Finite Group Databasebeta

← #29676323

Subgroups — #29676323

Order 15616.

580 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#21458803C211yesmaximal, characteristic
2#21458714C211yesmaximal, characteristic
3#21458436C211yesmaximal, characteristic, complemented
4#21445454C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445318C211yesmaximal, characteristic, complemented
7#21445311C211yesmaximal, characteristic, complemented
8#21445199C211yesmaximal, characteristic, complemented
9#21445087C211yesmaximal, characteristic, complemented
10#21445082C211yesmaximal, characteristic, complemented
11#21445025C211yesmaximal, characteristic, complemented
12#21444991C211yesmaximal, characteristic, complemented
13#21444731C211yesmaximal, characteristic
14#21444670C211yesmaximal, characteristic, complemented
15C61×#3328C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840168—21no—
19#16840160C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840144—21no—
23#16840141C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840101—21no—
26#16840091—21no—
27#16840062—21no—
28#16840057C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840049—21no—
31#16840047C2211yescharacteristic
32#16840039C2211yescharacteristic
33#16840017—21no—
34#16839984—21no—
35#16839981—21no—
36#16839967C2211yescharacteristic
37#16839964C2211yescharacteristic
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839872—21no—
41C4×#11758202—21no—
42C4×#11758199C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839803—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
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×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199D411yescharacteristic
72C2×#11758189—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519772—41no—
76#14519769—21no—
77#14519765—21no—
78#14519755—41no—
79#14519753—21no—
80#14519753—21no—
81C4×Dic122—21no—
82C4×D244—21no—
83C4×D244C2311yescharacteristic
84#14519735—21no—
85C4⋊C4×D61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710D411yescharacteristic
89#14519709—21no—
90#14519709—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—41no—
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519700—21no—
105#14519700—41no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112C4×#92418—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×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159Q16×C61—41no—
160Q16×C61—81no—
161M16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
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×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—41no—
183C42×C61C2411yescharacteristic
184#11758202—42no—
185#11758202—81no—
186#11758201—81no—
187#11758200—81no—
188#11758199—22no—
189#11758198—21no—
190#11758198—41no—
191#11758198—41no—
192#11758198—41no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—41no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758189—42no—
209C23×C61—21no—
210C22×D61—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—
219Q8×C61—82no—
220D4×C61—21no—
221D4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—82no—
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61H(5,𝔽2)11yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238D244—21no—
239D244—21no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—161no—
243Dic122—41no—
244Dic122—41no—
245Dic122—81no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418#13712yes—
255#20252—611nomaximal, Sylow
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61D4211yescharacteristic
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
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×C61C2×#13711yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57711yescharacteristic
275Dic61—41no—
276Dic61—81no—
277Dic61—81no—
278#3393—611no—
279#3384—611no—
280#3356—611no—
281#3328D6111yescharacteristic, complemented
282#1716—611no—
283#1699—611no—
284#1691—611no—
285#1690—611no—
286#1672—611no—
287#1652—611no—
288#1651—611no—
289#1643—611no—
290#1638—611no—
291#1594—611no—
292#1584—611no—
293C2×C61—81no—
294C2×C61#326711yescharacteristic
295C2×C61#327811yescharacteristic
296C2×C61#328911yescharacteristic
297D61—81no—
298#556—611no—
299#556C2×D6111yescharacteristic
300#554—611no—
301D4×Q8C2×D6111yescharacteristic
302#501—1221no—
303#498—611no—
304#498—611no—
305#498—611no—
306#495—1221no—
