Finite Group Databasebeta

← #29669484

Subgroups — #29669484

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#21458717C211yesmaximal, characteristic, complemented
2#21457640C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4D4×#11758199C211yesmaximal, characteristic
5#21445446C211yesmaximal, characteristic, complemented
6#21445302C211yesmaximal, characteristic, complemented
7#21445230C211yesmaximal, characteristic, complemented
8#21445196C211yesmaximal, characteristic, complemented
9#21445159C211yesmaximal, characteristic, complemented
10#21445000C211yesmaximal, characteristic, complemented
11#21444925C211yesmaximal, characteristic, complemented
12#21444888C211yesmaximal, characteristic, complemented
13#21444652C211yesmaximal, characteristic, complemented
14#21444640C211yesmaximal, characteristic, complemented
15C61×#1629C211yesmaximal, characteristic, complemented
16C22×#11758200—21no—
17C22×#11758199—21no—
18#16840473C2211yescharacteristic, complemented
19D4×Dic122C2211yescharacteristic, complemented
20D4×D244C2211yescharacteristic
21#16840169—21no—
22#16840158C2211yescharacteristic, complemented
23#16840138C2211yescharacteristic
24#16840134C2211yescharacteristic, complemented
25#16840110C2211yescharacteristic, complemented
26#16840109C2211yescharacteristic, complemented
27#16840082—21no—
28#16840060—21no—
29#16840051—21no—
30#16840043C2211yescharacteristic, complemented
31#16839996—21no—
32#16839992—21no—
33#16839989—21no—
34#16839967C2211yescharacteristic
35#16839963C2211yescharacteristic, complemented
36#16839959C2211yescharacteristic, complemented
37#16839957C2211yescharacteristic
38#16839954C2211yescharacteristic
39#16839914—21no—
40#16839913—21no—
41#16839900—21no—
42#16839896—21no—
43#16839895—21no—
44#16839889C2211yescharacteristic, complemented
45#16839871—21no—
46C4×#11758200C2211yescharacteristic
47C4×#11758199C2211yescharacteristic
48D4×#92418C2211yescharacteristic
49D4×#92418C2211yescharacteristic, complemented
50#16839827C2211yescharacteristic, complemented
51#102×D61—21no—
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839511C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839505C2211yescharacteristic, complemented
57#16839494C2211yescharacteristic, complemented
58#16839491C2211yescharacteristic, complemented
59#16839484C2211yescharacteristic, complemented
60D42×C61C2211yescharacteristic
61C61×#492C2211yescharacteristic, complemented
62C61×#476C2211yescharacteristic
63C61×#476C2211yescharacteristic, complemented
64C61×#331C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic, complemented
67C22×Dic122—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758200—44no—
76C2×#11758200D411yescharacteristic
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758199—21no—
81C2×#11758199—44no—
82C2×#11758199D411yescharacteristic
83C22×#92418—21no—
84C22×#92418—21no—
85C2×C8×D61—21no—
86#14519777C2311yescharacteristic
87#14519776—21no—
88#14519774C2311yescharacteristic
89#14519768—21no—
90#14519757—21no—
91#14519756—21no—
92#14519754—41no—
93#14519753—41no—
94#14519752—21no—
95#14519751—21no—
96#14519747—41no—
97C4×Dic122C2311yescharacteristic
98C4×D244C2311yescharacteristic
99D4×Dic61—21no—
100#14519739—21no—
101C4⋊C4×D61—21no—
102#14519711—21no—
103#14519710D411yescharacteristic
104#14519708—21no—
105#14519708—21no—
106#14519708D411yescharacteristic
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109#14519706—21no—
110#14519700—21no—
111#14519700D411yescharacteristic
112#14519699—21no—
113#14519699—21no—
114#14519699—41no—
115#14519698—21no—
116#14519698—21no—
117#14519698D411yescharacteristic
118#14519698D411yescharacteristic
119#14519697—21no—
120#14519697—21no—
121#14519697—21no—
122#14519697D411yescharacteristic
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519689—21no—
126#14519687—21no—
127C4×#92418C2311yescharacteristic
128C4×#92418C2311yescharacteristic
129C22×D4×C61—21no—
130C22×D4×C61—21no—
131C2×SD16×C61—41no—
132C4⋊Q8×C61C2311yescharacteristic
133#127×C61C2311yescharacteristic
134#121×C61—21no—
135#121×C61—21no—
136#120×C61—41no—
137C4×D4×C61C2311yescharacteristic
138C4×D4×C61C2311yescharacteristic
139#106×C61—21no—
