
51#16837358C2211yescharacteristic, complemented
52#16837357C2211yescharacteristic, complemented
53#16837356—21no—
54#16837354—21no—
55C4×#11745659—21no—
56#16837163C2211yescharacteristic, complemented
57#16837162C2211yescharacteristic, complemented
58#16837161C2211yescharacteristic, complemented
59#16837157C2211yescharacteristic, complemented
60#16837156C2211yescharacteristic, complemented
61#16837156C2211yescharacteristic, complemented
62C2×#108×C59C2211yescharacteristic, complemented
63C2×#104×C59C2211yescharacteristic
64C59×#416C2211yescharacteristic
65C59×#408C2211yescharacteristic
66C59×#405C2211yescharacteristic, complemented
67C59×#339C2211yescharacteristic, complemented
68C59×#336C2211yescharacteristic, complemented
69C2×#11745689C2×C411yescharacteristic
70C2×#11745685—21no—
71C2×#11745685C2311yescharacteristic
72C2×#11745687—21no—
73C2×#11745687C2×C411yescharacteristic
74#41×D59—22no—
75#41×D59—22no—
76#41×D59—22no—
77#41×D59—22no—
78C2×Q8×D59C2×C411yescharacteristic
79C2×D4×D59—21no—
80C2×D4×D59C2×C411yescharacteristic
81C22×C4×D59—21no—
82C22×C4×D59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745664C2311yescharacteristic
85C2×#11745664C2311yescharacteristic
86C2×#11745659—21no—
87C2×#11745659—22no—
88C2×#11745659—22no—
89C2×#11745659—22no—
90C2×#11745659—22no—
91C2×#11745659—21no—
92C2×#11745659C2×C411yescharacteristic
93C2×#11745659C2×C411yescharacteristic
94C2×#11745659C2×C411yescharacteristic
95C2×#11745659C2×C411yescharacteristic
96C2×#11745659D411yescharacteristic
97C2×#11745659D411yescharacteristic
98C2×#11745659D411yescharacteristic
99C2×#11745659D411yescharacteristic
100M16×D59—22no—
101M16×D59—22no—
102M16×D59—22no—
103M16×D59D414yes—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—21no—
107C2×C8×D59—21no—
108#14273686C2311yescharacteristic
109#14273685C2×C411yescharacteristic
110#14273685C2×C411yescharacteristic
111#14273684—21no—
112#14273683—21no—
113C4⋊C4×D59C2×C411yescharacteristic
114C4⋊C4×D59C2×C411yescharacteristic
115C22⋊C4×D59—21no—
116C2×C4×Dic59—21no—
117C2×C4×Dic59C2311yescharacteristic
118C42×D59—21no—
119C42×D59—22no—
120C42×D59—22no—
121#14273663—22no—
122#14273662—22no—
123#14273662—22no—
124#14273655—22no—
125#14273654—22no—
126#14273653—22no—
127#14273652C2×C411yescharacteristic, complemented
128#14273652C2×C411yescharacteristic, complemented
129#14273651C2×C411yescharacteristic, complemented
130#14273651C2×C411yescharacteristic, complemented
131#14273650C2×C411yescharacteristic, complemented
132#14273650C2×C411yescharacteristic, complemented
133#14273649C2×C411yescharacteristic, complemented
134#14273649C2×C411yescharacteristic, complemented
135#14273648C2×C411yescharacteristic, complemented
136#14273648C2×C411yescharacteristic, complemented
137#14273647C2×C411yescharacteristic, complemented
138#14273647C2×C411yescharacteristic, complemented
139C22⋊(C59⋊C8)—21no—
140C22⋊(C59⋊C8)—21no—
141(C2×D59)⋊C8—21no—
142(C2×D59)⋊C8—21no—
143(C2×D59)⋊C8—21no—
144(C2×D59)⋊C8—21no—
145#14273638—21no—
146#14273637—21no—
