Finite Group Databasebeta

← #30616680

Subgroups — #30616680

Order 15616.

1256 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
1C4×D61⋊M16C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461995C212yesmaximal, complemented
4#21461982C212yesmaximal, complemented
5#21461801C214yesmaximal, complemented
6C4×#14519842C214yesmaximal, complemented
7#21459116C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856—21no—
10C2×#14519842C2218yes—
11C4×#11758213C2212yes—
12C4×#11758213C2212yes—
13C4×#11758217—21no—
14C4×#11758217—21no—
15#16840721—21no—
16C4×D61⋊C8—21no—
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923C2212yes—
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923C2212yes—
21#16840698—21no—
22C42×#6923C2212yes—
23#16840632C2218yes—
24#16840317C411yescharacteristic, complemented
25#16840317C2211yescharacteristic
26#16840313C411yescharacteristic, complemented
27#16840313C2211yescharacteristic
28#16840312C411yescharacteristic, complemented
29#16840299—21no—
30#16840299C412yescomplemented
31#16840298—21no—
32#16840298C412yescomplemented
33#16840297—21no—
34#16840297—21no—
35#16840275—21no—
36#16840275C2212yes—
37#16840274—21no—
38C4×#11758226—21no—
39C4×#11758226C2212yes—
40#16840230—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#533C411yescharacteristic, complemented
43C2×#11758213C2314yes—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8—22no—
47#14519856—28no—
48C2×C4⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C4×#6923—22no—
51C2×C4×#6923—22no—
52C2×C4×#6923C2314yes—
53#14519842—216no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C4×#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C2×#11758226—21no—
61C2×#11758226C2312yes—
62C2×#11758222—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66#14519777C2×C411yescharacteristic
67#14519774C2×C411yescharacteristic
68#14519772—22no—
69#14519772—22no—
70#14519768—21no—
71#14519768C2×C412yes—
72#14519766—21no—
73#14519766C2×C412yes—
74#14519765—21no—
75#14519762—22no—
76#14519762—22no—
77#14519761—22no—
78#14519757—21no—
79#14519757—21no—
80#14519753—21no—
81#14519753C2×C412yes—
82#14519752—21no—
83#14519752—21no—
84#14519752—21no—
85#14519752C2×C412yes—
86#14519751—21no—
87#14519751C2×C412yes—
88#14519747—22no—
89Q8×Dic61—21no—
90Q8×Dic61C2×C412yes—
91#14519742—21no—
92#14519742—21no—
93C4×D244—22no—
94C4×D244—22no—
95C4×D244—21no—
96C4×D244C2×C412yes—
97#14519739—22no—
98#14519739—22no—
99#14519739—21no—
100#14519739—21no—
101#14519739—21no—
102#14519739C2×C412yes—
103#14519737—22no—
104#14519737—22no—
105#14519735—21no—
106#14519735—22no—
107#14519735—22no—
108#14519735C2312yes—
109#14519734—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C42×D61—22no—
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122C4⋊Q8×C61C2×C411yescharacteristic
123C4⋊Q8×C61C2×C411yescharacteristic
124#125×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61C2×C412yes—
127C4×Q8×C61—21no—
128C4×Q8×C61C2×C412yes—
129#117×C61—21no—
130C2×C42×C61C2×C411yescharacteristic
131C23×D61C2×D411yescharacteristic
132C22×#6923—24no—
133C2×Q8×C61—21no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C2×C22⋊D61—22no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142#11758226—28no—
143#11758226—44no—
144#11758222—44no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C22×C412yes—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—42no—
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2411yescharacteristic
168C2×Dic122—21no—
169C22⋊#6923—28no—
170#11758217—28no—
171C2×#92420—24no—
172C4⋊#6923—28no—
