Finite Group Databasebeta

← #29650743

Subgroups — #29650743

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456392C211yesmaximal, characteristic
2#21454796C211yesmaximal, characteristic, complemented
3#21454793C211yesmaximal, characteristic, complemented
4#21444670C211yesmaximal, characteristic, complemented
5#21444662C211yesmaximal, characteristic, complemented
6#21444659C211yesmaximal, characteristic, complemented
7#21444658C211yesmaximal, characteristic, complemented
8#21444653C211yesmaximal, characteristic, complemented
9#21444650C211yesmaximal, characteristic, complemented
10#21444647C211yesmaximal, characteristic, complemented
11#21444581C211yesmaximal, characteristic, complemented
12#21444278C211yesmaximal, characteristic, complemented
13#21444278C211yesmaximal, characteristic, complemented
14#322×D61C211yesmaximal, characteristic, complemented
15C61×#1584C211yesmaximal, characteristic, complemented
16#16840299C2211yescharacteristic
17#16840299C2211yescharacteristic
18#16840163C411yescharacteristic
19#16840147C411yescharacteristic
20#16840118C411yescharacteristic
21#16840118C411yescharacteristic
22#16840000C411yescharacteristic
23#16839999C411yescharacteristic
24#16839994C411yescharacteristic
25#16839994C411yescharacteristic
26#16839893C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×#11758201C2211yescharacteristic
30C4×D488C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839835—21no—
34#16839832—21no—
35C8×D244—21no—
36C8×D244C2211yescharacteristic
37#16839827—21no—
38#16839827C2211yescharacteristic
39#16839822—21no—
40#16839822—21no—
41#16839818C2211yescharacteristic
42#16839818C2211yescharacteristic
43#16839719—21no—
44#16839716—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758201C2×C411yescharacteristic
68C2×#11758201C2×C411yescharacteristic
69C2×D488C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75C2×C8×D61C2×C411yescharacteristic
76C2×C8×D61C2×C411yescharacteristic
77C2×C8×D61D411yescharacteristic
78C2×C8×D61D411yescharacteristic
79#14519772—21no—
80#14519772—21no—
81#14519768C2×C411yescharacteristic
82#14519768C2×C411yescharacteristic
83#14519766C2×C411yescharacteristic
84#14519766C2×C411yescharacteristic
85#14519762—21no—
86#14519762—21no—
87#14519753C2×C411yescharacteristic
88#14519753C2×C411yescharacteristic
89#14519752C2×C411yescharacteristic
90#14519752C2×C411yescharacteristic
91C4×D244—21no—
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95#14519734—21no—
96#14519734—21no—
97C42×D61C2311yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519701C2×C411yescharacteristic
106#14519701C2×C411yescharacteristic
107#14519699C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519697C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111#14519689—21no—
112#14519689—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118#14519687—21no—
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61C2×C411yescharacteristic
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D244—21no—
147C2×D244—21no—
148C2×D244C22×C411yescharacteristic
149C2×D244C22×C411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155Q16×C61—41no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61C22×C411yescharacteristic
160C2×C8×C61C22×C411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C411yescharacteristic
166C4⋊C4×C61C22×C411yescharacteristic
167C42×C61—21no—
168C42×C61—21no—
169C42×C61C2411yescharacteristic
170#11758201—41no—
171#11758201—41no—
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61C22×C411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61#4111yescharacteristic
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200D488—41no—
201#11758189—42no—
202#11758189—42no—
203C8×D61—22no—
204C8×D61—22no—
205C8×D61—41no—
206C8×D61—41no—
207C8×D61—42no—
208C8×D61—42no—
209C8×D61—42no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61C4×D411yescharacteristic
227C2×Dic61C4×D411yescharacteristic
228C2×Dic61C4×D411yescharacteristic
229D244—21no—
230D244—21no—
231D244—21no—
232D244—21no—
233D244—42no—
234D244—42no—
235C4×D61—22no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—41no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61#13512yes—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418#13512yes—
258#17978—611nomaximal, Sylow
259C22×C61C2×C4×D411yescharacteristic
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61#44412yes—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61#56811yescharacteristic
275C4×C61#56811yescharacteristic
276C4×C61C2×#13511yescharacteristic
277C4×C61C2×#13511yescharacteristic
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283#3168—611no—
284#2966—611no—
285#2966—611no—
286#1584—611no—
287#1584D6111yescharacteristic, complemented
288#1583—611no—
289#1583—611no—
290#1582—611no—
291#1582—611no—
292#1581—611no—
293#1581—611no—
294#1568—611no—
295#1494—611no—
