Finite Group Databasebeta

← #28595155

Subgroups — #28595155

Order 15104.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433551C211yesmaximal, characteristic
2C2×#16837522C211yesmaximal, characteristic, complemented
3C2×#16837517C211yesmaximal, characteristic, complemented
4#21432815C211yesmaximal, characteristic, complemented
5#21425015C211yesmaximal, characteristic, complemented
6#21424871C211yesmaximal, characteristic, complemented
7#21424744C211yesmaximal, characteristic, complemented
8#21424744C211yesmaximal, characteristic, complemented
9#21424423C211yesmaximal, characteristic, complemented
10#21424423C211yesmaximal, characteristic, complemented
11#21424116C211yesmaximal, characteristic, complemented
12#21423968C211yesmaximal, characteristic, complemented
13#21423942C211yesmaximal, characteristic, complemented
14#21423935C211yesmaximal, characteristic, complemented
15C59×#2875C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273733C2211yescharacteristic
19C2×#14273733C2211yescharacteristic
20#16837952C2211yescharacteristic
21#16837624C411yescharacteristic, complemented
22#16837624C411yescharacteristic, complemented
23#16837617C411yescharacteristic, complemented
24#16837617C411yescharacteristic, complemented
25#16837612C411yescharacteristic, complemented
26#16837607C411yescharacteristic, complemented
27#16837602C411yescharacteristic, complemented
28#16837597C411yescharacteristic, complemented
29#16837522—24no—
30#16837517—24no—
31#16837475—21no—
32#16837475—21no—
33#16837475—21no—
34#16837475—21no—
35C2×#14273662C2211yescharacteristic
36C2×#14273662C2211yescharacteristic
37#16837426C2211yescharacteristic
38C2×C4⋊(C59⋊C8)C2211yescharacteristic
39C2×#14273654C2211yescharacteristic
40C2×#14273654C2211yescharacteristic
41C2×#14273653C2211yescharacteristic
42C2×#14273653C2211yescharacteristic
43C2×#14273653C2211yescharacteristic
44C2×#14273653C2211yescharacteristic
45#16837396C2211yescharacteristic
46#16837396C2211yescharacteristic
47#16837368C2211yescharacteristic
48#16837368C2211yescharacteristic
49C2×#14273637C2211yescharacteristic
50C2×C8×Dic59C2211yescharacteristic
51C4×C4⋊Dic59C2211yescharacteristic
52#16837166C2211yescharacteristic
53#16837166C2211yescharacteristic
54#16837161C2211yescharacteristic
55#16837161C2211yescharacteristic
56#16837156C2211yescharacteristic
57#16837156C2211yescharacteristic
58C2×#131×C59C2211yescharacteristic
59C2×#131×C59C2211yescharacteristic
60C4×#41×C59C2211yescharacteristic
61C59×#405—21no—
62C59×#405—21no—
63C59×#405C2211yescharacteristic
64C59×#405C2211yescharacteristic
65C4×M16×C59—21no—
66C4×M16×C59C2211yescharacteristic
67C2×#97×C59—21no—
68C2×#97×C59C2211yescharacteristic
69C2×#11745685C2311yescharacteristic
70C2×#11745685C2311yescharacteristic
71#14273747—22no—
72#14273747—22no—
73#14273747—22no—
74#14273747—22no—
75C2×#11745672C2×C411yescharacteristic
76C2×#11745672C2×C411yescharacteristic
77C2×#11745670C2×C411yescharacteristic
78C2×#11745670C2×C411yescharacteristic
79C2×#11745671C2×C411yescharacteristic
80C2×#11745671C2×C411yescharacteristic
81C2×#11745669C2×C411yescharacteristic
82C2×#11745669C2×C411yescharacteristic
83#14273733—22no—
84#14273733—22no—
85#14273733—22no—
86#14273733—22no—
87C2×#11745664C2311yescharacteristic
88C2×#11745664C2311yescharacteristic
89C2×#11745659—21no—
90C2×#11745659—21no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—21no—
94C2×C8×D59—21no—
95#14273727C2×C411yescharacteristic
96#14273724C2×C411yescharacteristic
