Finite Group Databasebeta

← #29670751

Subgroups — #29670751

Order 15616.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458559C211yesmaximal, characteristic
2#21458504C211yesmaximal, characteristic
3#21458251C211yesmaximal, characteristic
4#21445468C211yesmaximal, characteristic, complemented
5#21445375C211yesmaximal, characteristic, complemented
6#21445279C211yesmaximal, characteristic, complemented
7#21445267C211yesmaximal, characteristic
8#21445213C211yesmaximal, characteristic, complemented
9#21445096C211yesmaximal, characteristic, complemented
10#21445087C211yesmaximal, characteristic
11#21445040C211yesmaximal, characteristic, complemented
12#21444990C211yesmaximal, characteristic
13#21444670C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic
15C61×#3363C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840485C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840124—21no—
21#16840119—21no—
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840102—21no—
26#16840102—21no—
27#16840066—21no—
28#16840049C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840044—21no—
32#16840039C2211yescharacteristic
33#16840000—21no—
34#16839984—21no—
35#16839984—21no—
36#16839972C2211yescharacteristic
37#16839972C2211yescharacteristic
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839867—21no—
41C4×#11758202—21no—
42C4×#11758201C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#16839799—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#487—21no—
59C61×#487C2211yescharacteristic
60C61×#477—21no—
61C61×#477C2211yescharacteristic
62C61×#462—21no—
63C61×#462C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×Q16×C61—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758201D411yescharacteristic
70C2×C8×D61—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519772—41no—
74#14519772—41no—
75#14519765—21no—
76#14519765—21no—
77#14519753—21no—
78#14519753—21no—
79C4×Dic122—21no—
80C4×Dic122—21no—
81C4×D244C2311yescharacteristic
82#14519735—21no—
83#14519735—21no—
84#14519711—21no—
85#14519711—21no—
86#14519710—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—41no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701—21no—
99#14519701—41no—
100#14519701D411yescharacteristic
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—41no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
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#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154Q16×C61—41no—
155Q16×C61—42no—
156C2×C8×C61—21no—
157C2×C8×C61C2×D411yescharacteristic
158C2×C8×C61C2×D411yescharacteristic
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—41no—
178C42×C61—41no—
179C42×C61C2411yescharacteristic
180#11758202—42no—
181#11758202—42no—
182#11758201—22no—
183#11758198—21no—
184#11758198—41no—
185#11758198—41no—
186#11758198—41no—
187#11758198—41no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—41no—
194#11758196—41no—
195C4×Dic61—41no—
196C4×Dic61—41no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C8×D61—42no—
204C22×D61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213Q8×C61—161no—
214Q8×C61#13512yes—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229D244—21no—
230D244—21no—
231C4×D61—41no—
232C4×D61—41no—
233Dic122—41no—
234Dic122—41no—
235Dic122—41no—
236Dic122—41no—
237C8×C61—21no—
238C8×C61—21no—
239C8×C61—41no—
240#92418—21no—
241#92418—21no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#19848—611nomaximal, Sylow
247C22×C61D4211yescharacteristic
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C4×C61—22no—
252C4×C61—21no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—81no—
259C4×C61—81no—
260C4×C61C2×#13511yescharacteristic
261C4×C61#57511yescharacteristic
262C4×C61#57811yescharacteristic
263C4×C61#57811yescharacteristic
264Dic61—41no—
265Dic61—81no—
266Dic61—81no—
267#3369—611no—
268#3364—611no—
269#3363D6111yescharacteristic, complemented
270#3342—611no—
271#1718—611no—
272#1700—611no—
273#1684—611no—
274#1683—611no—
275#1674—611no—
276#1653—611no—
277#1652—611no—
278#1645—611no—
279#1638—611no—
280#1584—611no—
281SD16⋊C8—611no—
282C2×C61#326911yescharacteristic
283C2×C61#328511yescharacteristic
284C2×C61#328911yescharacteristic
285D61—81no—
286Q82C2×D6111yescharacteristic
287#557C2×D6111yescharacteristic
288#556—611no—
289#556—611no—
290#500—611no—
291#498—611no—
292#489—1221no—
293#488—1221no—
294#487—21no—
295#487—611no—
296#487—611no—
297#487—611no—
298#487C2×D6111yescharacteristic
299#485—1221no—
