Finite Group Databasebeta

← #29649726

Subgroups — #29649726

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454934C211yesmaximal, characteristic, complemented
2#21454929C211yesmaximal, characteristic, complemented
3C4×#14519798C211yesmaximal, characteristic
4#21444690C211yesmaximal, characteristic, complemented
5#21444687C211yesmaximal, characteristic, complemented
6#21444686C211yesmaximal, characteristic, complemented
7#21444681C211yesmaximal, characteristic, complemented
8#21444663C211yesmaximal, characteristic, complemented
9#21444657C211yesmaximal, characteristic, complemented
10#21444654C211yesmaximal, characteristic, complemented
11#334×D61C211yesmaximal, characteristic, complemented
12#21444205C211yesmaximal, characteristic, complemented
13#21444203C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1583C211yesmaximal, characteristic, complemented
16C2×#14519798C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×#11758224C2211yescharacteristic
19#16839892C2211yescharacteristic
20#16839889C2211yescharacteristic
21Q8×#92418C2211yescharacteristic
22C4×#11758202C2211yescharacteristic
23#16839854C411yescharacteristic
24C4×#11758190C2211yescharacteristic
25SD16×Dic61C411yescharacteristic
26#16839849C411yescharacteristic
27C4×#11758199C2211yescharacteristic
28#16839842C411yescharacteristic
29#16839840C2211yescharacteristic
30#16839836—21no—
31#16839831—21no—
32C8×D244—21no—
33C8×D244C2211yescharacteristic
34#16839827—21no—
35#16839827C2211yescharacteristic
36#16839816—21no—
37#16839813—21no—
38#16839813C2211yescharacteristic
39#16839813C2211yescharacteristic
40#16839797C411yescharacteristic
41#16839785—21no—
42C4⋊C8×D61—21no—
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#16839757C411yescharacteristic
46#16839755C411yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
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×#11758194—21no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80Q8×Dic61C2×C411yescharacteristic
81C4×Dic122C2311yescharacteristic
82#14519742C2×C411yescharacteristic
83C4×D244—21no—
84C4×D244C2311yescharacteristic
85D4×Dic61C2×C411yescharacteristic
86#14519739—21no—
87#14519739C2×C411yescharacteristic
88C4×C22⋊D61—21no—
89#14519737—21no—
90#14519735—21no—
91#14519735C2×C411yescharacteristic
92#14519735C2×C411yescharacteristic
93#14519733—21no—
94C2×C4×Dic61—21no—
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706D411yescharacteristic
109#14519706D411yescharacteristic
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#14519689—21no—
120#14519689D411yescharacteristic
121#14519689D411yescharacteristic
122#14519687—21no—
123#14519687—21no—
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
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—
141C4×C8×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#11758226M1614yescomplemented
153#11758224—22no—
154#11758224—22no—
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—
165M16×C61—81no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
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
199#11758194—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758190—22no—
208C8×D61—22no—
209C8×D61—22no—
210C8×D61—81no—
211C8×D61—81no—
212C8×D61—81no—
213C8×D61—81no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217Q8×C61—21no—
218Q8×C61C2×M1612yes—
219D4×C61—21no—
220D4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—42no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—42no—
234C2×Dic61—81no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238D244—24no—
239D244—21no—
240D244C2×M1612yes—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—24no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—81no—
248C4×D61C2×M1612yes—
249C4×D61#13112yes—
250Dic122—21no—
251Dic122—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#17882—611nomaximal, Sylow
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61#43512yes—
277C4×C61—22no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61C22×M1611yescharacteristic
282C4×C61C2×#13111yescharacteristic
283C4×C61#57711yescharacteristic
284C4×C61#57711yescharacteristic
285Dic61—21no—
286Dic61—21no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61#43512yes—
291#2989—611no—
292#2988—611no—
293C4×#135—611no—
294#1587—611no—
295#1587—611no—
296#1586—611no—
297#1586—611no—
298#1583—611no—
299#1583D6111yescharacteristic, complemented
300#1582—611no—
301#1582—611no—
302C2×#334—611no—
303#1477—611no—
304#1477—611no—
305#1452—611no—
306C2×C61—81no—
307C2×C61C2×#43511yescharacteristic
308C2×C61#295211yescharacteristic
309C2×C61#295711yescharacteristic
310D61—22no—
311D61—42no—
312C2×#135—611no—
313C4×#41—611no—
314C4×#41—611no—
315#446—611no—
316#446—611no—
317C8×Q8—611no—
318C8×Q8C2×D6111yescharacteristic
319C4×Q16—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×SD16—611no—
324C4×SD16C2×D6111yescharacteristic
