Finite Group Databasebeta

← #29667595

Subgroups — #29667595

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#21457156C211yesmaximal, characteristic
2#21457037C211yesmaximal, characteristic
3#21456965C211yesmaximal, characteristic, complemented
4#21445401C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445325C211yesmaximal, characteristic, complemented
7#21445318C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445270C211yesmaximal, characteristic, complemented
10#21445201C211yesmaximal, characteristic, complemented
11#21445194C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444517C211yesmaximal, characteristic, complemented
14C2×#16839510C211yesmaximal, characteristic, complemented
15C61×#2994C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840172—21no—
19#16840160C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840121—21no—
22#16840113C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840093—21no—
25#16840093—21no—
26#16840090—21no—
27#16840073—21no—
28#16840066—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840052C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840048—21no—
34#16840048—21no—
35#16840047C2211yescharacteristic
36#16840042C2211yescharacteristic
37#16840001—21no—
38#16839989—21no—
39#16839981—21no—
40#16839972C2211yescharacteristic
41#16839967C2211yescharacteristic
42#16839819C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839510C2211yescharacteristic
51#16839510C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#435—21no—
61C8×D4×C61—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C22×#92418—21no—
71#14519777—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83#14519736—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519709—21no—
90#14519709—21no—
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519702—21no—
102#14519702—21no—
103#14519702—21no—
104#14519702—21no—
105#14519701—21no—
106#14519701—21no—
107#14519701—21no—
108#14519700—21no—
109#14519700—21no—
110#14519698—21no—
111#14519698—21no—
112#14519698—21no—
113C22⋊#92418—21no—
114#14519688—21no—
115C2×M16×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61D411yescharacteristic
120#124×C61D411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61D411yescharacteristic
123#121×C61D411yescharacteristic
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×C61C2×D411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×Dic61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—41no—
157C2×Dic122—82no—
158M16×C61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—81no—
162C2×C8×C61—81no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C42×C61—21no—
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184#11758202—81no—
185#11758200—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—41no—
195C4⋊Dic61—41no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C23×C61—21no—
205C23×C61#12111yescharacteristic
206Q8×C61—21no—
207Q8×C61—21no—
208D4×C61—21no—
209D4×C61—21no—
210D4×C61—42no—
211C2×C4×C61—22no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—82no—
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—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#19588—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61#47112yes—
256C22×C61C2×#12111yescharacteristic
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61#57711yescharacteristic
265C4×C61#57711yescharacteristic
266C4×C61#57811yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—81no—
269Dic61—81no—
270Dic61—81no—
271Dic61—81no—
272#3248—611no—
273#3238—611no—
274#3229—611no—
275#2994D6111yescharacteristic
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#1573—611no—
285#1552—611no—
286C2×#333—611no—
287C2×C61—22no—
288C2×C61—81no—
289C2×C61#304611yescharacteristic
290C2×C61#306311yescharacteristic
291C2×C61C2×#47111yescharacteristic
292#533—611no—
293C2×C4⋊Q8—611no—
294#529C2×D6111yescharacteristic
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#446C2×D6111yescharacteristic
320C8×Q8C2×D6111yescharacteristic
321#436C2×D6111yescharacteristic
322#435—21no—
323C8×D4—21no—
324C8×D4C2×D6111yescharacteristic
325#433—21no—
326#432—611no—
327#431C2×D6111yescharacteristic
328#424—21no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8C2×D6111yescharacteristic
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
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—21no—
348C22×C8—21no—
349C22×C8—21no—
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—21no—
359#125—1221no—
360#125D24411yescharacteristic
361#124D24411yescharacteristic
362#123—21no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C22⋊Q8D24411yescharacteristic
366#121D24411yescharacteristic
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8C22×D6111yescharacteristic
370C4×D4—21no—
371C4×D4C22×D6111yescharacteristic
372#117—21no—
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—21no—
389C4⋊C8—21no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
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—21no—
413C22⋊C8—1221no—
414C22⋊C8C22⋊D6111yescharacteristic
415C22⋊C8C22⋊D6111yescharacteristic
416#97—21no—
417#97—1221no—
418C4×C8—21no—
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—4882no—
426C2×Q8—2441no—
427C2×Q8C2×D24411yescharacteristic
428C2×D4—21no—
429C2×D4C2×D24411yescharacteristic
430C22×C4—21no—
431C22×C4—2441no—
432C22×C4C2×D24411yescharacteristic
433C22×C4#1175822211yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435Q16—4881no—
436SD16—4881no—
437M16—81no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—81no—
441C2×C8—81no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—4881no—
447C2×C8C2×C22⋊D6111yescharacteristic
448C2×C8C2×C22⋊D6111yescharacteristic
449C2×C8C2×C22⋊D6111yescharacteristic
450C2×C8C2×C22⋊D6111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
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—2441no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4C2×D24411yescharacteristic
468C4⋊C4C2×D24411yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—2441no—
475C42—21no—
476C42—2441no—
477C42C2×D24411yescharacteristic
478C42#1175822211yescharacteristic
479C42C2×C22⋊D6111yescharacteristic
480C42C23×D6111yescharacteristic
481C23—21no—
482C23#1451975111yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—4881no—
486Q8—4881no—
487Q8—4882no—
488Q8—2441no—
489Q8—2441no—
490Q8—2441no—
491Q8—2441no—
492D4—21no—
493D4—21no—
494D4—42no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—4882no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4#1451975111yescharacteristic
511C2×C4#1451975111yescharacteristic
512C2×C4#1451975111yescharacteristic
513C2×C4C22×C22⋊D6111yescharacteristic
514C2×C4C22×D24411yescharacteristic
515C2×C4C2×#1175822211yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—2441no—
523C8—2441no—
524C8—2441no—
525C8—2441no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22#1684002512yes—
532C22C2×#1451975111yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—4881no—
541C4—4881no—
542C4—4881no—
543C4—4881no—
544C4#1684057311yescharacteristic
545C4#1684057411yescharacteristic
546C4#1684057711yescharacteristic
547C4#1684057911yescharacteristic
548C2—22no—
549C2—81no—
550C2#2145536911yescharacteristic
551C2#2145551011yescharacteristic
552C2C2×#1684002511yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2994C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#2994D61
hypocenterC61#19588
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
3. #21456965C2semidirect
4. #21445401C2semidirect
5. #21445394C2semidirect
6. #21445325C2semidirect
7. #21445318C2semidirect
8. #21445277C2semidirect
9. #21445270C2semidirect
10. #21445201C2semidirect
11. #21445194C2semidirect
12. #21444604C2semidirect
13. #21444517C2semidirect
14. C2×#16839510C2semidirect
343. C61#19588semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214570372
#214569652
#214454012
#214453942
#214453252
#214453182
#214452772
#214452702
#214452012
#214451942
#214446042
#214445172
C2×#168395102
C61×#29942
#1958861