Finite Group Databasebeta

← #28495841

Subgroups — #28495841

Order 15104.

898 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837426C211yesmaximal, characteristic, complemented
2C22×#14273655C211yesmaximal, characteristic
3#21432613C211yesmaximal, characteristic
4C2×#16837384C211yesmaximal, characteristic
5#21423835C211yesmaximal, characteristic, complemented
6C2×C59⋊#338C211yesmaximal, characteristic, complemented
7C2×C59×#339C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11C22×#11745664C2211yescharacteristic
12#16837426—22no—
13#16837426—22no—
14C2×C4⋊(C59⋊C8)—22no—
15C2×#14273655—22no—
16C2×#14273655—21no—
17C2×#14273655—21no—
18C2×#14273655C414yescomplemented
19#16837410—21no—
20#16837406—21no—
21#16837401—22no—
22#16837396—22no—
23#16837384—22no—
24#16837384—22no—
25C2×#14273645—21no—
26C2×#14273643—21no—
27#16837171—22no—
28C59⋊#338—22no—
29C22×M16×C59C2211yescharacteristic
30C2×#117×C59C2211yescharacteristic
31C22×C42×C59C2211yescharacteristic
32C59×#339—21no—
33C59×#339—21no—
34C2×#11745685—21no—
35C2×#11745685—21no—
36C2×#11745685—21no—
37C2×#11745685—21no—
38C2×#11745685—21no—
39C2×#11745685—21no—
40C2×#11745685—21no—
41C2×#11745685—21no—
42C2×#11745685—21no—
43C2×#11745685—21no—
44C2×#11745685C2×C412yes—
45C2×#11745685Q812yes—
46C22×Dic118D411yescharacteristic
47C22×D236D411yescharacteristic
48C22×C22⋊D59—21no—
49C22×C4×D59—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664—21no—
54C2×#11745664—21no—
55C2×#11745664—21no—
56C2×#11745664—21no—
57C2×#11745664—21no—
58C2×#11745664—21no—
59C2×#11745664—21no—
60C2×#11745664—21no—
61C2×#11745664—21no—
62C2×#11745664—21no—
63C2×#11745664—21no—
64C2×#11745664—21no—
65C2×#11745664—21no—
66C2×#11745664C2×C412yes—
67C2×#11745664D412yes—
68C22×C59⋊C8—21no—
69C22×C59⋊C8—21no—
70C22×C59⋊C8D412yes—
71C4⋊(C59⋊C8)—28no—
72#14273655—24no—
73#14273655—24no—
74#14273650—24no—
75#14273647—24no—
76#14273645—24no—
77#14273643—24no—
78C23×C4×C59—21no—
79C23×C4×C59C2311yescharacteristic
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C2×M16×C59—21no—
83C2×M16×C59—21no—
84C2×M16×C59—21no—
85C2×M16×C59D412yes—
86C22×C8×C59—21no—
87#117×C59—21no—
88#117×C59—21no—
89#117×C59—21no—
90#117×C59—21no—
91C2×C4⋊C4×C59D412yes—
92C2×C22⋊C4×C59—21no—
93C2×C42×C59—21no—
94C2×C42×C59—21no—
95C2×C42×C59—21no—
96C2×C42×C59—21no—
97C2×C42×C59C2×C412yes—
98C2×C42×C59D412yes—
99C2×C42×C59D411yescharacteristic
100C2×C42×C59D411yescharacteristic
101C24×C59#4111yescharacteristic
102C23×D59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—44no—
109C22×C4×C59C22×C411yescharacteristic
110C22×C4×C59C2×D411yescharacteristic
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59C2×D411yescharacteristic
114C22×C4×C59C2×D411yescharacteristic
115C22×C4×C59C2×D411yescharacteristic
116C22×C4×C59C2×D411yescharacteristic
