Finite Group Databasebeta

← #29650662

Subgroups — #29650662

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456425C211yesmaximal, characteristic
2#21454970C211yesmaximal, characteristic
3#21454913C211yesmaximal, characteristic, complemented
4#21444729C211yesmaximal, characteristic, complemented
5#21444723C211yesmaximal, characteristic, complemented
6#21444717C211yesmaximal, characteristic, complemented
7#21444711C211yesmaximal, characteristic, complemented
8#21444639C211yesmaximal, characteristic, complemented
9#21444633C211yesmaximal, characteristic, complemented
10C8×Dic244C211yesmaximal, characteristic, complemented
11C8×#11758190C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic
14#21444275C211yesmaximal, characteristic, complemented
15C8×M16×C61C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840171C411yescharacteristic
19#16840156C411yescharacteristic
20#16840131C411yescharacteristic
21#16840122C411yescharacteristic
22#16840020C411yescharacteristic
23#16840020C411yescharacteristic
24#16840008C411yescharacteristic
25#16840008C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839892C2211yescharacteristic
28#16839892C2211yescharacteristic
29#16839891—21no—
30#16839891—21no—
31C8×Dic122C2211yescharacteristic
32C8×Dic122C2211yescharacteristic
33C8×Dic122C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×#11758190C2211yescharacteristic
37C4×#11758190C2211yescharacteristic
38#16839841C2211yescharacteristic
39#16839837—21no—
40#16839836—21no—
41C8×D244C2211yescharacteristic
42#16839822—21no—
43#16839820—21no—
44#16839820—21no—
45#16839819C2211yescharacteristic
46#16839787—21no—
47#16839786C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C4×M16×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C82×C61C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×Dic244C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×C8×D61—21no—
74#14519777C2×C411yescharacteristic
75#14519777C2×C411yescharacteristic
76#14519771—21no—
77#14519769—21no—
78#14519769C2×C411yescharacteristic
79#14519765C2×C411yescharacteristic
80#14519760—21no—
81#14519756—21no—
82#14519756C2×C411yescharacteristic
83#14519756C2×C411yescharacteristic
84#14519756C2×C411yescharacteristic
85#14519751C2×C411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122C2311yescharacteristic
88C4×Dic122C2311yescharacteristic
89C4×Dic122C2311yescharacteristic
90C4×D244C2311yescharacteristic
91C4×C22⋊D61—21no—
92#14519736—21no—
93#14519734—21no—
94#14519711C2×C411yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519702C2×C411yescharacteristic
113#14519702C2×C411yescharacteristic
114#14519702C2×C411yescharacteristic
115#14519699C2×C411yescharacteristic
116#14519699C2×C411yescharacteristic
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519688—21no—
121#14519687—21no—
122#14519687—21no—
123#14519687—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C2×M16×C61C2×C411yescharacteristic
128C2×M16×C61C2×C411yescharacteristic
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C22⋊C8×C61D411yescharacteristic
134C22⋊C8×C61D411yescharacteristic
135#97×C61C2×C411yescharacteristic
136#97×C61C2×C411yescharacteristic
137C4×C8×C61—21no—
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×D244C22×C411yescharacteristic
149C2×C4×D61—21no—
150C2×Dic122—21no—
151C2×Dic122C22×C411yescharacteristic
152C2×Dic122C22×C411yescharacteristic
153C2×Dic122C22×C411yescharacteristic
154M16×C61—22no—
155M16×C61—22no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—42no—
159C2×C8×C61C22×C411yescharacteristic
160C2×C8×C61C22×C411yescharacteristic
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C42×C61C22×C411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173C22⋊Dic61—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61C22×C411yescharacteristic
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201Dic244—22no—
202Dic244—22no—
203#11758190—22no—
204#11758190—22no—
205#11758189—81no—
206C8×D61—81no—
207C23×C61C4×D411yescharacteristic
208C22×D61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C22⋊D61—81no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228D244—21no—
229D244—21no—
230C4×D61—41no—
231C4×D61—41no—
232Dic122—21no—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—81no—
239C8×C61—22no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61#13112yes—
248C8×C61#13112yes—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#17969—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61C2×C4×D411yescharacteristic
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61C2×#13111yescharacteristic
266C4×C61C2×#13111yescharacteristic
267C4×C61#57711yescharacteristic
268C4×C61#57811yescharacteristic
269Dic61—41no—
270Dic61—41no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276#3172—611no—
277#2993—611no—
278#2985—611no—
279#1593—611no—
280#1592—611no—
281#1591—611no—
282#1590—611no—
283#1579—611no—
284SD16⋊C8—611no—
