Finite Group Databasebeta

← #30616722

Subgroups — #30616722

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462379C211yesmaximal, characteristic
2#21462297C211yesmaximal, characteristic
3#21462002C211yesmaximal, characteristic, complemented
4#21462001C211yesmaximal, characteristic, complemented
5#21461950C211yesmaximal, characteristic, complemented
6#21461946C211yesmaximal, characteristic, complemented
7#21461834C212yesmaximal
8#21461832C212yesmaximal
9#21461591C212yesmaximal, complemented
10C4×#14519840C212yesmaximal, complemented
11#541×D61C211yesmaximal, characteristic
12C2×D61⋊M16C2211yescharacteristic
13C22×D61⋊C8C2211yescharacteristic
14C2×#14519840C2212yes—
15C2×#14519840C2212yes—
16C2×#14519840C2212yes—
17C2×#14519840C2212yes—
18#16840727—22no—
19#16840726—22no—
20#16840721C2211yescharacteristic
21#16840721C2211yescharacteristic
22C4×D61⋊C8C2211yescharacteristic
23C4×D61⋊C8C2211yescharacteristic
24#16840712—22no—
25#16840711—22no—
26#16840708C2211yescharacteristic
27#16840706C2211yescharacteristic
28#16840704C2212yes—
29C4×C4⋊#6923C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32#16840635C2212yes—
33#16840635C2212yes—
34#16840375C411yescharacteristic, complemented
35#16840374C411yescharacteristic, complemented
36#16840373C411yescharacteristic, complemented
37#16840372C412yescomplemented
38#16840371—22no—
39#16840370C412yescomplemented
40#16840369—22no—
41C4⋊Q8×D61C2211yescharacteristic
42#126×D61—22no—
43#125×D61—22no—
44#125×D61C2211yescharacteristic
45C22⋊Q8×D61C2212yes—
46C4×Q8×D61C2212yes—
47#117×D61C2211yescharacteristic
48C61×#541C411yescharacteristic, complemented
49C2×#11758213—21no—
50D61⋊M16—22no—
51D61⋊M16—22no—
52C2×#11758217—21no—
53C2×D61⋊C8—21no—
54C2×D61⋊C8—22no—
55C2×D61⋊C8—22no—
56C2×D61⋊C8C2311yescharacteristic
57C2×D61⋊C8C2311yescharacteristic
58C2×D61⋊C8C2311yescharacteristic
59C2×D61⋊C8C2311yescharacteristic
60C22×#92420—21no—
61C2×C4⋊#6923—22no—
62C2×C4⋊#6923C2312yes—
63C2×C4⋊#6923C2312yes—
64C2×C22⋊#6923—22no—
65C2×C4×#6923—22no—
66#14519840—24no—
67#14519840—24no—
68#14519840—24no—
69#14519840—24no—
70#14519832—22no—
71#14519832—22no—
72C4×#92420—22no—
73C4×#92420—22no—
74(C2×#6923)⋊C4—22no—
75(C2×#6923)⋊C4—22no—
76(C2×#6923)⋊C4—22no—
77C2×Q8×D61C2312yes—
78C22×C4×D61C2311yescharacteristic
79#14519777C2×C411yescharacteristic
80#14519776—22no—
81#14519775C2×C412yes—
82#14519772—22no—
83#14519772—22no—
84#14519772—22no—
85#14519771—22no—
86#14519770—22no—
87#14519770—22no—
88#14519770—22no—
89#14519769—22no—
90#14519769C2×C411yescharacteristic
91#14519768—22no—
92#14519768—22no—
93#14519768C2×C412yes—
94#14519767—22no—
95#14519767—22no—
96#14519767—22no—
97#14519767—22no—
98#14519767—22no—
99#14519757C2×C412yes—
100#14519756C2×C412yes—
101#14519755—22no—
102#14519754—22no—
103#14519753C2×C412yes—
104Q8×Dic61C2×C412yes—
105C4×Dic122—22no—
106C4×Dic122C2×C412yes—
107#14519742—22no—
108#14519742C2×C412yes—
109#14519736C2×C411yescharacteristic
110#14519735D412yes—
111#14519734C2×C411yescharacteristic
112#14519734C2×C411yescharacteristic
113#14519733D412yes—
114C4⋊C4×D61—22no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61D412yes—
119C4⋊C4×D61C2312yes—
120C22⋊C4×D61—22no—
121C22⋊C4×D61D412yes—
122C42×D61—22no—
123C42×D61C2311yescharacteristic
124C42×D61C2311yescharacteristic
125C4⋊Q8×C61C2×C411yescharacteristic
126#126×C61—22no—
127#125×C61—22no—
128#125×C61C2×C411yescharacteristic
129C22⋊Q8×C61C2×C412yes—
130C4×Q8×C61C2×C412yes—
131#117×C61C2×C411yescharacteristic
132C23×D61C2×D411yescharacteristic
133C22×#6923—22no—
134C22×#6923—22no—
135C2×Q8×C61C22×C412yes—
136C22×C4×C61C22×C411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138Q8×D61—22no—
139Q8×D61—22no—
140Q8×D61—22no—
141Q8×D61—22no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61C22×C411yescharacteristic
149C2×C4×D61C2×D411yescharacteristic
150C2×C4×D61C2×D412yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2411yescharacteristic