173C4×#6923—28no—
174C4×#6923—28no—
175C4×#6923—44no—
176#11758213—24no—
177#11758213#4118yescomplemented
178D61⋊C8—28no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C42×C61—22no—
187C42×C61C22⋊C411yescharacteristic
188C42×C61C22⋊C411yescharacteristic
189C42×C61C22×C411yescharacteristic
190C42×C61C22×C411yescharacteristic
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199C4⋊Dic61—21no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C23×C61C2×C22⋊C411yescharacteristic
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—41no—
224C22×D61C2×C22⋊C411yescharacteristic
225C22×D61C22×D411yescharacteristic
226C2×#6923—28no—
227C2×#6923—44no—
228C2×#6923—44no—
229Q8×C61—24no—
230Q8×C61—42no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C23×C411yescharacteristic
242C22⋊D61—44no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C22×D411yescharacteristic
253D244—24no—
254D244—42no—
255D244—44no—
256D244—44no—
257D244—42no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61—44no—
271C4×D61#10414yescomplemented
272C4×D61C2×#4114yes—
273Dic122—42no—
274#92420—28no—
275#21382—611nomaximal, Sylow
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61C22×C22⋊C411yescharacteristic
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—44no—
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61C2×#10412yes—
289C2×D61#53212yes—
290#6923—48no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61C2×#10412yes—
297C4×C61#42112yes—
298C4×C61C4×#4112yes—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—42no—
304Dic61C2×#10412yes—
305Dic61#52512yes—
306#3444—611no—
307C2×C4×M16—611no—
308C4×#117—611no—
309#1986—612no—
310#1980—612no—
311#1871—614no—
312C4×#104—614no—
313C2×C61—41no—
314C2×C61#229711yescharacteristic
315C2×C61C22×#10411yescharacteristic
316C2×C61C2×#42111yescharacteristic
317D61—22no—
318D61—22no—
319D61—82no—
320C22×M16—612no—
321#533—611no—
322#533—611no—
323#533#692311yescharacteristic, complemented
324#532—611no—
325#532—611no—
326#532—611no—
327#529—612no—
328#529—612no—
329#529—1221no—
330#529—1221no—
331#529—1221no—
332#529—1221no—
333#525—612no—
334#525—1221no—
335#525—1221no—
336C4×#41—612no—
337C4×#41—1221no—
338C4×#41—1221no—
339C2×#117—1221no—
340C22×C42—611no—
341C2×#104—618no—
342C4×M16—612no—
343C4×M16—612no—
344C4×M16—1221no—
345C4×M16—1221no—
346C2×#97—1221no—
347C2×C4×C8—1221no—
348C4×C4⋊C4—612no—
349C4×C4⋊C4—1221no—
350C4×C22⋊C4—612no—
351C4×C22⋊C4—1221no—
352#376—1221no—
353C43—612no—
354#339—618no—
355C61#2138211yescharacteristic, complemented, Sylow
356C2×#41—612no—
357C2×#41—1221no—
358C2×#41—1221no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C2×M16—614no—
363C2×M16—1228no—
364C2×M16—1222no—
365C22×C8—1222no—
366C4⋊Q8—611no—
367C4⋊Q8C2×#692311yescharacteristic
368C4⋊Q8C2×#692311yescharacteristic
369#127—611no—
370#126—1222no—
371#126—1222no—
372#125—21no—
373#125—612no—
374#125—1221no—
375#124—612no—
376#124—1221no—
377#124—1221no—
378#123—1222no—
379#123—1222no—
380#123—1222no—
381C22⋊Q8—21no—
382C22⋊Q8—612no—
383C22⋊Q8—1221no—
384C22⋊Q8—1221no—
385C22⋊Q8—1221no—
386C22⋊Q8C2×#692312yes—
387#121—612no—
388#121—612no—
389#121—1221no—
390#121—1221no—
391#121—1221no—
392#121—1221no—
393#120—1222no—
394C4×Q8—21no—
395C4×Q8—612no—
396C4×Q8—1221no—
397C4×Q8—1221no—
398C4×Q8—1221no—
399C4×Q8C2×#692312yes—
400C4×D4—612no—
401C4×D4—612no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1221no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410C4×D4—1222no—
411C4×D4—1221no—
412#117—21no—
413#117—612no—
414#117—1222no—
415#117—1222no—
