Finite Group Databasebeta

← #29665134

Subgroups — #29665134

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457046C211yesmaximal, characteristic
2#21456201C211yesmaximal, characteristic, complemented
3#21454824C211yesmaximal, characteristic
4#21445403C211yesmaximal, characteristic, complemented
5#21445396C211yesmaximal, characteristic, complemented
6#21445375C211yesmaximal, characteristic, complemented
7#21445368C211yesmaximal, characteristic, complemented
8#21445279C211yesmaximal, characteristic, complemented
9#21445272C211yesmaximal, characteristic, complemented
10#21445251C211yesmaximal, characteristic, complemented
11#21445244C211yesmaximal, characteristic, complemented
12#21444584C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444505C211yesmaximal, characteristic, complemented
15C61×#3252C211yesmaximal, characteristic
16C2×#14519777C2211yescharacteristic
17#16840172—21no—
18#16840132—21no—
19#16840132—21no—
20#16840121—21no—
21#16840114C2211yescharacteristic
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840095—21no—
26#16840078—21no—
27#16840047C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16839893C2211yescharacteristic
32Q8×#92418C2211yescharacteristic
33#16839840—21no—
34#16839840C2211yescharacteristic
35#16839834—21no—
36D4×#92418C2211yescharacteristic
37#16839823—21no—
38#16839819C2211yescharacteristic
39#16839815C2211yescharacteristic
40#16839770—21no—
41#16839770—21no—
42#16839718—21no—
43C4×#11758194C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#479—21no—
59C61×#477C2211yescharacteristic
60C61×#476C2211yescharacteristic
61C61×#470—21no—
62C61×#468—21no—
63C61×#464—21no—
64C61×#462C2211yescharacteristic
65C61×#461C2211yescharacteristic
66C61×#423C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758194—21no—
69C2×#11758194D411yescharacteristic
70C2×#11758194D411yescharacteristic
71C22×#92418—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79#14519710—21no—
80#14519710—21no—
81#14519708—21no—
82#14519708—21no—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89#14519701—21no—
90#14519701—21no—
91#14519700—21no—
92#14519700—21no—
93#14519700—21no—
94#14519700—21no—
95#14519700—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519698—21no—
100#14519698—21no—
101C22⋊#92418—21no—
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105#14519688—21no—
106#14519688—21no—
107#14519688D411yescharacteristic
108#14519688D411yescharacteristic
109C4×#92418—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C2×Q16×C61—21no—
114C2×SD16×C61—21no—
115C2×M16×C61—21no—
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#126×C61—21no—
119#125×C61—21no—
120#125×C61D411yescharacteristic
121#124×C61D411yescharacteristic
122#123×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61D411yescharacteristic
126#121×C61D411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142#103×C61—21no—
143#102×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×Dic61—41no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—42no—
157C2×Dic122—42no—
158C2×Dic122—41no—
159Q16×C61—81no—
160SD16×C61—81no—
161M16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—41no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—41no—
193C4⋊Dic61—41no—
194#11758194—41no—
195#11758194—41no—
196#11758194—42no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—42no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—21no—
207C23×C61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—81no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—82no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—82no—
242C8×C61—41no—
243C8×C61—41no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#19381—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C2×#12111yescharacteristic
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61#57511yescharacteristic
270C4×C61#57511yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—81no—
274Dic61—81no—
275#3252D6111yescharacteristic
276#3239—611no—
277#3139—611no—
278#2969—611no—
279#1704—611no—
280#1703—611no—
281#1700—611no—
282#1699—611no—
283#1684—611no—
284#1683—611no—
285#1680—611no—
286#1679—611no—
287#1569—611no—
288#1554—611no—
289#1549—611no—
290C2×C61—41no—
291C2×C61—81no—
292C2×C61#304011yescharacteristic
293C2×C61#306311yescharacteristic
