Finite Group Databasebeta

← #30622372

Subgroups — #30622372

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462617C211yesmaximal, characteristic, complemented
2#21462518C211yesmaximal, characteristic
3#21462005C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461912C211yesmaximal, characteristic
6#21461912C211yesmaximal, characteristic
7#21461903C211yesmaximal, characteristic
8#21461902C211yesmaximal, characteristic
9#21461886C211yesmaximal, characteristic, complemented
10#21461884C211yesmaximal, characteristic, complemented
11#21461623C211yesmaximal, characteristic, complemented
12#21461622C211yesmaximal, characteristic, complemented
13C4⋊C8×#6923C211yesmaximal, characteristic, complemented
14C4×#14519842C211yesmaximal, characteristic
15#21455606C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840812—21no—
19#16840811—21no—
20#16840787—21no—
21#16840787—21no—
22#16840785—21no—
23#16840780—21no—
24C2×#14519848C2211yescharacteristic
25C2×#14519847C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840767C2211yescharacteristic
29D61⋊(C4⋊C8)C2211yescharacteristic
30C2×#14519842C2211yescharacteristic
31C2×#14519842C2211yescharacteristic
32#16840737C2211yescharacteristic
33#16840737C2211yescharacteristic
34#16840727C2211yescharacteristic
35#16840727C2211yescharacteristic
36#16840727C2211yescharacteristic
37#16840727C2211yescharacteristic
38C4×#11758213C2211yescharacteristic
39C2×C8×#6923C2211yescharacteristic
40C2×C8×#6923C2211yescharacteristic
41C42×#6923C2211yescharacteristic
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#16840318C2211yescharacteristic
53C4×#11758226C2211yescharacteristic
54#16840069C411yescharacteristic, complemented
55#16840063C411yescharacteristic, complemented
56#16840059C411yescharacteristic, complemented
57#16840055C411yescharacteristic, complemented
58#16840051C411yescharacteristic, complemented
59#16840045C411yescharacteristic, complemented
60#16840041C411yescharacteristic, complemented
61#16839799C2211yescharacteristic
62#16839797C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#16839757C2211yescharacteristic
65#16839757C2211yescharacteristic
66C61×#479C411yescharacteristic, complemented
67C2×#11758213C2311yescharacteristic
68C2×#11758213C2311yescharacteristic
69C2×#11758213C2311yescharacteristic
70C2×#11758213C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73C2×C4×#6923—21no—
74C2×C4×#6923—21no—
75C2×C4×#6923C2311yescharacteristic
76C2×C4×#6923C2311yescharacteristic
77#14519848—22no—
78#14519847—22no—
79#14519844—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844D411yescharacteristic
84#14519844D411yescharacteristic
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420D411yescharacteristic
88C4⋊#92420D411yescharacteristic
89#14519842—22no—
90#14519842—22no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104C4×#92420—21no—
105C8×#6923—22no—
106C8×#6923—22no—
107C2×#11758226C2311yescharacteristic
108C2×C8×D61C2311yescharacteristic
109C2×C8×D61C2311yescharacteristic
110#14519776C2×C411yescharacteristic
111#14519776C2×C411yescharacteristic
112#14519769C2×C411yescharacteristic
113#14519755—21no—
114#14519755—21no—
115Q8×Dic61C2×C411yescharacteristic
116#14519742—21no—
117#14519742—21no—
118C4×D244—21no—
119C4×D244C2×C411yescharacteristic
120#14519739—21no—
121#14519739C2×C411yescharacteristic
122#14519735—21no—
123#14519735C2311yescharacteristic
124#14519735C2311yescharacteristic
125#14519735C2311yescharacteristic
126C42×D61—21no—
127C42×D61C2311yescharacteristic
128#14519711C2×C411yescharacteristic
129#14519710C2×C411yescharacteristic
130#14519710C2×C411yescharacteristic
131#14519709C2×C411yescharacteristic
132#14519708C2×C411yescharacteristic
133#14519708C2×C411yescharacteristic
134C4⋊#92418C2×C411yescharacteristic
135#14519706C2×C411yescharacteristic
136#14519706C2×C411yescharacteristic
137#14519701C2×C411yescharacteristic
138#14519701C2×C411yescharacteristic
139#14519699C2×C411yescharacteristic
140#14519699C2×C411yescharacteristic
141#14519697C2×C411yescharacteristic
142#14519697C2×C411yescharacteristic
143#125×C61C2×C411yescharacteristic
144C4×Q8×C61C2×C411yescharacteristic
145#107×C61C2×C411yescharacteristic
146#106×C61C2×C411yescharacteristic
147C4⋊C8×C61C2×C411yescharacteristic
148#103×C61C2×C411yescharacteristic