416#117—1222no—
417#117—1221no—
418#117—1228no—
419C2×C4⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—614no—
433C2×C42—1222no—
434C2×C42—1222no—
435C2×C42—1222no—
436C2×C42C2×#692311yescharacteristic
437#104—12216no—
438#97—1222no—
439#97—1222no—
440C4×C8—1222no—
441C4×C8—1222no—
442#95—1222no—
443#95—1222no—
444C24—611no—
445#41—1228no—
446#41—2444no—
447#41—2444no—
448C2×Q8—21no—
449C2×Q8—1221no—
450C2×Q8C22×#692312yes—
451C2×D4—612no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1221no—
456C2×D4—1221no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1224no—
477C22×C4—1222no—
478C22×C4—2442no—
479C22×C4C22⋊#692311yescharacteristic
480C22×C4C22⋊#692311yescharacteristic
481C22×C4C22×#692311yescharacteristic
482M16—618no—
483M16—1224no—
484M16—1228no—
485C2×C8—1224no—
486C2×C8—1228no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—612no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1228no—
498C4⋊C4—1221no—
499C4⋊C4C22×#692312yes—
500C22⋊C4—22no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—1228no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C42—22no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—1222no—
524C42—1222no—
525C42—1228no—
526C42—1228no—
527C42—2444no—
528C42C22⋊#692311yescharacteristic
529C42C22⋊#692311yescharacteristic
530C42C22×#692311yescharacteristic
531C42C22×#692311yescharacteristic
532C23—611no—
533C23—611no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23—2441no—
538C23C2×C22⋊#692311yescharacteristic
539Q8—24no—
540Q8—42no—
541Q8—2442no—
542D4—1224no—
543D4—2442no—
544D4—2444no—
545D4—2444no—
546D4—2444no—
547D4—2442no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—614no—
556C2×C4—614no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1228no—
572C2×C4—1222no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4—2441no—
578C2×C4—2444no—
579C2×C4—2444no—
580C2×C4—2444no—
581C2×C4C2×C22⋊#692311yescharacteristic
582C2×C4C2×C22⋊#692311yescharacteristic
583C2×C4C2×C22⋊#692311yescharacteristic
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C2×C22⋊#692311yescharacteristic
586C2×C4C23×#692311yescharacteristic
587C8—1228no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—612no—
592C22—612no—
593C22—1221no—
594C22—1221no—
595C22—1221no—
596C22—1221no—
597C22—2444no—
598C22—2442no—
599C22—2442no—
600C22—2442no—
601C22C22×C22⋊#692311yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—42no—
606C4—42no—
607C4—612no—
608C4—612no—
609C4—1221no—
610C4—1221no—
611C4—1221no—
612C4—1221no—
613C4—2448no—
614C4—2442no—
615C4D61⋊#10412yes—
616C4#1684076112yes—
617C4#41×#692312yes—
618C2—41no—
619C2—1222no—
620C2—1222no—
621C2—4882no—
622C2#2146228011yescharacteristic
623C2C2×D61⋊#10411yescharacteristic
624C2C2×#1684076111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#533C4
socleC22×C61C22×C22⋊C4
prime radical#21459116C2
cosocleC2×C4×D61C24
hypercenter#533#6923
hypocenterC61#21382
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C4×D61⋊M16C2semidirect
2. C4×#14519856C2semidirect
3. #21461995C2semidirect
4. #21461982C2semidirect
5. #21461801C2semidirect
6. C4×#14519842C2semidirect
24. #16840317C4semidirect
26. #16840313C4semidirect
28. #16840312C4semidirect
30. #16840299C4semidirect
32. #16840298C4semidirect
42. C61×#533C4semidirect
177. #11758213#41semidirect
271. C4×D61#104semidirect
323. #533#6923semidirect
355. C61#21382semidirect

Maximal subgroups

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

subgroupindex
C4×D61⋊M162
C4×#145198562
#214619952
#214619822
#214618012
C4×#145198422
#214591162
#2138261