Finite Group Databasebeta

← #29646963

Subgroups — #29646963

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459416C211yesmaximal, characteristic
2#21454785C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21444281C212yesmaximal, complemented
5#21444255C212yesmaximal, complemented
6#21444247C211yesmaximal, characteristic, complemented
7#21444229C212yesmaximal, complemented
8#21444218C211yesmaximal, characteristic, complemented
9#21444203C212yesmaximal, complemented
10C2×#16839494C211yesmaximal, characteristic, complemented
11C61×#1492C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840498C411yescharacteristic
14#16840494—21no—
15#16840487C411yescharacteristic
16#16840486C411yescharacteristic
17#16840481—21no—
18#16840464C412yes—
19#16840455—22no—
20#16840432C411yescharacteristic
21#16840418C412yes—
22#16840308—21no—
23#16840294C2212yes—
24#16840292—22no—
25#41×Dic61—21no—
26C4×#11758222C2211yescharacteristic
27C4×#11758224C2212yes—
28C2×C4×Dic122C2211yescharacteristic
29#16839892—21no—
30#16839841—21no—
31#16839833—22no—
32#16839815C2211yescharacteristic
33#16839813C2212yes—
34#16839790—21no—
35#16839787—22no—
36#16839784C2212yes—
37C2×C4⋊#92418C2211yescharacteristic
38C4⋊C8×D61C2212yes—
39C4×#11758189C2212yes—
40#16839494C2211yescharacteristic
41#16839494C2211yescharacteristic
42#16839494C2211yescharacteristic
43#16839494C2211yescharacteristic
44#16839492C2212yes—
45#16839492C2212yes—
46D4⋊#92418C2212yes—
47D4⋊#92418C2212yes—
48C61×#532C2211yescharacteristic
49C61×#423C2211yescharacteristic
50C2×C4×C8×C61C2211yescharacteristic
51C61×D4⋊C8C2212yes—
52C61×D4⋊C8C2212yes—
53C2×#11758222D411yescharacteristic
54C2×#11758224C2×C412yes—
55C22×Dic122C2×C411yescharacteristic
56#14519785—44no—
57C2×#11758189—22no—
58C2×#11758189—22no—
59C22×#92418—21no—
60C2×C8×D61—22no—
61#14519775—21no—
62#14519773—21no—
63#14519772—22no—
64#14519770—22no—
65#14519770—22no—
66#14519768C2×C412yes—
67#14519767—22no—
68#14519766—21no—
69#14519764—21no—
70#14519764C2×C412yes—
71#14519763—22no—
72#14519761—22no—
73#14519759—22no—
74#14519758—22no—
75#14519757C2×C412yes—
76#14519754—22no—
77#14519749—22no—
78#14519749—22no—
79#14519749—22no—
80#14519748C2×C412yes—
81Q8×Dic61—21no—
82Q8×Dic61—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122C2×C411yescharacteristic
86C4×Dic122C2×C411yescharacteristic
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122D411yescharacteristic
89C4×Dic122C2311yescharacteristic
90C4×Dic122C2311yescharacteristic
91#14519742C2×C412yes—
92C4×D244C2×C411yescharacteristic
93C4×D244D411yescharacteristic
94D4×Dic61—22no—
95D4×Dic61—22no—
96D4×Dic61—21no—
97D4×Dic61—21no—
98D4×Dic61C2×C412yes—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61C2×C412yes—
102C4×C22⋊D61D412yes—
103#14519737—22no—
104#14519736—22no—
105#14519736D411yescharacteristic
106#14519735C2×C412yes—
107#14519734D412yes—
108#14519733—22no—
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×#11758196—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—22no—
113C42×D61C2312yes—
114C4⋊#92418—21no—
115C4⋊#92418—21no—
116C4⋊#92418C2311yescharacteristic
117C4⋊#92418C2311yescharacteristic
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121C22⋊#92418—21no—
122#14519689—22no—
123#14519687—22no—
124C4×#92418C2312yes—
125C2×#41×C61—21no—
126C2×M16×C61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2×C411yescharacteristic
129#127×C61C2×C411yescharacteristic
130#124×C61—21no—
131#121×C61—21no—
132#121×C61C2×C412yes—
133C4×D4×C61—21no—
134C4×D4×C61C2312yes—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C4×C8×C61—21no—
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141#41×C61—42no—
142#41×C61—42no—
143C2×Q8×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—22no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61C22⋊C412yes—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159#11758224—24no—
160#11758224—42no—
161#11758222—22no—
162#11758222—22no—
163C2×D244C22⋊C411yescharacteristic
164C2×C4×D61C22×C412yes—
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167C2×Dic122—22no—
168C2×Dic122—21no—
169C2×Dic122—41no—
170C2×Dic122C22⋊C411yescharacteristic