147#14273637—21no—
148C4×C59⋊C8—21no—
149C8×Dic59—21no—
150C8×Dic59—21no—
151C2×#41×C59C2311yescharacteristic
152C2×M16×C59C2311yescharacteristic
153C2×M16×C59C2311yescharacteristic
154C22×C8×C59C2311yescharacteristic
155C22×C8×C59C2311yescharacteristic
156#117×C59C2311yescharacteristic
157C2×C42×C59C2311yescharacteristic
158#108×C59—22no—
159#104×C59—22no—
160#103×C59C2×C411yescharacteristic, complemented
161#103×C59C2×C411yescharacteristic, complemented
162#102×C59C2×C411yescharacteristic, complemented
163#102×C59C2×C411yescharacteristic, complemented
164C22⋊C8×C59—21no—
165C22⋊C8×C59—21no—
166#97×C59—21no—
167C4×C8×C59—21no—
168C23×D59—21no—
169C23×D59#4111yescharacteristic
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—21no—
173#41×C59—21no—
174C2×Q8×C59C22×C411yescharacteristic
175C2×D4×C59—21no—
176C2×D4×C59C22×C411yescharacteristic
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59C2411yescharacteristic
180C2×C22⋊D59—21no—
181C2×C22⋊D59—21no—
182C2×C22⋊D59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185C22×Dic59#4111yescharacteristic
186#11745689—22no—
187#11745689—22no—
188Q8×D59—22no—
189Q8×D59—22no—
190#11745687—22no—
191#11745687—22no—
192#11745687—42no—
193#11745687—42no—
194D4×D59—22no—
195D4×D59—22no—
196D4×D59—42no—
197D4×D59—42no—
198#11745685—21no—
199#11745685—21no—
200#11745685—21no—
201#11745685—21no—
202#11745685—42no—
203#11745685—42no—
204C2×D236—21no—
205C2×D236C22×C411yescharacteristic
206C2×C4×D59—21no—
207C2×C4×D59—21no—
208C2×C4×D59—21no—
209C2×C4×D59—21no—
210C2×C4×D59—21no—
211C2×C4×D59—42no—
212C2×C4×D59—42no—
213C2×C4×D59—42no—
214C2×C4×D59—42no—
215C2×C4×D59—42no—
216C2×C4×D59C22×C411yescharacteristic
217C2×C4×D59C22×C411yescharacteristic
218C2×C4×D59C2×D412yes—
219C2×C4×D59C2×D411yescharacteristic
220C2×C4×D59C2×D411yescharacteristic
221C2×C4×D59#4112yes—
222C2×C4×D59#4112yes—
223C2×C4×D59#4112yes—
224C2×Dic118—21no—
225C2×Dic118C22×C411yescharacteristic
226M16×C59—21no—
227M16×C59—21no—
228M16×C59—21no—
229M16×C59C2×D412yes—
230C2×C8×C59—21no—
231C2×C8×C59—21no—
232C2×C8×C59—21no—
233C2×C8×C59—21no—
234C2×C8×C59—21no—
235C2×C8×C59—21no—
236C2×C8×C59C22×C411yescharacteristic
237C2×C8×C59C22×C411yescharacteristic
238C2×C8×C59C2×D411yescharacteristic
239C2×C8×C59C2×D411yescharacteristic
240C4⋊C4×C59C22×C411yescharacteristic
241C4⋊C4×C59C22×C411yescharacteristic
242C22⋊C4×C59—21no—
243C42×C59—21no—
244C42×C59—21no—
245C42×C59—21no—
246C22⋊Dic59—21no—
247(C2×D59)⋊C4—21no—
248(C2×D59)⋊C4—21no—
249C4⋊Dic59C22×C411yescharacteristic
250C4⋊Dic59C22×C411yescharacteristic
251Dic59⋊C4—21no—
252Dic59⋊C4—21no—
253C4×Dic59—21no—
254C4×Dic59—21no—
255C4×Dic59—21no—
256C4×Dic59—21no—
257C4×Dic59—21no—
258C4×Dic59—42no—
259#11745664—21no—
260#11745664—21no—
261#11745664—21no—
262#11745664C2×D412yes—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C2×C59⋊C8—21no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8C22×C411yescharacteristic
270C2×C59⋊C8C22×C411yescharacteristic
271C2×C59⋊C8C2×D411yescharacteristic
