Finite Group Databasebeta

← #29663062

Subgroups — #29663062

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456564C211yesmaximal, characteristic, complemented
2#21455890C211yesmaximal, characteristic
3#21455607C211yesmaximal, characteristic
4#21445394C211yesmaximal, characteristic, complemented
5#21445366C211yesmaximal, characteristic, complemented
6#21445318C211yesmaximal, characteristic, complemented
7#21445308C211yesmaximal, characteristic, complemented
8#21445277C211yesmaximal, characteristic, complemented
9#21445249C211yesmaximal, characteristic, complemented
10#21445201C211yesmaximal, characteristic, complemented
11#21445189C211yesmaximal, characteristic, complemented
12#21444571C211yesmaximal, characteristic, complemented
13#21444530C211yesmaximal, characteristic, complemented
14#21444520C211yesmaximal, characteristic, complemented
15C61×#2971C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840319C2211yescharacteristic
18#16840160C2211yescharacteristic
19#16840142C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840103—21no—
23#16840069—21no—
24#16840062—21no—
25#16840057C2211yescharacteristic
26#16840052C2211yescharacteristic
27#16840047C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840042C2211yescharacteristic
31#16840020—21no—
32#16840020—21no—
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839924—21no—
36#16839870—21no—
37#16839870—21no—
38C4×#11758202—21no—
39C4×#11758200—21no—
40#16839815C2211yescharacteristic
41#16839798—21no—
42C2×C4⋊#92418C2211yescharacteristic
43#16839758—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436—21no—
61C61×#436C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#432—21no—
64C61×#432C2211yescharacteristic
65C4×M16×C61—21no—
66C4×M16×C61C2211yescharacteristic
67C2×Dic244—21no—
68C2×Dic244—21no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519769—21no—
77#14519769—21no—
78#14519756—21no—
79#14519756—21no—
80#14519756—21no—
81#14519756—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86#14519736—21no—
87#14519736—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×#41×C61D411yescharacteristic
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61D411yescharacteristic
119C2×M16×C61D411yescharacteristic
120C4×Q8×C61D411yescharacteristic
121C4×Q8×C61C2311yescharacteristic
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61D411yescharacteristic
125C4×D4×C61C2311yescharacteristic
126#117×C61—21no—
127#117×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61—21no—
138#97×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159M16×C61—22no—
160M16×C61—41no—
161M16×C61—42no—
162M16×C61—42no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
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—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185#11758202—42no—
186#11758200—42no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195#11758196—41no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—41no—
200C4×Dic61—41no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206Dic244—42no—
207Dic244—42no—
208C23×C61—21no—
209C23×C61#12111yescharacteristic
210Q8×C61—21no—
211Q8×C61#13712yes—
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—42no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—42no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—81no—
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—41no—
242Dic122—41no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61#13512yes—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#19185—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×#12111yescharacteristic
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—22no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61C2×#13511yescharacteristic
270C4×C61C2×#13711yescharacteristic
271C4×C61#57511yescharacteristic
272C4×C61#57511yescharacteristic
273Dic61—81no—
274Dic61—81no—
275Dic61—81no—
276Dic61—81no—
277#3185—611no—
278#3107—611no—
279#3076—611no—
280#2971D6111yescharacteristic
281#1703—611no—
282#1699—611no—
283#1691—611no—
284#1689—611no—
285#1684—611no—
286#1680—611no—
287#1672—611no—
288#1670—611no—
289#1565—611no—
290#1554—611no—
291#1552—611no—
292C2×C61—41no—
293C2×C61—81no—
294C2×C61#303511yescharacteristic
295C2×C61#305611yescharacteristic
296C2×C61#306911yescharacteristic
297#533—611no—
298#533—611no—
299C4×#41C2×D6111yescharacteristic
300#498—611no—
301#494—611no—
302#487—611no—
