Finite Group Databasebeta

← #30622384

Subgroups — #30622384

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462613C211yesmaximal, characteristic, complemented
2#21462516C211yesmaximal, characteristic
3#21462007C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461915C211yesmaximal, characteristic
6#21461913C211yesmaximal, characteristic
7#21461901C211yesmaximal, characteristic
8#21461900C211yesmaximal, characteristic
9#21461886C211yesmaximal, characteristic, complemented
10#21461885C211yesmaximal, characteristic, complemented
11#21461627C211yesmaximal, characteristic, complemented
12#21461622C211yesmaximal, characteristic, complemented
13#21461608C211yesmaximal, characteristic, complemented
14#21461582C211yesmaximal, characteristic
15#21455608C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19Q8×#92420—21no—
20#16840786—21no—
21#16840786—21no—
22#16840782—21no—
23#16840779—21no—
24C2×#14519848C2211yescharacteristic
25C2×#14519847C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840767C2211yescharacteristic
29D61⋊(C4⋊C8)C2211yescharacteristic
30C2×#14519841C2211yescharacteristic
31C2×#14519841C2211yescharacteristic
32#16840736C2211yescharacteristic
33#16840736C2211yescharacteristic
34#16840727C2211yescharacteristic
35#16840727C2211yescharacteristic
36#16840727C2211yescharacteristic
37#16840727C2211yescharacteristic
38C4×#11758213C2211yescharacteristic
39C2×#14519831C2211yescharacteristic
40C2×C8×#6923C2211yescharacteristic
41#16840698C2211yescharacteristic
42#16840638C2211yescharacteristic
43#16840638C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840317C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840072C411yescharacteristic, complemented
55#16840072C411yescharacteristic, complemented
56#16840064C411yescharacteristic, complemented
57#16840064C411yescharacteristic, complemented
58#16840054C411yescharacteristic, complemented
59#16840048C411yescharacteristic, complemented
60#16840042C411yescharacteristic, complemented
61#16839797C2211yescharacteristic
62#16839797C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#16839755C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#476C411yescharacteristic, complemented
67C2×#11758213C2311yescharacteristic
68C2×#11758213C2311yescharacteristic
69C2×#11758213C2311yescharacteristic
70C2×#11758213C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73C2×C4×#6923C2311yescharacteristic
74C2×C4×#6923C2311yescharacteristic
75#14519848—22no—
76#14519847—22no—
77#14519844—21no—
78#14519844—21no—
79#14519844—21no—
80#14519844—21no—
81#14519844D411yescharacteristic
82#14519844D411yescharacteristic
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420D411yescharacteristic
86C4⋊#92420D411yescharacteristic
87#14519841—22no—
88#14519841—22no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832—21no—
98#14519831—22no—
99C4×#92420—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104C8×#6923—22no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107C2×#11758224C2311yescharacteristic
108C2×C8×D61C2311yescharacteristic
109C2×C8×D61C2311yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519768C2×C411yescharacteristic
112#14519768C2×C411yescharacteristic
113#14519757—21no—
114#14519753—21no—
115Q8×Dic61—21no—
116C4×Dic122C2×C411yescharacteristic
117#14519742—21no—
118#14519742C2×C411yescharacteristic
119D4×Dic61C2×C411yescharacteristic
120C4×C22⋊D61—21no—
121#14519737—21no—
122#14519735C2311yescharacteristic
123#14519735C2311yescharacteristic
124#14519735C2311yescharacteristic
125#14519733—21no—
126C2×C4×Dic61—21no—
127C42×D61C2311yescharacteristic
128#14519710C2×C411yescharacteristic
129#14519710C2×C411yescharacteristic
130#14519710C2×C411yescharacteristic
131#14519710C2×C411yescharacteristic
132#14519709C2×C411yescharacteristic
133#14519709C2×C411yescharacteristic
134C4⋊#92418C2×C411yescharacteristic
135#14519706C2×C411yescharacteristic
136#14519706C2×C411yescharacteristic
137#14519702C2×C411yescharacteristic
138#14519702C2×C411yescharacteristic
139#14519700C2×C411yescharacteristic
140#14519700C2×C411yescharacteristic
141#14519698C2×C411yescharacteristic
142#14519698C2×C411yescharacteristic
143C4⋊Q8×C61C2×C411yescharacteristic
144C4×D4×C61C2×C411yescharacteristic
145#106×C61C2×C411yescharacteristic
