Finite Group Databasebeta

← #29650647

Subgroups — #29650647

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#21456414C211yesmaximal, characteristic
2#21454970C211yesmaximal, characteristic, complemented
3#21454894C211yesmaximal, characteristic, complemented
4#21444734C211yesmaximal, characteristic, complemented
5#21444723C211yesmaximal, characteristic, complemented
6#21444711C211yesmaximal, characteristic, complemented
7#21444705C211yesmaximal, characteristic, complemented
8#21444644C211yesmaximal, characteristic, complemented
9#21444633C211yesmaximal, characteristic, complemented
10C8×#11758190C211yesmaximal, characteristic, complemented
11C8×D488C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic, complemented
14#21444271C211yesmaximal, characteristic, complemented
15C8×M16×C61C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840171C411yescharacteristic
19#16840151C411yescharacteristic
20#16840127C411yescharacteristic
21#16840122C411yescharacteristic
22#16840015C411yescharacteristic
23#16840015C411yescharacteristic
24#16840008C411yescharacteristic
25#16840008C411yescharacteristic
26#16839892C2211yescharacteristic
27C8×Dic122C2211yescharacteristic
28C4×#11758190C2211yescharacteristic
29C4×#11758190C2211yescharacteristic
30C4×D488C2211yescharacteristic
31C4×D488C2211yescharacteristic
32#16839841C2211yescharacteristic
33#16839841C2211yescharacteristic
34#16839841C2211yescharacteristic
35#16839837—21no—
36#16839836—21no—
37#16839832—21no—
38#16839832—21no—
39C8×D244C2211yescharacteristic
40C8×D244C2211yescharacteristic
41C8×D244C2211yescharacteristic
42#16839822—21no—
43#16839819C2211yescharacteristic
44#16839787—21no—
45#16839786C2211yescharacteristic
46#16839727—21no—
47#16839727—21no—
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839491C2211yescharacteristic
57#16839491C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C4×M16×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C82×C61C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×D488C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519777C2×C411yescharacteristic
80#14519774C2×C411yescharacteristic
81#14519771—21no—
82#14519769C2×C411yescharacteristic
83#14519765—21no—
84#14519765C2×C411yescharacteristic
85#14519760—21no—
86#14519756C2×C411yescharacteristic
87#14519751—21no—
88#14519751C2×C411yescharacteristic
89#14519751C2×C411yescharacteristic
90#14519751C2×C411yescharacteristic
91C4×Dic122C2311yescharacteristic
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95C4×D244C2311yescharacteristic
96C4×C22⋊D61—21no—
97#14519734—21no—
98#14519711C2×C411yescharacteristic
99#14519711C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101#14519709C2×C411yescharacteristic
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114#14519699C2×C411yescharacteristic
115#14519699C2×C411yescharacteristic
116#14519699C2×C411yescharacteristic
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519688—21no—
125#14519687—21no—
126C8×Dic61—21no—
127C2×M16×C61C2×C411yescharacteristic
128C2×M16×C61C2×C411yescharacteristic
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C22⋊C8×C61D411yescharacteristic
134C22⋊C8×C61D411yescharacteristic
135#97×C61C2×C411yescharacteristic
136#97×C61C2×C411yescharacteristic
137C4×C8×C61—21no—
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150#11758222—81no—
151#11758222—81no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244C22×C411yescharacteristic
155C2×D244C22×C411yescharacteristic
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162M16×C61—22no—
163M16×C61—22no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—42no—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192C4⋊Dic61C22×C411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203D488—22no—
204D488—22no—
205#11758190—22no—
206#11758190—22no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210C8×D61—81no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—81no—
229C22⋊D61—81no—
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236D244—21no—
237D244—21no—
238D244—21no—
239D244—21no—
240D244—21no—
241D244—21no—
242D244—81no—
243D244—81no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250Dic122—21no—
251Dic122—21no—
252Dic122—81no—
253C8×C61—22no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261C8×C61#13112yes—
262C8×C61#13112yes—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#17968—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61C2×C4×D411yescharacteristic
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61C2×#13111yescharacteristic
286C4×C61C2×#13111yescharacteristic
287C4×C61#57611yescharacteristic
288C4×C61#57711yescharacteristic
289Dic61—41no—
290Dic61—41no—
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294#3171—611no—
295#2993—611no—
296#2981—611no—
