Finite Group Databasebeta

← #29662738

Subgroups — #29662738

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C211yesmaximal, characteristic, complemented
2#21455873C211yesmaximal, characteristic
3#21454785C211yesmaximal, characteristic, complemented
4#21445398C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445384C211yesmaximal, characteristic, complemented
7#21445377C211yesmaximal, characteristic, complemented
8#21445322C211yesmaximal, characteristic, complemented
9#21445315C211yesmaximal, characteristic, complemented
10#21445288C211yesmaximal, characteristic, complemented
11#21445281C211yesmaximal, characteristic, complemented
12#21444567C211yesmaximal, characteristic, complemented
13#21444484C211yesmaximal, characteristic, complemented
14#21444481C211yesmaximal, characteristic, complemented
15C61×#3167C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100—21no—
18#16840083—21no—
19#16840054C2211yescharacteristic
20#16840049C2211yescharacteristic
21#16840044C2211yescharacteristic
22#16840039C2211yescharacteristic
23#16839969C2211yescharacteristic
24#16839964C2211yescharacteristic
25#16839959C2211yescharacteristic
26#16839954C2211yescharacteristic
27#16839922—21no—
28#16839905—21no—
29#16839892C2211yescharacteristic
30#16839892C2211yescharacteristic
31C4×#11758202—21no—
32C4×#11758201—21no—
33C4×#11758200—21no—
34C4×#11758199—21no—
35#16839841C2211yescharacteristic
36#16839841C2211yescharacteristic
37#16839833—21no—
38#16839833—21no—
39#16839815C2211yescharacteristic
40#16839815C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839813—21no—
43C4×#11758189—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#532C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#465—21no—
63C61×#465—21no—
64C4×SD16×C61—21no—
65C4×SD16×C61—21no—
66C2×C4×C8×C61C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74C4×Dic122D411yescharacteristic
75C4×Dic122C2311yescharacteristic
76C4×D244D411yescharacteristic
77C4×D244C2311yescharacteristic
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80#14519736D411yescharacteristic
81#14519734—21no—
82C42×D61—21no—
83#14519710—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93#14519706—21no—
94#14519706—21no—
95#14519701—21no—
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519698—21no—
100#14519698—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106#14519689—21no—
107#14519689—21no—
108#14519687—21no—
109#14519687—21no—
110C4×#92418—21no—
111C4×#92418—21no—
112C4×#92418—21no—
113C2×#41×C61—21no—
114C2×SD16×C61—21no—
115C2×SD16×C61—21no—
116C22×C8×C61D411yescharacteristic
117C22×C8×C61D411yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#125×C61—21no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140C4×C8×C61D411yescharacteristic
141C4×C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—82no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C22×C4×C61—41no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C2×C22⋊D61—21no—
157#11758222—41no—
158#11758222—41no—
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×Dic122C2×D411yescharacteristic
164SD16×C61—42no—
165SD16×C61—42no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—41no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61—21no—
189#11758202—42no—
190#11758201—42no—
191#11758200—42no—
192#11758199—42no—
193#11758198—21no—
194#11758198—21no—
195C4⋊Dic61C2×D411yescharacteristic
196C4⋊Dic61C2×D411yescharacteristic
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208#11758189—42no—
209#11758189—42no—
210C23×C61—41no—
211C23×C61#12111yescharacteristic
212C22×D61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—81no—
223D4×C61—82no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—82no—
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C22⋊D61—42no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243D244—21no—
244D244—21no—
245C4×D61—42no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—42no—
249Dic122—21no—
250Dic122—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61#13512yes—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19159—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61C2×#12111yescharacteristic
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#47112yes—
279C4×C61C2×#13511yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57511yescharacteristic
282C4×C61#57511yescharacteristic
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286#3167D6111yescharacteristic, complemented
287#3107—611no—
288#3106—611no—
289#2965—611no—
290#1704—611no—
291#1703—611no—
292#1702—611no—
293#1701—611no—
294#1692—611no—
295#1691—611no—
296#1686—611no—
297#1685—611no—
298#1564—611no—
299#1544—611no—
300#1543—611no—
301C2×C61—41no—
302C2×C61—161no—
303C2×C61#303511yescharacteristic
