Finite Group Databasebeta

← #28495844

Subgroups — #28495844

Order 15104.

974 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×#16837420C211yesmaximal, characteristic
2#21432613C211yesmaximal, characteristic
3#21426586C211yesmaximal, characteristic
4#21423805C211yesmaximal, characteristic, complemented
5C2×#16837158C211yesmaximal, characteristic, complemented
6#21423790C211yesmaximal, characteristic, complemented
7C59×#2296C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837420—22no—
13#16837420C414yescomplemented
14C2×#14273655—22no—
15#16837410—21no—
16#16837406—21no—
17#16837401—22no—
18#16837396—22no—
19#16837308—21no—
20#16837304—21no—
21#16837281—22no—
22C4×(C2×D59)⋊C4—22no—
23#16837161—22no—
24#16837158—22no—
25#16837157—22no—
26C2×#117×C59C2211yescharacteristic
27C2×#117×C59C2211yescharacteristic
28C22×C42×C59C2211yescharacteristic
29C59×#389—22no—
30C59×#385—22no—
31C4×C4⋊C4×C59—22no—
32C2×#11745685—21no—
33C2×#11745685—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×#11745685C2×C412yes—
43C2×#11745685Q812yes—
44C22×Dic118D411yescharacteristic
45C22×D236D411yescharacteristic
46C22×C22⋊D59—21no—
47C22×C4×D59—21no—
48C2×#11745664—21no—
49C2×#11745664—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×#11745664C2×C412yes—
60C22×C59⋊C8—21no—
61C22×C59⋊C8D412yes—
62#14273686—21no—
63#14273686—21no—
64#14273686—21no—
65#14273686—21no—
66C2×C4⋊Dic59—21no—
67C2×C22⋊Dic59—21no—
68C2×(C2×D59)⋊C4—24no—
69C2×C4×Dic59D412yes—
70#14273655—28no—
71#14273650—24no—
72#14273647—24no—
73C59⋊#95—24no—
74C23×C4×C59D412yes—
75C23×C4×C59C2311yescharacteristic
76#117×C59—21no—
77#117×C59—21no—
78#117×C59—21no—
79#117×C59—21no—
80#117×C59—21no—
81#117×C59—21no—
82#117×C59C2×C412yes—
83#117×C59D412yes—
84C2×C4⋊C4×C59—21no—
85C2×C4⋊C4×C59—24no—
86C2×C4⋊C4×C59D412yes—
87C2×C22⋊C4×C59—21no—
88C2×C22⋊C4×C59—21no—
89C2×C42×C59—21no—
90C2×C42×C59—21no—
91C2×C42×C59—21no—
92C2×C42×C59—21no—
93C2×C42×C59—21no—
94C2×C42×C59—21no—
95C2×C42×C59—21no—
96C2×C42×C59D412yes—
97#95×C59—24no—
98C24×C59C2×D411yescharacteristic
99C23×D59—21no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—44no—
106C22×C4×C59C22×C411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D411yescharacteristic
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59C2×Q811yescharacteristic
114C22×C4×C59#4111yescharacteristic
115C22×C4×C59#4111yescharacteristic
116C22×C4×C59#4111yescharacteristic
117C22×C4×C59#4111yescharacteristic
118C22×C4×C59#4111yescharacteristic
119C22×C4×C59#4111yescharacteristic
120C2×C22⋊D59—22no—
121C2×C22⋊D59—22no—
122C2×C22⋊D59—41no—
123C2×C22⋊D59—41no—
124C2×C22⋊D59—41no—
125C2×C22⋊D59—41no—
126C22×Dic59—21no—
127C22×Dic59—22no—
128#11745685—22no—
129#11745685—22no—
130#11745685—22no—
131#11745685—22no—
132#11745685—22no—
133#11745685—22no—
134#11745685—22no—
135#11745685—22no—
136#11745685—41no—
137#11745685—41no—
138#11745685—41no—
139#11745685—41no—
140#11745685—41no—
141#11745685—41no—
142#11745685—41no—
143#11745685—41no—
144C2×D236—21no—
145C2×D236—21no—
146C2×D236—21no—
147C2×D236—21no—
148C2×D236—21no—
149C2×D236C4⋊C412yescomplemented
150C2×C4×D59—22no—
151C2×C4×D59—22no—
152C2×C4×D59—41no—
153C2×C4×D59—41no—
154C2×C4×D59—41no—
155C2×C4×D59—41no—
156C2×Dic118—21no—
157C2×Dic118—21no—
158C2×Dic118—21no—
159C2×Dic118—21no—
160C2×Dic118—21no—
161C2×Dic118C4⋊C412yescomplemented
162C4⋊C4×C59—22no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—22no—
165C4⋊C4×C59—22no—
