Finite Group Databasebeta

← #28630110

Subgroups — #28630110

Order 15104.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837688C211yesmaximal, characteristic, complemented
2#21429917C211yesmaximal, characteristic
3#21426778C211yesmaximal, characteristic
4#21425529C211yesmaximal, characteristic
5#21425529C211yesmaximal, characteristic
6#21425300C211yesmaximal, characteristic
7#21425293C211yesmaximal, characteristic
8#21425043C211yesmaximal, characteristic, complemented
9#21424866C211yesmaximal, characteristic, complemented
10#21424834C211yesmaximal, characteristic, complemented
11#21424824C211yesmaximal, characteristic, complemented
12#21424786C211yesmaximal, characteristic, complemented
13#21424772C211yesmaximal, characteristic, complemented
14#21424112C211yesmaximal, characteristic, complemented
15C2×C59×#433C211yesmaximal, characteristic
16C2×#14273727C2211yescharacteristic
17C2×#14273706C2211yescharacteristic
18C2×C4×Dic118C2211yescharacteristic
19#16837688—24no—
20C2×#14273661C2211yescharacteristic
21C2×#14273659C2211yescharacteristic
22C2×#14273659C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24C2×#14273652C2211yescharacteristic
25C2×#14273652C2211yescharacteristic
26C2×#14273652C2211yescharacteristic
27C2×#14273652C2211yescharacteristic
28#16837341—21no—
29#16837338—21no—
30#16837322—21no—
31#16837314—21no—
32#16837308C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837300C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837297—21no—
37#16837296—21no—
38#16837290—21no—
39#16837283—21no—
40#16837268C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837262C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#433—24no—
55C2×C4⋊C8×C59C2211yescharacteristic
56C2×C4⋊C8×C59C2211yescharacteristic
57C2×C22⋊C8×C59C2211yescharacteristic
58C2×C22⋊C8×C59C2211yescharacteristic
59C2×#97×C59C2211yescharacteristic
60C2×C4×C8×C59C2211yescharacteristic
61C22×Dic118—21no—
62C22×Dic118C2311yescharacteristic
63#14273727—22no—
64#14273727—22no—
65#14273706—22no—
66#14273706—22no—
67C4×Dic118—22no—
68C4×Dic118—22no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×Dic59⋊C4—21no—
80C2×Dic59⋊C4—21no—
81C2×Dic59⋊C4—21no—
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C4×Dic59—21no—
87C2×C4×Dic59—21no—
88#14273661—22no—
89#14273659—22no—
90#14273659—22no—
91#14273659—22no—
92#14273652—22no—
93#14273652—22no—
94#14273652—22no—
95#14273652—22no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C23×C4×C59C2311yescharacteristic
108C22×C8×C59C2311yescharacteristic
109C22×C8×C59C2311yescharacteristic
110C22×C8×C59C2311yescharacteristic
111C22×C8×C59C2311yescharacteristic
112#117×C59—22no—
113#117×C59—22no—
114C2×C4⋊C4×C59D411yescharacteristic
115C2×C4⋊C4×C59D411yescharacteristic
116C2×C22⋊C4×C59D411yescharacteristic
117C2×C22⋊C4×C59D411yescharacteristic
118C2×C42×C59C2311yescharacteristic
119C2×C42×C59C2311yescharacteristic
120C4⋊C8×C59—22no—
121C4⋊C8×C59D414yes—
122C22⋊C8×C59—22no—
123C22⋊C8×C59—22no—
124#97×C59—22no—
125C4×C8×C59—22no—
126C24×C59C2×D411yescharacteristic
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59C2411yescharacteristic
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C2×Dic118—21no—
148C2×Dic118—21no—
149C2×Dic118—21no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118—42no—
153C2×Dic118—81no—
154C2×Dic118—81no—
155C2×Dic118#4112yes—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C2×C8×C59—21no—
163C2×C8×C59—21no—
164C2×C8×C59—21no—
165C2×C8×C59—21no—
166C2×C8×C59C2×D412yes—
167C2×C8×C59C2×D412yes—
168C4⋊C4×C59—22no—
169C4⋊C4×C59—22no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—22no—
172C42×C59—21no—
173C42×C59—21no—
174C42×C59C2×D412yes—
175C42×C59#4112yes—
176C22⋊Dic59—24no—
177C22⋊Dic59—81no—
178C22⋊Dic59—81no—
179C22⋊Dic59—81no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193C4⋊Dic59—42no—
194C4⋊Dic59#4112yes—