146#106×C61C2×C411yescharacteristic
147C4⋊C8×C61C2×C411yescharacteristic
148#102×C61C2×C411yescharacteristic
149#102×C61C2×C411yescharacteristic
150C22×#6923—21no—
151C22×#6923—21no—
152C2×Q8×C61—21no—
153C2×D4×C61C22×C411yescharacteristic
154C22×C4×C61—21no—
155C2×C22⋊D61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158#11758224—21no—
159#11758224—21no—
160#11758224—21no—
161#11758224—21no—
162C2×C4×D61#4111yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×C4×D61C2411yescharacteristic
165C2×Dic122—21no—
166C2×Dic122C22×C411yescharacteristic
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C4×#6923—21no—
176C4×#6923—21no—
177C4×#6923—21no—
178C4×#6923#4112yes—
179#11758213—21no—
180#11758213—21no—
181#11758213—21no—
182#11758213—21no—
183#11758213—21no—
184#11758213—21no—
185#11758213—21no—
186#11758213#4112yes—
187D61⋊C8—21no—
188D61⋊C8—21no—
189D61⋊C8—21no—
190D61⋊C8—21no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C4⋊C4×C61—21no—
194C4⋊C4×C61C22×C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C4⋊C4×C61C22×C411yescharacteristic
197C22⋊C4×C61—21no—
198C42×C61C22×C411yescharacteristic
199C22⋊Dic61—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209#11758196—21no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C2×#92418C22×C411yescharacteristic
222C2×#92418C22×C411yescharacteristic
223C8×D61—21no—
224C8×D61—21no—
225C8×D61—21no—
226C8×D61—21no—
227C23×C61—21no—
228C22×D61C2×#4111yescharacteristic
229C2×#6923—22no—
230C2×#6923—41no—
231C2×#6923—41no—
232C2×#6923—41no—
233C2×#6923—41no—
234C2×#6923—41no—
235Q8×C61—42no—
236D4×C61—21no—
237D4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—81no—
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C23×C411yescharacteristic
245C22⋊D61—41no—
246C22⋊D61—41no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—42no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61C4×D411yescharacteristic
255C2×Dic61C4×D411yescharacteristic
256C2×Dic61C22×D411yescharacteristic
257C4×D61—41no—
258C4×D61—41no—
259C4×D61C2×#4111yescharacteristic
260C4×D61C2×#4111yescharacteristic
261C4×D612−1+411yescharacteristic
262C4×D612−1+411yescharacteristic
263Dic122—21no—
264Dic122—21no—
265Dic122—81no—
266#92420—21no—
267#92420—21no—
268#92420—21no—
269#92420—21no—
270#92420—22no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274C8×C61—21no—
275C8×C61—21no—
276#92418—21no—
277#92418—21no—
278#23082—611nomaximal, Sylow
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C2×C4×D411yescharacteristic
283C2×D61—21no—
284C2×D61—21no—
285C2×D61#55211yescharacteristic
286C2×D61#55611yescharacteristic
287#6923—42no—
288#6923—81no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61C4×#4111yescharacteristic
295C4×C61#51911yescharacteristic
296Dic61—21no—
297Dic61—21no—
298Dic61—41no—
299Dic61—41no—
300Dic61—41no—
301Dic61—41no—
302Dic61#54711yescharacteristic
303Dic61#54811yescharacteristic
304#3076—611no—
305#2962—611no—
306#2925—611no—
307#1995—611no—
308#1950—611no—
309#1938—611no—
310#1937—611no—
311#1929—611no—
312#1929—611no—
313#1922—611no—
314#1922—611no—
315#1773—611no—
316#1772—611no—
317#1768—611no—
318#1759—611no—
319C2×C61—81no—
320C2×C61#236211yescharacteristic
321C2×C61#295511yescharacteristic
322C2×C61#295711yescharacteristic
323D61—21no—
324D61—21no—
325#533—611no—
326C4×#41—611no—
327#479—611no—
328#479—611no—
329#478—611no—
330#478—611no—
331#477—611no—
332#476#692311yescharacteristic, complemented
333#475—611no—
334#474—611no—
335#446—1221no—
336#446—1221no—
337#446—1221no—
338C8×Q8—1221no—
339#433—1221no—
340#433—1221no—
341#432—1221no—
342#431—1221no—
343C2×#108—611no—
344C2×#108—611no—
345#427—611no—
346#427—611no—
347#424—611no—
348#424—611no—
349#423—611no—
350C2×C4⋊C8—611no—
351C2×C4⋊C8—611no—
352C2×#104—611no—
353C2×#104—611no—
354#416—611no—
355#416—611no—
356#408—611no—
357#408—611no—
358#405—611no—
359#405—611no—
360#405—611no—
361#405—611no—
362C4×M16—611no—
363C2×#97—611no—
364C2×C4×C8—611no—
365#376—611no—
366#341—611no—
367#341—611no—
368#339—611no—
369#339—611no—
370#339—611no—
371#339—611no—
372#339—611no—
373#339—611no—
374#336—611no—
375#336—611no—
376C61#2308211yescharacteristic, complemented, Sylow
377C2×#41—611no—
