Finite Group Databasebeta

← #29651234

Subgroups — #29651234

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455886C211yesmaximal, characteristic
2#21454947C211yesmaximal, characteristic
3#21454917C211yesmaximal, characteristic, complemented
4#21444712C211yesmaximal, characteristic, complemented
5#21444698C211yesmaximal, characteristic, complemented
6#21444695C211yesmaximal, characteristic, complemented
7#21444689C211yesmaximal, characteristic, complemented
8#21444688C211yesmaximal, characteristic, complemented
9C8×Dic244C211yesmaximal, characteristic, complemented
10#21444623C211yesmaximal, characteristic, complemented
11#21444606C211yesmaximal, characteristic, complemented
12#21444272C211yesmaximal, characteristic, complemented
13#21444198C211yesmaximal, characteristic
14#21444101C211yesmaximal, characteristic, complemented
15C61×#1590C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4×#11758224C2211yescharacteristic
18#16840106C411yescharacteristic
19#16840102C411yescharacteristic
20#16840046C411yescharacteristic
21#16840040C411yescharacteristic
22#16839971C411yescharacteristic
23#16839965C411yescharacteristic
24#16839925C411yescharacteristic
25#16839921C411yescharacteristic
26#16839890—21no—
27#16839889C2211yescharacteristic
28Q8×#92418C2211yescharacteristic
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31#16839886—21no—
32#16839886C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758200C2211yescharacteristic
36#16839840C2211yescharacteristic
37#16839838—21no—
38#16839837—21no—
39#16839824—21no—
40#16839822—21no—
41#16839814C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839812—21no—
45#16839785—21no—
46#16839784C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×C8×D61—21no—
74#14519776C2×C411yescharacteristic
75#14519775C2×C411yescharacteristic
76#14519767—21no—
77#14519757C2×C411yescharacteristic
78#14519755—21no—
79#14519753C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82C4×Dic122C2311yescharacteristic
83#14519742C2×C411yescharacteristic
84D4×Dic61C2×C411yescharacteristic
85C4×C22⋊D61—21no—
86#14519737—21no—
87#14519735C2×C411yescharacteristic
88#14519734—21no—
89#14519733—21no—
90C2×C4×Dic61—21no—
91C42×D61C2311yescharacteristic
92#14519711C2×C411yescharacteristic
93#14519710C2×C411yescharacteristic
94#14519708C2×C411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519706—21no—
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689C2×C411yescharacteristic
116#14519689C2×C411yescharacteristic
117#14519689D411yescharacteristic
118#14519689D411yescharacteristic
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150#11758224—22no—
151#11758224—41no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158SD16×C61—41no—
159M16×C61—81no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61C22×C411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61C2411yescharacteristic
173C22⋊Dic61—21no—
174#11758202—22no—
175#11758200—41no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C22×C411yescharacteristic
181C4⋊Dic61C22×C411yescharacteristic
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204Dic244—22no—
205#11758189—81no—
206C8×D61—24no—
207C23×C61—21no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211D4×C61—21no—
212D4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61C23×C411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—42no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—42no—
227C2×Dic61—42no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—22no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240Dic122#13112yes—
241C8×C61—22no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—22no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#18019—611nomaximal, Sylow
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C2×C4×D411yescharacteristic
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61C2×#13111yescharacteristic
268C4×C61#56811yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—22no—
272Dic61—21no—
273Dic61—21no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277Dic61#44312yes—
278#3107—611no—
279#2991—611no—
280#2986—611no—
281#1590—611no—
282#1590D6111yescharacteristic, complemented
283#1588—611no—
284#1588—611no—
285#1587—611no—
286#1587—611no—
287C8×Q16—611no—
288C8×Q16—611no—
289#1574—611no—
290#1493—611no—
291#1476—611no—
292#1450—611no—
293C2×C61—81no—
294C2×C61#293311yescharacteristic
295C2×C61#294711yescharacteristic
296C2×C61C2×#44311yescharacteristic