195Dic59⋊C4—24no—
196Dic59⋊C4—42no—
197Dic59⋊C4—81no—
198Dic59⋊C4—81no—
199Dic59⋊C4—81no—
200C4×Dic59—42no—
201C4×Dic59—81no—
202C23×C59—21no—
203C23×C59—21no—
204C23×C59—21no—
205C23×C59—21no—
206C23×C59—21no—
207C23×C59—21no—
208C23×C59—21no—
209C23×C59C22×D411yescharacteristic
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59#12112yes—
228C2×C4×C59#12112yes—
229C2×C4×C59C22×D411yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C59C2×#4111yescharacteristic
232C2×C4×C59C2×#4111yescharacteristic
233C2×C4×C592−1+411yescharacteristic
234C2×C4×C592−1+411yescharacteristic
235C2×Dic59—22no—
236C2×Dic59—22no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259Dic118—22no—
260Dic118—22no—
261Dic118—41no—
262Dic118—41no—
263Dic118—84no—
264C8×C59—22no—
265C8×C59—22no—
266C8×C59—41no—
267C8×C59—41no—
268#24718—591nomaximal, Sylow
269C22×C59—41no—
270C22×C59—41no—
271C22×C59—41no—
272C22×C59—41no—
273C22×C59—41no—
274C22×C59—41no—
275C22×C59—41no—
276C22×C59C2×#12111yescharacteristic
277C22×C59#52511yescharacteristic
278C22×C59#53611yescharacteristic
279C22×C59#57711yescharacteristic
280C22×C59#57711yescharacteristic
281C22×C59#57711yescharacteristic
282C22×C59#57811yescharacteristic
283C4×C59—22no—
284C4×C59—22no—
285C4×C59—41no—
286C4×C59—41no—
287C4×C59—41no—
288C4×C59#54711yescharacteristic
289C4×C59#54811yescharacteristic
290C4×C59#55211yescharacteristic
291C4×C59#55611yescharacteristic
292Dic59—42no—
293Dic59—42no—
294Dic59—81no—
295Dic59—81no—
296Dic59—81no—
297Dic59—81no—
298Dic59—81no—
299Dic59—81no—
300C2×#475—591no—
301C2×#433D5911yescharacteristic
302#2628—591no—
303#2323—591no—
304#2077—591no—
305#2077—591no—
306#2036—591no—
307#2035—591no—
308#1987—591no—
309#1949—591no—
310#1943—591no—
311#1941—591no—
312#1935—591no—
313#1933—591no—
314#1805—591no—
315C2×C59—81no—
316C2×C59#241511yescharacteristic
317C2×C59#305711yescharacteristic
318C2×C59#306311yescharacteristic
319C2×C59#312111yescharacteristic
320C2×C59#312511yescharacteristic
321C2×C59#324211yescharacteristic
322C2×C59#324411yescharacteristic
323C2×C4⋊Q8—591no—
324C2×C22⋊Q8—591no—
325C2×C4×Q8—591no—
326C2×#117C2×D5911yescharacteristic
327#475—1184no—
328#433—24no—
329C2×#107—591no—
330C2×#106—591no—
331C2×#106—591no—
332C2×#106—591no—
333C2×C4⋊C8C2×D5911yescharacteristic
334C2×C4⋊C8C2×D5911yescharacteristic
335C2×#103—591no—
336C2×#103—591no—
337C2×#103—591no—
338C2×#103—591no—
339C2×C22⋊C8C2×D5911yescharacteristic
340C2×C22⋊C8C2×D5911yescharacteristic
341C2×#97C2×D5911yescharacteristic
342C2×C4×C8C2×D5911yescharacteristic
343#400—1181no—
344#399—1181no—
345#395—1181no—
346#393—1181no—
347#391—591no—
348#389—591no—
349#389—591no—
350#389—591no—
351#389—1181no—
352#388—1181no—
353#388—1181no—
354#387—1181no—
355#382—591no—
356#380—591no—
357#380—591no—
358#380—591no—
359C4×C4⋊C4—591no—
360#340—591no—
361#340—591no—
362#340—591no—
363#340—591no—
364#340—591no—
365#340—591no—
366#340—591no—
367#340—591no—
368C59#2471811yescharacteristic, complemented, Sylow
369C22×Q8—591no—
370C22×Q8—1181no—
371C23×C4C22×D5911yescharacteristic
372C22×C8C22×D5911yescharacteristic
373C22×C8C22×D5911yescharacteristic
374C22×C8C22×D5911yescharacteristic
375C22×C8C22×D5911yescharacteristic
376C4⋊Q8—1182no—
377C4⋊Q8—1182no—
378C22⋊Q8—1182no—
379C22⋊Q8—1182no—
380C4×Q8—1182no—
381C4×Q8—1182no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—591no—
385C2×C4⋊C4—591no—
386C2×C4⋊C4—591no—
387C2×C4⋊C4—591no—
388C2×C4⋊C4—591no—
389C2×C4⋊C4—591no—
390C2×C4⋊C4—591no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4—1181no—
395C2×C4⋊C4—1181no—
396C2×C4⋊C4—1181no—
397C2×C4⋊C4D23611yescharacteristic
398C2×C4⋊C4D23611yescharacteristic
399C2×C22⋊C4—1181no—
400C2×C22⋊C4—1181no—
401C2×C22⋊C4—1181no—
402C2×C22⋊C4—1181no—
403C2×C22⋊C4D23611yescharacteristic
404C2×C22⋊C4D23611yescharacteristic
405C2×C42—1181no—
406C2×C42—1181no—
407C2×C42C22×D5911yescharacteristic
