Finite Group Databasebeta

← #29649358

Subgroups — #29649358

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454949C211yesmaximal, characteristic
2#21454941C211yesmaximal, characteristic
3#21454783C211yesmaximal, characteristic
4#21444606C211yesmaximal, characteristic, complemented
5#21444606C211yesmaximal, characteristic, complemented
6#21444599C211yesmaximal, characteristic, complemented
7#21444596C211yesmaximal, characteristic, complemented
8#21444588C211yesmaximal, characteristic, complemented
9#21444584C211yesmaximal, characteristic, complemented
10#21444583C211yesmaximal, characteristic, complemented
11#21444573C211yesmaximal, characteristic, complemented
12#21444569C211yesmaximal, characteristic, complemented
13#21444568C211yesmaximal, characteristic, complemented
14#21444564C211yesmaximal, characteristic, complemented
15C61×#1570C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16839891—21no—
18#16839891C411yescharacteristic
19#16839891C411yescharacteristic
20#16839886—21no—
21#16839839—21no—
22#16839838—21no—
23#16839838—21no—
24#16839837C411yescharacteristic
25#16839837C411yescharacteristic
26#16839836C411yescharacteristic
27#16839836C411yescharacteristic
28#16839833—21no—
29#16839832—21no—
30#16839832C411yescharacteristic
31#16839832C411yescharacteristic
32C8×C22⋊D61—21no—
33#16839819C2211yescharacteristic
34#16839818C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839814C2211yescharacteristic
37#16839814C2211yescharacteristic
38#16839814C2211yescharacteristic
39#16839813C2211yescharacteristic
40#16839813C2211yescharacteristic
41#16839784C2211yescharacteristic
42#16839784C2211yescharacteristic
43#16839784C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45C4×#11758194C2211yescharacteristic
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839513C2211yescharacteristic
55#16839513C2211yescharacteristic
56#16839512C2211yescharacteristic
57#16839512C2211yescharacteristic
58#16839512C2211yescharacteristic
59#16839512C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222Q811yescharacteristic
68C2×#11758194C2×C411yescharacteristic
69C2×#11758194C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73C2×#11758189C2×C411yescharacteristic
74C2×#11758189C2×C411yescharacteristic
75C2×C8×D61—21no—
76C2×C8×D61C2×C411yescharacteristic
77C2×C8×D61C2×C411yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122D411yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244D411yescharacteristic
82C4×C22⋊D61C2×C411yescharacteristic
83C4×C22⋊D61C2×C411yescharacteristic
84C4×C22⋊D61D411yescharacteristic
85C4×C22⋊D61D411yescharacteristic
86#14519736Q811yescharacteristic
87#14519734Q811yescharacteristic
88#14519734Q811yescharacteristic
89C42×D61C2311yescharacteristic
90C42×D61C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519706—21no—
98#14519706—21no—
99#14519706C2×C411yescharacteristic
100#14519706C2×C411yescharacteristic
101#14519706C2×C411yescharacteristic
102#14519706C2×C411yescharacteristic
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105#14519689—21no—
106#14519689—21no—
107#14519689—21no—
108#14519689—21no—
109#14519689C2×C411yescharacteristic
110#14519689C2×C411yescharacteristic
111#14519689C2×C411yescharacteristic
112#14519689C2×C411yescharacteristic
113#14519688—21no—
114#14519688C2×C411yescharacteristic
115#14519688C2×C411yescharacteristic
116#14519687—21no—
117#14519687C2×C411yescharacteristic
118#14519687C2×C411yescharacteristic
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C8×Dic61—21no—
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61C2×C411yescharacteristic
126C8×Dic61C2×C411yescharacteristic
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2×C411yescharacteristic
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61C2×C411yescharacteristic
139C22⋊C8×C61C2×C411yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×Q811yescharacteristic
