Finite Group Databasebeta

← #29657979

Subgroups — #29657979

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457046C211yesmaximal, characteristic, complemented
2#21456843C211yesmaximal, characteristic, complemented
3C2×#16840158C211yesmaximal, characteristic, complemented
4#21445103C212yesmaximal, complemented
5#21445096C212yesmaximal, complemented
6#21445089C212yesmaximal, complemented
7#21445082C212yesmaximal, complemented
8#21444536C211yesmaximal, characteristic, complemented
9#21444279C211yesmaximal, characteristic, complemented
10#21444279C211yesmaximal, characteristic, complemented
11C61×#3552C211yesmaximal, characteristic
12C2×#14519777C2211yescharacteristic
13#16840172—21no—
14#16840158—22no—
15#16840158C2212yes—
16#16840158C2212yes—
17#16840157—21no—
18#16840132—21no—
19#16840121—21no—
20#16840095—21no—
21#16840078—21no—
22#16840047C2212yes—
23#16840042C2212yes—
24#16839972C2212yes—
25#16839967C2212yes—
26#16839917—21no—
27#16839900—21no—
28#16839819C2211yescharacteristic
29#16839819C2211yescharacteristic
30C2×#14519708—22no—
31C2×C4×#92418C2211yescharacteristic
32#16839508C2212yes—
33#16839508C2212yes—
34Q8⋊#92418C2212yes—
35Q8⋊#92418C2212yes—
36D4⋊#92418C2212yes—
37D4⋊#92418C2212yes—
38C61×#563—22no—
39C61×#557C2211yescharacteristic
40C61×#556C2211yescharacteristic
41C61×#554—21no—
42C61×#553—21no—
43D4×Q8×C61—21no—
44D4×Q8×C61C2211yescharacteristic
45C61×#548—21no—
46C61×#547C2211yescharacteristic
47C61×#544—21no—
48C61×#542—21no—
49C61×#541—21no—
50C61×#539—22no—
51C61×#536—21no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C61×#529C2211yescharacteristic
54C61×#529C2211yescharacteristic
55C22×Dic122—21no—
56C2×#11758202—22no—
57C2×#11758200—22no—
58C22×#92418—21no—
59#14519777—21no—
60#14519777—21no—
61#14519777—21no—
62#14519777C2312yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65#14519710—22no—
66#14519708—22no—
67#14519708—24no—
68#14519708—24no—
69C4⋊#92418C2312yes—
70C4⋊#92418C2312yes—
71#14519701—22no—
72#14519700—22no—
73#14519700—22no—
74#14519698—22no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77#14519688—21no—
78#14519688—21no—
79C4×#92418—21no—
80C4×#92418C2312yes—
81C2×#41×C61—21no—
82C22×Q8×C61—21no—
83C22×Q8×C61—21no—
84C4⋊Q8×C61—22no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61D412yes—
90C4⋊Q8×C61C2311yescharacteristic
91C4⋊Q8×C61C2311yescharacteristic
92#126×C61—22no—
93#126×C61—22no—
94#126×C61—22no—
95#126×C61—21no—
96#126×C61—21no—
97#125×C61—22no—
98#125×C61—22no—
99#125×C61—22no—
100#125×C61—21no—
101#125×C61D411yescharacteristic
102#125×C61D411yescharacteristic
103#124×C61—22no—
104#124×C61—21no—
105#124×C61D411yescharacteristic
106#124×C61D411yescharacteristic
107#123×C61—22no—
108#123×C61—22no—
109#123×C61—21no—
110#123×C61—21no—
111#123×C61—22no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—22no—
116C22⋊Q8×C61—22no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—22no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61D411yescharacteristic
122C22⋊Q8×C61D411yescharacteristic
123#121×C61—22no—
124#121×C61—21no—
125#121×C61D411yescharacteristic
126#121×C61D411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C4×D4×C61C2311yescharacteristic
138C4×D4×C61C2311yescharacteristic
139#117×C61—21no—
140#117×C61—21no—
141#117×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61D412yes—
145C2×C42×C61C2311yescharacteristic
146#41×C61—82no—
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—82no—
152C2×Q8×C61—82no—
153C2×Q8×C61C2×D411yescharacteristic
