Finite Group Databasebeta

← #29671523

Subgroups — #29671523

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458162C211yesmaximal, characteristic, complemented
2#21458126C211yesmaximal, characteristic, complemented
3#21457537C211yesmaximal, characteristic, complemented
4#21445415C211yesmaximal, characteristic, complemented
5#21445366C211yesmaximal, characteristic, complemented
6#21445363C211yesmaximal, characteristic, complemented
7#21445206C211yesmaximal, characteristic, complemented
8#21445182C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic, complemented
10#21445103C211yesmaximal, characteristic, complemented
11#21445102C211yesmaximal, characteristic, complemented
12#21445101C211yesmaximal, characteristic, complemented
13#21444702C211yesmaximal, characteristic, complemented
14D8×#92418C211yesmaximal, characteristic, complemented
15C61×#3330C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840417C2211yescharacteristic
18#16840416C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840141C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840099—21no—
25#16840075—21no—
26#16840073—21no—
27#16840042C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840039C2211yescharacteristic
30#16840007—21no—
31#16840001—21no—
32#16839996—21no—
33#16839967C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839964C2211yescharacteristic
36#16839924—21no—
37#16839922—21no—
38#16839904—21no—
39C4×#11758199C2211yescharacteristic
40#16839841C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43C2×#14519710—21no—
44#16839760—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#547C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#484—21no—
60C61×#474C2211yescharacteristic
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#417—21no—
67C2×#11758222—21no—
68C2×#11758224—21no—
69#14519797—44no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758199D411yescharacteristic
76C2×#11758189—21no—
77C22×#92418—21no—
78C22×#92418—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519761—41no—
82#14519759—41no—
83#14519757—21no—
84#14519756—21no—
85#14519751—21no—
86#14519748—21no—
87C4×D244C2311yescharacteristic
88C2×C4⋊Dic61—21no—
89C4⋊C4×D61—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—21no—
95#14519710D411yescharacteristic
96#14519708—41no—
97#14519708—41no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519702—21no—
102#14519702—21no—
103#14519701—21no—
104#14519700—21no—
105#14519700—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×SD16×C61—21no—
119C2×D8×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#123×C61—41no—
124#123×C61—41no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134#107×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—42no—
147#41×C61—81no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—41no—
163C22×Dic61—41no—
164#11758224—42no—
165#11758224—81no—
166#11758222—42no—
167#11758222—81no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—41no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173SD16×C61—81no—
174D8×C61—22no—
175M16×C61—81no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61—41no—
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C42×C61C2411yescharacteristic
194C22⋊Dic61—41no—
195#11758202—42no—
196#11758202—81no—
197#11758201—42no—
198#11758200—42no—
199#11758200—81no—
200#11758199—22no—
201#11758198—21no—
202#11758198—41no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—41no—
208C4⋊Dic61C2×D411yescharacteristic
209#11758196—41no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—42no—
215C2×#92418—42no—
216C2×#92418C2×D411yescharacteristic
217C2×#92418C2×D411yescharacteristic
218#11758189—81no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C22×D61—21no—
223Q8×C61—41no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—82no—
233D4×C61—82no—
234D4×C61#13512yescomplemented
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—82no—
247C2×C4×C61—82no—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C22⋊D61—82no—
252C22⋊D61—82no—
253C2×Dic61—21no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—82no—
257D244—21no—
258D244—21no—
259C4×D61—41no—
260C4×D61—41no—
261C4×D61—82no—
262Dic122—41no—
263Dic122—41no—
264Dic122—41no—
265Dic122—41no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—41no—
269#92418—22no—
270#92418—21no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#92418AGL(1,ℤ/8)12yes—
275#19902—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61D4211yescharacteristic
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C4×C61—21no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—81no—
294C4×C61—81no—
295C4×C61C2×#13511yescharacteristic
296C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C61#57611yescharacteristic
298C4×C61#57711yescharacteristic
299Dic61—41no—
300Dic61—81no—
301Dic61—81no—
302#3334—611no—
303#3330—611no—
304#3330D6111yescharacteristic, complemented
305#3283—611no—
306#1707—611no—
307#1699—611no—
308#1699—611no—
309#1673—611no—
310#1669—611no—
311#1654—611no—
312#1654—611no—
313#1654—611no—
314#1654—611no—
315#1589—611no—
316C8×D8—611no—
317C2×C61—42no—
318C2×C61—81no—
319C2×C61—81no—
320C2×C61#327211yescharacteristic
321C2×C61#328011yescharacteristic
322C2×C61#329311yescharacteristic
323D61—81no—
324C2×#135—1221no—
325#547—611no—
326#547—611no—
