Finite Group Databasebeta

← #29665149

Subgroups — #29665149

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457181C211yesmaximal, characteristic
2#21456215C211yesmaximal, characteristic, complemented
3#21454824C211yesmaximal, characteristic, complemented
4#21445403C211yesmaximal, characteristic, complemented
5#21445396C211yesmaximal, characteristic, complemented
6#21445361C211yesmaximal, characteristic, complemented
7#21445354C211yesmaximal, characteristic, complemented
8#21445279C211yesmaximal, characteristic, complemented
9#21445272C211yesmaximal, characteristic, complemented
10#21445237C211yesmaximal, characteristic, complemented
11#21445230C211yesmaximal, characteristic, complemented
12#21444587C211yesmaximal, characteristic, complemented
13#21444525C211yesmaximal, characteristic, complemented
14#21444500C211yesmaximal, characteristic, complemented
15C61×#3238C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840124—21no—
18#16840124—21no—
19#16840114C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840059—21no—
24#16840047C2211yescharacteristic
25#16840042C2211yescharacteristic
26#16840013—21no—
27#16840010—21no—
28#16839974—21no—
29#16839962C2211yescharacteristic
30#16839957C2211yescharacteristic
31#16839893C2211yescharacteristic
32Q8×#92418C2211yescharacteristic
33#16839840—21no—
34#16839840C2211yescharacteristic
35#16839834—21no—
36D4×#92418C2211yescharacteristic
37#16839823—21no—
38#16839815C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839761—21no—
41#16839761—21no—
42#16839718—21no—
43C4×#11758194C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C2×C4⋊Q8×C61C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#501—21no—
59C61×#489—21no—
60C61×#483—21no—
61C61×#480—21no—
62C61×#477C2211yescharacteristic
63C61×#477C2211yescharacteristic
64C61×#476C2211yescharacteristic
65C61×#476C2211yescharacteristic
66C61×#432C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201—21no—
69C2×#11758199—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194D411yescharacteristic
73C2×#11758194D411yescharacteristic
74C22×#92418—21no—
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519765—21no—
78#14519751—21no—
79#14519751—21no—
80C4×D244—21no—
81C4×D244—21no—
82#14519710—21no—
83#14519708—21no—
84C4⋊#92418—21no—
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91#14519701—21no—
92#14519700—21no—
93#14519700—21no—
94#14519700—21no—
95#14519700—21no—
96#14519698—21no—
97#14519697—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106#14519688—21no—
107#14519688D411yescharacteristic
108#14519688D411yescharacteristic
109C4×#92418—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C22×Q8×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—21no—
120#125×C61D411yescharacteristic
121#124×C61D411yescharacteristic
122#123×C61—21no—
123C22⋊Q8×C61D411yescharacteristic
124#121×C61D411yescharacteristic
125C4×Q8×C61C2311yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61C2311yescharacteristic
128#117×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—21no—
133#107×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×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—82no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61C2×D411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—41no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C2×C22⋊D61—41no—
157#11758222—42no—
158#11758222—42no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164C2×C8×C61—21no—
165C2×C8×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—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61—21no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188#11758201—81no—
189#11758199—81no—
190#11758198—41no—
191#11758198—41no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194#11758194—41no—
195#11758194—41no—
196#11758194—42no—
197#11758194—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—42no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C23×C61—21no—
208C23×C61#12111yescharacteristic
209C22×D61—41no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—82no—
213Q8×C61—81no—
214Q8×C61—81no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—81no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—82no—
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C22⋊D61—82no—
238C2×Dic61—41no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—81no—
244C4×D61—82no—
245Dic122—41no—
246Dic122—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#19382—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×#12111yescharacteristic
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61#57511yescharacteristic
278C4×C61#57511yescharacteristic
279C4×C61#57711yescharacteristic
280C4×C61#57811yescharacteristic
281Dic61—81no—
282#3251—611no—
283#3238D6111yescharacteristic, complemented
284#3141—611no—
285#2969—611no—
286#1704—611no—
287#1703—611no—
288#1698—611no—
289#1697—611no—
290#1684—611no—
291#1683—611no—
292#1678—611no—
