Finite Group Databasebeta

← #29665113

Subgroups — #29665113

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#21457193C211yesmaximal, characteristic, complemented
2#21456837C211yesmaximal, characteristic
3#21456193C211yesmaximal, characteristic, complemented
4#21454817C211yesmaximal, characteristic, complemented
5#21445386C211yesmaximal, characteristic, complemented
6#21445379C211yesmaximal, characteristic, complemented
7#21445358C211yesmaximal, characteristic, complemented
8#21445351C211yesmaximal, characteristic, complemented
9#21445262C211yesmaximal, characteristic, complemented
10#21445255C211yesmaximal, characteristic, complemented
11#21445234C211yesmaximal, characteristic, complemented
12#21445227C211yesmaximal, characteristic, complemented
13#21444584C211yesmaximal, characteristic, complemented
14#21444527C211yesmaximal, characteristic, complemented
15C61×#1545C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840149—21no—
19#16840126—21no—
20#16840126—21no—
21#16840126—21no—
22#16840108C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840108C2211yescharacteristic
26#16840070—21no—
27#16840058C2211yescharacteristic, complemented
28#16840053C2211yescharacteristic, complemented
29#16840020—21no—
30#16840008—21no—
31#16839985—21no—
32#16839973C2211yescharacteristic, complemented
33#16839968C2211yescharacteristic, complemented
34#16839959C2211yescharacteristic
35#16839959C2211yescharacteristic
36#16839954C2211yescharacteristic
37#16839954C2211yescharacteristic
38#16839913—21no—
39#16839896—21no—
40#16839889C2211yescharacteristic, complemented
41#16839886C2211yescharacteristic, complemented
42#16839839C2211yescharacteristic, complemented
43#16839837—21no—
44#16839836—21no—
45#16839827C2211yescharacteristic, complemented
46#16839821—21no—
47#16839819C2211yescharacteristic
48#16839767—21no—
49#16839767—21no—
50#16839716—21no—
51C4×#11758194C2211yescharacteristic
52#16839514C2211yescharacteristic, complemented
53#16839514C2211yescharacteristic, complemented
54#16839512C2211yescharacteristic, complemented
55#16839512C2211yescharacteristic, complemented
56#16839510C2211yescharacteristic, complemented
57#16839510C2211yescharacteristic, complemented
58#16839507C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C2×#127×C61C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C61×#331C2211yescharacteristic
64C61×#331C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×Dic244—21no—
68C2×#11758190—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758194D411yescharacteristic
74C2×#11758194D411yescharacteristic
75C2×#11758189—21no—
76C2×C8×D61—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519771—21no—
80#14519769—21no—
81#14519769D411yescharacteristic
82#14519765D411yescharacteristic
83#14519760—21no—
84#14519756—21no—
85#14519756—21no—
86#14519756D411yescharacteristic
87#14519751D411yescharacteristic
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93#14519736—21no—
94#14519734—21no—
95#14519711—21no—
96#14519709—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519706—21no—
101#14519702—21no—
102#14519702—21no—
103#14519702—21no—
104#14519699—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—21no—
110#14519698—21no—
111#14519698—21no—
112#14519698—21no—
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519698—21no—
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519688—21no—
121#14519688D411yescharacteristic
122#14519688D411yescharacteristic
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×D4×C61—21no—
128C22×D4×C61—21no—
129C22×D4×C61—21no—
130C2×M16×C61—21no—
131#127×C61—21no—
132#127×C61—21no—
133#127×C61—21no—
134#127×C61C2311yescharacteristic
135#127×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61—21no—
144C24×C61—41no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61—82no—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C2×C22⋊D61—21no—
163C2×D244C2×D411yescharacteristic
164C2×C4×D61—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122C2×D411yescharacteristic
168M16×C61—81no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C42×C61C2×D411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61#4111yescharacteristic
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178C22⋊Dic61—41no—
179#11758200—81no—
180#11758200—81no—
181#11758199—81no—
182#11758199—81no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C2×D411yescharacteristic
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—21no—
200C4×Dic61—41no—
201#11758194—41no—
202#11758194—41no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209Dic244—81no—
210#11758190—81no—
211#11758189—42no—
212C8×D61—42no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—82no—
216C23×C61—82no—
217C23×C61—82no—
218C23×C61#12111yescharacteristic
219C22×D61—21no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—81no—
229D4×C61—81no—
230D4×C61—82no—
231D4×C61—82no—
232D4×C61—82no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—41no—
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—81no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250D244—21no—
251D244—21no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—21no—
255Dic122—21no—
256Dic122—41no—
257Dic122—41no—
258Dic122—81no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—21no—
267#92418—41no—
268#92418—41no—
269#19380—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—164no—