303#487—611no—
304#485—1221no—
305#479—1221no—
306#478—1221no—
307#477—611no—
308#476—611no—
309#475—611no—
310#475—611no—
311#474—611no—
312#474—611no—
313#470—1221no—
314#470—1221no—
315#462—611no—
316#461—611no—
317#452—1221no—
318C8×Q8C2×D6111yescharacteristic
319C8×Q8C2×D6111yescharacteristic
320#441—1221no—
321#441—1221no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324#436—21no—
325#436—21no—
326#436C2×D6111yescharacteristic
327#436C2×D6111yescharacteristic
328#432—21no—
329#432C2×D6111yescharacteristic
330#431—611no—
331#427—1221no—
332C2×C4⋊C8—611no—
333#416—1221no—
334C4×M16—21no—
335C4×M16C2×D6111yescharacteristic
336#335—611no—
337#335—611no—
338#334—611no—
339#334—611no—
340#333—611no—
341#333—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348C61#1918511yescharacteristic, complemented, Sylow
349C2×#41D24411yescharacteristic
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16—1221no—
353C2×SD16—1221no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16C22⋊D6111yescharacteristic
357C2×M16C22⋊D6111yescharacteristic
358C22×C8—1221no—
359C4⋊Q8—611no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363#125—1221no—
364#125—1221no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C22⋊Q8—1221no—
368C22⋊Q8—1221no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8D24411yescharacteristic
374C4×Q8C22×D6111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4D24411yescharacteristic
378C4×D4C22×D6111yescharacteristic
379#117—21no—
380#117—1221no—
381#117—1221no—
382#117D24411yescharacteristic
383C2×C42—21no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#106—1221no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392#106—1221no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—1221no—
418#97—21no—
419#97C22⋊D6111yescharacteristic
420#97C22⋊D6111yescharacteristic
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—22no—
427#41—41no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8C2×D24411yescharacteristic
433C2×D4—21no—
434C2×D4C2×D24411yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D24411yescharacteristic
439C22×C4#1175822211yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441Q16—2442no—
442Q16—2442no—
443Q16—2442no—
444SD16—2442no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—42no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—2442no—
456C2×C8C2×C22⋊D6111yescharacteristic
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4C2×D24411yescharacteristic
475C4⋊C4C2×D24411yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—2441no—
485C42—2441no—
486C42C2×D24411yescharacteristic
487C42#1175822211yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—21no—
491C23#1451975111yescharacteristic
492Q8—21no—
493Q8—4881no—
494Q8—2441no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498Q8—2441no—
499Q8—2441no—
500Q8#1451981012yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4#1451975111yescharacteristic
521C2×C4#1451975111yescharacteristic
522C2×C4#1451975111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4C22×D24411yescharacteristic
525C2×C4C2×#1175822211yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8#1451979712yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×#1451975111yescharacteristic
543C4—21no—
544C4—22no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—4881no—
551C4—4881no—
552C4—4881no—
553C4—4881no—
554C4C2×#1451979711yescharacteristic
555C4C2×#1451981011yescharacteristic
556C4#1684056011yescharacteristic
557C4#1684056211yescharacteristic
558C2—41no—
559C2—81no—
560C2#2145527411yescharacteristic
561C2#2145544911yescharacteristic
562C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2971C2
socleC22×C61C2×#121
prime radicalC2×#41×C61D4
hypercenter#2971D61
hypocenterC61#19185
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #21456564C2semidirect
4. #21445394C2semidirect
5. #21445366C2semidirect
6. #21445318C2semidirect
7. #21445308C2semidirect
8. #21445277C2semidirect
9. #21445249C2semidirect
10. #21445201C2semidirect
11. #21445189C2semidirect
12. #21444571C2semidirect
13. #21444530C2semidirect
14. #21444520C2semidirect
348. C61#19185semidirect

Maximal subgroups

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

subgroupindex
#214565642
#214558902
#214556072
#214453942
#214453662
#214453182
#214453082
#214452772
#214452492
#214452012
#214451892
#214445712
#214445302
#214445202
C61×#29712
#1918561