Finite Group Databasebeta

← #29670359

Subgroups — #29670359

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458694C211yesmaximal, characteristic, complemented
2#21458459C211yesmaximal, characteristic, complemented
3#21457678C211yesmaximal, characteristic
4#21445466C211yesmaximal, characteristic, complemented
5#21445366C211yesmaximal, characteristic, complemented
6#21445274C211yesmaximal, characteristic, complemented
7#21445251C211yesmaximal, characteristic, complemented
8#21445196C211yesmaximal, characteristic, complemented
9#21445059C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic
11#21445026C211yesmaximal, characteristic, complemented
12#21444983C211yesmaximal, characteristic, complemented
13#21444660C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3331C211yesmaximal, characteristic
16#16840490C2211yescharacteristic
17D4×Dic122C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840161—21no—
20#16840158C2211yescharacteristic
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840111—21no—
25#16840092—21no—
26#16840066—21no—
27#16840062—21no—
28#16840054C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840046—21no—
31#16840044C2211yescharacteristic
32#16840042C2211yescharacteristic
33#16839989—21no—
34#16839967C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839965—21no—
37#16839900—21no—
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40#16839853—21no—
41C4×#11758200—21no—
42C4×#11758200C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519700—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#483—21no—
60C61×#476C2211yescharacteristic
61C61×#470—21no—
62C61×#462C2211yescharacteristic
63C61×#452—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#417—21no—
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200D411yescharacteristic
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519776—21no—
75#14519775—21no—
76#14519769—21no—
77#14519767—41no—
78#14519756—21no—
79#14519754—41no—
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83D4×Dic61—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—41no—
87#14519708—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—41no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700D411yescharacteristic
108#14519698—21no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×Q16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133#106×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—41no—
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C22×Dic61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—42no—
160C2×Dic122—41no—
161C2×Dic122—81no—
162C2×Dic122C2×D411yescharacteristic
163Q16×C61—81no—
164SD16×C61—22no—
165M16×C61—81no—
166C2×C8×C61—21no—
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×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758200—22no—
188#11758200—42no—
189#11758200—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—81no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—81no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—82no—
220D4×C61#13512yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—82no—
232C2×C4×C61—161no—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—82no—
241Dic122—21no—
242Dic122—41no—
243Dic122—41no—
244Dic122—41no—
245Dic122—41no—
246Dic122—82no—
247Dic122#13712yes—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—41no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#19822—611nomaximal, Sylow
258C22×C61—22no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61D4211yescharacteristic
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61C2×#13511yescharacteristic
273C4×C61C2×#13711yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57711yescharacteristic
276Dic61—22no—
277Dic61—41no—
278Dic61—81no—
279Dic61—81no—
280#3381—611no—
281#3359—611no—
282#3331D6111yescharacteristic
283#3298—611no—
284#1718—611no—
285#1699—611no—
286#1684—611no—
287#1680—611no—
288#1671—611no—
289#1648—611no—
290#1647—611no—
291#1643—611no—
292#1637—611no—
293#1583—611no—
294SD16⋊C8—611no—
295C2×C61—42no—
296C2×C61—81no—
297C2×C61#326611yescharacteristic
298C2×C61#328211yescharacteristic
299C2×C61#328911yescharacteristic
300#557—611no—
301#554C2×D6111yescharacteristic
302D4×Q8—611no—
303#547C2×D6111yescharacteristic
304#500—611no—
305#499—1221no—
306#498—611no—
307#487—611no—
308#487—611no—
309#487—611no—
310#487—1221no—
311#487C2×D6111yescharacteristic
312#483—21no—
313#483—1221no—
314#479—1221no—
315#478—1221no—