297D61—41no—
298#533—611no—
299C4×#41—611no—
300#485—611no—
301#485—611no—
302#475—611no—
303#474—611no—
304#462—611no—
305#461—611no—
306#452—611no—
307#452—611no—
308#446—611no—
309#446—1221no—
310#446C2×D6111yescharacteristic
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—1221no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16C2×D6111yescharacteristic
320#436—611no—
321#436—1221no—
322#436—1221no—
323#436C2×D6111yescharacteristic
324#433—1221no—
325#433—1221no—
326#431—611no—
327#431—611no—
328#431—611no—
329#431—1221no—
330#423—611no—
331#423—1221no—
332C2×C4×C8—611no—
333#335—611no—
334#335—611no—
335#334—611no—
336#334C2×D6111yescharacteristic
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8C2×D6111yescharacteristic
343D4⋊C8—611no—
344D4⋊C8C2×D6111yescharacteristic
345#322—611no—
346#322—611no—
347C82—611no—
348C82C2×D6111yescharacteristic
349C61#1801911yescharacteristic, complemented, Sylow
350C2×#41—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16C4×D6111yescharacteristic
355C2×M16—21no—
356C2×M16—1221no—
357C2×M16—1221no—
358C22×C8—1221no—
359C4⋊Q8—611no—
360C4⋊Q8—611no—
361#125—1221no—
362C22⋊Q8—611no—
363C22⋊Q8—611no—
364C22⋊Q8—1221no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8C22×D6111yescharacteristic
370C4×D4—611no—
371C4×D4—1221no—
372C4×D4—1221no—
373C4×D4C22×D6111yescharacteristic
374#117—611no—
375#117—1221no—
376#117—1221no—
377C2×C42—611no—
378C2×C42—1221no—
379#107—611no—
380#107—611no—
381#106—611no—
382#106C4×D6111yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103C4×D6111yescharacteristic
404#102—611no—
405#102C4×D6111yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—611no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—1221no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C4×C8C22×D6111yescharacteristic
427#41—1222no—
428#41—2441no—
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×Q8C2×C4×D6111yescharacteristic
433C2×D4—1221no—
434C2×D4C2×C4×D6111yescharacteristic
435C22×C4—21no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1221no—
440C22×C4—1221no—
441Q16—1222no—
442Q16—1222no—
443SD16—41no—
444SD16—2441no—
445M16—81no—
446M16—4881no—
447M16—4881no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—1224no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C4×D6111yescharacteristic
460C2×C8C2×C4×D6111yescharacteristic
461C2×C8D4×D6111yescharacteristic
462C2×C8D4×D6111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—611no—
465C4⋊C4—611no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4C2×C4×D6111yescharacteristic
475C4⋊C4C2×C4×D6111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42C23×D6111yescharacteristic
490C23—21no—
491C23—611no—
492Q8—21no—
493Q8—21no—
494Q8—612no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—21no—
500D4—21no—
501D4—2442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—1222no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—2442no—
520C2×C4—2442no—
521C2×C4C22×C4×D6111yescharacteristic
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4#41×D6111yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—1222no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—1221no—
542C22—1221no—
543C22—1221no—
544C22C4×D4×D6111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—612no—
550C4—1221no—
551C4—1221no—
552C4—1222no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4#131×D6111yescharacteristic
557C4#1684052811yescharacteristic
558C4#1684056811yescharacteristic
559C4#1684057611yescharacteristic
560C2—81no—
561C2—2441no—
562C2#2145454811yescharacteristic
563C2#2145465511yescharacteristic
564C2#443×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1590C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C2×C4
cosocleC42×C61C24
hypercenter#1590D61
hypocenterC61#18019
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
3. #21454917C2semidirect
4. #21444712C2semidirect
5. #21444698C2semidirect
6. #21444695C2semidirect
7. #21444689C2semidirect
8. #21444688C2semidirect
9. C8×Dic244C2semidirect
10. #21444623C2semidirect
11. #21444606C2semidirect
12. #21444272C2semidirect
14. #21444101C2semidirect
15. C61×#1590C2semidirect
282. #1590D61semidirect
349. C61#18019semidirect

Maximal subgroups

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

subgroupindex
#214558862
#214549472
#214549172
#214447122
#214446982
#214446952
#214446892
#214446882
C8×Dic2442
#214446232
#214446062
#214442722
#214441982
#214441012
C61×#15902
#1801961