Finite Group Databasebeta

← #30612175

Subgroups — #30612175

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462741C211yesmaximal, characteristic
2#21462740C211yesmaximal, characteristic
3#21461396C211yesmaximal, characteristic, complemented
4#21461395C211yesmaximal, characteristic, complemented
5#21461393C211yesmaximal, characteristic, complemented
6#21461392C211yesmaximal, characteristic, complemented
7#21461391C211yesmaximal, characteristic, complemented
8#21461390C211yesmaximal, characteristic, complemented
9#21461389C211yesmaximal, characteristic, complemented
10#21461388C211yesmaximal, characteristic, complemented
11#21461385C211yesmaximal, characteristic, complemented
12#21461384C211yesmaximal, characteristic, complemented
13#21461380C211yesmaximal, characteristic, complemented
14#21461378C211yesmaximal, characteristic, complemented
15#21454460C211yesmaximal, characteristic
16#16840814—21no—
17#16840812—21no—
18#16840796—21no—
19#16840795—21no—
20#16840794—21no—
21#16840792—21no—
22#16840791—21no—
23#16840791—21no—
24#16840784C2211yescharacteristic
25#16840784C2211yescharacteristic
26#16840784C2211yescharacteristic
27#16840783C2211yescharacteristic
28#16840781C2211yescharacteristic
29#16840778C2211yescharacteristic
30#16840766C2211yescharacteristic
31#16840766C2211yescharacteristic
32#16840766C2211yescharacteristic
33#16840765C2211yescharacteristic
34D61⋊(C4⋊C8)C2211yescharacteristic
35C2×C4⋊#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840626C2211yescharacteristic
39#16840626C2211yescharacteristic
40#16840626C2211yescharacteristic
41#16840626C2211yescharacteristic
42#16840625C2211yescharacteristic
43#16840625C2211yescharacteristic
44#16840625C2211yescharacteristic
45#16840625C2211yescharacteristic
46#16840624C2211yescharacteristic
47#16840624C2211yescharacteristic
48#16840623C2211yescharacteristic
49#16840623C2211yescharacteristic
50#16840623C2211yescharacteristic
51#16840623C2211yescharacteristic
52#16840230C2211yescharacteristic
53#16839824C411yescharacteristic
54#16839823C411yescharacteristic
55#16839821C411yescharacteristic
56#16839814C2211yescharacteristic
57#16839814C2211yescharacteristic
58#16839812C2211yescharacteristic
59#16839812C2211yescharacteristic
60#16839787C411yescharacteristic
61#16839787C411yescharacteristic
62#16839727C411yescharacteristic
63#16839727C411yescharacteristic
64#16839714C2211yescharacteristic
65C4×C8×D61C2211yescharacteristic
66C61×#433C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97C4×#92420—21no—
98C4×#92420—21no—
99C2×#11758222C2×C411yescharacteristic
100C2×#11758189C2×C411yescharacteristic
101C2×#11758189C2×C411yescharacteristic
102C2×C8×D61C2×C411yescharacteristic
103C2×C8×D61C2×C411yescharacteristic
104#14519742D411yescharacteristic
105#14519742Q811yescharacteristic
106#14519739D411yescharacteristic
107#14519739Q811yescharacteristic
108#14519737D411yescharacteristic
109#14519737D411yescharacteristic
110#14519737Q811yescharacteristic
111#14519737Q811yescharacteristic
112#14519734C2×C411yescharacteristic
113#14519734C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C42×D61C2311yescharacteristic
117C4⋊#92418C2×C411yescharacteristic
118C4⋊#92418C2×C411yescharacteristic
119#14519706C2×C411yescharacteristic
120#14519706C2×C411yescharacteristic
121#14519706C2×C411yescharacteristic
122#14519706C2×C411yescharacteristic
123C22⋊#92418C2×C411yescharacteristic
124C22⋊#92418C2×C411yescharacteristic
125#14519689C2×C411yescharacteristic
126#14519689C2×C411yescharacteristic
127#14519689C2×C411yescharacteristic
128#14519689C2×C411yescharacteristic
129#14519688C2×C411yescharacteristic
130C4×#92418C2×C411yescharacteristic
131C8×Dic61C2311yescharacteristic
132C8×Dic61C2311yescharacteristic
133C8×Dic61C2311yescharacteristic
134C8×Dic61C2311yescharacteristic
135#117×C61C2×C411yescharacteristic
136C4⋊C8×C61C2×C411yescharacteristic
137C4⋊C8×C61C2×C411yescharacteristic