145C2×C22⋊D61C4⋊C411yescharacteristic
146C2×C22⋊D61C4⋊C411yescharacteristic
147#11758222—42no—
148C2×D244C4⋊C411yescharacteristic
149C2×C4×D61C22×C411yescharacteristic
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×Q811yescharacteristic
154C2×C4×D61C2×Q811yescharacteristic
155C2×Dic122C4⋊C411yescharacteristic
156M16×C61—81no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—81no—
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C42×C61C22×C411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×Q811yescharacteristic
169C42×C61C2411yescharacteristic
170C22⋊Dic61C4⋊C411yescharacteristic
171C22⋊Dic61C4⋊C411yescharacteristic
172#11758198C4⋊C411yescharacteristic
173#11758198C4⋊C411yescharacteristic
174#11758198C4⋊C411yescharacteristic
175#11758198C4⋊C411yescharacteristic
176C4⋊Dic61C4⋊C411yescharacteristic
177C4⋊Dic61C4⋊C411yescharacteristic
178#11758196C4⋊C411yescharacteristic
179#11758196C4⋊C411yescharacteristic
180#11758196C4⋊C411yescharacteristic
181#11758196C4⋊C411yescharacteristic
182C4×Dic61C22×C411yescharacteristic
183C4×Dic61C22×C411yescharacteristic
184C4×Dic61C2×D411yescharacteristic
185C4×Dic61C2×D411yescharacteristic
186C4×Dic61C2×Q811yescharacteristic
187C4×Dic61C2×Q811yescharacteristic
188#11758194—22no—
189#11758194—41no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418C22×C411yescharacteristic
195C2×#92418C22×C411yescharacteristic
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198#11758189—22no—
199#11758189—41no—
200#11758189—81no—
201#11758189—81no—
202#11758189—81no—
203C8×D61—22no—
204C8×D61—41no—
205C8×D61—81no—
206C23×C61C2×C4⋊C411yescharacteristic
207C22×D61C2×C4⋊C411yescharacteristic
208C22×D61C2×C4⋊C411yescharacteristic
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C2×C4⋊C411yescharacteristic
216C2×C4×C61C2×C4⋊C411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×Q811yescharacteristic
220C22⋊D61—22no—
221C22⋊D61—41no—
222C2×Dic61C2×C4⋊C411yescharacteristic
223C2×Dic61C2×C4⋊C411yescharacteristic
224C2×Dic61C2×C4⋊C411yescharacteristic
225C2×Dic61C2×C4⋊C411yescharacteristic
226C2×Dic61C2×C4⋊C411yescharacteristic
227C2×Dic61C2×C4⋊C411yescharacteristic
228D244—41no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—22no—
238C4×D61—41no—
239Dic122—22no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418#13112yes—
256#17841—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61C22×C4⋊C411yescharacteristic
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61C2×#13111yescharacteristic
272C4×C61#56811yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57711yescharacteristic
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61—21no—
279Dic61—21no—
280Dic61#43012yes—
281#2991—611no—
282#2990—611no—
283#2965—611no—
284#1574—611no—
285#1574—611no—
286#1572—611no—
287#1572—611no—
288#1570—611no—
289#1570D6111yescharacteristic, complemented
290#1569—611no—
291#1569—611no—
292#1566—611no—
293#1565—611no—
294#1565—611no—
295#1564—611no—
296C2×C61—41no—
297C2×C61#290611yescharacteristic
298C2×C61#291211yescharacteristic
299C2×C61C2×#43011yescharacteristic
300D61—41no—
301D61—41no—
302C4×#41—611no—
303#446—611no—
304#446—611no—
305#446—1221no—
306C8×Q8—1221no—
307#436—611no—
308#436—611no—
309#436—1221no—
310#436—1221no—
311#436—1221no—
312#435—611no—
313#435—611no—
314#435—611no—
315#435—611no—
316#435—1221no—
317#435—1221no—
318C8×D4—1221no—
319#432—611no—
320#432—611no—
321#431—611no—
322#431—611no—
323#431—611no—
324#431—611no—
325#431—611no—
326#431—611no—
327#431C2×D6111yescharacteristic
328#423—611no—
329#423—611no—
330#423—611no—
331#423C2×D6111yescharacteristic
332C2×C4⋊C8—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334C4×M16—611no—
335C4×M16—611no—
336C2×C4×C8—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#334—611no—
344#334—611no—
345#334—611no—
346#334—611no—
347#334—611no—
348#334—611no—