140#106×C61—21no—
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143#102×C61—21no—
144#102×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147C23×D61—41no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C2×C22⋊D61—41no—
163C22×Dic61—41no—
164D4×D61—42no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—42no—
170C2×D244—41no—
171C2×D244—81no—
172C2×D244C2×D411yescharacteristic
173C2×C4×D61—21no—
174C2×C4×D61—41no—
175C2×Dic122—21no—
176C2×Dic122—42no—
177C2×Dic122—41no—
178C2×Dic122—81no—
179C2×Dic122C2×D411yescharacteristic
180SD16×C61—82no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—41no—
191C42×C61C2411yescharacteristic
192C22⋊Dic61—41no—
193#11758200—22no—
194#11758200—42no—
195#11758200—42no—
196#11758200—42no—
197#11758200—81no—
198#11758199—42no—
199#11758199—42no—
200#11758199—42no—
201#11758199—81no—
202#11758199SD1614yescomplemented
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—41no—
209C4⋊Dic61C2×D411yescharacteristic
210C4⋊Dic61C2×D411yescharacteristic
211#11758196—21no—
212#11758196—41no—
213#11758196—41no—
214C4×Dic61—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—42no—
218C2×#92418—42no—
219C2×#92418C2×D411yescharacteristic
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222C2×#92418C2×D411yescharacteristic
223#11758190—81no—
224C8×D61—81no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—41no—
228C23×C61—82no—
229C23×C61—82no—
230C23×C61—161no—
231C22×D61—21no—
232C22×D61—41no—
233C22×D61—82no—
234C22×D61—82no—
235C22×D61—161no—
236Q8×C61—81no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—81no—
244D4×C61—82no—
245D4×C61—82no—
246D4×C61C2×SD1612yes—
247D4×C61AGL(1,ℤ/8)12yes—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—41no—
263C2×Dic61—82no—
264D244—21no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—81no—
270D244—82no—
271D244C2×SD1612yescomplemented
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—161no—
275Dic122—21no—
276Dic122—21no—
277Dic122—41no—
278Dic122—41no—
279Dic122—82no—
280C8×C61—41no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—21no—
284#92418—21no—
285#92418—21no—
286#92418—41no—
287#92418—41no—
288#92418C2×SD1612yescomplemented
289#19763—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61—164no—
300C22×C61D4211yescharacteristic
301C2×D61—22no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—164no—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—81no—
312C4×C61C22×SD1611yescharacteristic
313C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C61#57611yescharacteristic
315C4×C61#57711yescharacteristic
316Dic61—41no—
317Dic61—41no—
318Dic61—41no—
319Dic61—81no—
320#3384—611no—
321#3295—611no—
322D4×SD16—611no—
323D4×D8—611no—
324#1715—611no—
325#1688—611no—
326#1677—611no—
327#1671—611no—
328#1665—611no—
329#1639—611no—
330#1629D6111yescharacteristic, complemented
331#1627—611no—
332#1622—611no—
333#1582—611no—
334#1580—611no—
335C2×C61—42no—
336C2×C61—42no—
337C2×C61—161no—
338C2×C61#326411yescharacteristic
339C2×C61D4×SD1611yescharacteristic
340C2×C61#328811yescharacteristic
341D61—42no—
342D61—161no—
343C22×SD16—1221no—
344C22×D8—1221no—
345#554—611no—
346D4×Q8—611no—
347D42—611no—
348D42C2×D6111yescharacteristic
349#501—1221no—
350#498—611no—
351#493—611no—
352#492—611no—
353#492C2×D6111yescharacteristic, complemented
354#486—611no—
355#486—611no—
356#481—1221no—
357#478—1221no—
358#476—1221no—
359#476C2×D6111yescharacteristic
360#476C2×D6111yescharacteristic, complemented
361#474—611no—
362#466—1221no—
363#465—1221no—
364#465—1221no—
365#461—611no—
366#460—611no—
367#460—611no—
368#459—611no—
369#459—611no—
370#450—1221no—
371#450—1221no—
372#448—1221no—
373#447—1221no—
374#447—1221no—
375#446—611no—
376#442—1221no—
377C4×SD16—611no—
378C4×D8—611no—
379C8×D4—611no—
380C8×D4—611no—
381C8×D4—611no—
382C2×#102—1221no—
383#334—611no—
384#334—611no—
385#333—611no—
386#332—611no—
387#331—611no—
388#331C2×D6111yescharacteristic, complemented
389Q8⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8C2×D6111yescharacteristic
392D4⋊C8C2×D6111yescharacteristic, complemented
393#322—611no—
394C61#1976311yescharacteristic, complemented, Sylow
