Finite Group Databasebeta

← #29670421

Subgroups — #29670421

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458479C211yesmaximal, characteristic, complemented
2#21458477C211yesmaximal, characteristic, complemented
3#21458135C211yesmaximal, characteristic, complemented
4#21445477C211yesmaximal, characteristic, complemented
5#21445354C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445228C211yesmaximal, characteristic, complemented
8#21445198C211yesmaximal, characteristic, complemented
9#21445004C211yesmaximal, characteristic, complemented
10#21444953C211yesmaximal, characteristic, complemented
11#21444951C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic
13#21444663C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15C61×#3335C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840141C2211yescharacteristic
19#16840119—21no—
20#16840118—21no—
21#16840112C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840090—21no—
26#16840061—21no—
27#16840059—21no—
28#16840057C2211yescharacteristic
29#16840054C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840018—21no—
32#16839979—21no—
33#16839977—21no—
34#16839969C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839924—21no—
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40C4×#11758200C2211yescharacteristic
41C4×#11758199—21no—
42#16839842—21no—
43#16839840C2211yescharacteristic
44#16839763—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#483—21no—
60C61×#481—21no—
61C61×#476C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#465—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#106×C61—21no—
67C2×#11758202—21no—
68C2×#11758202—41no—
69C2×#11758200D411yescharacteristic
70C2×#11758199—21no—
71C2×#11758199—21no—
72C2×#11758194—21no—
73#14519777C2311yescharacteristic
74#14519774C2311yescharacteristic
75#14519768—21no—
76#14519766—21no—
77#14519765—21no—
78#14519762—41no—
79#14519756—21no—
80#14519754—41no—
81C4×Dic122C2311yescharacteristic
82C4×D244—21no—
83D4×Dic61—21no—
84#14519739—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708D411yescharacteristic
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700D411yescharacteristic
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C22×C8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#125×C61—21no—
121#123×C61—41no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125#121×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×D4×C61—21no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132#106×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136#106×C61D411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—41no—
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C22×Dic61—41no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162C2×Dic122C2×D411yescharacteristic
163SD16×C61—41no—
164C2×C8×C61—21no—
165C2×C8×C61—42no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—21no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186#11758202—81no—
187#11758202—82no—
188#11758200—22no—
189#11758199—42no—
190#11758199—42no—
191#11758198—41no—
192#11758198—41no—
193#11758198—41no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—41no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200C4×Dic61—21no—
201#11758194—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C23×C61—21no—
209C23×C61—21no—
210C22×D61—41no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—81no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—82no—
220D4×C61#13512yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—82no—
232C2×C4×C61—161no—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—161no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—41no—
244D244—81no—
245C4×D61—161no—
246Dic122—21no—
247Dic122—21no—
248Dic122—81no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#19826—611nomaximal, Sylow
259C22×C61—22no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61D4211yescharacteristic
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61C2×#13511yescharacteristic
277C4×C61#57511yescharacteristic
278C4×C61#57711yescharacteristic
279C4×C61#57811yescharacteristic
280Dic61—41no—
281Dic61—41no—
282Dic61—81no—
283#3361—611no—
284#3361—611no—
285#3335D6111yescharacteristic, complemented
286#3331—611no—
287#1720—611no—
288#1697—611no—
289#1684—611no—
290#1677—611no—
291#1672—611no—
292#1640—611no—
293#1632—611no—
294#1632—611no—
295#1625—611no—
296#1583—611no—
297SD16⋊C8—611no—
298C2×C61—42no—
299C2×C61—81no—
300C2×C61#326911yescharacteristic
301C2×C61#328211yescharacteristic
302C2×C61#328811yescharacteristic
303D61—161no—
304#559—611no—
305#554—611no—
306#554C2×D6111yescharacteristic
307#547C2×D6111yescharacteristic
308#498C2×D6111yescharacteristic
309#494—611no—
310#488—1221no—