408C2×C42C22×D5911yescharacteristic
409#107—1182no—
410#106—1182no—
411#106—1182no—
412#106—1182no—
413C4⋊C8—22no—
414C4⋊C8C22⋊D5914yes—
415#103—1182no—
416#103—1182no—
417#103—1182no—
418#103—1182no—
419C22⋊C8—22no—
420C22⋊C8—22no—
421#97—22no—
422C4×C8—22no—
423#95—1181no—
424#95—1181no—
425#95—1181no—
426#95—1181no—
427#95—1181no—
428#95—1181no—
429#95—1181no—
430#95—1181no—
431#95—1181no—
432#95—1181no—
433#95—1181no—
434C24C2×D23611yescharacteristic
435C2×Q8—592no—
436C2×Q8—1181no—
437C2×Q8—1181no—
438C2×Q8—1181no—
439C2×Q8—1181no—
440C2×Q8—1181no—
441C2×Q8—4721no—
442C2×Q8—4721no—
443C2×Q8—2362no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1181no—
451C22×C4—1181no—
452C22×C4—1181no—
453C22×C4—1181no—
454C22×C4—1181no—
455C22×C4—1181no—
456C22×C4—1181no—
457C22×C4—1181no—
458C22×C4C2×D23611yescharacteristic
459C22×C4C2×D23611yescharacteristic
460C22×C4C2×D23611yescharacteristic
461C22×C4C2×D23611yescharacteristic
462C22×C4C2×D23611yescharacteristic
463C22×C4C23×D5911yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8C2×C22⋊D5912yes—
475C2×C8C2×C22⋊D5912yes—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—592no—
479C4⋊C4—1184no—
480C4⋊C4—1181no—
481C4⋊C4—1181no—
482C4⋊C4—1181no—
483C4⋊C4—1181no—
484C4⋊C4—1181no—
485C4⋊C4—1181no—
486C4⋊C4—1181no—
487C4⋊C4—1181no—
488C4⋊C4—1181no—
489C4⋊C4—1181no—
490C4⋊C4—1181no—
491C4⋊C4—1181no—
492C4⋊C4—1181no—
493C4⋊C4—4721no—
494C4⋊C4—4721no—
495C4⋊C4—4721no—
496C4⋊C4—2362no—
497C4⋊C4—2362no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—1184no—
501C22⋊C4—4721no—
502C22⋊C4—4721no—
503C22⋊C4—4721no—
504C42—21no—
505C42—21no—
506C42—4721no—
507C42—2362no—
508C42#1174568512yes—
509C42C2×C22⋊D5912yes—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×D23611yescharacteristic
518Q8—1182no—
519Q8—1182no—
520Q8—4724no—
521Q8—2361no—
522Q8—2361no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—1182no—
541C2×C4—1182no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2361no—
552C2×C4—2361no—
553C2×C4—2361no—
554C2×C4—2361no—
555C2×C4—2361no—
556C2×C4—2361no—
557C2×C4—2361no—
558C2×C4—2361no—
559C2×C4—2361no—
560C2×C4—2361no—
561C2×C4—2361no—
562C2×C4—2361no—
563C2×C4—2361no—
564C2×C4#1427370112yes—
565C2×C4#1427370112yes—
566C2×C4C22×C22⋊D5911yescharacteristic
567C2×C4#41×D5911yescharacteristic
568C2×C4#41×D5911yescharacteristic
569C2×C4C2×#1174568511yescharacteristic
570C2×C4#1427377411yescharacteristic
571C2×C4#1427377411yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1427370111yescharacteristic
584C22#1683791411yescharacteristic
585C22#1683797811yescharacteristic
586C22#1683821411yescharacteristic
587C22#1683821411yescharacteristic
588C22#1683821411yescharacteristic
589C22#1683821911yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—4721no—
596C4—4721no—
597C4—4721no—
598C4—4721no—
599C4—4721no—
600C4—4721no—
601C4—2362no—
602C4—2362no—
603C4#1683805111yescharacteristic
604C4#1683805911yescharacteristic
605C4#1683809111yescharacteristic
606C4#1683812011yescharacteristic
607C2—81no—
608C2#2142751911yescharacteristic
609C2#2143373511yescharacteristic
610C2#2143378711yescharacteristic
611C2#2143432711yescharacteristic
612C2#2143437511yescharacteristic
613C2#2143536611yescharacteristic
614C2#2143539611yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenterC2×#433D59
hypocenterC59#24718
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16837688C2semidirect
8. #21425043C2semidirect
9. #21424866C2semidirect
10. #21424834C2semidirect
11. #21424824C2semidirect
12. #21424786C2semidirect
13. #21424772C2semidirect
14. #21424112C2semidirect
368. C59#24718semidirect

Maximal subgroups

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

subgroupindex
C2×#168376882
#214299172
#214267782
#214255292
#214253002
#214252932
#214250432
#214248662
#214248342
#214248242
#214247862
#214247722
#214241122
C2×C59×#4332
#2471859