Finite Group Databasebeta

← #29650533

Subgroups — #29650533

Order 15616.

682 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#21456375C211yesmaximal, characteristic
2#21454750C211yesmaximal, characteristic, complemented
3#21454528C211yesmaximal, characteristic
4#21444711C211yesmaximal, characteristic, complemented
5#21444709C211yesmaximal, characteristic, complemented
6#21444707C211yesmaximal, characteristic, complemented
7#21444622C211yesmaximal, characteristic, complemented
8SD16×#92418C211yesmaximal, characteristic, complemented
9#21444618C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444573C211yesmaximal, characteristic, complemented
12#21444272C211yesmaximal, characteristic, complemented
13#21444268C211yesmaximal, characteristic
14C82×D61C211yesmaximal, characteristic, complemented
15C61×#1590C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840316C2211yescharacteristic
18#16840309C2211yescharacteristic
19#16840159C411yescharacteristic
20#16840133C411yescharacteristic
21#16840111C411yescharacteristic
22#16840107C411yescharacteristic
23#16839994C411yescharacteristic
24#16839992C411yescharacteristic
25#16839990C411yescharacteristic
26#16839988C411yescharacteristic
27#16839892C2211yescharacteristic
28#16839890—21no—
29Q8×#92418C2211yescharacteristic
30#16839886—21no—
31#16839886C2211yescharacteristic
32C4×#11758190C2211yescharacteristic
33C4×#11758201C2211yescharacteristic
34C4×#11758200C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839838—21no—
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839825—21no—
40#16839787—21no—
41#16839784C2211yescharacteristic
42#16839784C2211yescharacteristic
43#16839727—21no—
44#16839719—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57C8×#92418C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71#14519785—44no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80C2×C8×D61D411yescharacteristic
81C2×C8×D61D411yescharacteristic
82#14519776C2×C411yescharacteristic
83#14519776C2×C411yescharacteristic
84#14519775C2×C411yescharacteristic
85#14519773C2×C411yescharacteristic
86#14519767—21no—
87#14519763—21no—
88#14519757C2×C411yescharacteristic
89#14519755—21no—
90#14519753C2×C411yescharacteristic
91#14519752C2×C411yescharacteristic
92#14519750—21no—
93#14519748C2×C411yescharacteristic
94C4×Dic122—21no—
95C4×Dic122C2311yescharacteristic
96C4×D244C2311yescharacteristic
97C4×C22⋊D61—21no—
98#14519734—21no—
99C42×D61C2311yescharacteristic
100#14519709C2×C411yescharacteristic
101#14519708C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103C4⋊#92418—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519702C2×C411yescharacteristic
111#14519701C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115#14519697C2×C411yescharacteristic
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689—21no—
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61C2×C411yescharacteristic
131C2×M16×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—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151#11758222—42no—
152#11758222—42no—
153C2×D244—21no—
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61C22×C411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61#4111yescharacteristic
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162SD16×C61—22no—
163M16×C61—42no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758201—22no—
179#11758200—22no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—42no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205#11758190—22no—
206#11758189—42no—
207#11758189—42no—
208#11758189—42no—
209C8×D61—24no—
210C8×D61—22no—
211C8×D61—22no—
212C8×D61—22no—
213C8×D61—42no—
214C8×D61SD1614yescomplemented
215C23×C61—21no—
216C22×D61—21no—
217C22×D61C4×D411yescharacteristic
218Q8×C61—21no—
219Q8×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
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—42no—
231C22⋊D61—42no—
232C22⋊D61—42no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
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×D61C2×SD1612yes—
248C4×D61#13512yes—
249Dic122—21no—
250Dic122—21no—
251Dic122—42no—
252Dic122—42no—
253C8×C61—22no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61#13112yescomplemented
259C8×C61C2×SD1612yes—
260#92418—22no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418#13112yescomplemented
266#92418C2×SD1612yes—
267#17957—611nomaximal, Sylow
268C22×C61—41no—
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×D61C4×SD1612yes—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61C2×#13111yescharacteristic
283C4×C61C2×#13111yescharacteristic
284C4×C61C22×SD1611yescharacteristic
285C4×C61C2×#13511yescharacteristic
286Dic61—21no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61C4×SD1612yes—
291Dic61#44312yes—
292#3167—611no—
293#2960—611no—
294#2931—611no—
295#1590—611no—
296#1590—611no—
297#1590—611no—