349#334C2×D6111yescharacteristic
350#334C2×D6111yescharacteristic
351#334C2×D6111yescharacteristic
352#334C2×D6111yescharacteristic
353C61#1784111yescharacteristic, complemented, Sylow
354C2×#41—611no—
355C2×M16—21no—
356C2×M16—611no—
357C2×M16—611no—
358C2×M16—611no—
359C2×M16—611no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—21no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—1221no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×D4—611no—
370C4×D4—611no—
371C4×D4—611no—
372C4×D4—611no—
373C4×D4—611no—
374C4×D4—611no—
375#117—611no—
376#117—611no—
377#117—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42C22×D6111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C4×D6111yescharacteristic
396C4⋊C8C4×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401C22⋊C8—611no—
402C22⋊C8—611no—
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C4×D6111yescharacteristic
412C22⋊C8C4×D6111yescharacteristic
413#97—611no—
414#97—611no—
415#97—611no—
416#97—611no—
417#97—1221no—
418#97—1221no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8C22×D6111yescharacteristic
428C4×C8C22×D6111yescharacteristic
429#41—2442no—
430C2×Q8—611no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4C2×C4×D6111yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4Q8×D6111yescharacteristic
443M16—81no—
444M16—1222no—
445M16—1222no—
446M16—4881no—
447M16—4881no—
448M16—4881no—
449M16—2441no—
450M16—2441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—1222no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—4881no—
466C2×C8—2441no—
467C2×C8C2×C4×D6111yescharacteristic
468C2×C8C2×C4×D6111yescharacteristic
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C22⋊C4—611no—
478C22⋊C4—611no—
479C22⋊C4—611no—
480C22⋊C4—611no—
481C22⋊C4—611no—
482C22⋊C4—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42C2×C4×D6111yescharacteristic
490C42D4×D6111yescharacteristic
491C42Q8×D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—611no—
494C23—611no—
495C23C4⋊C4×D6111yescharacteristic
496Q8—1222no—
497D4—1222no—
498D4—2441no—
499D4—2441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—611no—
511C2×C4—1222no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—2441no—
521C2×C4C4⋊C4×D6111yescharacteristic
522C2×C4C4⋊C4×D6111yescharacteristic
523C2×C4C4⋊C4×D6111yescharacteristic
524C2×C4C22×C4×D6111yescharacteristic
525C2×C4C2×D4×D6111yescharacteristic
526C2×C4C2×Q8×D6111yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—612no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—1221no—
547C22—1221no—
548C22—1221no—
549C22—1221no—
550C22—1221no—
551C22—1221no—
552C22C2×C4⋊C4×D6111yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—612no—
558C4—1221no—
559C4—1221no—
560C4—1221no—
561C4—1221no—
562C4—1221no—
563C4#131×D6111yescharacteristic
564C4#1684052711yescharacteristic
565C4#1684056811yescharacteristic
566C4#1684056811yescharacteristic
567C2—41no—
568C2—2441no—
569C2—2441no—
570C2#2145438611yescharacteristic
571C2#2145441011yescharacteristic
572C2#430×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1570C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222Q8
cosocleC42×C61C24
hypercenter#1570D61
hypocenterC61#17841
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
4. #21444606C2semidirect
5. #21444606C2semidirect
6. #21444599C2semidirect
7. #21444596C2semidirect
8. #21444588C2semidirect
9. #21444584C2semidirect
10. #21444583C2semidirect
11. #21444573C2semidirect
12. #21444569C2semidirect
13. #21444568C2semidirect
14. #21444564C2semidirect
15. C61×#1570C2semidirect
289. #1570D61semidirect
353. C61#17841semidirect

Maximal subgroups

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

subgroupindex
#214549492
#214549412
#214547832
#214446062
#214445992
#214445962
#214445882
#214445842
#214445832
#214445732
#214445692
#214445682
#214445642
C61×#15702
#1784161