Finite Group Databasebeta

← #29676938

Subgroups — #29676938

Order 15616.

574 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#21458729C211yesmaximal, characteristic, complemented
2#21458557C211yesmaximal, characteristic, complemented
3#21458403C211yesmaximal, characteristic
4#21445427C211yesmaximal, characteristic, complemented
5#21445398C211yesmaximal, characteristic, complemented
6#21445394C211yesmaximal, characteristic, complemented
7#21445340C211yesmaximal, characteristic, complemented
8#21445335C211yesmaximal, characteristic, complemented
9#21445038C211yesmaximal, characteristic, complemented
10#21445033C211yesmaximal, characteristic, complemented
11#21444989C211yesmaximal, characteristic, complemented
12#21444970C211yesmaximal, characteristic
13#21444710C211yesmaximal, characteristic, complemented
14#21444707C211yesmaximal, characteristic, complemented
15C61×#3331C211yesmaximal, characteristic
16Q8×Dic122C2211yescharacteristic
17#16840482C2211yescharacteristic
18#16840172—21no—
19#16840165C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840120—21no—
22#16840114C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840097—21no—
26#16840083—21no—
27#16840066—21no—
28#16840054C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840046—21no—
32#16840044C2211yescharacteristic
33#16840042—21no—
34#16840042C2211yescharacteristic
35#16840006—21no—
36#16839982—21no—
37#16839972C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839892C2211yescharacteristic
40#16839866—21no—
41#16839862—21no—
42C4×#11758200C2211yescharacteristic
43#16839840C2211yescharacteristic
44#16839802—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
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—
67C2×#11758202—21no—
68C2×#11758200D411yescharacteristic
69C2×#11758194—21no—
70#14519777—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519776—21no—
74#14519776—41no—
75#14519770—41no—
76#14519764—21no—
77#14519756—21no—
78Q8×Dic61—21no—
79C4×Dic122—21no—
80C4×Dic122C2311yescharacteristic
81#14519742—21no—
82#14519736—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519702—21no—
99#14519702—21no—
100#14519701—41no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—41no—
105#14519700D411yescharacteristic
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
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—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—41no—
159C2×Dic122C2×D411yescharacteristic
160Q16×C61—81no—
161SD16×C61—41no—
162M16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—41no—
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—
181C42×C61—21no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185#11758202—42no—
186#11758200—22no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—41no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199#11758194—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—21no—
207C23×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—82no—
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—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—82no—
229C2×C4×C61—161no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237Dic122—21no—
238Dic122—21no—
239Dic122—41no—
240Dic122—41no—
241Dic122—81no—
242Dic122—161no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418#13712yes—
252#20293—611nomaximal, Sylow
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61D4211yescharacteristic
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61C2×#13711yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—41no—
272Dic61—41no—
273Dic61—81no—
274Dic61—81no—
275#3385—611no—
276#3369—611no—
277#3353—611no—
278#3331D6111yescharacteristic
279#1710—611no—
280#1704—611no—
281#1703—611no—
282#1695—611no—
283#1694—611no—
284#1645—611no—
285#1644—611no—
286#1638—611no—
287#1635—611no—
288#1590—611no—
289#1590—611no—
290C2×C61—81no—
291C2×C61—81no—
292C2×C61#327511yescharacteristic
293C2×C61#327611yescharacteristic
294C2×C61#329011yescharacteristic
295Q82—611no—
296#556—611no—
297#554C2×D6111yescharacteristic
298#547C2×D6111yescharacteristic
299#501—1221no—
300#500—611no—
301#500—611no—
302#489—1221no—
303#487—611no—
304#487—611no—
305#487—611no—
306#487C2×D6111yescharacteristic
307#484—1221no—
