Finite Group Databasebeta

← #29670470

Subgroups — #29670470

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458690C211yesmaximal, characteristic, complemented
2#21458490C211yesmaximal, characteristic
3#21458159C211yesmaximal, characteristic
4#21445476C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445237C211yesmaximal, characteristic, complemented
7#21445235C211yesmaximal, characteristic, complemented
8#21445199C211yesmaximal, characteristic, complemented
9#21445010C211yesmaximal, characteristic
10#21444959C211yesmaximal, characteristic, complemented
11#21444952C211yesmaximal, characteristic, complemented
12#21444915C211yesmaximal, characteristic, complemented
13#21444662C211yesmaximal, characteristic, complemented
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3363C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840434C2211yescharacteristic
18#16840161—21no—
19#16840158C2211yescharacteristic
20#16840141C2211yescharacteristic
21#16840110—21no—
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840077—21no—
26#16840069—21no—
27#16840059—21no—
28#16840057C2211yescharacteristic
29#16840057C2211yescharacteristic
30#16840049—21no—
31#16840049C2211yescharacteristic
32#16840039C2211yescharacteristic
33#16840011—21no—
34#16839962—21no—
35#16839962C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839923—21no—
38Q8×#92418C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C4×#11758201—21no—
41C4×#11758201—21no—
42C4×#11758201C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839762—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
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×#11758226—21no—
68C2×#11758202—41no—
69C2×#11758201—21no—
70C2×#11758201—21no—
71C2×#11758201D411yescharacteristic
72C2×#11758189—21no—
73#14519777C2311yescharacteristic
74#14519774—21no—
75#14519774C2311yescharacteristic
76#14519769—21no—
77#14519755—41no—
78#14519753—21no—
79#14519752—21no—
80#14519752—41no—
81C4×D244—21no—
82C4×D244—21no—
83C4×D244C2311yescharacteristic
84C4⋊C4×D61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701—21no—
99#14519701D411yescharacteristic
100#14519699—21no—
101#14519699—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110#14519689—21no—
111C4×#92418—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
150#11758226—42no—
151#11758226—81no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—41no—
156C2×D244—41no—
157C2×D244C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162Q16×C61—22no—
163Q16×C61—42no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—41no—
186C42×C61—41no—
187C42×C61C2411yescharacteristic
188#11758202—82no—
189#11758201—22no—
190#11758201—42no—
191#11758201—81no—
192#11758198—21no—
193#11758198—41no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—41no—
199#11758196—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206#11758189—81no—
207C22×D61—21no—
208C22×D61—41no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—81no—
216Q8×C61—161no—
217Q8×C61#13512yes—
218Q8×C61#13712yes—
219C2×C4×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×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61H(5,𝔽2)11yescharacteristic
230C2×Dic61—21no—
231C2×Dic61—41no—
232D244—21no—
233D244—21no—
234D244—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—82no—
239D244—81no—
240D244—161no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—82no—
244C4×D61—161no—
245Dic122—81no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#19829—611nomaximal, Sylow
256C22×C61D4211yescharacteristic
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—81no—
261C2×D61—81no—
262C2×D61—81no—
263C4×C61—22no—
264C4×C61—22no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61C2×#13511yescharacteristic
273C4×C61C2×#13711yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—41no—
277Dic61—81no—
278#3381—611no—
279#3363D6111yescharacteristic, complemented
280#3362—611no—
281#3333—611no—
282#1720—611no—
283#1703—611no—
284#1678—611no—
285#1678—611no—
286#1672—611no—
287#1641—611no—
288#1633—611no—
289#1632—611no—
290#1626—611no—
291#1583—611no—
292#1579—611no—
293C2×C61#327011yescharacteristic
294C2×C61#328211yescharacteristic
295C2×C61#328811yescharacteristic
296D61—81no—
297D61—161no—
298Q82C2×D6111yescharacteristic
299#557C2×D6111yescharacteristic
300#554—611no—
301#550—611no—
302#499—1221no—
303#498—611no—
304#494—611no—
305#487—21no—
306#487C2×D6111yescharacteristic
