Finite Group Databasebeta

← #29670876

Subgroups — #29670876

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458846C211yesmaximal, characteristic, complemented
2#21458234C211yesmaximal, characteristic
3#21458226C211yesmaximal, characteristic
4#21445454C211yesmaximal, characteristic, complemented
5#21445323C211yesmaximal, characteristic, complemented
6#21445239C211yesmaximal, characteristic, complemented
7#21445201C211yesmaximal, characteristic, complemented
8#21445182C211yesmaximal, characteristic, complemented
9#21445089C211yesmaximal, characteristic, complemented
10#21445087C211yesmaximal, characteristic, complemented
11#21445046C211yesmaximal, characteristic
12#21444977C211yesmaximal, characteristic, complemented
13#21444656C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic, complemented
15C61×#3364C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840477C2211yescharacteristic
18#16840160C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840154—21no—
22#16840141C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840101—21no—
25#16840100—21no—
26#16840086—21no—
27#16840085—21no—
28#16840057C2211yescharacteristic
29#16840057C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16840039C2211yescharacteristic
32#16839993—21no—
33#16839988—21no—
34#16839984—21no—
35#16839972C2211yescharacteristic
36#16839969—21no—
37#16839964C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839867—21no—
40C4×#11758201C2211yescharacteristic
41C8×D244C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839798—21no—
44#16839797—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
57C61×#556C2211yescharacteristic
58C61×#488—21no—
59C61×#487C2211yescharacteristic
60C61×#479—21no—
61C61×#474C2211yescharacteristic
62C61×#464—21no—
63C61×#462C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×Q16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758201—21no—
71C2×#11758201D411yescharacteristic
72C22×#92418—21no—
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519772—41no—
77#14519765—21no—
78#14519763—41no—
79#14519753—21no—
80#14519751—21no—
81#14519748—21no—
82C4×Dic122—21no—
83C4×D244C2311yescharacteristic
84#14519736—21no—
85#14519735—21no—
86#14519735—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—41no—
96#14519708D411yescharacteristic
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—41no—
107#14519698—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111#14519689—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×SD16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#126×C61—41no—
121#125×C61—21no—
122#125×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#107×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×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—41no—
151C2×D244C2×D411yescharacteristic
152C2×C4×D61—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155Q16×C61—42no—
156SD16×C61—41no—
157C2×C8×C61—21no—
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
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×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—41no—
179C42×C61—41no—
180C42×C61C2411yescharacteristic
181C22⋊Dic61—41no—
182#11758202—42no—
183#11758202—81no—
184#11758202—81no—
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—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—42no—
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—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217D4×C61—21no—
218D4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C22⋊D61—161no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235D244—21no—
236D244—21no—
237C4×D61—41no—
238C4×D61—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418#13512yes—
251#19856—611nomaximal, Sylow
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61D4211yescharacteristic
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61C2×#13511yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274#3398—611no—
275#3364D6111yescharacteristic, complemented
276#3340—611no—
277#3340—611no—
278#1716—611no—
279#1692—611no—
280#1679—611no—
281#1672—611no—
282#1669—611no—
283#1652—611no—
284#1652—611no—
285#1646—611no—
286#1636—611no—
287#1582—611no—
288SD16⋊C8—611no—
289C2×C61—81no—
290C2×C61#326911yescharacteristic
291C2×C61#328411yescharacteristic
292C2×C61#328911yescharacteristic
293D61—81no—
294#557C2×D6111yescharacteristic
295#556—611no—
296#556C2×D6111yescharacteristic
297#555—611no—
298#498—611no—
299#498—611no—
300#498—611no—
301#497—1221no—
302#494—611no—
303#488—21no—
304#487—611no—
305#487C2×D6111yescharacteristic
306#485—1221no—
307#485—1221no—
308#482—1221no—
309#482—1221no—
