Finite Group Databasebeta

← #29669480

Subgroups — #29669480

Order 15616.

756 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458716C211yesmaximal, characteristic, complemented
2#21457643C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445445C211yesmaximal, characteristic, complemented
5#21445300C211yesmaximal, characteristic, complemented
6#21445226C211yesmaximal, characteristic, complemented
7#21445194C211yesmaximal, characteristic, complemented
8#21445158C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic, complemented
10#21444935C211yesmaximal, characteristic, complemented
11#21444921C211yesmaximal, characteristic, complemented
12#21444889C211yesmaximal, characteristic, complemented
13#21444655C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15D4×D8×C61C211yesmaximal, characteristic
16C22×#11758200—21no—
17#16840469C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic, complemented
19#16840170—21no—
20#16840160C2211yescharacteristic, complemented
21#16840134C2211yescharacteristic, complemented
22#16840134C2211yescharacteristic, complemented
23#16840108C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic, complemented
25#16840078—21no—
26#16840064—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16840050—21no—
30#16840042C2211yescharacteristic, complemented
31#16839989—21no—
32#16839989—21no—
33#16839967C2211yescharacteristic
34#16839959C2211yescharacteristic, complemented
35#16839959C2211yescharacteristic, complemented
36#16839913—21no—
37#16839913—21no—
38#16839900—21no—
39#16839892C2211yescharacteristic, complemented
40#16839874—21no—
41C4×#11758200C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic, complemented
44C2×#14519698—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic, complemented
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54D4⋊#92418C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C22×D8×C61—21no—
57D42×C61C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#493C2211yescharacteristic
60C61×#466—21no—
61C61×#459C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C61×#447—21no—
65C4×D8×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—41no—
74C2×#11758200—44no—
75C2×#11758200D411yescharacteristic
76C22×#92418—21no—
77C22×#92418—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519776—21no—
81#14519768—21no—
82#14519756—21no—
83#14519756—21no—
84#14519754—41no—
85#14519754—41no—
86C4×Dic122C2311yescharacteristic
87D4×Dic61—21no—
88D4×Dic61—21no—
89C2×C4⋊Dic61—21no—
90#14519710—21no—
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708D411yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519700—21no—
101#14519700D411yescharacteristic
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519687—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C2×D8×C61—21no—
121C2×D8×C61—21no—
122C2×D8×C61—21no—
123C2×D8×C61—21no—
124C2×D8×C61—44no—
125C2×D8×C61D411yescharacteristic
126C22×C8×C61—21no—
127#127×C61C2311yescharacteristic
128#127×C61C2311yescharacteristic
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#120×C61—41no—
134#120×C61—41no—
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C4×D4×C61C2311yescharacteristic
138#107×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147C24×C61—41no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—81no—
163C2×D4×C61—81no—
164C2×D4×C61—81no—
165C2×D4×C61—81no—
166C2×D4×C61C2×D411yescharacteristic
167C2×D4×C61C2×D411yescharacteristic
168C2×D4×C61C2×D411yescharacteristic
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×Dic61—41no—
173C22×Dic61—41no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—42no—
177C2×Dic122—41no—
178C2×Dic122—81no—
179C2×Dic122C2×D411yescharacteristic
180D8×C61—42no—
181D8×C61—42no—
182D8×C61—42no—
183D8×C61—81no—
184D8×C61SD1614yescomplemented
185C2×C8×C61—21no—
186C2×C8×C61—42no—
187C2×C8×C61C2×D411yescharacteristic
188C2×C8×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C4⋊C4×C61C2×D411yescharacteristic
191C4⋊C4×C61C2×D411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C42×C61C2411yescharacteristic
198C22⋊Dic61—41no—
199C22⋊Dic61—41no—
200#11758200—22no—
201#11758200—42no—
202#11758200—42no—
