Finite Group Databasebeta

← #29670511

Subgroups — #29670511

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458504C211yesmaximal, characteristic, complemented
2#21458234C211yesmaximal, characteristic
3#21458113C211yesmaximal, characteristic
4#21445467C211yesmaximal, characteristic, complemented
5#21445368C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445239C211yesmaximal, characteristic, complemented
8#21445201C211yesmaximal, characteristic, complemented
9#21445074C211yesmaximal, characteristic, complemented
10#21445068C211yesmaximal, characteristic, complemented
11#21445045C211yesmaximal, characteristic
12#21444977C211yesmaximal, characteristic, complemented
13#21444663C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic, complemented
15C61×#3359C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840477C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840160C2211yescharacteristic
20#16840119—21no—
21#16840114C2211yescharacteristic
22#16840114C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840101—21no—
25#16840100—21no—
26#16840085—21no—
27#16840066—21no—
28#16840057C2211yescharacteristic
29#16840057C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16840039C2211yescharacteristic
32#16840010—21no—
33#16839988—21no—
34#16839984—21no—
35#16839972C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839901—21no—
38Q8×#92418C2211yescharacteristic
39C4×#11758202—21no—
40C4×#11758201C2211yescharacteristic
41#16839840C2211yescharacteristic
42C8×D244C2211yescharacteristic
43#16839797—21no—
44#16839771—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#557C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487—21no—
59C61×#487C2211yescharacteristic
60C61×#475—21no—
61C61×#475C2211yescharacteristic
62C61×#461—21no—
63C61×#461C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758201—21no—
69C2×#11758201D411yescharacteristic
70C2×#11758194—21no—
71C2×C8×D61—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519772—41no—
75#14519765—21no—
76#14519763—41no—
77#14519753—21no—
78#14519751—21no—
79#14519748—21no—
80C4×Dic122—21no—
81C4×D244C2311yescharacteristic
82#14519736—21no—
83#14519735—21no—
84#14519735—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—41no—
90#14519709—21no—
91#14519709—21no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—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—41no—
107#14519698—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#106×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C4×C8×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×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C2×C22⋊D61—41no—
155C2×D244C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159SD16×C61—41no—
160SD16×C61—42no—
161C2×C8×C61—21no—
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—41no—
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—41no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—41no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184#11758202—42no—
185#11758201—22no—
186#11758201—81no—
187#11758198—21no—
188#11758198—41no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—41no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199#11758194—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C8×D61—42no—
207C23×C61—21no—
208C22×D61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—82no—
217Q8×C61#13512yes—
218D4×C61—21no—
219D4×C61—21no—
220C2×C4×C61—21no—
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—82no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C22⋊D61—161no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237D244—21no—
238D244—21no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—41no—
242Dic122—41no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#19832—611nomaximal, Sylow
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61D4211yescharacteristic
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—22no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61C2×#13511yescharacteristic
270C4×C61#57511yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—41no—
274Dic61—81no—
275Dic61—81no—
276#3364—611no—
277#3359D6111yescharacteristic, complemented
278#3340—611no—
279#3329—611no—
280#1718—611no—
281#1699—611no—
282#1684—611no—
283#1679—611no—
284#1672—611no—
285#1650—611no—
286#1649—611no—
287#1646—611no—
288#1636—611no—
289#1583—611no—
290SD16⋊C8—611no—
291C2×C61—81no—
292C2×C61#326911yescharacteristic
293C2×C61#328211yescharacteristic
294C2×C61#328911yescharacteristic
295D61—81no—
296#557C2×D6111yescharacteristic
297#556—611no—
298#555—611no—