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×M16D6111yescharacteristic, complemented
309C2×C61—41no—
310C2×C61#293111yescharacteristic
311C2×C61#294611yescharacteristic
312C2×C61#295611yescharacteristic
313D61—81no—
314D61—81no—
315D61—81no—
316#532—611no—
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—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337#435—1221no—
338#435—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342#433—1221no—
343#432—611no—
344#431C2×D6111yescharacteristic
345#424—1221no—
346#423—611no—
347#408—1221no—
348#408—1221no—
349C4×M16C2×D6111yescharacteristic
350C2×C4×C8C2×D6111yescharacteristic
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#322C2×D6111yescharacteristic
364#322C2×D6111yescharacteristic
365C82C2×D6111yescharacteristic
366C82C2×D6111yescharacteristic
367C61#1796811yescharacteristic, complemented, Sylow
368C2×#41—1221no—
369C2×SD16—611no—
370C2×SD16—611no—
371C2×D8—611no—
372C2×D8—611no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16C4×D6111yescharacteristic
378C2×M16C4×D6111yescharacteristic
379C22×C8—21no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C4⋊Q8—611no—
384#127—611no—
385#126—1221no—
386#125—611no—
387#124—611no—
388#124—1221no—
389#123—1221no—
390C22⋊Q8—611no—
391#121—611no—
392#121—611no—
393#121—611no—
394#121—1221no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
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—611no—
410C4⋊C8—611no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8D24411yescharacteristic
415C4⋊C8D24411yescharacteristic
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—1221no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8D24411yescharacteristic
432C22⋊C8D24411yescharacteristic
433#97—1221no—
434#97—1221no—
435#97C4×D6111yescharacteristic
436#97C4×D6111yescharacteristic
437C4×C8—21no—
438C4×C8—1221no—
439C4×C8C22×D6111yescharacteristic
440C4×C8C22×D6111yescharacteristic
441C4×C8C22×D6111yescharacteristic
442C4×C8C22×D6111yescharacteristic
443C4×C8C22×D6111yescharacteristic
444C4×C8C22×D6111yescharacteristic
445#41—4881no—
446#41—4881no—
447C2×Q8—611no—
448C2×Q8—1221no—
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×D24411yescharacteristic
462C22×C4#1175822211yescharacteristic
463SD16—1222no—
464SD16—1222no—
465D8—1222no—
466D8—1222no—
467M16—22no—
468M16—22no—
469M16—4881no—
470M16—4881no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—4881no—
481C2×C8—4881no—
482C2×C8—4881no—
483C2×C8C2×C4×D6111yescharacteristic
484C2×C8C2×C4×D6111yescharacteristic
485C2×C8C2×C4×D6111yescharacteristic
486C2×C8C2×C4×D6111yescharacteristic
487C2×C8C2×D24411yescharacteristic
488C2×C8C2×D24411yescharacteristic
489C2×C8C2×D24411yescharacteristic
490C2×C8C2×D24411yescharacteristic
491C4⋊C4—611no—
492C4⋊C4—611no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—1221no—
510C42C2×C4×D6111yescharacteristic
511C42C2×D24411yescharacteristic
512C42#1175822211yescharacteristic
513C42C23×D6111yescharacteristic
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23C4×D24411yescharacteristic
518Q8—1221no—
519Q8—1221no—
520Q8—4881no—
521D4—1221no—
522D4—1221no—
523D4—1221no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C4×D24411yescharacteristic
549C2×C4C4×D24411yescharacteristic
550C2×C4C4×D24411yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C22×D24411yescharacteristic
553C2×C4C2×#1175822211yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C8#1451978312yes—
567C8#1451978312yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22C2×C4×D24411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—2441no—
586C4—2441no—
587C4—2441no—
588C4—2441no—
589C4—2441no—
590C4C2×#1451978311yescharacteristic
591C4C2×#1451978311yescharacteristic
592C4#1684056711yescharacteristic
593C4#1684057411yescharacteristic
594C2—41no—
595C2—4881no—
596C2—4881no—
597C2—4881no—
598C2#2145453211yescharacteristic
599C2#2145465311yescharacteristic
600C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×M16×C61C2
socleC22×C61C2×C4×D4
prime radical#21456414C2
cosocleC42×C61C24
hypercenterC8×M16D61
hypocenterC61#17968
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #21454970C2semidirect
3. #21454894C2semidirect
4. #21444734C2semidirect
5. #21444723C2semidirect
6. #21444711C2semidirect
7. #21444705C2semidirect
8. #21444644C2semidirect
9. #21444633C2semidirect
10. C8×#11758190C2semidirect
11. C8×D488C2semidirect
12. #21444586C2semidirect
13. #21444280C2semidirect
14. #21444271C2semidirect
15. C8×M16×C61C2semidirect
308. C8×M16D61semidirect
367. C61#17968semidirect

Maximal subgroups

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

subgroupindex
#214564142
#214549702
#214548942
#214447342
#214447232
#214447112
#214447052
#214446442
#214446332
C8×#117581902
C8×D4882
#214445862
#214442802
#214442712
C8×M16×C612
#1796861