Finite Group Databasebeta

← #29677104

Subgroups — #29677104

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#21458535C211yesmaximal, characteristic
2#21458102C211yesmaximal, characteristic, complemented
3#21458096C211yesmaximal, characteristic, complemented
4#21445427C211yesmaximal, characteristic, complemented
5#21445373C211yesmaximal, characteristic, complemented
6#21445370C211yesmaximal, characteristic, complemented
7#21445368C211yesmaximal, characteristic, complemented
8#21445364C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445073C211yesmaximal, characteristic, complemented
11#21445068C211yesmaximal, characteristic, complemented
12#21445067C211yesmaximal, characteristic, complemented
13#21444714C211yesmaximal, characteristic, complemented
14#21444704C211yesmaximal, characteristic
15C61×#3367C211yesmaximal, characteristic
16#16840482C2211yescharacteristic
17D4×Dic122C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840120—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840103—21no—
25#16840100—21no—
26#16840056—21no—
27#16840047C2211yescharacteristic
28#16840044C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840018—21no—
31#16840018—21no—
32#16839975—21no—
33#16839972C2211yescharacteristic
34#16839969C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839918—21no—
37#16839917—21no—
38#16839892C2211yescharacteristic
39#16839859—21no—
40C4×#11758202C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839771—21no—
44#16839770—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#556C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#487C2211yescharacteristic
60C61×#477—21no—
61C61×#474C2211yescharacteristic
62C61×#463—21no—
63C61×#461C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×D8×C61C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202D411yescharacteristic
71C2×#11758200—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519776—21no—
77#14519770—41no—
78#14519764—21no—
79#14519756—21no—
80#14519756—21no—
81#14519754—41no—
82C4×Dic122C2311yescharacteristic
83#14519742—21no—
84D4×Dic61—21no—
85#14519736—21no—
86#14519710—21no—
87#14519710—41no—
88#14519710—41no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519702—21no—
97#14519702—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701D411yescharacteristic
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×SD16×C61—21no—
117C2×D8×C61D411yescharacteristic
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#126×C61—41no—
122#124×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C22×Dic61—41no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—42no—
159C2×Dic122—41no—
160C2×Dic122—81no—
161C2×Dic122C2×D411yescharacteristic
162SD16×C61—42no—
163D8×C61—41no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—41no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—41no—
186C22⋊Dic61—41no—
187C22⋊Dic61—41no—
188#11758202—41no—
189#11758202—81no—
190#11758202—81no—
191#11758200—42no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C2×D411yescharacteristic
197#11758196—21no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202#11758194—81no—
203#11758194—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C23×C61—21no—
211C23×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—82no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—82no—
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—82no—
242Dic122—21no—
243Dic122—21no—
244Dic122—41no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—82no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—22no—
253#92418—21no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#20306—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61D4211yescharacteristic
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61#57511yescharacteristic
274C4×C61#57511yescharacteristic
275C4×C61#57611yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—41no—
278Dic61—41no—
279Dic61—81no—
280Dic61—81no—
281#3367—611no—
282#3367D6111yescharacteristic
283#3328—611no—
284#3328—611no—
285#1710—611no—
286#1700—611no—
287#1700—611no—
288#1699—611no—
289#1699—611no—
290#1650—611no—
291#1650—611no—
292#1649—611no—
293#1649—611no—
294#1591—611no—
295#1589—611no—
296C2×C61—81no—
297C2×C61—81no—
298C2×C61#327311yescharacteristic
299C2×C61#327711yescharacteristic
300C2×C61#329311yescharacteristic
301#556—611no—
