Finite Group Databasebeta

← #29667580

Subgroups — #29667580

Order 15616.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457192C211yesmaximal, characteristic
2#21456994C211yesmaximal, characteristic
3#21456980C211yesmaximal, characteristic, complemented
4#21445394C211yesmaximal, characteristic, complemented
5#21445373C211yesmaximal, characteristic, complemented
6#21445347C211yesmaximal, characteristic, complemented
7#21445318C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445242C211yesmaximal, characteristic, complemented
10#21445218C211yesmaximal, characteristic, complemented
11#21445201C211yesmaximal, characteristic, complemented
12#21444608C211yesmaximal, characteristic, complemented
13#21444507C211yesmaximal, characteristic, complemented
14#21444477C211yesmaximal, characteristic, complemented
15C61×#2994C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840319C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840161—21no—
20#16840160C2211yescharacteristic
21#16840116—21no—
22#16840113C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840104—21no—
25#16840104—21no—
26#16840100—21no—
27#16840083—21no—
28#16840070—21no—
29#16840070—21no—
30#16840066—21no—
31#16840057C2211yescharacteristic
32#16840057C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840052C2211yescharacteristic
35#16840047C2211yescharacteristic
36#16840042C2211yescharacteristic
37#16840018—21no—
38#16840006—21no—
39#16839981—21no—
40#16839972C2211yescharacteristic
41#16839967C2211yescharacteristic
42#16839815C2211yescharacteristic
43#16839786C2211yescharacteristic
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
67C2×#11758202—21no—
68C2×#11758200—21no—
69C2×#11758194—21no—
70#14519777C2311yescharacteristic
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519769—21no—
75#14519769—21no—
76#14519756—21no—
77#14519756—21no—
78#14519756—21no—
79#14519756—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84#14519736—21no—
85#14519736—21no—
86#14519711—21no—
87#14519711—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—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—
114C4×#92418—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
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155M16×C61—81no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—81no—
159C2×C8×C61—81no—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61C2×D411yescharacteristic
169C4⋊C4×C61C2×D411yescharacteristic
170C22⋊C4×C61—21no—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—41no—
181C22⋊Dic61—41no—
182#11758202—81no—
183#11758200—81no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—41no—
197C4×Dic61—41no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C23×C61—21no—
204C23×C61#12111yescharacteristic
205Q8×C61—21no—
206Q8×C61—21no—
207D4×C61—21no—
208D4×C61—21no—
209D4×C61—42no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230Dic122—41no—
231Dic122—41no—
232Dic122—41no—
233Dic122—41no—
234Dic122—81no—
235Dic122—81no—
236C8×C61—21no—
237C8×C61—21no—
238C8×C61—21no—
239C8×C61—21no—
240C8×C61—41no—
241C8×C61—41no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#19587—611nomaximal, Sylow
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61C2×#12111yescharacteristic
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61#57711yescharacteristic
262C4×C61#57711yescharacteristic
263C4×C61#57811yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—81no—
266Dic61—81no—
267Dic61—81no—
268Dic61—81no—
269#3252—611no—
270#3233—611no—
271#3231—611no—
272#2994D6111yescharacteristic
273#1703—611no—
274#1700—611no—
275#1696—611no—
276#1691—611no—
277#1684—611no—
278#1679—611no—
279#1675—611no—
280#1672—611no—
281#1574—611no—
282#1550—611no—
283#1542—611no—
284C2×C61—41no—
285C2×C61—81no—
286C2×C61#304611yescharacteristic
287C2×C61#306311yescharacteristic
288C2×C61#306711yescharacteristic
289#533—611no—
290#533—611no—
291#529C2×D6111yescharacteristic
292#500—611no—
293#499—1221no—
294#498—611no—
295#488—1221no—
296#487—611no—
297#487—611no—
298#485—1221no—
299#485—1221no—
300#485—1221no—
301#482—1221no—
302#479—1221no—
303#479—1221no—
304#479—1221no—
305#477—611no—
306#477—611no—
307#476—611no—
308#476—611no—
309#475—611no—
310#474—611no—
311#470—1221no—
312#468—1221no—
313#464—1221no—
314#462—611no—
315#461—611no—
316#446C2×D6111yescharacteristic