308#483—21no—
309#482—1221no—
310#479—1221no—
311#477—611no—
312#476—611no—
313#476—611no—
314#476C2×D6111yescharacteristic
315#475—611no—
316#475—1221no—
317#474—611no—
318#474—1221no—
319#470—21no—
320#468—1221no—
321#464—1221no—
322#462—611no—
323#462C2×D6111yescharacteristic
324#452—21no—
325#446—611no—
326#446—611no—
327#441—1221no—
328#440—1221no—
329C4×SD16—611no—
330C4×SD16C2×D6111yescharacteristic
331#436—611no—
332#436C2×D6111yescharacteristic
333#428—1221no—
334#417—21no—
335#334—611no—
336#334—611no—
337#333—611no—
338#333—611no—
339#332—611no—
340#332—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345C82—611no—
346C61#2029311yescharacteristic, complemented, Sylow
347C2×#41—21no—
348C2×Q16—21no—
349C2×Q16—1221no—
350C2×SD16—611no—
351C2×SD16C22⋊D6111yescharacteristic
352C2×M16—21no—
353C2×M16—1221no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8—2441no—
359C4⋊Q8C22×D6111yescharacteristic
360C4⋊Q8C22×D6111yescharacteristic
361#126—2441no—
362#125—21no—
363#124—1221no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—1221no—
369#121—21no—
370C4×Q8—611no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8—1221no—
374C4×Q8C22×D6111yescharacteristic
375C4×D4—21no—
376C4×D4C22×D6111yescharacteristic
377C4×D4C22×D6111yescharacteristic
378#117—1221no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#106—21no—
388#106—611no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392#106C22⋊D6111yescharacteristic
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—611no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—2441no—
409#103—2441no—
410#103C22⋊D6111yescharacteristic
411#102—21no—
412#102—611no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102C22⋊D6111yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—1221no—
419#97—1221no—
420#97—1221no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8C22×D6111yescharacteristic
424#41—42no—
425#41—81no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—2441no—
432C2×Q8C2×C22⋊D6111yescharacteristic
433C2×D4—41no—
434C2×D4D4×D6111yescharacteristic
435C2×D4C2×C22⋊D6111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440Q16—81no—
441Q16—2442no—
442SD16—41no—
443SD16—1222no—
444M16—81no—
445M16—2442no—
446C2×C8—21no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8C2×C22⋊D6111yescharacteristic
454C2×C8C2×C22⋊D6111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4D4×D6111yescharacteristic
473C4⋊C4C2×C22⋊D6111yescharacteristic
474C4⋊C4C2×C22⋊D6111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C42—21no—
482C42—1221no—
483C42—2441no—
484C42—2441no—
485C42C23×D6111yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—1221no—
494Q8—1221no—
495Q8—9761no—
496Q8—4881no—
497Q8—2441no—
498Q8—2441no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—82no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—82no—
515C2×C4—161no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C22×C22⋊D6111yescharacteristic
522C2×C4#1451982211yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—612no—
527C8—1221no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D4×C22⋊D6111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—4881no—
547C4—4881no—
548C4—2441no—
549C4—2441no—
550C4#137×D6111yescharacteristic
551C4#1684056011yescharacteristic
552C4#1684057311yescharacteristic
553C4#1684057811yescharacteristic
554C2—81no—
555C2—81no—
556C2#2145744611yescharacteristic
557C2#2145745911yescharacteristic
558C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3331C2
socleC22×C61D42
prime radicalC61×#547C22
hypercenter#3331D61
hypocenterC61#20293
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. #21458729C2semidirect
2. #21458557C2semidirect
4. #21445427C2semidirect
5. #21445398C2semidirect
6. #21445394C2semidirect
7. #21445340C2semidirect
8. #21445335C2semidirect
9. #21445038C2semidirect
10. #21445033C2semidirect
11. #21444989C2semidirect
13. #21444710C2semidirect
14. #21444707C2semidirect
346. C61#20293semidirect

Maximal subgroups

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

subgroupindex
#214587292
#214585572
#214584032
#214454272
#214453982
#214453942
#214453402
#214453352
#214450382
#214450332
#214449892
#214449702
#214447102
#214447072
C61×#33312
#2029361