Finite Group Databasebeta

← #29663488

Subgroups — #29663488

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457150C211yesmaximal, characteristic, complemented
2#21457146C211yesmaximal, characteristic
3#21456379C211yesmaximal, characteristic, complemented
4#21454788C211yesmaximal, characteristic, complemented
5#21445324C211yesmaximal, characteristic, complemented
6#21445317C211yesmaximal, characteristic, complemented
7#21445294C211yesmaximal, characteristic, complemented
8#21445287C211yesmaximal, characteristic, complemented
9#21445276C211yesmaximal, characteristic, complemented
10#21445269C211yesmaximal, characteristic, complemented
11#21445266C211yesmaximal, characteristic, complemented
12#21445259C211yesmaximal, characteristic, complemented
13C2×#16839514C211yesmaximal, characteristic, complemented
14#21444515C211yesmaximal, characteristic, complemented
15C61×#1552C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840069—21no—
23#16840063—21no—
24#16840058C2211yescharacteristic
25#16840053C2211yescharacteristic
26#16840044C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840001—21no—
29#16839998—21no—
30#16839993—21no—
31#16839993—21no—
32#16839993—21no—
33#16839991—21no—
34#16839984—21no—
35#16839978—21no—
36#16839969C2211yescharacteristic
37#16839964C2211yescharacteristic
38#16839963C2211yescharacteristic
39#16839958C2211yescharacteristic
40#16839889C2211yescharacteristic
41#16839886C2211yescharacteristic
42C4×#11758201—21no—
43C4×#11758201—21no—
44#16839839C2211yescharacteristic
45#16839830—21no—
46#16839827C2211yescharacteristic
47#16839825—21no—
48#16839824—21no—
49C2×C4⋊#92418C2211yescharacteristic
50#16839719—21no—
51C2×C4×#92418C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839514C2211yescharacteristic
55#16839514C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758190—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×D488—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C22×#92418D411yescharacteristic
77C22×#92418D411yescharacteristic
78C2×C8×D61—21no—
79#14519777C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519771—21no—
82#14519769D411yescharacteristic
83#14519765—21no—
84#14519765D411yescharacteristic
85#14519760—21no—
86#14519756D411yescharacteristic
87#14519751—21no—
88#14519751—21no—
89#14519751D411yescharacteristic
90C4×Dic122C2311yescharacteristic
91C4×D244—21no—
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×C22⋊D61—21no—
95#14519734—21no—
96#14519711—21no—
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100#14519708—21no—
101#14519708—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519701—21no—
109#14519701—21no—
110#14519701—21no—
111#14519701—21no—
112#14519700—21no—
113#14519699—21no—
114#14519699—21no—
115#14519699—21no—
116#14519697—21no—
117#14519697—21no—
118#14519697—21no—
119#14519689—21no—
120#14519689—21no—
121#14519687—21no—
122C4×#92418D411yescharacteristic
123C4×#92418D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×Q8×C61—21no—
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143#97×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—41no—
151#11758222—82no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122C2×D411yescharacteristic
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—81no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C42×C61—41no—
173C42×C61C2×D411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61#4111yescharacteristic
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758202—81no—
179#11758201—42no—
180#11758201—42no—
181#11758201—81no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—41no—
187#11758198—41no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61C2×D411yescharacteristic
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197C2×#92418—22no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—41no—
201C2×#92418—81no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206D488—81no—
207#11758190—81no—
208#11758189—42no—
209C8×D61—42no—
210C23×C61#12111yescharacteristic
211C22×D61—21no—
212C22×D61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217C2×C4×C61—22no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—42no—
231C22⋊D61—82no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236D244—21no—
237D244—21no—
238D244—41no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—81no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—82no—
246Dic122—21no—
247Dic122—21no—
248Dic122—81no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—41no—
257#92418—41no—
258#92418#13512yes—
259#19229—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61#47112yes—
263C22×C61C2×#12111yescharacteristic
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61C2×#13511yescharacteristic
277C4×C61#57511yescharacteristic
278C4×C61#57611yescharacteristic
279C4×C61#57811yescharacteristic
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—81no—
284#3248—611no—
285#3247—611no—
286#3167—611no—
287#2966—611no—
288#1692—611no—
289#1691—611no—
290#1686—611no—
291#1685—611no—
292#1684—611no—
293#1683—611no—
294#1682—611no—
295#1681—611no—
296C2×#335—611no—
297#1552D6111yescharacteristic, complemented
298#1551—611no—
