Finite Group Databasebeta

← #29649539

Subgroups — #29649539

Order 15616.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454784C211yesmaximal, characteristic, complemented
2C8×#11758224C211yesmaximal, characteristic, complemented
3C4×#14519798C211yesmaximal, characteristic
4#21444672C211yesmaximal, characteristic, complemented
5#21444667C211yesmaximal, characteristic, complemented
6#21444664C211yesmaximal, characteristic, complemented
7#21444661C211yesmaximal, characteristic, complemented
8#21444656C211yesmaximal, characteristic, complemented
9#21444648C211yesmaximal, characteristic, complemented
10#21444645C211yesmaximal, characteristic, complemented
11#21444564C211yesmaximal, characteristic, complemented
12#21444200C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic, complemented
14#322×D61C211yesmaximal, characteristic, complemented
15C61×#1582C211yesmaximal, characteristic, complemented
16C2×#14519798C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×#11758224C2211yescharacteristic
19#16839893C2211yescharacteristic
20C8×Dic122C2211yescharacteristic
21#16839886C2211yescharacteristic
22C4×#11758202C2211yescharacteristic
23#16839854C411yescharacteristic
24C4×#11758190C2211yescharacteristic
25SD16×Dic61C411yescharacteristic
26#16839849C411yescharacteristic
27C4×#11758199C2211yescharacteristic
28#16839842C411yescharacteristic
29#16839841C2211yescharacteristic
30#16839839C2211yescharacteristic
31#16839835—21no—
32#16839832—21no—
33D4×#92418C2211yescharacteristic
34C8×C22⋊D61—21no—
35#16839825—21no—
36#16839814—21no—
37#16839814C2211yescharacteristic
38#16839814C2211yescharacteristic
39#16839812—21no—
40#16839797C411yescharacteristic
41#16839757C411yescharacteristic
42#16839755C411yescharacteristic
43#16839714—21no—
44C2×C8×Dic61—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758226C2×C411yescharacteristic
68C2×#11758224C2×C411yescharacteristic
69#14519798—24no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758190C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61C2×C411yescharacteristic
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61D411yescharacteristic
80C2×C8×D61D411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82C4×Dic122C2311yescharacteristic
83#14519742C2×C411yescharacteristic
84C4×D244—21no—
85C4×D244C2311yescharacteristic
86D4×Dic61C2×C411yescharacteristic
87#14519739—21no—
88#14519739C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90#14519737—21no—
91#14519735—21no—
92#14519735C2×C411yescharacteristic
93#14519735C2×C411yescharacteristic
94#14519733—21no—
95C2×C4×Dic61—21no—
96C42×D61—21no—
97C42×D61C2311yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519700C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112C22⋊#92418—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118C4×#92418C2311yescharacteristic
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C8×Dic61—21no—
122C8×Dic61—21no—
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61C2×C411yescharacteristic
131C22×C8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#106×C61C2×C411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151#11758226—22no—
152#11758226—22no—
153#11758224—22no—
154#11758224M1614yescomplemented
155C2×D244—21no—
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61#4111yescharacteristic
163C2×Dic122C22×C411yescharacteristic
164SD16×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—42no—
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C22⋊C4×C61—21no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758202—22no—
181#11758199—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—42no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758190—22no—
208#11758189—42no—
209#11758189—42no—
210C8×D61—22no—
211C8×D61—22no—
212C8×D61—22no—
213C8×D61—22no—
214C8×D61—42no—
215C23×C61—21no—
216C22×D61—21no—
217C22×D61C4×D411yescharacteristic
218Q8×C61—21no—
219Q8×C61—21no—
220D4×C61—21no—
221D4×C61C2×M1612yes—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—24no—
231C2×Dic61—21no—
232C2×Dic61—24no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—42no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238C2×Dic61C4×D411yescharacteristic
239D244—21no—
240D244—21no—
241D244—42no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—22no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—42no—
248C4×D61—42no—
249C4×D61C2×M1612yes—
250C4×D61#13112yes—
251Dic122—21no—
252Dic122C2×M1612yes—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61#13512yescomplemented
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418#13512yescomplemented
267#17863—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×C4×D411yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61#43512yes—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61C22×M1611yescharacteristic
283C4×C61C2×#13111yescharacteristic
284C4×C61C2×#13511yescharacteristic
285C4×C61C2×#13511yescharacteristic
286Dic61—22no—
287Dic61—21no—
288Dic61—41no—
289Dic61—41no—
290Dic61#43512yes—
291Dic61#44412yes—
292#2965—611no—
293C8×#41—611no—
294C4×#135—611no—
295#1584—611no—
296#1584—611no—
297#1583—611no—
298#1583—611no—
299#1582—611no—
300#1582D6111yescharacteristic, complemented
301#1581—611no—
302#1581—611no—
303#1564—611no—
304#1476—611no—
305#1476—611no—
306C2×#322—611no—
307C2×C61—42no—