166C4⋊C4×C59—48no—
167C22⋊C4×C59—22no—
168C22⋊C4×C59—22no—
169C22⋊C4×C59—41no—
170C22⋊C4×C59—41no—
171C42×C59—22no—
172C42×C59—41no—
173C42×C59—41no—
174C42×C59—41no—
175C42×C59—41no—
176C42×C59—41no—
177C42×C59—41no—
178C42×C59C22⋊C414yescomplemented
179C22⋊Dic59—41no—
180C22⋊Dic59—41no—
181(C2×D59)⋊C4—48no—
182C4⋊Dic59—41no—
183C4⋊Dic59—41no—
184C4×Dic59—22no—
185C4×Dic59—22no—
186#11745664—22no—
187#11745664—22no—
188#11745664—41no—
189#11745664—41no—
190#11745664—41no—
191#11745664—41no—
192#11745664—41no—
193#11745664—41no—
194C2×C59⋊C8—22no—
195C2×C59⋊C8—22no—
196C2×C59⋊C8—22no—
197C2×C59⋊C8—22no—
198C2×C59⋊C8—41no—
199C2×C59⋊C8—41no—
200C23×C59—42no—
201C23×C59C4×D411yescharacteristic
202C23×C59#12011yescharacteristic
203C23×C59#12011yescharacteristic
204C23×C59#12111yescharacteristic
205C23×C59#12111yescharacteristic
206C23×C59C22⋊Q811yescharacteristic
207C23×C59#12411yescharacteristic
208C22×D59—22no—
209C22×D59—44no—
210C22×D59—41no—
211C22×D59—41no—
212C2×C4×C59—24no—
213C2×C4×C59—24no—
214C2×C4×C59—24no—
215C2×C4×C59—24no—
216C2×C4×C59—44no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—44no—
222C2×C4×C59—42no—
223C2×C4×C59C2×C22⋊C411yescharacteristic
224C2×C4×C59C2×C4⋊C411yescharacteristic
225C2×C4×C59#11711yescharacteristic
226C2×C4×C59C4×D411yescharacteristic
227C2×C4×C59C4×D411yescharacteristic
228C2×C4×C59C4×D411yescharacteristic
229C2×C4×C59#12011yescharacteristic
230C2×C4×C59#12111yescharacteristic
231C2×C4×C59#12111yescharacteristic
232C2×C4×C59#12111yescharacteristic
233C2×C4×C59#12111yescharacteristic
234C2×C4×C59#12111yescharacteristic
235C2×C4×C59#12111yescharacteristic
236C2×C4×C59C22⋊Q811yescharacteristic
237C2×C4×C59C22⋊Q811yescharacteristic
238C2×C4×C59C22⋊Q811yescharacteristic
239C2×C4×C59C22⋊Q811yescharacteristic
240C2×C4×C59C22⋊Q811yescharacteristic
241C2×C4×C59#12311yescharacteristic
242C2×C4×C59#12311yescharacteristic
243C2×C4×C59#12311yescharacteristic
244C2×C4×C59#12311yescharacteristic
245C2×C4×C59#12311yescharacteristic
246C2×C4×C59#12411yescharacteristic
247C2×C4×C59#12411yescharacteristic
248C2×C4×C59#12611yescharacteristic
249C2×C4×C59#12611yescharacteristic
250C2×C4×C59#12711yescharacteristic
251C22⋊D59—42no—
252C22⋊D59—42no—
253C22⋊D59—42no—
254C22⋊D59—42no—
255C2×Dic59—22no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—44no—
259C2×Dic59—42no—
260D236—22no—
261D236—22no—
262D236—41no—
263D236—41no—
264C4×D59—42no—
265C4×D59—42no—
266C4×D59—42no—
267C4×D59—42no—
268Dic118—22no—
269Dic118—22no—
270Dic118—41no—
271Dic118—41no—
272C59⋊C8—42no—
273C59⋊C8—42no—
274#11083—591nomaximal, Sylow
275C22×C59—22no—
276C22×C59—22no—
277C22×C59—22no—
278C22×C59—41no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59#38511yescharacteristic
283C22×C59#38611yescharacteristic
284C22×C59#38811yescharacteristic
285C22×C59#39211yescharacteristic
286C22×C59#39311yescharacteristic
287C22×C59#39411yescharacteristic
288C22×C59#39611yescharacteristic
289C2×D59—44no—
290C2×D59—42no—
291C2×D59—82no—
292C2×D59—82no—
293C4×C59—44no—
294C4×C59—44no—
295C4×C59—82no—
296C4×C59#38011yescharacteristic
297C4×C59#38511yescharacteristic
298C4×C59#38811yescharacteristic
299C4×C59#39011yescharacteristic
300C4×C59#39411yescharacteristic
301C4×C59#39611yescharacteristic
302C4×C59#39711yescharacteristic
303C4×C59#39911yescharacteristic
304Dic59—42no—
305Dic59—82no—
306C2×#421—591no—
307#2896—591no—
308#2297—591no—
309#2296D5911yescharacteristic, complemented
