Finite Group Databasebeta

← #29670931

Subgroups — #29670931

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458466C211yesmaximal, characteristic, complemented
2#21458403C211yesmaximal, characteristic, complemented
3#21458176C211yesmaximal, characteristic, complemented
4#21445494C211yesmaximal, characteristic, complemented
5#21445316C211yesmaximal, characteristic, complemented
6#21445270C211yesmaximal, characteristic, complemented
7#21445206C211yesmaximal, characteristic, complemented
8#21445186C211yesmaximal, characteristic, complemented
9#21445073C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic, complemented
11#21445024C211yesmaximal, characteristic, complemented
12#21444970C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15C61×#3283C211yesmaximal, characteristic
16#16840482C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840115—21no—
22#16840114C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840097—21no—
25#16840092—21no—
26#16840083—21no—
27#16840078—21no—
28#16840068—21no—
29#16840052C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840044C2211yescharacteristic
32#16840044C2211yescharacteristic
33#16840042C2211yescharacteristic
34#16840006—21no—
35#16839989—21no—
36#16839975—21no—
37#16839967C2211yescharacteristic
38C8×Dic122C2211yescharacteristic
39#16839853—21no—
40C4×#11758200C2211yescharacteristic
41#16839840C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839802—21no—
44C2×#14519708—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839492C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C2×#135×C61—21no—
57C61×#547C2211yescharacteristic
58C61×#547C2211yescharacteristic
59C61×#494C2211yescharacteristic
60C61×#467—21no—
61C61×#461C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#452—21no—
64C61×#452—21no—
65C4×D8×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758200D411yescharacteristic
69C2×#11758194—21no—
70C22×#92418—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519770—41no—
74#14519768—21no—
75#14519764—21no—
76#14519756—21no—
77#14519756—21no—
78#14519754—41no—
79C4×Dic122C2311yescharacteristic
80#14519742—21no—
81D4×Dic61—21no—
82#14519736—21no—
83C2×C4⋊Dic61—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—41no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519702—21no—
100#14519702—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—41no—
105#14519700D411yescharacteristic
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117#135×C61—44no—
118C2×Q16×C61—21no—
119C2×Q16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×D8×C61D411yescharacteristic
123C22×C8×C61—21no—
124C4⋊Q8×C61C2311yescharacteristic
125C4⋊Q8×C61C2311yescharacteristic
126#123×C61—41no—
127#123×C61—41no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137#107×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—42no—
147#41×C61—81no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C22×Dic61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C2×D411yescharacteristic
165Q16×C61—42no—
166Q16×C61—81no—
167SD16×C61—42no—
168SD16×C61—42no—
169D8×C61—22no—
170C2×C8×C61—21no—
171C2×C8×C61—42no—
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C42×C61C2411yescharacteristic
189C22⋊Dic61—41no—
190C22⋊Dic61—41no—
191C22⋊Dic61—41no—
192#11758200—22no—
193#11758200—42no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—41no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—41no—
205#11758194—42no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—42no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—82no—
226D4×C61—82no—
227D4×C61AGL(1,ℤ/8)12yes—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—82no—
240C2×C4×C61—82no—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—161no—
249Dic122—21no—
250Dic122—21no—
251Dic122—41no—
252Dic122—41no—
253Dic122—81no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418#13512yescomplemented
263#19860—611nomaximal, Sylow
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61D4211yescharacteristic
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61C2×#13511yescharacteristic
281C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C61#57711yescharacteristic
283C4×C61#57811yescharacteristic
284Dic61—41no—
285Dic61—41no—
286Dic61—81no—
287Dic61—81no—
288#3360—611no—
289#3353—611no—
290#3335—611no—
291#3283D6111yescharacteristic
292#1723—611no—
293#1691—611no—
294#1683—611no—
295#1673—611no—
296#1670—611no—
297#1650—611no—
298#1647—611no—
299#1643—611no—
300#1635—611no—
301#1581—611no—
302SD16⋊C8—611no—
303C2×C61—42no—
304C2×C61—81no—
305C2×C61—81no—
306C2×C61#326511yescharacteristic
