Finite Group Databasebeta

← #29665102

Subgroups — #29665102

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457193C211yesmaximal, characteristic
2#21457042C211yesmaximal, characteristic
3#21456365C211yesmaximal, characteristic, complemented
4#21454823C211yesmaximal, characteristic
5#21445348C211yesmaximal, characteristic, complemented
6#21445343C211yesmaximal, characteristic, complemented
7#21445326C211yesmaximal, characteristic, complemented
8#21445319C211yesmaximal, characteristic, complemented
9#21445224C211yesmaximal, characteristic, complemented
10#21445219C211yesmaximal, characteristic, complemented
11#21445202C211yesmaximal, characteristic, complemented
12#21445195C211yesmaximal, characteristic, complemented
13#21444530C211yesmaximal, characteristic, complemented
14#21444501C211yesmaximal, characteristic, complemented
15C61×#1569C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840296C2211yescharacteristic
19#16840171—21no—
20#16840171—21no—
21#16840171—21no—
22#16840167C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840160C2211yescharacteristic
25#16840160C2211yescharacteristic
26#16840122—21no—
27#16840093—21no—
28#16840076—21no—
29#16840070—21no—
30#16840058C2211yescharacteristic
31#16840058C2211yescharacteristic
32#16840058C2211yescharacteristic
33#16840053C2211yescharacteristic
34#16840053C2211yescharacteristic
35#16840053C2211yescharacteristic
36#16840020—21no—
37#16840008—21no—
38#16839985—21no—
39#16839973C2211yescharacteristic
40#16839968C2211yescharacteristic
41#16839892C2211yescharacteristic
42C8×Dic122C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839838—21no—
45#16839831—21no—
46C8×D244C2211yescharacteristic
47#16839824—21no—
48#16839815C2211yescharacteristic
49#16839804—21no—
50#16839804—21no—
51#16839719—21no—
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839510C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839509C2211yescharacteristic
59#16839509C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C22×Dic122—21no—
68C2×Dic244—21no—
69C2×#11758190—21no—
70C2×#11758189—21no—
71C2×C8×D61—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519771—21no—
80#14519769—21no—
81#14519769D411yescharacteristic
82#14519765D411yescharacteristic
83#14519760—21no—
84#14519756—21no—
85#14519756—21no—
86#14519756D411yescharacteristic
87#14519751D411yescharacteristic
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93#14519736—21no—
94#14519734—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97#14519711—21no—
98#14519711—21no—
99#14519711—21no—
100#14519711—21no—
101#14519711—21no—
102#14519711—21no—
103#14519711—21no—
104#14519709—21no—
105#14519709—21no—
106#14519709—21no—
107#14519709—21no—
108#14519709—21no—
109#14519709—21no—
110#14519709—21no—
111C4⋊#92418C2311yescharacteristic
112C4⋊#92418C2311yescharacteristic
113#14519706—21no—
114#14519706—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519702—21no—
120#14519699—21no—
121#14519699—21no—
122#14519699—21no—
123C22⋊#92418—21no—
124#14519689—21no—
125#14519689—21no—
126#14519687—21no—
127C4×#92418—21no—
128C8×Dic61—21no—
129C2×M16×C61—21no—
130C2×M16×C61D411yescharacteristic
131C2×M16×C61D411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139#97×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—41no—
149C2×D244C2×D411yescharacteristic
150C2×C4×D61—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—41no—
156C2×Dic122—82no—
157C2×Dic122C2×D411yescharacteristic
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—81no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61#4111yescharacteristic
172C42×C61C2411yescharacteristic
173C22⋊Dic61—21no—
174C22⋊Dic61—41no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—41no—
188C4⋊Dic61—41no—
189C4⋊Dic61C2×D411yescharacteristic
190C4⋊Dic61C2×D411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201Dic244—81no—
202#11758190—81no—
203#11758189—42no—
204C8×D61—42no—
205C23×C61#12111yescharacteristic
206C22×D61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61#12111yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C22⋊D61—81no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—82no—
227D244—21no—
228D244—21no—
229C4×D61—41no—
230C4×D61—41no—
231Dic122—21no—
232Dic122—21no—
233Dic122—41no—
234Dic122—41no—
235Dic122—82no—
236Dic122—81no—
237Dic122—81no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61#13712yes—
246C8×C61#13712yes—
247#92418—41no—
248#92418—41no—
249#19379—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61C2×#12111yescharacteristic
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61C2×#13711yescharacteristic
262C4×C61C2×#13711yescharacteristic
263C4×C61#57711yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—41no—
266Dic61—41no—
267Dic61—41no—
268Dic61—81no—
269Dic61—81no—
270Dic61—81no—
271Dic61—81no—
272#3252—611no—
273#3238—611no—
274#3165—611no—
275#2969—611no—
276#1696—611no—
277#1695—611no—
278#1692—611no—
279#1691—611no—
280#1676—611no—
