Finite Group Databasebeta

← #29667597

Subgroups — #29667597

Order 15616.

568 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#21457157C211yesmaximal, characteristic
2#21457042C211yesmaximal, characteristic
3#21456965C211yesmaximal, characteristic, complemented
4#21454981C211yesmaximal, characteristic
5#21445402C211yesmaximal, characteristic, complemented
6#21445395C211yesmaximal, characteristic, complemented
7#21445326C211yesmaximal, characteristic, complemented
8#21445319C211yesmaximal, characteristic, complemented
9#21445278C211yesmaximal, characteristic, complemented
10#21445271C211yesmaximal, characteristic, complemented
11#21445202C211yesmaximal, characteristic, complemented
12#21445195C211yesmaximal, characteristic, complemented
13#21444520C211yesmaximal, characteristic, complemented
14C2×#16839510C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840296C2211yescharacteristic
19#16840171—21no—
20#16840160C2211yescharacteristic
21#16840160C2211yescharacteristic
22#16840122—21no—
23#16840113C2211yescharacteristic
24#16840113C2211yescharacteristic
25#16840093—21no—
26#16840093—21no—
27#16840093—21no—
28#16840076—21no—
29#16840070—21no—
30#16840058C2211yescharacteristic
31#16840058C2211yescharacteristic
32#16840053C2211yescharacteristic
33#16840053C2211yescharacteristic
34#16840048—21no—
35#16840048—21no—
36#16840048C2211yescharacteristic
37#16840043C2211yescharacteristic
38#16840003—21no—
39#16839991—21no—
40#16839985—21no—
41#16839973C2211yescharacteristic
42#16839968C2211yescharacteristic
43#16839892C2211yescharacteristic
44C8×Dic122C2211yescharacteristic
45#16839841C2211yescharacteristic
46#16839830—21no—
47C8×D244C2211yescharacteristic
48#16839825—21no—
49#16839822—21no—
50#16839787—21no—
51C2×C4⋊#92418C2211yescharacteristic
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839510C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C22×Dic122—21no—
68C2×Dic244—21no—
69C2×#11758190—21no—
70C2×#11758189—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519771—21no—
81#14519769—21no—
82#14519769D411yescharacteristic
83#14519765D411yescharacteristic
84#14519760—21no—
85#14519756—21no—
86#14519756—21no—
87#14519756D411yescharacteristic
88#14519751D411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122C2311yescharacteristic
92C4×D244C2311yescharacteristic
93C4×C22⋊D61—21no—
94#14519736—21no—
95#14519734—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98#14519711—21no—
99#14519711—21no—
100#14519711—21no—
101#14519709—21no—
102#14519709—21no—
103#14519709—21no—
104#14519709—21no—
105#14519709—21no—
106#14519709—21no—
107#14519709—21no—
108C4⋊#92418—21no—
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519702—21no—
120#14519702—21no—
121#14519702—21no—
122#14519699—21no—
123#14519699—21no—
124#14519699—21no—
125#14519689—21no—
126#14519689—21no—
127#14519687—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141#97×C61—21no—
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
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—41no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—41no—
186C4⋊Dic61—41no—
187C4⋊Dic61C2×D411yescharacteristic
188C4⋊Dic61C2×D411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—41no—
194#11758196—41no—
195C4×Dic61—21no—
196C4×Dic61—41no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200Dic244—81no—
201#11758190—81no—
202#11758189—81no—
203C8×D61—81no—
204C23×C61#12111yescharacteristic
205C22×D61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61#12111yescharacteristic
212C2×C4×C61#12111yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C22⋊D61—42no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—82no—
226D244—21no—
227D244—21no—
228C4×D61—41no—
229C4×D61—41no—
230Dic122—21no—
231Dic122—21no—
232Dic122—41no—
233Dic122—41no—
234Dic122—41no—
235Dic122—41no—
236Dic122—82no—
237Dic122—81no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—41no—
248#92418—41no—
249#19588—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61#47112yes—
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×C61#57711yescharacteristic
262C4×C61#57711yescharacteristic
263C4×C61#57811yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—41no—
266Dic61—41no—
267Dic61—41no—
268Dic61—81no—
269Dic61—81no—
270Dic61—81no—
271Dic61—81no—
272#3248—611no—
273#3238—611no—
274#3229—611no—
275#2994—611no—
276#1704—611no—
277#1703—611no—
278#1692—611no—