378C2×M16—611no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—611no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386C4⋊Q8—611no—
387C4⋊Q8C2×#692311yescharacteristic
388#125—611no—
389#125—611no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C4×Q8—611no—
393C4×Q8—611no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4C2×#692311yescharacteristic
400#117—611no—
401#117—611no—
402#117—611no—
403#117—1221no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—1221no—
408#108—1222no—
409#108—1222no—
410#107—611no—
411#107—611no—
412#107—611no—
413#107—611no—
414#106—611no—
415#106—611no—
416#106C2×#692311yescharacteristic
417#106C2×#692311yescharacteristic
418C4⋊C8—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—1221no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431C4⋊C8C2×#692311yescharacteristic
432#104—1222no—
433#104—1222no—
434#103—611no—
435#103—611no—
436#103—611no—
437#103—611no—
438#102—611no—
439#102—611no—
440#102C2×#692311yescharacteristic
441#102C2×#692311yescharacteristic
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—1222no—
447#97—1221no—
448#97—1221no—
449#97—1221no—
450#97—1221no—
451#97—1221no—
452C4×C8—1222no—
453C4×C8—1221no—
454C4×C8—1221no—
455C4×C8—1221no—
456C4×C8—1221no—
457C4×C8—1221no—
458#95—1221no—
459#95—1221no—
460#41—1221no—
461#41—1221no—
462#41—1221no—
463#41—1221no—
464C2×Q8—21no—
465C2×Q8—611no—
466C2×Q8—1221no—
467C2×D4—1221no—
468C2×D4C22×#692311yescharacteristic
469C22×C4—21no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477M16—612no—
478M16—1221no—
479M16—1221no—
480M16—1221no—
481M16—1221no—
482M16—1221no—
483M16—1221no—
484M16—1221no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—611no—
490C2×C8—611no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8C22×#692311yescharacteristic
504C2×C8C22×#692311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—611no—
507C4⋊C4—611no—
508C4⋊C4—611no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4C22×#692311yescharacteristic
517C4⋊C4C22×#692311yescharacteristic
518C4⋊C4C22×#692311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—612no—
528C42—1221no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42C22×#692311yescharacteristic
537C23—21no—
538C23—611no—
539Q8—42no—
540Q8—1221no—
541Q8—1221no—
542Q8—4881no—
543D4—21no—
544D4—21no—
545D4—2441no—
546D4—2441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—81no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—1222no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2442no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4D4×#692311yescharacteristic
574C2×C4D4×#692311yescharacteristic
575C2×C4C23×#692311yescharacteristic
576C8—21no—
577C8—21no—
578C8—1221no—
579C8—1221no—
580C8—1221no—
581C8—1221no—
582C8—1222no—
583C8—1221no—
584C8—1221no—
585C8—2441no—
586C8—2441no—
587C8—2441no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—611no—
592C22—611no—
593C22—1221no—
594C22—1221no—
595C22C2×D4×#692311yescharacteristic
596C4—21no—
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—611no—
602C4—611no—
603C4—1221no—
604C4—1221no—
605C4—4881no—
606C4—2442no—
607C4—2441no—
608C4—2441no—
609C4—2441no—
610C4—2441no—
611C4#41×#692311yescharacteristic
612C4#1684083011yescharacteristic
613C2—81no—
614C2—1221no—
615C2—1221no—
616C2#2146234511yescharacteristic
617C2#2146259111yescharacteristic
618C2#2146259711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#476C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C23
cosocleC2×C4×D61C24
hypercenter#476#6923
hypocenterC61#23082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #21462613C2semidirect
3. #21462007C2semidirect
4. #21461935C2semidirect
9. #21461886C2semidirect
10. #21461885C2semidirect
11. #21461627C2semidirect
12. #21461622C2semidirect
13. #21461608C2semidirect
54. #16840072C4semidirect
55. #16840072C4semidirect
56. #16840064C4semidirect
57. #16840064C4semidirect
58. #16840054C4semidirect
59. #16840048C4semidirect
60. #16840042C4semidirect
66. C61×#476C4semidirect
332. #476#6923semidirect
376. C61#23082semidirect

Maximal subgroups

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

subgroupindex
#214626132
#214625162
#214620072
#214619352
#214619152
#214619132
#214619012
#214619002
#214618862
#214618852
#214616272
#214616222
#214616082
#214615822
#214556082
#2308261