97#14273715C2×C411yescharacteristic
98#14273715C2×C411yescharacteristic
99#14273701—21no—
100#14273701—21no—
101C4×D236—21no—
102C4×D236—21no—
103C2×C4⋊Dic59—21no—
104C2×C4×Dic59C2311yescharacteristic
105C2×C4×Dic59C2311yescharacteristic
106#14273662—22no—
107#14273662—22no—
108C4⋊(C59⋊C8)—21no—
109C4⋊(C59⋊C8)—21no—
110C4⋊(C59⋊C8)C2×C411yescharacteristic
111C4⋊(C59⋊C8)C2×C411yescharacteristic
112C4⋊(C59⋊C8)C2×C411yescharacteristic
113C4⋊(C59⋊C8)C2×C411yescharacteristic
114#14273654—22no—
115#14273654—22no—
116#14273653—22no—
117#14273653—22no—
118#14273653—22no—
119#14273653—22no—
120#14273650C2×C411yescharacteristic
121#14273650C2×C411yescharacteristic
122#14273650C2×C411yescharacteristic
123#14273650C2×C411yescharacteristic
124#14273647C2×C411yescharacteristic
125#14273647C2×C411yescharacteristic
126#14273647C2×C411yescharacteristic
127#14273647C2×C411yescharacteristic
128(C2×D59)⋊C8—21no—
129(C2×D59)⋊C8—21no—
130(C2×D59)⋊C8—21no—
131(C2×D59)⋊C8—21no—
132#14273637—22no—
133C8×Dic59—22no—
134C59⋊#95—21no—
135C2×#41×C59C2311yescharacteristic
136#131×C59—22no—
137#131×C59—22no—
138#131×C59—22no—
139#131×C59D414yescomplemented
140C2×M16×C59—21no—
141C2×M16×C59—21no—
142C2×M16×C59C2311yescharacteristic
143C2×M16×C59C2311yescharacteristic
144C22×C8×C59—21no—
145C22×C8×C59—21no—
146C22×C8×C59C2311yescharacteristic
147C22×C8×C59C2311yescharacteristic
148C4×Q8×C59C2×C411yescharacteristic
149C4×Q8×C59C2×C411yescharacteristic
150C4×D4×C59—21no—
151C4×D4×C59—21no—
152C4×D4×C59C2×C411yescharacteristic
153C4×D4×C59C2×C411yescharacteristic
154#117×C59—21no—
155#117×C59C2311yescharacteristic
156C2×C42×C59—21no—
157C2×C42×C59C2311yescharacteristic
158#97×C59—21no—
159#97×C59—21no—
160#97×C59—21no—
161#97×C59D411yescharacteristic
162#97×C59D411yescharacteristic
163#97×C59D411yescharacteristic
164#97×C59D411yescharacteristic
165C4×C8×C59—21no—
166C4×C8×C59—21no—
167C4×C8×C59—21no—
168#41×C59—21no—
169#41×C59—21no—
170#41×C59C2×D412yes—
171#41×C59#4112yes—
172C2×Q8×C59C22×C411yescharacteristic
173C2×D4×C59—21no—
174C2×D4×C59C22×C411yescharacteristic
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59#4111yescharacteristic
179C22×C4×C59#4111yescharacteristic
180C22×C4×C59C2411yescharacteristic
181C2×C22⋊D59—21no—
182C2×C22⋊D59—21no—
183C22×Dic59—21no—
184C22×Dic59—21no—
185#11745685—21no—
186#11745685—21no—
187#11745685—21no—
188#11745685—21no—
189#11745685—21no—
190#11745685—21no—
191#11745685—21no—
192#11745685—21no—
193C2×D236—21no—
194C2×D236—21no—
195C2×D236C22×C411yescharacteristic
196C2×D236C22×C411yescharacteristic
197C2×C4×D59—21no—
198C2×C4×D59—21no—
199C2×Dic118C22×C411yescharacteristic
200C2×Dic118C22×C411yescharacteristic
201M16×C59—24no—
202M16×C59—21no—
203M16×C59—21no—
204M16×C59—24no—
205M16×C59C2×D412yes—
206M16×C59#4112yes—
207C2×C8×C59—24no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—24no—
213C2×C8×C59C2×D411yescharacteristic
214C2×C8×C59C2×D411yescharacteristic
215C2×C8×C59C2×D412yes—
216C2×C8×C59C2×D411yescharacteristic
217C2×C8×C59C2×D411yescharacteristic
218C2×C8×C59#4112yes—
219C4⋊C4×C59—21no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59C22×C411yescharacteristic
222C4⋊C4×C59C22×C411yescharacteristic
223C22⋊C4×C59—21no—
224C22⋊C4×C59—21no—
225C22⋊C4×C59—21no—
226C42×C59—21no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59C22×C411yescharacteristic
230C42×C59C22×C411yescharacteristic
231C42×C59C2×D411yescharacteristic
232C42×C59C2×D411yescharacteristic
