Finite Group Databasebeta

← #29676977

Subgroups — #29676977

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#21458631C211yesmaximal, characteristic, complemented
2#21458611C211yesmaximal, characteristic
3#21458555C211yesmaximal, characteristic, complemented
4#21445432C211yesmaximal, characteristic, complemented
5#21445399C211yesmaximal, characteristic, complemented
6#21445389C211yesmaximal, characteristic, complemented
7#21445370C211yesmaximal, characteristic, complemented
8#21445352C211yesmaximal, characteristic
9#21445038C211yesmaximal, characteristic, complemented
10#21445004C211yesmaximal, characteristic, complemented
11#21444984C211yesmaximal, characteristic, complemented
12#21444929C211yesmaximal, characteristic
13#21444716C211yesmaximal, characteristic, complemented
14#21444707C211yesmaximal, characteristic, complemented
15C61×#3328C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17Q8×Dic122C2211yescharacteristic
18#16840124—21no—
19#16840123—21no—
20#16840121—21no—
21#16840114C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840057C2211yescharacteristic
27#16840052C2211yescharacteristic
28#16840049—21no—
29#16840047—21no—
30#16840044C2211yescharacteristic
31#16840041—21no—
32#16839986—21no—
33#16839981—21no—
34#16839977—21no—
35#16839969C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839957C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839872—21no—
42#16839867—21no—
43#16839865—21no—
44C4×#11758200C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#556C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#475C2211yescharacteristic
61C61×#470—21no—
62C61×#462C2211yescharacteristic
63C61×#451—21no—
64C4×Q16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#419—21no—
67C2×#11758202—21no—
68C2×#11758200D411yescharacteristic
69C2×#11758201—21no—
70C2×#11758199—21no—
71#14519777—21no—
72#14519777C2311yescharacteristic
73#14519776—21no—
74#14519776—41no—
75#14519774C2311yescharacteristic
76#14519766—21no—
77#14519765—21no—
78#14519762—41no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82C4×D244—21no—
83#14519739—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87#14519708D411yescharacteristic
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93#14519706—21no—
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519700—21no—
99#14519700—41no—
100#14519700D411yescharacteristic
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519688—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#126×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×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
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122—41no—
160C2×Dic122C2×D411yescharacteristic
161Q16×C61—41no—
162Q16×C61—81no—
163M16×C61—81no—
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—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—41no—
185C42×C61C2411yescharacteristic
186#11758202—42no—
187#11758201—42no—
188#11758200—41no—
189#11758199—42no—
190#11758198—41no—
191#11758198—41no—
192#11758198—41no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—41no—
196C4⋊Dic61C2×D411yescharacteristic
197#11758196—21no—
198#11758196—41no—
199C4×Dic61—21no—
200C4×Dic61—41no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C23×C61—21no—
208C22×D61—41no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—82no—
218D4×C61—21no—
219D4×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×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—82no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236D244—41no—
237D244—41no—
238D244—41no—
239D244—41no—
240D244—81no—
241C4×D61—161no—
242Dic122—21no—
243Dic122—21no—
244Dic122—81no—
245Dic122—161no—
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#20296—611nomaximal, Sylow
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61D4211yescharacteristic
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—81no—
270C4×C61—81no—
271C4×C61#57511yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57811yescharacteristic
275Dic61—41no—
276Dic61—41no—
277Dic61—81no—
278#3375—611no—
279#3373—611no—
280#3369—611no—
281#3328D6111yescharacteristic, complemented
282#1711—611no—
283#1704—611no—
284#1702—611no—
285#1700—611no—
286#1697—611no—
287#1645—611no—
288#1640—611no—
289#1637—611no—
290#1628—611no—
291#1591—611no—
292#1590—611no—
293C2×C61—81no—
294C2×C61#327511yescharacteristic