154C2×Q8×C61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—22no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×Dic61—41no—
169C2×Dic122—22no—
170C2×Dic122—41no—
171C2×Dic122—82no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C2×D411yescharacteristic
191C4⋊C4×C61C2×D412yes—
192C4⋊C4×C61C2×D412yes—
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—21no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊C4×C61—21no—
210C42×C61—22no—
211C42×C61—22no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61C2×D411yescharacteristic
215C42×C61C2×D411yescharacteristic
216C42×C61C2×D411yescharacteristic
217C42×C61C2411yescharacteristic
218#11758202—82no—
219#11758200—82no—
220C4⋊Dic61—22no—
221C4⋊Dic61—22no—
222C4⋊Dic61—41no—
223C4⋊Dic61—41no—
224C2×#92418—24no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—22no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61#12011yescharacteristic
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—42no—
234Q8×C61—42no—
235Q8×C61—82no—
236Q8×C61—82no—
237D4×C61—22no—
238D4×C61—22no—
239D4×C61—42no—
240D4×C61—42no—
241D4×C61—82no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—82no—
256C2×C4×C61—82no—
257C2×C4×C61—82no—
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61#12011yescharacteristic
260C2×C4×C61#12011yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×Dic61—42no—
265C2×Dic61—82no—
266Dic122—42no—
267Dic122—42no—
268Dic122—82no—
269#92418—24no—
270#92418—42no—
271#92418—42no—
272#18700—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61#45612yes—
282C22×C61C2×#12011yescharacteristic
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—42no—
289C4×C61—41no—
290C4×C61—42no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61#57712yes—
296C4×C61#57712yes—
297Dic61—82no—
298#3552D6111yescharacteristic
299#3239—611no—
300#3218—611no—
301C2×#498—611no—
302#1654—612no—
303#1653—612no—
304#1652—612no—
305#1651—612no—
306#1556—611no—
307#1494—611no—
308#1494—611no—
309C2×C61—22no—
310C2×C61—81no—
311C2×C61—81no—
312C2×C61#300911yescharacteristic
313C2×C61#301011yescharacteristic
314C2×C61C2×#45611yescharacteristic
315#563—22no—
316#557C2×D6111yescharacteristic
317#556C2×D6111yescharacteristic
318#554—21no—
319#553—21no—
320D4×Q8—21no—
321D4×Q8C2×D6111yescharacteristic
322#548—21no—
323#547C2×D6111yescharacteristic
324#544—21no—
325#542—21no—
326#541—21no—
327#539—22no—
328#536—21no—
329C2×C4⋊Q8—611no—
330C2×C4⋊Q8C2×D6111yescharacteristic
331#529C2×D6111yescharacteristic
332#529C2×D6111yescharacteristic
333#501—1221no—
334#498—612no—
335#498—612no—
336#498—1222no—
337#497—1221no—
338#491—1221no—
339#489—1221no—
340#484—1221no—
341#481—1221no—
342#475—612no—
343#474—612no—
344#462—612no—
345#461—612no—
346#451—1221no—
347#448—1221no—
348#432—611no—
349#432—611no—
350C2×#106—1222no—
351C2×C4×C8—611no—
352#332—612no—
353#332—612no—
354Q8⋊C8—612no—
355Q8⋊C8—612no—
356D4⋊C8—612no—
357D4⋊C8—612no—
358C61#1870011yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C22×Q8—21no—
362C22×Q8—1221no—
363C2×Q16—1222no—
364C2×SD16—1222no—
365C22×C8—1221no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—612no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8C22⋊D6112yes—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#126—22no—
379#126—22no—
380#126—22no—
381#126—21no—
382#126—21no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—21no—
387#125C22⋊D6111yescharacteristic
388#125C22⋊D6111yescharacteristic
389#124—22no—
390#124—21no—
391#124C22⋊D6111yescharacteristic
392#124C22⋊D6111yescharacteristic