298#1590D6111yescharacteristic, complemented
299C8×SD16—611no—
300C8×SD16—611no—
301C8×SD16—611no—
302C8×SD16—611no—
303#1566—611no—
304#1493—611no—
305#1492—611no—
306C2×C82—611no—
307C2×C61—81no—
308C2×C61#293111yescharacteristic
309C2×C61C2×C4×SD1611yescharacteristic
310C2×C61C2×#44311yescharacteristic
311D61—22no—
312D61—81no—
313C2×#131—1221no—
314#533—611no—
315#532—611no—
316#498—611no—
317#492—611no—
318#487—611no—
319#486—611no—
320#465—611no—
321#465—611no—
322#465—611no—
323#465—611no—
324#446—611no—
325#446—1221no—
326#446C2×D6111yescharacteristic
327C8×Q8—611no—
328C8×Q8—611no—
329C8×Q8—1221no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×SD16C2×D6111yescharacteristic
334#436—611no—
335#436—1221no—
336#436C2×D6111yescharacteristic
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—1221no—
340#424—1221no—
341#423—611no—
342#423—611no—
343#408—1221no—
344#405—1221no—
345C2×C4×C8—611no—
346C2×C4×C8—611no—
347C2×C4×C8—611no—
348#334—611no—
349#334—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
360C82—611no—
361C82—611no—
362C82—611no—
363C82C2×D6111yescharacteristic
364C61#1795711yescharacteristic, complemented, Sylow
365C2×#41—1221no—
366C2×SD16—611no—
367C2×SD16—611no—
368C2×SD16—611no—
369C2×SD16C4×D6111yescharacteristic
370#131—2444no—
371C2×M16—21no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383C4⋊Q8—611no—
384C4⋊Q8—611no—
385#127—611no—
386#125—1221no—
387#124—1221no—
388C22⋊Q8—611no—
389C22⋊Q8—611no—
390C22⋊Q8—1221no—
391#121—611no—
392#121—611no—
393#121—1221no—
394C4×Q8—611no—
395C4×Q8—1221no—
396C4×Q8C22×D6111yescharacteristic
397C4×D4—611no—
398C4×D4—1221no—
399C4×D4C22×D6111yescharacteristic
400#117—1221no—
401C2×C42—611no—
402#106—611no—
403#106—611no—
404#106—611no—
405#106C4×D6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416#103—611no—
417#103—611no—
418#103—611no—
419#103C4×D6111yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102C4×D6111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428#97—21no—
429#97—1221no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442C4×C8C22×D6111yescharacteristic
443#41—2442no—
444#41—2442no—
445C2×Q8—611no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—611no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4C2×C4×D6111yescharacteristic
455C22×C4—21no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460SD16—22no—
461SD16—1222no—
462SD16—1222no—
463SD16—1222no—
464M16—42no—
465M16—2442no—
466M16—2442no—
467M16—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—614no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1224no—
479C2×C8—1221no—
480C2×C8—1222no—
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⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C2×C4×D6111yescharacteristic
500C4⋊C4C2×C4×D6111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—21no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—1221no—
512C42C23×D6111yescharacteristic
513C23—21no—
514C23—611no—
515C23—1221no—
516Q8—21no—
517Q8—21no—
518Q8—1221no—
519Q8—1221no—
520Q8—2442no—
521Q8—2442no—
522D4—21no—
523D4—21no—
524D4—1221no—
525D4—1221no—
526D4—2442no—
527D4—2442no—
528D4—2442no—
529D4—2442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—611no—
540C2×C4—1222no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C22×C4×D6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4#41×D6111yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—612no—
557C8—612no—
558C8—1222no—
559C8—1221no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8#1451978512yescomplemented
564C8SD16×D6112yes—
565C22—41no—
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—1221no—
582C4—2441no—
583C4—2441no—
584C4—2441no—
585C4#131×D6111yescharacteristic
586C4C2×#1451978511yescharacteristic
587C4C2×SD16×D6111yescharacteristic
588C4#135×D6111yescharacteristic
589C2—81no—
590C2—1222no—
591C2—4881no—
592C2#2145452811yescharacteristic
593C2C4×SD16×D6111yescharacteristic
594C2#443×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1590C2
socleC22×C61C2×C4×D4
prime radical#16840309C22
cosocleC42×C61C24
hypercenter#1590D61
hypocenterC61#17957
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #21454750C2semidirect
4. #21444711C2semidirect
5. #21444709C2semidirect
6. #21444707C2semidirect
7. #21444622C2semidirect
8. SD16×#92418C2semidirect
9. #21444618C2semidirect
10. #21444616C2semidirect
11. #21444573C2semidirect
12. #21444272C2semidirect
14. C82×D61C2semidirect
15. C61×#1590C2semidirect
214. C8×D61SD16semidirect
258. C8×C61#131semidirect
265. #92418#131semidirect
298. #1590D61semidirect
364. C61#17957semidirect
563. C8#14519785semidirect

Maximal subgroups

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

subgroupindex
#214563752
#214547502
#214545282
#214447112
#214447092
#214447072
#214446222
SD16×#924182
#214446182
#214446162
#214445732
#214442722
#214442682
C82×D612
C61×#15902
#1795761