Finite Group Databasebeta

← #29665130

Subgroups — #29665130

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457192C211yesmaximal, characteristic
2#21457046C211yesmaximal, characteristic
3#21456200C211yesmaximal, characteristic, complemented
4#21445401C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445373C211yesmaximal, characteristic, complemented
7#21445366C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445270C211yesmaximal, characteristic, complemented
10#21445249C211yesmaximal, characteristic, complemented
11#21445242C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444527C211yesmaximal, characteristic, complemented
14#21444503C211yesmaximal, characteristic, complemented
15C61×#2969C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840172—21no—
19#16840131—21no—
20#16840131—21no—
21#16840121—21no—
22#16840113C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840113C2211yescharacteristic
25#16840113C2211yescharacteristic
26#16840095—21no—
27#16840078—21no—
28#16840066—21no—
29#16840057C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840047C2211yescharacteristic
32#16840047C2211yescharacteristic
33#16840042C2211yescharacteristic
34#16840042C2211yescharacteristic
35#16840018—21no—
36#16840006—21no—
37#16839981—21no—
38#16839972C2211yescharacteristic
39#16839967C2211yescharacteristic
40#16839819C2211yescharacteristic
41#16839786C2211yescharacteristic
42#16839772—21no—
43#16839772—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
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
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758194—21no—
71#14519777—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83#14519736—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#14519702—21no—
102#14519702—21no—
103#14519702—21no—
104#14519702—21no—
105#14519701—21no—
106#14519701—21no—
107#14519701—21no—
108#14519700—21no—
109#14519700—21no—
110#14519698—21no—
111#14519698—21no—
112#14519698—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
151C22×Dic61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—42no—
157C2×Dic122—42no—
158C2×Dic122—41no—
159M16×C61—41no—
160M16×C61—41no—
161M16×C61—42no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—42no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C42×C61—21no—
181C42×C61C2×D411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61#4111yescharacteristic
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186#11758202—81no—
187#11758200—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—41no—
197C4⋊Dic61—41no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—41no—
201#11758194—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C23×C61—21no—
207C23×C61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210D4×C61—21no—
211D4×C61—21no—
212D4×C61—81no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—82no—
234Dic122—41no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—82no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#19381—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C2×#12111yescharacteristic
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61#57511yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—81no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275#3252—611no—
276#3239—611no—
277#3139—611no—
278#2969D6111yescharacteristic
279#1704—611no—
280#1703—611no—
281#1700—611no—
282#1699—611no—
283#1684—611no—
284#1683—611no—
285#1680—611no—
286#1679—611no—
287#1569—611no—
288#1554—611no—
289#1549—611no—
290C2×C61—41no—
291C2×C61—81no—
292C2×C61#304011yescharacteristic
293C2×C61#306311yescharacteristic
294C2×C61#306911yescharacteristic
295#533—611no—
296C2×C4⋊Q8—611no—
297#529C2×D6111yescharacteristic
298#501—1221no—
299#491—1221no—
300#491—1221no—
301#489—1221no—
302#487—611no—
303#487—611no—
304#487—611no—
305#487—611no—
306#484—1221no—
307#481—1221no—
308#479—1221no—
309#477—611no—
310#476—611no—
311#475—611no—
312#475—611no—
313#474—611no—
314#474—611no—
315#470—1221no—
316#468—1221no—
317#464—1221no—
318#462—611no—
319#461—611no—
320#446C2×D6111yescharacteristic
321C8×Q8C2×D6111yescharacteristic
322#436—21no—
323#436C2×D6111yescharacteristic
324#435—21no—
325C8×D4C2×D6111yescharacteristic
326#433—21no—
327#432—611no—
328#431C2×D6111yescharacteristic
329#423—611no—
330#419—1221no—
331#419—1221no—
332#405—21no—
333C4×M16C2×D6111yescharacteristic
334#335—611no—
335#335—611no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346C61#1938111yescharacteristic, complemented, Sylow
347C22×Q8—1221no—
348C2×Q16—1221no—
349C2×SD16—1221no—
350C2×M16—21no—
351C2×M16—1221no—
352C2×M16C22⋊D6111yescharacteristic
353C2×M16C22⋊D6111yescharacteristic
354C22×C8—21no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362#126—21no—
363#125—1221no—
364#125D24411yescharacteristic
365#124D24411yescharacteristic
366#123—21no—
367C22⋊Q8—1221no—
368C22⋊Q8—1221no—
369C22⋊Q8D24411yescharacteristic
370#121D24411yescharacteristic
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8C22×D6111yescharacteristic
374C4×D4—21no—
375C4×D4C22×D6111yescharacteristic
376#117—21no—
377#117—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#102—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—1221no—
416#97—21no—
417#97—1221no—
418#97C22⋊D6111yescharacteristic
419#97C22⋊D6111yescharacteristic
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—2442no—
429C2×Q8—2442no—
430C2×Q8—2441no—
431C2×Q8C2×D24411yescharacteristic
432C2×D4—21no—
433C2×D4C2×D24411yescharacteristic
434C22×C4—21no—
435C22×C4—2441no—
436C22×C4C2×D24411yescharacteristic
437C22×C4#1175822211yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439Q16—4881no—
440SD16—4881no—
441M16—41no—
442M16—41no—
443M16—42no—
444M16—4881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8C2×C22⋊D6111yescharacteristic
453C2×C8C2×C22⋊D6111yescharacteristic
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4C2×D24411yescharacteristic
473C4⋊C4C2×D24411yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—2441no—
480C42—21no—
481C42—2441no—
482C42C2×D24411yescharacteristic
483C42#1175822211yescharacteristic
484C42C2×C22⋊D6111yescharacteristic
485C42C23×D6111yescharacteristic
486C23—21no—
487C23#1451975111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—4881no—
491Q8—4882no—
492Q8—2441no—
493Q8—2441no—
494Q8—2441no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—4882no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451975111yescharacteristic
517C2×C4#1451975111yescharacteristic
518C2×C4#1451975111yescharacteristic
519C2×C4C22×C22⋊D6111yescharacteristic
520C2×C4C22×D24411yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#1451975111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—4881no—
547C4—4881no—
548C4—4881no—
549C4—4881no—
550C4#1684056011yescharacteristic
551C4#1684056011yescharacteristic
552C4#1684057411yescharacteristic
553C4#1684057911yescharacteristic
554C2—41no—
555C2—81no—
556C2#2145531311yescharacteristic
557C2#2145551011yescharacteristic
558C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2969C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#2969D61
hypocenterC61#19381
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
3. #21456200C2semidirect
4. #21445401C2semidirect
5. #21445394C2semidirect
6. #21445373C2semidirect
7. #21445366C2semidirect
8. #21445277C2semidirect
9. #21445270C2semidirect
10. #21445249C2semidirect
11. #21445242C2semidirect
12. #21444586C2semidirect
13. #21444527C2semidirect
14. #21444503C2semidirect
346. C61#19381semidirect

Maximal subgroups

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

subgroupindex
#214571922
#214570462
#214562002
#214454012
#214453942
#214453732
#214453662
#214452772
#214452702
#214452492
#214452422
#214445862
#214445272
#214445032
C61×#29692
#1938161