Finite Group Databasebeta

← #29721525

Subgroups — #29721525

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455637C211yesmaximal, characteristic
2C4×#14519808C211yesmaximal, characteristic
3#21454484C211yesmaximal, characteristic
4#21447265C211yesmaximal, characteristic
5#21447260C211yesmaximal, characteristic
6#21447119C211yesmaximal, characteristic
7#21447119C211yesmaximal, characteristic
8#21446813C211yesmaximal, characteristic, complemented
9#21446602C211yesmaximal, characteristic, complemented
10#21446597C211yesmaximal, characteristic, complemented
11#21446595C211yesmaximal, characteristic, complemented
12#21446471C211yesmaximal, characteristic, complemented
13#21446471C211yesmaximal, characteristic, complemented
14#21445815C211yesmaximal, characteristic, complemented
15C2×C61×#479C211yesmaximal, characteristic, complemented
16C2×#14519808C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840066—21no—
19#16840066—21no—
20#16840059—21no—
21#16840059—21no—
22#16839867—21no—
23#16839860—21no—
24C4×#11758202—21no—
25C4×#11758201—21no—
26#16839822—21no—
27#16839822—21no—
28#16839818—21no—
29#16839814—21no—
30C2×#14519713C2211yescharacteristic
31C2×#14519713C2211yescharacteristic
32#16839802C2211yescharacteristic
33#16839802C2211yescharacteristic
34#16839802C2211yescharacteristic
35#16839786C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839771C2211yescharacteristic
38#16839761C2211yescharacteristic
39#16839761C2211yescharacteristic
40#16839761C2211yescharacteristic
41C2×#14519696C2211yescharacteristic
42C2×#14519696C2211yescharacteristic
43#16839728C2211yescharacteristic
44#16839728C2211yescharacteristic
45#16839717C2211yescharacteristic
46#16839717C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839531C2211yescharacteristic
49#16839531C2211yescharacteristic
50#16839531C2211yescharacteristic
51#16839531C2211yescharacteristic
52#16839531C2211yescharacteristic
53#16839531C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C61×#479—21no—
59C61×#479—21no—
60C61×#479—21no—
61C61×#479—21no—
62C2×#107×C61C2211yescharacteristic
63C2×#106×C61C2211yescharacteristic
64C2×C4⋊C8×C61C2211yescharacteristic
65C2×#103×C61C2211yescharacteristic
66C2×#103×C61C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519808—22no—
69#14519808—22no—
70C2×#11758202—21no—
71C2×#11758201—21no—
72C2×#11758194C2311yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C4×Dic122D411yescharacteristic
79C4×Dic122D411yescharacteristic
80C4×D244D411yescharacteristic
81C4×D244D411yescharacteristic
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519736C2311yescharacteristic
85#14519734—21no—
86C42×D61—21no—
87#14519713—22no—
88#14519713—22no—
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418—21no—
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418—21no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519696—22no—
108#14519696—22no—
109#14519689—21no—
110#14519689—21no—
111#14519689—21no—
112#14519689—21no—
113#14519688—21no—
114#14519687—21no—
115#14519687—21no—
116C4×#92418—21no—
117C8×Dic61—21no—
118C8×Dic61—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—21no—
124#125×C61—21no—
125#125×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61C2311yescharacteristic
138#107×C61—21no—
139#107×C61—21no—
140#106×C61—21no—
141#106×C61—21no—
142C4⋊C8×C61D411yescharacteristic
143C4⋊C8×C61D411yescharacteristic
144C4⋊C8×C61D411yescharacteristic
145C4⋊C8×C61D411yescharacteristic
146#103×C61—21no—
147#103×C61—21no—
148#103×C61—21no—
149#103×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61#4112yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61#4111yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—21no—
164#11758222—21no—
165#11758222—21no—
166#11758222—21no—
167#11758222—21no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×Dic122C2×D411yescharacteristic
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
