Finite Group Databasebeta

← #29676893

Subgroups — #29676893

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458524C211yesmaximal, characteristic, complemented
2#21458140C211yesmaximal, characteristic, complemented
3#21458135C211yesmaximal, characteristic, complemented
4#21445432C211yesmaximal, characteristic, complemented
5#21445392C211yesmaximal, characteristic, complemented
6#21445382C211yesmaximal, characteristic, complemented
7#21445370C211yesmaximal, characteristic, complemented
8#21445352C211yesmaximal, characteristic, complemented
9#21445024C211yesmaximal, characteristic, complemented
10#21445011C211yesmaximal, characteristic, complemented
11#21444970C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444707C211yesmaximal, characteristic, complemented
14#21444704C211yesmaximal, characteristic, complemented
15C61×#3330C211yesmaximal, characteristic, complemented
16#16840469C2211yescharacteristic
17#16840433C2211yescharacteristic
18#16840125—21no—
19#16840114C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840090—21no—
25#16840080—21no—
26#16840065—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840044C2211yescharacteristic
30#16840018—21no—
31#16840013—21no—
32#16839969C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839955—21no—
36#16839924—21no—
37#16839905—21no—
38#16839892C2211yescharacteristic
39#16839871—21no—
40C4×#11758200C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839763—21no—
44#16839761—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51#16839492C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#547C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#484—21no—
60C61×#474C2211yescharacteristic
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#417—21no—
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758200D411yescharacteristic
70C2×#11758199—21no—
71C2×#11758199—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74#14519777C2311yescharacteristic
75#14519774C2311yescharacteristic
76#14519773—21no—
77#14519768—21no—
78#14519756—21no—
79#14519754—41no—
80#14519751—21no—
81#14519750—41no—
82C4×Dic122C2311yescharacteristic
83D4×Dic61—21no—
84#14519739—21no—
85C2×C4⋊Dic61—21no—
86#14519708—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708D411yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93#14519706—21no—
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97#14519700—21no—
98#14519700—41no—
99#14519700D411yescharacteristic
100#14519699—21no—
101#14519699—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×SD16×C61—21no—
118C2×D8×C61D411yescharacteristic
119C2×M16×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#123×C61—41no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
146#41×C61—81no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C22×Dic61—41no—
163#11758222—42no—
164#11758222—81no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×C4×D61—41no—
169C2×Dic122—21no—
170C2×Dic122C2×D411yescharacteristic
171SD16×C61—81no—
172D8×C61—41no—
173M16×C61—81no—
174C2×C8×C61—21no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61—41no—
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61—41no—
191C42×C61C2411yescharacteristic
192C22⋊Dic61—41no—
193#11758202—81no—
194#11758200—41no—
195#11758199—42no—
196#11758199—81no—
197#11758198—41no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—41no—
201C4⋊Dic61C2×D411yescharacteristic
202#11758196—21no—
203#11758196—41no—
204C4×Dic61—21no—
205#11758194—81no—
206#11758194—81no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C22×D61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—82no—
228D4×C61—82no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—82no—
241C2×C4×C61—82no—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61H(5,𝔽2)11yescharacteristic
245C22⋊D61—82no—
246C22⋊D61—161no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—41no—
250C2×Dic61—161no—
251D244—41no—
252D244—41no—
253D244—41no—
254D244—41no—
255D244—81no—
256C4×D61—82no—
257Dic122—21no—
258Dic122—21no—
259Dic122—81no—
260C8×C61—21no—
261C8×C61—21no—
262C8×C61—41no—
263#92418—21no—
264#92418—21no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#20290—611nomaximal, Sylow
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61D4211yescharacteristic
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—81no—
288C4×C61—81no—
289C4×C61#57511yescharacteristic
290C4×C61#57511yescharacteristic
291C4×C61#57611yescharacteristic
292C4×C61#57711yescharacteristic
293Dic61—41no—
294Dic61—41no—
295Dic61—81no—
296#3366—611no—
297#3332—611no—
298#3331—611no—
299#3330D6111yescharacteristic, complemented
300#1711—611no—
301#1703—611no—
302#1701—611no—
303#1700—611no—
304#1697—611no—
305#1643—611no—
306#1641—611no—
307#1635—611no—
308#1625—611no—
309#1590—611no—
310#1589—611no—
311C2×C61—81no—
312C2×C61—81no—
313C2×C61—81no—
314C2×C61#327311yescharacteristic
315C2×C61#327511yescharacteristic
316C2×C61#329011yescharacteristic
317D61—161no—
318#554—611no—
319#550—611no—
