Finite Group Databasebeta

← #29650644

Subgroups — #29650644

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#21456410C211yesmaximal, characteristic
2#21454967C211yesmaximal, characteristic, complemented
3#21454893C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444724C211yesmaximal, characteristic, complemented
6#21444710C211yesmaximal, characteristic, complemented
7#21444703C211yesmaximal, characteristic, complemented
8#21444644C211yesmaximal, characteristic, complemented
9C8×#11758201C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444585C211yesmaximal, characteristic, complemented
12#21444278C211yesmaximal, characteristic, complemented
13#21444268C211yesmaximal, characteristic, complemented
14#21444098C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16#16840309C2211yescharacteristic
17#16840299C2211yescharacteristic
18#16840169C411yescharacteristic
19#16840148C411yescharacteristic
20#16840125C411yescharacteristic
21#16840123C411yescharacteristic
22#16840016C411yescharacteristic
23#16840014C411yescharacteristic
24#16840011C411yescharacteristic
25#16840005C411yescharacteristic
26#16839893C2211yescharacteristic
27C4×#11758201C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30#16839841—21no—
31#16839840C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839836—21no—
35#16839833—21no—
36#16839832—21no—
37C8×D244C2211yescharacteristic
38C8×D244C2211yescharacteristic
39#16839821—21no—
40#16839818C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839787—21no—
43#16839784C2211yescharacteristic
44#16839728—21no—
45#16839727—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839512C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201C2×C411yescharacteristic
69C2×D488C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189C2×C411yescharacteristic
76C2×#11758189C2×C411yescharacteristic
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80#14519776C2×C411yescharacteristic
81#14519773C2×C411yescharacteristic
82#14519772—21no—
83#14519768C2×C411yescharacteristic
84#14519766C2×C411yescharacteristic
85#14519763—21no—
86#14519762—21no—
87#14519753C2×C411yescharacteristic
88#14519752C2×C411yescharacteristic
89#14519752C2×C411yescharacteristic
90#14519750—21no—
91#14519748C2×C411yescharacteristic
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95C4×C22⋊D61—21no—
96#14519734—21no—
97C42×D61C2311yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689D411yescharacteristic
120#14519689D411yescharacteristic
121#14519688—21no—
122#14519687—21no—
123#14519687C2×C411yescharacteristic
124#14519687C2×C411yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
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×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61C22×C411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61#4111yescharacteristic
161C2×Dic122—21no—
162SD16×C61—22no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—81no—
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758201—22no—
179#11758199—22no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204D488—22no—
205#11758189—22no—
206#11758189—22no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210C8×D61—42no—
211C8×D61—81no—
212C8×D61—81no—
213C23×C61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217Q8×C61—21no—
218Q8×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—81no—
230C22⋊D61—81no—
231C22⋊D61—81no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237D244—21no—
238D244—21no—
239D244—21no—
240D244—21no—
241D244—81no—
242D244—81no—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—81no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61#13112yes—
260#92418—22no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418#13112yes—
267#17968—611nomaximal, Sylow
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×C4×D411yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61C2×#13111yescharacteristic
286C4×C61C2×#13111yescharacteristic
287C4×C61#57611yescharacteristic
288C4×C61#57711yescharacteristic
289Dic61—21no—
290Dic61—21no—
291Dic61—21no—
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⋊C8D6111yescharacteristic, complemented
303C8×SD16—611no—
304C8×D8—611no—
305#1569—611no—
306#1494—611no—
307#1492—611no—
308C8×M16—611no—
309C2×C61—81no—
310C2×C61#293111yescharacteristic