307#486—611no—
308#486—611no—
309#486—611no—
310#486—1221no—
311#480—1221no—
312#479—1221no—
313#478—1221no—
314#477—21no—
315#477—611no—
316#477—611no—
317#477C2×D6111yescharacteristic
318#476—611no—
319#476—1221no—
320#474—611no—
321#468—1221no—
322#462—21no—
323#462C2×D6111yescharacteristic
324#460—611no—
325#460—611no—
326#460—1221no—
327#452—1221no—
328C8×Q8—611no—
329C8×Q8—611no—
330C8×Q8C2×D6111yescharacteristic
331C4×Q16—21no—
332C4×Q16C2×D6111yescharacteristic
333C4×SD16—611no—
334C4×SD16—1221no—
335C4×SD16—1221no—
336#436—611no—
337#417—1221no—
338#334—611no—
339#334—611no—
340#333—611no—
341#333—611no—
342#332—611no—
343#331—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347D4⋊C8—611no—
348#322—611no—
349C61#1982911yescharacteristic, complemented, Sylow
350C2×#41—1221no—
351C2×Q16—21no—
352C2×Q16—2441no—
353C2×Q16C22⋊D6111yescharacteristic
354C2×SD16—611no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×M16—1221no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8—611no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#127—611no—
366#127—1221no—
367#125—21no—
368#125—41no—
369#125—1221no—
370C22⋊Q8—1221no—
371C22⋊Q8—2441no—
372#121—1221no—
373#121—2441no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C22×D6111yescharacteristic
379C4×Q8C22×D6111yescharacteristic
380C4×Q8C22×D6111yescharacteristic
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C2×C4⋊C4—1221no—
385#107—21no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107C22⋊D6111yescharacteristic
390#106—611no—
391#106—1221no—
392#106—1221no—
393#106—1221no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—611no—
406#103—1221no—
407#103—1221no—
408#103C22⋊D6111yescharacteristic
409#103C22⋊D6111yescharacteristic
410#102—611no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#102—2441no—
420C22⋊C8—1221no—
421C4×C8—21no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427#41—4881no—
428#41—2442no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—1221no—
433C2×Q8D4×D6111yescharacteristic
434C2×Q8C2×C22⋊D6111yescharacteristic
435C2×Q8C2×C22⋊D6111yescharacteristic
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—2441no—
441C2×D4—2441no—
442C22×C4—1221no—
443C22×C4—2441no—
444C22×C4—2441no—
445Q16—22no—
446Q16—42no—
447Q16—4882no—
448SD16—1222no—
449SD16—4881no—
450SD16—2442no—
451M16—4881no—
452C2×C8—21no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4D4×D6111yescharacteristic
479C4⋊C4C2×C22⋊D6111yescharacteristic
480C4⋊C4C2×C22⋊D6111yescharacteristic
481C22⋊C4—1221no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42—41no—
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23—2441no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—161no—
500Q8—4881no—
501Q8#1451979712yes—
502Q8#1451980912yes—
503D4—1221no—
504D4—1221no—
505D4—9761no—
506D4—4881no—
507D4—4882no—
508D4—2441no—
509D4—2441no—
510D4—2441no—
511D4—2441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—1221no—
521C2×C4—9761no—
522C2×C4—4882no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C22×C22⋊D6111yescharacteristic
528C2×C4#1451982211yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C22—4881no—
539C22—4881no—
540C22—4881no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22D4×C22⋊D6111yescharacteristic
545C4—22no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—4881no—
555C4—2441no—
556C4C2×#1451979711yescharacteristic
557C4C2×#1451980911yescharacteristic
558C4#1684057011yescharacteristic
559C4#1684057511yescharacteristic
560C2—9761no—
561C2—4881no—
562C2#2145738911yescharacteristic
563C2#2145752711yescharacteristic
564C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3363C2
socleC22×C61D42
prime radical#16840434C22
hypercenter#3363D61
hypocenterC61#19829
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
1. #21458690C2semidirect
4. #21445476C2semidirect
5. #21445391C2semidirect
6. #21445237C2semidirect
7. #21445235C2semidirect
8. #21445199C2semidirect
10. #21444959C2semidirect
11. #21444952C2semidirect
12. #21444915C2semidirect
13. #21444662C2semidirect
14. #21444638C2semidirect
15. C61×#3363C2semidirect
279. #3363D61semidirect
349. C61#19829semidirect

Maximal subgroups

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

subgroupindex
#214586902
#214584902
#214581592
#214454762
#214453912
#214452372
#214452352
#214451992
#214450102
#214449592
#214449522
#214449152
#214446622
#214446382
C61×#33632
#1982961