Finite Group Databasebeta

← #29650625

Subgroups — #29650625

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456423C211yesmaximal, characteristic
2#21454796C211yesmaximal, characteristic
3#21454748C211yesmaximal, characteristic, complemented
4#21444716C211yesmaximal, characteristic, complemented
5#21444713C211yesmaximal, characteristic, complemented
6#21444708C211yesmaximal, characteristic, complemented
7#21444706C211yesmaximal, characteristic, complemented
8#21444636C211yesmaximal, characteristic, complemented
9#21444633C211yesmaximal, characteristic, complemented
10#21444629C211yesmaximal, characteristic, complemented
11#21444583C211yesmaximal, characteristic, complemented
12#21444290C211yesmaximal, characteristic, complemented
13#21444283C211yesmaximal, characteristic
14#21444098C211yesmaximal, characteristic, complemented
15C61×#1579C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17#16840299C2211yescharacteristic
18#16840170C411yescharacteristic
19#16840155C411yescharacteristic
20#16840129C411yescharacteristic
21#16840123C411yescharacteristic
22#16840019C411yescharacteristic
23#16840017C411yescharacteristic
24#16840011C411yescharacteristic
25#16840009C411yescharacteristic
26#16839893C2211yescharacteristic
27#16839893C2211yescharacteristic
28#16839891—21no—
29#16839889C2211yescharacteristic
30C8×Dic122—21no—
31C8×Dic122C2211yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758190C2211yescharacteristic
34C4×#11758201C2211yescharacteristic
35#16839839C2211yescharacteristic
36#16839832—21no—
37C8×D244—21no—
38C8×D244C2211yescharacteristic
39#16839822—21no—
40#16839818C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839787—21no—
43#16839784C2211yescharacteristic
44#16839716—21no—
45#16839716—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758190C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189C2×C411yescharacteristic
73C2×#11758189C2×C411yescharacteristic
74C2×C8×D61—21no—
75C2×C8×D61D411yescharacteristic
76C2×C8×D61D411yescharacteristic
77#14519776C2×C411yescharacteristic
78#14519775C2×C411yescharacteristic
79#14519772—21no—
80#14519768C2×C411yescharacteristic
81#14519767—21no—
82#14519766C2×C411yescharacteristic
83#14519762—21no—
84#14519757C2×C411yescharacteristic
85#14519755—21no—
86#14519753C2×C411yescharacteristic
87#14519753C2×C411yescharacteristic
88#14519752C2×C411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91C4×D244—21no—
92C4×D244C2311yescharacteristic
93#14519734—21no—
94#14519734—21no—
95C42×D61C2311yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519702C2×C411yescharacteristic
108#14519701C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118#14519688—21no—
119#14519687—21no—
120#14519687—21no—
121#14519687C2×C411yescharacteristic
122#14519687C2×C411yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139C4×C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D244—21no—
147C2×D244C22×C411yescharacteristic
148C2×C4×D61—21no—
149C2×C4×D61C22×C411yescharacteristic
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61#4111yescharacteristic
152C2×Dic122—21no—
153C2×Dic122C22×C411yescharacteristic
154Q16×C61—22no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61C22×C411yescharacteristic
159C2×C8×C61C22×C411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61C22×C411yescharacteristic
165C4⋊C4×C61C22×C411yescharacteristic
166C42×C61—21no—
167C42×C61—21no—
168C42×C61C2411yescharacteristic
169#11758202—22no—
170#11758201—22no—
171#11758198—21no—
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178C4⋊Dic61—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×Dic61C22×C411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61#4111yescharacteristic
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200#11758190—22no—
201#11758189—22no—
202#11758189—22no—
203#11758189—42no—
204#11758189—42no—
205C8×D61—22no—
206C8×D61—41no—
207C8×D61—42no—
208C22×D61—21no—
209C22×D61C4×D411yescharacteristic
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61C23×C411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226C2×Dic61C4×D411yescharacteristic
227D244—21no—
228D244—21no—
229D244—42no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—41no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61#13112yes—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418#13112yes—
253#92418#13712yes—
254#17967—611nomaximal, Sylow
255C22×C61C2×C4×D411yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61C2×#13111yescharacteristic
268C4×C61C2×#13111yescharacteristic
269C4×C61C2×#13711yescharacteristic
270C4×C61#57511yescharacteristic
271Dic61—21no—
272Dic61—21no—
273Dic61—21no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3172—611no—
278#2966—611no—
279#2960—611no—
280#1591—611no—
281#1591—611no—
282#1590—611no—
283#1590—611no—
284#1579—611no—
285#1579D6111yescharacteristic, complemented
286SD16⋊C8—611no—
287SD16⋊C8—611no—