393#123—22no—
394#123—22no—
395#123—21no—
396#123—21no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8C22⋊D6111yescharacteristic
408C22⋊Q8C22⋊D6111yescharacteristic
409#121—22no—
410#121—21no—
411#121C22⋊D6111yescharacteristic
412#121C22⋊D6111yescharacteristic
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C22×D6111yescharacteristic
417C4×Q8C22×D6111yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4C22×D6111yescharacteristic
424C4×D4C22×D6111yescharacteristic
425#117—21no—
426#117—21no—
427#117—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C22⋊D6112yes—
433C2×C42C22×D6111yescharacteristic
434#107—1222no—
435#106—1224no—
436#106—1224no—
437#106—1222no—
438C4⋊C8—612no—
439C4⋊C8—612no—
440#103—1222no—
441#103—1222no—
442#103—1222no—
443#102—1222no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—1221no—
447#97—1221no—
448C4×C8—612no—
449C4×C8—1221no—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—82no—
456C2×Q8—82no—
457C2×Q8—1222no—
458C2×Q8—4882no—
459C2×Q8—2441no—
460C2×Q8C2×C22⋊D6111yescharacteristic
461C2×Q8C2×C22⋊D6111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4C2×C22⋊D6111yescharacteristic
466C2×D4C2×C22⋊D6111yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—2441no—
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476Q16—4882no—
477SD16—4882no—
478C2×C8—1224no—
479C2×C8—1222no—
480C2×C8—1222no—
481C2×C8—1222no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—2441no—
503C4⋊C4—2441no—
504C4⋊C4C2×C22⋊D6111yescharacteristic
505C4⋊C4C2×C22⋊D6111yescharacteristic
506C4⋊C4C2×C22⋊D6112yes—
507C4⋊C4C2×C22⋊D6112yes—
508C4⋊C4C2×C22⋊D6111yescharacteristic
509C4⋊C4C2×C22⋊D6111yescharacteristic
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C42—22no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42C2×C22⋊D6111yescharacteristic
529C42C2×C22⋊D6111yescharacteristic
530C42C2×C22⋊D6111yescharacteristic
531C42C23×D6111yescharacteristic
532C23—21no—
533C23—21no—
534C23#1451974611yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—42no—
538Q8—42no—
539Q8—82no—
540Q8—82no—
541Q8—4882no—
542Q8—2442no—
543Q8—2442no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—4882no—
566C2×C4—2442no—
567C2×C4#1451974611yescharacteristic
568C2×C4#1451974611yescharacteristic
569C2×C4#1451974611yescharacteristic
570C2×C4C22×C22⋊D6111yescharacteristic
571C2×C4C22×C22⋊D6111yescharacteristic
572C2×C4C22×C22⋊D6111yescharacteristic
573C8—1224no—
574C8—2442no—
575C8—2442no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22#1683994512yes—
585C22C2×#1451974611yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—42no—
598C4—4882no—
599C4#1684057012yes—
600C4#1684057312yes—
601C2—22no—
602C2—81no—
603C2—81no—
604C2#2145509611yescharacteristic
605C2#2145510511yescharacteristic
606C2C2×#1683994511yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3552C2
socleC22×C61C2×#120
hypercenter#3552D61
hypocenterC61#18700
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3552

Complements

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

NH ≅ G/Ntype
1. #21457046C2semidirect
2. #21456843C2semidirect
3. C2×#16840158C2semidirect
4. #21445103C2semidirect
5. #21445096C2semidirect
6. #21445089C2semidirect
7. #21445082C2semidirect
8. #21444536C2semidirect
9. #21444279C2semidirect
10. #21444279C2semidirect
358. C61#18700semidirect

Maximal subgroups

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

subgroupindex
#214570462
#214568432
C2×#168401582
#214451032
#214450962
#214450892
#214450822
#214445362
#214442792
C61×#35522
#1870061