Finite Group Databasebeta

← #29669991

Subgroups — #29669991

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458618C211yesmaximal, characteristic, complemented
2#21458459C211yesmaximal, characteristic
3#21457689C211yesmaximal, characteristic
4#21445463C211yesmaximal, characteristic, complemented
5#21445403C211yesmaximal, characteristic, complemented
6#21445249C211yesmaximal, characteristic, complemented
7#21445240C211yesmaximal, characteristic
8#21445198C211yesmaximal, characteristic, complemented
9#21445067C211yesmaximal, characteristic
10#21445061C211yesmaximal, characteristic, complemented
11#21445026C211yesmaximal, characteristic
12#21444975C211yesmaximal, characteristic, complemented
13#21444656C211yesmaximal, characteristic
14#21444636C211yesmaximal, characteristic, complemented
15C61×#3381C211yesmaximal, characteristic
16#16840490C2211yescharacteristic
17D4×Dic122C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840130—21no—
20#16840114C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840111—21no—
25#16840097—21no—
26#16840069—21no—
27#16840054C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840046—21no—
31#16840001—21no—
32#16839972C2211yescharacteristic
33#16839969—21no—
34#16839969C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839965—21no—
37#16839917—21no—
38#16839893C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40#16839867—21no—
41C4×#11758202C2211yescharacteristic
42#16839853—21no—
43D4×#92418C2211yescharacteristic
44C2×#14519700—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#499—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#478—21no—
62C61×#477C2211yescharacteristic
63C61×#474C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202D411yescharacteristic
71C2×#11758200—21no—
72C22×#92418—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519775—21no—
77#14519769—21no—
78#14519767—41no—
79#14519756—21no—
80#14519754—41no—
81C4×Dic122—21no—
82C4×Dic122C2311yescharacteristic
83#14519742—21no—
84D4×Dic61—21no—
85#14519710—21no—
86#14519710—41no—
87#14519710D411yescharacteristic
88#14519708—21no—
89#14519708—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519702—21no—
96#14519702—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—41no—
103#14519701D411yescharacteristic
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700—21no—
109#14519700D411yescharacteristic
110C22⋊#92418—21no—
111#14519688—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×SD16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61—41no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#106×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
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—
150C22×C4×C61—41no—
151C22×Dic61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—42no—
155C2×Dic122—41no—
156C2×Dic122—81no—
157C2×Dic122C2×D411yescharacteristic
158SD16×C61—22no—
159C2×C8×C61—21no—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—41no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182C22⋊Dic61—41no—
183#11758202—22no—
184#11758202—42no—
185#11758202—81no—
186#11758200—42no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—21no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—81no—
214D4×C61—21no—
215D4×C61#13712yes—
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×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—161no—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61H(5,𝔽2)11yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—82no—
234Dic122—21no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—82no—
240Dic122#13512yes—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244#92418—21no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#19797—611nomaximal, Sylow
251C22×C61—22no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61D4211yescharacteristic
255C4×C61—21no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61C2×#13511yescharacteristic
264C4×C61C2×#13711yescharacteristic
265C4×C61#57711yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—22no—
268Dic61—41no—
269Dic61—81no—
270Dic61—81no—
271#3381D6111yescharacteristic
272#3374—611no—
273#3359—611no—
274#3299—611no—
275#1718—611no—
276#1704—611no—
277#1680—611no—
278#1679—611no—
279#1672—611no—
280#1649—611no—
281#1648—611no—
282#1643—611no—
283#1636—611no—
284#1582—611no—
285#1579—611no—
286C2×C61—42no—
287C2×C61#327011yescharacteristic
288C2×C61#328211yescharacteristic
289C2×C61#328911yescharacteristic
290#557—611no—
291#557C2×D6111yescharacteristic