138C22⋊C8×C61C2×C411yescharacteristic
139C22⋊C8×C61C2×C411yescharacteristic
140#97×C61C2×C411yescharacteristic
141C4×C8×C61C2×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C2×C22⋊D61C4⋊C411yescharacteristic
144C2×C22⋊D61C4⋊C411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×Q811yescharacteristic
147#11758222—41no—
148#11758222—41no—
149C2×D244C4⋊C411yescharacteristic
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C22×C411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×Q811yescharacteristic
155C2×C4×D61C2×Q811yescharacteristic
156C2×Dic122C4⋊C411yescharacteristic
157#11758217—81no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—81no—
167#11758213—81no—
168#11758213—81no—
169#11758213—81no—
170D61⋊C8—81no—
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C4⋊C4×C61C4⋊C411yescharacteristic
176C4⋊C4×C61C4⋊C411yescharacteristic
177C22⋊C4×C61C4⋊C411yescharacteristic
178C22⋊C4×C61C4⋊C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180C42×C61C22×C411yescharacteristic
181#11758198C4⋊C411yescharacteristic
182#11758198C4⋊C411yescharacteristic
183#11758198C4⋊C411yescharacteristic
184#11758198C4⋊C411yescharacteristic
185#11758196C4⋊C411yescharacteristic
186#11758196C4⋊C411yescharacteristic
187#11758196C4⋊C411yescharacteristic
188#11758196C4⋊C411yescharacteristic
189C4×Dic61C22×C411yescharacteristic
190C4×Dic61C2×D411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×Q811yescharacteristic
194C4×Dic61C2×Q811yescharacteristic
195C4×Dic61C2×Q811yescharacteristic
196C4×Dic61C2411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201#11758189—41no—
202#11758189—41no—
203C8×D61—41no—
204C8×D61—41no—
205C23×C61C2×C4⋊C411yescharacteristic
206C22×D61C2×C4⋊C411yescharacteristic
207C22×D61C2×C4⋊C411yescharacteristic
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61C2×C4⋊C411yescharacteristic
211C2×C4×C61C2×C4⋊C411yescharacteristic
212C2×C4×C61C2×C4⋊C411yescharacteristic
213C2×C4×C61C2×C4⋊C411yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C23×C411yescharacteristic
216C22⋊D61—41no—
217C22⋊D61—41no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—41no—
221C2×Dic61C2×C4⋊C411yescharacteristic
222C2×Dic61C2×C4⋊C411yescharacteristic
223C2×Dic61C2×C4⋊C411yescharacteristic
224C2×Dic61C2×C4⋊C411yescharacteristic
225C2×Dic61C22×D411yescharacteristic
226C2×Dic61C22×Q811yescharacteristic
227D244—41no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—41no—
237C4×D61—41no—
238Dic122—41no—
239#92420—41no—
240#92420—41no—
241#92420—41no—
242#92420—41no—
243#92420—41no—
244#92420—41no—
245#92420—41no—
246#92420—41no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#17825—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61C22×C4⋊C411yescharacteristic
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61#56811yescharacteristic
272C4×C61#56811yescharacteristic
273Dic61—21no—
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61#57611yescharacteristic
279Dic61#57811yescharacteristic
280#2989—611no—
281#2989—611no—
282#2922—611no—
283#1574—611no—
284#1574—611no—
285#1573—611no—
286#1573—611no—
287#1572—611no—
288#1572—611no—
289#1571—611no—
290#1571—611no—
291#1569—611no—
292#1569—611no—
293#1568—611no—
294#1567—611no—
295C2×C61—41no—
296C2×C61#290511yescharacteristic
297C2×C61#291311yescharacteristic
298C2×C61#291611yescharacteristic
299D61—41no—
300D61—41no—
301C4×#41—611no—
302#446—1221no—
303#446—1221no—
304#436—1221no—
305#436—1221no—
306#435—1221no—
307#435—1221no—
308#435—1221no—
309#435—1221no—
310#433—611no—
311#433—611no—
312#433—611no—
313#433#692311yescharacteristic
314#432—611no—
315#432—611no—
316#432—611no—
317#432—611no—
318#431—611no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431—611no—
324#424—611no—
325#424—611no—
326#423—611no—
327#423—611no—
328#423—611no—
329#423—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332#408—611no—
333#408—611no—
