Finite Group Databasebeta

← #30610583

Subgroups — #30610583

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic, complemented
2C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
3#21461170C214yesmaximal, complemented
4#21461169C212yesmaximal, complemented
5#21461165C212yesmaximal, complemented
6#21461111C214yesmaximal, complemented
7#21459114C211yesmaximal, characteristic
8C22×D61⋊C8—21no—
9#16840784—21no—
10#16840783C2212yes—
11#16840781C2212yes—
12#16840778—21no—
13#16840766C2212yes—
14#16840733—21no—
15C4×#11758213—21no—
16C4×D61⋊C8—21no—
17C4×D61⋊C8—21no—
18C4×D61⋊C8C2212yes—
19C4×D61⋊C8C2212yes—
20C2×C4×#92420—21no—
21C2×C4×#92420C2212yes—
22#16840612C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24#16840319C411yescharacteristic
25#16840317C411yescharacteristic
26#16840317C2211yescharacteristic
27#16840310C411yescharacteristic
28#16840310C2211yescharacteristic
29#16840294—21no—
30#16840294C412yes—
31#16840293—21no—
32#16840293C2212yes—
33#16840291—21no—
34#16840291—21no—
35#16840272—21no—
36#16840272C412yes—
37#16840269—21no—
38#41×Dic61—21no—
39C4×#11758224—21no—
40C4×#11758224C2212yes—
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic
43C2×#11758213—22no—
44C2×D61⋊C8—28no—
45C2×D61⋊C8—22no—
46C2×D61⋊C8—22no—
47C22×#92420—22no—
48C4⋊#92420—22no—
49C4⋊#92420C2314yes—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53C4×#92420—22no—
54C4×#92420—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C4×#92420C2314yes—
58C2×#11758224—21no—
59C2×#11758224C2×C412yes—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63#14519777C2×C411yescharacteristic
64#14519777C2×C411yescharacteristic
65#14519770—22no—
66#14519770—22no—
67#14519769—21no—
68#14519768—21no—
69#14519768C2×C412yes—
70#14519764—21no—
71#14519764C2×C412yes—
72#14519759—22no—
73#14519759—22no—
74#14519758—22no—
75#14519757—21no—
76#14519757C2×C412yes—
77#14519756—21no—
78#14519756C2×C412yes—
79#14519753—21no—
80#14519753—21no—
81#14519748—21no—
82#14519748—21no—
83#14519748—21no—
84#14519748C2×C412yes—
85#14519745—22no—
86Q8×Dic61—21no—
87Q8×Dic61—21no—
88C4×Dic122—21no—
89C4×Dic122C2×C412yes—
90#14519742—21no—
91#14519742C2312yes—
92D4×Dic61—22no—
93D4×Dic61—22no—
94D4×Dic61—21no—
95D4×Dic61—21no—
96D4×Dic61—21no—
97D4×Dic61C2312yes—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100#14519737—22no—
101#14519737—22no—
102#14519736—21no—
103#14519736—22no—
104#14519735—21no—
105#14519735C2×C412yes—
106#14519733—22no—
107#14519733—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C2×#41×C61—21no—
121C4⋊Q8×C61C2×C411yescharacteristic
122#127×C61C2×C411yescharacteristic
123#124×C61—21no—
124#121×C61—21no—
125#121×C61C2×C412yes—
126C4×D4×C61—21no—
127C4×D4×C61C2×C412yes—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61C22⋊C411yescharacteristic
130#41×C61—44no—
131C2×Q8×C61—21no—
132C2×D4×C61—22no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61C22×C412yes—
136C22×C4×C61—22no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61C22⋊C411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147#11758224—28no—
148#11758224—44no—
149C2×C4×D61—24no—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×Dic122—21no—
165C2×Dic122C22×C412yes—
166C2×#92420—28no—
167C2×#92420—24no—
168C2×#92420—24no—
169#11758213—44no—
170D61⋊C8—28no—
171D61⋊C8—28no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C412yes—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C42×C61C22⋊C411yescharacteristic
177C42×C61C22⋊C411yescharacteristic
178C42×C61C22×C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185#11758198—22no—
186#11758198—22no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61C22×C412yes—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61—22no—
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22×C411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2411yescharacteristic
212C23×C61—22no—
213C23×C61C2×C22⋊C411yescharacteristic
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61C2×C22⋊C411yescharacteristic
218C22×D61C2×C22⋊C411yescharacteristic
219Q8×C61—42no—
220D4×C61—24no—
221D4×C61—44no—
222D4×C61—42no—
223D4×C61—42no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—44no—
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—
236C22⋊D61—44no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—44no—
243C2×Dic61—44no—
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249C2×Dic61C22×D411yescharacteristic
250C4×D61—22no—
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#13114yes—
261C4×D61#13514yes—
262Dic122—24no—
263Dic122—42no—
264#92420—28no—
265#92420—44no—
266#17473—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61C2×#10412yes—
273C22×C61C22×C22⋊C411yescharacteristic
274C2×D61—28no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61#40812yes—
280C2×D61#41612yes—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—42no—
284C4×C61#41612yes—
285C4×C61C2×#10412yes—
286C4×C61C2×#10412yes—
287C4×C61C2×#13112yes—
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—21no—
292Dic61—42no—
293Dic61—42no—
294Dic61#40812yes—
295Dic61C2×#13512yes—
296#3444—611no—
297#2920—611no—
298C22×C4×C8—611no—
