Finite Group Databasebeta

← #29669870

Subgroups — #29669870

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458609C211yesmaximal, characteristic, complemented
2#21458479C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445455C211yesmaximal, characteristic, complemented
5#21445356C211yesmaximal, characteristic, complemented
6#21445256C211yesmaximal, characteristic, complemented
7#21445230C211yesmaximal, characteristic, complemented
8#21445165C211yesmaximal, characteristic, complemented
9#21445026C211yesmaximal, characteristic, complemented
10#21444983C211yesmaximal, characteristic, complemented
11#21444877C211yesmaximal, characteristic, complemented
12#21444873C211yesmaximal, characteristic
13#21444655C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3295C211yesmaximal, characteristic, complemented
16C22×#11758200—21no—
17#16840497C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840134C2211yescharacteristic
21#16840123—21no—
22#16840119—21no—
23#16840112C2211yescharacteristic, complemented
24#16840110C2211yescharacteristic, complemented
25#16840109C2211yescharacteristic, complemented
26#16840059—21no—
27#16840054C2211yescharacteristic, complemented
28#16840051—21no—
29#16840047C2211yescharacteristic, complemented
30#16839989—21no—
31#16839979—21no—
32#16839977—21no—
33#16839967C2211yescharacteristic
34#16839959C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839913—21no—
38#16839900—21no—
39#16839892C2211yescharacteristic, complemented
40Q8×#92418C2211yescharacteristic, complemented
41#16839871—21no—
42C4×#11758200C2211yescharacteristic
43C4×#11758199—21no—
44D4×#92418C2211yescharacteristic
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839492C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#481—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#460C2211yescharacteristic
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—44no—
73C2×#11758200D411yescharacteristic
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—41no—
77C22×#92418—21no—
78#14519777C2311yescharacteristic
79#14519776—21no—
80#14519774C2311yescharacteristic
81#14519766—21no—
82#14519765—21no—
83#14519762—41no—
84#14519756—21no—
85#14519754—41no—
86C4×Dic122C2311yescharacteristic
87C4×D244—21no—
88D4×Dic61—21no—
89#14519739—21no—
90#14519710—21no—
91#14519708—21no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519701—21no—
99#14519701—41no—
100#14519700—21no—
101#14519700—21no—
102#14519700D411yescharacteristic
103#14519699—21no—
104#14519699—21no—
105#14519698—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—21no—
111C22⋊#92418—21no—
112#14519687—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C22×C8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—81no—
156C2×D4×C61—81no—
157C2×D4×C61C2×D411yescharacteristic
158C2×D4×C61C2×D411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—41no—
162C22×Dic61—41no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×C4×D61—41no—
167C2×Dic122—21no—
168C2×Dic122—42no—
169C2×Dic122—41no—
170C2×Dic122—81no—
171C2×Dic122C2×D411yescharacteristic
172SD16×C61—22no—
173SD16×C61—81no—
174C2×C8×C61—21no—
175C2×C8×C61—81no—
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61—41no—
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C42×C61—21no—
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—82no—
201#11758198—41no—
202#11758198—41no—
203#11758198—41no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C2×D411yescharacteristic
207#11758196—21no—
208#11758196—41no—
209C4×Dic61—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—42no—
215C2×#92418C2×D411yescharacteristic
216C2×#92418C2×D411yescharacteristic
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—41no—
220C23×C61—82no—
221C23×C61—82no—
222C23×C61—161no—
223C22×D61—41no—
224Q8×C61—21no—
225Q8×C61—21no—
226Q8×C61—81no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—41no—
232D4×C61—41no—
233D4×C61—81no—
234D4×C61—82no—
235D4×C61—82no—
236D4×C61#13512yes—
237D4×C61AGL(1,ℤ/8)12yes—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—161no—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—41no—
254C2×Dic61—82no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—41no—
259D244—81no—
260C4×D61—161no—
261Dic122—21no—
262Dic122—21no—
263Dic122—41no—
264Dic122—41no—
265Dic122—82no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—41no—
269#92418—21no—
270#92418—21no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#19789—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—164no—
286C22×C61D4211yescharacteristic
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—81no—
296C4×C61C2×#13511yescharacteristic
297C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C61#57711yescharacteristic
299C4×C61#57711yescharacteristic
300Dic61—41no—
301Dic61—41no—
302Dic61—81no—
303#3373—611no—
304#3361—611no—
305#3295D6111yescharacteristic, complemented
306D4×SD16—611no—
307#1717—611no—
308#1698—611no—
309#1681—611no—
310#1677—611no—
311#1666—611no—
312#1643—611no—
313#1637—611no—
314#1620—611no—
315#1619—611no—
316#1582—611no—
317SD16⋊C8—611no—
318C2×C61—42no—
319C2×C61—42no—
320C2×C61—161no—
321C2×C61#326511yescharacteristic
322C2×C61#328211yescharacteristic
323C2×C61#328811yescharacteristic
324D61—161no—
325C22×SD16—1221no—
326#559—611no—
327#554C2×D6111yescharacteristic
328D4×Q8—611no—
329D42C2×D6111yescharacteristic
330#493—611no—
331#492—611no—
332#489—1221no—
333#488—1221no—
334#487—611no—
335#486—611no—
336#486—611no—
337#486C2×D6111yescharacteristic