171C2×Dic122C22×C411yescharacteristic
172C2×Dic122C22×C411yescharacteristic
173M16×C61—42no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—22no—
177C2×C8×C61—42no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61C22×C412yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C42×C61C22×C411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61C2411yescharacteristic
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61C22⋊C412yes—
191#11758198—22no—
192#11758198—22no—
193#11758198C22⋊C412yes—
194#11758198C22⋊C412yes—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22⋊C411yescharacteristic
199C4⋊Dic61C22⋊C411yescharacteristic
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206#11758196—22no—
207#11758196—22no—
208#11758196C22⋊C412yes—
209#11758196C22⋊C412yes—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61C22×C412yes—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C2×#92418—22no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—42no—
223#11758189—44no—
224#11758189—44no—
225C8×D61—44no—
226C23×C61—22no—
227C23×C61C2×C22⋊C411yescharacteristic
228C22×D61C2×C22⋊C412yes—
229Q8×C61—42no—
230D4×C61—22no—
231D4×C61—22no—
232D4×C61—44no—
233D4×C61—42no—
234D4×C61—81no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61AGL(1,ℤ/8)12yes—
245C2×C4×C61#13712yes—
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C22⋊D61—24no—
250C22⋊D61—44no—
251C22⋊D61—82no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—44no—
257C2×Dic61—42no—
258C2×Dic61—82no—
259C2×Dic61—81no—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263D244—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—42no—
269Dic122—21no—
270Dic122—22no—
271Dic122—21no—
272Dic122—21no—
273Dic122—42no—
274Dic122#13112yescomplemented
275C8×C61—22no—
276C8×C61—41no—
277C8×C61—42no—
278#92418—42no—
279#92418—41no—
280#92418—41no—
281#17515—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61#41712yes—
288C22×C61C22×C22⋊C411yescharacteristic
289C2×D61—22no—
290C2×D61—22no—
291C2×D61—22no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—42no—
296C4×C61#41712yes—
297C4×C61C2×#13111yescharacteristic
298C4×C61#56811yescharacteristic
299C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C61C2×#13711yescharacteristic
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—22no—
305Dic61—41no—
306Dic61—41no—
307Dic61—41no—
308#3480—611no—
309#2965—611no—
310#2906—611no—
311#1495—612no—
312#1492D6111yescharacteristic, complemented
313#1489—612no—
314#1487—611no—
315#1483—612no—
316#1480—611no—
317#1477—612no—
318C2×Q8⋊C8—611no—
319C2×C61—22no—
320C2×C61—82no—
321C2×C61#288011yescharacteristic
322C2×C61C2×#41711yescharacteristic
323C2×C61#290111yescharacteristic
324D61—42no—
325C2×#131—1221no—
326#559—611no—
327#559—1221no—
328#557—611no—
329#556—611no—
330#556—1221no—
331#553—612no—
332#553—1222no—
333#550—611no—
334#548—612no—
335#532—1221no—
336#532C2×D6111yescharacteristic
337#529—612no—
338#529—1222no—
339C4×#41—611no—
340C4×#41—612no—
341C4×#41—1221no—
342C2×C4×Q8—611no—
343#446—1221no—
344#436—1221no—
345#435—1222no—
346#431—611no—
347#431—612no—
348#424—1222no—
349#424—1221no—
350#423—612no—
351#423C2×D6111yescharacteristic
352C2×C4⋊C8—611no—
353C2×C4⋊C8—612no—
354C4×M16—612no—
355C2×C4×C8C2×D6111yescharacteristic
356Q8⋊C8—612no—
357Q8⋊C8—612no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360Q8⋊C8—611no—
361Q8⋊C8—611no—
362D4⋊C8—612no—
363D4⋊C8—612no—
364D4⋊C8C2×D6112yes—
365D4⋊C8C2×D6112yes—
366C61#1751511yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×#41—611no—
369C2×#41—612no—
370C22×Q8—611no—
371#131—2444no—
372C2×M16—21no—
373C2×M16—1222no—
374C2×M16—1222no—
375C22×C8—21no—
376C22×C8—1222no—
377C22×C8—1221no—
378C4⋊Q8—1221no—
379C4⋊Q8C4×D6111yescharacteristic
380#127—1221no—
381#127C4×D6111yescharacteristic
382#126—1222no—
383#126—1222no—
384#126—1222no—
385#125—612no—
386#125—1222no—
387#124—21no—
388#124—612no—
389#124—1222no—
390#124—1221no—
391#124—1221no—
392#123—1222no—
393#123—1222no—
394#123—1222no—
395C22⋊Q8—612no—
396C22⋊Q8—1222no—
397#121—21no—
398#121—612no—
399#121—1222no—
400#121—1222no—
401#121—1222no—
402#121C4×D6112yes—