272C2×C59⋊C8C2×D411yescharacteristic
273#11745659—22no—
274#11745659—22no—
275#11745659—22no—
276#11745659—22no—
277#11745659—24no—
278#11745659—22no—
279#11745659—22no—
280#11745659—22no—
281#11745659—22no—
282#11745659—42no—
283C8×D59—24no—
284C8×D59—42no—
285C23×C59—21no—
286C23×C59C2×#4111yescharacteristic
287C22×D59—21no—
288C22×D59—41no—
289C22×D59—41no—
290C22×D59—42no—
291C22×D59—81no—
292C22×D59—81no—
293C22×D59C4×D411yescharacteristic
294C22×D59C4×D411yescharacteristic
295C22×D59#12412yes—
296C22×D59#12612yes—
297Q8×C59—21no—
298Q8×C59—21no—
299D4×C59—21no—
300D4×C59—21no—
301D4×C59—41no—
302D4×C59—41no—
303C2×C4×C59—22no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59C23×C411yescharacteristic
312C2×C4×C59C22×D411yescharacteristic
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4111yescharacteristic
315C2×C4×C59C2×#4111yescharacteristic
316C2×C4×C59C2×#4111yescharacteristic
317C22⋊D59—41no—
318C22⋊D59—41no—
319C22⋊D59—42no—
320C22⋊D59—42no—
321C2×Dic59—22no—
322C2×Dic59—21no—
323C2×Dic59—21no—
324C2×Dic59—21no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—42no—
328C2×Dic59C4×D411yescharacteristic
329C2×Dic59C4×D411yescharacteristic
330C2×Dic59#12412yes—
331C2×Dic59#12612yes—
332D236—21no—
333D236—21no—
334D236—42no—
335C4×D59—48no—
336C4×D59—42no—
337C4×D59—41no—
338C4×D59—41no—
339C4×D59—42no—
340C4×D59—81no—
341C4×D59—81no—
342C4×D59#11712yes—
343C4×D59#11712yes—
344C4×D59C4×D412yes—
345C4×D59C4×D412yes—
346C4×D59#12112yes—
347C4×D59#12112yes—
348C4×D59#12312yes—
349C4×D59#12312yes—
350Dic118—21no—
351Dic118—21no—
352Dic118—42no—
353C8×C59—21no—
354C8×C59—21no—
355C8×C59—22no—
356C8×C59—21no—
357C8×C59—21no—
358C8×C59—41no—
359C59⋊C8—21no—
360C59⋊C8—21no—
361C59⋊C8—22no—
362C59⋊C8—21no—
363C59⋊C8—21no—
364C59⋊C8—41no—
365#21071—591nomaximal, Sylow
366C22×C59—21no—
367C22×C59—21no—
368C22×C59—41no—
369C22×C59—41no—
370C22×C59—41no—
371C22×C59C2×C4×D411yescharacteristic
372C22×C59C2×#12411yescharacteristic
373C22×C59C2×#12611yescharacteristic
374C2×D59—21no—
375C2×D59—21no—
376C2×D59—21no—
377C2×D59—21no—
378C2×D59—42no—
379C2×D59—42no—
380C2×D59—41no—
381C2×D59—41no—
382C2×D59—41no—
383C2×D59—84no—
384C2×D59#38812yes—
385C2×D59#38812yes—
386C4×C59—42no—
387C4×C59—41no—
388C4×C59—41no—
389C4×C59—41no—
390C4×C59C2×#11711yescharacteristic
391C4×C59C2×C4×D411yescharacteristic
392C4×C59C2×#12111yescharacteristic
393C4×C59C2×#12311yescharacteristic
394Dic59—42no—
395Dic59—41no—
396Dic59—41no—
397Dic59—41no—
398Dic59#38812yes—
399Dic59#38812yes—
400C2×#430—591no—
401C22×#104—591no—
402#2896—591no—
403#2879—591no—
404#2873—591no—
405#1929—591no—
406#1929—591no—
407#1929—591no—
408#1929—591no—
409#1929—591no—
410#1929—591no—
411#1929—591no—
412#1929D5911yescharacteristic, complemented
413C2×#339—591no—
414#1728—591no—
415C2×C59—21no—
416C2×C59—21no—
417C2×C59—81no—
418C2×C59C2×#38811yescharacteristic
419C2×C59#295611yescharacteristic
420C2×C59#295611yescharacteristic
421D59—22no—
422D59—22no—
423D59—81no—
424C22×#41—591no—
425C22×M16—591no—
426C22×M16—591no—
