Finite Group Databasebeta

← #30611433

Subgroups — #30611433

Order 15616.

1144 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
1C2×C4×#11758213C211yesmaximal, characteristic, complemented
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3#21461277C212yesmaximal, complemented
4#21461275C212yesmaximal, complemented
5#21461272C214yesmaximal, complemented
6#21461271C214yesmaximal, complemented
7#21459116C211yesmaximal, characteristic
8C22×#11758213—21no—
9C2×D61⋊M16—21no—
10C4×#11758213—21no—
11C4×#11758213—21no—
12C4×#11758213—21no—
13C4×#11758213C2212yes—
14C4×#11758213C2212yes—
15C4×#11758213C2212yes—
16C4×#11758217—21no—
17C4×#11758217C2212yes—
18#16840721C2212yes—
19C2×#14519832C2212yes—
20C4×D61⋊C8—21no—
21C2×C4×#92420—21no—
22#16840619C2218yescomplemented
23#16840618C2218yescomplemented
24#16840317C411yescharacteristic
25#16840317C2211yescharacteristic
26#16840313C411yescharacteristic
27#16840313C2211yescharacteristic
28#16840312C411yescharacteristic
29#16840299—21no—
30#16840299C2212yes—
31#16840298—21no—
32#16840298C2212yes—
33#16840297—21no—
34#16840297—21no—
35#16840275—21no—
36#16840275C412yes—
37#16840274—21no—
38C4×#11758226—21no—
39C4×#11758226C412yes—
40#16840230—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#533C411yescharacteristic
43C2×#11758213—28no—
44C2×#11758213—22no—
45C2×#11758213—22no—
46C2×#11758213—22no—
47D61⋊M16—28no—
48C2×#11758217—22no—
49C2×D61⋊C8—22no—
50C22×#92420—22no—
51#14519832—22no—
52#14519832—22no—
53#14519832C2314yes—
54#14519832C2314yes—
55C4×#92420—22no—
56C4×#92420—22no—
57C4×#92420—22no—
58C4×#92420—22no—
59C2×#11758226—21no—
60C2×#11758226C2×C412yes—
61C2×#11758222—21no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65#14519777C2×C411yescharacteristic
66#14519774C2×C411yescharacteristic
67#14519772—22no—
68#14519772—22no—
69#14519768—21no—
70#14519768C2312yes—
71#14519766—21no—
72#14519766C2312yes—
73#14519765—21no—
74#14519762—22no—
75#14519762—22no—
76#14519761—22no—
77#14519757—21no—
78#14519757—21no—
79#14519753—21no—
80#14519753C2×C412yes—
81#14519752—21no—
82#14519752—21no—
83#14519752—21no—
84#14519752C2×C412yes—
85#14519751—21no—
86#14519751C2×C412yes—
87#14519747—22no—
88Q8×Dic61—21no—
89Q8×Dic61C2×C412yes—
90#14519742—21no—
91#14519742—21no—
92C4×D244—22no—
93C4×D244—22no—
94C4×D244—21no—
95C4×D244C2×C412yes—
96#14519739—22no—
97#14519739—22no—
98#14519739—21no—
99#14519739—21no—
100#14519739—21no—
101#14519739C2×C412yes—
102#14519737—22no—
103#14519737—22no—
104#14519735—21no—
105#14519735—22no—
106#14519735—22no—
107#14519735C2×C412yes—
108#14519734—22no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C4⋊Q8×C61C2×C411yescharacteristic
122C4⋊Q8×C61C2×C411yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61C2×C412yes—
126C4×Q8×C61—21no—
127C4×Q8×C61C2×C412yes—
128#117×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C22⋊C411yescharacteristic
131C2×Q8×C61—21no—
132C2×Q8×C61C22×C412yes—
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C2×C22⋊D61—22no—
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140#11758226—44no—
141#11758226—44no—
142#11758222—44no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244C22×C412yes—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—42no—
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×Dic122—21no—
167#11758217—28no—
168C2×#92420—28no—
169C2×#92420—24no—
170C2×#92420—24no—
171#11758213—28no—
172#11758213—28no—
173#11758213—28no—
