Finite Group Databasebeta

← #28495923

Subgroups — #28495923

Order 15104.

868 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432659C211yesmaximal, characteristic, complemented
2C2×#16837420C211yesmaximal, characteristic
3C2×#16837418C211yesmaximal, characteristic
4C2×#16837375C211yesmaximal, characteristic
5#21423828C211yesmaximal, characteristic, complemented
6#21423805C211yesmaximal, characteristic, complemented
7C59×#1733C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C2×#14273686C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837430—22no—
13#16837428—22no—
14#16837425—22no—
15#16837420—22no—
16#16837420—22no—
17#16837418—22no—
18#16837418—22no—
19C2×#14273655—22no—
20C2×#14273653—22no—
21#16837375—22no—
22#16837375C414yescomplemented
23C2×#14273641—22no—
24#16837168—22no—
25#16837161—22no—
26C22×M16×C59C2211yescharacteristic
27C2×#117×C59C2211yescharacteristic
28C2×#117×C59C2211yescharacteristic
29C59×#339—22no—
30C2×#11745685—21no—
31C2×#11745685—21no—
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×#11745685C2×C412yes—
41C2×#11745685D412yes—
42C22×Dic118Q811yescharacteristic
43C22×D236Q811yescharacteristic
44C22×C22⋊D59—21no—
45C22×C4×D59—21no—
46C2×#11745664—21no—
47C2×#11745664—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664—21no—
51C2×#11745664D412yes—
52C22×C59⋊C8—21no—
53#14273686—21no—
54#14273686—21no—
55#14273686—21no—
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686C2×C412yes—
60#14273686D412yes—
61C2×C4⋊Dic59—21no—
62C2×C4⋊Dic59—21no—
63C2×C22⋊Dic59—21no—
64C2×C22⋊Dic59D412yes—
65C2×C4×Dic59—21no—
66C2×C4×Dic59D412yes—
67Dic59⋊C8—28no—
68#14273655—28no—
69#14273653—28no—
70#14273641—28no—
71C23×C4×C59C2311yescharacteristic
72C2×M16×C59—21no—
73C2×M16×C59—21no—
74C2×M16×C59—21no—
75C2×M16×C59—21no—
76C2×M16×C59—21no—
77C2×M16×C59D412yes—
78C22×C8×C59—21no—
79#117×C59—21no—
80#117×C59—21no—
81#117×C59—21no—
82#117×C59—21no—
83#117×C59—21no—
84#117×C59—21no—
85#117×C59C2×C412yes—
86#117×C59D412yes—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59—21no—
89C2×C22⋊C4×C59—21no—
90C2×C22⋊C4×C59—21no—
91C2×C42×C59—21no—
92C2×C42×C59—21no—
93C24×C59C2×D411yescharacteristic
94C23×D59—21no—
95C22×C4×C59—41no—
96C22×C4×C59—41no—
97C22×C4×C59C22×C411yescharacteristic
98C22×C4×C59C2×D411yescharacteristic
99C22×C4×C59C2×D411yescharacteristic
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×Q811yescharacteristic
105C22×C4×C59#4111yescharacteristic
106C22×C4×C59#4111yescharacteristic
107C22×C4×C59#4111yescharacteristic
108C22×C4×C59#4111yescharacteristic
109C22×C4×C59#4111yescharacteristic
110C22×C4×C59#4111yescharacteristic
111C2×C22⋊D59—22no—
112C2×C22⋊D59—22no—
113C2×C22⋊D59—41no—
114C2×C22⋊D59—41no—
115C2×C22⋊D59—41no—
116C2×C22⋊D59—41no—
117C22×Dic59—21no—
118C22×Dic59—22no—
119C22×Dic59—22no—
120#11745685—22no—
121#11745685—22no—
122#11745685—22no—
123#11745685—22no—
124#11745685—22no—
125#11745685—22no—
126#11745685—22no—
127#11745685—22no—
128#11745685—41no—
129#11745685—41no—
130#11745685—41no—
131#11745685—41no—
132#11745685—41no—
133#11745685—41no—
134#11745685—41no—
135#11745685—41no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236—21no—
140C2×D236—21no—
141C2×D236C4⋊C412yes—
142C2×C4×D59—22no—
143C2×C4×D59—22no—
144C2×C4×D59—41no—
145C2×C4×D59—41no—
146C2×C4×D59—41no—
147C2×C4×D59—41no—
148C2×Dic118—21no—
149C2×Dic118—21no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118—21no—