317C8×Q8C2×D6111yescharacteristic
318#436C2×D6111yescharacteristic
319#435—21no—
320C8×D4—21no—
321C8×D4C2×D6111yescharacteristic
322#433—21no—
323#431—611no—
324#431C2×D6111yescharacteristic
325#424—21no—
326#423—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328#335—611no—
329#335—611no—
330#334—611no—
331#334—611no—
332#333—611no—
333#333—611no—
334#333—611no—
335#333—611no—
336#332—611no—
337#332—611no—
338#332—611no—
339#332—611no—
340C61#1958711yescharacteristic, complemented, Sylow
341C2×Q16—1221no—
342C2×SD16—1221no—
343C2×M16—21no—
344C2×M16—1221no—
345C22×C8—21no—
346C22×C8—21no—
347C4⋊Q8—611no—
348C4⋊Q8—611no—
349C4⋊Q8—611no—
350C4⋊Q8—611no—
351#126—21no—
352#125—1221no—
353#125—1221no—
354#125D24411yescharacteristic
355#124D24411yescharacteristic
356#123—21no—
357C22⋊Q8—1221no—
358C22⋊Q8—1221no—
359C22⋊Q8—1221no—
360C22⋊Q8—1221no—
361C22⋊Q8D24411yescharacteristic
362#121D24411yescharacteristic
363C4×Q8—1221no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D6111yescharacteristic
370#117—21no—
371#117—1221no—
372#117—1221no—
373C2×C42C22×D6111yescharacteristic
374#107—1221no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#106—1221no—
380#106—1221no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8C22⋊D6111yescharacteristic
393C4⋊C8C22⋊D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#102—1221no—
406#102—1221no—
407#102—1221no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C4×C8C22×D6111yescharacteristic
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8C2×D24411yescharacteristic
423C2×D4—21no—
424C2×D4C2×D24411yescharacteristic
425C22×C4—21no—
426C22×C4C2×D24411yescharacteristic
427C22×C4#1175822211yescharacteristic
428C22×C4C2×C22⋊D6111yescharacteristic
429Q16—4881no—
430SD16—4881no—
431M16—81no—
432M16—4881no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—81no—
436C2×C8—81no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8C2×C22⋊D6111yescharacteristic
442C2×C8C2×C22⋊D6111yescharacteristic
443C2×C8C2×C22⋊D6111yescharacteristic
444C2×C8C2×C22⋊D6111yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—1221no—
450C4⋊C4—1221no—
451C4⋊C4—1221no—
452C4⋊C4—1221no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—2441no—
458C4⋊C4—2441no—
459C4⋊C4—2441no—
460C4⋊C4—2441no—
461C4⋊C4C2×D24411yescharacteristic
462C4⋊C4C2×D24411yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—2441no—
469C22⋊C4—2441no—
470C42—21no—
471C42—2441no—
472C42—2441no—
473C42C2×D24411yescharacteristic
474C42#1175822211yescharacteristic
475C42C2×C22⋊D6111yescharacteristic
476C42C23×D6111yescharacteristic
477C23—21no—
478C23#1451975111yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—4881no—
482Q8—4881no—
483Q8—2441no—
484Q8—2441no—
485Q8—2441no—
486Q8—2441no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4#1451975111yescharacteristic
505C2×C4#1451975111yescharacteristic
506C2×C4#1451975111yescharacteristic
507C2×C4C22×C22⋊D6111yescharacteristic
508C2×C4C22×D24411yescharacteristic
509C2×C4C2×#1175822211yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—2441no—
517C8—2441no—
518C8—2441no—
519C8—2441no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#1451975111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—4881no—
535C4—4881no—
536C4—4881no—
537C4—4881no—
538C4#1684057311yescharacteristic
539C4#1684057411yescharacteristic
540C4#1684057711yescharacteristic
541C4#1684057911yescharacteristic
542C2—41no—
543C2—81no—
544C2#2145536911yescharacteristic
545C2#2145551011yescharacteristic
546C2#2145553911yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2994C2
socleC22×C61C2×#121
prime radical#121×C61D4
hypercenter#2994D61
hypocenterC61#19587
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. #21456980C2semidirect
4. #21445394C2semidirect
5. #21445373C2semidirect
6. #21445347C2semidirect
7. #21445318C2semidirect
8. #21445277C2semidirect
9. #21445242C2semidirect
10. #21445218C2semidirect
11. #21445201C2semidirect
12. #21444608C2semidirect
13. #21444507C2semidirect
14. #21444477C2semidirect
340. C61#19587semidirect

Maximal subgroups

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

subgroupindex
#214571922
#214569942
#214569802
#214453942
#214453732
#214453472
#214453182
#214452772
#214452422
#214452182
#214452012
#214446082
#214445072
#214444772
C61×#29942
#1958761