427C22×M16—591no—
428C22×M16—591no—
429C2×#117—591no—
430C22×C42—591no—
431#430—1184no—
432C2×#108—591no—
433C2×#108—591no—
434C2×#108—591no—
435C2×#108C2×D5911yescharacteristic, complemented
436C2×#104—591no—
437C2×#104—591no—
438C2×#104—591no—
439C2×#104—1184no—
440C2×#104C2×D5911yescharacteristic
441#419—591no—
442#419—591no—
443#418—591no—
444#418—591no—
445#417—591no—
446#417—591no—
447#417—591no—
448#417—591no—
449#416—591no—
450#416—591no—
451#416—591no—
452#416C2×D5911yescharacteristic
453#408—591no—
454#408—591no—
455#408—591no—
456#408—1181no—
457#408—1181no—
458#408C2×D5911yescharacteristic
459#407—1181no—
460#407—1181no—
461#405—591no—
462#405—591no—
463#405—591no—
464#405—1181no—
465#405—1181no—
466#405C2×D5911yescharacteristic, complemented
467C4×M16—1181no—
468C4×M16—1181no—
469#339—591no—
470#339—591no—
471#339—591no—
472#339C2×D5911yescharacteristic, complemented
473#336—591no—
474#336—591no—
475#336—591no—
476#336C2×D5911yescharacteristic, complemented
477C59#2107111yescharacteristic, complemented, Sylow
478C2×#41—591no—
479C2×#41—591no—
480C2×#41—591no—
481C2×#41—1181no—
482C2×#41—1181no—
483C2×#41—1182no—
484C2×#41—1182no—
485C2×#41—1182no—
486C2×#41—1182no—
487C2×#41C22×D5911yescharacteristic
488C22×Q8—591no—
489C22×D4—591no—
490C22×D4—1181no—
491C23×C4—591no—
492C23×C4—1181no—
493C23×C4—1181no—
494C2×M16—591no—
495C2×M16—591no—
496C2×M16—591no—
497C2×M16—591no—
498C2×M16—591no—
499C2×M16—591no—
500C2×M16—591no—
501C2×M16—591no—
502C2×M16—591no—
503C2×M16—594no—
504C2×M16—591no—
505C2×M16—1181no—
506C2×M16—1182no—
507C2×M16—1182no—
508C2×M16—1182no—
509C2×M16—1182no—
510C2×M16—1181no—
511C2×M16—1182no—
512C2×M16—1182no—
513C2×M16—1182no—
514C2×M16C22×D5911yescharacteristic
515C2×M16C22×D5911yescharacteristic
516C22×C8—591no—
517C22×C8—591no—
518C22×C8—1181no—
519C22×C8—1181no—
520C22×C8C22×D5911yescharacteristic
521C22×C8C22×D5911yescharacteristic
522#117—591no—
523#117—591no—
524#117—591no—
525#117—1181no—
526#117—1181no—
527#117C22×D5911yescharacteristic
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C22⋊C4—1181no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42—1182no—
534C2×C42—1182no—
535C2×C42—1181no—
536C2×C42C22×D5911yescharacteristic
537#108—22no—
538#108—1182no—
539#108—1182no—
540#108—1182no—
541#104—22no—
542#104—1182no—
543#104—1182no—
544#104—1182no—
545#103—591no—
546#103—591no—
547#103—591no—
548#103—591no—
549#103—591no—
550#103—591no—
551#103C4×D5911yescharacteristic, complemented
552#103C4×D5911yescharacteristic, complemented
553#102—591no—
554#102—591no—
555#102—591no—
556#102—591no—
557#102—591no—
558#102—591no—
559#102C4×D5911yescharacteristic, complemented
560#102C4×D5911yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—1181no—
564C22⋊C8—1181no—
565C22⋊C8—1181no—
566C22⋊C8—1181no—
567C22⋊C8—1181no—
568C22⋊C8—1181no—
569#97—21no—
570#97—1181no—
571#97—1181no—
572#97—1181no—
573C4×C8—21no—
574C4×C8—1181no—
575C4×C8—1181no—
576C4×C8—1181no—
577C24—591no—
578C24—1181no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—1182no—