281#1675—611no—
282#1672—611no—
283#1671—611no—
284#1569D6111yescharacteristic, complemented
285#1554—611no—
286#1548—611no—
287C2×C61—41no—
288C2×C61#303911yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61#306811yescharacteristic
291D61—81no—
292#533—611no—
293C2×C4⋊Q8—611no—
294#529—611no—
295#501—1221no—
296#501—1221no—
297#501—1221no—
298#500—611no—
299#500—611no—
300#498—611no—
301#498—611no—
302#489—1221no—
303#483—1221no—
304#480—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#477—611no—
309#476—611no—
310#476—611no—
311#476—611no—
312#470—1221no—
313#468—1221no—
314#464—1221no—
315#462—611no—
316#461—611no—
317#446—611no—
318C8×Q8—611no—
319#436—611no—
320#436—1221no—
321#435—1221no—
322C8×D4—611no—
323#433—1221no—
324#432C2×D6111yescharacteristic
325#431—611no—
326#428—1221no—
327#428—1221no—
328#423C2×D6111yescharacteristic
329#405—1221no—
330C4×M16C2×D6111yescharacteristic
331#335C2×D6111yescharacteristic
332#335C2×D6111yescharacteristic
333#334C2×D6111yescharacteristic
334#334C2×D6111yescharacteristic
335#333—611no—
336#333—611no—
337#333—611no—
338#333—611no—
339#333—611no—
340#333—611no—
341#332—611no—
342#332—611no—
343C61#1937911yescharacteristic, complemented, Sylow
344C22×Q8—1221no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—21no—
348C2×M16—1221no—
349C2×M16D24411yescharacteristic
350C2×M16D24411yescharacteristic
351C22×C8—1221no—
352C4⋊Q8—611no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8—1221no—
359#126—1221no—
360#125—611no—
361#125—1221no—
362#124—611no—
363#123—1221no—
364C22⋊Q8—611no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367#121—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×D4—611no—
372C4×D4—1221no—
373#117—1221no—
374#117—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C42C22×D6111yescharacteristic
378#107—1221no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392C4⋊C8—21no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#102—1221no—
407#102—1221no—
408#102—1221no—
409C22⋊C8—21no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—1221no—
415#97D24411yescharacteristic
416#97D24411yescharacteristic
417C4×C8—1221no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C2×Q8—611no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—4882no—
427C2×Q8—2441no—
428C2×D4—611no—
429C2×D4—1221no—
430C22×C4—1221no—
431C22×C4—2441no—
432C22×C4C2×D24411yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4#1175822611yescharacteristic
435Q16—4881no—
436SD16—4881no—
437M16—22no—
438M16—22no—
439M16—81no—
440M16—2442no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—2442no—
448C2×C8C2×D24411yescharacteristic
449C2×C8C2×D24411yescharacteristic
450C2×C8C2×D24411yescharacteristic
451C2×C8C2×D24411yescharacteristic
452C4⋊C4—611no—
453C4⋊C4—611no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—2441no—
476C42—1221no—
477C42—2441no—
478C42C2×D24411yescharacteristic
479C42D4×D6111yescharacteristic
480C42#1175822611yescharacteristic
481C42C23×D6111yescharacteristic
482C23—1221no—
483C23#1451975211yescharacteristic
484Q8—1221no—
485Q8—1221no—
486Q8—4881no—
487Q8—4881no—
488Q8—4881no—
489Q8—4882no—
490Q8—2441no—
491Q8—2441no—
492D4—1221no—
493D4—1221no—
494D4—4881no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—4882no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4#1451975211yescharacteristic
511C2×C4#1451975211yescharacteristic
512C2×C4#1451975211yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×D24411yescharacteristic
515C2×C4C2×#1175822611yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—2441no—
523C8—2441no—
524C8#1451981012yes—
525C8#1451981012yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—2441no—
530C22—2441no—
531C22—2441no—
532C22C2×#1451975211yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—4881no—
538C4—4881no—
539C4—4881no—
540C4—4881no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4C2×#1451981011yescharacteristic
545C4C2×#1451981011yescharacteristic
546C4#1684057211yescharacteristic
547C4#1684057811yescharacteristic
548C2—41no—
549C2—4881no—
550C2#2145530711yescharacteristic
551C2#2145551111yescharacteristic
552C2#2145554811yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1569C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1569D61
hypocenterC61#19379
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #21456365C2semidirect
5. #21445348C2semidirect
6. #21445343C2semidirect
7. #21445326C2semidirect
8. #21445319C2semidirect
9. #21445224C2semidirect
10. #21445219C2semidirect
11. #21445202C2semidirect
12. #21445195C2semidirect
13. #21444530C2semidirect
14. #21444501C2semidirect
15. C61×#1569C2semidirect
284. #1569D61semidirect
343. C61#19379semidirect

Maximal subgroups

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

subgroupindex
#214571932
#214570422
#214563652
#214548232
#214453482
#214453432
#214453262
#214453192
#214452242
#214452192
#214452022
#214451952
#214445302
#214445012
C61×#15692
#1937961