Finite Group Databasebeta

← #29650548

Subgroups — #29650548

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456383C211yesmaximal, characteristic
2#21454795C211yesmaximal, characteristic, complemented
3#21454788C211yesmaximal, characteristic, complemented
4#21444713C211yesmaximal, characteristic, complemented
5#21444712C211yesmaximal, characteristic, complemented
6#21444706C211yesmaximal, characteristic, complemented
7#21444701C211yesmaximal, characteristic, complemented
8#21444623C211yesmaximal, characteristic, complemented
9#21444622C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444580C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic, complemented
14C2×C8×#92418C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840161C411yescharacteristic
18#16840144C411yescharacteristic
19#16840119C411yescharacteristic
20#16840116C411yescharacteristic
21#16840001C411yescharacteristic
22#16839996C411yescharacteristic
23#16839993C411yescharacteristic
24#16839989C411yescharacteristic
25#16839893C2211yescharacteristic
26#16839889C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758199C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839839C2211yescharacteristic
35#16839834—21no—
36#16839830—21no—
37D4×#92418—21no—
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839825—21no—
41#16839824—21no—
42#16839823—21no—
43#16839819C2211yescharacteristic
44#16839719—21no—
45#16839718—21no—
46C2×C4×#92418C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56C8×#92418C2211yescharacteristic
57C8×#92418C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C22×#92418—21no—
74C22×#92418C2×C411yescharacteristic
75C22×#92418C2×C411yescharacteristic
76C22×#92418D411yescharacteristic
77C22×#92418D411yescharacteristic
78C2×C8×D61—21no—
79#14519771—21no—
80#14519769C2×C411yescharacteristic
81#14519765C2×C411yescharacteristic
82#14519760—21no—
83#14519756C2×C411yescharacteristic
84#14519751C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×D244C2311yescharacteristic
87C4×C22⋊D61—21no—
88#14519734—21no—
89#14519710C2×C411yescharacteristic
90#14519710C2×C411yescharacteristic
91#14519708C2×C411yescharacteristic
92#14519708C2×C411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701C2×C411yescharacteristic
100#14519701C2×C411yescharacteristic
101#14519700C2×C411yescharacteristic
102#14519700C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110#14519689—21no—
111#14519689—21no—
112#14519688—21no—
113#14519688—21no—
114#14519687—21no—
115C4×#92418—21no—
116C4×#92418C2×C411yescharacteristic
117C4×#92418C2×C411yescharacteristic
118C4×#92418D411yescharacteristic
119C4×#92418D411yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C22×C8×C61—21no—
126#126×C61—21no—
127#125×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×Dic122C22×C411yescharacteristic
155C2×C8×C61—24no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61C22×C411yescharacteristic
165C4⋊C4×C61C22×C411yescharacteristic
166C22⋊C4×C61—21no—
167C22⋊C4×C61—21no—
168C22⋊C4×C61—21no—
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61C22×C411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61#4111yescharacteristic
175C42×C61C2411yescharacteristic
176C22⋊Dic61—21no—
177#11758202—22no—
178#11758201—22no—
179#11758200—22no—
180#11758199—22no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61C22×C411yescharacteristic
186C4⋊Dic61C22×C411yescharacteristic
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192#11758194—42no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—22no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—42no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758189—42no—
209C8×D61—42no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—42no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—42no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238D244—21no—
239D244—21no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—21no—
243Dic122—21no—
244C8×C61—22no—
245C8×C61—22no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#92418#13112yes—
255#92418#13112yes—
256#92418#13512yes—
257#92418#13512yes—
258#17959—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61#44312yes—
265C22×C61C2×C4×D411yescharacteristic
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61C2×#13111yescharacteristic
277C4×C61C2×#13111yescharacteristic
278C4×C61C2×#13511yescharacteristic
279C4×C61C2×#13511yescharacteristic
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283#3168—611no—
284#2966—611no—
285#2966—611no—
286#1591—611no—
287#1590—611no—
288#1590—611no—
289#1589—611no—
290C8×Q16—611no—
291C8×SD16—611no—
292C8×SD16—611no—
293C8×D8—611no—
294#1568—611no—
295#1494—611no—
296#1494D6111yescharacteristic, complemented
297C2×C82—611no—
298C2×C61—22no—
299C2×C61—81no—
300C2×C61#293111yescharacteristic
301C2×C61C4×#13511yescharacteristic
302C2×C61C2×#44311yescharacteristic
303D61—81no—
304#529—611no—
305#529C2×D6111yescharacteristic