584#41—1182no—
585#41—1182no—
586#41—1182no—
587#41—1181no—
588#41—1181no—
589#41—1181no—
590#41—1181no—
591#41—2362no—
592#41—2362no—
593#41—2362no—
594#41—2362no—
595C2×Q8—591no—
596C2×Q8—1181no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8C2×C4×D5911yescharacteristic
600C2×D4—21no—
601C2×D4—591no—
602C2×D4—1181no—
603C2×D4—1182no—
604C2×D4—1182no—
605C2×D4—1181no—
606C2×D4—1181no—
607C2×D4—1181no—
608C2×D4—2362no—
609C2×D4—2362no—
610C2×D4C2×C4×D5911yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—591no—
614C22×C4—591no—
615C22×C4—591no—
616C22×C4—592no—
617C22×C4—591no—
618C22×C4—591no—
619C22×C4—592no—
620C22×C4—592no—
621C22×C4—592no—
622C22×C4—1181no—
623C22×C4—1181no—
624C22×C4—1181no—
625C22×C4—1181no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—2362no—
630C22×C4—2362no—
631C22×C4—2362no—
632C22×C4—2362no—
633C22×C4—2362no—
634C22×C4C23×D5911yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—592no—
639M16—1184no—
640M16—1182no—
641M16—1182no—
642M16—1182no—
643M16—1182no—
644M16—1182no—
645M16—1182no—
646M16—1182no—
647M16—1182no—
648M16—1181no—
649M16—1181no—
650M16—1181no—
651M16—2362no—
652M16D4×D5912yes—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—591no—
660C2×C8—591no—
661C2×C8—591no—
662C2×C8—591no—
663C2×C8—1184no—
664C2×C8—1181no—
665C2×C8—1181no—
666C2×C8—1181no—
667C2×C8—1181no—
668C2×C8—1181no—
669C2×C8—1181no—
670C2×C8—2362no—
671C2×C8C2×C4×D5911yescharacteristic
672C2×C8C2×C4×D5911yescharacteristic
673C2×C8D4×D5911yescharacteristic
674C2×C8D4×D5911yescharacteristic
675C4⋊C4—591no—
676C4⋊C4—591no—
677C4⋊C4—1181no—
678C4⋊C4—1181no—
679C4⋊C4C2×C4×D5911yescharacteristic
680C4⋊C4C2×C4×D5911yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—1181no—
683C22⋊C4—1181no—
684C22⋊C4—1181no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—1181no—
689C42—1181no—
690C42—1181no—
691C42—1181no—
692C42—1181no—
693C42—2362no—
694C23—21no—
695C23—591no—
696C23—591no—
697C23—592no—
698C23—592no—
699C23—1181no—
700C23—4721no—
701C23—4721no—
702C23—2361no—
703C23—2361no—
704C23—2362no—
705C23#41×D5911yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—1181no—
709Q8—1181no—
710Q8—2362no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—1181no—
716D4—1181no—
717D4—2362no—
718D4—2362no—
719D4—2362no—
720D4—2361no—
721D4—2361no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—592no—
731C2×C4—592no—
732C2×C4—591no—
733C2×C4—591no—
734C2×C4—592no—
735C2×C4—592no—
736C2×C4—592no—
737C2×C4—592no—
738C2×C4—592no—
739C2×C4—592no—
740C2×C4—592no—
741C2×C4—592no—
742C2×C4—1182no—
743C2×C4—1181no—
744C2×C4—1181no—
745C2×C4—1181no—
746C2×C4—4721no—
747C2×C4—4721no—
748C2×C4—2362no—
749C2×C4—2362no—
750C2×C4—2368no—
751C2×C4—2362no—
752C2×C4—2361no—
753C2×C4—2361no—
754C2×C4—2361no—
755C2×C4—2361no—
756C2×C4C22×C4×D5911yescharacteristic
757C2×C4C2×D4×D5911yescharacteristic
758C2×C4C2×D4×D5911yescharacteristic
759C2×C4#41×D5911yescharacteristic
760C2×C4#41×D5911yescharacteristic
761C2×C4#41×D5911yescharacteristic
