Finite Group Databasebeta

← #29670781

Subgroups — #29670781

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458829C211yesmaximal, characteristic
2#21458633C211yesmaximal, characteristic, complemented
3#21458515C211yesmaximal, characteristic, complemented
4#21445461C211yesmaximal, characteristic
5#21445389C211yesmaximal, characteristic, complemented
6#21445274C211yesmaximal, characteristic, complemented
7#21445237C211yesmaximal, characteristic, complemented
8#21445179C211yesmaximal, characteristic
9#21445003C211yesmaximal, characteristic, complemented
10#21444939C211yesmaximal, characteristic, complemented
11#21444915C211yesmaximal, characteristic, complemented
12#21444897C211yesmaximal, characteristic, complemented
13#21444670C211yesmaximal, characteristic, complemented
14#21444636C211yesmaximal, characteristic, complemented
15C61×#3363C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840497C2211yescharacteristic
18#16840147—21no—
19#16840139C2211yescharacteristic
20#16840136C2211yescharacteristic
21#16840124—21no—
22#16840119—21no—
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16840110C2211yescharacteristic
26#16840059—21no—
27#16840054C2211yescharacteristic
28#16840044C2211yescharacteristic
29#16840039—21no—
30#16839984—21no—
31#16839984—21no—
32#16839980—21no—
33#16839980—21no—
34#16839962C2211yescharacteristic
35#16839962C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839962C2211yescharacteristic
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839860—21no—
42C4×#11758202C2211yescharacteristic
43C4×#11758201—21no—
44#16839844—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839505C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
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×#11758202D411yescharacteristic
68C2×#11758201—21no—
69C2×#11758201—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—41no—
73C2×D488—21no—
74C2×D488—21no—
75#14519774C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519766—21no—
78#14519766—21no—
79#14519765—21no—
80#14519765—21no—
81#14519762—41no—
82#14519762—41no—
83C4×Dic122C2311yescharacteristic
84C4×D244—21no—
85C4×D244—21no—
86#14519739—21no—
87#14519739—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519701D411yescharacteristic
98#14519700—21no—
99#14519700—21no—
100#14519700D411yescharacteristic
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519688—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
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×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×Dic122C2×D411yescharacteristic
159Q16×C61—41no—
160Q16×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—21no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—41no—
183C42×C61—41no—
184C42×C61C2411yescharacteristic
185#11758202—22no—
186#11758201—42no—
187#11758201—42no—
188#11758201—81no—
189#11758201—81no—
190#11758201—82no—
191#11758198—41no—
192#11758198—41no—
193#11758198—41no—
194#11758198—41no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199C4×Dic61—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206D488—42no—
207D488—81no—
208C22×D61—41no—
209C22×D61—41no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218Q8×C61—161no—
219Q8×C61#13512yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233D244—41no—
234D244—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—41no—
239D244—41no—
240D244—41no—
241D244—81no—
242D244—81no—
243C4×D61—161no—
244C4×D61—161no—
245Dic122—21no—
246Dic122—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#19850—611nomaximal, Sylow
257C22×C61D4211yescharacteristic
258C2×D61—81no—
259C2×D61—81no—
260C2×D61—81no—
261C2×D61—81no—
262C2×D61—81no—
263C2×D61—81no—
264C4×C61—22no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61C2×#13511yescharacteristic
274C4×C61#57511yescharacteristic
275C4×C61#57711yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—41no—
278Dic61—41no—
279#3396—611no—
280#3375—611no—
281#3365—611no—
282#3363D6111yescharacteristic, complemented
283#1717—611no—
284#1702—611no—
285#1684—611no—
286#1678—611no—
287#1668—611no—
288#1640—611no—
289#1630—611no—
290#1626—611no—
291#1623—611no—
292#1584—611no—
293#1579—611no—
294C2×C61#327111yescharacteristic
295C2×C61#328511yescharacteristic
296C2×C61#328811yescharacteristic
297D61—161no—
298D61—161no—
299#559—611no—
300#559—611no—
301Q82C2×D6111yescharacteristic
302#557C2×D6111yescharacteristic
303#495—1221no—
304#493—611no—
305#492—611no—
306#489—1221no—