154C2×Dic122—22no—
155C2×Dic122C22×C412yes—
156C22⋊#6923—82no—
157#11758217—24no—
158C2×#92420—24no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C4⋊#6923—22no—
164C4⋊#6923—22no—
165C4⋊#6923—22no—
166C4⋊#6923—22no—
167C4⋊#6923—82no—
168C4×#6923—82no—
169#11758213—24no—
170D61⋊C8—24no—
171D61⋊C8—21no—
172D61⋊C8—21no—
173D61⋊C8—21no—
174D61⋊C8—21no—
175D61⋊C8#4112yes—
176D61⋊C8#4112yes—
177D61⋊C8#4112yes—
178D61⋊C8#4112yes—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C22⋊C412yes—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C22⋊C4×C61C22⋊C412yes—
187C42×C61—22no—
188C42×C61C22×C411yescharacteristic
189C42×C61C22×C411yescharacteristic
190C22⋊Dic61—22no—
191C22⋊Dic61C22⋊C412yes—
192#11758198—22no—
193#11758198—22no—
194#11758198C22⋊C412yes—
195#11758198C22⋊C412yes—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61C22⋊C412yes—
201C4⋊Dic61C22×C412yes—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196C22⋊C412yes—
212#11758196C22⋊C412yes—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C23×C61C2×C22⋊C411yescharacteristic
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61C22×D411yescharacteristic
227C2×#6923—42no—
228C2×#6923—42no—
229C2×#6923—42no—
230C2×#6923—42no—
231C2×#6923—42no—
232C2×#6923—42no—
233Q8×C61—22no—
234Q8×C61—22no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61C2×C22⋊C412yes—
240C2×C4×C61C2×C22⋊C412yes—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61C2×C22⋊C412yes—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61—21no—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61C2×#4111yescharacteristic
266C4×D61C2×#4111yescharacteristic
267C4×D61C2×#4111yescharacteristic
268C4×D61C2×#4111yescharacteristic
269Dic122—22no—
270Dic122—22no—
271Dic122—42no—
272Dic122—42no—
273#92420—22no—
274#92420—22no—
275#92420—22no—
276#92420—22no—
277#21413—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—21no—
280C22×C61C22×C22⋊C411yescharacteristic
281C2×D61—22no—
282C2×D61—21no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—42no—
286C2×D61#53211yescharacteristic
287C2×D61#53211yescharacteristic
288C2×D61#57712yes—
289C2×D61#57812yes—
290#6923—82no—
291#6923—82no—
292C4×C61—22no—
293C4×C61—22no—
294C4×C61—21no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61C4×#4111yescharacteristic
298C4×C61C4×#4111yescharacteristic
299Dic61—22no—
300Dic61—22no—
301Dic61—21no—
302Dic61—42no—
303Dic61—42no—
304Dic61#52511yescharacteristic
305Dic61#52511yescharacteristic
306C2×#541—611no—
307C2×#405—611no—
308#2314—611no—
309#1992—611no—
310#1991—611no—
311#1960—611no—
312#1956—611no—
313#1894—612no—
314#1892—612no—
315#1763—612no—
316C4×#103—612no—
317C2×C61—41no—
318C2×C61#229711yescharacteristic
319C2×C61#289812yes—
320D61—41no—
321D61#317411yescharacteristic
322D61#317711yescharacteristic
323D61#317812yes—
324C22×M16—611no—
325C23×C8—611no—
326#541—611no—
327#541—611no—
328#541—612no—
329#541—612no—
330#541—611no—
331#541—1222no—
332#541—1222no—
333#541#692311yescharacteristic, complemented
334C2×C4⋊Q8—611no—
335C2×#126—1222no—
336C2×#125—611no—
337C2×#125—1222no—
338C2×C22⋊Q8—612no—
339C2×C4×Q8—612no—
340C2×#117—611no—
341C2×#103—612no—
342C2×#103—612no—
343C2×#103—612no—
344C2×#103—612no—
345#405—1222no—
346#405—1222no—
347C2×#97—611no—
348C2×#97—611no—
349C2×C4×C8—611no—
350C2×C4×C8—611no—
351#388—1222no—
352#387—1222no—
353#384—611no—
354#382—611no—
355#380—612no—
356C4×C4⋊C4—612no—
357#340—612no—
358#340—612no—
359#340—612no—
360#340—612no—
361C61#2141311yescharacteristic, complemented, Sylow
362C22×Q8—612no—
363C23×C4—611no—
364C2×M16—1222no—
365C2×M16—1222no—
366C2×M16—1221no—
367C2×M16—1221no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—611no—
372C22×C8—1222no—
373C22×C8—1222no—
374C22×C8—1221no—
375C22×C8—1221no—
376C4⋊Q8—612no—
377C4⋊Q8—611no—
378C4⋊Q8—1222no—
379C4⋊Q8C2×#692311yescharacteristic
380#126—22no—
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#126—1222no—
