Finite Group Databasebeta

← #29665115

Subgroups — #29665115

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457192C211yesmaximal, characteristic, complemented
2#21456834C211yesmaximal, characteristic
3#21456194C211yesmaximal, characteristic, complemented
4#21445387C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445359C211yesmaximal, characteristic, complemented
7#21445352C211yesmaximal, characteristic, complemented
8#21445263C211yesmaximal, characteristic, complemented
9#21445256C211yesmaximal, characteristic, complemented
10#21445235C211yesmaximal, characteristic, complemented
11#21445228C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444527C211yesmaximal, characteristic, complemented
14#21444486C211yesmaximal, characteristic, complemented
15C61×#2969C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C2×#14519774C2211yescharacteristic
18#16840152—21no—
19#16840128—21no—
20#16840127—21no—
21#16840127—21no—
22#16840109C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840066—21no—
27#16840057C2211yescharacteristic, complemented
28#16840052C2211yescharacteristic, complemented
29#16840018—21no—
30#16840006—21no—
31#16839981—21no—
32#16839972C2211yescharacteristic, complemented
33#16839967C2211yescharacteristic, complemented
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839957C2211yescharacteristic
38#16839912—21no—
39#16839895—21no—
40#16839819C2211yescharacteristic
41#16839786C2211yescharacteristic
42#16839768—21no—
43#16839768—21no—
44#16839515C2211yescharacteristic, complemented
45#16839515C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839513C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839510C2211yescharacteristic, complemented
50#16839507C2211yescharacteristic, complemented
51#16839507C2211yescharacteristic, complemented
52#16839505C2211yescharacteristic
53#16839505C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic, complemented
58C8×Q8×C61C2211yescharacteristic, complemented
59C61×#436—21no—
60C61×#436C2211yescharacteristic, complemented
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#405—21no—
66C4×M16×C61C2211yescharacteristic
67C22×D244—21no—
68C22×D244—21no—
69C22×D244—21no—
70C2×#11758202—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758194—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519774—21no—
80#14519774—21no—
81#14519774—21no—
82#14519774C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519769—21no—
85#14519756—21no—
86#14519756—21no—
87C4×Dic122—21no—
88C4×Dic122—21no—
89#14519736—21no—
90#14519710—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519699—21no—
101#14519699—21no—
102#14519699—21no—
103#14519699—21no—
104#14519699—21no—
105#14519699—21no—
106#14519699—21no—
107#14519699—21no—
108#14519698—21no—
109#14519697—21no—
110#14519697—21no—
111#14519697—21no—
112#14519697—21no—
113C22⋊#92418—21no—
114#14519688—21no—
115C2×M16×C61—21no—
116C2×M16×C61D411yescharacteristic
117C2×M16×C61D411yescharacteristic
118C22×C8×C61—21no—
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×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61—21no—
138#97×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61C2×D411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C2×D411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—42no—
159C2×D244—42no—
160C2×D244—41no—
161C2×D244—41no—
162C2×D244—41no—
163C2×D244—81no—
164C2×D244—81no—
165C2×D244—82no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168M16×C61—41no—
169M16×C61—41no—
170M16×C61—42no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—42no—
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C42×C61—21no—
190C42×C61C2×D411yescharacteristic
191C42×C61C2×D411yescharacteristic
192C42×C61#4111yescharacteristic
193C42×C61C2411yescharacteristic