334C4×M16—611no—
335C2×C4×C8—611no—
336#335—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—611no—
344#335—611no—
345#335—611no—
346#334—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334—611no—
351#334—611no—
352C61#1782511yescharacteristic, complemented, Sylow
353C2×#41—611no—
354C2×M16—611no—
355C2×M16—611no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—1221no—
363C22×C8—1221no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×D4—611no—
367C4×D4—611no—
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—611no—
371C4×D4—611no—
372#117—611no—
373#117—611no—
374#117C2×#692311yescharacteristic
375C2×C42—611no—
376C2×C42—611no—
377C2×C42—611no—
378C4⋊C8—611no—
379C4⋊C8—611no—
380C4⋊C8—611no—
381C4⋊C8—611no—
382C4⋊C8—611no—
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—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C2×#692311yescharacteristic
399C4⋊C8C2×#692311yescharacteristic
400C22⋊C8—611no—
401C22⋊C8—611no—
402C22⋊C8—611no—
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—611no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8C2×#692311yescharacteristic
413C22⋊C8C2×#692311yescharacteristic
414#97—611no—
415#97—1221no—
416#97—1221no—
417#97—1221no—
418#97—1221no—
419#97C2×#692311yescharacteristic
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8C2×#692311yescharacteristic
428#41—2441no—
429#41—2441no—
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×C4—611no—
441C22×C4—611no—
442C22×C4C22×#692311yescharacteristic
443M16—4881no—
444M16—4881no—
445M16—4881no—
446M16—4881no—
447M16—2441no—
448M16—2441no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—4881no—
462C2×C8—4881no—
463C2×C8—2441no—
464C2×C8—2441no—
465C2×C8C22×#692311yescharacteristic
466C2×C8C22×#692311yescharacteristic
467C2×C8C22×#692311yescharacteristic
468C2×C8C22×#692311yescharacteristic
469C4⋊C4—611no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4C4⋊#692311yescharacteristic
474C4⋊C4C4⋊#692311yescharacteristic
475C22⋊C4—611no—
476C22⋊C4—611no—
477C22⋊C4—611no—
478C22⋊C4—611no—
479C22⋊C4C4⋊#692311yescharacteristic
480C22⋊C4C4⋊#692311yescharacteristic
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42C22×#692311yescharacteristic
490C42C22×#692311yescharacteristic
491C23—611no—
492C23—611no—
493C23C2×C4⋊#692311yescharacteristic
494Q8—2441no—
495D4—2441no—
496D4—2441no—
497D4—2441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4C2×C4⋊#692311yescharacteristic
520C2×C4C2×C4⋊#692311yescharacteristic
521C2×C4C2×C4⋊#692311yescharacteristic
522C2×C4C2×C4⋊#692311yescharacteristic
523C2×C4C2×C4⋊#692311yescharacteristic
524C2×C4C23×#692311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—1221no—
545C22—1221no—
546C22—1221no—
547C22—1221no—
548C22—1221no—
549C22—1221no—
550C22C22×C4⋊#692311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—611no—
557C4—611no—
558C4—1221no—
559C4—1221no—
560C4—1221no—
561C4—1221no—
562C4—1221no—
563C4#1684084111yescharacteristic
564C4#1684084111yescharacteristic
565C2—41no—
566C2—2441no—
567C2—2441no—
568C2#2146246211yescharacteristic
569C2#2146247411yescharacteristic
570C2#2146248011yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#433C4
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#433#6923
hypocenterC61#17825
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #21461396C2semidirect
4. #21461395C2semidirect
5. #21461393C2semidirect
6. #21461392C2semidirect
7. #21461391C2semidirect
8. #21461390C2semidirect
9. #21461389C2semidirect
10. #21461388C2semidirect
11. #21461385C2semidirect
12. #21461384C2semidirect
13. #21461380C2semidirect
14. #21461378C2semidirect
352. C61#17825semidirect

Maximal subgroups

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

subgroupindex
#214627412
#214627402
#214613962
#214613952
#214613932
#214613922
#214613912
#214613902
#214613892
#214613882
#214613852
#214613842
#214613802
#214613782
#214544602
#1782561