279#1691—611no—
280#1684—611no—
281#1683—611no—
282#1672—611no—
283#1671—611no—
284#1573D6111yescharacteristic, complemented
285#1552—611no—
286C2×#333—611no—
287C2×C61—22no—
288C2×C61#304611yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61C2×#47111yescharacteristic
291D61—81no—
292#533—611no—
293C2×C4⋊Q8—611no—
294#529—611no—
295#501—1221no—
296#498—611no—
297#498—611no—
298#489—1221no—
299#487—611no—
300#487—611no—
301#483—1221no—
302#483—1221no—
303#483—1221no—
304#480—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#476—611no—
309#476—611no—
310#475—611no—
311#475—1221no—
312#475—1221no—
313#474—611no—
314#467—1221no—
315#465—1221no—
316#464—1221no—
317#462—611no—
318#461—611no—
319#446—611no—
320C8×Q8—611no—
321#436—611no—
322#435—1221no—
323C8×D4—611no—
324C8×D4—1221no—
325#433—1221no—
326#432C2×D6111yescharacteristic
327#431C2×D6111yescharacteristic
328#424—1221no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8C2×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#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343C61#1958811yescharacteristic, complemented, Sylow
344C22×Q8—1221no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—1221no—
348C22×C8—21no—
349C22×C8—1221no—
350C22×C8—1221no—
351C4⋊Q8—611no—
352C4⋊Q8—611no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358#126—1221no—
359#125—611no—
360#125—1221no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364C22⋊Q8—1221no—
365C22⋊Q8—1221no—
366#121—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×D4—611no—
371C4×D4—1221no—
372#117—1221no—
373#117—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#106—1221no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—21no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8D24411yescharacteristic
394C4⋊C8D24411yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#102—1221no—
409#102—1221no—
410#102—1221no—
411C22⋊C8—21no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8D24411yescharacteristic
415C22⋊C8D24411yescharacteristic
416#97—21no—
417#97—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—4881no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—81no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—4881no—
446C2×C8—4881no—
447C2×C8C2×D24411yescharacteristic
448C2×C8C2×D24411yescharacteristic
449C2×C8C2×D24411yescharacteristic
450C2×C8C2×D24411yescharacteristic
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
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—2441no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—2441no—
475C42—1221no—
476C42—2441no—
477C42C2×D24411yescharacteristic
478C42D4×D6111yescharacteristic
479C42#1175822611yescharacteristic
480C42C23×D6111yescharacteristic
481C23—1221no—
482C23#1451975211yescharacteristic
483Q8—1221no—
484Q8—1221no—
485Q8—4881no—
486Q8—4881no—
487Q8—4882no—
488Q8—2441no—
489Q8—2441no—
490Q8—2441no—
491Q8—2441no—
492D4—1221no—
493D4—1221no—
494D4—2442no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
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—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—2441no—
525C8—2441no—
526C22—21no—
527C22—21no—
528C22—2441no—
529C22—2441no—
530C22—2441no—
531C22#1684002612yes—
532C22C2×#1451975211yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—4881no—
538C4—4881no—
539C4—4881no—
540C4—4881no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4#1684057211yescharacteristic
545C4#1684057411yescharacteristic
546C4#1684057811yescharacteristic
547C4#1684057911yescharacteristic
548C2—22no—
549C2—4881no—
550C2#2145537111yescharacteristic
551C2#2145551111yescharacteristic
552C2C2×#1684002611yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1573D61
hypocenterC61#19588
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #21456965C2semidirect
5. #21445402C2semidirect
6. #21445395C2semidirect
7. #21445326C2semidirect
8. #21445319C2semidirect
9. #21445278C2semidirect
10. #21445271C2semidirect
11. #21445202C2semidirect
12. #21445195C2semidirect
13. #21444520C2semidirect
14. C2×#16839510C2semidirect
15. C61×#1573C2semidirect
284. #1573D61semidirect
343. C61#19588semidirect

Maximal subgroups

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

subgroupindex
#214571572
#214570422
#214569652
#214549812
#214454022
#214453952
#214453262
#214453192
#214452782
#214452712
#214452022
#214451952
#214445202
C2×#168395102
C61×#15732
#1958861