308C2×C61C2×#43511yescharacteristic
309C2×C61C4×#13511yescharacteristic
310C2×C61C2×#44411yescharacteristic
311D61—22no—
312D61—81no—
313C2×#135—611no—
314C4×#41—611no—
315C4×#41—611no—
316#446—611no—
317#446C2×D6111yescharacteristic
318C8×Q8—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×Q16—611no—
322C4×SD16—611no—
323C4×SD16—611no—
324C4×SD16—611no—
325C4×SD16C2×D6111yescharacteristic
326C4×D8—611no—
327C4×D8—611no—
328#436—611no—
329#436—611no—
330#435—1221no—
331#435—1221no—
332C8×D4—611no—
333C8×D4—1221no—
334C8×D4—1221no—
335C8×D4C2×D6111yescharacteristic
336#431—611no—
337#431—611no—
338#431—1221no—
339#431—1221no—
340#427—611no—
341#416—611no—
342#416—611no—
343C4×M16—1221no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346C2×C4×C8—611no—
347C2×C4×C8—1221no—
348#335—611no—
349#335—611no—
350#334—611no—
351#334C2×D6111yescharacteristic
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8—611no—
355Q8⋊C8C2×D6111yescharacteristic
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8C2×D6111yescharacteristic
360#322—611no—
361#322—611no—
362#322—611no—
363#322C2×D6111yescharacteristic
364C61#1786311yescharacteristic, complemented, Sylow
365C2×#41—611no—
366C2×#41—611no—
367#135—1224no—
368C2×Q16—611no—
369C2×SD16—611no—
370C2×SD16C4×D6111yescharacteristic
371C2×D8—611no—
372C2×M16—1221no—
373C2×M16—1221no—
374C22×C8—21no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—1221no—
380C22×C8—1221no—
381C4×Q8—611no—
382C4×Q8—611no—
383C4×Q8—611no—
384C4×Q8C22×D6111yescharacteristic
385C4×D4—611no—
386C4×D4—611no—
387C4×D4—611no—
388C4×D4—1221no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4C22×D6111yescharacteristic
393#117—611no—
394#117—611no—
395#117—1221no—
396#117—1221no—
397C2×C42—611no—
398C2×C42—1221no—
399C2×C42—1221no—
400#107—611no—
401#107—611no—
402#106—611no—
403#106C4×D6111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—611no—
413#103—611no—
414#103—611no—
415#103C4×D6111yescharacteristic
416#102—611no—
417#102—611no—
418#102—611no—
419#102C4×D6111yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—21no—
427#97—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442C4×C8C22×D6111yescharacteristic
443#41—614no—
444#41—1222no—
445#41—1222no—
446#41—1222no—
447C2×Q8—611no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—611no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4C2×C4×D6111yescharacteristic
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462Q16—1222no—
463SD16—22no—
464SD16—1222no—
465D8—1222no—
466M16—2442no—
467M16—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1222no—
479C2×C8—1222no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—2442no—
484C2×C8—2442no—
485C2×C8C2×C4×D6111yescharacteristic
486C2×C8C2×C4×D6111yescharacteristic
487C2×C8D4×D6111yescharacteristic
488C2×C8D4×D6111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—611no—
491C4⋊C4—611no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4C2×C4×D6111yescharacteristic
496C4⋊C4C2×C4×D6111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C42—21no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42C23×D6111yescharacteristic
513C23—21no—
514C23—611no—
515C23—1221no—
516Q8—21no—
517Q8—21no—
518Q8—612no—
519Q8—1221no—
520D4—21no—
521D4—1224no—
522D4—1221no—
523D4—1221no—
524D4—2442no—
525D4M16×D6112yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—611no—
532C2×C4—611no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—611no—
536C2×C4—1222no—
537C2×C4—1224no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C22×C4×D6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4#41×D6111yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—612no—
558C8—1221no—
559C8—1221no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8#1451979812yescomplemented
565C22—22no—
566C22—41no—
567C22—41no—
568C22—612no—
569C22—1221no—
570C22—1221no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22C4×D4×D6111yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—612no—
580C4—612no—
581C4—1222no—
582C4—1221no—
583C4—2441no—
584C4—2441no—
585C4C2×M16×D6111yescharacteristic
586C4#131×D6111yescharacteristic
587C4#135×D6111yescharacteristic
588C4C2×#1451979811yescharacteristic
589C2—42no—
590C2—1222no—
591C2—4881no—
592C2#435×D6111yescharacteristic
593C2C4×#1451979811yescharacteristic
594C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1582C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519798C4
cosocleC42×C61C24
hypercenter#1582D61
hypocenterC61#17863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #21454784C2semidirect
2. C8×#11758224C2semidirect
4. #21444672C2semidirect
5. #21444667C2semidirect
6. #21444664C2semidirect
7. #21444661C2semidirect
8. #21444656C2semidirect
9. #21444648C2semidirect
10. #21444645C2semidirect
11. #21444564C2semidirect
12. #21444200C2semidirect
13. #21444198C2semidirect
14. #322×D61C2semidirect
15. C61×#1582C2semidirect
154. #11758224M16semidirect
259. C8×C61#135semidirect
266. #92418#135semidirect
300. #1582D61semidirect
364. C61#17863semidirect
564. C8#14519798semidirect

Maximal subgroups

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

subgroupindex
#214547842
C8×#117582242
C4×#145197982
#214446722
#214446672
#214446642
#214446612
#214446562
#214446482
#214446452
#214445642
#214442002
#214441982
#322×D612
C61×#15822
#1786361