Finite Group Databasebeta

← #29650643

Subgroups — #29650643

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456408C211yesmaximal, characteristic
2#21454970C211yesmaximal, characteristic, complemented
3#21444731C211yesmaximal, characteristic, complemented
4#21444721C211yesmaximal, characteristic, complemented
5#21444707C211yesmaximal, characteristic, complemented
6#21444702C211yesmaximal, characteristic, complemented
7#21444641C211yesmaximal, characteristic, complemented
8#21444631C211yesmaximal, characteristic, complemented
9C8×#11758200C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444587C211yesmaximal, characteristic, complemented
12#21444277C211yesmaximal, characteristic, complemented
13#21444270C211yesmaximal, characteristic, complemented
14#21444100C211yesmaximal, characteristic, complemented
15C61×#2981C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168C411yescharacteristic
18#16840149C411yescharacteristic
19#16840126C411yescharacteristic
20#16840124C411yescharacteristic
21#16840013C411yescharacteristic
22#16840013C411yescharacteristic
23#16840006C411yescharacteristic
24#16840006C411yescharacteristic
25#16839892C2211yescharacteristic
26C8×Dic122C2211yescharacteristic
27C4×#11758200C2211yescharacteristic
28C4×#11758200C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839837—21no—
33#16839836—21no—
34C8×D244C2211yescharacteristic
35#16839822—21no—
36#16839787—21no—
37#16839786C2211yescharacteristic
38C4×#11758194C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44#16839492C2211yescharacteristic
45#16839492C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54C8×#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C61×#436C2211yescharacteristic
58C61×#436C2211yescharacteristic
59C61×#435—21no—
60C61×#435—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#432C2211yescharacteristic
64C61×#431C2211yescharacteristic
65C61×#408—21no—
66C61×#408—21no—
67C2×#11758200C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758194C2×C411yescharacteristic
73C2×#11758194C2×C411yescharacteristic
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769C2×C411yescharacteristic
79#14519765C2×C411yescharacteristic
80#14519760—21no—
81#14519756C2×C411yescharacteristic
82#14519751C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519706—21no—
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519698C2×C411yescharacteristic
99#14519698C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103#14519697C2×C411yescharacteristic
104#14519689—21no—
105#14519689—21no—
106#14519688C2×C411yescharacteristic
107#14519688C2×C411yescharacteristic
108#14519687—21no—
109C4×#92418—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C22×C8×C61—21no—
119C22×C8×C61—21no—
120C4⋊Q8×C61C2×C411yescharacteristic
121#127×C61C2×C411yescharacteristic
122#124×C61—21no—
123#121×C61—21no—
124#121×C61C2×C411yescharacteristic
125#121×C61C2×C411yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—81no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61C22×C411yescharacteristic
152C2×D4×C61C22×C411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C2×C22⋊D61—21no—
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×Dic122C22×C411yescharacteristic
162M16×C61—81no—
163M16×C61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—81no—
167C2×C8×C61—81no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊C4×C61—21no—
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183C22⋊Dic61—21no—
184#11758200—22no—
185#11758200—22no—
186#11758199—22no—
187#11758199—22no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199#11758194—22no—
200#11758194—22no—
201#11758194—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—42no—
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211#11758189—81no—
212C8×D61—81no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C4×D411yescharacteristic
216C22×D61—21no—
217Q8×C61—81no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—81no—
223D4×C61—81no—
224D4×C61—81no—
225D4×C61—81no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C22⋊D61—81no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247D244—21no—
248D244—21no—
249C4×D61—41no—
250C4×D61—41no—
251Dic122—21no—
252Dic122—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—22no—
260#92418—21no—
261#92418—21no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418#13112yes—
266#92418#13112yes—
267#17968—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61C2×C4×D411yescharacteristic
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289C4×C61#57611yescharacteristic
290C4×C61#57711yescharacteristic
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294#3171—611no—
295#2993—611no—
296#2981D6111yescharacteristic, complemented
297#1594—611no—
298#1592—611no—
299#1590—611no—
300#1589—611no—
301#1580—611no—
302SD16⋊C8—611no—
303C8×SD16—611no—
304C8×D8—611no—
305#1569—611no—
306#1494—611no—
307#1492—611no—
308C8×M16—611no—
309C2×C61—41no—
310C2×C61—81no—
311C2×C61—81no—
312C2×C61#293111yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295611yescharacteristic