300#485—1221no—
301#479—1221no—
302#477—21no—
303#477C2×D6111yescharacteristic
304#476—611no—
305#475—611no—
306#475—611no—
307#475—1221no—
308#474—611no—
309#467—1221no—
310#464—1221no—
311#464—1221no—
312#462—21no—
313#462—611no—
314#462—611no—
315#462C2×D6111yescharacteristic
316#446—611no—
317C8×Q8—611no—
318C8×Q8C2×D6111yescharacteristic
319#441—1221no—
320C4×Q16—21no—
321C4×Q16—1221no—
322C4×Q16C2×D6111yescharacteristic
323C4×SD16—611no—
324C8×D4—611no—
325#427—1221no—
326#335—611no—
327#335—611no—
328#333—611no—
329#332—611no—
330#332—611no—
331#332—611no—
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335D4⋊C8—611no—
336#322—611no—
337C61#1984811yescharacteristic, complemented, Sylow
338C2×Q16—21no—
339C2×Q16—1221no—
340C2×Q16—1221no—
341C2×Q16C22⋊D6111yescharacteristic
342C2×SD16—611no—
343C22×C8—1221no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—41no—
348C4⋊Q8—611no—
349C4⋊Q8—611no—
350C4⋊Q8C22×D6111yescharacteristic
351C4⋊Q8C22×D6111yescharacteristic
352#126—2441no—
353#126—2441no—
354#125—21no—
355#125—41no—
356#124—1221no—
357#124—1221no—
358C22⋊Q8—1221no—
359C22⋊Q8—1221no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8C22×D6111yescharacteristic
367C4×Q8C22×D6111yescharacteristic
368C4×Q8C22×D6111yescharacteristic
369C4×D4—611no—
370#117—1221no—
371#117—1221no—
372#107—21no—
373#107—1221no—
374#107—1221no—
375#107—1221no—
376#107C22⋊D6111yescharacteristic
377#106—611no—
378#106—1221no—
379#106—1221no—
380#106—1221no—
381#106—2441no—
382C4⋊C8—21no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8C22×D6111yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—611no—
394#103—1221no—
395#103—1221no—
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—2441no—
403#103C22⋊D6111yescharacteristic
404#103C22⋊D6111yescharacteristic
405#102—611no—
406#102—1221no—
407#102—1221no—
408C22⋊C8—1221no—
409#97—1221no—
410C4×C8—21no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8—1221no—
414C4×C8C22×D6111yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—41no—
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8D4×D6111yescharacteristic
421C2×Q8C2×C22⋊D6111yescharacteristic
422C2×Q8C2×C22⋊D6111yescharacteristic
423C2×D4—611no—
424C22×C4—1221no—
425Q16—41no—
426Q16—42no—
427Q16—2442no—
428Q16—2442no—
429SD16—1222no—
430C2×C8—21no—
431C2×C8—611no—
432C2×C8—611no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—2442no—
438C2×C8C2×C22⋊D6111yescharacteristic
439C2×C8C2×C22⋊D6111yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—2441no—
458C4⋊C4—2441no—
459C4⋊C4D4×D6111yescharacteristic
460C4⋊C4C2×C22⋊D6111yescharacteristic
461C4⋊C4C2×C22⋊D6111yescharacteristic
462C22⋊C4—1221no—
463C22⋊C4—2441no—
464C22⋊C4—2441no—
465C22⋊C4—2441no—
466C22⋊C4—2441no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42—2441no—
473C42—2441no—
474C42C23×D6111yescharacteristic
475C23—1221no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—161no—
485Q8—2441no—
486Q8—2441no—
487Q8—2441no—
488Q8—2441no—
489Q8#1451980012yes—
490D4—1221no—
491D4—1221no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—1221no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4C2×D4×D6111yescharacteristic
506C2×C4C22×C22⋊D6111yescharacteristic
507C2×C4#1451982211yescharacteristic
508C8—21no—
509C8—21no—
510C8—41no—
511C8—1221no—
512C8—1221no—
513C8—2441no—
514C8—2441no—
515C8—2441no—
516C8—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22D4×C22⋊D6111yescharacteristic
521C4—22no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—81no—
529C4—81no—
530C4—4881no—
531C4—4881no—
532C4—2441no—
533C4C2×#1451980011yescharacteristic
534C4#1684056011yescharacteristic
535C4#1684057511yescharacteristic
536C4#1684057711yescharacteristic
537C2—4881no—
538C2#2145737511yescharacteristic
539C2#2145756011yescharacteristic
540C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3363C2
socleC22×C61D42
prime radicalC2×D244C2×D4
hypercenter#3363D61
hypocenterC61#19848
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
4. #21445468C2semidirect
5. #21445375C2semidirect
6. #21445279C2semidirect
8. #21445213C2semidirect
9. #21445096C2semidirect
11. #21445040C2semidirect
13. #21444670C2semidirect
15. C61×#3363C2semidirect
269. #3363D61semidirect
337. C61#19848semidirect

Maximal subgroups

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

subgroupindex
#214585592
#214585042
#214582512
#214454682
#214453752
#214452792
#214452672
#214452132
#214450962
#214450872
#214450402
#214449902
#214446702
#214446292
C61×#33632
#1984861