Finite Group Databasebeta

← #29650654

Subgroups — #29650654

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#21456426C211yesmaximal, characteristic
2#21454913C211yesmaximal, characteristic, complemented
3#21444726C211yesmaximal, characteristic, complemented
4#21444721C211yesmaximal, characteristic, complemented
5#21444714C211yesmaximal, characteristic, complemented
6#21444707C211yesmaximal, characteristic, complemented
7#21444636C211yesmaximal, characteristic, complemented
8#21444631C211yesmaximal, characteristic, complemented
9C8×#11758202C211yesmaximal, characteristic, complemented
10C8×#11758200C211yesmaximal, characteristic, complemented
11#21444584C211yesmaximal, characteristic, complemented
12#21444279C211yesmaximal, characteristic
13#21444273C211yesmaximal, characteristic, complemented
14#21444100C211yesmaximal, characteristic, complemented
15C61×#2993C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840172C411yescharacteristic
18#16840157C411yescharacteristic
19#16840132C411yescharacteristic
20#16840121C411yescharacteristic
21#16840018C411yescharacteristic
22#16840018C411yescharacteristic
23#16840006C411yescharacteristic
24#16840006C411yescharacteristic
25#16839892C2211yescharacteristic
26#16839892C2211yescharacteristic
27#16839891—21no—
28#16839891—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31C4×#11758202C2211yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758200C2211yescharacteristic
34C4×#11758200C2211yescharacteristic
35#16839820—21no—
36#16839820—21no—
37#16839819C2211yescharacteristic
38C4×#11758194C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46#16839492C2211yescharacteristic
47#16839492C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54C8×#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436C2211yescharacteristic
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C61×#423C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758194C2×C411yescharacteristic
72C2×#11758194C2×C411yescharacteristic
73C22×#92418—21no—
74#14519777C2×C411yescharacteristic
75#14519777C2×C411yescharacteristic
76#14519769—21no—
77#14519756—21no—
78#14519756C2×C411yescharacteristic
79#14519756C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82C4×Dic122C2311yescharacteristic
83#14519736—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90#14519706—21no—
91#14519706—21no—
92#14519706—21no—
93#14519706—21no—
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519700C2×C411yescharacteristic
99#14519700C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102C22⋊#92418—21no—
103#14519688—21no—
104#14519688C2×C411yescharacteristic
105#14519688C2×C411yescharacteristic
106#14519687—21no—
107#14519687—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C8×Dic61—21no—
114C8×Dic61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61C2×C411yescharacteristic
120#124×C61C2×C411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123#121×C61C2×C411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×Dic122—21no—
152C2×Dic122C22×C411yescharacteristic
153C2×Dic122C22×C411yescharacteristic
154M16×C61—81no—
155M16×C61—81no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—81no—
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C42×C61—21no—
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180C22⋊Dic61—21no—
181#11758202—22no—
182#11758202—22no—
183#11758200—22no—
184#11758200—22no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196#11758194—22no—
197#11758194—22no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—42no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C23×C61—21no—
208C23×C61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211D4×C61—21no—
212D4×C61—21no—
213D4×C61—81no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245#92418—22no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418#13112yes—
252#92418#13112yes—
253#17969—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61C2×C4×D411yescharacteristic
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61C2×#13111yescharacteristic
269C4×C61C2×#13111yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276#3172—611no—
277#2993D6111yescharacteristic
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×M16—611no—
291C2×C61—41no—
292C2×C61—81no—
293C2×C61#293111yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295611yescharacteristic