153C2×Dic118C4⋊C412yes—
154M16×C59—22no—
155M16×C59—22no—
156M16×C59—41no—
157M16×C59—41no—
158C2×C8×C59—22no—
159C2×C8×C59—41no—
160C2×C8×C59—41no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—41no—
164C4⋊C4×C59—41no—
165C22⋊C4×C59—22no—
166C22⋊C4×C59—22no—
167C22⋊C4×C59—41no—
168C22⋊C4×C59—41no—
169C42×C59—22no—
170C42×C59—22no—
171C42×C59—41no—
172C42×C59—41no—
173C22⋊Dic59—22no—
174C22⋊Dic59—41no—
175C22⋊Dic59—41no—
176C22⋊Dic59C22⋊C414yes—
177C4⋊Dic59—22no—
178C4⋊Dic59—22no—
179C4⋊Dic59—41no—
180C4⋊Dic59—41no—
181C4×Dic59—22no—
182C4×Dic59—22no—
183C4×Dic59—22no—
184C4×Dic59—22no—
185#11745664—22no—
186#11745664—22no—
187#11745664—41no—
188#11745664—41no—
189C2×C59⋊C8—22no—
190C2×C59⋊C8—41no—
191C2×C59⋊C8—41no—
192C23×C59—81no—
193C23×C59C2×C22⋊C411yescharacteristic
194C23×C59#12111yescharacteristic
195C23×C59#12111yescharacteristic
196C23×C59#12111yescharacteristic
197C23×C59#12111yescharacteristic
198C23×C59#12111yescharacteristic
199C23×C59C22⋊Q811yescharacteristic
200C22×D59—22no—
201C22×D59—41no—
202C22×D59—41no—
203C22×D59—82no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59—82no—
207C2×C4×C59—82no—
208C2×C4×C59C2×C4⋊C411yescharacteristic
209C2×C4×C59#11711yescharacteristic
210C2×C4×C59C4×D411yescharacteristic
211C2×C4×C59C4×D411yescharacteristic
212C2×C4×C59C4×D411yescharacteristic
213C2×C4×C59C4×D411yescharacteristic
214C2×C4×C59#12011yescharacteristic
215C2×C4×C59#12011yescharacteristic
216C2×C4×C59#12011yescharacteristic
217C2×C4×C59#12111yescharacteristic
218C2×C4×C59#12111yescharacteristic
219C2×C4×C59#12111yescharacteristic
220C2×C4×C59C22⋊Q811yescharacteristic
221C2×C4×C59C22⋊Q811yescharacteristic
222C2×C4×C59C22⋊Q811yescharacteristic
223C2×C4×C59C22⋊Q811yescharacteristic
224C2×C4×C59C22⋊Q811yescharacteristic
225C2×C4×C59#12311yescharacteristic
226C2×C4×C59#12311yescharacteristic
227C2×C4×C59#12311yescharacteristic
228C2×C4×C59#12311yescharacteristic
229C2×C4×C59#12311yescharacteristic
230C2×C4×C59#12411yescharacteristic
231C2×C4×C59#12411yescharacteristic
232C2×C4×C59#12411yescharacteristic
233C2×C4×C59#12611yescharacteristic
234C2×C4×C59#12611yescharacteristic
235C2×C4×C59#12711yescharacteristic
236C22⋊D59—42no—
237C22⋊D59—42no—
238C22⋊D59—42no—
239C22⋊D59—42no—
240C2×Dic59—22no—
241C2×Dic59—24no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—42no—
245C2×Dic59—82no—
246C2×Dic59—82no—
247D236—22no—
248D236—22no—
249D236—41no—
250D236—41no—
251C4×D59—42no—
252C4×D59—42no—
253C4×D59—42no—
254C4×D59—42no—
255Dic118—22no—
256Dic118—22no—
257Dic118—41no—
258Dic118—41no—
259C8×C59—42no—
260C59⋊C8—42no—
261#11094—591nomaximal, Sylow
262C22×C59—41no—
263C22×C59—41no—
264C22×C59—41no—
265C22×C59—41no—
266C22×C59—41no—
267C22×C59—41no—
268C22×C59—41no—
269C22×C59#38011yescharacteristic
270C22×C59#38611yescharacteristic
271C22×C59#39011yescharacteristic
272C22×C59#39411yescharacteristic
273C22×C59#39411yescharacteristic
274C22×C59#39611yescharacteristic
275C22×C59#39611yescharacteristic
276C2×D59—42no—
277C2×D59—82no—
278C2×D59—82no—
279C2×D59—82no—
280C4×C59—82no—
281C4×C59—82no—
282C4×C59#38511yescharacteristic
283C4×C59#38511yescharacteristic
284C4×C59#38811yescharacteristic
285C4×C59#38811yescharacteristic
286C4×C59#39211yescharacteristic
287C4×C59#39311yescharacteristic
288C4×C59#39711yescharacteristic
289C4×C59#39911yescharacteristic
290Dic59—44no—
291Dic59—42no—
292Dic59—82no—
293#2905—591no—