306#499—611no—
307#495—611no—
308#488—611no—
309#488—611no—
310#467—611no—
311#466—611no—
312#465—611no—
313#465—611no—
314#446—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C4×Q16—611no—
319C4×SD16—611no—
320C4×SD16—611no—
321C4×D8—611no—
322#436—611no—
323#436—611no—
324#435—1221no—
325#435—1221no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330#433—1221no—
331#433—1221no—
332#432—611no—
333#432C2×D6111yescharacteristic
334#405—1221no—
335#405—1221no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8C2×D6111yescharacteristic
339#335—611no—
340#335—611no—
341#334—611no—
342#334—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8C2×D6111yescharacteristic
346Q8⋊C8C2×D6111yescharacteristic
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8C2×D6111yescharacteristic
350D4⋊C8C2×D6111yescharacteristic
351C82—611no—
352C82—611no—
353C82—611no—
354C82—611no—
355C61#1795911yescharacteristic, complemented, Sylow
356C2×Q16—611no—
357C2×SD16—611no—
358C2×SD16—611no—
359C2×D8—611no—
360C2×M16—1221no—
361C2×M16—1221no—
362C22×C8—21no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—1221no—
368C22×C8—1221no—
369#126—21no—
370#126—1221no—
371#125—611no—
372#125C4×D6111yescharacteristic
373#124—611no—
374#124C4×D6111yescharacteristic
375#123—21no—
376#123—1221no—
377C22⋊Q8—611no—
378C22⋊Q8C4×D6111yescharacteristic
379#121—611no—
380#121C4×D6111yescharacteristic
381C4×Q8—611no—
382C4×Q8C22×D6111yescharacteristic
383C4×D4—21no—
384C4×D4—611no—
385C4×D4—1221no—
386C4×D4C22×D6111yescharacteristic
387#117—21no—
388#117—1221no—
389C2×C42C22×D6111yescharacteristic
390#107—611no—
391#107—611no—
392#106—611no—
393#106—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402#103—611no—
403#103—611no—
404#103—611no—
405#103—611no—
406#102—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410C22⋊C8—21no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—21no—
417#97—1221no—
418#97—1221no—
419#97—1221no—
420C4×C8—21no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8C22×D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C2×Q8—611no—
434C2×Q8C2×C4×D6111yescharacteristic
435C2×D4—21no—
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4C2×C4×D6111yescharacteristic
439C22×C4—21no—
440C22×C4—1221no—
441C22×C4C2×C4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443C22×C4#1175822411yescharacteristic
444Q16—1222no—
445SD16—1222no—
446SD16—1222no—
447D8—1222no—
448M16—2442no—
449M16—2442no—
450C2×C8—24no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1222no—
464C2×C8—1222no—
465C2×C8—1222no—
466C2×C8—1222no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—2442no—
470C2×C8—2442no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C4×D6111yescharacteristic
482C4⋊C4C2×C4×D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—1221no—
495C42C2×C4×D6111yescharacteristic
496C42D4×D6111yescharacteristic
497C42#1175822411yescharacteristic
498C42C23×D6111yescharacteristic
499C23—21no—
500C23—1221no—
501C23#1451973711yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1221no—
505Q8—1221no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—1221no—
510D4—1221no—
511D4—2442no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4#1451973711yescharacteristic
528C2×C4#1451973711yescharacteristic
529C2×C4#1451973711yescharacteristic
530C2×C4C22×C4×D6111yescharacteristic
531C2×C4C2×D4×D6111yescharacteristic
532C2×C4C2×#1175822411yescharacteristic
533C8—22no—
534C8—22no—
535C8—41no—
536C8—41no—
537C8—612no—
538C8—612no—
539C8—612no—
540C8—612no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—2441no—
546C8—2441no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22#1683987612yes—
556C22C2×#1451973711yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—2441no—
565C4—2441no—
566C4—2441no—
567C4#131×D6111yescharacteristic
568C4#131×D6111yescharacteristic
569C4#135×D6111yescharacteristic
570C4#135×D6111yescharacteristic
571C2—22no—
572C2—81no—
573C2—4881no—
574C2#2145452711yescharacteristic
575C2#2145458711yescharacteristic
576C2C2×#1683987611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C2×C4×D4
prime radical#16839996C4
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#17959
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454795C2semidirect
3. #21454788C2semidirect
4. #21444713C2semidirect
5. #21444712C2semidirect
6. #21444706C2semidirect
7. #21444701C2semidirect
8. #21444623C2semidirect
9. #21444622C2semidirect
10. #21444616C2semidirect
11. #21444611C2semidirect
12. #21444580C2semidirect
13. #21444280C2semidirect
14. C2×C8×#92418C2semidirect
15. C61×#1494C2semidirect
296. #1494D61semidirect
355. C61#17959semidirect

Maximal subgroups

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

subgroupindex
#214563832
#214547952
#214547882
#214447132
#214447122
#214447062
#214447012
#214446232
#214446222
#214446162
#214446112
#214445802
#214442802
C2×C8×#924182
C61×#14942
#1795961