117C22×C4×C59C2×Q811yescharacteristic
118C22×C4×C59#4111yescharacteristic
119C22×C4×C59#4111yescharacteristic
120C22×C4×C59#4111yescharacteristic
121C22×C4×C59#4111yescharacteristic
122C22×C4×C59#4111yescharacteristic
123C2×C22⋊D59—22no—
124C2×C22⋊D59—22no—
125C2×C22⋊D59—41no—
126C2×C22⋊D59—41no—
127C2×C22⋊D59—41no—
128C2×C22⋊D59—41no—
129C22×Dic59—21no—
130#11745685—22no—
131#11745685—22no—
132#11745685—22no—
133#11745685—22no—
134#11745685—22no—
135#11745685—22no—
136#11745685—22no—
137#11745685—22no—
138#11745685—41no—
139#11745685—41no—
140#11745685—41no—
141#11745685—41no—
142#11745685—41no—
143#11745685—41no—
144#11745685—41no—
145#11745685—41no—
146C2×D236—21no—
147C2×D236—21no—
148C2×D236—21no—
149C2×D236—21no—
150C2×D236—21no—
151C2×D236C4⋊C412yes—
152C2×C4×D59—22no—
153C2×C4×D59—22no—
154C2×C4×D59—41no—
155C2×C4×D59—41no—
156C2×C4×D59—41no—
157C2×C4×D59—41no—
158C2×Dic118—21no—
159C2×Dic118—21no—
160C2×Dic118—21no—
161C2×Dic118—21no—
162C2×Dic118—21no—
163C2×Dic118C4⋊C412yes—
164M16×C59—22no—
165M16×C59—22no—
166M16×C59—41no—
167M16×C59—41no—
168C2×C8×C59—22no—
169C2×C8×C59—41no—
170C2×C8×C59—41no—
171C4⋊C4×C59—22no—
172C4⋊C4×C59—22no—
173C22⋊C4×C59—41no—
174C22⋊C4×C59—41no—
175C42×C59—22no—
176C42×C59—22no—
177C42×C59—21no—
178C42×C59—21no—
179C42×C59—41no—
180C42×C59—41no—
181C42×C59C22⋊C412yes—
182C42×C59C22⋊C412yes—
183#11745664—22no—
184#11745664—22no—
185#11745664—22no—
186#11745664—22no—
187#11745664—41no—
188#11745664—41no—
189#11745664—41no—
190#11745664—41no—
191#11745664—41no—
192#11745664—41no—
193#11745664—41no—
194#11745664—41no—
195C2×C59⋊C8—22no—
196C2×C59⋊C8—22no—
197C2×C59⋊C8—22no—
198C2×C59⋊C8—22no—
199C2×C59⋊C8—22no—
200C2×C59⋊C8—41no—
201C2×C59⋊C8—41no—
202C2×C59⋊C8—41no—
203C2×C59⋊C8—41no—
204C23×C59—42no—
205C23×C59C4×D411yescharacteristic
206C23×C59#12111yescharacteristic
207C23×C59C22⋊Q811yescharacteristic
208C23×C59#12311yescharacteristic
209C23×C59#12311yescharacteristic
210C23×C59#12311yescharacteristic
211C23×C59#12611yescharacteristic
212C22×D59—22no—
213C22×D59—41no—
214C22×D59—41no—
215C22×D59—82no—
216C2×C4×C59—24no—
217C2×C4×C59—22no—
218C2×C4×C59—22no—
219C2×C4×C59—44no—
220C2×C4×C59—44no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—82no—
224C2×C4×C59C2×C22⋊C411yescharacteristic
225C2×C4×C59C2×C4⋊C411yescharacteristic
226C2×C4×C59#11711yescharacteristic
227C2×C4×C59C4×D411yescharacteristic
228C2×C4×C59C4×D411yescharacteristic
229C2×C4×C59C4×D411yescharacteristic
230C2×C4×C59#12011yescharacteristic
231C2×C4×C59#12011yescharacteristic
232C2×C4×C59#12011yescharacteristic
233C2×C4×C59#12111yescharacteristic
234C2×C4×C59#12111yescharacteristic
235C2×C4×C59#12111yescharacteristic
236C2×C4×C59#12111yescharacteristic
237C2×C4×C59#12111yescharacteristic
238C2×C4×C59#12111yescharacteristic
239C2×C4×C59#12111yescharacteristic