174D61⋊C8—28no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61C22×C412yes—
181C22⋊C4×C61—22no—
182C42×C61—22no—
183C42×C61C22⋊C411yescharacteristic
184C42×C61C22⋊C411yescharacteristic
185C42×C61C22×C411yescharacteristic
186C42×C61C22×C411yescharacteristic
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22×C412yes—
199#11758196—22no—
200#11758196—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22×C411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2411yescharacteristic
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—41no—
220C22×D61C2×C22⋊C411yescharacteristic
221C22×D61C2×C22⋊C411yescharacteristic
222Q8×C61—42no—
223Q8×C61—42no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—41no—
228C2×C4×C61#10414yes—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C23×C411yescharacteristic
235C22⋊D61—44no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61C2×C22⋊C411yescharacteristic
241C2×Dic61C2×C22⋊C411yescharacteristic
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C22×D411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246D244—42no—
247D244—44no—
248D244—44no—
249D244—42no—
250D244—42no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—44no—
263C4×D61—44no—
264C4×D61—44no—
265C4×D61#10414yes—
266Dic122—42no—
267#92420—28no—
268#92420—28no—
269#17638—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61C2×#10412yes—
273C22×C61C22×C22⋊C411yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—44no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—42no—
283C2×D61C2×#10412yes—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61C2×#10412yes—
290C4×C61C2×#10412yes—
291C4×C61C2×#10412yes—
292Dic61—21no—
293Dic61—21no—
294Dic61—21no—
295Dic61—21no—
296Dic61—42no—
297Dic61#41312yes—
298Dic61C2×#10412yes—
299#3444—611no—
300C2×C4×M16—611no—
301C2×C4×M16—611no—
302#1526—612no—
303#1525—612no—
304#1524—614no—
305#1524—614no—
306C2×C61—22no—
307C2×C61C2×#41311yescharacteristic
308C2×C61C22×#10411yescharacteristic
309C2×C61C22×#10411yescharacteristic
310D61—22no—
311D61—41no—
312D61—82no—
313C22×M16—1221no—
314C22×M16—1221no—
315#533—611no—
316#533—611no—
317#533#692311yescharacteristic
318#532—611no—
319#532—611no—
320#532—611no—
321#529—612no—
322#529—612no—
323#529—1221no—
324#529—1221no—
325#529—1221no—
326#529—1221no—
327#525—612no—
328#525—1221no—
329#525—1221no—
330C4×#41—612no—
331C4×#41—1221no—
332C4×#41—1221no—
333C22×C42—611no—
334C4×M16—612no—
335C4×M16—612no—
336C4×M16—612no—
337C4×M16—612no—
338C4×M16—1221no—
339C4×M16—1221no—
340C4×M16—1221no—
341C4×M16—1221no—
342C2×#97—612no—
343C2×#97—612no—
344C2×C4×C8—1221no—
345C2×C4×C8—1221no—
346#330—618no—
347#329—618no—
348C61#1763811yescharacteristic, complemented, Sylow
349C2×#41—612no—
350C2×#41—1221no—
351C2×#41—1221no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C2×M16—1222no—
356C2×M16—1222no—
357C2×M16—1222no—
358C2×M16—1222no—
359C2×M16—1228no—
360C2×M16—1228no—
361C22×C8—1222no—
362C22×C8—1222no—
363C4⋊Q8—611no—
364C4⋊Q8C2×#692311yescharacteristic
365C4⋊Q8C2×#692311yescharacteristic
366#127—611no—
367#126—1222no—
368#126—1222no—
369#125—21no—
370#125—612no—
371#125—1221no—
372#124—612no—
373#124—1221no—
374#124—1221no—
375#123—1222no—
376#123—1222no—
377#123—1222no—
378C22⋊Q8—21no—
379C22⋊Q8—612no—
380C22⋊Q8—1221no—
381C22⋊Q8—1221no—
382C22⋊Q8—1221no—
383C22⋊Q8C2×#692312yes—
384#121—612no—
385#121—612no—
386#121—1221no—
387#121—1221no—
388#121—1221no—