327#547C2×D6111yescharacteristic
328#547C2×D6111yescharacteristic
329#500—611no—
330#498—611no—
331#498—611no—
332#494—611no—
333#487—611no—
334#487C2×D6111yescharacteristic
335#484—21no—
336#484—1221no—
337#480—1221no—
338#480—1221no—
339#474—611no—
340#474—611no—
341#474—611no—
342#474C2×D6111yescharacteristic
343#468—21no—
344#468—1221no—
345#467—1221no—
346#466—1221no—
347#461—611no—
348#461—611no—
349#461—611no—
350#461C2×D6111yescharacteristic
351#452—1221no—
352#452—1221no—
353#449—21no—
354#449—1221no—
355C4×D8—611no—
356C4×D8C2×D6111yescharacteristic
357#436—611no—
358#436C2×D6111yescharacteristic
359C8×D4—611no—
360C8×D4—611no—
361C2×#107—1221no—
362#417—21no—
363#417—1221no—
364#335—611no—
365#335—611no—
366#332—611no—
367#332—611no—
368#332—611no—
369#332—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374C82—611no—
375C61#1990211yescharacteristic, complemented, Sylow
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—1221no—
379C2×#41—1221no—
380#135—2444no—
381C2×Q16—1221no—
382C2×Q16—1221no—
383C2×SD16—21no—
384C2×SD16—1221no—
385C2×SD16—1221no—
386C2×SD16—1221no—
387C2×D8—611no—
388C2×D8C22⋊D6111yescharacteristic
389C2×M16—21no—
390C2×M16—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C4⋊Q8—611no—
394C4⋊Q8—611no—
395C4⋊Q8C22×D6111yescharacteristic
396C4⋊Q8C22×D6111yescharacteristic
397#123—41no—
398#123—41no—
399#123—2441no—
400#123—2441no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—1221no—
404C22⋊Q8—1221no—
405#121—21no—
406#121—21no—
407#121—1221no—
408#121—1221no—
409C4×D4—611no—
410C4×D4C22×D6111yescharacteristic
411C4×D4C22×D6111yescharacteristic
412C4×D4C22×D6111yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417#107—21no—
418#107—611no—
419#107—1221no—
420#107—1221no—
421#107—1221no—
422#107—1221no—
423#107—1221no—
424#107C22⋊D6111yescharacteristic
425#106—2441no—
426#106—2441no—
427C4⋊C8—611no—
428C4⋊C8—611no—
429C4⋊C8—611no—
430C4⋊C8C22×D6111yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—1221no—
435#103—1221no—
436#103—1221no—
437#103—1221no—
438#103—1221no—
439#102—21no—
440#102—611no—
441#102—611no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102C22⋊D6111yescharacteristic
446#102C22⋊D6111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8C22×D6111yescharacteristic
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458#41—4881no—
459#41—4881no—
460#41—2442no—
461#41—2442no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—611no—
469C2×D4—2441no—
470C2×D4—2441no—
471C2×D4D4×D6111yescharacteristic
472C2×D4C2×C22⋊D6111yescharacteristic
473C2×D4C2×C22⋊D6111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—1221no—
480C22×C4—2441no—
481C22×C4—2441no—
482Q16—4881no—
483Q16—2442no—
484SD16—81no—
485SD16—4881no—
486SD16—2442no—
487SD16—2442no—
488D8—22no—
489D8—1222no—
490M16—81no—
491M16—4881no—
492C2×C8—21no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—2442no—
500C2×C8—2442no—
501C2×C8C2×C22⋊D6111yescharacteristic
502C2×C8C2×C22⋊D6111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—611no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—2441no—
515C4⋊C4—2441no—
516C4⋊C4D4×D6111yescharacteristic
517C4⋊C4C2×C22⋊D6111yescharacteristic
518C4⋊C4C2×C22⋊D6111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—1221no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C42C23×D6111yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—1221no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—2441no—
537Q8—2441no—
538Q8—2441no—
539Q8—2441no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—82no—
546D4—82no—
547D4—1221no—
548D4—1221no—
549D4—4882no—
550D4—4882no—
551D4#1451979712yescomplemented
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—1221no—
566C2×C4—4882no—
567C2×C4—4882no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C2×D4×D6111yescharacteristic
573C2×C4C22×C22⋊D6111yescharacteristic
574C2×C4#1451982211yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—612no—
579C8—1222no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—2441no—
594C22—2441no—
595C22—2441no—
596C22D4×C22⋊D6111yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—4881no—
604C4—4881no—
605C4—2441no—
606C4C2×#1451979711yescharacteristic
607C4AGL(1,ℤ/8)×D6111yescharacteristic
608C4#1684056511yescharacteristic
609C4#1684057211yescharacteristic
610C2—42no—
611C2—81no—
612C2—81no—
613C2—4881no—
614C2#2145741311yescharacteristic
615C2#2145750011yescharacteristic
616C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3330C2
socleC22×C61D42
hypercenter#3330D61
hypocenterC61#19902
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #21458162C2semidirect
2. #21458126C2semidirect
3. #21457537C2semidirect
4. #21445415C2semidirect
5. #21445366C2semidirect
6. #21445363C2semidirect
7. #21445206C2semidirect
8. #21445182C2semidirect
9. #21445103C2semidirect
10. #21445103C2semidirect
11. #21445102C2semidirect
12. #21445101C2semidirect
13. #21444702C2semidirect
14. D8×#92418C2semidirect
15. C61×#3330C2semidirect
234. D4×C61#135semidirect
304. #3330D61semidirect
375. C61#19902semidirect
551. D4#14519797semidirect

Maximal subgroups

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

subgroupindex
#214581622
#214581262
#214575372
#214454152
#214453662
#214453632
#214452062
#214451822
#214451032
#214451022
#214451012
#214447022
D8×#924182
C61×#33302
#1990261