338#481—21no—
339#478—1221no—
340#477—611no—
341#476—1221no—
342#476C2×D6111yescharacteristic
343#475—611no—
344#465—21no—
345#465—1221no—
346#463—1221no—
347#463—1221no—
348#461—611no—
349#460—611no—
350#460C2×D6111yescharacteristic
351#459—611no—
352#459—611no—
353#450—21no—
354#450—1221no—
355#448—1221no—
356#446—611no—
357C8×Q8—611no—
358#442—1221no—
359C4×SD16—611no—
360C4×SD16C2×D6111yescharacteristic
361C4×D8—1221no—
362C8×D4—611no—
363C8×D4C2×D6111yescharacteristic
364C2×#102—21no—
365#335—611no—
366#334—611no—
367#333—611no—
368#332—611no—
369#331—611no—
370#331—611no—
371Q8⋊C8—611no—
372Q8⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376C61#1978911yescharacteristic, complemented, Sylow
377C22×Q8—1221no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—611no—
382C2×SD16—1221no—
383C2×SD16—1221no—
384C2×SD16—1221no—
385C2×SD16—1221no—
386C2×SD16—2444no—
387C2×SD16C22⋊D6111yescharacteristic
388C2×D8—1221no—
389C2×D8—1221no—
390C2×D8—2441no—
391C22×C8—21no—
392C22×C8—1221no—
393C4⋊Q8—611no—
394C4⋊Q8—1221no—
395C4⋊Q8C22×D6111yescharacteristic
396#127—611no—
397#127C22×D6111yescharacteristic
398#125—21no—
399#124—1221no—
400#124—1221no—
401#123—2441no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—1221no—
405C22⋊Q8—2441no—
406#121—21no—
407#121—21no—
408#120—41no—
409C4×Q8—611no—
410C4×Q8C22×D6111yescharacteristic
411C4×D4—21no—
412C4×D4—1221no—
413C4×D4—1221no—
414C4×D4—1221no—
415C4×D4C22×D6111yescharacteristic
416C4×D4C22×D6111yescharacteristic
417C2×C4⋊C4—21no—
418#107—1221no—
419#106—21no—
420#106—611no—
421#106—1221no—
422#106C22⋊D6111yescharacteristic
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8C22×D6111yescharacteristic
429#103—611no—
430#103—1221no—
431#103—1221no—
432#103—1221no—
433#103—2441no—
434#103C22⋊D6111yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—611no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102C22⋊D6111yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—1221no—
450#97—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—1221no—
454C4×C8C22×D6111yescharacteristic
455C24—41no—
456C2×Q8—21no—
457C2×Q8—611no—
458C2×Q8—1221no—
459C2×Q8—4881no—
460C2×Q8—2441no—
461C2×Q8—2442no—
462C2×Q8C2×C22⋊D6111yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4D4×D6111yescharacteristic
476C2×D4C2×C22⋊D6111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—2441no—
481C22×C4—2441no—
482SD16—22no—
483SD16—81no—
484SD16—1222no—
485SD16—4881no—
486SD16—2442no—
487SD16—2442no—
488SD16—2442no—
489D8—4882no—
490D8—2442no—
491D8—2442no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—2442no—
501C2×C8C2×C22⋊D6111yescharacteristic
502C2×C8C2×C22⋊D6111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—611no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—2441no—
513C4⋊C4D4×D6111yescharacteristic
514C4⋊C4C2×C22⋊D6111yescharacteristic
515C4⋊C4C2×C22⋊D6111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—2441no—
521C22⋊C4—2441no—
522C22⋊C4—2441no—
523C22⋊C4—2441no—
524C42—21no—
525C42—1221no—
526C42C23×D6111yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—82no—
531C23—82no—
532C23—161no—
533C23—2441no—
534Q8—21no—
535Q8—21no—
536Q8—81no—
537Q8—1221no—
538Q8—1221no—
539Q8—4882no—
540Q8—2441no—
541Q8—2441no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—4881no—
552D4—2441no—
553D4—2441no—
554D4—2441no—
555D4—2441no—
556D4#1451979712yes—
557D4#1451980412yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—161no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—9761no—
571C2×C4—4882no—
572C2×C4—2441no—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C22×C22⋊D6111yescharacteristic
575C2×C4#1451982211yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—1221no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8—2441no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—164no—
595C22—4881no—
596C22—4881no—
597C22—4881no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—4881no—
606C4—2441no—
607C4—2441no—
608C4C2×#1451979711yescharacteristic
609C4C2×#1451980411yescharacteristic
610C4#1684056811yescharacteristic
611C4#1684057311yescharacteristic
612C2—42no—
613C2—42no—
614C2—161no—
615C2—9761no—
616C2#2145731411yescharacteristic
617C2#2145752211yescharacteristic
618C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3295C2
socleC22×C61D42
prime radical#21444873C2
hypercenter#3295D61
hypocenterC61#19789
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #21458609C2semidirect
2. #21458479C2semidirect
3. D4×#11758200C2semidirect
4. #21445455C2semidirect
5. #21445356C2semidirect
6. #21445256C2semidirect
7. #21445230C2semidirect
8. #21445165C2semidirect
9. #21445026C2semidirect
10. #21444983C2semidirect
11. #21444877C2semidirect
13. #21444655C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3295C2semidirect
17. #16840497C22semidirect
23. #16840112C22semidirect
24. #16840110C22semidirect
25. #16840109C22semidirect
27. #16840054C22semidirect
29. #16840047C22semidirect
39. #16839892C22semidirect
40. Q8×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839507C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
52. #16839492C22semidirect
55. #16839483C22semidirect
305. #3295D61semidirect
376. C61#19789semidirect

Maximal subgroups

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

subgroupindex
#214586092
#214584792
D4×#117582002
#214454552
#214453562
#214452562
#214452302
#214451652
#214450262
#214449832
#214448772
#214448732
#214446552
SD16⋊#924182
C61×#32952
#1978961