Finite Group Databasebeta

← #29663778

Subgroups — #29663778

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic
2#21456994C211yesmaximal, characteristic, complemented
3#21456537C211yesmaximal, characteristic, complemented
4#21445401C211yesmaximal, characteristic, complemented
5#21445359C211yesmaximal, characteristic, complemented
6#21445342C211yesmaximal, characteristic, complemented
7#21445284C211yesmaximal, characteristic, complemented
8#21445270C211yesmaximal, characteristic, complemented
9#21445228C211yesmaximal, characteristic, complemented
10#21445223C211yesmaximal, characteristic, complemented
11#21445167C211yesmaximal, characteristic, complemented
12#21444571C211yesmaximal, characteristic, complemented
13#21444479C211yesmaximal, characteristic, complemented
14#21444474C211yesmaximal, characteristic, complemented
15C61×#2969C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840312C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840161—21no—
20#16840135C2211yescharacteristic
21#16840116—21no—
22#16840113C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840100—21no—
25#16840083—21no—
26#16840059—21no—
27#16840057C2211yescharacteristic
28#16840057C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840047C2211yescharacteristic
32#16840042C2211yescharacteristic
33#16840008—21no—
34#16840008—21no—
35#16839996—21no—
36#16839993—21no—
37#16839974—21no—
38#16839962C2211yescharacteristic
39#16839957C2211yescharacteristic
40#16839864—21no—
41#16839864—21no—
42#16839815C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839510C2211yescharacteristic
51#16839510C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436C2211yescharacteristic
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#405—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190—21no—
69C2×#11758190—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C22×#92418—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519769—21no—
78#14519765—21no—
79#14519756—21no—
80#14519756—21no—
81#14519751—21no—
82#14519751—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×D244—21no—
86C4×D244—21no—
87#14519736—21no—
88#14519711—21no—
89#14519711—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519702—21no—
102#14519702—21no—
103#14519701—21no—
104#14519701—21no—
105#14519701—21no—
106#14519699—21no—
107#14519699—21no—
108#14519698—21no—
109#14519698—21no—
110#14519698—21no—
111#14519697—21no—
112#14519697—21no—
113C22⋊#92418—21no—
114C4×#92418—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
144C2×Q8×C61C2×D411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—41no—
152#11758222—82no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61—42no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—42no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C42×C61—21no—
182C42×C61C2×D411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61#4111yescharacteristic
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758201—81no—
188#11758199—81no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205#11758190—42no—
206#11758190—42no—
207C23×C61—21no—
208C23×C61#12111yescharacteristic
209C22×D61—41no—
210Q8×C61—21no—
211Q8×C61—21no—
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—81no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C22⋊D61—82no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—41no—
239D244—81no—
240C4×D61—82no—
241Dic122—41no—
242Dic122—41no—
243Dic122—81no—
244Dic122—81no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61#13512yes—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#19253—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61C2×#12111yescharacteristic
263C2×D61—81no—
264C2×D61—81no—
265C2×D61—81no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61C2×#13511yescharacteristic
274C4×C61#57511yescharacteristic
275C4×C61#57711yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—81no—
278Dic61—81no—
279Dic61—81no—
280#3247—611no—
281#3233—611no—
282#3182—611no—
283#2969D6111yescharacteristic, complemented
284#1704—611no—
285#1698—611no—
286#1695—611no—
287#1685—611no—
288#1683—611no—
289#1677—611no—
290#1676—611no—
291#1666—611no—
292#1565—611no—
293#1543—611no—
294#1542—611no—
295C2×C61—41no—
296C2×C61—81no—
297C2×C61#303511yescharacteristic
298C2×C61#306311yescharacteristic
299C2×C61#306811yescharacteristic
300D61—161no—
301#533—611no—
302#532—611no—
303#529C2×D6111yescharacteristic
304#500—611no—
305#499—1221no—
306#492—611no—
307#488—1221no—
308#487—611no—
309#486—611no—
310#485—1221no—
311#482—1221no—
312#478—1221no—
313#477—611no—
314#477—611no—
315#476—611no—
316#476—611no—
