Finite Group Databasebeta

← #29667629

Subgroups — #29667629

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457156C211yesmaximal, characteristic
2#21456970C211yesmaximal, characteristic, complemented
3#21454979C211yesmaximal, characteristic
4#21445375C211yesmaximal, characteristic, complemented
5#21445368C211yesmaximal, characteristic, complemented
6#21445335C211yesmaximal, characteristic, complemented
7#21445330C211yesmaximal, characteristic, complemented
8#21445251C211yesmaximal, characteristic, complemented
9#21445244C211yesmaximal, characteristic, complemented
10#21445211C211yesmaximal, characteristic, complemented
11#21445206C211yesmaximal, characteristic, complemented
12#21444605C211yesmaximal, characteristic, complemented
13#21444520C211yesmaximal, characteristic, complemented
14C2×#16839508C211yesmaximal, characteristic, complemented
15C61×#3218C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840165C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840114C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840097—21no—
22#16840097—21no—
23#16840066—21no—
24#16840054—21no—
25#16840054—21no—
26#16840047C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840001—21no—
29#16839989—21no—
30#16839981—21no—
31#16839972C2211yescharacteristic
32#16839967C2211yescharacteristic
33#16839893C2211yescharacteristic
34Q8×#92418C2211yescharacteristic
35#16839840C2211yescharacteristic
36#16839834—21no—
37D4×#92418—21no—
38D4×#92418C2211yescharacteristic
39#16839823—21no—
40#16839815C2211yescharacteristic
41#16839789—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56C2×C4⋊Q8×C61C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#497—21no—
59C61×#491—21no—
60C61×#462C2211yescharacteristic
61C61×#462C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#461C2211yescharacteristic
64C61×#451—21no—
65C61×#448—21no—
66C61×#432C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758200—21no—
69C2×#11758194—21no—
70C22×#92418—21no—
71C22×#92418—21no—
72C22×#92418—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519769—21no—
76#14519756—21no—
77#14519756—21no—
78C4×Dic122—21no—
79C4×Dic122—21no—
80#14519736—21no—
81#14519710—21no—
82#14519710—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418D411yescharacteristic
92C4⋊#92418D411yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519698—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107C22⋊#92418D411yescharacteristic
108C22⋊#92418D411yescharacteristic
109#14519688—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C22×Q8×C61—21no—
114C2×Q16×C61—21no—
115C2×Q16×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#126×C61—21no—
124#125×C61D411yescharacteristic
125#124×C61D411yescharacteristic
126#123×C61—21no—
127C22⋊Q8×C61D411yescharacteristic
128#121×C61D411yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C22⋊C8×C61—21no—
143#97×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C2×Dic122—21no—
158C2×Dic122—21no—
159Q16×C61—81no—
160Q16×C61—81no—
161SD16×C61—81no—
162SD16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×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—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C42×C61—21no—
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61#4111yescharacteristic
186C42×C61C2411yescharacteristic
187C22⋊Dic61—41no—
188#11758202—81no—
189#11758200—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—41no—
197#11758194—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—81no—
203C2×#92418—81no—
204C2×#92418—81no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C23×C61—21no—
210C23×C61#12111yescharacteristic
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—82no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—42no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
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—82no—
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×Dic61—41no—
241C2×Dic61—41no—
242Dic122—41no—
243Dic122—41no—
244Dic122—41no—
245Dic122—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#19590—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61#47312yes—
263C22×C61C2×#12111yescharacteristic
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61#57611yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57711yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—81no—
278Dic61—81no—
279#3248—611no—
280#3230—611no—
281#3218D6111yescharacteristic
282#2994—611no—
283#1700—611no—
284#1699—611no—
285#1694—611no—
286#1693—611no—