310#1733—591no—
311C2×H(3,ℤ/4)—591no—
312#1728—591no—
313C2×C59—21no—
314C2×C59—21no—
315C2×C59—21no—
316C2×C59—21no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59#143911yescharacteristic
320C2×C59#201012yes—
321D59—82no—
322C22×#41—591no—
323C22×M16—591no—
324C22×M16—591no—
325C2×#117—591no—
326C2×#117C2×D5911yescharacteristic
327C2×#117C2×D5911yescharacteristic
328C22×C42C2×D5911yescharacteristic
329#421—594no—
330#421—1182no—
331C2×#104—1182no—
332#419—1181no—
333#418—1181no—
334#417—1182no—
335#416—1182no—
336#391—1181no—
337#390—1181no—
338#389—22no—
339#386—1182no—
340#385—22no—
341C4×C4⋊C4—22no—
342C4×C22⋊C4—1182no—
343#339—1182no—
344H(3,ℤ/4)—1182no—
345#336—1182no—
346C59#1108311yescharacteristic, complemented, Sylow
347C2×#41—592no—
348C2×#41—592no—
349C2×#41—1181no—
350C2×#41—1181no—
351C2×#41—1181no—
352C2×#41—1181no—
353C2×#41—1181no—
354C2×#41—1181no—
355C2×#41—1181no—
356C2×#41—1181no—
357C2×#41—1181no—
358C2×#41—1181no—
359C22×Q8—591no—
360C22×D4—591no—
361C22×D4—1181no—
362C23×C4—1181no—
363C23×C4C22⋊D5912yes—
364C23×C4C22×D5911yescharacteristic
365C2×M16—592no—
366C2×M16—1181no—
367C2×M16—1181no—
368C2×M16—1181no—
369C2×M16—1181no—
370C2×M16—1181no—
371C2×M16—1181no—
372C2×M16—1181no—
373C2×M16—1181no—
374C2×M16—1181no—
375C2×M16—1181no—
376C2×M16—1181no—
377C22×C8—592no—
378C22×C8—1181no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—1181no—
386#117—1181no—
387#117—1181no—
388#117—1181no—
389#117C4×D5912yes—
390#117D23612yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4C22⋊D5912yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—1184no—
398C2×C22⋊C4—1181no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—592no—
407C2×C42C22⋊D5912yes—
408#104—1188no—
409#103—1184no—
410#102—1184no—
411#95—24no—
412#95—1184no—
413C24—1181no—
414C24C2×C22⋊D5911yescharacteristic
415#41—1182no—
416#41—1182no—
417#41—1182no—
418#41—1182no—
419#41—1182no—
420#41—1182no—
421#41—1182no—
422#41—1182no—
423#41—2361no—
424#41—2361no—
425#41—2361no—
426#41—2361no—
427#41—2361no—
428#41—2361no—
429#41—2361no—
430#41—2361no—
431C2×Q8—592no—
432C2×Q8—1181no—
433C2×Q8—1181no—
434C2×Q8—1181no—
435C2×Q8—1181no—
436C2×Q8—1181no—
437C2×D4—592no—
438C2×D4—1182no—
439C2×D4—1182no—
440C2×D4—1181no—
441C2×D4—1181no—
442C2×D4—1181no—
443C2×D4—1181no—
444C2×D4—1181no—
445C2×D4—2361no—
446C2×D4—2361no—
447C2×D4—2361no—
448C2×D4—2361no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—1181no—
456C22×C4—1182no—
457C22×C4—1182no—
458C22×C4—1182no—
459C22×C4—2361no—
460C22×C4—2361no—
461C22×C4—2361no—
462C22×C4—2361no—
463C22×C4C2×C4×D5911yescharacteristic
464C22×C4C2×D23611yescharacteristic
465C22×C4#1174568511yescharacteristic
466C22×C4#1174568511yescharacteristic
467C22×C4D4×D5911yescharacteristic
468C22×C4D4×D5911yescharacteristic
469C22×C4D4×D5911yescharacteristic
470C22×C4#1174568711yescharacteristic
471C22×C4Q8×D5911yescharacteristic
472C22×C4#1174568911yescharacteristic
473C22×C4#1174568911yescharacteristic
474C22×C4#1174568911yescharacteristic
475C22×C4C2×C22⋊D5911yescharacteristic
476C22×C4C2×C22⋊D5911yescharacteristic
477M16—1182no—
478M16—1182no—
479M16—2361no—
480M16—2361no—
481M16—2361no—
482M16—2361no—
483M16—2361no—
484M16—2361no—
485C2×C8—1182no—
486C2×C8—1182no—
487C2×C8—1182no—
488C2×C8—1182no—
489C2×C8—2361no—
490C2×C8—2361no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—48no—
496C4⋊C4—2361no—