307C2×C61#328311yescharacteristic
308C2×C61#328911yescharacteristic
309C2×#135—21no—
310#556—611no—
311#554—611no—
312#547C2×D6111yescharacteristic
313#547C2×D6111yescharacteristic
314#500—611no—
315#500—611no—
316#498—611no—
317#494C2×D6111yescharacteristic
318#488—1221no—
319#487—611no—
320#487—611no—
321#484—1221no—
322#483—1221no—
323#482—1221no—
324#481—1221no—
325#479—1221no—
326#476—611no—
327#476—611no—
328#475—611no—
329#475—611no—
330#474—611no—
331#468—1221no—
332#467—21no—
333#465—1221no—
334#463—1221no—
335#461—611no—
336#461C2×D6111yescharacteristic
337#461C2×D6111yescharacteristic
338#452—21no—
339#452—21no—
340C8×Q8—611no—
341C4×SD16—611no—
342C4×SD16—1221no—
343C4×D8C2×D6111yescharacteristic
344#436—611no—
345C8×D4—611no—
346C8×D4C2×D6111yescharacteristic
347#428—1221no—
348C2×#106—1221no—
349#335—611no—
350#335—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355Q8⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360C61#1986011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C2×#41—21no—
363#135—44no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—611no—
369C2×SD16—1221no—
370C2×D8C22⋊D6111yescharacteristic
371C2×M16—1221no—
372C22×C8—21no—
373C22×C8—1221no—
374C4⋊Q8—611no—
375C4⋊Q8—611no—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#126—2441no—
379#125—1221no—
380#124—1221no—
381#123—41no—
382#123—41no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—2441no—
388#121—21no—
389#121—21no—
390C4×Q8—611no—
391C4×Q8—1221no—
392C4×D4—1221no—
393C4×D4C22×D6111yescharacteristic
394C4×D4C22×D6111yescharacteristic
395C4×D4C22×D6111yescharacteristic
396#117—1221no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—1221no—
400#107—1221no—
401#107—1221no—
402#107—1221no—
403#107—2441no—
404#107C22⋊D6111yescharacteristic
405#106—611no—
406#106—1221no—
407#106—1221no—
408#106—1221no—
409#106—1221no—
410#106—1221no—
411#106—1221no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417#103—21no—
418#103—21no—
419#103—611no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—2441no—
426#102—611no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102C22⋊D6111yescharacteristic
431#102C22⋊D6111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8C22×D6111yescharacteristic
439#41—42no—
440#41—42no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—611no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4D4×D6111yescharacteristic
451C2×D4C2×C22⋊D6111yescharacteristic
452C2×D4C2×C22⋊D6111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—2441no—
459Q16—42no—
460Q16—81no—
461SD16—42no—
462SD16—42no—
463SD16—1222no—
464SD16—2442no—
465D8—22no—
466M16—2442no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—2442no—
476C2×C8C2×C22⋊D6111yescharacteristic
477C2×C8C2×C22⋊D6111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4D4×D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C4⋊C4C2×C22⋊D6111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—1221no—
505C42—2441no—
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—1221no—
515Q8—1221no—
516Q8—4881no—
517Q8—2441no—
518Q8—2441no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—82no—
525D4—82no—
526D4#1451980312yes—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—9761no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4#1451982211yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—612no—
552C8—1221no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—4881no—
574C4—4881no—
575C4—2441no—
576C4—2441no—
577C4#135×D6111yescharacteristic
578C4C2×#1451980311yescharacteristic
579C4#1684057311yescharacteristic
580C4#1684057611yescharacteristic
581C2—42no—
582C2—81no—
583C2—81no—
584C2#2145731011yescharacteristic
585C2#2145753511yescharacteristic
586C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3283C2
socleC22×C61D42
hypercenter#3283D61
hypocenterC61#19860
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #21458466C2semidirect
2. #21458403C2semidirect
3. #21458176C2semidirect
4. #21445494C2semidirect
5. #21445316C2semidirect
6. #21445270C2semidirect
7. #21445206C2semidirect
8. #21445186C2semidirect
9. #21445073C2semidirect
10. #21445054C2semidirect
11. #21445024C2semidirect
12. #21444970C2semidirect
13. #21444649C2semidirect
14. #21444631C2semidirect
262. #92418#135semidirect
360. C61#19860semidirect

Maximal subgroups

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

subgroupindex
#214584662
#214584032
#214581762
#214454942
#214453162
#214452702
#214452062
#214451862
#214450732
#214450542
#214450242
#214449702
#214446492
#214446312
C61×#32832
#1986061