395C22×Q8—1221no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—1221no—
399C22×D4—1221no—
400C2×SD16—41no—
401C2×SD16—611no—
402C2×SD16—1221no—
403C2×SD16—1221no—
404C2×SD16—1221no—
405C2×SD16—1221no—
406C2×SD16—1221no—
407C2×SD16—2444no—
408C2×D8—611no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8—1221no—
413C2×D8—2444no—
414C22×C8—1221no—
415C22×C8—1221no—
416C22×C8—1221no—
417C4⋊Q8—611no—
418C4⋊Q8—1221no—
419C4⋊Q8C22×D6111yescharacteristic
420#127—611no—
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—1221no—
430#121—1221no—
431#120—41no—
432#120—2441no—
433C4×Q8—611no—
434C4×D4—611no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4C22×D6111yescharacteristic
438C4×D4C22×D6111yescharacteristic
439C2×C4⋊C4—1221no—
440#107—611no—
441#107—1221no—
442#106—21no—
443#106—21no—
444#106—611no—
445#106—1221no—
446#106—1221no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—1221no—
450C4⋊C8C22×D6111yescharacteristic
451C4⋊C8C22×D6111yescharacteristic
452#103—611no—
453#103—1221no—
454#102—21no—
455#102—21no—
456#102—611no—
457#102—611no—
458#102—611no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—1221no—
464#102—1221no—
465#102—1221no—
466#102—2441no—
467C22⋊C8—1221no—
468C22⋊C8—1221no—
469C22⋊C8—1221no—
470#97—1221no—
471C4×C8—611no—
472C4×C8—611no—
473C4×C8C22×D6111yescharacteristic
474C24—41no—
475C24—2441no—
476C2×Q8—21no—
477C2×Q8—611no—
478C2×Q8—1221no—
479C2×Q8—4881no—
480C2×Q8—2441no—
481C2×Q8—2442no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4—611no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—4881no—
496C2×D4—4881no—
497C2×D4—2441no—
498C2×D4—2442no—
499C2×D4—2441no—
500C2×D4—2442no—
501C2×D4D4×D6111yescharacteristic
502C2×D4D4×D6111yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—1221no—
506C22×C4—2441no—
507C22×C4—2441no—
508SD16—82no—
509SD16—1222no—
510SD16—4881no—
511SD16—4881no—
512SD16—2442no—
513SD16—2442no—
514SD16—2442no—
515D8—614no—
516D8—4881no—
517D8—2442no—
518D8—2442no—
519D8—2442no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—611no—
524C2×C8—611no—
525C2×C8—611no—
526C2×C8—611no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—4881no—
530C2×C8—2442no—
531C2×C8—2442no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—611no—
535C4⋊C4—611no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2441no—
540C4⋊C4—2441no—
541C4⋊C4—2441no—
542C4⋊C4D4×D6111yescharacteristic
543C4⋊C4D4×D6111yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—1221no—
548C22⋊C4—2441no—
549C22⋊C4—2441no—
550C22⋊C4—2441no—
551C42—1221no—
552C42C23×D6111yescharacteristic
553C23—21no—
554C23—21no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—1221no—
560C23—9761no—
561C23—4882no—
562C23—4882no—
563C23—2441no—
564Q8—81no—
565Q8—1221no—
566Q8—1221no—
567Q8—4882no—
568Q8—2441no—
569Q8—2441no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—81no—
577D4—82no—
578D4—82no—
579D4—612no—
580D4—1221no—
581D4—4881no—
582D4—4882no—
583D4—4882no—
584D4—2441no—
585D4—2441no—
586D4—2441no—
587D4—2441no—
588D4SD16×D6112yes—
589D4#1451980412yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—9761no—
601C2×C4—4882no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4#1451982211yescharacteristic
608C8—41no—
609C8—41no—
610C8—41no—
611C8—612no—
612C8—1221no—
613C8—1221no—
614C8—1221no—
615C8—2441no—
616C8—2441no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—164no—
627C22—1222no—
628C22—9764no—
629C22—4881no—
630C22—4881no—
631C22—4881no—
632C22—2441no—
633C22—2441no—
634C22#1684039411yescharacteristic
635C4—21no—
636C4—41no—
637C4—41no—
638C4—81no—
639C4—4881no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C4C2×SD16×D6111yescharacteristic
644C4C2×#1451980411yescharacteristic
645C4#1684056611yescharacteristic
646C4#1684057211yescharacteristic
647C2—42no—
648C2—42no—
649C2—161no—
650C2—9761no—
651C2—2442no—
652C2#2145730311yescharacteristic
653C2#2145751311yescharacteristic
654C2#2145758011yescharacteristic
subgroupG/H
centerC22#16840394
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1629C2
socleC22×C61D42
prime radicalD4×#11758199C2
hypercenter#1629D61
hypocenterC61#19763
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1629