302#556C2×D6111yescharacteristic
303D4×Q8—611no—
304D4×Q8C2×D6111yescharacteristic
305#500—611no—
306#500—611no—
307#489—21no—
308#489—1221no—
309#487—611no—
310#487—611no—
311#487—611no—
312#487C2×D6111yescharacteristic
313#485—1221no—
314#485—1221no—
315#477—21no—
316#477—1221no—
317#475—611no—
318#475—611no—
319#474—611no—
320#474C2×D6111yescharacteristic
321#470—1221no—
322#470—1221no—
323#463—21no—
324#463—1221no—
325#462—611no—
326#462—611no—
327#461—611no—
328#461C2×D6111yescharacteristic
329#451—1221no—
330#451—1221no—
331#446—611no—
332#446C2×D6111yescharacteristic
333#440—21no—
334#440—1221no—
335C4×Q16—611no—
336C4×D8C2×D6111yescharacteristic
337#436—611no—
338#436—611no—
339#419—1221no—
340#419—1221no—
341#335—611no—
342#335—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351C82—611no—
352C61#2030611yescharacteristic, complemented, Sylow
353C22×Q8—21no—
354C22×Q8—1221no—
355C2×Q16—611no—
356C2×Q16—1221no—
357C2×Q16—1221no—
358C2×SD16—21no—
359C2×SD16—1221no—
360C2×D8C22⋊D6111yescharacteristic
361C2×M16—1221no—
362C2×M16—1221no—
363C4⋊Q8—21no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#126—41no—
370#126—2441no—
371#124—21no—
372#124—1221no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C22⋊Q8—2441no—
379C4×Q8—21no—
380C4×Q8—611no—
381C4×Q8—1221no—
382C4×Q8C22×D6111yescharacteristic
383C4×D4—21no—
384C4×D4—1221no—
385C4×D4C22×D6111yescharacteristic
386C4×D4C22×D6111yescharacteristic
387#117—21no—
388#117—1221no—
389#107—21no—
390#107—611no—
391#107—1221no—
392#107—2441no—
393#107—2441no—
394#107C22⋊D6111yescharacteristic
395#106—1221no—
396#106—1221no—
397C4⋊C8—21no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—611no—
407#103—611no—
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#103—1221no—
418#103—1221no—
419#102—21no—
420#102—1221no—
421#102C22⋊D6111yescharacteristic
422#102C22⋊D6111yescharacteristic
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425#97—21no—
426#97—1221no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8C22×D6111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—611no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—4881no—
439C2×Q8—2441no—
440C2×Q8—2442no—
441C2×Q8D4×D6111yescharacteristic
442C2×D4C2×C22⋊D6111yescharacteristic
443C2×D4C2×C22⋊D6111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—2441no—
448Q16—4881no—
449Q16—4881no—
450Q16—2441no—
451SD16—42no—
452SD16—2442no—
453D8—41no—
454M16—4881no—
455M16—4881no—
456C2×C8—21no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—611no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4D4×D6111yescharacteristic
481C4⋊C4C2×C22⋊D6111yescharacteristic
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C22⋊C4—2441no—
491C42—21no—
492C42—41no—
493C42—1221no—
494C42—2441no—
495C42C23×D6111yescharacteristic
496C23—21no—
497C23—21no—
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—82no—
505Q8—1221no—
506Q8—1221no—
507Q8—4882no—
508Q8—2441no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—4882no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4#1451982211yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—1222no—
539C8—1221no—
540C8—1221no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22D4×C22⋊D6111yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—4881no—
559C4—4881no—
560C4—2441no—
561C4—2441no—
562C4#1684055811yescharacteristic
563C4#1684056011yescharacteristic
564C4#1684056611yescharacteristic
565C4#1684057711yescharacteristic
566C2—81no—
567C2—81no—
568C2#2145742411yescharacteristic
569C2#2145747211yescharacteristic
570C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3367C2
socleC22×C61D42
prime radicalC2×D8×C61D4
hypercenter#3367D61
hypocenterC61#20306
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
2. #21458102C2semidirect
3. #21458096C2semidirect
4. #21445427C2semidirect
5. #21445373C2semidirect
6. #21445370C2semidirect
7. #21445368C2semidirect
8. #21445364C2semidirect
9. #21445075C2semidirect
10. #21445073C2semidirect
11. #21445068C2semidirect
12. #21445067C2semidirect
13. #21444714C2semidirect
352. C61#20306semidirect

Maximal subgroups

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

subgroupindex
#214585352
#214581022
#214580962
#214454272
#214453732
#214453702
#214453682
#214453642
#214450752
#214450732
#214450682
#214450672
#214447142
#214447042
C61×#33672
#2030661