296#533—611no—
297#529C2×D6111yescharacteristic
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—1221no—
309#446—1221no—
310#446C2×D6111yescharacteristic
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8C2×D6111yescharacteristic
314C4×Q16—611no—
315C4×Q16—611no—
316C4×SD16—611no—
317C4×SD16—611no—
318#436—21no—
319#436C2×D6111yescharacteristic
320#435—21no—
321C8×D4C2×D6111yescharacteristic
322#433—21no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431C2×D6111yescharacteristic
327#424—21no—
328#423C2×D6111yescharacteristic
329C4×M16—611no—
330C2×C4×C8—611no—
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#322—611no—
344#322—611no—
345C82—611no—
346C82—611no—
347C61#1796911yescharacteristic, complemented, Sylow
348C2×Q16—611no—
349C2×Q16—611no—
350C2×SD16—611no—
351C2×SD16—611no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—611no—
355C2×M16—611no—
356C22×C8—21no—
357C22×C8—1221no—
358C4⋊Q8—611no—
359C4⋊Q8—611no—
360#126—21no—
361#125—1221no—
362#125C4×D6111yescharacteristic
363#124C4×D6111yescharacteristic
364#123—21no—
365C22⋊Q8—611no—
366C22⋊Q8—611no—
367C22⋊Q8—1221no—
368C22⋊Q8C4×D6111yescharacteristic
369#121C4×D6111yescharacteristic
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—1221no—
373C4×Q8C22×D6111yescharacteristic
374C4×D4—21no—
375C4×D4C22×D6111yescharacteristic
376#117—21no—
377#117—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22⋊D6111yescharacteristic
393C4⋊C8C22⋊D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
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—21no—
405C22⋊C8—21no—
406C22⋊C8—1221no—
407C22⋊C8C22⋊D6111yescharacteristic
408C22⋊C8C22⋊D6111yescharacteristic
409#97—21no—
410#97—611no—
411#97—611no—
412#97—1221no—
413#97—1221no—
414#97—1221no—
415C4×C8—21no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C2×Q8—611no—
426C2×Q8—611no—
427C2×Q8—1221no—
428C2×Q8C2×C4×D6111yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D6111yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D6111yescharacteristic
433C22×C4#1175822211yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435Q16—1222no—
436Q16—1222no—
437SD16—1222no—
438SD16—1222no—
439M16—81no—
440M16—81no—
441M16—1222no—
442M16—1222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—2442no—
455C2×C8C2×C22⋊D6111yescharacteristic
456C2×C8C2×C22⋊D6111yescharacteristic
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
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⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42#1175822211yescharacteristic
486C42C2×C22⋊D6111yescharacteristic
487C42C23×D6111yescharacteristic
488C23—21no—
489C23C4×C22⋊D6111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—1221no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4C4×C22⋊D6111yescharacteristic
515C2×C4C4×C22⋊D6111yescharacteristic
516C2×C4C4×C22⋊D6111yescharacteristic
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C22×C22⋊D6111yescharacteristic
519C2×C4C2×#1175822211yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—612no—
527C8—612no—
528C8—1222no—
529C8—1221no—
530C8—1221no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D6111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2441no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4#131×D6111yescharacteristic
553C4#131×D6111yescharacteristic
554C4#1684057311yescharacteristic
555C4#1684057711yescharacteristic
556C2—41no—
557C2—81no—
558C2#2145452911yescharacteristic
559C2#2145465811yescharacteristic
560C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2993C2
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC42×C61C24
hypercenter#2993D61
hypocenterC61#17969
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #21454913C2semidirect
3. #21444726C2semidirect
4. #21444721C2semidirect
5. #21444714C2semidirect
6. #21444707C2semidirect
7. #21444636C2semidirect
8. #21444631C2semidirect
9. C8×#11758202C2semidirect
10. C8×#11758200C2semidirect
11. #21444584C2semidirect
13. #21444273C2semidirect
14. #21444100C2semidirect
347. C61#17969semidirect

Maximal subgroups

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

subgroupindex
#214564262
#214549132
#214447262
#214447212
#214447142
#214447072
#214446362
#214446312
C8×#117582022
C8×#117582002
#214445842
#214442792
#214442732
#214441002
C61×#29932
#1796961