317#475—611no—
318#474—611no—
319#468—1221no—
320#468—1221no—
321#466—1221no—
322#465—1221no—
323#463—1221no—
324#460—611no—
325#459—611no—
326#446C2×D6111yescharacteristic
327C8×Q8C2×D6111yescharacteristic
328#440—1221no—
329#440—1221no—
330#436—21no—
331#436C2×D6111yescharacteristic
332#435—21no—
333C8×D4C2×D6111yescharacteristic
334#433—21no—
335#431—611no—
336#431C2×D6111yescharacteristic
337C2×C4⋊C8—611no—
338#405—21no—
339C4×M16C2×D6111yescharacteristic
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344#333—611no—
345#333—611no—
346#333—611no—
347#333—611no—
348#332—611no—
349#332—611no—
350#331—611no—
351#331—611no—
352C61#1925311yescharacteristic, complemented, Sylow
353C2×#41—1221no—
354C2×SD16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×D8—1221no—
358C2×M16—21no—
359C2×M16C22⋊D6111yescharacteristic
360C2×M16C22⋊D6111yescharacteristic
361C22×C8—21no—
362C22×C8—1221no—
363C4⋊Q8—611no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366#127—611no—
367#126—21no—
368#125—1221no—
369#125D24411yescharacteristic
370#124—1221no—
371#124D24411yescharacteristic
372#123—21no—
373C22⋊Q8—1221no—
374C22⋊Q8—1221no—
375C22⋊Q8D24411yescharacteristic
376#121—1221no—
377#121—1221no—
378#121D24411yescharacteristic
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×Q8C22×D6111yescharacteristic
382C4×D4—21no—
383C4×D4—1221no—
384C4×D4—1221no—
385C4×D4C22×D6111yescharacteristic
386#117—21no—
387#117—1221no—
388C2×C42C22×D6111yescharacteristic
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—1221no—
393#107—1221no—
394#106—1221no—
395#106—1221no—
396#106—1221no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—1221no—
422#97—21no—
423#97C22⋊D6111yescharacteristic
424#97C22⋊D6111yescharacteristic
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429C4×C8C22×D6111yescharacteristic
430#41—4882no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×Q8C2×D24411yescharacteristic
435C2×D4—21no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—2441no—
440C2×D4C2×D24411yescharacteristic
441C22×C4—21no—
442C22×C4—2441no—
443C22×C4C2×D24411yescharacteristic
444C22×C4#1175822211yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446SD16—4881no—
447SD16—2442no—
448SD16—2442no—
449D8—4881no—
450M16—22no—
451M16—41no—
452M16—42no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—42no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—4881no—
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—2441no—
476C4⋊C4—2441no—
477C4⋊C4C2×D24411yescharacteristic
478C4⋊C4C2×D24411yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C22⋊C4—2441no—
487C42—21no—
488C42—2441no—
489C42C2×D24411yescharacteristic
490C42#1175822211yescharacteristic
491C42C2×C22⋊D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—21no—
494C23—2441no—
495C23#1451975111yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—4881no—
499Q8—4881no—
500Q8—2441no—
501Q8—2441no—
502D4—21no—
503D4—21no—
504D4—81no—
505D4—4881no—
506D4—4882no—
507D4—2441no—
508D4—2441no—
509D4—2441no—
510D4—2441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—4882no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4#1451975111yescharacteristic
526C2×C4#1451975111yescharacteristic
527C2×C4#1451975111yescharacteristic
528C2×C4C22×C22⋊D6111yescharacteristic
529C2×C4C22×D24411yescharacteristic
530C2×C4C2×#1175822211yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8#1451979712yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22C2×#1451975111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—4881no—
559C4—4881no—
560C4—4881no—
561C4C2×#1451979711yescharacteristic
562C4#1684056011yescharacteristic
563C4#1684057411yescharacteristic
564C4#1684057911yescharacteristic
565C2—41no—
566C2—81no—
567C2—9761no—
568C2#2145527411yescharacteristic
569C2#2145551011yescharacteristic
570C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2969C2
socleC22×C61C2×#121
prime radical#21457145C2
hypercenter#2969D61
hypocenterC61#19253
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
2. #21456994C2semidirect
3. #21456537C2semidirect
4. #21445401C2semidirect
5. #21445359C2semidirect
6. #21445342C2semidirect
7. #21445284C2semidirect
8. #21445270C2semidirect
9. #21445228C2semidirect
10. #21445223C2semidirect
11. #21445167C2semidirect
12. #21444571C2semidirect
13. #21444479C2semidirect
14. #21444474C2semidirect
15. C61×#2969C2semidirect
283. #2969D61semidirect
352. C61#19253semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214569942
#214565372
#214454012
#214453592
#214453422
#214452842
#214452702
#214452282
#214452232
#214451672
#214445712
#214444792
#214444742
C61×#29692
#1925361