299C2×C61—22no—
300C2×C61#303511yescharacteristic
301C2×C61#306111yescharacteristic
302C2×C61C2×#47111yescharacteristic
303D61—81no—
304D61—161no—
305#533C2×D6111yescharacteristic
306#532—611no—
307#529—611no—
308#498—611no—
309#492—611no—
310#487—611no—
311#486—611no—
312#479—1221no—
313#478—1221no—
314#477—611no—
315#476—611no—
316#475—611no—
317#474—611no—
318#467—1221no—
319#466—1221no—
320#465—1221no—
321#465—1221no—
322#465—1221no—
323#465—1221no—
324#464—1221no—
325#463—1221no—
326#462—611no—
327#461—611no—
328#460—611no—
329#459—611no—
330#446—611no—
331C8×Q8—611no—
332C4×SD16—1221no—
333C4×SD16—1221no—
334#436—611no—
335#435—1221no—
336C8×D4—611no—
337C8×D4—1221no—
338#433—1221no—
339#432C2×D6111yescharacteristic
340C2×C4⋊C8—611no—
341C2×C4⋊C8C2×D6111yescharacteristic
342#405—1221no—
343C2×C4×C8—611no—
344#335—611no—
345#335—611no—
346#335—611no—
347#335—611no—
348#333—611no—
349#333—611no—
350#332C2×D6111yescharacteristic
351#332C2×D6111yescharacteristic
352#332C2×D6111yescharacteristic
353#332C2×D6111yescharacteristic
354#331—611no—
355#331—611no—
356C61#1922911yescharacteristic, complemented, Sylow
357C2×#41—1221no—
358C2×Q16—1221no—
359C2×SD16—1221no—
360C2×SD16—1221no—
361C2×SD16—1221no—
362C2×SD16—1221no—
363C2×D8—1221no—
364C2×M16—1221no—
365C22×C8—21no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—1221no—
369C22×C8—1221no—
370C4⋊Q8—611no—
371C4⋊Q8C22×D6111yescharacteristic
372C4⋊Q8C22×D6111yescharacteristic
373#127—611no—
374#126—1221no—
375#125—21no—
376#125—611no—
377#124—611no—
378#124—1221no—
379#123—1221no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—611no—
383#121—611no—
384#121—1221no—
385#121—1221no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—611no—
389C4×D4—611no—
390C4×D4—1221no—
391C4×D4—1221no—
392C4×D4—1221no—
393#117—21no—
394#117—1221no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#107—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8C22×D6111yescharacteristic
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424C22⋊C8—21no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427#97—21no—
428#97—1221no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—1221no—
434#41—4882no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—611no—
438C2×Q8—1221no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—2441no—
445C22×C4—1221no—
446C22×C4—2441no—
447C22×C4#1175822211yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4D4×D6111yescharacteristic
450Q16—4881no—
451SD16—4881no—
452SD16—4881no—
453SD16—2442no—
454SD16—2442no—
455D8—4881no—
456M16—2442no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1222no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—2442no—
471C2×C8—2441no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—611no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C22⋊C4—41no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—2441no—
493C22⋊C4—2441no—
494C42—41no—
495C42—1221no—
496C42#1175822211yescharacteristic
497C42D4×D6111yescharacteristic
498C42D4×D6111yescharacteristic
499C42C23×D6111yescharacteristic
500C23—1221no—
501C23—2441no—
502C23#1451975011yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—1221no—
508Q8—1221no—
509Q8—4881no—
510D4—1221no—
511D4—1221no—
512D4—4881no—
513D4—4882no—
514D4—2442no—
515D4—2441no—
516D4—2441no—
517D4—2441no—
518D4—2441no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—4882no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4#1451975011yescharacteristic
534C2×C4#1451975011yescharacteristic
535C2×C4#1451975011yescharacteristic
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C2×D4×D6111yescharacteristic
538C2×C4C2×#1175822211yescharacteristic
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—612no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—4881no—
552C22—4881no—
553C22—4881no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22#1684002812yes—
558C22C2×#1451975011yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—81no—
564C4—81no—
565C4—4881no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4#135×D6111yescharacteristic
570C4#1684055911yescharacteristic
571C4#1684056611yescharacteristic
572C4#1684057811yescharacteristic
573C2—22no—
574C2—9761no—
575C2—4881no—
576C2#2145527211yescharacteristic
577C2#2145548811yescharacteristic
578C2C2×#1684002811yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C2×#121
prime radical#21457146C2
hypercenter#1552D61
hypocenterC61#19229
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
1. #21457150C2semidirect
3. #21456379C2semidirect
4. #21454788C2semidirect
5. #21445324C2semidirect
6. #21445317C2semidirect
7. #21445294C2semidirect
8. #21445287C2semidirect
9. #21445276C2semidirect
10. #21445269C2semidirect
11. #21445266C2semidirect
12. #21445259C2semidirect
13. C2×#16839514C2semidirect
14. #21444515C2semidirect
15. C61×#1552C2semidirect
297. #1552D61semidirect
356. C61#19229semidirect

Maximal subgroups

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

subgroupindex
#214571502
#214571462
#214563792
#214547882
#214453242
#214453172
#214452942
#214452872
#214452762
#214452692
#214452662
#214452592
C2×#168395142
#214445152
C61×#15522
#1922961