285C8×Q16—611no—
286C8×SD16—611no—
287#1569—611no—
288#1494—611no—
289#1493—611no—
290C8×M16D6111yescharacteristic, complemented
291C2×C61—41no—
292C2×C61#293111yescharacteristic
293C2×C61#294711yescharacteristic
294C2×C61#295611yescharacteristic
295D61—81no—
296#533—611no—
297#529—611no—
298#501—611no—
299#497—611no—
300#491—611no—
301#489—611no—
302#470—611no—
303#470—611no—
304#468—611no—
305#468—611no—
306#446—611no—
307#446—611no—
308#446—611no—
309#446—1221no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C4×Q16—611no—
315C4×Q16—611no—
316C4×SD16—611no—
317C4×SD16—611no—
318#436—611no—
319#436—1221no—
320#435—1221no—
321C8×D4—611no—
322#433—1221no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431C2×D6111yescharacteristic
327#424—1221no—
328#423—611no—
329C4×M16C2×D6111yescharacteristic
330C2×C4×C8C2×D6111yescharacteristic
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341D4⋊C8—611no—
342D4⋊C8—611no—
343#322C2×D6111yescharacteristic
344#322C2×D6111yescharacteristic
345C82C2×D6111yescharacteristic
346C82C2×D6111yescharacteristic
347C61#1796911yescharacteristic, complemented, Sylow
348C2×Q16—611no—
349C2×Q16—611no—
350C2×SD16—611no—
351C2×SD16—611no—
352C2×M16—1221no—
353C2×M16—1221no—
354C2×M16C4×D6111yescharacteristic
355C2×M16C4×D6111yescharacteristic
356C22×C8—21no—
357C22×C8—1221no—
358C4⋊Q8—611no—
359C4⋊Q8—611no—
360#126—1221no—
361#125—611no—
362#125—1221no—
363#124—611no—
364#123—1221no—
365C22⋊Q8—611no—
366C22⋊Q8—611no—
367C22⋊Q8—611no—
368C22⋊Q8—1221no—
369#121—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×D4—611no—
375C4×D4—1221no—
376#117—1221no—
377#117—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8D24411yescharacteristic
395C4⋊C8D24411yescharacteristic
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#102—611no—
403#102—611no—
404C22⋊C8—1221no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8D24411yescharacteristic
408C22⋊C8D24411yescharacteristic
409#97—1221no—
410#97—1221no—
411#97—1221no—
412#97—1221no—
413#97C4×D6111yescharacteristic
414#97C4×D6111yescharacteristic
415C4×C8—21no—
416C4×C8—1221no—
417C4×C8—1221no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C4×C8C22×D6111yescharacteristic
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C2×Q8—611no—
426C2×Q8—611no—
427C2×Q8—611no—
428C2×Q8—1221no—
429C2×D4—611no—
430C2×D4—1221no—
431C22×C4—1221no—
432C22×C4C2×C4×D6111yescharacteristic
433C22×C4C2×D24411yescharacteristic
434C22×C4#1175822211yescharacteristic
435Q16—1222no—
436Q16—1222no—
437SD16—1222no—
438SD16—1222no—
439M16—22no—
440M16—22no—
441M16—4881no—
442M16—4881no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—4881no—
451C2×C8C2×C4×D6111yescharacteristic
452C2×C8C2×C4×D6111yescharacteristic
453C2×C8C2×C4×D6111yescharacteristic
454C2×C8C2×C4×D6111yescharacteristic
455C2×C8C2×D24411yescharacteristic
456C2×C8C2×D24411yescharacteristic
457C2×C8C2×D24411yescharacteristic
458C2×C8C2×D24411yescharacteristic
459C4⋊C4—611no—
460C4⋊C4—611no—
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42C2×D24411yescharacteristic
486C42#1175822211yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23C4×D24411yescharacteristic
490Q8—1221no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497D4—1221no—
498D4—1221no—
499D4—4881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4C4×D24411yescharacteristic
515C2×C4C4×D24411yescharacteristic
516C2×C4C4×D24411yescharacteristic
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C22×D24411yescharacteristic
519C2×C4C2×#1175822211yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8#1451978312yes—
533C8#1451978312yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22C2×C4×D24411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—2441no—
546C4—2441no—
547C4—2441no—
548C4—2441no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4C2×#1451978311yescharacteristic
553C4C2×#1451978311yescharacteristic
554C4#1684057411yescharacteristic
555C4#1684057911yescharacteristic
556C2—41no—
557C2—4881no—
558C2#2145453211yescharacteristic
559C2#2145466411yescharacteristic
560C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×M16×C61C2
socleC22×C61C2×C4×D4
prime radical#14519751C2×C4
cosocleC42×C61C24
hypercenterC8×M16D61
hypocenterC61#17969
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
3. #21454913C2semidirect
4. #21444729C2semidirect
5. #21444723C2semidirect
6. #21444717C2semidirect
7. #21444711C2semidirect
8. #21444639C2semidirect
9. #21444633C2semidirect
10. C8×Dic244C2semidirect
11. C8×#11758190C2semidirect
12. #21444586C2semidirect
14. #21444275C2semidirect
15. C8×M16×C61C2semidirect
290. C8×M16D61semidirect
347. C61#17969semidirect

Maximal subgroups

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

subgroupindex
#214564252
#214549702
#214549132
#214447292
#214447232
#214447172
#214447112
#214446392
#214446332
C8×Dic2442
C8×#117581902
#214445862
#214442802
#214442752
C8×M16×C612
#1796961