497C4⋊C4—2361no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—2368no—
503C22⋊C4—2361no—
504C22⋊C4—2361no—
505C42—22no—
506C42—41no—
507C42—41no—
508C42—41no—
509C42—41no—
510C42—41no—
511C42—41no—
512C42—1182no—
513C42—1182no—
514C42(C2×D59)⋊C414yescomplemented
515C23—42no—
516C23—1182no—
517C23—2364no—
518C23—2361no—
519C23—2361no—
520C23C4×C22⋊D5911yescharacteristic
521C23#1427369511yescharacteristic
522C23#1427369611yescharacteristic
523C23#1427369911yescharacteristic
524C23#1427370111yescharacteristic
525C23#1427370311yescharacteristic
526C23#1427371611yescharacteristic
527Q8—1182no—
528Q8—1182no—
529Q8—2361no—
530Q8—2361no—
531D4—1182no—
532D4—1182no—
533D4—2362no—
534D4—2362no—
535D4—2362no—
536D4—2362no—
537D4—2361no—
538D4—2361no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—1182no—
551C2×C4—2364no—
552C2×C4—2362no—
553C2×C4—2361no—
554C2×C4—2361no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4—2362no—
559C2×C4C2×(C2×D59)⋊C411yescharacteristic
560C2×C4C4⋊C4×D5911yescharacteristic
561C2×C4#1427368511yescharacteristic
562C2×C4C4×C22⋊D5911yescharacteristic
563C2×C4#1427368911yescharacteristic
564C2×C4#1427368911yescharacteristic
565C2×C4#1427369511yescharacteristic
566C2×C4#1427369811yescharacteristic
567C2×C4#1427369911yescharacteristic
568C2×C4#1427370111yescharacteristic
569C2×C4#1427370211yescharacteristic
570C2×C4#1427370211yescharacteristic
571C2×C4#1427370211yescharacteristic
572C2×C4#1427370311yescharacteristic
573C2×C4#1427370311yescharacteristic
574C2×C4#1427370511yescharacteristic
575C2×C4#1427370511yescharacteristic
576C2×C4#1427370711yescharacteristic
577C2×C4#1427371011yescharacteristic
578C2×C4#1427371211yescharacteristic
579C2×C4#1427371211yescharacteristic
580C2×C4#1427371211yescharacteristic
581C2×C4#1427371211yescharacteristic
582C2×C4#1427371611yescharacteristic
583C2×C4#1427371611yescharacteristic
584C2×C4#1427372211yescharacteristic
585C2×C4#1427372211yescharacteristic
586C2×C4#1427372311yescharacteristic
587C8—2362no—
588C8—2362no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—4722no—
597C22—4722no—
598C22—2364no—
599C22—2362no—
600C22#1683727311yescharacteristic
601C22#1683728111yescharacteristic
602C22#1683729211yescharacteristic
603C22#1683731011yescharacteristic
604C22#1683731311yescharacteristic
605C22#1683731911yescharacteristic
606C22#1683732411yescharacteristic
607C4—44no—
608C4—44no—
609C4—82no—
610C4—4722no—
611C4—2362no—
612C4#1683725911yescharacteristic
613C4#1683727311yescharacteristic
614C4#1683729211yescharacteristic
615C4#1683730311yescharacteristic
616C4#1683731911yescharacteristic
617C4#1683732411yescharacteristic
618C4#1683732811yescharacteristic
619C4#1683733711yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—4722no—
627C2#2142233811yescharacteristic
628C2#2142516112yes—
subgroupG/H
centerC2×C4#14273723
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2296C2
socleC22×C59#392
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenter#2296D59
hypocenterC59#11083
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
4. #21423805C2semidirect
5. C2×#16837158C2semidirect
6. #21423790C2semidirect
7. C59×#2296C2semidirect
13. #16837420C4semidirect
149. C2×D236C4⋊C4semidirect
161. C2×Dic118C4⋊C4semidirect
178. C42×C59C22⋊C4semidirect
309. #2296D59semidirect
346. C59#11083semidirect
514. C42(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168374202
#214326132
#214265862
#214238052
C2×#168371582
#214237902
C59×#22962
#1108359