149#103×C61C2×C411yescharacteristic
150C22×#6923—21no—
151C22×#6923—21no—
152C2×Q8×C61C22×C411yescharacteristic
153#11758226—21no—
154#11758226—21no—
155#11758226—21no—
156#11758226—21no—
157C2×D244—21no—
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61#4111yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×C4×D61C2411yescharacteristic
165C2×Dic122—21no—
166C2×Dic122—21no—
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—24no—
176C4×#6923—21no—
177C4×#6923—21no—
178C4×#6923—21no—
179C4×#6923—42no—
180C4×#6923#4112yes—
181#11758213—21no—
182#11758213—21no—
183#11758213—21no—
184#11758213—21no—
185#11758213—21no—
186#11758213—21no—
187#11758213—21no—
188#11758213#4112yes—
189D61⋊C8—21no—
190D61⋊C8—21no—
191D61⋊C8—21no—
192D61⋊C8—21no—
193C2×C8×C61C22×C411yescharacteristic
194C2×C8×C61C22×C411yescharacteristic
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61C22×C411yescharacteristic
199C4⋊C4×C61C22×C411yescharacteristic
200C4⋊C4×C61C22×C411yescharacteristic
201C42×C61—21no—
202C42×C61C22×C411yescharacteristic
203#11758198—21no—
204#11758198—21no—
205#11758198—21no—
206#11758198—21no—
207#11758198—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C22×C411yescharacteristic
210C4⋊Dic61C22×C411yescharacteristic
211C4⋊Dic61C22×C411yescharacteristic
212#11758196—21no—
213#11758196—21no—
214#11758196—21no—
215#11758196—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C2×#92418C22×C411yescharacteristic
224C2×#92418C22×C411yescharacteristic
225C8×D61—21no—
226C8×D61—21no—
227C8×D61—21no—
228C8×D61—21no—
229C22×D61—21no—
230C22×D61C2×#4111yescharacteristic
231C2×#6923—22no—
232C2×#6923—22no—
233C2×#6923—22no—
234C2×#6923—22no—
235C2×#6923—41no—
236C2×#6923—41no—
237Q8×C61—21no—
238Q8×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C23×C411yescharacteristic
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61C4×D411yescharacteristic
250C2×Dic61C4×D411yescharacteristic
251C2×Dic61C22×D411yescharacteristic
252D244—21no—
253D244—21no—
254D244—41no—
255D244—41no—
256C4×D61—22no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—42no—
261C4×D61—81no—
262C4×D61C2×#4111yescharacteristic
263C4×D61C2×#4111yescharacteristic
264C4×D612−1+411yescharacteristic
265C4×D612−1+411yescharacteristic
266Dic122—42no—
267Dic122—81no—
268#92420—21no—
269#92420—21no—
270#92420—21no—
271#92420—21no—
272#92420—22no—
273#92420—41no—
274#92420—41no—
275#92420—41no—
276C8×C61—21no—
277C8×C61—21no—
278#92418—21no—
279#92418—21no—
280#23080—611nomaximal, Sylow
281C22×C61C2×C4×D411yescharacteristic
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61#55211yescharacteristic
288C2×D61#55611yescharacteristic
289#6923—24no—
290#6923—42no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61C4×#4111yescharacteristic
298C4×C61#51911yescharacteristic
299Dic61—21no—
300Dic61—41no—
301Dic61—41no—
302Dic61—41no—
303Dic61#44312yes—
304Dic61#54711yescharacteristic
305Dic61#54811yescharacteristic
306#3076—611no—
307#2962—611no—
308#2925—611no—
309#1994—611no—
310#1950—611no—
311#1937—611no—
312#1937—611no—
313#1929—611no—
314#1929—611no—
315#1922—611no—
316#1922—611no—
317#1772—611no—
318#1772—611no—
319C4×C4⋊C8—611no—
320C4×#104—611no—
321C2×C61#236211yescharacteristic
322C2×C61C2×#44311yescharacteristic
323C2×C61#295611yescharacteristic
324D61—21no—
325D61—21no—
326D61—81no—
327#533—611no—
328C4×#41—611no—
329#479—611no—
330#479#692311yescharacteristic, complemented
331#478—611no—
332#478—611no—
333#477—611no—
334#476—611no—
335#475—611no—
336#474—611no—
337#446—1221no—
338#446—1221no—
339#446—1221no—
340C8×Q8—1221no—
341#433—1221no—
342#433—1221no—
343#432—1221no—
344#431—1221no—
345C2×#108—611no—
346C2×#108—611no—
347#427—611no—
348#427—611no—
349#424—611no—
350#424—611no—
351#423—611no—
352C2×C4⋊C8—611no—
353C2×C4⋊C8—611no—
354C2×#104—611no—
355C2×#104—611no—
356#416—611no—
357#416—611no—
358#408—611no—
359#408—611no—
360#405—611no—
361#405—611no—
362#405—611no—
363#405—611no—
364C4×M16—611no—
365C2×C4×C8—611no—
366C2×C4×C8—611no—
367C43—611no—
368#341—611no—
369#341—611no—
370#339—611no—
371#339—611no—
372#339—611no—
373#339—611no—
374#339—611no—
375#339—611no—
376#336—611no—
377#336—611no—
378C61#2308011yescharacteristic, complemented, Sylow
379C2×#41—611no—
380C2×M16—611no—
381C2×M16—611no—
382C2×M16—611no—