288#1569—611no—
289#1497—611no—
290#1495—611no—
291C8×M16—611no—
292C2×C61#293111yescharacteristic
293C2×C61C4×#13711yescharacteristic
294C2×C61#295511yescharacteristic
295D61—41no—
296D61—81no—
297#533—611no—
298#529—611no—
299#501—611no—
300#497—611no—
301#491—611no—
302#489—611no—
303#470—611no—
304#470—611no—
305#468—611no—
306#468—611no—
307#446—611no—
308#446—611no—
309#446—611no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—1221no—
313C8×Q8C2×D6111yescharacteristic
314C8×Q8C2×D6111yescharacteristic
315C4×Q16—611no—
316C4×Q16C2×D6111yescharacteristic
317C4×SD16—611no—
318C4×SD16—611no—
319#436—611no—
320#435—1221no—
321C8×D4—611no—
322C8×D4—1221no—
323#433—1221no—
324#432—611no—
325#431—611no—
326#424—1221no—
327#423—611no—
328#405—1221no—
329#405—1221no—
330C4×M16—611no—
331C2×C4×C8—611no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334C2×D6111yescharacteristic
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8C2×D6111yescharacteristic
341Q8⋊C8C2×D6111yescharacteristic
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322C2×D6111yescharacteristic
346C82—611no—
347C82—611no—
348C61#1796711yescharacteristic, complemented, Sylow
349C2×Q16—611no—
350C2×Q16C4×D6111yescharacteristic
351C2×SD16—611no—
352C2×SD16—611no—
353C2×M16—611no—
354C2×M16—611no—
355C2×M16—1221no—
356C2×M16—1221no—
357C22×C8—611no—
358C22×C8—611no—
359C22×C8—1221no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362#126—1221no—
363#125—611no—
364#125—1221no—
365#124—611no—
366#123—1221no—
367C22⋊Q8—611no—
368C22⋊Q8—611no—
369C22⋊Q8—611no—
370C22⋊Q8—1221no—
371#121—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×Q8C22×D6111yescharacteristic
375C4×Q8C22×D6111yescharacteristic
376C4×D4—611no—
377C4×D4—1221no—
378#117—1221no—
379#117—1221no—
380C2×C42—611no—
381#107—611no—
382#107C4×D6111yescharacteristic
383#106—611no—
384#106—611no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103C4×D6111yescharacteristic
402#103C4×D6111yescharacteristic
403#102—611no—
404#102—611no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409#97—611no—
410#97—611no—
411#97—1221no—
412#97—1221no—
413#97—1221no—
414#97—1221no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C2×Q8—611no—
427C2×Q8—1221no—
428C2×Q8C2×C4×D6111yescharacteristic
429C2×Q8C2×C4×D6111yescharacteristic
430C2×D4—611no—
431C2×D4—1221no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—1221no—
436Q16—22no—
437Q16—1222no—
438SD16—1222no—
439SD16—1222no—
440M16—1222no—
441M16—1222no—
442M16—2442no—
443M16—2442no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—1222no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—2441no—
456C2×C8—2442no—
457C2×C8C2×C4×D6111yescharacteristic
458C2×C8C2×C4×D6111yescharacteristic
459C2×C8D4×D6111yescharacteristic
460C2×C8D4×D6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—611no—
464C4⋊C4—611no—
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—
474C4⋊C4C2×C4×D6111yescharacteristic
475C4⋊C4C2×C4×D6111yescharacteristic
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C42—21no—
484C42—21no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—1221no—
489C42C23×D6111yescharacteristic
490C23—611no—
491C23—1221no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—1221no—
500D4—1221no—
501D4—2442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
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×C4C22×C4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4#41×D6111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—612no—
529C8—612no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8#1451978312yes—
536C22—1221no—
537C22—1221no—
538C22—1221no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C4×D4×D6111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—1221no—
549C4—1221no—
550C4—1221no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4C2×#1451978311yescharacteristic
556C4#137×D6111yescharacteristic
557C4#1684056111yescharacteristic
558C2—4881no—
559C2—2441no—
560C2#2145452611yescharacteristic
561C2#2145463511yescharacteristic
562C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1579C2
socleC22×C61C2×C4×D4
prime radical#14519752C2×C4
cosocleC42×C61C24
hypercenter#1579D61
hypocenterC61#17967
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #21454748C2semidirect
4. #21444716C2semidirect
5. #21444713C2semidirect
6. #21444708C2semidirect
7. #21444706C2semidirect
8. #21444636C2semidirect
9. #21444633C2semidirect
10. #21444629C2semidirect
11. #21444583C2semidirect
12. #21444290C2semidirect
14. #21444098C2semidirect
15. C61×#1579C2semidirect
285. #1579D61semidirect
348. C61#17967semidirect

Maximal subgroups

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

subgroupindex
#214564232
#214547962
#214547482
#214447162
#214447132
#214447082
#214447062
#214446362
#214446332
#214446292
#214445832
#214442902
#214442832
#214440982
C61×#15792
#1796761