280C22×C61C2×#12111yescharacteristic
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61#57511yescharacteristic
289C4×C61#57511yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57711yescharacteristic
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61—81no—
296Dic61—81no—
297#3252—611no—
298#3217—611no—
299#3138—611no—
300#2969—611no—
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#1545D6111yescharacteristic, complemented
312C2×C61—41no—
313C2×C61—161no—
314C2×C61—161no—
315C2×C61#304011yescharacteristic
316C2×C61#306211yescharacteristic
317C2×C61#306811yescharacteristic
318D61—81no—
319#533—611no—
320C2×#127C2×D6111yescharacteristic
321#529—611no—
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#446—611no—
345C8×Q8—611no—
346#436—611no—
347#436—1221no—
348#435—1221no—
349C8×D4—611no—
350#433—1221no—
351#432—611no—
352#431C2×D6111yescharacteristic
353#423C2×D6111yescharacteristic
354#418—1221no—
355#418—1221no—
356#405—1221no—
357C4×M16—611no—
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#331C2×D6111yescharacteristic
367#331C2×D6111yescharacteristic
368#331C2×D6111yescharacteristic
369#331C2×D6111yescharacteristic
370C61#1938011yescharacteristic, complemented, Sylow
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—1221no—
375C2×SD16—1221no—
376C2×SD16—1221no—
377C2×SD16—1221no—
378C2×D8—1221no—
379C2×D8—1221no—
380C2×M16—21no—
381C2×M16—611no—
382C2×M16—611no—
383C2×M16—1221no—
384C22×C8—1221no—
385C4⋊Q8—611no—
386C4⋊Q8—611no—
387#127—21no—
388#127—21no—
389#127—21no—
390#127C22×D6111yescharacteristic
391#127C22×D6111yescharacteristic
392#126—1221no—
393#125—611no—
394#125—1221no—
395#124—611no—
396#123—1221no—
397C22⋊Q8—611no—
398C22⋊Q8—1221no—
399C22⋊Q8—1221no—
400#121—611no—
401C4×Q8—611no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×D4—611no—
405C4×D4—1221no—
406#117—1221no—
407#117—1221no—
408C2×C42C22×D6111yescharacteristic
409#107—1221no—
410#106—1221no—
411C4⋊C8—21no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
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—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440#97—611no—
441#97—611no—
442#97—1221no—
443#97—1221no—
444C4×C8—21no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—1221no—
448C24—41no—
449C2×Q8—611no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—82no—
466C2×D4—611no—
467C2×D4—1221no—
468C22×C4—1221no—
469C22×C4#1175822211yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472Q16—4881no—
473SD16—4881no—
474SD16—4881no—
475SD16—4881no—
476D8—4881no—
477D8—4881no—
478M16—81no—
479M16—2442no—
480M16—2441no—
481M16—2441no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—611no—
489C2×C8—611no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—2442no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—2441no—
504C4⋊C4—2441no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—2441no—
511C42—1221no—
512C42—2441no—
513C42#1175822211yescharacteristic
514C42D4×D6111yescharacteristic
515C42D4×D6111yescharacteristic
516C42C23×D6111yescharacteristic
517C23—41no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—82no—
522C23—1221no—
523C23#1451975011yescharacteristic
524Q8—1221no—
525Q8—1221no—
526Q8—4881no—
527Q8—2441no—
528Q8—2441no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—1221no—
543D4—1221no—
544D4—4881no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4#1451975011yescharacteristic
558C2×C4#1451975011yescharacteristic
559C2×C4#1451975011yescharacteristic
560C2×C4C2×D4×D6111yescharacteristic
561C2×C4C2×D4×D6111yescharacteristic
562C2×C4C2×#1175822211yescharacteristic
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—164no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22C2×#1451975011yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—4881no—
592C4—4881no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4#1684055811yescharacteristic
597C4#1684055811yescharacteristic
598C4#1684056311yescharacteristic
599C4#1684056811yescharacteristic
600C2—41no—
601C2—161no—
602C2—161no—
603C2—4881no—
604C2#2145531211yescharacteristic
605C2#2145549711yescharacteristic
606C2#2145554611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1545C2
socleC22×C61C2×#121
prime radical#21456837C2
hypercenter#1545D61
hypocenterC61#19380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #21457193C2semidirect
3. #21456193C2semidirect
4. #21454817C2semidirect
5. #21445386C2semidirect
6. #21445379C2semidirect
7. #21445358C2semidirect
8. #21445351C2semidirect
9. #21445262C2semidirect
10. #21445255C2semidirect
11. #21445234C2semidirect
12. #21445227C2semidirect
13. #21444584C2semidirect
14. #21444527C2semidirect
15. C61×#1545C2semidirect
27. #16840058C22semidirect
28. #16840053C22semidirect
32. #16839973C22semidirect
33. #16839968C22semidirect
40. #16839889C22semidirect
41. #16839886C22semidirect
42. #16839839C22semidirect
45. #16839827C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839512C22semidirect
55. #16839512C22semidirect
56. #16839510C22semidirect
57. #16839510C22semidirect
58. #16839507C22semidirect
59. #16839507C22semidirect
311. #1545D61semidirect
370. C61#19380semidirect

Maximal subgroups

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

subgroupindex
#214571932
#214568372
#214561932
#214548172
#214453862
#214453792
#214453582
#214453512
#214452622
#214452552
#214452342
#214452272
#214445842
#214445272
C61×#15452
#1938061