240C2×C4×C59C22⋊Q811yescharacteristic
241C2×C4×C59C22⋊Q811yescharacteristic
242C2×C4×C59C22⋊Q811yescharacteristic
243C2×C4×C59C22⋊Q811yescharacteristic
244C2×C4×C59C22⋊Q811yescharacteristic
245C2×C4×C59#12311yescharacteristic
246C2×C4×C59#12311yescharacteristic
247C2×C4×C59#12411yescharacteristic
248C2×C4×C59#12411yescharacteristic
249C2×C4×C59#12411yescharacteristic
250C2×C4×C59#12611yescharacteristic
251C2×C4×C59#12711yescharacteristic
252C22⋊D59—42no—
253C22⋊D59—42no—
254C22⋊D59—42no—
255C22⋊D59—42no—
256C2×Dic59—22no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259D236—22no—
260D236—22no—
261D236—41no—
262D236—41no—
263C4×D59—42no—
264C4×D59—42no—
265C4×D59—42no—
266C4×D59—42no—
267Dic118—22no—
268Dic118—22no—
269Dic118—41no—
270Dic118—41no—
271C8×C59—42no—
272C59⋊C8—42no—
273C59⋊C8—42no—
274C59⋊C8—42no—
275#11082—591nomaximal, Sylow
276C22×C59—22no—
277C22×C59—22no—
278C22×C59—22no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59#38511yescharacteristic
284C22×C59#38611yescharacteristic
285C22×C59#38811yescharacteristic
286C22×C59#39411yescharacteristic
287C22×C59#39611yescharacteristic
288C22×C59#39711yescharacteristic
289C22×C59#39911yescharacteristic
290C2×D59—42no—
291C2×D59—82no—
292C2×D59—82no—
293C2×D59—82no—
294C4×C59—24no—
295C4×C59—42no—
296C4×C59—82no—
297C4×C59#38011yescharacteristic
298C4×C59#38511yescharacteristic
299C4×C59#38811yescharacteristic
300C4×C59#39011yescharacteristic
301C4×C59#39211yescharacteristic
302C4×C59#39311yescharacteristic
303C4×C59#39411yescharacteristic
304C4×C59#39611yescharacteristic
305Dic59—42no—
306C2×#423—591no—
307C22×#104—591no—
308#2896—591no—
309C2×#413—591no—
310#1742—591no—
311C2×#339D5911yescharacteristic, complemented
312C2×#338—591no—
313C2×C59—21no—
314C2×C59—21no—
315C2×C59—21no—
316C2×C59—21no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59#143911yescharacteristic
320C2×C59#205012yes—
321D59—82no—
322C22×#41—591no—
323C22×M16—591no—
324C22×M16—591no—
325C22×M16—591no—
326C22×M16C2×D5911yescharacteristic
327C2×#117C2×D5911yescharacteristic
328C22×C42C2×D5911yescharacteristic
329#423—1182no—
330#423—1182no—
331C2×C4⋊C8—1182no—
332C2×#104—594no—
333C2×#104—1182no—
334C2×#104—1181no—
335C2×#104—1181no—
336#419—1181no—
337#418—1181no—
338#417—1182no—
339#416—1182no—
340#413—1182no—
341#413—1182no—
342C2×#101—1181no—
343C2×#100—1181no—
344#343—1182no—
345#339—21no—
346#339—21no—
347#338—1182no—
348C59#1108211yescharacteristic, complemented, Sylow
349C2×#41—592no—
350C2×#41—592no—
351C2×#41—1181no—
352C2×#41—1181no—
353C2×#41—1181no—
354C2×#41—1181no—
355C2×#41—1181no—
356C2×#41—1181no—
357C2×#41—1181no—
358C2×#41—1181no—
359C2×#41—1181no—
360C2×#41—1181no—
361C22×Q8—591no—
362C22×D4—591no—
363C22×D4—1181no—
364C23×C4—21no—
365C23×C4—1181no—
366C23×C4C22×D5911yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—592no—