292#554C2×D6111yescharacteristic
293D4×Q8—611no—
294#500—611no—
295#499—21no—
296#498C2×D6111yescharacteristic
297#491—1221no—
298#487—611no—
299#487—611no—
300#487—611no—
301#487—611no—
302#487—1221no—
303#484—1221no—
304#479—21no—
305#479—1221no—
306#478—21no—
307#477—611no—
308#477C2×D6111yescharacteristic
309#475—611no—
310#475—611no—
311#475—1221no—
312#474C2×D6111yescharacteristic
313#467—1221no—
314#462—611no—
315#462—611no—
316#462—1221no—
317#461—611no—
318#461—1221no—
319#451—1221no—
320#446—611no—
321C8×Q8—611no—
322C8×Q8C2×D6111yescharacteristic
323#441—1221no—
324C4×Q16—611no—
325C4×SD16—21no—
326C4×SD16—1221no—
327C4×SD16C2×D6111yescharacteristic
328C8×D4—611no—
329C2×#103—1221no—
330#334—611no—
331#334—611no—
332#333—611no—
333#332—611no—
334#332—611no—
335#332—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339D4⋊C8—611no—
340#322—611no—
341C61#1979711yescharacteristic, complemented, Sylow
342C22×Q8—1221no—
343C2×Q16—611no—
344C2×Q16—1221no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×SD16C22⋊D6111yescharacteristic
348C22×C8—1221no—
349C4⋊Q8—21no—
350C4⋊Q8—611no—
351C4⋊Q8—611no—
352C4⋊Q8—1221no—
353C4⋊Q8—1221no—
354C4⋊Q8C22×D6111yescharacteristic
355C4⋊Q8C22×D6111yescharacteristic
356#125—21no—
357#125—21no—
358#125—41no—
359#125—1221no—
360#125—2441no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—1221no—
364C22⋊Q8—2441no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4—1221no—
374C4×D4C22×D6111yescharacteristic
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—611no—
379#107—1221no—
380#107—2441no—
381#106—21no—
382#106—21no—
383#106—1221no—
384#106—1221no—
385#106C22⋊D6111yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22×D6111yescharacteristic
393#103—21no—
394#103—611no—
395#103—611no—
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—2441no—
409#103C22⋊D6111yescharacteristic
410#102—21no—
411#102C22⋊D6111yescharacteristic
412C22⋊C8—1221no—
413#97—1221no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—1221no—
418C4×C8C22×D6111yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—611no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—4881no—
425C2×Q8—2441no—
426C2×Q8—2442no—
427C2×Q8D4×D6111yescharacteristic
428C2×Q8C2×C22⋊D6111yescharacteristic
429C2×D4C2×C22⋊D6111yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—2441no—
433Q16—1222no—
434Q16—4881no—
435Q16—2442no—
436SD16—22no—
437SD16—2442no—
438C2×C8—21no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—4881no—
446C2×C8C2×C22⋊D6111yescharacteristic
447C2×C8C2×C22⋊D6111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—611no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4D4×D6111yescharacteristic
470C4⋊C4C2×C22⋊D6111yescharacteristic
471C4⋊C4C2×C22⋊D6111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—2441no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—1221no—
479C42—2441no—
480C42C23×D6111yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—612no—
490Q8—1221no—
491Q8—4882no—
492Q8—2441no—
493Q8—2441no—
494Q8—2441no—
495Q8—2441no—
496D4—21no—
497D4#1451980812yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—161no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—4882no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×C22⋊D6111yescharacteristic
515C2×C4#1451982211yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—1221no—
520C8—1221no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C8—2441no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D4×C22⋊D6111yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—1222no—
538C4—4881no—
539C4—4881no—
540C4—2441no—
541C4#135×D6111yescharacteristic
542C4C2×#1451980811yescharacteristic
543C4#1684056911yescharacteristic
544C4#1684057711yescharacteristic
545C2—42no—
546C2#2145739011yescharacteristic
547C2#2145752011yescharacteristic
548C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3381C2
socleC22×C61D42
prime radicalC2×D4×C61C2×D4
hypercenter#3381D61
hypocenterC61#19797
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #21458618C2semidirect
4. #21445463C2semidirect
5. #21445403C2semidirect
6. #21445249C2semidirect
8. #21445198C2semidirect
10. #21445061C2semidirect
12. #21444975C2semidirect
14. #21444636C2semidirect
341. C61#19797semidirect

Maximal subgroups

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

subgroupindex
#214586182
#214584592
#214576892
#214454632
#214454032
#214452492
#214452402
#214451982
#214450672
#214450612
#214450262
#214449752
#214446562
#214446362
C61×#33812
#1979761