762C8—22no—
763C8—21no—
764C8—21no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—1182no—
769C8—1181no—
770C8—1181no—
771C8—1181no—
772C8—1181no—
773C8—2361no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—592no—
780C22—592no—
781C22—1181no—
782C22—1181no—
783C22—1181no—
784C22—1181no—
785C22—4724no—
786C22—2362no—
787C22—2362no—
788C22—2361no—
789C22—2361no—
790C22—2361no—
791C22C4×D4×D5911yescharacteristic
792C22#124×D5911yescharacteristic
793C22#126×D5911yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—592no—
799C4—592no—
800C4—2362no—
801C4—2361no—
802C4—2361no—
803C4—2361no—
804C4#117×D5911yescharacteristic
805C4C4×D4×D5911yescharacteristic
806C4#121×D5911yescharacteristic
807C4#123×D5911yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—1182no—
812C2—1182no—
813C2—4721no—
814C2#388×D5911yescharacteristic
815C2#2143300111yescharacteristic
816C2#2143300411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1929C2
socleC22×C59C2×C4×D4
prime radicalC2×#41×D59C22
cosocleC22×C4×C59C24
hypercenter#1929D59
hypocenterC59#21071
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#16837449C2semidirect
5. #21432512C2semidirect
6. #21424747C2semidirect
7. #21424746C2semidirect
8. #21424745C2semidirect
9. #21424744C2semidirect
10. #21424743C2semidirect
11. #21424742C2semidirect
12. #21424741C2semidirect
13. #339×D59C2semidirect
14. #21423788C2semidirect
15. C59×#1929C2semidirect
24. C2×#14273663C22semidirect
25. C2×#14273662C22semidirect
26. C2×#14273662C22semidirect
31. #16837409C4semidirect
32. #16837409C4semidirect
33. #16837405C4semidirect
34. #16837405C4semidirect
35. #16837402C4semidirect
36. #16837402C4semidirect
37. #16837400C4semidirect
38. #16837400C4semidirect
49. #16837360C22semidirect
51. #16837358C22semidirect
52. #16837357C22semidirect
56. #16837163C22semidirect
57. #16837162C22semidirect
58. #16837161C22semidirect
59. #16837157C22semidirect
60. #16837156C22semidirect
61. #16837156C22semidirect
62. C2×#108×C59C22semidirect
66. C59×#405C22semidirect
67. C59×#339C22semidirect
68. C59×#336C22semidirect
127. #14273652C2×C4semidirect
128. #14273652C2×C4semidirect
129. #14273651C2×C4semidirect
130. #14273651C2×C4semidirect
131. #14273650C2×C4semidirect
132. #14273650C2×C4semidirect
133. #14273649C2×C4semidirect
134. #14273649C2×C4semidirect
135. #14273648C2×C4semidirect
136. #14273648C2×C4semidirect
137. #14273647C2×C4semidirect
138. #14273647C2×C4semidirect
160. #103×C59C2×C4semidirect
161. #103×C59C2×C4semidirect
162. #102×C59C2×C4semidirect
163. #102×C59C2×C4semidirect
412. #1929D59semidirect
435. C2×#108C2×D59semidirect
466. #405C2×D59semidirect
472. #339C2×D59semidirect
476. #336C2×D59semidirect
477. C59#21071semidirect
551. #103C4×D59semidirect
552. #103C4×D59semidirect
559. #102C4×D59semidirect
560. #102C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374492
C2×#104×D592
#214326112
#214325382
#214325122
#214247472
#214247462
#214247452
#214247442
#214247432
#214247422
#214247412
#339×D592
#214237882
C59×#19292
#2107159