373C2×M16—592no—
374C2×M16—1181no—
375C2×M16—1181no—
376C2×M16—1181no—
377C2×M16—1181no—
378C2×M16—1181no—
379C2×M16—1181no—
380C2×M16—1181no—
381C2×M16—1181no—
382C2×M16—1181no—
383C2×M16—1181no—
384C2×M16—1181no—
385C2×M16—1181no—
386C2×M16—1181no—
387C2×M16—1181no—
388C2×M16—1181no—
389C2×M16—1181no—
390C2×M16D23612yes—
391C22×C8—21no—
392C22×C8—592no—
393C22×C8—1181no—
394C22×C8—1181no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4D23612yes—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C4×D5912yes—
406C2×C42D23612yes—
407C2×C42C22⋊D5911yescharacteristic
408C2×C42C22⋊D5911yescharacteristic
409C4⋊C8—1188no—
410#104—1184no—
411#104—1184no—
412#103—1184no—
413#102—1184no—
414#101—1184no—
415#100—1184no—
416C24—1181no—
417C24#1174568711yescharacteristic
418#41—1182no—
419#41—1182no—
420#41—1182no—
421#41—1182no—
422#41—1182no—
423#41—1182no—
424#41—1182no—
425#41—1182no—
426#41—2361no—
427#41—2361no—
428#41—2361no—
429#41—2361no—
430#41—2361no—
431#41—2361no—
432#41—2361no—
433#41—2361no—
434C2×Q8—592no—
435C2×Q8—1181no—
436C2×Q8—1181no—
437C2×Q8—1181no—
438C2×Q8—1181no—
439C2×Q8—1181no—
440C2×D4—592no—
441C2×D4—1182no—
442C2×D4—1182no—
443C2×D4—1181no—
444C2×D4—1181no—
445C2×D4—1181no—
446C2×D4—1181no—
447C2×D4—1181no—
448C2×D4—2361no—
449C2×D4—2361no—
450C2×D4—2361no—
451C2×D4—2361no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—1181no—
459C22×C4—1182no—
460C22×C4—1182no—
461C22×C4—2361no—
462C22×C4—2361no—
463C22×C4—2361no—
464C22×C4—2361no—
465C22×C4C2×C4×D5911yescharacteristic
466C22×C4C2×D23611yescharacteristic
467C22×C4C2×D23611yescharacteristic
468C22×C4C2×D23611yescharacteristic
469C22×C4#1174568511yescharacteristic
470C22×C4#1174568511yescharacteristic
471C22×C4D4×D5911yescharacteristic
472C22×C4D4×D5911yescharacteristic
473C22×C4D4×D5911yescharacteristic
474C22×C4#1174568711yescharacteristic
475C22×C4#1174568711yescharacteristic
476C22×C4Q8×D5911yescharacteristic
477C22×C4#1174568911yescharacteristic
478C22×C4C2×C22⋊D5911yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—1182no—
484M16—1182no—
485M16—1182no—
486M16—1182no—
487M16—2361no—
488M16—2361no—
489M16—2361no—
490M16—2361no—
491M16—2361no—
492M16—2361no—
493M16—2361no—
494M16—2361no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—1182no—
499C2×C8—1182no—
500C2×C8—1182no—
501C2×C8—1182no—
502C2×C8—1182no—
503C2×C8—2361no—
504C2×C8—2361no—
505C2×C8—2361no—
506C2×C8—2361no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42—41no—
517C42(C2×D59)⋊C412yes—
518C42(C2×D59)⋊C412yes—
519C23—42no—
520C23—1182no—
521C23—4722no—
522C23—2361no—
523C23—2361no—
524C23(C22⋊D59)⋊C411yescharacteristic
525C23#1427369911yescharacteristic
526C23#1427370711yescharacteristic
527C23#1427370911yescharacteristic
528C23#1427371111yescharacteristic
529C23#1427371111yescharacteristic