Complements

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

NH ≅ G/Ntype
1. #21458717C2semidirect
2. #21457640C2semidirect
3. D4×#11758200C2semidirect
5. #21445446C2semidirect
6. #21445302C2semidirect
7. #21445230C2semidirect
8. #21445196C2semidirect
9. #21445159C2semidirect
10. #21445000C2semidirect
11. #21444925C2semidirect
12. #21444888C2semidirect
13. #21444652C2semidirect
14. #21444640C2semidirect
15. C61×#1629C2semidirect
18. #16840473C22semidirect
19. D4×Dic122C22semidirect
22. #16840158C22semidirect
24. #16840134C22semidirect
25. #16840110C22semidirect
26. #16840109C22semidirect
30. #16840043C22semidirect
35. #16839963C22semidirect
36. #16839959C22semidirect
44. #16839889C22semidirect
49. D4×#92418C22semidirect
50. #16839827C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839511C22semidirect
55. #16839509C22semidirect
56. #16839505C22semidirect
57. #16839494C22semidirect
58. #16839491C22semidirect
59. #16839484C22semidirect
61. C61×#492C22semidirect
63. C61×#476C22semidirect
64. C61×#331C22semidirect
66. C61×D4⋊C8C22semidirect
202. #11758199SD16semidirect
271. D244C2×SD16semidirect
288. #92418C2×SD16semidirect
330. #1629D61semidirect
353. #492C2×D61semidirect
360. #476C2×D61semidirect
388. #331C2×D61semidirect
392. D4⋊C8C2×D61semidirect
394. C61#19763semidirect

Maximal subgroups

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

subgroupindex
#214587172
#214576402
D4×#117582002
D4×#117581992
#214454462
#214453022
#214452302
#214451962
#214451592
#214450002
#214449252
#214448882
#214446522
#214446402
C61×#16292
#1976361