304C2×C61#305411yescharacteristic
305C2×C61C2×#47111yescharacteristic
306D61—81no—
307#533C2×D6111yescharacteristic
308#532C2×D6111yescharacteristic
309C4×#41—611no—
310#498C2×D6111yescharacteristic
311#492C2×D6111yescharacteristic
312#487C2×D6111yescharacteristic
313#486C2×D6111yescharacteristic
314#485—1221no—
315#482—1221no—
316#477—611no—
317#476—611no—
318#475—611no—
319#474—611no—
320#465—21no—
321#465—21no—
322#462—611no—
323#461—611no—
324#460—611no—
325#459—611no—
326#452—1221no—
327#449—1221no—
328#446—611no—
329#446—611no—
330C4×Q16—1221no—
331C4×SD16—21no—
332C4×SD16—21no—
333C4×SD16—1221no—
334C4×SD16—1221no—
335C4×D8—1221no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#431—611no—
341#431—611no—
342#431—611no—
343#431—1221no—
344C4×M16—1221no—
345C2×C4×C8C2×D6111yescharacteristic
346#335—611no—
347#335—611no—
348#334—611no—
349#334—611no—
350#333—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#331—611no—
357#331—611no—
358C61#1915911yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C2×#41—611no—
361C2×Q16—1221no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C22×C8C22⋊D6111yescharacteristic
370C22×C8C22⋊D6111yescharacteristic
371C4⋊Q8C22×D6111yescharacteristic
372C4⋊Q8C22×D6111yescharacteristic
373C4⋊Q8C22×D6111yescharacteristic
374#127C22×D6111yescharacteristic
375#125—21no—
376#124—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—21no—
380#121—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—611no—
384C4×Q8—611no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—611no—
388C4×D4—611no—
389C4×D4—1221no—
390C4×D4—1221no—
391#117—21no—
392#117—611no—
393#117—1221no—
394C2×C42—1221no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#107—1221no—
398#106—21no—
399#106—21no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410#103—21no—
411#103—21no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#102—21no—
417#102—21no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427#97—1221no—
428#97—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22⋊D6111yescharacteristic
433C4×C8C22⋊D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—82no—
437#41—2441no—
438#41—2441no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—611no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—611no—
448C2×D4—1221no—
449C22×C4—41no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4D4×D6111yescharacteristic
454C22×C4#1175822411yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—2442no—
457SD16—42no—
458SD16—42no—
459SD16—2442no—
460SD16—2442no—
461D8—2442no—
462M16—2442no—
463M16—2442no—
464C2×C8—22no—
465C2×C8—41no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C2×C8C2×C22⋊D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—611no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C42—41no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42D4×D6111yescharacteristic
499C42#1175822411yescharacteristic
500C42C2×C22⋊D6111yescharacteristic
501C42C23×D6111yescharacteristic
502C23—41no—
503C23—1221no—
504C23#1451974811yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—81no—
510Q8—1221no—
511Q8—1221no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—1221no—
519D4—1221no—
520D4—2442no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4#1451974811yescharacteristic
538C2×C4#1451974811yescharacteristic
539C2×C4#1451974811yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C22×C22⋊D6111yescharacteristic
542C2×C4C2×#1175822411yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8#1451979712yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22C2×#1451974811yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—2441no—
570C4—2441no—
571C4—2441no—
572C4#1684002212yes—
573C4C2×#1451979711yescharacteristic
574C4#1684055911yescharacteristic
575C4#1684055911yescharacteristic
576C4#1684056011yescharacteristic
577C2—41no—
578C2—161no—
579C2—4881no—
580C2#2145526811yescharacteristic
581C2#2145542411yescharacteristic
582C2C2×#1684002211yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3167C2
socleC22×C61C2×#121
prime radical#21455873C2
hypercenter#3167D61
hypocenterC61#19159
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #21455884C2semidirect
3. #21454785C2semidirect
4. #21445398C2semidirect
5. #21445391C2semidirect
6. #21445384C2semidirect
7. #21445377C2semidirect
8. #21445322C2semidirect
9. #21445315C2semidirect
10. #21445288C2semidirect
11. #21445281C2semidirect
12. #21444567C2semidirect
13. #21444484C2semidirect
14. #21444481C2semidirect
15. C61×#3167C2semidirect
286. #3167D61semidirect
358. C61#19159semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214558732
#214547852
#214453982
#214453912
#214453842
#214453772
#214453222
#214453152
#214452882
#214452812
#214445672
#214444842
#214444812
C61×#31672
#1915961