233#11745672—22no—
234#11745672—22no—
235#11745671—22no—
236#11745671—22no—
237#11745670—22no—
238#11745670—22no—
239#11745669—22no—
240#11745669—22no—
241(C2×D59)⋊C4—21no—
242(C2×D59)⋊C4—21no—
243(C2×D59)⋊C4—21no—
244(C2×D59)⋊C4—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—42no—
248C4×Dic59—21no—
249C4×Dic59—21no—
250C4×Dic59—21no—
251C4×Dic59—21no—
252#11745664—21no—
253#11745664—21no—
254#11745664—21no—
255#11745664—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8C22×C411yescharacteristic
263C2×C59⋊C8C22×C411yescharacteristic
264C2×C59⋊C8C22×C411yescharacteristic
265C2×C59⋊C8C22×C411yescharacteristic
266#11745659—42no—
267#11745659—42no—
268C8×D59—42no—
269C8×D59—42no—
270C23×C59—21no—
271C23×C59C2×#4111yescharacteristic
272C22×D59—21no—
273C22×D59—21no—
274Q8×C59—21no—
275Q8×C59C4×D412yes—
276D4×C59—22no—
277D4×C59—22no—
278D4×C59—21no—
279D4×C59C4×D412yes—
280C2×C4×C59—21no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—81no—
288C2×C4×C59—81no—
289C2×C4×C59C4×D411yescharacteristic
290C2×C4×C59C4×D411yescharacteristic
291C2×C4×C59C4×D411yescharacteristic
292C2×C4×C59C4×D411yescharacteristic
293C2×C4×C59C23×C411yescharacteristic
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C22×D411yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59C2×#4111yescharacteristic
298C2×C4×C59C2×#4111yescharacteristic
299C22⋊D59—41no—
300C22⋊D59—41no—
301C22⋊D59—41no—
302C22⋊D59—41no—
303C2×Dic59—22no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311D236—21no—
312D236—21no—
313D236—21no—
314D236—21no—
315D236—81no—
316D236—81no—
317C4×D59—41no—
318C4×D59—41no—
319C4×D59—41no—
320C4×D59—41no—
321Dic118—21no—
322Dic118—21no—
323Dic118—21no—
324Dic118—21no—
325C8×C59—22no—
326C8×C59—21no—
327C8×C59—22no—
328C8×C59—21no—
329C8×C59#12112yes—
330C8×C59#12112yes—
331C59⋊C8—21no—
332C59⋊C8—21no—
333C59⋊C8—21no—
334C59⋊C8—21no—
335C59⋊C8—41no—
336C59⋊C8—41no—
337#21519—591nomaximal, Sylow
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—22no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59C2×C4×D411yescharacteristic
344C22×C59#52911yescharacteristic
345C22×C59#53211yescharacteristic
346C2×D59—41no—
347C2×D59—41no—
348C2×D59—41no—
349C2×D59—41no—
350C2×D59—41no—
351C2×D59—41no—
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—21no—
356C4×C59—22no—
357C4×C59—41no—
358C4×C59—41no—
359C4×C59C2×C4×D411yescharacteristic
360C4×C59C4×#4111yescharacteristic
361C4×C59C2×#12111yescharacteristic
362C4×C59#52511yescharacteristic
363Dic59—42no—
364Dic59—41no—
365Dic59—41no—
366Dic59—81no—
367#3035—591no—
368C2×#444—591no—
369C2×#443—591no—
370#2932—591no—
371#2875D5911yescharacteristic, complemented
372#1980—591no—
373#1950—591no—
374#1929—591no—
375#1929—591no—
376#1876—591no—
377#1876—591no—
378#1806—591no—
379#1771—591no—
380#1765—591no—
381#1764—591no—
382C2×C59—21no—
383C2×C59—21no—
384C2×C59—42no—
385C2×C59C4×#12111yescharacteristic
386C2×C59#295611yescharacteristic
387C2×C59#295711yescharacteristic
388D59—81no—
389D59—81no—
390C2×#135—591no—
391C2×#135—591no—
392C2×#131—591no—
393C2×#131—591no—
394C2×#131C2×D5911yescharacteristic
395C2×#131C2×D5911yescharacteristic
396#532—591no—
397C4×#41C2×D5911yescharacteristic
398#464—591no—
399#464—591no—
400#463—591no—
401#463—591no—
402#462—591no—
403#461—591no—
404#460—591no—
405#459—591no—
406#444—1184no—
407#443—1184no—
408#435—1181no—
409#435—1181no—
410#435—1181no—
411#435—1181no—
412C2×#108—591no—
413C2×#108—591no—
414#423—591no—
415C2×C4⋊C8—591no—