294C2×C61#306911yescharacteristic
295#533C2×D6111yescharacteristic
296C2×C4⋊Q8—611no—
297#529C2×D6111yescharacteristic
298#501—1221no—
299#491—1221no—
300#491—1221no—
301#489—1221no—
302#487—611no—
303#487—611no—
304#487—611no—
305#487—611no—
306#484—1221no—
307#481—1221no—
308#479—21no—
309#477C2×D6111yescharacteristic
310#476C2×D6111yescharacteristic
311#475—611no—
312#475—611no—
313#474—611no—
314#474—611no—
315#470—21no—
316#468—21no—
317#464—21no—
318#462C2×D6111yescharacteristic
319#461C2×D6111yescharacteristic
320#446—611no—
321C8×Q8—611no—
322#436—611no—
323#436—1221no—
324#435—1221no—
325C8×D4—611no—
326#433—1221no—
327#432—611no—
328#431—611no—
329#423C2×D6111yescharacteristic
330#419—1221no—
331#419—1221no—
332#405—1221no—
333C4×M16—611no—
334#335—611no—
335#335—611no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346C61#1938111yescharacteristic, complemented, Sylow
347C22×Q8—1221no—
348C2×Q16—21no—
349C2×SD16—21no—
350C2×M16—21no—
351C2×M16—611no—
352C2×M16—611no—
353C2×M16—1221no—
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—1221no—
358C4⋊Q8—1221no—
359C4⋊Q8—1221no—
360C4⋊Q8C22×D6111yescharacteristic
361C4⋊Q8C22×D6111yescharacteristic
362#126—21no—
363#125—21no—
364#125C22⋊D6111yescharacteristic
365#124C22⋊D6111yescharacteristic
366#123—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8C22⋊D6111yescharacteristic
370#121C22⋊D6111yescharacteristic
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C22×D6111yescharacteristic
374C4×D4—21no—
375C4×D4C22×D6111yescharacteristic
376#117—21no—
377#117—21no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—21no—
382#107—1221no—
383#107—1221no—
384#106—21no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—21no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#102—21no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—611no—
417#97—611no—
418#97—1221no—
419#97—1221no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—2442no—
429C2×Q8—2442no—
430C2×Q8—2441no—
431C2×Q8C2×C22⋊D6111yescharacteristic
432C2×D4—21no—
433C2×D4C2×C22⋊D6111yescharacteristic
434C22×C4—21no—
435C22×C4—2441no—
436C22×C4D4×D6111yescharacteristic
437C22×C4#1175822411yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439Q16—81no—
440SD16—81no—
441M16—81no—
442M16—2441no—
443M16—2441no—
444M16—2442no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—2442no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4C2×C22⋊D6111yescharacteristic
473C4⋊C4C2×C22⋊D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C42—21no—
481C42—41no—
482C42D4×D6111yescharacteristic
483C42#1175822411yescharacteristic
484C42C2×C22⋊D6111yescharacteristic
485C42C23×D6111yescharacteristic
486C23—21no—
487C23#1451974911yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—4882no—
494Q8—2441no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—4882no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451974911yescharacteristic
517C2×C4#1451974911yescharacteristic
518C2×C4#1451974911yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822411yescharacteristic
522C8—41no—
523C8—41no—
524C8—1221no—
525C8—1221no—
526C8—1221no—
527C8—1221no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#1451974911yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—4881no—
549C4—4881no—
550C4#1684056111yescharacteristic
551C4#1684056111yescharacteristic
552C4#1684057311yescharacteristic
553C4#1684057711yescharacteristic
554C2—41no—
555C2—81no—
556C2#2145531511yescharacteristic
557C2#2145551211yescharacteristic
558C2#2145555811yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3252C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#3252D61
hypocenterC61#19381
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #21456201C2semidirect
4. #21445403C2semidirect
5. #21445396C2semidirect
6. #21445375C2semidirect
7. #21445368C2semidirect
8. #21445279C2semidirect
9. #21445272C2semidirect
10. #21445251C2semidirect
11. #21445244C2semidirect
12. #21444584C2semidirect
13. #21444529C2semidirect
14. #21444505C2semidirect
346. C61#19381semidirect

Maximal subgroups

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

subgroupindex
#214570462
#214562012
#214548242
#214454032
#214453962
#214453752
#214453682
#214452792
#214452722
#214452512
#214452442
#214445842
#214445292
#214445052
C61×#32522
#1938161