385#126—1222no—
386#126—1222no—
387#126—1222no—
388#125—22no—
389#125—612no—
390#125—611no—
391#125—1222no—
392#125—1222no—
393#125—1222no—
394#125—1222no—
395#125—1222no—
396#125—1222no—
397#125—1222no—
398#125—1222no—
399#125C2×#692311yescharacteristic
400C22⋊Q8—612no—
401C22⋊Q8—612no—
402C22⋊Q8—612no—
403C22⋊Q8—1222no—
404C22⋊Q8—1222no—
405C22⋊Q8C2×#692312yes—
406C4×Q8—612no—
407C4×Q8—612no—
408C4×Q8—612no—
409C4×Q8—1222no—
410C4×Q8—1222no—
411C4×Q8C2×#692312yes—
412#117—611no—
413#117—612no—
414#117—612no—
415#117—611no—
416#117—611no—
417#117C2×#692311yescharacteristic
418C2×C4⋊C4—612no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—612no—
421C2×C4⋊C4—612no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1222no—
426C2×C4⋊C4—1222no—
427C2×C22⋊C4—612no—
428C2×C22⋊C4—1222no—
429C2×C22⋊C4—1222no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—1222no—
433C2×C42—1222no—
434#103—1224no—
435#103—1224no—
436#103—1224no—
437#103—1224no—
438#97—1222no—
439#97—1222no—
440C4×C8—1222no—
441C4×C8—1222no—
442#95—1222no—
443#95—1222no—
444#95—1222no—
445C24—611no—
446C2×Q8—612no—
447C2×Q8—1222no—
448C2×Q8—1222no—
449C2×Q8—1222no—
450C2×Q8—1222no—
451C2×Q8—1222no—
452C2×Q8C22×#692312yes—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4C22×#692311yescharacteristic
469M16—1224no—
470M16—1224no—
471C2×C8—612no—
472C2×C8—612no—
473C2×C8—612no—
474C2×C8—612no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1224no—
484C2×C8—1224no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—612no—
490C4⋊C4—612no—
491C4⋊C4—612no—
492C4⋊C4—612no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—4882no—
511C4⋊C4C22⋊#692312yes—
512C4⋊C4C22×#692312yes—
513C22⋊C4—22no—
514C22⋊C4—612no—
515C22⋊C4—612no—
516C22⋊C4—612no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—4882no—
521C22⋊C4C22⋊#692312yes—
522C42—22no—
523C42—612no—
524C42—612no—
525C42—611no—
526C42—611no—
527C42—1222no—
528C42—1222no—
529C42—1222no—
530C42—4882no—
531C42C22×#692311yescharacteristic
532C42C22×#692311yescharacteristic
533C23—611no—
534C23—611no—
535C23—1222no—
536C23—1221no—
537C23—1221no—
538C23—1222no—
539C23C2×C22⋊#692311yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—1222no—
543Q8—1222no—
544Q8—2442no—
545Q8—2442no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—611no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4C2×C22⋊#692312yes—
583C2×C4C2×C22⋊#692312yes—
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C23×#692311yescharacteristic
586C8—1222no—
587C8—1222no—
588C8—1222no—
589C8—1222no—
590C22—21no—
591C22—22no—
592C22—611no—
593C22—611no—
594C22—612no—
595C22—612no—
596C22—1221no—
597C22—1222no—
598C22—2441no—
599C22—2442no—
600C22—2441no—
601C22C22×C22⋊#692311yescharacteristic
602C4—21no—
603C4—22no—
604C4—22no—
605C4—42no—
606C4—42no—
607C4—611no—
608C4—611no—
609C4—1221no—
610C4—1222no—
611C4—1222no—
612C4—4882no—
613C4—4882no—
614C4—2442no—
615C4—2442no—
616C4#41×#692311yescharacteristic
617C4#41×#692311yescharacteristic
618C2—41no—
619C2—611no—
620C2—612no—
621C2—611no—
622C2—2441no—
623C2#2146228011yescharacteristic
624C2#2146244112yes—
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#541C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#541#6923
hypocenterC61#21413
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #21462002C2semidirect
4. #21462001C2semidirect
5. #21461950C2semidirect
6. #21461946C2semidirect
9. #21461591C2semidirect
10. C4×#14519840C2semidirect
34. #16840375C4semidirect
35. #16840374C4semidirect
36. #16840373C4semidirect
37. #16840372C4semidirect
39. #16840370C4semidirect
48. C61×#541C4semidirect
333. #541#6923semidirect
361. C61#21413semidirect

Maximal subgroups

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

subgroupindex
#214623792
#214622972
#214620022
#214620012
#214619502
#214619462
#214618342
#214618322
#214615912
C4×#145198402
#541×D612
#2141361