Finite Group Databasebeta

← #29667604

Subgroups — #29667604

Order 15616.

602 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#21457139C211yesmaximal, characteristic
2#21456846C211yesmaximal, characteristic, complemented
3#21454981C211yesmaximal, characteristic, complemented
4#21445384C211yesmaximal, characteristic, complemented
5#21445377C211yesmaximal, characteristic, complemented
6#21445322C211yesmaximal, characteristic, complemented
7#21445315C211yesmaximal, characteristic, complemented
8#21445260C211yesmaximal, characteristic, complemented
9#21445253C211yesmaximal, characteristic, complemented
10#21445198C211yesmaximal, characteristic, complemented
11#21445191C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444514C211yesmaximal, characteristic, complemented
14C2×#16839508C211yesmaximal, characteristic, complemented
15C61×#3227C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840154—21no—
18#16840130—21no—
19#16840062—21no—
20#16840054C2211yescharacteristic
21#16840049C2211yescharacteristic
22#16839996—21no—
23#16839989—21no—
24#16839977—21no—
25#16839969C2211yescharacteristic
26#16839969C2211yescharacteristic
27#16839964C2211yescharacteristic
28#16839964C2211yescharacteristic
29#16839959C2211yescharacteristic
30#16839954C2211yescharacteristic
31#16839918—21no—
32#16839901—21no—
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839830—21no—
37C8×D244C2211yescharacteristic
38#16839825—21no—
39#16839822—21no—
40#16839819C2211yescharacteristic
41#16839787—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
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×#532C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#498C2211yescharacteristic
60C61×#486C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#481—21no—
63C61×#481—21no—
64C61×#476—21no—
65C61×#476—21no—
66C61×#431C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769D411yescharacteristic
79#14519765D411yescharacteristic
80#14519760—21no—
81#14519756D411yescharacteristic
82#14519751D411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519700—21no—
104#14519698—21no—
105#14519698—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111#14519687—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C22×Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—21no—
123#121×C61—21no—
124#121×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#106×C61—21no—
131#106×C61—21no—
132#106×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊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×Q8×C61—41no—
149C2×Q8×C61—81no—
150C2×Q8×C61—81no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C22×C4×C61—41no—
156C22×C4×C61—41no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C2×C22⋊D61—21no—
161C2×D244C2×D411yescharacteristic
162C2×C4×D61—21no—
163C2×Dic122C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
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—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C42×C61#4111yescharacteristic
181C42×C61C2411yescharacteristic
182C22⋊Dic61—21no—
183#11758202—81no—
184#11758202—81no—
185#11758201—81no—
186#11758201—81no—
187#11758200—81no—
188#11758199—81no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61C2×D411yescharacteristic
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—81no—
207C2×#92418—81no—
208#11758189—81no—
209C8×D61—81no—
210C23×C61—41no—
211C23×C61#12111yescharacteristic
212C22×D61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—82no—
218Q8×C61—81no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—81no—
224D4×C61—82no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—82no—
234C2×C4×C61—82no—
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C22⋊D61—42no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245D244—21no—
246D244—21no—
247C4×D61—41no—
248C4×D61—41no—
249Dic122—21no—
250Dic122—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19589—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61#47112yes—
268C22×C61C2×#12111yescharacteristic
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61#57611yescharacteristic
280C4×C61#57711yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286#3247—611no—
287#3227D6111yescharacteristic, complemented
288#3218—611no—
289#2994—611no—
290#1702—611no—
291#1701—611no—
292#1692—611no—
293#1691—611no—
294#1682—611no—
295#1681—611no—
296#1672—611no—
297#1671—611no—
298#1573—611no—
299#1551—611no—
300C2×#332—611no—
301C2×C61—22no—
302C2×C61—161no—
303C2×C61#304611yescharacteristic
304C2×C61#306211yescharacteristic
305C2×C61C2×#47111yescharacteristic
306D61—81no—
307#532C2×D6111yescharacteristic
308C2×C4⋊Q8C2×D6111yescharacteristic
309#529—611no—
310#498C2×D6111yescharacteristic
311#498C2×D6111yescharacteristic
312#497—1221no—
313#491—1221no—
314#486C2×D6111yescharacteristic
315#486C2×D6111yescharacteristic
316#481—21no—
317#481—21no—
318#478—1221no—
319#477—611no—
320#476—21no—
321#476—21no—
322#476—611no—
323#466—1221no—
324#465—1221no—
325#463—1221no—
326#462—611no—
327#462—611no—
328#461—611no—
329#461—611no—
330#460—611no—
331#459—611no—
332#451—1221no—
333#448—1221no—
334#446—611no—
335C8×Q8—611no—
336#436—611no—
337#435—1221no—
338C8×D4—611no—
339C8×D4—1221no—
340#433—1221no—
341#432—611no—
342#431C2×D6111yescharacteristic
343#424—1221no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8—611no—
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#1958911yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C22×D6111yescharacteristic
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377#127C22×D6111yescharacteristic
378#126—1221no—
379#125—611no—
380#124—21no—
381#124—611no—
382#123—1221no—
383C22⋊Q8—611no—
384#121—21no—
385#121—21no—
386#121—611no—
387C4×Q8—611no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—611no—
391C4×D4—1221no—
392#117—1221no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
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—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8C22⋊D6111yescharacteristic
413C4⋊C8C22⋊D6111yescharacteristic
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8C22⋊D6111yescharacteristic
430C22⋊C8C22⋊D6111yescharacteristic
431#97—1221no—
432#97—1221no—
433C4×C8—1221no—
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8—611no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—611no—
449C2×D4—1221no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—1221no—
453C22×C4D4×D6111yescharacteristic
454C22×C4#1175822411yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—4881no—
457Q16—4881no—
458SD16—4881no—
459SD16—4881no—
460SD16—4881no—
461D8—4881no—
462M16—4881no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8—4881no—
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—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—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—82no—
511Q8—1221no—
512Q8—1221no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—81no—
518D4—82no—
519D4—1221no—
520D4—1221no—
521D4—2442no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
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—21no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C22—21no—
554C22—21no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22#1684002212yes—
562C22C2×#1451974811yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—2441no—
571C4—2441no—
572C4—2441no—
573C4#1684056611yescharacteristic
574C4#1684057011yescharacteristic
575C4#1684057211yescharacteristic
576C4#1684057711yescharacteristic
577C2—22no—
578C2—161no—
579C2—4881no—
580C2#2145536511yescharacteristic
581C2#2145549311yescharacteristic
582C2C2×#1684002211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3227C2
socleC22×C61C2×#121
prime radical#21457139C2
hypercenter#3227D61
hypocenterC61#19589
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #21456846C2semidirect
3. #21454981C2semidirect
4. #21445384C2semidirect
5. #21445377C2semidirect
6. #21445322C2semidirect
7. #21445315C2semidirect
8. #21445260C2semidirect
9. #21445253C2semidirect
10. #21445198C2semidirect
11. #21445191C2semidirect
12. #21444604C2semidirect
13. #21444514C2semidirect
14. C2×#16839508C2semidirect
15. C61×#3227C2semidirect
287. #3227D61semidirect
358. C61#19589semidirect

Maximal subgroups

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

subgroupindex
#214571392
#214568462
#214549812
#214453842
#214453772
#214453222
#214453152
#214452602
#214452532
#214451982
#214451912
#214446042
#214445142
C2×#168395082
C61×#32272
#1958961