325C4×D8—611no—
326C4×D8—611no—
327#436—611no—
328#436C2×D6111yescharacteristic
329#435—1221no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—611no—
333C8×D4—1221no—
334C8×D4—1221no—
335#432—1221no—
336#431—611no—
337#431—611no—
338#431—1221no—
339#427—611no—
340#423—1221no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8—1221no—
344#416—611no—
345#416—611no—
346C2×C4×C8—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334C2×D6111yescharacteristic
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8C2×D6111yescharacteristic
355D4⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8C2×D6111yescharacteristic
359#322—611no—
360#322—611no—
361#322—611no—
362#322C2×D6111yescharacteristic
363C61#1788211yescharacteristic, complemented, Sylow
364C2×#41—611no—
365C2×#41—611no—
366#135—1224no—
367C2×Q16—611no—
368C2×SD16—611no—
369C2×SD16C4×D6111yescharacteristic
370C2×D8—611no—
371C2×M16—21no—
372C2×M16—1221no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—1221no—
376C22×C8—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×Q8C22×D6111yescharacteristic
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4—1221no—
390C4×D4C22×D6111yescharacteristic
391#117—611no—
392#117—611no—
393#117—1221no—
394#117—1221no—
395C2×C42—611no—
396C2×C42—1221no—
397C2×C42—1221no—
398#107—611no—
399#107—611no—
400#106—611no—
401#106C4×D6111yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8C22×D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415#103—611no—
416#103—611no—
417#103—611no—
418#103C4×D6111yescharacteristic
419#102—611no—
420#102—611no—
421#102—611no—
422#102C4×D6111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—611no—
425C22⋊C8—611no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430#97—1221no—
431#97—1221no—
432C4×C8—21no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—1221no—
439C4×C8C22×D6111yescharacteristic
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442#41—614no—
443#41—1222no—
444#41—1222no—
445#41—1222no—
446C2×Q8—611no—
447C2×Q8C2×C4×D6111yescharacteristic
448C2×D4—611no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4C2×C4×D6111yescharacteristic
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461Q16—1222no—
462SD16—22no—
463SD16—1222no—
464D8—1222no—
465M16—81no—
466M16—4881no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—4881no—
480C2×C8—4881no—
481C2×C8—4881no—
482C2×C8—4881no—
483C2×C8C2×C4×D6111yescharacteristic
484C2×C8C2×C4×D6111yescharacteristic
485C2×C8D4×D6111yescharacteristic
486C2×C8D4×D6111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—611no—
489C4⋊C4—611no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4C2×C4×D6111yescharacteristic
494C4⋊C4C2×C4×D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C42—21no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42C23×D6111yescharacteristic
511C23—21no—
512C23—611no—
513C23—1221no—
514Q8—21no—
515Q8—1221no—
516Q8—1221no—
517Q8M16×D6112yes—
518D4—21no—
519D4—21no—
520D4—612no—
521D4—1224no—
522D4—1221no—
523D4—2442no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—611no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—611no—
533C2×C4—611no—
534C2×C4—1224no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—4881no—
541C2×C4—4881no—
542C2×C4—2441no—
543C2×C4—2442no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—1221no—
557C8—1221no—
558C8—1221no—
559C8—1221no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—612no—
567C22—1221no—
568C22—1221no—
569C22—1222no—
570C22—2441no—
571C22—2441no—
572C22C4×D4×D6111yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—612no—
578C4—1221no—
579C4—1221no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4C2×M16×D6111yescharacteristic
584C4#131×D6111yescharacteristic
585C4#1684056811yescharacteristic
586C4#1684056911yescharacteristic
587C2—81no—
588C2—1222no—
589C2—2442no—
590C2#435×D6111yescharacteristic
591C2#2145469711yescharacteristic
592C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1583C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519798C4
cosocleC42×C61C24
hypercenter#1583D61
hypocenterC61#17882
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
1. #21454934C2semidirect
2. #21454929C2semidirect
4. #21444690C2semidirect
5. #21444687C2semidirect
6. #21444686C2semidirect
7. #21444681C2semidirect
8. #21444663C2semidirect
9. #21444657C2semidirect
10. #21444654C2semidirect
11. #334×D61C2semidirect
12. #21444205C2semidirect
13. #21444203C2semidirect
14. #21444110C2semidirect
15. C61×#1583C2semidirect
152. #11758226M16semidirect
299. #1583D61semidirect
363. C61#17882semidirect

Maximal subgroups

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

subgroupindex
#214549342
#214549292
C4×#145197982
#214446902
#214446872
#214446862
#214446812
#214446632
#214446572
#214446542
#334×D612
#214442052
#214442032
#214441102
C61×#15832
#1788261