299#1494—614no—
300#1493—612no—
301#1492—612no—
302#1476—614no—
303C2×C61—22no—
304C2×C61—82no—
305C2×C61C2×#40811yescharacteristic
306C2×C61C2×#41611yescharacteristic
307C2×C61C22×#10411yescharacteristic
308D61—22no—
309D61—22no—
310C23×C8—1221no—
311#533—611no—
312#533—611no—
313#533—611no—
314#532—611no—
315#532—611no—
316#532#692311yescharacteristic
317#529—612no—
318#529—612no—
319#529—1221no—
320#529—1221no—
321#529—1221no—
322#529—1221no—
323#525—612no—
324#525—1221no—
325#525—1221no—
326C4×#41—612no—
327C4×#41—1221no—
328C4×#41—1221no—
329C22×C42—611no—
330#432—612no—
331#432—1221no—
332#431—612no—
333#431—1221no—
334#423—612no—
335#407—1221no—
336C4×M16—1221no—
337C2×C4×C8—612no—
338C2×C4×C8—612no—
339C2×C4×C8—612no—
340C2×C4×C8—1221no—
341C2×C4×C8—1221no—
342C2×C4×C8—1221no—
343Q8⋊C8—618no—
344D4⋊C8—618no—
345C61#1747311yescharacteristic, complemented, Sylow
346C2×#41—21no—
347C2×#41—612no—
348C2×#41—1221no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C2×M16—1222no—
353C22×C8—1222no—
354C22×C8—1222no—
355C22×C8—1222no—
356C22×C8—1228no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359C4⋊Q8C2×#692311yescharacteristic
360#127C2×#692311yescharacteristic
361#126—1222no—
362#126—1222no—
363#125—612no—
364#125—1221no—
365#125—1221no—
366#124—21no—
367#124—612no—
368#124—1221no—
369#123—1222no—
370#123—1222no—
371#123—1222no—
372C22⋊Q8—612no—
373C22⋊Q8—612no—
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378#121—21no—
379#121—612no—
380#121—1221no—
381#121—1221no—
382#121—1221no—
383#121C2×#692312yes—
384#120—1222no—
385C4×Q8—612no—
386C4×Q8—612no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8—1221no—
391C4×D4—21no—
392C4×D4—612no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1222no—
402C4×D4C2×#692312yes—
403#117—612no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407#117—1221no—
408#117—1221no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—1222no—
421C2×C42C2×#692311yescharacteristic
422C4⋊C8—614no—
423C4⋊C8—1222no—
424C22⋊C8—1222no—
425C22⋊C8—1222no—
426#97—1222no—
427C4×C8—614no—
428C4×C8—1222no—
429C4×C8—1222no—
430C4×C8—1222no—
431C4×C8—1222no—
432C24—611no—
433#41—44no—
434#41—1228no—
435#41—2444no—
436C2×Q8—21no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4C22×#692312yes—
445C22×C4—22no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
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—1224no—
462C22×C4—1224no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1224no—
466C22×C4C22⋊#692311yescharacteristic
467C22×C4C22⋊#692311yescharacteristic
468C22×C4C22×#692311yescharacteristic
469M16—2444no—
470C2×C8—1224no—
471C2×C8—1228no—
472C2×C8—1228no—
473C2×C8—1228no—
474C2×C8—1224no—
475C4⋊C4—21no—
476C4⋊C4—612no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4C22×#692312yes—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—1222no—
490C22⋊C4—1222no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—1222no—
509C42—1222no—
510C42—1222no—
511C42C22⋊#692311yescharacteristic
512C42C22⋊#692311yescharacteristic
513C42C22×#692311yescharacteristic
514C42C22×#692311yescharacteristic
515C23—22no—
516C23—611no—
517C23—611no—
518C23—1222no—
519C23—1222no—
520C23—1222no—
521C23C2×C22⋊#692311yescharacteristic
522Q8—42no—
523Q8—1224no—
524Q8—2442no—
525D4—24no—
526D4—44no—
527D4—42no—
528D4—42no—
529D4—2444no—
530D4—2444no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—44no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—614no—
538C2×C4—614no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1222no—
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—2444no—
559C2×C4—2444no—
560C2×C4#1451984114yes—
561C2×C4C2×C22⋊#692311yescharacteristic
562C2×C4C2×C22⋊#692311yescharacteristic
563C2×C4C2×C22⋊#692311yescharacteristic
564C2×C4C2×C22⋊#692311yescharacteristic
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4C23×#692311yescharacteristic
567C8—1228no—
568C8—2444no—
569C22—21no—
570C22—21no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—612no—
575C22—612no—
576C22—1228no—
577C22—1221no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22C2×#1451984112yes—
582C22C22×C22⋊#692311yescharacteristic
583C4—21no—
584C4—21no—
585C4—42no—
586C4—612no—
587C4—612no—
588C4—1221no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—2442no—
593C4—2442no—
594C4#1684075212yes—
595C4C2×#1451984112yes—
596C4C2×#1451984112yes—
597C4D61⋊#13112yes—
598C2—22no—
599C2—82no—
600C2—1222no—
601C2—1222no—
602C2D61⋊#40811yescharacteristic
603C2C2×#1684075211yescharacteristic
604C2C22×#1451984111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#532C4
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC4×Dic61C24
hypercenter#532#6923
hypocenterC61#17473
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C2×C4×D61⋊C8C2semidirect
3. #21461170C2semidirect
4. #21461169C2semidirect
5. #21461165C2semidirect
6. #21461111C2semidirect
22. #16840612C22semidirect
23. D4⋊#92420C22semidirect
345. C61#17473semidirect

Maximal subgroups

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

subgroupindex
#214624962
C2×C4×D61⋊C82
#214611702
#214611692
#214611652
#214611112
#214591142
#1747361