293#1677—611no—
294#1569—611no—
295#1553—611no—
296#1548—611no—
297C2×C61—41no—
298C2×C61—81no—
299C2×C61#304011yescharacteristic
300C2×C61#306311yescharacteristic
301C2×C61#306811yescharacteristic
302D61—161no—
303#532—611no—
304C2×C4⋊Q8C2×D6111yescharacteristic
305#529C2×D6111yescharacteristic
306#501—21no—
307#489—21no—
308#489—1221no—
309#489—1221no—
310#487—611no—
311#487—611no—
312#486—611no—
313#486—611no—
314#483—21no—
315#480—21no—
316#478—1221no—
317#477C2×D6111yescharacteristic
318#477C2×D6111yescharacteristic
319#476C2×D6111yescharacteristic
320#476C2×D6111yescharacteristic
321#475—611no—
322#474—611no—
323#469—1221no—
324#468—1221no—
325#463—1221no—
326#460—611no—
327#459—611no—
328#446—611no—
329C8×Q8—611no—
330#436—611no—
331#436—1221no—
332#435—1221no—
333C8×D4—611no—
334#433—1221no—
335#432C2×D6111yescharacteristic
336#431—611no—
337#423—611no—
338#417—1221no—
339#417—1221no—
340#405—1221no—
341C4×M16—611no—
342#335—611no—
343#335—611no—
344#334—611no—
345#334—611no—
346#333—611no—
347#333—611no—
348#333—611no—
349#333—611no—
350#332—611no—
351#332—611no—
352#331—611no—
353#331—611no—
354C61#1938211yescharacteristic, complemented, Sylow
355C2×#41—1221no—
356C22×Q8—21no—
357C2×SD16—1221no—
358C2×D8—1221no—
359C2×M16—611no—
360C2×M16—611no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—1221no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—611no—
368C4⋊Q8C22×D6111yescharacteristic
369C4⋊Q8C22×D6111yescharacteristic
370#127—611no—
371#126—21no—
372#125C22⋊D6111yescharacteristic
373#124—1221no—
374#124C22⋊D6111yescharacteristic
375#123—21no—
376C22⋊Q8C22⋊D6111yescharacteristic
377#121—1221no—
378#121—1221no—
379#121C22⋊D6111yescharacteristic
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C22×D6111yescharacteristic
389#107—21no—
390#107—21no—
391#107—1221no—
392#106—21no—
393#106—21no—
394#106—1221no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404#103—21no—
405#103—21no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—21no—
412#102—21no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420C22⋊C8—21no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—21no—
425#97—611no—
426#97—611no—
427#97—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432#41—2442no—
433#41—2442no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—82no—
438C2×Q8—1221no—
439C2×Q8C2×C22⋊D6111yescharacteristic
440C2×D4—21no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—2441no—
445C2×D4C2×C22⋊D6111yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—2441no—
449C22×C4D4×D6111yescharacteristic
450C22×C4#1175822411yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452SD16—4881no—
453D8—4881no—
454M16—4881no—
455M16—2441no—
456M16—2441no—
457M16—2442no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—2442no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C22⋊D6111yescharacteristic
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C42—21no—
491C42D4×D6111yescharacteristic
492C42#1175822411yescharacteristic
493C42C2×C22⋊D6111yescharacteristic
494C42C23×D6111yescharacteristic
495C23—21no—
496C23—2441no—
497C23#1451974911yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—81no—
501Q8—81no—
502Q8—82no—
503Q8—2441no—
504Q8—2441no—
505D4—21no—
506D4—21no—
507D4—81no—
508D4—4881no—
509D4—4882no—
510D4—2441no—
511D4—2441no—
512D4—2441no—
513D4—2441no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—4882no—
528C2×C4—2441no—
529C2×C4#1451974911yescharacteristic
530C2×C4#1451974911yescharacteristic
531C2×C4#1451974911yescharacteristic
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4C2×#1175822411yescharacteristic
535C8—41no—
536C8—41no—
537C8—1221no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—4881no—
552C22—4881no—
553C22—4881no—
554C22C2×#1451974911yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—4881no—
565C4#1684056111yescharacteristic
566C4#1684056111yescharacteristic
567C4#1684057011yescharacteristic
568C4#1684057711yescharacteristic
569C2—41no—
570C2—81no—
571C2—9761no—
572C2#2145531511yescharacteristic
573C2#2145550611yescharacteristic
574C2#2145554411yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3238C2
socleC22×C61C2×#121
prime radical#21457181C2
hypercenter#3238D61
hypocenterC61#19382
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. #21456215C2semidirect
3. #21454824C2semidirect
4. #21445403C2semidirect
5. #21445396C2semidirect
6. #21445361C2semidirect
7. #21445354C2semidirect
8. #21445279C2semidirect
9. #21445272C2semidirect
10. #21445237C2semidirect
11. #21445230C2semidirect
12. #21444587C2semidirect
13. #21444525C2semidirect
14. #21444500C2semidirect
15. C61×#3238C2semidirect
283. #3238D61semidirect
354. C61#19382semidirect

Maximal subgroups

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

subgroupindex
#214571812
#214562152
#214548242
#214454032
#214453962
#214453612
#214453542
#214452792
#214452722
#214452372
#214452302
#214445872
#214445252
#214445002
C61×#32382
#1938261