Finite Group Databasebeta

← #29665513

Subgroups — #29665513

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456966C211yesmaximal, characteristic, complemented
2#21455631C211yesmaximal, characteristic
3#21455600C211yesmaximal, characteristic
4#21454926C211yesmaximal, characteristic
5#21445276C211yesmaximal, characteristic, complemented
6#21445274C211yesmaximal, characteristic, complemented
7#21445268C211yesmaximal, characteristic, complemented
8#21445224C211yesmaximal, characteristic, complemented
9#21445222C211yesmaximal, characteristic, complemented
10#21445218C211yesmaximal, characteristic, complemented
11#21445216C211yesmaximal, characteristic, complemented
12#21444592C211yesmaximal, characteristic, complemented
13#21444508C211yesmaximal, characteristic, complemented
14#333×D61C211yesmaximal, characteristic, complemented
15C61×#1683C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×#11758224C2211yescharacteristic
19#16840167C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840096—21no—
23#16840096—21no—
24#16840068—21no—
25#16840060—21no—
26#16840058C2211yescharacteristic
27#16840058C2211yescharacteristic
28#16840055—21no—
29#16840055—21no—
30#16840054C2211yescharacteristic
31#16840052C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840046—21no—
34#16840044C2211yescharacteristic
35#16840040—21no—
36C8×Dic122C2211yescharacteristic
37#16839886C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39C8×C22⋊D61—21no—
40#16839825—21no—
41#16839813C2211yescharacteristic
42#16839812—21no—
43#16839801—21no—
44#16839799—21no—
45#16839784C2211yescharacteristic
46C2×#14519706—21no—
47C4⋊C8×D61C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49#16839760—21no—
50#16839755—21no—
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839508C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#476C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758224D411yescharacteristic
68C2×Q8×D61—21no—
69C2×#11758189—21no—
70C22×#92418—21no—
71C2×C8×D61—21no—
72C2×C8×D61—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519776—21no—
77#14519775—21no—
78#14519768—21no—
79#14519757—21no—
80#14519753—21no—
81Q8×Dic61—21no—
82C4×Dic122C2311yescharacteristic
83#14519742—21no—
84#14519742D411yescharacteristic
85D4×Dic61D411yescharacteristic
86C4×C22⋊D61—21no—
87#14519737—21no—
88#14519735—21no—
89#14519735D411yescharacteristic
90#14519733—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C2×C4×Dic61—21no—
94C42×D61C2311yescharacteristic
95#14519711—21no—
96#14519711—21no—
97#14519711—21no—
98#14519711—21no—
99#14519710—21no—
100#14519710—21no—
101#14519710—21no—
102#14519708—21no—
103#14519708—21no—
104#14519708—21no—
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519706D411yescharacteristic
114#14519706D411yescharacteristic
115#14519702—21no—
116#14519702—21no—
117#14519701—21no—
118#14519701—21no—
119#14519700—21no—
120#14519700—21no—
121#14519698—21no—
122#14519698—21no—
123C22⋊#92418—21no—
124#14519689D411yescharacteristic
125#14519689D411yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#107×C61—21no—
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151Q8×D61—82no—
152#11758224—22no—
153#11758224Q1614yes—
154C2×C4×D61—41no—
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—41no—
161C2×Dic122C2×D411yescharacteristic
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—81no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C22⋊C4×C61—21no—
174C42×C61C2411yescharacteristic
175C22⋊Dic61—21no—
176#11758198—21no—
177#11758198—41no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—41no—
183C4⋊Dic61C2×D411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—41no—
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202#11758189—42no—
203C8×D61—42no—
204C8×D61—81no—
205C23×C61—21no—
206C22×D61#12111yescharacteristic
207Q8×C61—41no—
208Q8×C61—41no—
209Q8×C61—81no—
210D4×C61—21no—
211D4×C61C2×Q1612yes—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C22⋊D61—24no—
221C2×Dic61—21no—
222C2×Dic61—24no—
223C2×Dic61—21no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—81no—
227C2×Dic61#12111yescharacteristic
228C2×Dic61#12111yescharacteristic
229C2×Dic61#12111yescharacteristic
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—41no—
233C4×D61—82no—
234C4×D61C2×Q1612yes—
235C4×D61#13512yes—
236Dic122—21no—
237Dic122—82no—
238Dic122—81no—
239Dic122—81no—
240Dic122C2×Q1612yes—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#19417—611nomaximal, Sylow
252C22×C61—22no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61C2×#12111yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61#46712yes—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61C22×Q1611yescharacteristic
264C4×C61C2×#13511yescharacteristic
265C4×C61#57711yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—21no—
268Dic61—22no—
269Dic61—21no—
270Dic61—41no—
271Dic61—81no—
272Dic61—81no—
273Dic61#46712yes—
274#3230—611no—
275#3079—611no—
276#3076—611no—