203#11758200—42no—
204#11758200—81no—
205#11758200—81no—
206#11758200—82no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—41no—
212C4⋊Dic61C2×D411yescharacteristic
213#11758196—21no—
214#11758196—41no—
215#11758196—41no—
216C4×Dic61—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—42no—
222C2×#92418—81no—
223C2×#92418C2×D411yescharacteristic
224C2×#92418C2×D411yescharacteristic
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—82no—
231C23×C61—82no—
232C23×C61—82no—
233C23×C61—82no—
234C23×C61—161no—
235C23×C61—161no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—41no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—81no—
248D4×C61—81no—
249D4×C61—82no—
250D4×C61—82no—
251D4×C61—82no—
252D4×C61—82no—
253D4×C61C2×SD1612yes—
254D4×C61C2×SD1612yescomplemented
255D4×C61AGL(1,ℤ/8)12yes—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—82no—
273C2×Dic61—161no—
274Dic122—21no—
275Dic122—21no—
276Dic122—41no—
277Dic122—41no—
278Dic122—82no—
279Dic122—81no—
280C8×C61—21no—
281C8×C61—41no—
282C8×C61C2×SD1612yescomplemented
283#92418—21no—
284#92418—21no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#92418—41no—
289#19763—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61—81no—
304C22×C61—81no—
305C22×C61—164no—
306C22×C61—164no—
307C22×C61D4211yescharacteristic
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61C22×SD1611yescharacteristic
313C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C61#57611yescharacteristic
315C4×C61#57711yescharacteristic
316Dic61—41no—
317Dic61—41no—
318Dic61—81no—
319Dic61—81no—
320#3384—611no—
321#3295—611no—
322D4×SD16—611no—
323D4×D8D6111yescharacteristic
324#1715—611no—
325#1688—611no—
326#1677—611no—
327#1671—611no—
328#1665—611no—
329#1639—611no—
330#1629—611no—
331#1627—611no—
332#1622—611no—
333#1582—611no—
334#1580—611no—
335C2×C61—42no—
336C2×C61—42no—
337C2×C61—42no—
338C2×C61—161no—
339C2×C61—161no—
340C2×C61#326411yescharacteristic
341C2×C61D4×SD1611yescharacteristic
342C2×C61#328811yescharacteristic
343C22×SD16—1221no—
344C22×D8—21no—
345#554—611no—
346D4×Q8—611no—
347D42C2×D6111yescharacteristic
348D42C2×D6111yescharacteristic
349#501—1221no—
350#498—611no—
351#493C2×D6111yescharacteristic
352#492—611no—
353#492—611no—
354#486—611no—
355#486—611no—
356#481—1221no—
357#478—1221no—
358#476—611no—
359#476—611no—
360#476—1221no—
361#474—611no—
362#466—21no—
363#465—1221no—
364#465—1221no—
365#461—611no—
366#460—611no—
367#460—611no—
368#459C2×D6111yescharacteristic
369#459C2×D6111yescharacteristic
370#450—1221no—
371#450—1221no—
372#448—1221no—
373#447—21no—
374#447—21no—
375#446—611no—
376#442—1221no—
377C4×SD16—611no—
378C4×D8C2×D6111yescharacteristic
379C8×D4—611no—
380C8×D4—611no—
381C8×D4C2×D6111yescharacteristic
382C2×#102—1221no—
383#334—611no—
384#334—611no—
385#333—611no—
386#332—611no—
387#331—611no—
388#331—611no—
389Q8⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8—611no—
392D4⋊C8—611no—
393#322—611no—
394C61#1976311yescharacteristic, complemented, Sylow
395C22×Q8—1221no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—21no—
400C2×SD16—611no—
401C2×SD16—1221no—
402C2×SD16—1221no—
403C2×SD16—1221no—
404C2×SD16—1221no—
405C2×SD16—1221no—
406C2×SD16—2441no—
407C2×SD16—2444no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—21no—
411C2×D8—21no—
412C2×D8—44no—
413C2×D8C22⋊D6111yescharacteristic
414C22×C8—21no—
415C22×C8—1221no—
416C22×C8—1221no—
417C4⋊Q8—611no—
418C4⋊Q8—611no—
419C4⋊Q8—1221no—
420#127C22×D6111yescharacteristic
421#127C22×D6111yescharacteristic
422#125—1221no—
423C22⋊Q8—1221no—
424C22⋊Q8—1221no—
425C22⋊Q8—2441no—
426C22⋊Q8—2441no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#120—41no—
432#120—41no—
433C4×Q8—611no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438C4×D4C22×D6111yescharacteristic
439C2×C4⋊C4—1221no—
440#107—1221no—
441#107C22⋊D6111yescharacteristic
442#106—611no—
443#106—1221no—
444#106—1221no—
445#106—1221no—
446#106—1221no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—611no—
450C4⋊C8—1221no—
451C4⋊C8C22×D6111yescharacteristic
452#103—611no—
453#103—1221no—
454#102—21no—
455#102—21no—