311#488—1221no—
312#487—611no—
313#486—611no—
314#486—611no—
315#486—611no—
316#483—21no—
317#483—1221no—
318#481—21no—
319#478—1221no—
320#478—1221no—
321#477—611no—
322#477—611no—
323#476—611no—
324#476C2×D6111yescharacteristic
325#475C2×D6111yescharacteristic
326#470—1221no—
327#465—21no—
328#463—1221no—
329#463—1221no—
330#462—611no—
331#459—611no—
332#459—611no—
333#452—1221no—
334C8×Q8—611no—
335C8×Q8—611no—
336C4×SD16—611no—
337C4×SD16C2×D6111yescharacteristic
338C4×D8—1221no—
339C4×D8—1221no—
340#436—611no—
341C8×D4C2×D6111yescharacteristic
342C2×#106—21no—
343#417—1221no—
344#335—611no—
345#334—611no—
346#333—611no—
347#333—611no—
348#332—611no—
349#331—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352D4⋊C8—611no—
353D4⋊C8—611no—
354#322—611no—
355C61#1982611yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×Q16—1221no—
358C2×Q16—2441no—
359C2×SD16—611no—
360C2×SD16C22⋊D6111yescharacteristic
361C2×D8—1221no—
362C2×D8—1221no—
363C2×M16—1221no—
364C22×C8—21no—
365C4⋊Q8—611no—
366C4⋊Q8C22×D6111yescharacteristic
367C4⋊Q8C22×D6111yescharacteristic
368#127—611no—
369#125—21no—
370#125—1221no—
371#124—1221no—
372#124—1221no—
373#123—41no—
374#123—2441no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—41no—
378C22⋊Q8—1221no—
379C22⋊Q8—2441no—
380#121—21no—
381C4×Q8—611no—
382C4×Q8C22×D6111yescharacteristic
383C4×D4—21no—
384C4×D4—1221no—
385C4×D4—1221no—
386C4×D4—1221no—
387C4×D4C22×D6111yescharacteristic
388C4×D4C22×D6111yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—1221no—
392#107—1221no—
393#107—1221no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—611no—
399#106—1221no—
400#106C22⋊D6111yescharacteristic
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8C22×D6111yescharacteristic
407#103—21no—
408#103—611no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103C22⋊D6111yescharacteristic
415#102—21no—
416#102—611no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—2441no—
425#102C22⋊D6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—611no—
438C2×Q8—1221no—
439C2×Q8C2×C22⋊D6111yescharacteristic
440C2×D4—41no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4D4×D6111yescharacteristic
445C2×D4C2×C22⋊D6111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—2441no—
451C22×C4—2441no—
452Q16—4881no—
453Q16—4882no—
454SD16—41no—
455SD16—1222no—
456D8—2442no—
457D8—2442no—
458M16—4881no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8C2×C22⋊D6111yescharacteristic
468C2×C8C2×C22⋊D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—611no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—2441no—
482C4⋊C4—2441no—
483C4⋊C4D4×D6111yescharacteristic
484C4⋊C4C2×C22⋊D6111yescharacteristic
485C4⋊C4C2×C22⋊D6111yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—2441no—
491C22⋊C4—2441no—
492C22⋊C4—2441no—
493C22⋊C4—2441no—
494C42—21no—
495C42—1221no—
496C42C23×D6111yescharacteristic
497C23—21no—
498C23—21no—
499C23—2441no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—1221no—
506Q8—1221no—
507Q8—4881no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—82no—
512D4—4881no—
513D4—2441no—
514D4—2441no—
515D4—2441no—
516D4—2441no—
517D4#1451979812yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—9761no—
533C2×C4—9761no—
534C2×C4—2441no—
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4C22×C22⋊D6111yescharacteristic
537C2×C4#1451982211yescharacteristic
538C8—21no—
539C8—21no—
540C8—41no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—4881no—
554C22—4881no—
555C22—4881no—
556C22D4×C22⋊D6111yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—4881no—
565C4—2441no—
566C4—2441no—
567C4C2×#1451979811yescharacteristic
568C4#1684056011yescharacteristic
569C4#1684056811yescharacteristic
570C4#1684057711yescharacteristic
571C2—42no—
572C2—81no—
573C2—9761no—
574C2#2145737011yescharacteristic
575C2#2145752611yescharacteristic
576C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3335C2
socleC22×C61D42
prime radical#21444908C2
hypercenter#3335D61
hypocenterC61#19826
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #21458479C2semidirect
2. #21458477C2semidirect
3. #21458135C2semidirect
4. #21445477C2semidirect
5. #21445354C2semidirect
6. #21445275C2semidirect
7. #21445228C2semidirect
8. #21445198C2semidirect
9. #21445004C2semidirect
10. #21444953C2semidirect
11. #21444951C2semidirect
13. #21444663C2semidirect
14. #21444631C2semidirect
15. C61×#3335C2semidirect
285. #3335D61semidirect
355. C61#19826semidirect

Maximal subgroups

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

subgroupindex
#214584792
#214584772
#214581352
#214454772
#214453542
#214452752
#214452282
#214451982
#214450042
#214449532
#214449512
#214449082
#214446632
#214446312
C61×#33352
#1982661