Finite Group Databasebeta

← #29676951

Subgroups — #29676951

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458611C211yesmaximal, characteristic, complemented
2#21458609C211yesmaximal, characteristic, complemented
3#21458107C211yesmaximal, characteristic, complemented
4#21445422C211yesmaximal, characteristic, complemented
5#21445403C211yesmaximal, characteristic, complemented
6#21445398C211yesmaximal, characteristic, complemented
7#21445382C211yesmaximal, characteristic, complemented
8#21445380C211yesmaximal, characteristic, complemented
9#21445082C211yesmaximal, characteristic, complemented
10#21445080C211yesmaximal, characteristic, complemented
11#21444939C211yesmaximal, characteristic, complemented
12#21444902C211yesmaximal, characteristic
13#21444710C211yesmaximal, characteristic, complemented
14#21444707C211yesmaximal, characteristic, complemented
15C61×#3329C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17D4×Dic122C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840124—21no—
21#16840123—21no—
22#16840114C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840103—21no—
26#16840054C2211yescharacteristic
27#16840051—21no—
28#16840049—21no—
29#16840047C2211yescharacteristic
30#16840044C2211yescharacteristic
31#16840006—21no—
32#16839979—21no—
33#16839977—21no—
34#16839967C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839900—21no—
38#16839893C2211yescharacteristic
39#16839892C2211yescharacteristic
40#16839872—21no—
41#16839871—21no—
42C4×#11758200C2211yescharacteristic
43#16839840C2211yescharacteristic
44#16839770—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#555C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#477C2211yescharacteristic
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#448—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#419—21no—
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200D411yescharacteristic
70C2×#11758201—41no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758194—21no—
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519774C2311yescharacteristic
77#14519766—21no—
78#14519765—21no—
79#14519762—41no—
80#14519756—21no—
81#14519754—41no—
82C4×Dic122C2311yescharacteristic
83C4×D244—21no—
84D4×Dic61—21no—
85#14519739—21no—
86#14519710—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708—41no—
90#14519708D411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519701—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700D411yescharacteristic
103#14519699—21no—
104#14519699—21no—
105#14519698D411yescharacteristic
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110C22⋊#92418—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#124×C61—41no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125#121×C61—21no—
126#121×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61—21no—
133#107×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—41no—
156C22×Dic61—41no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162C2×Dic122—42no—
163C2×Dic122—41no—
164C2×Dic122—81no—
165C2×Dic122C2×D411yescharacteristic
166SD16×C61—41no—
167SD16×C61—81no—
168M16×C61—81no—
169C2×C8×C61—21no—
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—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C22⋊C4×C61—41no—
186C42×C61—21no—
187C42×C61—41no—
188C42×C61C2411yescharacteristic
189C22⋊Dic61—41no—
190#11758201—82no—
191#11758200—41no—
192#11758200—81no—
193#11758199—42no—
194#11758199—42no—
195#11758198—41no—
196#11758198—41no—
197#11758198—41no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C2×D411yescharacteristic
201#11758196—21no—
202#11758196—41no—
203C4×Dic61—21no—
204#11758194—81no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C23×C61—21no—
212C23×C61—21no—
213C22×D61—41no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—81no—
219Q8×C61—82no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—161no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—82no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—82no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—81no—
248C4×D61—161no—
249Dic122—21no—
250Dic122—21no—
251Dic122—41no—
252Dic122—41no—
253Dic122—82no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257#92418—22no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#20294—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61D4211yescharacteristic
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—81no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61#57511yescharacteristic
282C4×C61#57511yescharacteristic
283C4×C61#57711yescharacteristic
284C4×C61#57711yescharacteristic
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288#3373—611no—
289#3373—611no—
290#3329—611no—
291#3329D6111yescharacteristic, complemented
292#1708—611no—
293#1704—611no—
294#1704—611no—
295#1701—611no—
296#1701—611no—
297#1651—611no—
298#1651—611no—
299#1630—611no—
300#1624—611no—
301#1590—611no—
302#1590—611no—
303C2×C61—81no—
304C2×C61—81no—
305C2×C61#327511yescharacteristic
306C2×C61#327511yescharacteristic