316#477—611no—
317#476C2×D6111yescharacteristic
318#475—611no—
319#475—611no—
320#475—1221no—
321#474—611no—
322#470—21no—
323#465—1221no—
324#462C2×D6111yescharacteristic
325#461—611no—
326#461—611no—
327#461—1221no—
328#452—21no—
329#448—1221no—
330C8×Q8—611no—
331C8×Q8—611no—
332C4×SD16—611no—
333C4×SD16—1221no—
334C4×SD16—1221no—
335C4×SD16C2×D6111yescharacteristic
336#436C2×D6111yescharacteristic
337C8×D4—611no—
338#417—21no—
339C2×#103—1221no—
340#335—611no—
341#334—611no—
342#333—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350#322—611no—
351C61#1982211yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—1221no—
354C2×Q16—21no—
355C2×SD16—611no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×SD16C22⋊D6111yescharacteristic
359C2×M16—21no—
360C22×C8—1221no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8—1221no—
364C4⋊Q8—1221no—
365C4⋊Q8C22×D6111yescharacteristic
366C4⋊Q8C22×D6111yescharacteristic
367#125—21no—
368#125—1221no—
369#125—2441no—
370#123—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374C22⋊Q8—1221no—
375C22⋊Q8—2441no—
376#121—21no—
377C4×Q8—611no—
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384C4×D4C22×D6111yescharacteristic
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387#107—1221no—
388#107—1221no—
389#107—2441no—
390#106—21no—
391#106—611no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395#106—1221no—
396#106C22⋊D6111yescharacteristic
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—611no—
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—2441no—
417#103C22⋊D6111yescharacteristic
418#102—21no—
419#102—611no—
420#102—1221no—
421#102C22⋊D6111yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—1221no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429#41—42no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—611no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—4881no—
437C2×Q8—2441no—
438C2×Q8—2442no—
439C2×Q8C2×C22⋊D6111yescharacteristic
440C2×D4—41no—
441C2×D4D4×D6111yescharacteristic
442C2×D4C2×C22⋊D6111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—2441no—
448Q16—81no—
449SD16—22no—
450SD16—1222no—
451SD16—4881no—
452SD16—2442no—
453M16—81no—
454C2×C8—21no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—4881no—
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
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⋊C4—2441no—
481C4⋊C4—2441no—
482C4⋊C4D4×D6111yescharacteristic
483C4⋊C4C2×C22⋊D6111yescharacteristic
484C4⋊C4C2×C22⋊D6111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—2441no—
490C42—21no—
491C42—1221no—
492C42—2441no—
493C42C23×D6111yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—612no—
502Q8—1221no—
503Q8—4882no—
504Q8—2441no—
505Q8—2441no—
506Q8—2441no—
507Q8—2441no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—82no—
512D4#1451979712yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—161no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—4882no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4C2×D4×D6111yescharacteristic
531C2×C4C22×C22⋊D6111yescharacteristic
532C2×C4#1451982211yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—1221no—
537C8—1221no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D4×C22⋊D6111yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—1222no—
557C4—4881no—
558C4—4881no—
559C4—2441no—
560C4C2×#1451979711yescharacteristic
561C4#137×D6111yescharacteristic
562C4#1684057111yescharacteristic
563C4#1684057311yescharacteristic
564C2—42no—
565C2—81no—
566C2#2145732311yescharacteristic
567C2#2145752211yescharacteristic
568C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3331C2
socleC22×C61D42
prime radicalC61×#547C22
hypercenter#3331D61
hypocenterC61#19822
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3331

Complements

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

NH ≅ G/Ntype
1. #21458694C2semidirect
2. #21458459C2semidirect
4. #21445466C2semidirect
5. #21445366C2semidirect
6. #21445274C2semidirect
7. #21445251C2semidirect
8. #21445196C2semidirect
9. #21445059C2semidirect
11. #21445026C2semidirect
12. #21444983C2semidirect
13. #21444660C2semidirect
14. SD16⋊#92418C2semidirect
351. C61#19822semidirect

Maximal subgroups

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

subgroupindex
#214586942
#214584592
#214576782
#214454662
#214453662
#214452742
#214452512
#214451962
#214450592
#214450542
#214450262
#214449832
#214446602
SD16⋊#924182
C61×#33312
#1982261