530C23#1427372211yescharacteristic
531Q8—1182no—
532Q8—1182no—
533Q8—2361no—
534Q8—2361no—
535D4—1182no—
536D4—1182no—
537D4—2362no—
538D4—2362no—
539D4—2362no—
540D4—2362no—
541D4—2361no—
542D4—2361no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—1182no—
552C2×C4—2361no—
553C2×C4—2361no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4C2×(C2×D59)⋊C411yescharacteristic
559C2×C4C4⋊C4×D5911yescharacteristic
560C2×C4#1427368511yescharacteristic
561C2×C4(C22⋊D59)⋊C411yescharacteristic
562C2×C4C4×D23611yescharacteristic
563C2×C4C4×D23611yescharacteristic
564C2×C4#1427369711yescharacteristic
565C2×C4#1427369711yescharacteristic
566C2×C4#1427369711yescharacteristic
567C2×C4#1427369811yescharacteristic
568C2×C4#1427369911yescharacteristic
569C2×C4#1427370111yescharacteristic
570C2×C4#1427370111yescharacteristic
571C2×C4#1427370211yescharacteristic
572C2×C4#1427370211yescharacteristic
573C2×C4#1427370211yescharacteristic
574C2×C4#1427370311yescharacteristic
575C2×C4#1427370511yescharacteristic
576C2×C4#1427370511yescharacteristic
577C2×C4#1427370711yescharacteristic
578C2×C4#1427370711yescharacteristic
579C2×C4#1427370911yescharacteristic
580C2×C4#1427371111yescharacteristic
581C2×C4#1427371311yescharacteristic
582C2×C4#1427371311yescharacteristic
583C2×C4#1427371511yescharacteristic
584C2×C4#1427372211yescharacteristic
585C2×C4#1427372411yescharacteristic
586C8—42no—
587C8—2362no—
588C8—2362no—
589C8—2362no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—4722no—
598C22—4722no—
599C22—4722no—
600C22—2362no—
601C22#1683727611yescharacteristic
602C22#1683727911yescharacteristic
603C22#1683729411yescharacteristic
604C22#1683731811yescharacteristic
605C22#1683732411yescharacteristic
606C22#1683732911yescharacteristic
607C22#1683733911yescharacteristic
608C4—24no—
609C4—42no—
610C4—82no—
611C4—2362no—
612C4#1683725911yescharacteristic
613C4#1683727611yescharacteristic
614C4#1683729411yescharacteristic
615C4#1683730411yescharacteristic
616C4#1683731211yescharacteristic
617C4#1683731511yescharacteristic
618C4#1683731811yescharacteristic
619C4#1683732411yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—4722no—
627C2#2142234211yescharacteristic
628C2#2142538212yes—
subgroupG/H
centerC2×C4#14273713
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#339C2
socleC22×C59#394
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×#339D59
hypocenterC59#11082
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#16837426C2semidirect
5. #21423835C2semidirect
6. C2×C59⋊#338C2semidirect
7. C2×C59×#339C2semidirect
18. C2×#14273655C4semidirect
311. C2×#339D59semidirect
348. C59#11082semidirect

Maximal subgroups

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

subgroupindex
C2×#168374262
C22×#142736552
#214326132
C2×#168373842
#214238352
C2×C59⋊#3382
C2×C59×#3392
#1108259