Finite Group Databasebeta

← #29677031

Subgroups — #29677031

Order 15616.

578 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#21458596C211yesmaximal, characteristic, complemented
2#21458548C211yesmaximal, characteristic
3#21458159C211yesmaximal, characteristic
4#21445432C211yesmaximal, characteristic, complemented
5#21445399C211yesmaximal, characteristic, complemented
6#21445389C211yesmaximal, characteristic, complemented
7#21445363C211yesmaximal, characteristic, complemented
8#21445359C211yesmaximal, characteristic, complemented
9#21445031C211yesmaximal, characteristic, complemented
10#21445018C211yesmaximal, characteristic
11#21444977C211yesmaximal, characteristic, complemented
12#21444915C211yesmaximal, characteristic, complemented
13#21444716C211yesmaximal, characteristic, complemented
14#21444709C211yesmaximal, characteristic, complemented
15C61×#3374C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840434C2211yescharacteristic
18#16840130—21no—
19#16840128—21no—
20#16840114C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840077—21no—
26#16840069—21no—
27#16840059—21no—
28#16840057C2211yescharacteristic
29#16840057C2211yescharacteristic
30#16840039C2211yescharacteristic
31#16840011—21no—
32#16839964—21no—
33#16839964C2211yescharacteristic
34#16839962—21no—
35#16839962C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839923—21no—
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839860—21no—
41#16839860—21no—
42C4×#11758201C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839762—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#491—21no—
59C61×#487C2211yescharacteristic
60C61×#479—21no—
61C61×#475C2211yescharacteristic
62C61×#462—21no—
63C61×#462C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#441—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758226—21no—
68C2×#11758201—21no—
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#14519708D411yescharacteristic
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701D411yescharacteristic
100#14519700—41no—
101#14519699—21no—
102#14519699—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122#125×C61—21no—
123#125×C61—41no—
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×C61D411yescharacteristic
133#106×C61—21no—
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
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149#11758226—42no—
150#11758226—81no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—41no—
155C2×D244—41no—
156C2×D244C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×Dic122—21no—
161Q16×C61—41no—
162Q16×C61—42no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C4⋊C4×C61—21no—
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—41no—
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#11758201—41no—
189#11758201—42no—
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—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
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—81no—
239D244—82no—
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#20300—611nomaximal, Sylow
256C22×C61D4211yescharacteristic
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—81no—
261C2×D61—81no—
262C2×D61—81no—
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61#57511yescharacteristic
273C4×C61#57511yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—41no—
277Dic61—81no—
278#3374D6111yescharacteristic, complemented
279#3372—611no—
280#3368—611no—
281#3333—611no—
282#1711—611no—
283#1704—611no—
284#1702—611no—
285#1699—611no—
286#1698—611no—
287#1644—611no—
288#1642—611no—
289#1636—611no—
290#1626—611no—
291#1591—611no—
292#1590—611no—
293C2×C61#327511yescharacteristic
294C2×C61#327711yescharacteristic
295C2×C61#329011yescharacteristic
296D61—81no—
297D61—161no—
298#557C2×D6111yescharacteristic
299#557C2×D6111yescharacteristic
300#554—611no—
301#550—611no—
302#491—21no—
303#491—1221no—
304#490—1221no—
305#487—611no—
306#487—611no—
307#487C2×D6111yescharacteristic
308#486—611no—
309#486—611no—
310#486—611no—
311#480—1221no—
312#479—21no—
313#479—1221no—
314#478—1221no—
315#477—611no—
316#477—611no—
317#475C2×D6111yescharacteristic
318#474—611no—
319#468—1221no—
320#462—21no—
321#462C2×D6111yescharacteristic
322#461—611no—
323#461—1221no—
324#460—611no—
325#460—611no—
326#460—1221no—
327#452—1221no—
328#446—611no—
329#446—611no—
330#446C2×D6111yescharacteristic
331#441—21no—
332#440—1221no—
333#440—1221no—
334C4×Q16C2×D6111yescharacteristic
335C4×SD16—611no—
336#436—611no—
337#417—1221no—
338#335—611no—
339#334—611no—
340#333—611no—
341#332—611no—
342#332—611no—
343#331—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347D4⋊C8—611no—
348C82—611no—
349C61#2030011yescharacteristic, complemented, Sylow
350C2×#41—1221no—
351C2×Q16—21no—
352C2×Q16C22⋊D6111yescharacteristic
353C2×SD16—611no—
354C2×SD16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×M16—1221no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—611no—
361C4⋊Q8C22×D6111yescharacteristic
362C4⋊Q8C22×D6111yescharacteristic
363#127—611no—
364#127—1221no—
365#125—21no—
366#125—21no—
367#125—41no—
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—1221no—
386#107—1221no—
387#107—1221no—
388#107C22⋊D6111yescharacteristic
389#106—21no—
390#106—611no—
391C4⋊C8—21no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—611no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—2441no—
409#103C22⋊D6111yescharacteristic
410#103C22⋊D6111yescharacteristic
411#102—611no—
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—
421#97—21no—
422#97—1221no—
423#97—1221no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8C22×D6111yescharacteristic
427#41—4881no—
428#41—2442no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—1221no—
432C2×Q8D4×D6111yescharacteristic
433C2×Q8C2×C22⋊D6111yescharacteristic
434C2×Q8C2×C22⋊D6111yescharacteristic
435C2×D4—611no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—2441no—
440C2×D4—2441no—
441C22×C4—1221no—
442C22×C4—2441no—
443C22×C4—2441no—
444Q16—41no—
445Q16—42no—
446SD16—4881no—
447SD16—2441no—
448SD16—2442no—
449SD16—2442no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
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—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—4881no—
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—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—4881no—
555C4—2441no—
556C4#1684056011yescharacteristic
557C4#1684056111yescharacteristic
558C4#1684057011yescharacteristic
559C4#1684057811yescharacteristic
560C2—9761no—
561C2—4881no—
562C2#2145745111yescharacteristic
563C2#2145747011yescharacteristic
564C2#2145760511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3374C2
socleC22×C61D42
prime radical#16840434C22
hypercenter#3374D61
hypocenterC61#20300
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3374

Complements

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

NH ≅ G/Ntype
1. #21458596C2semidirect
4. #21445432C2semidirect
5. #21445399C2semidirect
6. #21445389C2semidirect
7. #21445363C2semidirect
8. #21445359C2semidirect
9. #21445031C2semidirect
11. #21444977C2semidirect
12. #21444915C2semidirect
13. #21444716C2semidirect
14. #21444709C2semidirect
15. C61×#3374C2semidirect
278. #3374D61semidirect
349. C61#20300semidirect

Maximal subgroups

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

subgroupindex
#214585962
#214585482
#214581592
#214454322
#214453992
#214453892
#214453632
#214453592
#214450312
#214450182
#214449772
#214449152
#214447162
#214447092
C61×#33742
#2030061