194C22⋊Dic61—41no—
195#11758202—81no—
196#11758201—81no—
197#11758201—81no—
198#11758200—81no—
199#11758199—81no—
200#11758199—81no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205#11758196—41no—
206#11758196—41no—
207C4×Dic61—41no—
208#11758194—81no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C23×C61—21no—
214C23×C61#12111yescharacteristic
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—82no—
218C22×D61—82no—
219C22×D61—82no—
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—81no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×Dic61—41no—
242C2×Dic61—41no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—41no—
251D244—81no—
252D244—81no—
253D244—82no—
254D244—82no—
255D244—82no—
256Dic122—41no—
257Dic122—41no—
258Dic122—81no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—21no—
262C8×C61—21no—
263C8×C61—41no—
264C8×C61—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#19380—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×#12111yescharacteristic
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—81no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—164no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61#57511yescharacteristic
292C4×C61#57511yescharacteristic
293C4×C61#57611yescharacteristic
294C4×C61#57711yescharacteristic
295Dic61—81no—
296Dic61—81no—
297#3252—611no—
298#3217—611no—
299#3138—611no—
300#2969D6111yescharacteristic, complemented
301#1702—611no—
302#1701—611no—
303#1698—611no—
304#1697—611no—
305#1682—611no—
306#1681—611no—
307#1678—611no—
308#1677—611no—
309#1569—611no—
310#1554—611no—
311#1545—611no—
312C2×C61—41no—
313C2×C61—81no—
314C2×C61#304011yescharacteristic
315C2×C61#306211yescharacteristic
316C2×C61#306811yescharacteristic
317D61—161no—
318D61—161no—
319#533—611no—
320C2×#127—611no—
321#529C2×D6111yescharacteristic
322#496—1221no—
323#490—1221no—
324#490—1221no—
325#490—1221no—
326#486—611no—
327#486—611no—
328#486—611no—
329#486—611no—
330#479—1221no—
331#477—611no—
332#476—611no—
333#470—1221no—
334#468—1221no—
335#464—1221no—
336#462—611no—
337#461—611no—
338#460—611no—
339#460—611no—
340#459—611no—
341#459—611no—
342#450—1221no—
343#447—1221no—
344#446C2×D6111yescharacteristic, complemented
345C8×Q8C2×D6111yescharacteristic, complemented
346#436—21no—
347#436C2×D6111yescharacteristic, complemented
348#435—21no—
349C8×D4C2×D6111yescharacteristic, complemented
350#433—21no—
351#432—611no—
352#431C2×D6111yescharacteristic
353#423—611no—
354#418—1221no—
355#418—1221no—
356#405—21no—
357C4×M16C2×D6111yescharacteristic
358#335—611no—
359#335—611no—
360#334—611no—
361#334—611no—
362#333—611no—
363#333—611no—
364#332—611no—
365#332—611no—
366#331—611no—
367#331—611no—
368#331—611no—
369#331—611no—
370C61#1938011yescharacteristic, complemented, Sylow
371C22×D4—1221no—
372C22×D4—1221no—
373C22×D4—1221no—
374C2×Q16—1221no—
375C2×SD16—1221no—
376C2×SD16—1221no—
377C2×SD16—1221no—
378C2×D8—1221no—
379C2×D8—1221no—
380C2×M16—21no—
381C2×M16—1221no—
382C2×M16C22⋊D6111yescharacteristic
383C2×M16C22⋊D6111yescharacteristic
384C22×C8—21no—
385C4⋊Q8—611no—
386C4⋊Q8—611no—
387#127—611no—
388#127—611no—
389#127—1221no—
390#127—1221no—
391#127—1221no—
392#126—21no—
393#125—1221no—
394#125D24411yescharacteristic
395#124D24411yescharacteristic
396#123—21no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399C22⋊Q8D24411yescharacteristic
400#121D24411yescharacteristic
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×Q8C22×D6111yescharacteristic
404C4×D4—21no—
405C4×D4C22×D6111yescharacteristic
406#117—21no—
407#117—1221no—
408C2×C42C22×D6111yescharacteristic
409#107—1221no—
410#106—1221no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8C22×D6111yescharacteristic
419C4⋊C8C22×D6111yescharacteristic