416C2×#104—591no—
417C2×#104—591no—
418C2×#104—591no—
419C2×#104—591no—
420C2×#104—591no—
421C2×#104—591no—
422#416—591no—
423#416—591no—
424#408—591no—
425#408—591no—
426#405—21no—
427#405—21no—
428#405C2×D5911yescharacteristic
429#405C2×D5911yescharacteristic
430C4×M16—21no—
431C4×M16C2×D5911yescharacteristic
432C2×#97—21no—
433C2×#97—591no—
434C2×#97C2×D5911yescharacteristic
435C2×C4×C8—591no—
436C4×C4⋊C4—591no—
437#341—591no—
438#341—591no—
439#339—591no—
440#339—591no—
441#336—591no—
442#336—591no—
443C59#2151911yescharacteristic, complemented, Sylow
444C2×#41—591no—
445C2×#41—591no—
446C2×#41C22×D5911yescharacteristic
447#135—1182no—
448#135—1182no—
449#135—1182no—
450#135—1182no—
451C2×Q16—591no—
452C2×Q16—591no—
453C2×SD16—591no—
454C2×SD16—591no—
455C2×SD16—591no—
456C2×SD16—591no—
457C2×D8—591no—
458C2×D8—591no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—1182no—
463#131—1182no—
464#131—1182no—
465#131—1182no—
466#131D23614yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—591no—
470C2×M16—591no—
471C2×M16—1181no—
472C2×M16—1181no—
473C2×M16C22×D5911yescharacteristic
474C2×M16C22×D5911yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—1181no—
480C22×C8—1181no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8—591no—
484#127—591no—
485#124—591no—
486#124—591no—
487#121—1181no—
488#121—1181no—
489C4×Q8C4×D5911yescharacteristic
490C4×Q8C4×D5911yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—1181no—
494C4×D4—1181no—
495C4×D4C4×D5911yescharacteristic
496C4×D4C4×D5911yescharacteristic
497#117—21no—
498#117C22×D5911yescharacteristic
499C2×C4⋊C4—1181no—
500C2×C42—21no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42C22×D5911yescharacteristic
504#108—1182no—
505#108—1182no—
506C4⋊C8—591no—
507C4⋊C8—591no—
508C4⋊C8—591no—
509C4⋊C8—591no—
510C4⋊C8—1181no—
511C4⋊C8—1181no—
512#104—1182no—
513#104—1182no—
514#104—1182no—
515#104—1182no—
516#104—1182no—
517#104—1182no—
518#103—591no—
519#103—591no—
520#103—591no—
521#103—591no—
522#102—591no—
523#102—591no—
524#102—591no—
525#102—591no—
526C22⋊C8—1181no—
527C22⋊C8—1181no—
528C22⋊C8—1181no—
529C22⋊C8—1181no—
530#97—21no—
531#97—21no—
532#97—21no—
533#97—1182no—
534#97C22⋊D5911yescharacteristic
535#97C22⋊D5911yescharacteristic
536#97C22⋊D5911yescharacteristic
537#97C22⋊D5911yescharacteristic
538C4×C8—21no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—1182no—
542#95—1181no—
543#41—21no—
544#41—21no—
545#41—1181no—
546#41—1181no—
547#41—1181no—
548#41—1181no—
549#41—1181no—
550#41—1181no—
551#41—1181no—
552#41—1181no—
553#41C2×D23612yes—
554#41#1174568512yes—
555C2×Q8—591no—
556C2×Q8—591no—
557C2×Q8C2×C4×D5911yescharacteristic
558C2×D4—21no—
559C2×D4—591no—
560C2×D4—591no—
561C2×D4—1181no—
562C2×D4—1181no—
563C2×D4—1181no—
564C2×D4—1181no—
565C2×D4C2×C4×D5911yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4#1174568511yescharacteristic
574C22×C4#1174568511yescharacteristic
575C22×C4C23×D5911yescharacteristic
576Q16—1182no—
577Q16—1182no—
578SD16—1182no—
579SD16—1182no—
580SD16—1182no—
581SD16—1182no—
582D8—1182no—
583D8—1182no—
584M16—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—1181no—
589M16—1181no—
590M16—1181no—
591M16—1181no—
592M16—2362no—
593M16—2362no—
594M16C2×D23612yes—
595M16#1174568512yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—24no—
602C2×C8—591no—
603C2×C8—591no—
604C2×C8—591no—
605C2×C8—591no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—2362no—
613C2×C8—2362no—
