Finite Group Databasebeta

← #30610882

Subgroups — #30610882

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462750C211yesmaximal, characteristic, complemented
2#21462503C211yesmaximal, characteristic, complemented
3#21461176C212yesmaximal, complemented
4#21461168C211yesmaximal, characteristic, complemented
5#21461157C211yesmaximal, characteristic, complemented
6#21461147C212yesmaximal, complemented
7#21461142C211yesmaximal, characteristic, complemented
8#21461132C212yesmaximal, complemented
9#21461121C212yesmaximal, complemented
10#21461113C211yesmaximal, characteristic, complemented
11#21459440C211yesmaximal, characteristic
12#16840811—21no—
13#16840797—21no—
14#16840795—22no—
15#16840786—22no—
16#16840781C2211yescharacteristic
17#16840779C2212yes—
18#16840778C2212yes—
19#16840778C2212yes—
20#16840769—21no—
21#16840766C2211yescharacteristic
22#16840765C2212yes—
23#16840736—21no—
24C4×#11758213C2211yescharacteristic
25C4×D61⋊C8C2211yescharacteristic
26Q8⋊#92420C2211yescharacteristic
27Q8⋊#92420C2211yescharacteristic
28Q8⋊#92420C2212yes—
29Q8⋊#92420C2212yes—
30Q8⋊#92420C2212yes—
31Q8⋊#92420C2212yes—
32Q8⋊#92420C2212yes—
33#16840610C2211yescharacteristic
34#16840610C2211yescharacteristic
35#16840610C2212yes—
36#16840491C411yescharacteristic
37#16840486—21no—
38#16840486C411yescharacteristic
39#16840454—22no—
40#16840454C412yes—
41#16840423C412yes—
42#16840416—21no—
43#16840416C411yescharacteristic
44#16840317—21no—
45#16840317C2211yescharacteristic
46#16840298—22no—
47#16840298C2212yes—
48C4×#11758226C2211yescharacteristic
49C4×#11758224—21no—
50C4×#11758224C2211yescharacteristic
51C2×Q8×Dic61C2212yes—
52D4×Q8×C61C411yescharacteristic
53C2×#11758213—21no—
54C2×#11758213—21no—
55C2×#11758217—22no—
56C2×D61⋊C8—21no—
57#14519844—22no—
58#14519844—22no—
59C4⋊#92420—21no—
60C4⋊#92420—22no—
61C4⋊#92420C2311yescharacteristic
62C4⋊#92420C2312yes—
63C4⋊#92420C2311yescharacteristic
64#14519834—21no—
65C22⋊#92420—22no—
66C22⋊#92420—22no—
67C22⋊#92420—22no—
68#14519832—21no—
69C4×#92420—21no—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C2×#11758226C2×C411yescharacteristic
76C2×#11758224—21no—
77C2×#11758224D411yescharacteristic
78#14519777—21no—
79#14519777C2×C411yescharacteristic
80#14519772—22no—
81#14519772—22no—
82#14519772—22no—
83#14519768—22no—
84#14519768—22no—
85#14519768—21no—
86#14519768C2×C412yes—
87#14519766—22no—
88#14519766C2×C412yes—
89#14519761—22no—
90#14519761—22no—
91#14519761—22no—
92#14519757—21no—
93#14519757—21no—
94#14519757—21no—
95#14519753—22no—
96#14519753C2×C412yes—
97#14519751—22no—
98#14519751C2×C412yes—
99Q8×Dic61—22no—
100Q8×Dic61—22no—
101Q8×Dic61C2×C412yes—
102Q8×Dic61C2×C412yes—
103Q8×Dic61C2311yescharacteristic
104Q8×Dic61C2312yes—
105C4×Dic122—21no—
106C4×Dic122C2×C411yescharacteristic
107#14519742—21no—
108#14519742D411yescharacteristic
109C4×D244—21no—
110C4×D244C2×C411yescharacteristic
111D4×Dic61D411yescharacteristic
112#14519739—21no—
113#14519739C2311yescharacteristic
114C4×C22⋊D61—22no—
115C4×C22⋊D61C2×C412yes—
116#14519737—22no—
117#14519737D412yes—
118#14519735—21no—
119#14519735—21no—
120#14519735—21no—
121#14519735—22no—
122#14519735C2×C411yescharacteristic
123#14519735D411yescharacteristic
124#14519733—22no—
125#14519733D412yes—
126C2×C4⋊Dic61—22no—
127C2×C4⋊Dic61C2×C412yes—
128C2×C4×Dic61—22no—
129C2×C4×Dic61C2312yes—
130C42×D61—21no—
131C42×D61C2311yescharacteristic
132C22×Q8×C61C2×C412yes—
133C4⋊Q8×C61—21no—
134C4⋊Q8×C61C2×C411yescharacteristic
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61C2×C412yes—
137C4×Q8×C61C2×C411yescharacteristic
138C4×D4×C61—21no—
139C4×D4×C61C2×C411yescharacteristic
140C2×Q8×C61—22no—
141C2×Q8×C61—24no—
142C2×Q8×C61—42no—
143C2×Q8×C61C22×C412yes—
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22⋊C411yescharacteristic
146C22×C4×C61—22no—
147C22×C4×C61C22×C412yes—
148C2×C22⋊D61—22no—
149C2×C22⋊D61C22⋊C412yes—
150C22×Dic61—22no—
151C22×Dic61C2×D412yes—
152C22×Dic61C2×D412yes—
153#11758226—22no—
154#11758226—41no—
155#11758224—42no—
156#11758224—44no—
157C2×D244—21no—
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61C22×C411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×Dic122—21no—
