Finite Group Databasebeta

← #29667627

Subgroups — #29667627

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#21457157C211yesmaximal, characteristic
2#21456972C211yesmaximal, characteristic, complemented
3#21456848C211yesmaximal, characteristic
4#21454981C211yesmaximal, characteristic
5#21445374C211yesmaximal, characteristic, complemented
6#21445367C211yesmaximal, characteristic, complemented
7#21445338C211yesmaximal, characteristic, complemented
8#21445333C211yesmaximal, characteristic, complemented
9#21445250C211yesmaximal, characteristic, complemented
10#21445243C211yesmaximal, characteristic, complemented
11#21445214C211yesmaximal, characteristic, complemented
12#21445209C211yesmaximal, characteristic, complemented
13#21444520C211yesmaximal, characteristic, complemented
14C2×#16839509C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840296C2211yescharacteristic
19#16840167C2211yescharacteristic
20#16840167C2211yescharacteristic
21#16840156—21no—
22#16840131—21no—
23#16840113C2211yescharacteristic
24#16840113C2211yescharacteristic
25#16840098—21no—
26#16840098—21no—
27#16840070—21no—
28#16840058—21no—
29#16840058—21no—
30#16840048C2211yescharacteristic
31#16840043C2211yescharacteristic
32#16840003—21no—
33#16839991—21no—
34#16839985—21no—
35#16839973C2211yescharacteristic
36#16839973C2211yescharacteristic
37#16839973C2211yescharacteristic
38#16839968C2211yescharacteristic
39#16839968C2211yescharacteristic
40#16839968C2211yescharacteristic
41#16839920—21no—
42#16839903—21no—
43#16839892C2211yescharacteristic
44C8×Dic122C2211yescharacteristic
45#16839841C2211yescharacteristic
46#16839830—21no—
47C8×D244C2211yescharacteristic
48#16839825—21no—
49#16839822—21no—
50#16839787—21no—
51C2×C4⋊#92418C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C22×Dic122—21no—
68C2×Dic244—21no—
69C2×Dic244—21no—
70C2×Dic244—21no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758190—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519777—21no—
78#14519777—21no—
79#14519777—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519777C2311yescharacteristic
83#14519777C2311yescharacteristic
84#14519771—21no—
85#14519769—21no—
86#14519769D411yescharacteristic
87#14519765D411yescharacteristic
88#14519760—21no—
89#14519756—21no—
90#14519756—21no—
91#14519756D411yescharacteristic
92#14519751D411yescharacteristic
93C4×Dic122—21no—
94C4×Dic122—21no—
95C4×Dic122C2311yescharacteristic
96C4×D244C2311yescharacteristic
97C4×C22⋊D61—21no—
98#14519736—21no—
99#14519734—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102#14519711—21no—
103#14519711—21no—
104#14519711—21no—
105#14519711—21no—
106#14519711—21no—
107#14519709—21no—
108C4⋊#92418—21no—
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519702—21no—
120#14519702—21no—
121#14519702—21no—
122#14519702—21no—
123#14519702—21no—
124#14519699—21no—
125#14519689—21no—
126#14519689—21no—
127#14519687—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—41no—
149C2×D244C2×D411yescharacteristic
150C2×C4×D61—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—41no—
156C2×Dic122—81no—
157C2×Dic122—81no—
158C2×Dic122C2×D411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—81no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61#4111yescharacteristic
171C42×C61C2411yescharacteristic
172C22⋊Dic61—21no—
173C22⋊Dic61—41no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—41no—
187C4⋊Dic61—41no—
188C4⋊Dic61C2×D411yescharacteristic
189C4⋊Dic61C2×D411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201Dic244—81no—
202Dic244—81no—
203Dic244—81no—
204#11758190—81no—
205#11758190—81no—
206#11758190—81no—
207#11758189—81no—
208C8×D61—81no—
209C23×C61#12111yescharacteristic
210C22×D61—21no—
211C2×C4×C61—22no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61#12111yescharacteristic
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C22⋊D61—42no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—82no—
231D244—21no—
232D244—21no—
233C4×D61—41no—
234C4×D61—41no—
235Dic122—21no—
236Dic122—21no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—41no—
242Dic122—41no—
243Dic122—41no—
244Dic122—41no—
245Dic122—82no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254#92418—41no—
255#92418—41no—
256#19590—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61#47312yes—
260C22×C61C2×#12111yescharacteristic
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61#57611yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—81no—
276Dic61—81no—
277Dic61—81no—
278Dic61—81no—
279#3248—611no—
280#3230—611no—
281#3218—611no—