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—41no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C42×C61—41no—
194C42×C61—41no—
195C42×C61C2×D411yescharacteristic
196C42×C61C2×D411yescharacteristic
197C42×C61C2×D411yescharacteristic
198C42×C61C2×D411yescharacteristic
199C22⋊Dic61—21no—
200#11758202—24no—
201#11758201—24no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61C2×D411yescharacteristic
205C4⋊Dic61C2×D411yescharacteristic
206#11758196—21no—
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211#11758194—21no—
212#11758194—21no—
213#11758194—21no—
214#11758194—21no—
215#11758194—21no—
216#11758194—21no—
217#11758194—21no—
218#11758194—21no—
219#11758194—21no—
220#11758194—21no—
221#11758194—21no—
222#11758194#4112yes—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C23×C61C2×#4111yescharacteristic
230C22×D61—21no—
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—41no—
234Q8×C61—41no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—81no—
244C2×C4×C61—81no—
245C2×C4×C61—81no—
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61#12111yescharacteristic
248C2×C4×C61#12111yescharacteristic
249C2×C4×C61#12111yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C612−1+411yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C22⋊D61—41no—
257C22⋊D61—41no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261D244—21no—
262D244—21no—
263C4×D61—42no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—81no—
267Dic122—21no—
268Dic122—21no—
269C8×C61—21no—
270C8×C61—21no—
271C8×C61—21no—
272C8×C61—21no—
273#92418—22no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#92418—41no—
279#24725—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61C2×#12111yescharacteristic
283C22×C61#55211yescharacteristic
284C22×C61#55611yescharacteristic
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—42no—
293C4×C61—81no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61#52511yescharacteristic
297C4×C61#53611yescharacteristic
298C4×C61#54711yescharacteristic
299C4×C61#54811yescharacteristic
300Dic61—41no—
301Dic61—41no—
302Dic61—41no—
303#3080—611no—
304C2×#479D6111yescharacteristic, complemented
305C4×#137—611no—
306#2925—611no—
307#2079—611no—
308#2078—611no—
309#2052—611no—
310#2052—611no—
311#1998—611no—
312#1952—611no—
313#1951—611no—
314#1950—611no—
315#1930—611no—
316#1930—611no—
317#1801—611no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61#241511yescharacteristic
321C2×C61#306711yescharacteristic
322C2×C61#306911yescharacteristic
323D61—81no—
324C2×#137—611no—
325C2×#125C2×D6111yescharacteristic
326C4×#41—611no—
327C2×C4×Q8C2×D6111yescharacteristic
328#479—21no—
329#479—21no—
330#479—21no—
331#479—21no—
332#479—1221no—
333#479—1221no—
334#478—1221no—
335#478—1221no—
336#441—1221no—
337#440—1221no—
338C4×Q16—1221no—
339C4×SD16—1221no—
340#433—1221no—
341#433—1221no—
342#432—1221no—
343#431—1221no—
344C2×#108—611no—
345C2×#108—611no—
346#428—611no—
347#428—611no—
348#428—611no—
349C2×#107C2×D6111yescharacteristic
350C2×#106C2×D6111yescharacteristic
351#423—611no—
352#423—611no—
353C2×C4⋊C8C2×D6111yescharacteristic
354#419—611no—
355#417—611no—
356#417—611no—
357#417—611no—
358C2×#103C2×D6111yescharacteristic
359C2×#103C2×D6111yescharacteristic
360C2×#101—611no—
361C2×#101—611no—
362#408—611no—
363#408—611no—
364#405—611no—
365#405—611no—
366C4×M16—611no—
367#343—611no—
368#343—611no—
369#343—611no—
370#343—611no—
371#343—611no—
372#343—611no—
373#341—611no—
374#341—611no—
375C61#2472511yescharacteristic, complemented, Sylow
376C2×#41—611no—
377C22×Q8C22×D6111yescharacteristic
378#137—1222no—
379#137—1222no—
380C2×Q16—1221no—
381C2×SD16—1221no—
382C2×M16—611no—
383C2×M16—611no—
384C2×M16—611no—
385C2×M16—611no—
386C2×M16—611no—
387C2×M16—611no—
388C22×C8C22×D6111yescharacteristic
389C22×C8C22×D6111yescharacteristic
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—611no—
399C4×Q8—611no—
400C4×D4—611no—
401C4×D4—611no—
402C4×D4—1221no—
403C4×D4—1221no—
404#117—611no—