299D4×Q8C2×D6111yescharacteristic
300#500—611no—
301#498—611no—
302#488—1221no—
303#487—21no—
304#487—611no—
305#487—611no—
306#487—611no—
307#487C2×D6111yescharacteristic
308#485—1221no—
309#485—1221no—
310#482—1221no—
311#479—1221no—
312#477—611no—
313#477—611no—
314#475—21no—
315#475C2×D6111yescharacteristic
316#474—611no—
317#474—611no—
318#468—1221no—
319#465—1221no—
320#464—1221no—
321#462—611no—
322#461—21no—
323#461—611no—
324#461C2×D6111yescharacteristic
325#448—1221no—
326C8×Q8—611no—
327C8×Q8C2×D6111yescharacteristic
328C4×Q16—1221no—
329C4×SD16—21no—
330C4×SD16—611no—
331C4×SD16C2×D6111yescharacteristic
332#436—611no—
333C8×D4—611no—
334#427—1221no—
335#419—1221no—
336#335—611no—
337#334—611no—
338#333—611no—
339#332—611no—
340#332—611no—
341#332—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344D4⋊C8—611no—
345D4⋊C8—611no—
346#322—611no—
347C61#1983211yescharacteristic, complemented, Sylow
348C22×Q8—21no—
349C2×Q16—1221no—
350C2×SD16—21no—
351C2×SD16—611no—
352C2×SD16—1221no—
353C2×SD16C22⋊D6111yescharacteristic
354C2×M16—1221no—
355C22×C8—1221no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—611no—
359C4⋊Q8—611no—
360C4⋊Q8C22×D6111yescharacteristic
361C4⋊Q8C22×D6111yescharacteristic
362#126—2441no—
363#125—21no—
364#125—41no—
365#124—1221no—
366#124—2441no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369C22⋊Q8—1221no—
370#121—1221no—
371#121—1221no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—1221no—
375C4×Q8C22×D6111yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×D4—21no—
378C4×D4—611no—
379C4×D4C22×D6111yescharacteristic
380#117—1221no—
381#117—1221no—
382#117—1221no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#107—2441no—
388#106—21no—
389#106—611no—
390#106—1221no—
391#106—1221no—
392#106C22⋊D6111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—611no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—2441no—
413#103C22⋊D6111yescharacteristic
414#102—611no—
415#102—1221no—
416#102—1221no—
417#102C22⋊D6111yescharacteristic
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C4×C8—21no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—42no—
429C2×Q8—81no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8D4×D6111yescharacteristic
433C2×Q8C2×C22⋊D6111yescharacteristic
434C2×D4—611no—
435C2×D4—2441no—
436C2×D4C2×C22⋊D6111yescharacteristic
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—1221no—
440Q16—2442no—
441SD16—41no—
442SD16—42no—
443SD16—1222no—
444SD16—4881no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—2442no—
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—2441no—
472C4⋊C4D4×D6111yescharacteristic
473C4⋊C4C2×C22⋊D6111yescharacteristic
474C4⋊C4C2×C22⋊D6111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—1221no—
478C22⋊C4—2441no—
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C22⋊C4—2441no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—2441no—
486C42—2441no—
487C42C23×D6111yescharacteristic
488C23—21no—
489C23—1221no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8—4881no—
499Q8—2441no—
500Q8—2441no—
501Q8#1451979812yes—
502D4—21no—
503D4—21no—
504D4—1221no—
505D4—1221no—
506D4—9761no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—1221no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4#1451982211yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22D4×C22⋊D6111yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—4881no—
550C4—4881no—
551C4—2441no—
552C4C2×#1451979811yescharacteristic
553C4#1684056011yescharacteristic
554C4#1684056811yescharacteristic
555C4#1684057711yescharacteristic
556C2—81no—
557C2—4881no—
558C2#2145737511yescharacteristic
559C2#2145752611yescharacteristic
560C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3359C2
socleC22×C61D42
prime radical#16840477C22
hypercenter#3359D61
hypocenterC61#19832
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3359

Complements

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

NH ≅ G/Ntype
1. #21458504C2semidirect
4. #21445467C2semidirect
5. #21445368C2semidirect
6. #21445275C2semidirect
7. #21445239C2semidirect
8. #21445201C2semidirect
9. #21445074C2semidirect
10. #21445068C2semidirect
12. #21444977C2semidirect
13. #21444663C2semidirect
14. #21444629C2semidirect
15. C61×#3359C2semidirect
277. #3359D61semidirect
347. C61#19832semidirect

Maximal subgroups

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

subgroupindex
#214585042
#214582342
#214581132
#214454672
#214453682
#214452752
#214452392
#214452012
#214450742
#214450682
#214450452
#214449772
#214446632
#214446292
C61×#33592
#1983261