307#488—1221no—
308#487—21no—
309#487C2×D6111yescharacteristic
310#486—611no—
311#486—611no—
312#486—611no—
313#478—1221no—
314#477—21no—
315#477—611no—
316#477C2×D6111yescharacteristic
317#475—611no—
318#474—1221no—
319#464—1221no—
320#464—1221no—
321#463—1221no—
322#463—1221no—
323#462—21no—
324#462C2×D6111yescharacteristic
325#460—611no—
326#460—611no—
327#460—611no—
328#460—611no—
329#446—611no—
330C8×Q8—611no—
331C8×Q8—611no—
332C8×Q8C2×D6111yescharacteristic
333#440—1221no—
334C4×Q16—21no—
335C4×Q16—611no—
336C4×Q16C2×D6111yescharacteristic
337C4×SD16—1221no—
338C4×D8—1221no—
339#335—611no—
340#334—611no—
341#333—611no—
342#332—611no—
343#331—611no—
344#331—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349#322—611no—
350C61#1985011yescharacteristic, complemented, Sylow
351C2×Q16—21no—
352C2×Q16—611no—
353C2×Q16C22⋊D6111yescharacteristic
354C2×SD16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×SD16—2441no—
359C2×D8—1221no—
360C2×D8—1221no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8C22×D6111yescharacteristic
366C4⋊Q8C22×D6111yescharacteristic
367#127—611no—
368#127—611no—
369#125—21no—
370#125—41no—
371#124—1221no—
372#124—1221no—
373#124—1221no—
374#124—1221no—
375#123—2441no—
376#123—2441no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—611no—
382C4×Q8C22×D6111yescharacteristic
383C4×Q8C22×D6111yescharacteristic
384C4×Q8C22×D6111yescharacteristic
385C4×D4—1221no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1221no—
389#107—21no—
390#107—611no—
391#107—1221no—
392#107C22⋊D6111yescharacteristic
393#106—1221no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C22×D6111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—611no—
407#103—611no—
408#103—1221no—
409#103—1221no—
410#103C22⋊D6111yescharacteristic
411#103C22⋊D6111yescharacteristic
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—2441no—
421#97—1221no—
422C4×C8—21no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8C22×D6111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—611no—
432C2×Q8D4×D6111yescharacteristic
433C2×Q8C2×C22⋊D6111yescharacteristic
434C2×Q8C2×C22⋊D6111yescharacteristic
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—1221no—
441C22×C4—2441no—
442C22×C4—2441no—
443Q16—41no—
444Q16—42no—
445Q16—1222no—
446SD16—4882no—
447SD16—4881no—
448SD16—4881no—
449SD16—2442no—
450SD16—2442no—
451D8—4881no—
452D8—2442no—
453C2×C8—21no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4D4×D6111yescharacteristic
477C4⋊C4C2×C22⋊D6111yescharacteristic
478C4⋊C4C2×C22⋊D6111yescharacteristic
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42—41no—
490C42—1221no—
491C42C23×D6111yescharacteristic
492C23—2441no—
493C23—2441no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—161no—
503Q8—1221no—
504Q8—1221no—
505Q8#1451980012yes—
506D4—4881no—
507D4—4881no—
508D4—2441no—
509D4—2441no—
510D4—2441no—
511D4—2441no—
512D4—2441no—
513D4—2441no—
514D4—2441no—
515D4—2441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—9761no—
527C2×C4—9761no—
528C2×C4C2×D4×D6111yescharacteristic
529C2×C4C22×C22⋊D6111yescharacteristic
530C2×C4#1451982211yescharacteristic
531C8—21no—
532C8—21no—
533C8—41no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C22—4881no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22—4881no—
545C22—4881no—
546C22D4×C22⋊D6111yescharacteristic
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—2441no—
557C4—2441no—
558C4C2×#1451980011yescharacteristic
559C4#1684056011yescharacteristic
560C4#1684057011yescharacteristic
561C4#1684057511yescharacteristic
562C2—9761no—
563C2—9761no—
564C2#2145740511yescharacteristic
565C2#2145756011yescharacteristic
566C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3363C2
socleC22×C61D42
prime radical#16840139C22
hypercenter#3363D61
hypocenterC61#19850
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
2. #21458633C2semidirect
3. #21458515C2semidirect
5. #21445389C2semidirect
6. #21445274C2semidirect
7. #21445237C2semidirect
9. #21445003C2semidirect
10. #21444939C2semidirect
11. #21444915C2semidirect
12. #21444897C2semidirect
13. #21444670C2semidirect
14. #21444636C2semidirect
15. C61×#3363C2semidirect
282. #3363D61semidirect
350. C61#19850semidirect

Maximal subgroups

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

subgroupindex
#214588292
#214586332
#214585152
#214454612
#214453892
#214452742
#214452372
#214451792
#214450032
#214449392
#214449152
#214448972
#214446702
#214446362
C61×#33632
#1985061