383C2×M16—611no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388C4⋊Q8—611no—
389C4⋊Q8—611no—
390#125—611no—
391#125C2×#692311yescharacteristic
392C22⋊Q8—1221no—
393C22⋊Q8—1221no—
394C4×Q8—611no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8C2×#692311yescharacteristic
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—1221no—
401C4×D4—1221no—
402#117—611no—
403#117—611no—
404#117—611no—
405#117—1221no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1221no—
412#108—1222no—
413#108—1222no—
414#107—611no—
415#107—611no—
416#107—611no—
417#107C2×#692311yescharacteristic
418#106—611no—
419#106—611no—
420#106—611no—
421#106C2×#692311yescharacteristic
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—611no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431C4⋊C8—1221no—
432C4⋊C8—1221no—
433C4⋊C8—1221no—
434C4⋊C8—1221no—
435C4⋊C8C2×#692311yescharacteristic
436#104—1222no—
437#104—1222no—
438#103—611no—
439#103—611no—
440#103C2×#692311yescharacteristic
441#103C2×#692311yescharacteristic
442#102—611no—
443#102—611no—
444#102—611no—
445#102—611no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450#97—1221no—
451#97—1221no—
452#97—1221no—
453#97—1221no—
454#97—1221no—
455C4×C8—1222no—
456C4×C8—1222no—
457C4×C8—1221no—
458C4×C8—1221no—
459C4×C8—1221no—
460C4×C8—1221no—
461C4×C8—1221no—
462#41—1221no—
463#41—1221no—
464#41—1221no—
465#41—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8C22×#692311yescharacteristic
469C2×D4—611no—
470C2×D4—1221no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479M16—612no—
480M16—1221no—
481M16—1221no—
482M16—1221no—
483M16—1221no—
484M16—1221no—
485M16—1221no—
486M16—1221no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—611no—
490C2×C8—611no—
491C2×C8—611no—
492C2×C8—611no—
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×C8—1221no—
504C2×C8—1221no—
505C2×C8C22×#692311yescharacteristic
506C2×C8C22×#692311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—611no—
511C4⋊C4—611no—
512C4⋊C4—611no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4C22×#692311yescharacteristic
519C4⋊C4C22×#692311yescharacteristic
520C4⋊C4C22×#692311yescharacteristic
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42—21no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—612no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C42—1221no—
538C42—1224no—
539C42—2442no—
540C42C22×#692311yescharacteristic
541C23—611no—
542C23—1221no—
543Q8—21no—
544Q8—21no—
545Q8—4881no—
546Q8—2442no—
547D4—1221no—
548D4—1221no—
549D4—2441no—
550D4—2441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—4881no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4D4×#692311yescharacteristic
578C2×C4D4×#692311yescharacteristic
579C2×C4C23×#692311yescharacteristic
580C8—21no—
581C8—21no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1222no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—611no—
593C22—611no—
594C22—1221no—
595C22—1221no—
596C22—2441no—
597C22—2441no—
598C22—2441no—
599C22C2×D4×#692311yescharacteristic
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—612no—
607C4—611no—
608C4—611no—
609C4—1224no—
610C4—1221no—
611C4—2442no—
612C4—2441no—
613C4—2441no—
614C4—2441no—
615C4#41×#692311yescharacteristic
616C4#1684083011yescharacteristic
617C2—1221no—
618C2—1221no—
619C2—4881no—
620C2#2146234511yescharacteristic
621C2D61⋊#44311yescharacteristic
622C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758226C23
cosocleC2×C4×D61C24
hypercenter#479#6923
hypocenterC61#23080
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #21462617C2semidirect
3. #21462005C2semidirect
4. #21461935C2semidirect
9. #21461886C2semidirect
10. #21461884C2semidirect
11. #21461623C2semidirect
12. #21461622C2semidirect
13. C4⋊C8×#6923C2semidirect
54. #16840069C4semidirect
55. #16840063C4semidirect
56. #16840059C4semidirect
57. #16840055C4semidirect
58. #16840051C4semidirect
59. #16840045C4semidirect
60. #16840041C4semidirect
66. C61×#479C4semidirect
330. #479#6923semidirect
378. C61#23080semidirect

Maximal subgroups

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

subgroupindex
#214626172
#214625182
#214620052
#214619352
#214619122
#214619032
#214619022
#214618862
#214618842
#214616232
#214616222
C4⋊C8×#69232
C4×#145198422
#214556062
#2308061