320#547C2×D6111yescharacteristic
321#547C2×D6111yescharacteristic
322#490—1221no—
323#487—611no—
324#487—611no—
325#487C2×D6111yescharacteristic
326#486—611no—
327#486—611no—
328#486—611no—
329#484—21no—
330#483—1221no—
331#481—1221no—
332#478—1221no—
333#476—611no—
334#476—611no—
335#475—611no—
336#474C2×D6111yescharacteristic
337#470—1221no—
338#469—1221no—
339#468—21no—
340#462—611no—
341#461C2×D6111yescharacteristic
342#459—611no—
343#459—611no—
344#459—1221no—
345#452—1221no—
346#449—21no—
347#449—1221no—
348#446—611no—
349#442—1221no—
350C4×SD16—611no—
351C4×D8C2×D6111yescharacteristic
352#436—611no—
353#436—611no—
354#436C2×D6111yescharacteristic
355#417—21no—
356#417—1221no—
357#417—1221no—
358#335—611no—
359#334—611no—
360#333—611no—
361#332—611no—
362#332—611no—
363#331—611no—
364Q8⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368C82—611no—
369C61#2029011yescharacteristic, complemented, Sylow
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—1221no—
373C2×Q16—1221no—
374C2×SD16—21no—
375C2×SD16—611no—
376C2×D8—1221no—
377C2×D8—1221no—
378C2×D8C22⋊D6111yescharacteristic
379C2×M16—21no—
380C2×M16—1221no—
381C2×M16—1221no—
382C4⋊Q8—611no—
383C4⋊Q8C22×D6111yescharacteristic
384C4⋊Q8C22×D6111yescharacteristic
385#127—611no—
386#127—1221no—
387#125—1221no—
388#123—41no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—1221no—
393C22⋊Q8—2441no—
394#121—21no—
395#121—21no—
396#121—1221no—
397#121—2441no—
398C4×Q8—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4C22×D6111yescharacteristic
402C4×D4C22×D6111yescharacteristic
403C4×D4C22×D6111yescharacteristic
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—1221no—
407#107—21no—
408#107C22⋊D6111yescharacteristic
409#106—611no—
410#106—1221no—
411#106—1221no—
412#106—1221no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8C22×D6111yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—611no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#103—2441no—
427#102—21no—
428#102—611no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436#102—1221no—
437#102—2441no—
438#102C22⋊D6111yescharacteristic
439#102C22⋊D6111yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443#97—1221no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8C22×D6111yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451#41—4881no—
452#41—2442no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—611no—
456C2×Q8—1221no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—2441no—
463C2×D4—2441no—
464C2×D4D4×D6111yescharacteristic
465C2×D4C2×C22⋊D6111yescharacteristic
466C2×D4C2×C22⋊D6111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—2441no—
473C22×C4—2441no—
474Q16—4881no—
475SD16—81no—
476SD16—2441no—
477D8—41no—
478D8—4881no—
479D8—2442no—
480M16—81no—
481M16—4881no—
482M16—4881no—
483C2×C8—21no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—611no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—2441no—
503C4⋊C4—2441no—
504C4⋊C4D4×D6111yescharacteristic
505C4⋊C4C2×C22⋊D6111yescharacteristic
506C4⋊C4C2×C22⋊D6111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—2441no—
513C22⋊C4—2441no—
514C42—1221no—
515C42C23×D6111yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—2441no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—1221no—
525Q8—1221no—
526Q8—4881no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—82no—
534D4—82no—
535D4—9761no—
536D4—4881no—
537D4—4882no—
538D4—2441no—
539D4—2441no—
540D4—2441no—
541D4—2441no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—9761no—
558C2×C4—4882no—
559C2×C4—2441no—
560C2×C4C2×D4×D6111yescharacteristic
561C2×C4C22×C22⋊D6111yescharacteristic
562C2×C4#1451982211yescharacteristic
563C8—21no—
564C8—21no—
565C8—41no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22D4×C22⋊D6111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—4881no—
592C4—2441no—
593C4—2441no—
594C4#1684055811yescharacteristic
595C4#1684056011yescharacteristic
596C4#1684056611yescharacteristic
597C4#1684057311yescharacteristic
598C2—81no—
599C2—81no—
600C2—81no—
601C2—9761no—
602C2#2145742411yescharacteristic
603C2#2145744611yescharacteristic
604C2#2145760511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3330C2
socleC22×C61D42
hypercenter#3330D61
hypocenterC61#20290
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #21458524C2semidirect
2. #21458140C2semidirect
3. #21458135C2semidirect
4. #21445432C2semidirect
5. #21445392C2semidirect
6. #21445382C2semidirect
7. #21445370C2semidirect
8. #21445352C2semidirect
9. #21445024C2semidirect
10. #21445011C2semidirect
11. #21444970C2semidirect
12. #21444908C2semidirect
13. #21444707C2semidirect
14. #21444704C2semidirect
15. C61×#3330C2semidirect
299. #3330D61semidirect
369. C61#20290semidirect

Maximal subgroups

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

subgroupindex
#214585242
#214581402
#214581352
#214454322
#214453922
#214453822
#214453702
#214453522
#214450242
#214450112
#214449702
#214449082
#214447072
#214447042
C61×#33302
#2029061