Finite Group Databasebeta

← #29665145

Subgroups — #29665145

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#21457037C211yesmaximal, characteristic, complemented
3#21456213C211yesmaximal, characteristic, complemented
4#21445401C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445359C211yesmaximal, characteristic, complemented
7#21445352C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445270C211yesmaximal, characteristic, complemented
10#21445235C211yesmaximal, characteristic, complemented
11#21445228C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444522C211yesmaximal, characteristic, complemented
14#21444499C211yesmaximal, characteristic, complemented
15C61×#2969C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840172—21no—
19#16840122—21no—
20#16840122—21no—
21#16840121—21no—
22#16840113C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840090—21no—
27#16840073—21no—
28#16840059—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840052C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840047C2211yescharacteristic
34#16840042C2211yescharacteristic
35#16840013—21no—
36#16840010—21no—
37#16839974—21no—
38#16839962C2211yescharacteristic
39#16839957C2211yescharacteristic
40#16839819C2211yescharacteristic
41#16839786C2211yescharacteristic
42#16839764—21no—
43#16839764—21no—
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—
68C22×Dic122—21no—
69C2×#11758201—21no—
70C2×#11758199—21no—
71C2×#11758194—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519765—21no—
80#14519751—21no—
81#14519751—21no—
82C4×D244—21no—
83C4×D244—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519699—21no—
105#14519699—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—
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
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—
152C22×Dic61—41no—
153#11758222—42no—
154#11758222—42no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—41no—
163C2×Dic122—82no—
164M16×C61—41no—
165M16×C61—41no—
166M16×C61—42no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—42no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C42×C61—21no—
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61#4111yescharacteristic
189C42×C61C2411yescharacteristic
190#11758201—81no—
191#11758199—81no—
192#11758198—41no—
193#11758198—41no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—41no—
201C4⋊Dic61—41no—
202#11758194—81no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
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—
235C2×Dic61—82no—
236D244—41no—
237D244—41no—
238D244—41no—
239D244—41no—
240D244—81no—
241C4×D61—82no—
242Dic122—41no—
243Dic122—41no—
244Dic122—82no—
245Dic122—81no—
246Dic122—81no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252C8×C61—41no—
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#57511yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57811yescharacteristic
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282#3251—611no—
283#3238—611no—
284#3141—611no—
285#2969D6111yescharacteristic, complemented
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⋊Q8—611no—
305#529C2×D6111yescharacteristic
306#501—1221no—
307#489—1221no—
308#489—1221no—
309#489—1221no—
310#487—611no—
311#487—611no—
312#486—611no—
313#486—611no—
314#483—1221no—
315#480—1221no—
316#478—1221no—
317#477—611no—
318#477—611no—
319#476—611no—
320#476—611no—
321#475—611no—
322#474—611no—
323#469—1221no—
324#468—1221no—
325#463—1221no—
326#460—611no—
327#459—611no—
328#446C2×D6111yescharacteristic
329C8×Q8C2×D6111yescharacteristic
330#436—21no—
331#436C2×D6111yescharacteristic
332#435—21no—
333C8×D4C2×D6111yescharacteristic
334#433—21no—
335#432—611no—
336#431C2×D6111yescharacteristic
337#423—611no—
338#417—1221no—
339#417—1221no—
340#405—21no—
341C4×M16C2×D6111yescharacteristic
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—1221no—
357C2×SD16—1221no—
358C2×D8—1221no—
359C2×M16—21no—
360C2×M16—1221no—
361C2×M16C22⋊D6111yescharacteristic
362C2×M16C22⋊D6111yescharacteristic
363C22×C8—21no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8—1221no—
370#127—611no—
371#126—21no—
372#125D24411yescharacteristic
373#124—1221no—
374#124D24411yescharacteristic
375#123—21no—
376C22⋊Q8D24411yescharacteristic
377#121—1221no—
378#121—1221no—
379#121D24411yescharacteristic
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—21no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C42C22×D6111yescharacteristic
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404#103—1221no—
405#103—1221no—
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—
418#102—1221no—
419#102—1221no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—1221no—
424#97—21no—
425#97—1221no—
426#97C22⋊D6111yescharacteristic
427#97C22⋊D6111yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432#41—2442no—
433#41—2442no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—4882no—
438C2×Q8—2441no—
439C2×Q8C2×D24411yescharacteristic
440C2×D4—21no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—2441no—
445C2×D4C2×D24411yescharacteristic
446C22×C4—21no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4C2×D24411yescharacteristic
450C22×C4#1175822211yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452SD16—4881no—
453D8—4881no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—4881no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8C2×C22⋊D6111yescharacteristic
466C2×C8C2×C22⋊D6111yescharacteristic
467C2×C8C2×C22⋊D6111yescharacteristic
468C2×C8C2×C22⋊D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4C2×D24411yescharacteristic
482C4⋊C4C2×D24411yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C42—21no—
491C42C2×D24411yescharacteristic
492C42#1175822211yescharacteristic
493C42C2×C22⋊D6111yescharacteristic
494C42C23×D6111yescharacteristic
495C23—21no—
496C23—2441no—
497C23#1451975111yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—4881no—
501Q8—4881no—
502Q8—4882no—
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—4882no—
525C2×C4—4882no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451975111yescharacteristic
530C2×C4#1451975111yescharacteristic
531C2×C4#1451975111yescharacteristic
532C2×C4C22×C22⋊D6111yescharacteristic
533C2×C4C22×D24411yescharacteristic
534C2×C4C2×#1175822211yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
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×#1451975111yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—4881no—
563C4—4881no—
564C4—4881no—
565C4#1684056011yescharacteristic
566C4#1684056011yescharacteristic
567C4#1684057411yescharacteristic
568C4#1684057911yescharacteristic
569C2—41no—
570C2—81no—
571C2—9761no—
572C2#2145531311yescharacteristic
573C2#2145551011yescharacteristic
574C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2969C2
socleC22×C61C2×#121
prime radical#21457181C2
hypercenter#2969D61
hypocenterC61#19382
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. #21457037C2semidirect
3. #21456213C2semidirect
4. #21445401C2semidirect
5. #21445394C2semidirect
6. #21445359C2semidirect
7. #21445352C2semidirect
8. #21445277C2semidirect
9. #21445270C2semidirect
10. #21445235C2semidirect
11. #21445228C2semidirect
12. #21444586C2semidirect
13. #21444522C2semidirect
14. #21444499C2semidirect
15. C61×#2969C2semidirect
285. #2969D61semidirect
354. C61#19382semidirect

Maximal subgroups

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

subgroupindex
#214571812
#214570372
#214562132
#214454012
#214453942
#214453592
#214453522
#214452772
#214452702
#214452352
#214452282
#214445862
#214445222
#214444992
C61×#29692
#1938261