389#121—1221no—
390#120—1222no—
391C4×Q8—21no—
392C4×Q8—612no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8C2×#692312yes—
397C4×D4—612no—
398C4×D4—612no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1221no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1221no—
409#117—21no—
410#117—612no—
411#117—1222no—
412#117—1222no—
413#117—1222no—
414#117—1221no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—1222no—
427C2×C42C2×#692311yescharacteristic
428#97—614no—
429#97—614no—
430#97—1222no—
431#97—1222no—
432C4×C8—1222no—
433C4×C8—1222no—
434C4×C8—1222no—
435C4×C8—1222no—
436C24—611no—
437#41—2444no—
438#41—2444no—
439#41—2444no—
440C2×Q8—21no—
441C2×Q8—1221no—
442C2×Q8C22×#692312yes—
443C2×D4—612no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1222no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1224no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—2442no—
470C22×C4C22⋊#692311yescharacteristic
471C22×C4C22⋊#692311yescharacteristic
472C22×C4C22×#692311yescharacteristic
473M16—1228no—
474M16—1228no—
475M16—1228no—
476M16—1228no—
477C2×C8—1224no—
478C2×C8—1224no—
479C2×C8—1228no—
480C2×C8—1228no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—612no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1221no—
492C4⋊C4C22×#692312yes—
493C22⋊C4—22no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C42—22no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—1222no—
516C42—1222no—
517C42C22⋊#692311yescharacteristic
518C42C22⋊#692311yescharacteristic
519C42C22×#692311yescharacteristic
520C42C22×#692311yescharacteristic
521C23—611no—
522C23—611no—
523C23—1222no—
524C23—1222no—
525C23—1222no—
526C23—2441no—
527C23C2×C22⋊#692311yescharacteristic
528Q8—42no—
529Q8—42no—
530Q8—2442no—
531D4—2442no—
532D4—2444no—
533D4—2444no—
534D4—2444no—
535D4—2442no—
536D4—2442no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—614no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2444no—
564C2×C4—2444no—
565C2×C4—2444no—
566C2×C4#1451984214yes—
567C2×C4C2×C22⋊#692311yescharacteristic
568C2×C4C2×C22⋊#692311yescharacteristic
569C2×C4C2×C22⋊#692311yescharacteristic
570C2×C4C2×C22⋊#692311yescharacteristic
571C2×C4C2×C22⋊#692311yescharacteristic
572C2×C4C23×#692311yescharacteristic
573C8—1228no—
574C8—1228no—
575C22—21no—
576C22—21no—
577C22—612no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22—1221no—
582C22—1221no—
583C22—2444no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22C2×#1451984212yes—
588C22C22×C22⋊#692311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—612no—
595C4—612no—
596C4—1221no—
597C4—1221no—
598C4—1221no—
599C4—1221no—
600C4—2442no—
601C4D61⋊#10412yes—
602C4C2×#1451984212yes—
603C4C2×#1451984212yes—
604C2—22no—
605C2—1222no—
606C2—4882no—
607C2—2441no—
608C2D61⋊#41311yescharacteristic
609C2C2×D61⋊#10411yescharacteristic
610C2C22×#1451984211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#533C4
socleC22×C61C22×C22⋊C4
prime radical#21459116C2
cosocleC4×Dic61C24
hypercenter#533#6923
hypocenterC61#17638
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758213C2semidirect
2. C4×D61⋊M16C2semidirect
3. #21461277C2semidirect
4. #21461275C2semidirect
5. #21461272C2semidirect
6. #21461271C2semidirect
22. #16840619C22semidirect
23. #16840618C22semidirect
348. C61#17638semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582132
C4×D61⋊M162
#214612772
#214612752
#214612722
#214612712
#214591162
#1763861