294C2×#421—591no—
295C2×#421—591no—
296C2×#410—591no—
297#1740—591no—
298#1733—591no—
299#1733D5911yescharacteristic, complemented
300C2×C59—21no—
301C2×C59—21no—
302C2×C59—21no—
303C2×C59—21no—
304C2×C59—21no—
305C2×C59—21no—
306C2×C59—21no—
307C2×C59#143911yescharacteristic
308D59—82no—
309C22×#41—591no—
310C22×M16—591no—
311C22×M16C2×D5911yescharacteristic
312C2×#117—591no—
313C2×#117—591no—
314C2×#117C2×D5911yescharacteristic
315C2×#117C2×D5911yescharacteristic
316#424—1182no—
317#424—1182no—
318#423—1182no—
319#421—1182no—
320#421—1182no—
321#421—1182no—
322#421—1182no—
323C2×#104—1182no—
324C2×#104—1182no—
325#410—594no—
326#410—1182no—
327C2×#99—1182no—
328#342—1182no—
329#339—22no—
330#339—1182no—
331C59#1109411yescharacteristic, complemented, Sylow
332C2×#41—592no—
333C2×#41—592no—
334C2×#41—1181no—
335C2×#41—1181no—
336C2×#41—1181no—
337C2×#41—1181no—
338C2×#41—1181no—
339C2×#41—1181no—
340C2×#41—1181no—
341C2×#41—1181no—
342C2×#41—1181no—
343C2×#41—1181no—
344C22×Q8—591no—
345C22×D4—591no—
346C22×D4—1181no—
347C23×C4—1181no—
348C23×C4C22×D5911yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—592no—
355C2×M16—1181no—
356C2×M16—1181no—
357C2×M16—1181no—
358C2×M16—1181no—
359C2×M16—1181no—
360C2×M16D23612yes—
361C22×C8—21no—
362C22×C8—1181no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—592no—
370#117—592no—
371#117—1181no—
372#117—1181no—
373#117—1181no—
374#117—1181no—
375#117—1181no—
376#117—1181no—
377#117C4×D5912yes—
378#117C22⋊D5912yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—1181no—
382C2×C4⋊C4—1181no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—592no—
386C2×C22⋊C4—1181no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—592no—
390C2×C42—1181no—
391C4⋊C8—1188no—
392#104—1188no—
393#104—1188no—
394#99—1188no—
395C24—1181no—
396C24D4×D5911yescharacteristic
397#41—1182no—
398#41—1182no—
399#41—1182no—
400#41—1182no—
401#41—1182no—
402#41—1182no—
403#41—1182no—
404#41—1182no—
405#41—2361no—
406#41—2361no—
407#41—2361no—
408#41—2361no—
409#41—2361no—
410#41—2361no—
411#41—2361no—
412#41—2361no—
413C2×Q8—592no—
414C2×Q8—1181no—
415C2×Q8—1181no—
416C2×Q8—1181no—
417C2×Q8—1181no—
418C2×Q8—1181no—
419C2×D4—592no—
420C2×D4—1182no—
421C2×D4—1182no—
422C2×D4—1181no—
423C2×D4—1181no—
424C2×D4—1181no—
425C2×D4—1181no—
426C2×D4—1181no—
427C2×D4—2361no—
428C2×D4—2361no—
429C2×D4—2361no—
430C2×D4—2361no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—1182no—
434C22×C4—1181no—
435C22×C4—1182no—
436C22×C4—1182no—
437C22×C4—1182no—
438C22×C4—2361no—
439C22×C4—2361no—
440C22×C4—2361no—
441C22×C4—2361no—
442C22×C4C2×C4×D5911yescharacteristic
443C22×C4C2×D23611yescharacteristic
444C22×C4#1174568511yescharacteristic
445C22×C4#1174568511yescharacteristic
446C22×C4#1174568511yescharacteristic
447C22×C4#1174568511yescharacteristic
448C22×C4D4×D5911yescharacteristic
449C22×C4D4×D5911yescharacteristic
450C22×C4D4×D5911yescharacteristic
451C22×C4D4×D5911yescharacteristic
452C22×C4#1174568711yescharacteristic
453C22×C4Q8×D5911yescharacteristic
454C22×C4#1174568911yescharacteristic
455C22×C4C2×C22⋊D5911yescharacteristic
456M16—22no—
457M16—22no—
458M16—41no—
459M16—41no—
460M16—1182no—
461M16—1182no—
462M16—2361no—
463M16—2361no—
464C2×C8—22no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—1182no—
468C2×C8—2361no—
469C2×C8—2361no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—1182no—
475C4⋊C4—1182no—