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#1573D6111yescharacteristic, complemented
292#1552—611no—
293C2×#332—611no—
294C2×C61—22no—
295C2×C61#304611yescharacteristic
296C2×C61#306211yescharacteristic
297C2×C61C2×#47311yescharacteristic
298D61—81no—
299#533—611no—
300C2×C4⋊Q8—611no—
301#529—611no—
302#500—611no—
303#500—611no—
304#497—1221no—
305#491—1221no—
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#462—611no—
320#462—611no—
321#461—611no—
322#461—611no—
323#461—611no—
324#451—1221no—
325#448—1221no—
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#431C2×D6111yescharacteristic
335#424—1221no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8C2×D6111yescharacteristic
338#335C2×D6111yescharacteristic
339#335C2×D6111yescharacteristic
340#334C2×D6111yescharacteristic
341#334C2×D6111yescharacteristic
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—1221no—
352C2×Q16—1221no—
353C2×Q16—1221no—
354C2×Q16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×M16—1221no—
359C22×C8—21no—
360C22×C8—1221no—
361C22×C8—1221no—
362C4⋊Q8—611no—
363C4⋊Q8—611no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369#126—1221no—
370#125—611no—
371#125—1221no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377#121—611no—
378C4×Q8—611no—
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×D4—611no—
382C4×D4—1221no—
383#117—1221no—
384#117—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C42C22×D6111yescharacteristic
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—1221no—
393#106—1221no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8D24411yescharacteristic
401C4⋊C8D24411yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
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—1221no—
420C22⋊C8—1221no—
421C22⋊C8D24411yescharacteristic
422C22⋊C8D24411yescharacteristic
423#97—21no—
424#97—1221no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427C4×C8C22×D6111yescharacteristic
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—4881no—
434C2×Q8—4881no—
435C2×Q8—2441no—
436C2×D4—611no—
437C2×D4—1221no—
438C22×C4—1221no—
439C22×C4—2441no—
440C22×C4C2×D24411yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4#1175822611yescharacteristic
443Q16—4881no—
444Q16—4881no—
445Q16—4881no—
446SD16—4881no—
447SD16—4881no—
448SD16—4881no—
449M16—4881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—4881no—
458C2×C8—4881no—
459C2×C8C2×D24411yescharacteristic
460C2×C8C2×D24411yescharacteristic
461C2×C8C2×D24411yescharacteristic
462C2×C8C2×D24411yescharacteristic
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—2441no—
487C42—1221no—
488C42—2441no—
489C42C2×D24411yescharacteristic
490C42D4×D6111yescharacteristic
491C42#1175822611yescharacteristic
492C42C23×D6111yescharacteristic
493C23—1221no—
494C23#1451975211yescharacteristic
495Q8—1221no—
496Q8—1221no—
497Q8—4882no—
498Q8—2441no—
499Q8—2441no—
500Q8—2441no—
501Q8—2441no—
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—1221no—
507D4—1221no—
508D4—2442no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—4882no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4#1451975211yescharacteristic
525C2×C4#1451975211yescharacteristic
526C2×C4#1451975211yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C2×C4C22×D24411yescharacteristic
529C2×C4C2×#1175822611yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—2441no—
539C8—2441no—
540C22—21no—
541C22—21no—
542C22—2441no—
543C22—2441no—
544C22—2441no—
545C22#1684003812yes—
546C22C2×#1451975211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—4881no—
552C4—4881no—
553C4—4881no—
554C4—4881no—
555C4—2441no—
556C4—2441no—
557C4—2441no—
558C4#1684056611yescharacteristic
559C4#1684057111yescharacteristic
560C4#1684057411yescharacteristic
561C4#1684057911yescharacteristic
562C2—22no—
563C2—4881no—
564C2#2145537111yescharacteristic
565C2#2145550011yescharacteristic
566C2C2×#1684003811yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1573D61
hypocenterC61#19590
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #21456972C2semidirect
5. #21445374C2semidirect
6. #21445367C2semidirect
7. #21445338C2semidirect
8. #21445333C2semidirect
9. #21445250C2semidirect
10. #21445243C2semidirect
11. #21445214C2semidirect
12. #21445209C2semidirect
13. #21444520C2semidirect
14. C2×#16839509C2semidirect
15. C61×#1573C2semidirect
291. #1573D61semidirect
350. C61#19590semidirect

Maximal subgroups

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

subgroupindex
#214571572
#214569722
#214568482
#214549812
#214453742
#214453672
#214453382
#214453332
#214452502
#214452432
#214452142
#214452092
#214445202
C2×#168395092
C61×#15732
#1959061