287#1680—611no—
288#1679—611no—
289#1674—611no—
290#1673—611no—
291#1573—611no—
292#1552—611no—
293C2×#332—611no—
294C2×C61—22no—
295C2×C61—81no—
296C2×C61#304611yescharacteristic
297C2×C61#306211yescharacteristic
298C2×C61C2×#47311yescharacteristic
299#533—611no—
300C2×C4⋊Q8C2×D6111yescharacteristic
301#529C2×D6111yescharacteristic
302#500—611no—
303#500—611no—
304#497—21no—
305#491—21no—
306#487—611no—
307#487—611no—
308#484—1221no—
309#484—1221no—
310#479—1221no—
311#477—1221no—
312#477—1221no—
313#475—611no—
314#474—611no—
315#467—1221no—
316#465—1221no—
317#464—1221no—
318#462—611no—
319#462C2×D6111yescharacteristic
320#462C2×D6111yescharacteristic
321#461—611no—
322#461C2×D6111yescharacteristic
323#461C2×D6111yescharacteristic
324#451—21no—
325#448—21no—
326#446—611no—
327C8×Q8—611no—
328#436—611no—
329#435—1221no—
330C8×D4—611no—
331C8×D4—1221no—
332#433—1221no—
333#432C2×D6111yescharacteristic
334#431—611no—
335#424—1221no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338#335—611no—
339#335—611no—
340#334—611no—
341#334—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348#332—611no—
349#332—611no—
350C61#1959011yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—1221no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—1221no—
358C2×M16—1221no—
359C22×C8—1221no—
360C22×C8—1221no—
361C22×C8—1221no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#126—21no—
370#125—1221no—
371#125C22⋊D6111yescharacteristic
372#124C22⋊D6111yescharacteristic
373#123—21no—
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376C22⋊Q8C22⋊D6111yescharacteristic
377#121C22⋊D6111yescharacteristic
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4C22×D6111yescharacteristic
383#117—21no—
384#117—1221no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C22×D6111yescharacteristic
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—1221no—
393#106—1221no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#102—1221no—
418C22⋊C8—21no—
419C22⋊C8—611no—
420C22⋊C8—611no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423#97—21no—
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8C2×C22⋊D6111yescharacteristic
436C2×D4—21no—
437C2×D4C2×C22⋊D6111yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4D4×D6111yescharacteristic
441C22×C4#1175822411yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443Q16—81no—
444Q16—81no—
445Q16—4881no—
446SD16—81no—
447SD16—81no—
448SD16—4881no—
449M16—4881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—4881no—
461C2×C8—4881no—
462C2×C8—4881no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4C2×C22⋊D6111yescharacteristic
480C4⋊C4C2×C22⋊D6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—2441no—
487C42—21no—
488C42—2441no—
489C42D4×D6111yescharacteristic
490C42#1175822411yescharacteristic
491C42C2×C22⋊D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—21no—
494C23#1451974911yescharacteristic
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—21no—
507D4—21no—
508D4—42no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4#1451974911yescharacteristic
525C2×C4#1451974911yescharacteristic
526C2×C4#1451974911yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C2×C4C22×C22⋊D6111yescharacteristic
529C2×C4C2×#1175822411yescharacteristic
530C8—41no—
531C8—41no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C22—21no—
541C22—21no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#1684003512yes—
546C22C2×#1451974911yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—4881no—
557C4—4881no—
558C4#1684056511yescharacteristic
559C4#1684057111yescharacteristic
560C4#1684057311yescharacteristic
561C4#1684057811yescharacteristic
562C2—22no—
563C2—81no—
564C2#2145537311yescharacteristic
565C2#2145549511yescharacteristic
566C2C2×#1684003511yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3218C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#3218D61
hypocenterC61#19590
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. #21456970C2semidirect
4. #21445375C2semidirect
5. #21445368C2semidirect
6. #21445335C2semidirect
7. #21445330C2semidirect
8. #21445251C2semidirect
9. #21445244C2semidirect
10. #21445211C2semidirect
11. #21445206C2semidirect
12. #21444605C2semidirect
13. #21444520C2semidirect
14. C2×#16839508C2semidirect
350. C61#19590semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214569702
#214549792
#214453752
#214453682
#214453352
#214453302
#214452512
#214452442
#214452112
#214452062
#214446052
#214445202
C2×#168395082
C61×#32182
#1959061