311C2×C61#294611yescharacteristic
312C2×C61#295611yescharacteristic
313D61—41no—
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×Q8C2×D6111yescharacteristic
328C4×SD16—611no—
329C4×SD16C2×D6111yescharacteristic
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×D4C2×D6111yescharacteristic
342#433—1221no—
343#432—611no—
344#431—611no—
345#424—1221no—
346#423—611no—
347#408—1221no—
348#408—1221no—
349C4×M16—611no—
350C2×C4×C8—611no—
351#335—611no—
352#335C2×D6111yescharacteristic
353#334—611no—
354#334—611no—
355Q8⋊C8—611no—
356Q8⋊C8C2×D6111yescharacteristic
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8C2×D6111yescharacteristic
363#322—611no—
364#322C2×D6111yescharacteristic
365C82—611no—
366C82—611no—
367C61#1796811yescharacteristic, complemented, Sylow
368C2×#41—1221no—
369C2×SD16—611no—
370C2×SD16C4×D6111yescharacteristic
371C2×D8—611no—
372C2×D8—611no—
373C2×M16—611no—
374C2×M16—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
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×Q8C22×D6111yescharacteristic
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—1221no—
399C4×D4—1221no—
400C4×D4C22×D6111yescharacteristic
401#117—1221no—
402C2×C42—611no—
403#107—611no—
404#107—611no—
405#106—611no—
406#106C4×D6111yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416#103—611no—
417#103C4×D6111yescharacteristic
418#102—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102C4×D6111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—611no—
426C22⋊C8—611no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—611no—
434#97—611no—
435#97—1221no—
436#97—1221no—
437C4×C8—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—1221no—
442C4×C8C22×D6111yescharacteristic
443C4×C8C22×D6111yescharacteristic
444C4×C8C22×D6111yescharacteristic
445#41—4881no—
446#41—4881no—
447C2×Q8—1221no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4C2×C4×D6111yescharacteristic
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1221no—
462C22×C4—1221no—
463SD16—22no—
464SD16—1222no—
465D8—1222no—
466D8—1222no—
467M16—1222no—
468M16—1222no—
469M16—4881no—
470M16—4881no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
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—4881no—
485C2×C8—4881no—
486C2×C8—2442no—
487C2×C8C2×C4×D6111yescharacteristic
488C2×C8C2×C4×D6111yescharacteristic
489C2×C8D4×D6111yescharacteristic
490C2×C8D4×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—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—21no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—611no—
516C23—1221no—
517C23—1221no—
518Q8—21no—
519Q8—21no—
520Q8—4881no—
521D4—21no—
522D4—21no—
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—41no—
536C2×C4—41no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—612no—
561C8—1222no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8#1451978312yes—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—1221no—
572C22—1221no—
573C22—1221no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22C4×D4×D6111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—1221no—
586C4—1221no—
587C4—1221no—
588C4—2441no—
589C4—2441no—
590C4#131×D6111yescharacteristic
591C4C2×#1451978311yescharacteristic
592C4#1684056611yescharacteristic
593C4#1684057111yescharacteristic
594C2—81no—
595C2—4881no—
596C2—4881no—
597C2—2441no—
598C2#2145452611yescharacteristic
599C2#2145465011yescharacteristic
600C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×SD16⋊C8C2
socleC22×C61C2×C4×D4
prime radical#21456410C2
cosocleC42×C61C24
hypercenterSD16⋊C8D61
hypocenterC61#17968
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454967C2semidirect
3. #21454893C2semidirect
4. #21444730C2semidirect
5. #21444724C2semidirect
6. #21444710C2semidirect
7. #21444703C2semidirect
8. #21444644C2semidirect
9. C8×#11758201C2semidirect
10. C8×#11758199C2semidirect
11. #21444585C2semidirect
12. #21444278C2semidirect
13. #21444268C2semidirect
14. #21444098C2semidirect
15. C61×SD16⋊C8C2semidirect
302. SD16⋊C8D61semidirect
367. C61#17968semidirect

Maximal subgroups

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

subgroupindex
#214564102
#214549672
#214548932
#214447302
#214447242
#214447102
#214447032
#214446442
C8×#117582012
C8×#117581992
#214445852
#214442782
#214442682
#214440982
C61×SD16⋊C82
#1796861