310#479—21no—
311#477—611no—
312#477—611no—
313#474—611no—
314#474—611no—
315#474C2×D6111yescharacteristic
316#465—1221no—
317#465—1221no—
318#464—21no—
319#464—1221no—
320#462—611no—
321#462—1221no—
322#462C2×D6111yescharacteristic
323#461—611no—
324#446—611no—
325C8×Q8C2×D6111yescharacteristic
326#441—1221no—
327C4×Q16—21no—
328C4×SD16—611no—
329C4×SD16C2×D6111yescharacteristic
330C8×D4—611no—
331C8×D4—611no—
332#427—1221no—
333#427—1221no—
334#335—611no—
335#334—611no—
336#333—611no—
337#332—611no—
338#332—611no—
339#332—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345C61#1985611yescharacteristic, complemented, Sylow
346C2×Q16—21no—
347C2×Q16—1221no—
348C2×Q16—1221no—
349C2×Q16—1221no—
350C2×SD16—611no—
351C2×SD16—1221no—
352C2×SD16C22⋊D6111yescharacteristic
353C22×C8—1221no—
354C22×C8—1221no—
355C4⋊Q8—21no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8C22×D6111yescharacteristic
359C4⋊Q8C22×D6111yescharacteristic
360#126—41no—
361#126—2441no—
362#125—21no—
363#125—41no—
364#124—21no—
365#124—1221no—
366#124—2441no—
367C22⋊Q8—21no—
368C22⋊Q8—1221no—
369#121—1221no—
370#121—1221no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—1221no—
375C4×Q8C22×D6111yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×D4—611no—
378C4×D4C22×D6111yescharacteristic
379#117—21no—
380#117—1221no—
381#117—1221no—
382#117—1221no—
383#107—21no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#106—611no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392#106—1221no—
393#106—2441no—
394#106C22⋊D6111yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—611no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—2441no—
410#103C22⋊D6111yescharacteristic
411#102—21no—
412#102—611no—
413#102—1221no—
414#102—1221no—
415#102C22⋊D6111yescharacteristic
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418#97—1221no—
419C4×C8—21no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8C22×D6111yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8D4×D6111yescharacteristic
428C2×Q8C2×C22⋊D6111yescharacteristic
429C2×D4—611no—
430C2×D4—2441no—
431C2×D4C2×C22⋊D6111yescharacteristic
432C22×C4—21no—
433C22×C4—1221no—
434Q16—42no—
435Q16—4881no—
436Q16—4881no—
437Q16—2442no—
438SD16—41no—
439SD16—1222no—
440SD16—4881no—
441C2×C8—21no—
442C2×C8—611no—
443C2×C8—611no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—2442no—
449C2×C8—2442no—
450C2×C8C2×C22⋊D6111yescharacteristic
451C2×C8C2×C22⋊D6111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—611no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—2441no—
468C4⋊C4D4×D6111yescharacteristic
469C4⋊C4C2×C22⋊D6111yescharacteristic
470C4⋊C4C2×C22⋊D6111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—1221no—
475C22⋊C4—2441no—
476C22⋊C4—2441no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—2441no—
484C42—2441no—
485C42C23×D6111yescharacteristic
486C23—21no—
487C23—1221no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—4881no—
497Q8—2441no—
498Q8—2441no—
499D4—21no—
500D4—21no—
501D4—1221no—
502D4—1221no—
503D4—9761no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—1221no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C22×C22⋊D6111yescharacteristic
520C2×C4#1451982211yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—612no—
525C8—1221no—
526C8—2441no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—2441no—
534C22—2441no—
535C22—2441no—
536C22D4×C22⋊D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—81no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4#135×D6111yescharacteristic
549C4#1684056011yescharacteristic
550C4#1684056911yescharacteristic
551C4#1684057711yescharacteristic
552C2—81no—
553C2—4881no—
554C2#2145737511yescharacteristic
555C2#2145754311yescharacteristic
556C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3364C2
socleC22×C61D42
prime radical#16840477C22
hypercenter#3364D61
hypocenterC61#19856
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3364

Complements

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

NH ≅ G/Ntype
1. #21458846C2semidirect
4. #21445454C2semidirect
5. #21445323C2semidirect
6. #21445239C2semidirect
7. #21445201C2semidirect
8. #21445182C2semidirect
9. #21445089C2semidirect
10. #21445087C2semidirect
12. #21444977C2semidirect
13. #21444656C2semidirect
14. #21444629C2semidirect
15. C61×#3364C2semidirect
275. #3364D61semidirect
345. C61#19856semidirect

Maximal subgroups

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

subgroupindex
#214588462
#214582342
#214582262
#214454542
#214453232
#214452392
#214452012
#214451822
#214450892
#214450872
#214450462
#214449772
#214446562
#214446292
C61×#33642
#1985661