456#102—611no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—1221no—
464#102—2441no—
465#102C22⋊D6111yescharacteristic
466#102C22⋊D6111yescharacteristic
467C22⋊C8—21no—
468C22⋊C8—1221no—
469C22⋊C8—1221no—
470#97—1221no—
471C4×C8—611no—
472C4×C8—611no—
473C4×C8C22×D6111yescharacteristic
474C24—41no—
475C24—41no—
476C2×Q8—611no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×Q8—4881no—
480C2×Q8—2441no—
481C2×Q8—2442no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4D4×D6111yescharacteristic
501C2×D4C2×C22⋊D6111yescharacteristic
502C2×D4C2×C22⋊D6111yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—2441no—
507C22×C4—2441no—
508SD16—1222no—
509SD16—4881no—
510SD16—4881no—
511SD16—4882no—
512SD16—2442no—
513SD16—2442no—
514SD16—2442no—
515D8—42no—
516D8—42no—
517D8—42no—
518D8—81no—
519D8#1175820014yescomplemented
520C2×C8—21no—
521C2×C8—42no—
522C2×C8—611no—
523C2×C8—611no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—4881no—
529C2×C8—2442no—
530C2×C8C2×C22⋊D6111yescharacteristic
531C2×C8C2×C22⋊D6111yescharacteristic
532C4⋊C4—611no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—2441no—
539C4⋊C4—2441no—
540C4⋊C4—2441no—
541C4⋊C4D4×D6111yescharacteristic
542C4⋊C4C2×C22⋊D6111yescharacteristic
543C4⋊C4C2×C22⋊D6111yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—2441no—
550C22⋊C4—2441no—
551C42—1221no—
552C42C23×D6111yescharacteristic
553C23—21no—
554C23—21no—
555C23—21no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23—161no—
563C23—161no—
564Q8—1221no—
565Q8—1221no—
566Q8—4881no—
567Q8—4882no—
568Q8—2441no—
569Q8—2441no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—81no—
582D4—81no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587D4C2×#1175820012yes—
588D4C2×#1175820012yescomplemented
589D4#1451980112yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—9761no—
602C2×C4—4882no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C22×C22⋊D6111yescharacteristic
607C2×C4#1451982211yescharacteristic
608C8—21no—
609C8—41no—
610C8—1221no—
611C8—1221no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C8—2441no—
616C8C2×#1175820012yescomplemented
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—164no—
633C22—164no—
634C22D4×C22⋊D6111yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—4881no—
640C4—4881no—
641C4—2441no—
642C4—2441no—
643C4C22×#1175820011yescharacteristic
644C4C2×#1451980111yescharacteristic
645C4#1684056311yescharacteristic
646C4#1684057311yescharacteristic
647C2—42no—
648C2—42no—
649C2—42no—
650C2—161no—
651C2—161no—
652C2#2145729911yescharacteristic
653C2D4×#1175820011yescharacteristic
654C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalD4×D8×C61C2
socleC22×C61D42
hypercenterD4×D8D61
hypocenterC61#19763
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #21458716C2semidirect
2. #21457643C2semidirect
3. D4×#11758200C2semidirect
4. #21445445C2semidirect
5. #21445300C2semidirect
6. #21445226C2semidirect
7. #21445194C2semidirect
8. #21445158C2semidirect
9. #21444998C2semidirect
10. #21444935C2semidirect
11. #21444921C2semidirect
12. #21444889C2semidirect
13. #21444655C2semidirect
14. #21444643C2semidirect
17. #16840469C22semidirect
18. D4×Dic122C22semidirect
20. #16840160C22semidirect
21. #16840134C22semidirect
22. #16840134C22semidirect
23. #16840108C22semidirect
24. #16840108C22semidirect
28. #16840052C22semidirect
30. #16840042C22semidirect
34. #16839959C22semidirect
35. #16839959C22semidirect
39. #16839892C22semidirect
42. D4×#92418C22semidirect
43. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839507C22semidirect
49. #16839506C22semidirect
50. #16839506C22semidirect
51. #16839492C22semidirect
53. D4⋊#92418C22semidirect
54. D4⋊#92418C22semidirect
55. #16839483C22semidirect
184. D8×C61SD16semidirect
254. D4×C61C2×SD16semidirect
282. C8×C61C2×SD16semidirect
394. C61#19763semidirect
519. D8#11758200semidirect
588. D4C2×#11758200semidirect
616. C8C2×#11758200semidirect

Maximal subgroups

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

subgroupindex
#214587162
#214576432
D4×#117582002
#214454452
#214453002
#214452262
#214451942
#214451582
#214449982
#214449352
#214449212
#214448892
#214446552
#214446432
D4×D8×C612
#1976361