307C2×C61#329111yescharacteristic
308D61—161no—
309#559—611no—
310#555C2×D6111yescharacteristic
311D4×Q8—611no—
312D4×Q8C2×D6111yescharacteristic
313#498—611no—
314#492—611no—
315#489—1221no—
316#489—1221no—
317#487—611no—
318#487C2×D6111yescharacteristic
319#486—611no—
320#486—611no—
321#485—21no—
322#485—1221no—
323#477—611no—
324#477C2×D6111yescharacteristic
325#476—1221no—
326#476—1221no—
327#475—611no—
328#475—611no—
329#468—21no—
330#468—1221no—
331#463—1221no—
332#463—1221no—
333#461—611no—
334#461C2×D6111yescharacteristic
335#459—611no—
336#459—611no—
337#448—21no—
338#448—1221no—
339#446—611no—
340#446—611no—
341#442—1221no—
342#442—1221no—
343C4×SD16—611no—
344C4×SD16C2×D6111yescharacteristic
345#436—611no—
346#436C2×D6111yescharacteristic
347#419—21no—
348#419—1221no—
349#334—611no—
350#334—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#331—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359C82—611no—
360C61#2029411yescharacteristic, complemented, Sylow
361C22×Q8—21no—
362C22×Q8—1221no—
363C2×SD16—21no—
364C2×SD16—611no—
365C2×SD16—1221no—
366C2×SD16—2441no—
367C2×SD16C22⋊D6111yescharacteristic
368C2×D8—1221no—
369C2×D8—1221no—
370C2×M16—21no—
371C2×M16—1221no—
372C4⋊Q8—21no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377#127—611no—
378#124—41no—
379#124—1221no—
380#124—1221no—
381#123—2441no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C22⋊Q8—1221no—
385C22⋊Q8—2441no—
386#121—21no—
387#121—21no—
388C4×Q8—611no—
389C4×Q8C22×D6111yescharacteristic
390C4×D4—21no—
391C4×D4—1221no—
392C4×D4—1221no—
393C4×D4—1221no—
394C4×D4C22×D6111yescharacteristic
395C4×D4C22×D6111yescharacteristic
396#117—21no—
397#117—21no—
398#107—21no—
399#107—1221no—
400#106—611no—
401#106—1221no—
402#106—1221no—
403#106—2441no—
404#106C22⋊D6111yescharacteristic
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—611no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103C22⋊D6111yescharacteristic
423#102—611no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102C22⋊D6111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—1221no—
433#97—1221no—
434#97—1221no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8C22×D6111yescharacteristic
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8—611no—
444C2×Q8—1221no—
445C2×Q8—4881no—
446C2×Q8—2441no—
447C2×Q8—2442no—
448C2×Q8C2×C22⋊D6111yescharacteristic
449C2×D4—41no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4D4×D6111yescharacteristic
454C2×D4C2×C22⋊D6111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—2441no—
459C22×C4—2441no—
460SD16—41no—
461SD16—81no—
462SD16—4882no—
463SD16—4881no—
464SD16—2441no—
465D8—2442no—
466D8—2442no—
467M16—81no—
468M16—4881no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8C2×C22⋊D6111yescharacteristic
477C2×C8C2×C22⋊D6111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—2441no—
489C4⋊C4D4×D6111yescharacteristic
490C4⋊C4C2×C22⋊D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C22⋊C4—2441no—
501C42—21no—
502C42—41no—
503C42—1221no—
504C42C23×D6111yescharacteristic
505C23—21no—
506C23—21no—
507C23—2441no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—81no—
513Q8—82no—
514Q8—1221no—
515Q8—1221no—
516Q8—4882no—
517Q8—2441no—
518Q8—2441no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—161no—
524D4—4881no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528D4—2441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—9761no—
543C2×C4—4882no—
544C2×C4—2441no—
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4#1451982211yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—1222no—
552C8—1221no—
553C8—1221no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—4881no—
564C22—4881no—
565C22—4881no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—4881no—
575C4—2441no—
576C4—2441no—
577C4#1684056011yescharacteristic
578C4#1684056111yescharacteristic
579C4#1684057111yescharacteristic
580C4#1684057311yescharacteristic
581C2—81no—
582C2—81no—
583C2—9761no—
584C2#2145744411yescharacteristic
585C2#2145744611yescharacteristic
586C2#2145761011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3329C2
socleC22×C61D42
prime radical#21444902C2
hypercenter#3329D61
hypocenterC61#20294
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3329

Complements

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

NH ≅ G/Ntype
1. #21458611C2semidirect
2. #21458609C2semidirect
3. #21458107C2semidirect
4. #21445422C2semidirect
5. #21445403C2semidirect
6. #21445398C2semidirect
7. #21445382C2semidirect
8. #21445380C2semidirect
9. #21445082C2semidirect
10. #21445080C2semidirect
11. #21444939C2semidirect
13. #21444710C2semidirect
14. #21444707C2semidirect
15. C61×#3329C2semidirect
291. #3329D61semidirect
360. C61#20294semidirect

Maximal subgroups

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

subgroupindex
#214586112
#214586092
#214581072
#214454222
#214454032
#214453982
#214453822
#214453802
#214450822
#214450802
#214449392
#214449022
#214447102
#214447072
C61×#33292
#2029461