295C2×C61#327711yescharacteristic
296C2×C61#329011yescharacteristic
297D61—161no—
298#559—611no—
299Q82—611no—
300#556C2×D6111yescharacteristic
301D4×Q8C2×D6111yescharacteristic
302#489—1221no—
303#489—1221no—
304#489—1221no—
305#487—611no—
306#487—611no—
307#487C2×D6111yescharacteristic
308#486—611no—
309#486—611no—
310#486—611no—
311#485—21no—
312#477—611no—
313#476—611no—
314#476—1221no—
315#475—611no—
316#475—1221no—
317#475C2×D6111yescharacteristic
318#474—1221no—
319#470—21no—
320#464—1221no—
321#464—1221no—
322#463—1221no—
323#462—611no—
324#462C2×D6111yescharacteristic
325#460—611no—
326#459—611no—
327#451—21no—
328#446—611no—
329#446—611no—
330#446—611no—
331#442—1221no—
332#441—1221no—
333#440—1221no—
334C4×Q16C2×D6111yescharacteristic
335C4×SD16—611no—
336#436C2×D6111yescharacteristic
337#419—21no—
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#2029611yescharacteristic, complemented, Sylow
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—1221no—
353C2×Q16C22⋊D6111yescharacteristic
354C2×SD16—611no—
355C2×SD16—1221no—
356C2×D8—1221no—
357C2×M16—21no—
358C4⋊Q8—21no—
359C4⋊Q8—611no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362C4⋊Q8—2441no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#127—611no—
366#126—41no—
367#124—21no—
368#124—1221no—
369#124—1221no—
370#123—2441no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374C4×Q8—21no—
375C4×Q8—611no—
376C4×Q8—1221no—
377C4×Q8—1221no—
378C4×Q8C22×D6111yescharacteristic
379C4×Q8C22×D6111yescharacteristic
380C4×D4—21no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384#117—21no—
385#107—1221no—
386#107C22⋊D6111yescharacteristic
387#106—21no—
388#106—611no—
389#106—1221no—
390#106—1221no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
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—21no—
421#97—1221no—
422#97—1221no—
423#97—1221no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8C22×D6111yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8—611no—
433C2×Q8—1221no—
434C2×Q8—2441no—
435C2×Q8C2×C22⋊D6111yescharacteristic
436C2×Q8C2×C22⋊D6111yescharacteristic
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4D4×D6111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—2441no—
444Q16—41no—
445Q16—81no—
446Q16—2442no—
447SD16—2441no—
448SD16—2442no—
449D8—2442no—
450M16—81no—
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—41no—
467C4⋊C4—41no—
468C4⋊C4—611no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4D4×D6111yescharacteristic
475C4⋊C4C2×C22⋊D6111yescharacteristic
476C4⋊C4C2×C22⋊D6111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42—1221no—
488C42—2441no—
489C42C23×D6111yescharacteristic
490C23—21no—
491C23—2441no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—82no—
501Q8—1221no—
502Q8—1221no—
503Q8—9761no—
504Q8—4881no—
505D4—21no—
506D4—21no—
507D4—4881no—
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—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—9761no—
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—41no—
539C22—41no—
540C22—41no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22D4×C22⋊D6111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—4881no—
554C4—2441no—
555C4—2441no—
556C4#1684056011yescharacteristic
557C4#1684056111yescharacteristic
558C4#1684057311yescharacteristic
559C4#1684057811yescharacteristic
560C2—81no—
561C2—9761no—
562C2#2145744611yescharacteristic
563C2#2145747011yescharacteristic
564C2#2145760511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3328C2
socleC22×C61D42
prime radical#16839957C22
hypercenter#3328D61
hypocenterC61#20296
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3328

Complements

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

NH ≅ G/Ntype
1. #21458631C2semidirect
3. #21458555C2semidirect
4. #21445432C2semidirect
5. #21445399C2semidirect
6. #21445389C2semidirect
7. #21445370C2semidirect
9. #21445038C2semidirect
10. #21445004C2semidirect
11. #21444984C2semidirect
13. #21444716C2semidirect
14. #21444707C2semidirect
15. C61×#3328C2semidirect
281. #3328D61semidirect
349. C61#20296semidirect

Maximal subgroups

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

subgroupindex
#214586312
#214586112
#214585552
#214454322
#214453992
#214453892
#214453702
#214453522
#214450382
#214450042
#214449842
#214449292
#214447162
#214447072
C61×#33282
#2029661