296#1494—611no—
297C2×#322—611no—
298C2×C61#293211yescharacteristic
299C2×C61C4×#13511yescharacteristic
300C2×C61C2×#44411yescharacteristic
301D61—22no—
302D61—81no—
303D61—81no—
304#529—611no—
305#529—611no—
306#499—611no—
307#495—611no—
308#488—611no—
309#488—611no—
310#467—611no—
311#466—611no—
312#465—611no—
313#465—611no—
314#446—611no—
315#446C2×D6111yescharacteristic
316C8×Q8—611no—
317C8×Q8C2×D6111yescharacteristic
318C4×Q16C2×D6111yescharacteristic
319C4×SD16—611no—
320C4×SD16—611no—
321C4×D8—611no—
322#436—611no—
323#436—611no—
324#435—1221no—
325#435—1221no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330#433—1221no—
331#433—1221no—
332#432—611no—
333#432—611no—
334#405—1221no—
335#405—1221no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339#335—611no—
340#335C2×D6111yescharacteristic
341#334—611no—
342#334—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8C2×D6111yescharacteristic
346Q8⋊C8C2×D6111yescharacteristic
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351#322—611no—
352#322—611no—
353#322—611no—
354#322C2×D6111yescharacteristic
355C61#1797811yescharacteristic, complemented, Sylow
356C2×Q16C4×D6111yescharacteristic
357C2×SD16—611no—
358C2×SD16—611no—
359C2×D8—611no—
360C2×M16—1221no—
361C2×M16—1221no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8—1221no—
369#126—1221no—
370#126—1221no—
371#125—611no—
372#125—611no—
373#124—611no—
374#124—611no—
375#123—1221no—
376#123—1221no—
377C22⋊Q8—611no—
378C22⋊Q8—611no—
379#121—611no—
380#121—611no—
381C4×Q8C22×D6111yescharacteristic
382C4×Q8C22×D6111yescharacteristic
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—1221no—
386C4×D4—1221no—
387#117—1221no—
388#117—1221no—
389C2×C42—611no—
390#107—611no—
391#107C4×D6111yescharacteristic
392#106—611no—
393#106—611no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402#103—611no—
403#103—611no—
404#103C4×D6111yescharacteristic
405#103C4×D6111yescharacteristic
406#102—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—21no—
417#97—1221no—
418#97—1221no—
419#97—1221no—
420C4×C8—21no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C2×Q8C2×C4×D6111yescharacteristic
434C2×Q8C2×C4×D6111yescharacteristic
435C2×D4—611no—
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4—1221no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—1221no—
443C22×C4—1221no—
444Q16—41no—
445SD16—2441no—
446SD16—2441no—
447D8—2441no—
448M16—2442no—
449M16—2442no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1222no—
458C2×C8—1222no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—2441no—
463C2×C8—2441no—
464C2×C8—2442no—
465C2×C8—2442no—
466C2×C8—2442no—
467C2×C8C2×C4×D6111yescharacteristic
468C2×C8C2×C4×D6111yescharacteristic
469C2×C8D4×D6111yescharacteristic
470C2×C8D4×D6111yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C4×D6111yescharacteristic
482C4⋊C4C2×C4×D6111yescharacteristic
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—21no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42C23×D6111yescharacteristic
499C23—611no—
500C23—1221no—
501C23—1221no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506D4—1221no—
507D4—1221no—
508D4—1221no—
509D4—1221no—
510D4—2442no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—1222no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4C22×C4×D6111yescharacteristic
531C2×C4C2×D4×D6111yescharacteristic
532C2×C4#41×D6111yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—612no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8#1451980012yes—
547C22—612no—
548C22—1221no—
549C22—1221no—
550C22—2441no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22C4×D4×D6111yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—1221no—
563C4—1221no—
564C4—1221no—
565C4—2441no—
566C4—2441no—
567C4#1684052711yescharacteristic
568C4#1684052811yescharacteristic
569C4#135×D6111yescharacteristic
570C4C2×#1451980011yescharacteristic
571C2—1222no—
572C2—4881no—
573C2—4881no—
574C2#2145453311yescharacteristic
575C2C4×#1451980011yescharacteristic
576C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radical#16839999C4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61#17978
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. #21454796C2semidirect
3. #21454793C2semidirect
4. #21444670C2semidirect
5. #21444662C2semidirect
6. #21444659C2semidirect
7. #21444658C2semidirect
8. #21444653C2semidirect
9. #21444650C2semidirect
10. #21444647C2semidirect
11. #21444581C2semidirect
12. #21444278C2semidirect
13. #21444278C2semidirect
14. #322×D61C2semidirect
15. C61×#1584C2semidirect
287. #1584D61semidirect
355. C61#17978semidirect

Maximal subgroups

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

subgroupindex
#214563922
#214547962
#214547932
#214446702
#214446622
#214446592
#214446582
#214446532
#214446502
#214446472
#214445812
#214442782
#322×D612
C61×#15842
#1797861