405#117—1221no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C42—21no—
413C2×C42—1221no—
414C2×C42C22×D6111yescharacteristic
415#108—1222no—
416#108—1222no—
417#107—21no—
418#107—21no—
419#107—1221no—
420#107—1221no—
421#107—1221no—
422#106—21no—
423#106—21no—
424#106—1221no—
425#106—1221no—
426#106—1221no—
427C4⋊C8—1221no—
428C4⋊C8—1221no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431C4⋊C8C22⋊D6111yescharacteristic
432C4⋊C8C22⋊D6111yescharacteristic
433C4⋊C8C22⋊D6111yescharacteristic
434C4⋊C8C22⋊D6111yescharacteristic
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—1221no—
440#103—1221no—
441#103—1221no—
442#103—1221no—
443#103—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#101—1222no—
448#101—1222no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1221no—
453#97—1221no—
454#97—1221no—
455#97—1221no—
456C4×C8—1221no—
457C4×C8—1221no—
458C4×C8—1221no—
459#41—1221no—
460#41—1221no—
461#41—1221no—
462#41—1221no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—611no—
469C2×Q8#1175822612yes—
470C2×D4—611no—
471C2×D4—1221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4#1175822411yescharacteristic
480C22×C4#1175822411yescharacteristic
481C22×C4C23×D6111yescharacteristic
482Q16—1224no—
483SD16—1224no—
484M16—612no—
485M16—1221no—
486M16—1221no—
487M16—1221no—
488M16—1221no—
489M16—1221no—
490M16—1221no—
491M16—1221no—
492M16—1221no—
493M16—1221no—
494M16—1221no—
495M16—1221no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8C2×C22⋊D6111yescharacteristic
507C2×C8C2×C22⋊D6111yescharacteristic
508C2×C8C2×C22⋊D6111yescharacteristic
509C2×C8C2×C22⋊D6111yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—611no—
523C4⋊C4—611no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C22⋊C4—1221no—
529C42—41no—
530C42—41no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42D4×D6111yescharacteristic
535C42D4×D6111yescharacteristic
536C42C2×C22⋊D6111yescharacteristic
537C42C2×C22⋊D6111yescharacteristic
538C23—1221no—
539C23C2×#1175822411yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544Q8—1221no—
545Q8—1221no—
546D4—1221no—
547D4—1221no—
548D4—2441no—
549D4—2441no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—4881no—
565C2×C4—2442no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4#1451974811yescharacteristic
569C2×C4#1451974811yescharacteristic
570C2×C4#1451974811yescharacteristic
571C2×C4#1451974811yescharacteristic
572C2×C4C2×D4×D6111yescharacteristic
573C2×C4C22×C22⋊D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4C2×#1175822611yescharacteristic
576C2×C4#1451982411yescharacteristic
577C2×C4#1451982511yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—1222no—
583C8—2441no—
584C8—2441no—
585C8—2441no—
586C8—2441no—
587C8—2441no—
588C22—21no—
589C22—21no—
590C22—2441no—
591C22—2441no—
592C22—2441no—
593C22C2×#1451974811yescharacteristic
594C22#1684045411yescharacteristic
595C22#1684048311yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—2441no—
605C4—2441no—
606C4—2441no—
607C4#1684027511yescharacteristic
608C4#1684033511yescharacteristic
609C4#1684041111yescharacteristic
610C4#1684042311yescharacteristic
611C2—21no—
612C2—21no—
613C2—4881no—
614C2#2144924411yescharacteristic
615C2#2145553511yescharacteristic
616C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#479C2
socleC22×C61C2×#121
prime radicalC2×#11758222C23
hypercenterC2×#479D61
hypocenterC61#24725
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
8. #21446813C2semidirect
9. #21446602C2semidirect
10. #21446597C2semidirect
11. #21446595C2semidirect
12. #21446471C2semidirect
13. #21446471C2semidirect
14. #21445815C2semidirect
15. C2×C61×#479C2semidirect
304. C2×#479D61semidirect
375. C61#24725semidirect

Maximal subgroups

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

subgroupindex
#214556372
C4×#145198082
#214544842
#214472652
#214472602
#214471192
#214468132
#214466022
#214465972
#214465952
#214464712
#214458152
C2×C61×#4792
#2472561