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—1221no—
440#97—21no—
441#97—1221no—
442#97C22⋊D6111yescharacteristic
443#97C22⋊D6111yescharacteristic
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—2441no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8C2×D24411yescharacteristic
452C2×D4—21no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—4881no—
460C2×D4—4881no—
461C2×D4—4882no—
462C2×D4—2442no—
463C2×D4—2442no—
464C2×D4—2441no—
465C2×D4—2441no—
466C2×D4—2441no—
467C2×D4C2×D24411yescharacteristic
468C22×C4—21no—
469C22×C4C2×D24411yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472Q16—4881no—
473SD16—4881no—
474SD16—4881no—
475SD16—4881no—
476D8—4881no—
477D8—4881no—
478M16—41no—
479M16—41no—
480M16—42no—
481M16—4881no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C2×C8C2×C22⋊D6111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—2441no—
502C4⋊C4—2441no—
503C4⋊C4C2×D24411yescharacteristic
504C4⋊C4C2×D24411yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—2441no—
511C42—21no—
512C42—2441no—
513C42C2×D24411yescharacteristic
514C42#1175822211yescharacteristic
515C42C2×C22⋊D6111yescharacteristic
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—4882no—
519C23—4882no—
520C23—4882no—
521C23—2441no—
522C23—2441no—
523C23#1451975111yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—4881no—
527Q8—2441no—
528Q8—2441no—
529D4—21no—
530D4—21no—
531D4—81no—
532D4—4881no—
533D4—4881no—
534D4—4882no—
535D4—4882no—
536D4—4882no—
537D4—2441no—
538D4—2441no—
539D4—2441no—
540D4—2441no—
541D4—2441no—
542D4—2441no—
543D4—2441no—
544D4—2441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4#1451975111yescharacteristic
558C2×C4#1451975111yescharacteristic
559C2×C4#1451975111yescharacteristic
560C2×C4C22×C22⋊D6111yescharacteristic
561C2×C4C22×D24411yescharacteristic
562C2×C4C2×#1175822211yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—9764no—
580C22—4881no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22—4881no—
585C22—4881no—
586C22C2×#1451975111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—4881no—
595C4—4881no—
596C4#1684056011yescharacteristic
597C4#1684056011yescharacteristic
598C4#1684056711yescharacteristic
599C4#1684057411yescharacteristic
600C2—41no—
601C2—81no—
602C2—9761no—
603C2—9761no—
604C2#2145531311yescharacteristic
605C2#2145549911yescharacteristic
606C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2969C2
socleC22×C61C2×#121
prime radical#21456834C2
hypercenter#2969D61
hypocenterC61#19380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #21457192C2semidirect
3. #21456194C2semidirect
4. #21445387C2semidirect
5. #21445380C2semidirect
6. #21445359C2semidirect
7. #21445352C2semidirect
8. #21445263C2semidirect
9. #21445256C2semidirect
10. #21445235C2semidirect
11. #21445228C2semidirect
12. #21444586C2semidirect
13. #21444527C2semidirect
14. #21444486C2semidirect
15. C61×#2969C2semidirect
27. #16840057C22semidirect
28. #16840052C22semidirect
32. #16839972C22semidirect
33. #16839967C22semidirect
44. #16839515C22semidirect
45. #16839515C22semidirect
46. #16839513C22semidirect
47. #16839513C22semidirect
48. #16839510C22semidirect
49. #16839510C22semidirect
50. #16839507C22semidirect
51. #16839507C22semidirect
57. C61×#446C22semidirect
58. C8×Q8×C61C22semidirect
60. C61×#436C22semidirect
62. C8×D4×C61C22semidirect
300. #2969D61semidirect
344. #446C2×D61semidirect
345. C8×Q8C2×D61semidirect
347. #436C2×D61semidirect
349. C8×D4C2×D61semidirect
370. C61#19380semidirect

Maximal subgroups

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

subgroupindex
#214571922
#214568342
#214561942
#214453872
#214453802
#214453592
#214453522
#214452632
#214452562
#214452352
#214452282
#214445862
#214445272
#214444862
C61×#29692
#1938061