614C2×C8C2×D23612yes—
615C2×C8#1174568512yes—
616C2×C8C2×C22⋊D5911yescharacteristic
617C2×C8C2×C22⋊D5911yescharacteristic
618C2×C8C2×C22⋊D5911yescharacteristic
619C2×C8C2×C22⋊D5911yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—2362no—
625C4⋊C4C2×C4×D5911yescharacteristic
626C4⋊C4C2×C4×D5911yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—1181no—
631C22⋊C4—1181no—
632C22⋊C4—1181no—
633C22⋊C4—1181no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1181no—
638C42—1181no—
639C42—1181no—
640C42—1181no—
641C42C2×C4×D5911yescharacteristic
642C42C2×C4×D5911yescharacteristic
643C42C2×C22⋊D5911yescharacteristic
644C42C2×C22⋊D5911yescharacteristic
645C23—21no—
646C23—1181no—
647C23—1181no—
648C23C2×#1174568511yescharacteristic
649Q8—21no—
650Q8—1181no—
651Q8—1181no—
652Q8—1181no—
653Q8—1181no—
654Q8C4×D23612yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—1181no—
659D4—1181no—
660D4—1181no—
661D4—1181no—
662D4—4721no—
663D4—4721no—
664D4—2361no—
665D4—2361no—
666D4—2361no—
667D4—2361no—
668D4C4×D23612yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—1182no—
679C2×C4—1181no—
680C2×C4—1181no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4C4×C22⋊D5911yescharacteristic
691C2×C4C4×C22⋊D5911yescharacteristic
692C2×C4C4×C22⋊D5911yescharacteristic
693C2×C4C4×C22⋊D5911yescharacteristic
694C2×C4C22×C4×D5911yescharacteristic
695C2×C4C22×C22⋊D5911yescharacteristic
696C2×C4C22×D23611yescharacteristic
697C2×C4C2×#1174568511yescharacteristic
698C2×C4C2×#1174568511yescharacteristic
699C2×C4C2×#1174568511yescharacteristic
700C8—22no—
701C8—21no—
702C8—22no—
703C8—21no—
704C8—1181no—
705C8—1181no—
706C8—1181no—
707C8—1181no—
708C8—2361no—
709C8—2361no—
710C8#1427370112yes—
711C8#1427370112yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—2361no—
718C22—2361no—
719C22—2361no—
720C22—2361no—
721C22—2361no—
722C22—2361no—
723C22C2×C4×C22⋊D5911yescharacteristic
724C22#1683793611yescharacteristic
725C22#1683795211yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—4721no—
734C4—2362no—
735C4—2361no—
736C4—2361no—
737C4C2×C4×D23611yescharacteristic
738C4C4×#1174568511yescharacteristic
739C4C2×#1427370111yescharacteristic
740C4#1683791311yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—4721no—
745C2—4721no—
746C2C4×#1427370111yescharacteristic
747C2#2143300311yescharacteristic
748C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2875C2
socleC22×C59C2×C4×D4
prime radical#21433551C2
cosocleC22×C4×C59C24
hypercenter#2875D59
hypocenterC59#21519
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C2×#16837522C2semidirect
3. C2×#16837517C2semidirect
4. #21432815C2semidirect
5. #21425015C2semidirect
6. #21424871C2semidirect
7. #21424744C2semidirect
8. #21424744C2semidirect
9. #21424423C2semidirect
10. #21424423C2semidirect
11. #21424116C2semidirect
12. #21423968C2semidirect
13. #21423942C2semidirect
14. #21423935C2semidirect
15. C59×#2875C2semidirect
21. #16837624C4semidirect
22. #16837624C4semidirect
23. #16837617C4semidirect
24. #16837617C4semidirect
25. #16837612C4semidirect
26. #16837607C4semidirect
27. #16837602C4semidirect
28. #16837597C4semidirect
139. #131×C59D4semidirect
371. #2875D59semidirect
443. C59#21519semidirect
466. #131D236semidirect

Maximal subgroups

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

subgroupindex
#214335512
C2×#168375222
C2×#168375172
#214328152
#214250152
#214248712
#214247442
#214244232
#214241162
#214239682
#214239422
#214239352
C59×#28752
#2151959