277#2988—611no—
278#1684—611no—
279#1684—611no—
280#1683—611no—
281#1683D6111yescharacteristic, complemented
282#1676—611no—
283#1676—611no—
284#1675—611no—
285#1675—611no—
286#1571—611no—
287#1550—611no—
288C2×#333—611no—
289C2×C61—42no—
290C2×C61#304611yescharacteristic
291C2×C61C2×#46711yescharacteristic
292C2×C61#306811yescharacteristic
293D61—22no—
294#533—611no—
295C2×C4⋊Q8—611no—
296C4×#41—611no—
297#500—611no—
298#500—611no—
299#487—611no—
300#487C2×D6111yescharacteristic
301#484—1221no—
302#484—1221no—
303#479—1221no—
304#478—1221no—
305#477—611no—
306#477—611no—
307#477—611no—
308#477—1221no—
309#477—1221no—
310#476—611no—
311#476—611no—
312#476C2×D6111yescharacteristic
313#475—611no—
314#475—1221no—
315#474—1221no—
316#474C2×D6111yescharacteristic
317C8×Q8—611no—
318C8×Q8—611no—
319C8×D4—611no—
320C8×D4—1221no—
321C8×D4—1221no—
322C8×D4C2×D6111yescharacteristic
323#431—611no—
324#431—1221no—
325#428—1221no—
326#427—1221no—
327#423—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—1221no—
331#417—1221no—
332#416—1221no—
333#335—611no—
334#335—611no—
335#335—611no—
336#335C2×D6111yescharacteristic
337#333—611no—
338#333—611no—
339#333—611no—
340#333—611no—
341#333—611no—
342#333C2×D6111yescharacteristic
343#332—611no—
344#332C2×D6111yescharacteristic
345C61#1941711yescharacteristic, complemented, Sylow
346C2×#41—611no—
347C22×Q8—1221no—
348C2×M16—1221no—
349C22×C8—21no—
350C22×C8—1221no—
351C22×C8—1221no—
352C22×C8—1221no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8C22×D6111yescharacteristic
359C4⋊Q8C22×D6111yescharacteristic
360#125—1221no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×D4—611no—
368C4×D4—1221no—
369C4×D4—1221no—
370C4×D4C22×D6111yescharacteristic
371#117—611no—
372#117—1221no—
373#117—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C42—611no—
377C2×C42—1221no—
378#107—21no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#106—21no—
387#106—1221no—
388#106—1221no—
389#106—1221no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—21no—
412#102—21no—
413#102—1221no—
414#102—1221no—
415C22⋊C8—21no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—1221no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423#41—614no—
424#41—1222no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—611no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8—4882no—
431C2×Q8—2441no—
432C2×D4—1221no—
433C2×D4D4×D6111yescharacteristic
434C22×C4—21no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—2441no—
441M16—2442no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—4881no—
452C2×C8—4881no—
453C2×C8—2442no—
454C2×C8D4×D6111yescharacteristic
455C2×C8D4×D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—611no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4D4×D6111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—2441no—
476C42—611no—
477C42—611no—
478C42—611no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—2441no—
483C42C23×D6111yescharacteristic
484C23—21no—
485C23—611no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—612no—
490Q8—1221no—
491Q8—4881no—
492Q8—4881no—
493Q8—4882no—
494D4—21no—
495D4—1224no—
496D4Q16×D6112yes—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—611no—
503C2×C4—612no—
504C2×C4—612no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—1224no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4882no—
513C2×C4—4881no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4C2×D4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4#41×D6111yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—1221no—
526C8—1221no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—612no—
534C22—1221no—
535C22—1221no—
536C22#121×D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—612no—
542C4—1221no—
543C4—1222no—
544C4—1221no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4C2×Q16×D6111yescharacteristic
549C4#135×D6111yescharacteristic
550C4#1684057211yescharacteristic
551C4#1684057611yescharacteristic
552C2—42no—
553C2—1222no—
554C2#2145537011yescharacteristic
555C2#467×D6111yescharacteristic
556C2#2145554211yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1683C2
socleC22×C61C2×#121
prime radicalC2×#11758224D4
hypercenter#1683D61
hypocenterC61#19417
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

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

NH ≅ G/Ntype
1. #21456966C2semidirect
5. #21445276C2semidirect
6. #21445274C2semidirect
7. #21445268C2semidirect
8. #21445224C2semidirect
9. #21445222C2semidirect
10. #21445218C2semidirect
11. #21445216C2semidirect
12. #21444592C2semidirect
13. #21444508C2semidirect
14. #333×D61C2semidirect
15. C61×#1683C2semidirect
281. #1683D61semidirect
345. C61#19417semidirect

Maximal subgroups

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

subgroupindex
#214569662
#214556312
#214556002
#214549262
#214452762
#214452742
#214452682
#214452242
#214452222
#214452182
#214452162
#214445922
#214445082
#333×D612
C61×#16832
#1941761