Finite Group Databasebeta

← #29650659

Subgroups — #29650659

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#21456423C211yesmaximal, characteristic
2#21454967C211yesmaximal, characteristic
3#21454910C211yesmaximal, characteristic, complemented
4#21444725C211yesmaximal, characteristic, complemented
5#21444724C211yesmaximal, characteristic, complemented
6#21444716C211yesmaximal, characteristic, complemented
7#21444708C211yesmaximal, characteristic, complemented
8#21444633C211yesmaximal, characteristic, complemented
9C8×#11758202C211yesmaximal, characteristic, complemented
10C8×#11758201C211yesmaximal, characteristic, complemented
11#21444583C211yesmaximal, characteristic, complemented
12#21444278C211yesmaximal, characteristic
13#21444272C211yesmaximal, characteristic, complemented
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#16839892—21no—
29#16839891—21no—
30#16839889C2211yescharacteristic
31C8×Dic122C2211yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758190C2211yescharacteristic
34C4×#11758201C2211yescharacteristic
35#16839841—21no—
36#16839839C2211yescharacteristic
37#16839832—21no—
38C8×D244C2211yescharacteristic
39#16839822—21no—
40#16839821—21no—
41#16839821—21no—
42#16839818C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839787—21no—
45#16839784C2211yescharacteristic
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×D61—21no—
76#14519776C2×C411yescharacteristic
77#14519775C2×C411yescharacteristic
78#14519772—21no—
79#14519768C2×C411yescharacteristic
80#14519767—21no—
81#14519766C2×C411yescharacteristic
82#14519762—21no—
83#14519757C2×C411yescharacteristic
84#14519755—21no—
85#14519753C2×C411yescharacteristic
86#14519753C2×C411yescharacteristic
87#14519752C2×C411yescharacteristic
88C4×Dic122—21no—
89C4×Dic122C2311yescharacteristic
90C4×D244—21no—
91C4×D244C2311yescharacteristic
92#14519734—21no—
93#14519734—21no—
94C42×D61C2311yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418—21no—
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
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#14519689D411yescharacteristic
117#14519689D411yescharacteristic
118#14519688—21no—
119#14519688—21no—
120#14519687—21no—
121#14519687—21no—
122#14519687C2×C411yescharacteristic
123#14519687C2×C411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61—21no—
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—81no—
204#11758189—81no—
205C8×D61—42no—
206C8×D61—81no—
207C22×D61—21no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61C4×D411yescharacteristic
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226D244—21no—
227D244—21no—
228D244—81no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—41no—
236Dic122—21no—
237Dic122—21no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61#13112yes—
246#92418—22no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418#13112yes—
253#17969—611nomaximal, Sylow
254C22×C61C2×C4×D411yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—21no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61C2×#13111yescharacteristic
267C4×C61C2×#13111yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—21no—
271Dic61—21no—
272Dic61—21no—
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#1579D6111yescharacteristic, complemented
284SD16⋊C8—611no—
285C8×Q16—611no—
286C8×SD16—611no—
287#1569—611no—
288#1494—611no—
289#1493—611no—
290C8×M16—611no—
291C2×C61#293111yescharacteristic
292C2×C61#294711yescharacteristic
293C2×C61#295611yescharacteristic
294D61—41no—
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×Q8C2×D6111yescharacteristic
313C8×Q8C2×D6111yescharacteristic
314C4×Q16—611no—
315C4×Q16C2×D6111yescharacteristic
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#431—611no—
327#424—1221no—
328#423—611no—
329C4×M16—611no—
330C2×C4×C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334C2×D6111yescharacteristic
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8C2×D6111yescharacteristic
340Q8⋊C8C2×D6111yescharacteristic
341D4⋊C8—611no—
342D4⋊C8—611no—
343#322—611no—
344#322C2×D6111yescharacteristic
345C82—611no—
346C82—611no—
347C61#1796911yescharacteristic, complemented, Sylow
348C2×Q16—611no—
349C2×Q16C4×D6111yescharacteristic
350C2×SD16—611no—
351C2×SD16—611no—
352C2×M16—611no—
353C2×M16—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—1221no—
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—1221no—
372C4×Q8C22×D6111yescharacteristic
373C4×Q8C22×D6111yescharacteristic
374C4×D4—611no—
375C4×D4—1221no—
376#117—1221no—
377#117—1221no—
378C2×C42—611no—
379#107—611no—
380#107C4×D6111yescharacteristic
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103C4×D6111yescharacteristic
401#103C4×D6111yescharacteristic
402#102—611no—
403#102—611no—
404C22⋊C8—611no—
405C22⋊C8—611no—
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—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C2×Q8—611no—
426C2×Q8—1221no—
427C2×Q8C2×C4×D6111yescharacteristic
428C2×Q8C2×C4×D6111yescharacteristic
429C2×D4—611no—
430C2×D4—1221no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1221no—
435Q16—22no—
436Q16—1222no—
437SD16—1222no—
438SD16—1222no—
439M16—1222no—
440M16—1222no—
441M16—4881no—
442M16—4881no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—4881no—
454C2×C8—2442no—
455C2×C8C2×C4×D6111yescharacteristic
456C2×C8C2×C4×D6111yescharacteristic
457C2×C8D4×D6111yescharacteristic
458C2×C8D4×D6111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
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⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—21no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—1221no—
487C42C23×D6111yescharacteristic
488C23—611no—
489C23—1221no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
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—611no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4#41×D6111yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—612no—
527C8—1222no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—2441no—
532C8—2441no—
533C8#1451978312yes—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22C4×D4×D6111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—1221no—
547C4—1221no—
548C4—1221no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4#131×D6111yescharacteristic
553C4C2×#1451978311yescharacteristic
554C4#1684057111yescharacteristic
555C4#1684057811yescharacteristic
556C2—4881no—
557C2—2441no—
558C2#2145452611yescharacteristic
559C2#2145466111yescharacteristic
560C2#2145472711yescharacteristic
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#17969
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. #21454910C2semidirect
4. #21444725C2semidirect
5. #21444724C2semidirect
6. #21444716C2semidirect
7. #21444708C2semidirect
8. #21444633C2semidirect
9. C8×#11758202C2semidirect
10. C8×#11758201C2semidirect
11. #21444583C2semidirect
13. #21444272C2semidirect
14. #21444098C2semidirect
15. C61×#1579C2semidirect
283. #1579D61semidirect
347. C61#17969semidirect

Maximal subgroups

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

subgroupindex
#214564232
#214549672
#214549102
#214447252
#214447242
#214447162
#214447082
#214446332
C8×#117582022
C8×#117582012
#214445832
#214442782
#214442722
#214440982
C61×#15792
#1796961