Finite Group Databasebeta

← #29663973

Subgroups — #29663973

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D61C211yesmaximal, characteristic, complemented
2#21455629C211yesmaximal, characteristic
3#21455303C211yesmaximal, characteristic
4C8×#11758226C211yesmaximal, characteristic
5#21445251C211yesmaximal, characteristic, complemented
6#21445249C211yesmaximal, characteristic, complemented
7#21445247C211yesmaximal, characteristic, complemented
8#21445245C211yesmaximal, characteristic, complemented
9#21445243C211yesmaximal, characteristic, complemented
10#21445241C211yesmaximal, characteristic, complemented
11#21445239C211yesmaximal, characteristic, complemented
12#21444573C211yesmaximal, characteristic, complemented
13#21444502C211yesmaximal, characteristic, complemented
14#21444489C211yesmaximal, characteristic, complemented
15C61×#1680C211yesmaximal, characteristic, complemented
16C2×#14519809—21no—
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×#11758226C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840111—21no—
24#16840111—21no—
25#16840055—21no—
26#16840051—21no—
27#16840047C2211yescharacteristic
28#16840043C2211yescharacteristic
29#16840039C2211yescharacteristic
30#16839972C2211yescharacteristic
31#16839970—21no—
32#16839968C2211yescharacteristic
33#16839966—21no—
34#16839964C2211yescharacteristic
35Q8×#92418C2211yescharacteristic
36C8×D244—21no—
37C8×D244C2211yescharacteristic
38#16839827—21no—
39#16839827C2211yescharacteristic
40#16839814—21no—
41#16839814C2211yescharacteristic
42#16839801—21no—
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45#16839769—21no—
46#16839762—21no—
47#103×D61—21no—
48#103×D61—21no—
49C4×C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839508C2211yescharacteristic
57#16839508C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#475C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758226D411yescharacteristic
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70#14519809—44no—
71C2×#11758202—21no—
72C2×#11758190—21no—
73C2×#11758201—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519776—21no—
86#14519775—21no—
87#14519775—21no—
88Q8×Dic61D411yescharacteristic
89C4×D244—21no—
90C4×D244C2311yescharacteristic
91#14519739—21no—
92#14519739D411yescharacteristic
93#14519735—21no—
94#14519735D411yescharacteristic
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C42×D61—21no—
100C42×D61C2311yescharacteristic
101#14519711—21no—
102#14519710—21no—
103#14519708—21no—
104C4⋊#92418—21no—
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108#14519706—21no—
109#14519706—21no—
110#14519702—21no—
111#14519702—21no—
112#14519702—21no—
113#14519701—21no—
114#14519701—21no—
115#14519701—21no—
116#14519701—21no—
117#14519700—21no—
118#14519700—21no—
119#14519700—21no—
120#14519699—21no—
121#14519697—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125C4×#92418—21no—
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×Q16×C61—21no—
131C4⋊Q8×C61C2311yescharacteristic
132C4⋊Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142#103×C61—21no—
143C4×C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148#11758226—22no—
149#11758226SD1614yes—
150Q8×D61—42no—
151Q8×D61—42no—
152Q8×D61—42no—
153Q8×D61—42no—
154C2×D244—21no—
155C2×D244C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—41no—
167C2×Dic122—41no—
168Q16×C61—42no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
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—21no—
179C4⋊C4×C61C2×D411yescharacteristic
180C42×C61—21no—
181C42×C61C2411yescharacteristic
182#11758202—42no—
183#11758201—42no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61#4111yescharacteristic
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758190—42no—
208#11758189—42no—
209#11758189—42no—
210C8×D61—41no—
211C8×D61—41no—
212C8×D61—42no—
213C8×D61—42no—
214C22×D61—21no—
215C22×D61#12111yescharacteristic
216Q8×C61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61C2×SD1612yes—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61#12111yescharacteristic
233C2×Dic61#12111yescharacteristic
234C2×Dic61#12111yescharacteristic
235D244—24no—
236D244—21no—
237D244C2×SD1612yes—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—24no—
241C4×D61—22no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—42no—
245C4×D61—82no—
246C4×D61—82no—
247C4×D61C2×SD1612yes—
248C4×D61#13512yes—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—82no—
254Dic122—82no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—21no—
261#92418—21no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#19275—611nomaximal, Sylow
266C22×C61C2×#12111yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—22no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61#46512yes—
273C4×C61—22no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61C22×SD1611yescharacteristic
279C4×C61C2×#13511yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57511yescharacteristic
282Dic61—21no—
283Dic61—41no—
284Dic61—81no—
285Dic61—81no—
286Dic61#46512yes—
287Dic61#47312yes—
288C2×#487—611no—
289#3079—611no—
290#3039—611no—