166C2×Dic122C22⋊C411yescharacteristic
167#11758217—82no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—22no—
172C2×#92420—21no—
173C2×#92420—22no—
174#11758213—42no—
175#11758213—81no—
176D61⋊C8—42no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61C22⋊C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—22no—
184C22⋊C4×C61C22⋊C412yes—
185C42×C61—21no—
186C42×C61C22×C411yescharacteristic
187C22⋊Dic61C22⋊C412yes—
188#11758198—22no—
189#11758198—21no—
190#11758198—21no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—21no—
195#11758198C22⋊C412yes—
196C4⋊Dic61—22no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—21no—
202C4⋊Dic61—22no—
203C4⋊Dic61C22⋊C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C412yes—
206#11758196—22no—
207#11758196—22no—
208#11758196C22⋊C412yes—
209#11758196C22⋊C412yes—
210C4×Dic61—21no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—21no—
214C4×Dic61—22no—
215C4×Dic61C22×C412yes—
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C4×Dic61C2411yescharacteristic
221C23×C61C2×C22⋊C412yes—
222C22×D61—21no—
223C22×D61C2×C22⋊C411yescharacteristic
224Q8×C61—21no—
225Q8×C61—22no—
226Q8×C61—22no—
227Q8×C61—44no—
228Q8×C61#13112yes—
229D4×C61—22no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—21no—
235C2×C4×C61—44no—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C23×C411yescharacteristic
240C22⋊D61—42no—
241C22⋊D61—44no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—42no—
247C2×Dic61—44no—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C22×D411yescharacteristic
252C2×Dic61C22×D411yescharacteristic
253D244—21no—
254D244—21no—
255D244—42no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—22no—
259C4×D61—21no—
260C4×D61—21no—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61—41no—
264C4×D61—41no—
265Dic122—22no—
266Dic122—42no—
267#92420—41no—
268#92420—41no—
269#92420—42no—
270#92420—42no—
271#92420—41no—
272#92420—41no—
273#17525—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61C22×C22⋊C411yescharacteristic
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—41no—
289C4×C61#42112yes—
290C4×C61C2×#13111yescharacteristic
291C4×C61#56811yescharacteristic
292Dic61—21no—
293Dic61—22no—
294Dic61—21no—
295Dic61—22no—
296Dic61—42no—
297Dic61—41no—
298Dic61#57711yescharacteristic
299Dic61#57811yescharacteristic
300#3482—611no—
301#2991—611no—
302#2922—611no—
303#1495—612no—
304#1493—611no—
305#1489—611no—
306#1487—612no—
307#1485—611no—
308#1482—612no—
309#1479—612no—
310#1476—611no—
311C2×C61—42no—
312C2×C61#288011yescharacteristic
313C2×C61#289811yescharacteristic
314C2×C61C2×#42111yescharacteristic
315D61—41no—
316D61—81no—
317#557—611no—
318#556—611no—
319#556—1221no—
320#552—612no—
321#552—1222no—
322D4×Q8#692311yescharacteristic
323#548—612no—
324#547—611no—
325#547—1221no—
326#533—611no—
327#533—1221no—
328#529—612no—
329#529—1222no—
330C4×#41—611no—
331C4×#41—611no—
332C4×#41—1221no—
333C2×C4×Q8—612no—
334C8×Q8—1221no—
335#436—1222no—
336#436—1221no—
337#433—1222no—
338#431—612no—
339#431—612no—
340#431—612no—
341#431—611no—
342#424—1221no—
343#423—612no—
344#423—611no—
345#408—1221no—
346C4×M16—611no—
347C2×C4×C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350Q8⋊C8—612no—
351Q8⋊C8—612no—
352Q8⋊C8—612no—
353Q8⋊C8—612no—
354Q8⋊C8—612no—
355D4⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—612no—
358C61#1752511yescharacteristic, complemented, Sylow
359C2×#41—611no—
360C2×#41—611no—
361C2×#41—1221no—
362C22×Q8C2×#692312yes—
363C2×M16—1222no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
367C4⋊Q8—21no—
368C4⋊Q8—611no—
369C4⋊Q8—1221no—
370C4⋊Q8C2×#692311yescharacteristic
371#126—1222no—
372#126—1222no—
373#126—1222no—
374#125—612no—
375#125—1221no—
376#125—1222no—
377#125—1222no—
378#124—612no—
379#124—1222no—
380#123—1222no—
381#123—1222no—
382#123—1222no—
383C22⋊Q8—22no—
384C22⋊Q8—612no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—1222no—
388C22⋊Q8—1221no—
389C22⋊Q8C2×#692312yes—
390#121—612no—
391#121—1222no—
392C4×Q8—611no—
393C4×Q8—611no—
394C4×Q8—611no—
395C4×Q8—612no—
396C4×Q8—612no—
