Finite Group Databasebeta

← #29667619

Subgroups — #29667619

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457150C211yesmaximal, characteristic
2#21456846C211yesmaximal, characteristic
3#21454981C211yesmaximal, characteristic
4#21445370C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445334C211yesmaximal, characteristic, complemented
7#21445329C211yesmaximal, characteristic, complemented
8#21445246C211yesmaximal, characteristic, complemented
9#21445239C211yesmaximal, characteristic, complemented
10#21445210C211yesmaximal, characteristic, complemented
11#21445205C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444519C211yesmaximal, characteristic, complemented
14C2×#16839508C211yesmaximal, characteristic, complemented
15C61×#3230C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840154—21no—
18#16840130—21no—
19#16840069—21no—
20#16840044C2211yescharacteristic
21#16840039C2211yescharacteristic
22#16840001—21no—
23#16839993—21no—
24#16839984—21no—
25#16839969C2211yescharacteristic
26#16839969C2211yescharacteristic
27#16839969C2211yescharacteristic
28#16839964C2211yescharacteristic
29#16839964C2211yescharacteristic
30#16839964C2211yescharacteristic
31#16839918—21no—
32#16839901—21no—
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839830—21no—
37C8×D244C2211yescharacteristic
38#16839825—21no—
39#16839822—21no—
40#16839819C2211yescharacteristic
41#16839787—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#500C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#484—21no—
63C61×#484—21no—
64C61×#477—21no—
65C61×#477—21no—
66C61×#431C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769D411yescharacteristic
79#14519765D411yescharacteristic
80#14519760—21no—
81#14519756D411yescharacteristic
82#14519751D411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—21no—
105#14519700—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111#14519687—21no—
112C8×Dic61—21no—
113C22×Q8×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126#117×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#107×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61—81no—
150C2×Q8×C61—81no—
151C22×C4×C61—41no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×D244C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×Dic122C2×D411yescharacteristic
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×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C42×C61—41no—
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61#4111yescharacteristic
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758202—81no—
183#11758202—81no—
184#11758202—81no—
185#11758201—81no—
186#11758201—81no—
187#11758201—81no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C2×D411yescharacteristic
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—81no—
206C2×#92418—81no—
207#11758189—81no—
208C8×D61—81no—
209C23×C61#12111yescharacteristic
210C22×D61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—82no—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—82no—
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—42no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240D244—21no—
241D244—21no—
242C4×D61—41no—
243C4×D61—41no—
244Dic122—21no—
245Dic122—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#19590—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61#47312yes—
260C22×C61C2×#12111yescharacteristic
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61#57611yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—41no—
277Dic61—41no—
278Dic61—41no—
279#3248—611no—
280#3230D6111yescharacteristic, complemented
281#3218—611no—
282#2994—611no—
283#1700—611no—
284#1699—611no—
285#1694—611no—
286#1693—611no—
287#1680—611no—
288#1679—611no—
289#1674—611no—
290#1673—611no—
291#1573—611no—
292#1552—611no—
293C2×#332—611no—
294C2×C61—22no—
295C2×C61#304611yescharacteristic
296C2×C61#306211yescharacteristic
297C2×C61C2×#47311yescharacteristic
298D61—81no—
299#533C2×D6111yescharacteristic
300C2×C4⋊Q8C2×D6111yescharacteristic
301#529—611no—
302#500C2×D6111yescharacteristic
303#500C2×D6111yescharacteristic
304#497—1221no—
305#491—1221no—
306#487C2×D6111yescharacteristic
307#487C2×D6111yescharacteristic
308#484—21no—
309#484—21no—
310#479—1221no—
311#477—21no—
312#477—21no—
313#475—611no—
314#474—611no—
315#467—1221no—
316#465—1221no—
317#464—1221no—
318#462—611no—
319#462—611no—
320#462—611no—
321#461—611no—
322#461—611no—
323#461—611no—
324#451—1221no—
325#448—1221no—
326#446—611no—
327C8×Q8—611no—
328#436—611no—
329#435—1221no—
330C8×D4—611no—
331C8×D4—1221no—
332#433—1221no—
333#432—611no—
334#431C2×D6111yescharacteristic
335#424—1221no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338#335—611no—
339#335—611no—
340#334—611no—
341#334—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348#332—611no—
349#332—611no—
350C61#1959011yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C2×Q16—1221no—
353C2×Q16—1221no—
354C2×Q16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×M16—1221no—
359C22×C8—1221no—
360C22×C8—1221no—
361C22×C8—1221no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C22×D6111yescharacteristic
366C4⋊Q8C22×D6111yescharacteristic
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#126—1221no—
370#125—21no—
371#125—611no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—611no—
377#121—611no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—611no—
381C4×D4—611no—
382C4×D4—1221no—
383#117—21no—
384#117—1221no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C22×D6111yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—1221no—
393#106—1221no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8C22⋊D6111yescharacteristic
405C4⋊C8C22⋊D6111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#102—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8C22⋊D6111yescharacteristic
422C22⋊C8C22⋊D6111yescharacteristic
423#97—1221no—
424#97—1221no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427C4×C8C22×D6111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8—611no—
436C2×D4—611no—
437C2×D4—1221no—
438C22×C4—41no—
439C22×C4—1221no—
440C22×C4D4×D6111yescharacteristic
441C22×C4#1175822411yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443Q16—4881no—
444Q16—4881no—
445Q16—4881no—
446SD16—4881no—
447SD16—4881no—
448SD16—4881no—
449M16—4881no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—4881no—
457C2×C8—4881no—
458C2×C8—4881no—
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C22⋊C4—41no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C42—41no—
488C42—1221no—
489C42D4×D6111yescharacteristic
490C42#1175822411yescharacteristic
491C42C2×C22⋊D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—1221no—
494C23#1451974811yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—82no—
504Q8—1221no—
505Q8—1221no—
506D4—1221no—
507D4—1221no—
508D4—2442no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4#1451974811yescharacteristic
525C2×C4#1451974811yescharacteristic
526C2×C4#1451974811yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C2×C4C22×C22⋊D6111yescharacteristic
529C2×C4C2×#1175822411yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C22—21no—
541C22—21no—
542C22—2441no—
543C22—2441no—
544C22—2441no—
545C22#1684003412yes—
546C22C2×#1451974811yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—2441no—
556C4—2441no—
557C4—2441no—
558C4#1684056611yescharacteristic
559C4#1684057011yescharacteristic
560C4#1684057211yescharacteristic
561C4#1684057711yescharacteristic
562C2—22no—
563C2—4881no—
564C2#2145536511yescharacteristic
565C2#2145549311yescharacteristic
566C2C2×#1684003411yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3230C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#3230D61
hypocenterC61#19590
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #21445370C2semidirect
5. #21445363C2semidirect
6. #21445334C2semidirect
7. #21445329C2semidirect
8. #21445246C2semidirect
9. #21445239C2semidirect
10. #21445210C2semidirect
11. #21445205C2semidirect
12. #21444604C2semidirect
13. #21444519C2semidirect
14. C2×#16839508C2semidirect
15. C61×#3230C2semidirect
280. #3230D61semidirect
350. C61#19590semidirect

Maximal subgroups

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

subgroupindex
#214571502
#214568462
#214549812
#214453702
#214453632
#214453342
#214453292
#214452462
#214452392
#214452102
#214452052
#214446042
#214445192
C2×#168395082
C61×#32302
#1959061