291C8×#41—611no—
292#1680—611no—
293#1680—611no—
294#1680—611no—
295#1680D6111yescharacteristic, complemented
296#1679—611no—
297#1679—611no—
298#1679—611no—
299#1679—611no—
300#1566—611no—
301#1549—611no—
302#1546—611no—
303C2×C61#304011yescharacteristic
304C2×C61C2×#46511yescharacteristic
305C2×C61C2×#47311yescharacteristic
306D61—22no—
307D61—42no—
308C2×#137—1221no—
309C2×C4⋊Q8—611no—
310C2×C4⋊Q8—611no—
311C4×#41—611no—
312#487—611no—
313#487—611no—
314#487—611no—
315#487—1221no—
316#487—1221no—
317#487C2×D6111yescharacteristic
318#477—1221no—
319#476—1221no—
320#475—611no—
321#475C2×D6111yescharacteristic
322#474—611no—
323#474—611no—
324#462—611no—
325#462—1221no—
326#462C2×D6111yescharacteristic
327#461—611no—
328#461—611no—
329#461—1221no—
330C8×Q8—611no—
331C8×Q8C2×D6111yescharacteristic
332C8×D4—611no—
333C8×D4—611no—
334C8×D4—1221no—
335C8×D4—1221no—
336#431—611no—
337#431—1221no—
338#428—1221no—
339#423—611no—
340#423—611no—
341#419—1221no—
342#417—1221no—
343C2×#103—1221no—
344C2×#103—1221no—
345C2×C4×C8—611no—
346C2×C4×C8—1221no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334C2×D6111yescharacteristic
351#332—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332C2×D6111yescharacteristic
358#332C2×D6111yescharacteristic
359C61#1927511yescharacteristic, complemented, Sylow
360C2×#41—611no—
361C22×Q8—1221no—
362C22×Q8—1221no—
363#137—2444no—
364C2×Q16—21no—
365C2×Q16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C22×C8—611no—
371C22×C8—611no—
372C22×C8—1221no—
373C22×C8—1221no—
374C4⋊Q8—611no—
375C4⋊Q8—611no—
376C4⋊Q8—1221no—
377C4⋊Q8—1221no—
378C4⋊Q8—1221no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8C22×D6111yescharacteristic
383C4⋊Q8C22×D6111yescharacteristic
384C4×Q8—611no—
385C4×Q8C22×D6111yescharacteristic
386C4×D4—611no—
387C4×D4—611no—
388C4×D4—1221no—
389C4×D4—1221no—
390#117—611no—
391#117—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C42—611no—
397C2×C42—1221no—
398#107—1221no—
399#107—1221no—
400#106—21no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#102—1221no—
427#102—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C4×C8—21no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438#41—614no—
439#41—1222no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—2441no—
445C2×Q8—2441no—
446C2×Q8—2442no—
447C2×Q8—2442no—
448C2×Q8—2442no—
449C2×Q8—2442no—
450C2×Q8D4×D6111yescharacteristic
451C2×D4—611no—
452C2×D4—1221no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—2441no—
460C22×C4—2441no—
461Q16—42no—
462Q16—2442no—
463SD16—2442no—
464SD16—2442no—
465M16—2442no—
466M16—2442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—2441no—
476C2×C8—2441no—
477C2×C8—2442no—
478C2×C8—2442no—
479C2×C8D4×D6111yescharacteristic
480C2×C8D4×D6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—611no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C4⋊C4D4×D6111yescharacteristic
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C42—21no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—1221no—
505C42—1221no—
506C42C23×D6111yescharacteristic
507C23—611no—
508C23—1221no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—4882no—
515Q8—4882no—
516Q8—2441no—
517Q8—2441no—
518Q8—2441no—
519Q8—2441no—
520Q8SD16×D6112yes—
521D4—612no—
522D4—1224no—
523D4—1221no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—611no—
533C2×C4—1222no—
534C2×C4—1224no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—4882no—
539C2×C4—4882no—
540C2×C4—2442no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4#41×D6111yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—1221no—
554C8—1221no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C22—612no—
559C22—1221no—
560C22—1221no—
561C22—1222no—
562C22—2441no—
563C22—2441no—
564C22#121×D6111yescharacteristic
565C4—22no—
566C4—21no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—612no—
571C4—612no—
572C4—1221no—
573C4—4881no—
574C4—4881no—
575C4—2441no—
576C4C2×SD16×D6111yescharacteristic
577C4#135×D6111yescharacteristic
578C4#1684055911yescharacteristic
579C4#1684056111yescharacteristic
580C2—1222no—
581C2—2442no—
582C2#2145531011yescharacteristic
583C2#465×D6111yescharacteristic
584C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1680C2
socleC22×C61C2×#121
prime radicalC2×#11758226D4
hypercenter#1680D61
hypocenterC61#19275
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1680

Complements

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

NH ≅ G/Ntype
1. #487×D61C2semidirect
5. #21445251C2semidirect
6. #21445249C2semidirect
7. #21445247C2semidirect
8. #21445245C2semidirect
9. #21445243C2semidirect
10. #21445241C2semidirect
11. #21445239C2semidirect
12. #21444573C2semidirect
13. #21444502C2semidirect
14. #21444489C2semidirect
15. C61×#1680C2semidirect
295. #1680D61semidirect
359. C61#19275semidirect

Maximal subgroups

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

subgroupindex
#487×D612
#214556292
#214553032
C8×#117582262
#214452512
#214452492
#214452472
#214452452
#214452432
#214452412
#214452392
#214445732
#214445022
#214444892
C61×#16802
#1927561