307#494—611no—
308#487—611no—
309#487C2×D6111yescharacteristic
310#485—21no—
311#485—1221no—
312#483—1221no—
313#478—1221no—
314#477—611no—
315#476—611no—
316#476—1221no—
317#475—611no—
318#475C2×D6111yescharacteristic
319#474—611no—
320#470—21no—
321#470—1221no—
322#464—1221no—
323#464—1221no—
324#462C2×D6111yescharacteristic
325#461—611no—
326#461—611no—
327#451—21no—
328#446—611no—
329C8×Q8—611no—
330#442—1221no—
331C4×Q16—1221no—
332C4×Q16C2×D6111yescharacteristic
333C4×D8—611no—
334#436—611no—
335#436C2×D6111yescharacteristic
336#428—1221no—
337#419—21no—
338#335—611no—
339#334—611no—
340#333—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348#322—611no—
349C61#2025211yescharacteristic, complemented, Sylow
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—1221no—
353C2×Q16—1221no—
354C2×Q16C22⋊D6111yescharacteristic
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×D8—611no—
358C2×M16—21no—
359C2×M16—1221no—
360C4⋊Q8—21no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365#126—41no—
366#126—2441no—
367#125—1221no—
368#124—21no—
369#124—1221no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—1221no—
374C22⋊Q8—1221no—
375C22⋊Q8—2441no—
376C4×Q8—21no—
377C4×Q8—1221no—
378C4×Q8C22×D6111yescharacteristic
379C4×Q8C22×D6111yescharacteristic
380C4×D4—21no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384#117—21no—
385#117—1221no—
386C2×C4⋊C4—1221no—
387#107—611no—
388#107—1221no—
389#107—1221no—
390#107C22⋊D6111yescharacteristic
391#106—21no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395#106—1221no—
396#106—1221no—
397#106—1221no—
398#106—2441no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8C22×D6111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—2441no—
414#103C22⋊D6111yescharacteristic
415#103C22⋊D6111yescharacteristic
416#102—611no—
417#102—611no—
418#102—1221no—
419#102—1221no—
420C22⋊C8—21no—
421C22⋊C8—1221no—
422#97—1221no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×Q8C2×C22⋊D6111yescharacteristic
435C2×Q8C2×C22⋊D6111yescharacteristic
436C2×D4—611no—
437C2×D4D4×D6111yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—1221no—
441C22×C4—2441no—
442Q16—41no—
443Q16—81no—
444Q16—4881no—
445Q16—2442no—
446SD16—4881no—
447SD16—4881no—
448D8—1222no—
449M16—81no—
450M16—2442no—
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—1221no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C4⋊C4—2441no—
476C4⋊C4D4×D6111yescharacteristic
477C4⋊C4C2×C22⋊D6111yescharacteristic
478C4⋊C4C2×C22⋊D6111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—1221no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C22⋊C4—2441no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—2441no—
491C42C23×D6111yescharacteristic
492C23—21no—
493C23—1221no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—82no—
503Q8—4881no—
504Q8—2441no—
505Q8—2441no—
506D4—21no—
507D4—21no—
508D4—1221no—
509D4—1221no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—1221no—
521C2×C4—9761no—
522C2×C4—2441no—
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—612no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22D4×C22⋊D6111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—4881no—
554C4—4881no—
555C4—2441no—
556C4#137×D6111yescharacteristic
557C4#1684056011yescharacteristic
558C4#1684057111yescharacteristic
559C4#1684057311yescharacteristic
560C2—81no—
561C2—4881no—
562C2#2145734011yescharacteristic
563C2#2145747911yescharacteristic
564C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3328C2
socleC22×C61D42
prime radicalC2×#11758199D4
hypercenter#3328D61
hypocenterC61#20252
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3328

Complements

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

NH ≅ G/Ntype
3. #21458436C2semidirect
4. #21445454C2semidirect
5. #21445363C2semidirect
6. #21445318C2semidirect
7. #21445311C2semidirect
8. #21445199C2semidirect
9. #21445087C2semidirect
10. #21445082C2semidirect
11. #21445025C2semidirect
12. #21444991C2semidirect
14. #21444670C2semidirect
15. C61×#3328C2semidirect
281. #3328D61semidirect
349. C61#20252semidirect

Maximal subgroups

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

subgroupindex
#214588032
#214587142
#214584362
#214454542
#214453632
#214453182
#214453112
#214451992
#214450872
#214450822
#214450252
#214449912
#214447312
#214446702
C61×#33282
#2025261