403C4×Q8—611no—
404C4×Q8—611no—
405C4×Q8—612no—
406C4×Q8—611no—
407C4×Q8—611no—
408C4×Q8—611no—
409C4×Q8—611no—
410C4×Q8—1221no—
411C4×Q8—1221no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×D4—21no—
415C4×D4—612no—
416C4×D4—612no—
417C4×D4—612no—
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4C22×D6112yes—
428#117—611no—
429#117—612no—
430#117—612no—
431#117—1222no—
432#117—1222no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1221no—
435C2×C42—612no—
436C2×C42—1222no—
437C2×C42—1221no—
438C2×C42C22×D6111yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—1222no—
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8C22×D6112yes—
448C22⋊C8—1222no—
449C22⋊C8—1221no—
450#97—1222no—
451C4×C8—21no—
452C4×C8—612no—
453C4×C8C22×D6111yescharacteristic
454C4×C8C22×D6111yescharacteristic
455#41—42no—
456#41—42no—
457#41—1222no—
458#41—1222no—
459#41—1224no—
460#41—2442no—
461C2×Q8—21no—
462C2×Q8—611no—
463C2×Q8—611no—
464C2×Q8—611no—
465C2×Q8—1222no—
466C2×Q8—1221no—
467C2×Q8—2441no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—612no—
472C2×D4—611no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4C2×C4×D6112yes—
476C22×C4—22no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487M16—42no—
488M16—2444no—
489M16—2444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—42no—
494C2×C8—1222no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—2444no—
498C2×C8—2442no—
499C4⋊C4—21no—
500C4⋊C4—612no—
501C4⋊C4—612no—
502C4⋊C4—611no—
503C4⋊C4—611no—
504C4⋊C4—611no—
505C4⋊C4—611no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4C2×C4×D6112yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—612no—
519C22⋊C4—612no—
520C22⋊C4—612no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C42—612no—
528C42—612no—
529C42—612no—
530C42—1222no—
531C42—1222no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42C2×C4×D6111yescharacteristic
537C42D4×D6111yescharacteristic
538C42D4×D6111yescharacteristic
539C42C23×D6111yescharacteristic
540C23—22no—
541C23—612no—
542C23C22⋊C4×D6111yescharacteristic
543Q8—42no—
544Q8—612no—
545Q8—1221no—
546Q8—1222no—
547Q8—1221no—
548Q8—1221no—
549Q8—2442no—
550D4—22no—
551D4—22no—
552D4—44no—
553D4—42no—
554D4—81no—
555D4—1224no—
556D4—1222no—
557D4—4882no—
558D4—2444no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—1221no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—4882no—
577C2×C4—4881no—
578C2×C4—2442no—
579C2×C4—2444no—
580C2×C4—2442no—
581C2×C4C22⋊C4×D6111yescharacteristic
582C2×C4C22⋊C4×D6111yescharacteristic
583C2×C4C22⋊C4×D6111yescharacteristic
584C2×C4#1451980112yes—
585C2×C4#1451980612yes—
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C2×D4×D6111yescharacteristic
589C8—22no—
590C8—41no—
591C8—42no—
592C8—2442no—
593C8—2441no—
594C8—2441no—
595C22—21no—
596C22—21no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—1222no—
601C22—1222no—
602C22—1222no—
603C22#1683976012yes—
604C22C2×C22⋊C4×D6111yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—1222no—
610C4—1222no—
611C4—1222no—
612C4—1222no—
613C4—2441no—
614C4—2441no—
615C4—2441no—
616C4#1683976012yes—
617C4#131×D6111yescharacteristic
618C4#1684052711yescharacteristic
619C4C2×#1451980111yescharacteristic
620C4C2×#1451980611yescharacteristic
621C2—22no—
622C2—82no—
623C2—2442no—
624C2#2145426711yescharacteristic
625C2C2×#1683976011yescharacteristic
626C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1492C2
socleC22×C61C22×C22⋊C4
prime radical#21459416C2
cosocleC42×C61C24
hypercenter#1492D61
hypocenterC61#17515
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #21454785C2semidirect
3. #21454388C2semidirect
4. #21444281C2semidirect
5. #21444255C2semidirect
6. #21444247C2semidirect
7. #21444229C2semidirect
8. #21444218C2semidirect
9. #21444203C2semidirect
10. C2×#16839494C2semidirect
11. C61×#1492C2semidirect
274. Dic122#131semidirect
312. #1492D61semidirect
366. C61#17515semidirect

Maximal subgroups

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

subgroupindex
#214594162
#214547852
#214543882
#214442812
#214442552
#214442472
#214442292
#214442182
#214442032
C2×#168394942
C61×#14922
#1751561