397C4×Q8—612no—
398C4×Q8—1221no—
399C4×Q8—1221no—
400C4×Q8—1222no—
401C4×Q8—1222no—
402C4×Q8C2×#692311yescharacteristic
403C4×D4—21no—
404C4×D4—611no—
405C4×D4—612no—
406C4×D4—612no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1221no—
413C4×D4C2×#692311yescharacteristic
414#117—611no—
415#117—612no—
416#117—611no—
417#117—1221no—
418#117—1222no—
419#117—1222no—
420#117—1221no—
421#117—1221no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—1222no—
424C2×C42—612no—
425C2×C42—611no—
426C2×C42—1221no—
427C2×C42—1222no—
428C4⋊C8—611no—
429C4⋊C8—612no—
430C4⋊C8—611no—
431C4⋊C8—1221no—
432C4⋊C8—1222no—
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435C22⋊C8—1222no—
436C22⋊C8—1222no—
437C22⋊C8—1222no—
438C22⋊C8—1221no—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—612no—
443C4×C8—1221no—
444C4×C8—1221no—
445C4×C8—1222no—
446#41—1222no—
447#41—2442no—
448#41—2441no—
449#41—2444no—
450C2×Q8—22no—
451C2×Q8—24no—
452C2×Q8—42no—
453C2×Q8—611no—
454C2×Q8—1221no—
455C2×Q8C22×#692312yes—
456C2×Q8C22×#692311yescharacteristic
457C2×D4—612no—
458C2×D4—611no—
459C2×D4—1221no—
460C2×D4—1222no—
461C2×D4C22⋊#692311yescharacteristic
462C22×C4—22no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1222no—
471C22×C4—1221no—
472C22×C4C22×#692312yes—
473M16—4881no—
474M16—4882no—
475M16—2442no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1222no—
479C2×C8—1221no—
480C2×C8—1222no—
481C2×C8—1221no—
482C2×C8—2442no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—612no—
488C4⋊C4—612no—
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—612no—
492C4⋊C4—1221no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1221no—
501C4⋊C4C22⋊#692311yescharacteristic
502C4⋊C4C22×#692311yescharacteristic
503C22⋊C4—22no—
504C22⋊C4—612no—
505C22⋊C4—612no—
506C22⋊C4—1221no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1221no—
510C22⋊C4—1222no—
511C22⋊C4—1221no—
512C22⋊C4—1222no—
513C22⋊C4C22⋊#692312yes—
514C42—21no—
515C42—611no—
516C42—611no—
517C42—612no—
518C42—612no—
519C42—611no—
520C42—612no—
521C42—1221no—
522C42—1221no—
523C42—1222no—
524C42—1222no—
525C42—1222no—
526C42C22×#692311yescharacteristic
527C23—611no—
528C23—1221no—
529C23C2×C22⋊#692312yes—
530Q8—21no—
531Q8—22no—
532Q8—22no—
533Q8—44no—
534Q8—1222no—
535Q8—2442no—
536Q8#1451986412yes—
537D4—22no—
538D4—1221no—
539D4—1221no—
540D4—2442no—
541D4—2442no—
542D4—2444no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—44no—
549C2×C4—611no—
550C2×C4—612no—
551C2×C4—611no—
552C2×C4—612no—
553C2×C4—611no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1222no—
563C2×C4—2442no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2442no—
567C2×C4—2444no—
568C2×C4—2442no—
569C2×C4C2×C22⋊#692312yes—
570C2×C4C2×C22⋊#692311yescharacteristic
571C2×C4C2×C22⋊#692311yescharacteristic
572C2×C4C23×#692311yescharacteristic
573C8—2441no—
574C8—2442no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C8—2442no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—1221no—
583C22—1221no—
584C22—1221no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22C22×C22⋊#692311yescharacteristic
589C4—22no—
590C4—22no—
591C4—21no—
592C4—42no—
593C4—41no—
594C4—611no—
595C4—611no—
596C4—1221no—
597C4—1222no—
598C4—1221no—
599C4—1222no—
600C4—2441no—
601C4—2442no—
602C4#1684076112yes—
603C4C2×#1451986411yescharacteristic
604C4#1684084011yescharacteristic
605C2—42no—
606C2—4881no—
607C2—2441no—
608C2#2146240711yescharacteristic
609C2#2146244111yescharacteristic
610C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459440C2
cosocleC4×Dic61C24
hypercenterD4×Q8#6923
hypocenterC61#17525
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462750C2semidirect
2. #21462503C2semidirect
3. #21461176C2semidirect
4. #21461168C2semidirect
5. #21461157C2semidirect
6. #21461147C2semidirect
7. #21461142C2semidirect
8. #21461132C2semidirect
9. #21461121C2semidirect
10. #21461113C2semidirect
358. C61#17525semidirect

Maximal subgroups

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

subgroupindex
#214627502
#214625032
#214611762
#214611682
#214611572
#214611472
#214611422
#214611322
#214611212
#214611132
#214594402
#1752561