315D61—81no—
316#532C2×D6111yescharacteristic
317#529—611no—
318#501—611no—
319#496—611no—
320#490—611no—
321#489—611no—
322#469—611no—
323#469—611no—
324#468—611no—
325#468—611no—
326#446—611no—
327C8×Q8—611no—
328C4×SD16—611no—
329C4×SD16—611no—
330C4×D8—611no—
331C4×D8—611no—
332#436—611no—
333#436—1221no—
334#436C2×D6111yescharacteristic
335#436C2×D6111yescharacteristic
336#435—21no—
337#435—21no—
338#435—1221no—
339C8×D4—611no—
340C8×D4C2×D6111yescharacteristic
341C8×D4C2×D6111yescharacteristic
342#433—1221no—
343#432C2×D6111yescharacteristic
344#431C2×D6111yescharacteristic
345#424—1221no—
346#423—611no—
347#408—21no—
348#408—21no—
349C4×M16—611no—
350C2×C4×C8—611no—
351#335—611no—
352#335—611no—
353#334—611no—
354#334—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363#322—611no—
364#322—611no—
365C82—611no—
366C82—611no—
367C61#1796811yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×SD16—611no—
370C2×SD16—611no—
371C2×D8—611no—
372C2×D8—611no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—611no—
376C2×M16—611no—
377C2×M16—1221no—
378C2×M16—1221no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—1221no—
382C22×C8—1221no—
383C4⋊Q8C4×D6111yescharacteristic
384#127C4×D6111yescharacteristic
385#126—1221no—
386#125—611no—
387#124—21no—
388#124—611no—
389#123—1221no—
390C22⋊Q8—611no—
391#121—21no—
392#121—611no—
393#121C4×D6111yescharacteristic
394#121C4×D6111yescharacteristic
395C4×Q8—611no—
396C4×D4—21no—
397C4×D4—611no—
398C4×D4—1221no—
399C4×D4C22×D6111yescharacteristic
400C4×D4C22×D6111yescharacteristic
401#117—1221no—
402C2×C42C22×D6111yescharacteristic
403#107—611no—
404#107—611no—
405#106—611no—
406#106—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8C22⋊D6111yescharacteristic
413C4⋊C8C22⋊D6111yescharacteristic
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416#103—611no—
417#103—611no—
418#102—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8C22⋊D6111yescharacteristic
432C22⋊C8C22⋊D6111yescharacteristic
433#97—21no—
434#97—611no—
435#97—611no—
436#97—1221no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—1221no—
442C4×C8—1221no—
443C4×C8C22×D6111yescharacteristic
444C4×C8C22×D6111yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—611no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—611no—
454C2×D4—1221no—
455C2×D4C2×C4×D6111yescharacteristic
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—1221no—
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4#1175822211yescharacteristic
462C22×C4C2×C22⋊D6111yescharacteristic
463SD16—1222no—
464SD16—1222no—
465D8—1222no—
466D8—1222no—
467M16—81no—
468M16—81no—
469M16—1222no—
470M16—1222no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—4881no—
486C2×C8—2442no—
487C2×C8C2×C22⋊D6111yescharacteristic
488C2×C8C2×C22⋊D6111yescharacteristic
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—611no—
493C4⋊C4—611no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4C2×C4×D6111yescharacteristic
499C4⋊C4C2×C4×D6111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—1221no—
510C42C2×C4×D6111yescharacteristic
511C42#1175822211yescharacteristic
512C42C2×C22⋊D6111yescharacteristic
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—21no—
516C23—1221no—
517C23C4×C22⋊D6111yescharacteristic
518Q8—81no—
519Q8—1221no—
520Q8—1221no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—1221no—
530D4—1221no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C4×C22⋊D6111yescharacteristic
549C2×C4C4×C22⋊D6111yescharacteristic
550C2×C4C4×C22⋊D6111yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C22×C22⋊D6111yescharacteristic
553C2×C4C2×#1175822211yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—612no—
561C8—612no—
562C8—1222no—
563C8—1221no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22C2×C4×C22⋊D6111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—2441no—
588C4—2441no—
589C4—2441no—
590C4#131×D6111yescharacteristic
591C4#131×D6111yescharacteristic
592C4#1684056511yescharacteristic
593C4#1684057311yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—4881no—
598C2#2145452911yescharacteristic
599C2#2145465111yescharacteristic
600C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2981C2
socleC22×C61C2×C4×D4
prime radical#21456408C2
cosocleC42×C61C24
hypercenter#2981D61
hypocenterC61#17968
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #21454970C2semidirect
3. #21444731C2semidirect
4. #21444721C2semidirect
5. #21444707C2semidirect
6. #21444702C2semidirect
7. #21444641C2semidirect
8. #21444631C2semidirect
9. C8×#11758200C2semidirect
10. C8×#11758199C2semidirect
11. #21444587C2semidirect
12. #21444277C2semidirect
13. #21444270C2semidirect
14. #21444100C2semidirect
15. C61×#2981C2semidirect
296. #2981D61semidirect
367. C61#17968semidirect

Maximal subgroups

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

subgroupindex
#214564082
#214549702
#214447312
#214447212
#214447072
#214447022
#214446412
#214446312
C8×#117582002
C8×#117581992
#214445872
#214442772
#214442702
#214441002
C61×#29812
#1796861