476C4⋊C4—2361no—
477C4⋊C4—2361no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—594no—
483C22⋊C4—1182no—
484C22⋊C4—2361no—
485C22⋊C4—2361no—
486C42—22no—
487C42—22no—
488C42—41no—
489C42—41no—
490C42—1182no—
491C42—1182no—
492C42—1182no—
493C42—1182no—
494C23—81no—
495C23—1182no—
496C23—4722no—
497C23—2361no—
498C23—2361no—
499C23C22⋊C4×D5911yescharacteristic
500C23#1427369911yescharacteristic
501C23#1427370011yescharacteristic
502C23#1427370011yescharacteristic
503C23#1427370011yescharacteristic
504C23#1427370211yescharacteristic
505C23#1427370511yescharacteristic
506Q8—1182no—
507Q8—1182no—
508Q8—2361no—
509Q8—2361no—
510D4—1182no—
511D4—1182no—
512D4—2362no—
513D4—2362no—
514D4—2362no—
515D4—2362no—
516D4—2361no—
517D4—2361no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—1182no—
523C2×C4—1184no—
524C2×C4—4722no—
525C2×C4—4722no—
526C2×C4—2362no—
527C2×C4—2361no—
528C2×C4—2361no—
529C2×C4—2362no—
530C2×C4—2362no—
531C2×C4—2362no—
532C2×C4—2362no—
533C2×C4C4⋊C4×D5911yescharacteristic
534C2×C4#1427368411yescharacteristic
535C2×C4(C22⋊D59)⋊C411yescharacteristic
536C2×C4C4×C22⋊D5911yescharacteristic
537C2×C4#1427368911yescharacteristic
538C2×C4C4×D23611yescharacteristic
539C2×C4#1427369511yescharacteristic
540C2×C4#1427369711yescharacteristic
541C2×C4#1427369711yescharacteristic
542C2×C4#1427370011yescharacteristic
543C2×C4#1427370011yescharacteristic
544C2×C4#1427370111yescharacteristic
545C2×C4#1427370311yescharacteristic
546C2×C4#1427370511yescharacteristic
547C2×C4#1427370511yescharacteristic
548C2×C4#1427370511yescharacteristic
549C2×C4#1427370711yescharacteristic
550C2×C4#1427370911yescharacteristic
551C2×C4#1427371011yescharacteristic
552C2×C4#1427371211yescharacteristic
553C2×C4#1427371211yescharacteristic
554C2×C4#1427371211yescharacteristic
555C2×C4#1427371311yescharacteristic
556C2×C4#1427371311yescharacteristic
557C2×C4#1427371511yescharacteristic
558C2×C4#1427372111yescharacteristic
559C2×C4#1427372211yescharacteristic
560C2×C4#1427372311yescharacteristic
561C8—42no—
562C8—2362no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—4722no—
571C22—4722no—
572C22—4722no—
573C22—2362no—
574C22#1683726111yescharacteristic
575C22#1683728011yescharacteristic
576C22#1683730211yescharacteristic
577C22#1683731711yescharacteristic
578C22#1683732011yescharacteristic
579C22#1683732411yescharacteristic
580C22#1683732611yescharacteristic
581C4—82no—
582C4—82no—
583C4—4722no—
584C4—2364no—
585C4—2362no—
586C4#1683727311yescharacteristic
587C4#1683727611yescharacteristic
588C4#1683729111yescharacteristic
589C4#1683729311yescharacteristic
590C4#1683731111yescharacteristic
591C4#1683731511yescharacteristic
592C4#1683733111yescharacteristic
593C4#1683733711yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—4722no—
602C2#2142234011yescharacteristic
subgroupG/H
centerC4#16837311
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1733C2
socleC2×C59#1439
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenter#1733D59
hypocenterC59#11094
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. #21432659C2semidirect
5. #21423828C2semidirect
6. #21423805C2semidirect
7. C59×#1733C2semidirect
22. #16837375C4semidirect
299. #1733D59semidirect
331. C59#11094semidirect

Maximal subgroups

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

subgroupindex
#214326592
C2×#168374202
C2×#168374182
C2×#168373752
#214238282
#214238052
C59×#17332
#1109459