Finite Group Databasebeta

← #29665525

Subgroups — #29665525

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456980C211yesmaximal, characteristic, complemented
2#21455981C211yesmaximal, characteristic
3#21455890C211yesmaximal, characteristic
4#21445277C211yesmaximal, characteristic, complemented
5#21445270C211yesmaximal, characteristic, complemented
6#21445249C211yesmaximal, characteristic, complemented
7#21445242C211yesmaximal, characteristic, complemented
8#21445213C211yesmaximal, characteristic, complemented
9#21445208C211yesmaximal, characteristic, complemented
10#21445201C211yesmaximal, characteristic, complemented
11#21445194C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444517C211yesmaximal, characteristic, complemented
14#21444477C211yesmaximal, characteristic, complemented
15C61×#2988C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840319C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840160C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840104—21no—
23#16840104—21no—
24#16840103—21no—
25#16840103—21no—
26#16840070—21no—
27#16840070—21no—
28#16840057C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16839972C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839924—21no—
37#16839924—21no—
38#16839867—21no—
39#16839862—21no—
40C4×#11758202—21no—
41C4×#11758200—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839507C2211yescharacteristic
55#16839507C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C8×D4×C61—21no—
60C8×D4×C61—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#431—21no—
64C61×#431C2211yescharacteristic
65C2×C4⋊C8×C61—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519769—21no—
76#14519769—21no—
77#14519756—21no—
78#14519756—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85#14519736—21no—
86#14519736—21no—
87#14519711—21no—
88#14519711—21no—
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519702—21no—
100#14519702—21no—
101#14519702—21no—
102#14519702—21no—
103#14519701—21no—
104#14519701—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700—21no—
109#14519698—21no—
110#14519698—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519688—21no—
114C4×#92418—21no—
115C2×#41×C61D411yescharacteristic
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61—21no—
119C4×Q8×C61D411yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61D411yescharacteristic
124C4×D4×C61C2311yescharacteristic
125#117×C61—21no—
126#117×C61D411yescharacteristic
127C2×C42×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
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
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—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—81no—
162C2×C8×C61—81no—
163C2×C8×C61—81no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C42×C61#4111yescharacteristic
181C42×C61C2411yescharacteristic
182C22⋊Dic61—41no—
183C22⋊Dic61—41no—
184#11758202—42no—
185#11758202—42no—
186#11758200—42no—
187#11758200—42no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—41no—
201C4×Dic61—41no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C23×C61—21no—
207C23×C61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61#13512yes—
210D4×C61—24no—
211D4×C61—21no—
212D4×C61#13512yes—
213C2×C4×C61—24no—
214C2×C4×C61—21no—
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—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—81no—
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#19418—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—22no—
256C22×C61—21no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C2×#12111yescharacteristic
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—22no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61C2×#13511yescharacteristic
268C4×C61C2×#13511yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—81no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275#3231—611no—
276#3116—611no—
277#3107—611no—
278#2988D6111yescharacteristic
279#1684—611no—
280#1683—611no—
281#1680—611no—
282#1679—611no—
283#1674—611no—
284#1673—611no—
285#1672—611no—
286#1671—611no—
287#1572—611no—
288#1552—611no—
289#1542—611no—
290C2×C61—41no—
291C2×C61—42no—
292C2×C61#304611yescharacteristic
293C2×C61#305011yescharacteristic
294C2×C61#306911yescharacteristic
295#533—611no—
296#533—611no—
297C4×#41C2×D6111yescharacteristic
298#500—611no—
299#498—611no—
300#487—611no—
301#487—611no—
302#485—1221no—
303#485—1221no—
304#485—1221no—
305#485—1221no—
306#479—1221no—
307#479—1221no—
308#477—611no—
309#476—611no—
310#475—611no—
311#474—611no—
312#462—611no—
313#462—611no—
314#461—611no—
315#461—611no—
316#452—1221no—
317#452—1221no—
318C8×Q8C2×D6111yescharacteristic
319C8×Q8C2×D6111yescharacteristic
320#441—1221no—
321#440—1221no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324C8×D4—21no—
325C8×D4—21no—
326C8×D4C2×D6111yescharacteristic
327C8×D4C2×D6111yescharacteristic
328#432—611no—
329#431—21no—
330#431—611no—
331#431C2×D6111yescharacteristic
332C2×C4⋊C8—21no—
333C2×C4⋊C8C2×D6111yescharacteristic
334#335—611no—
335#335—611no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346C61#1941811yescharacteristic, complemented, Sylow
347C2×#41D24411yescharacteristic
348C2×Q16—1221no—
349C2×Q16—1221no—
350C2×SD16—1221no—
351C2×SD16—1221no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360#125—1221no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8D24411yescharacteristic
370C4×Q8C22×D6111yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D24411yescharacteristic
374C4×D4C22×D6111yescharacteristic
375#117—21no—
376#117—1221no—
377#117—1221no—
378#117D24411yescharacteristic
379C2×C42—21no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8C22⋊D6111yescharacteristic
397C4⋊C8C22⋊D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
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#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8C22⋊D6111yescharacteristic
417C22⋊C8C22⋊D6111yescharacteristic
418#97—1221no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424#41—22no—
425#41—22no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8C2×D24411yescharacteristic
431C2×D4—21no—
432C2×D4C2×D24411yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D24411yescharacteristic
437C22×C4#1175822211yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439Q16—2442no—
440Q16—2442no—
441SD16—2442no—
442SD16—2442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8C2×C22⋊D6111yescharacteristic
453C2×C8C2×C22⋊D6111yescharacteristic
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
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—
470C4⋊C4C2×D24411yescharacteristic
471C4⋊C4C2×D24411yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—2441no—
476C22⋊C4—2441no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—2441no—
481C42—2441no—
482C42C2×D24411yescharacteristic
483C42#1175822211yescharacteristic
484C42C2×C22⋊D6111yescharacteristic
485C42C23×D6111yescharacteristic
486C23—21no—
487C23#1451975111yescharacteristic
488Q8—21no—
489Q8—4881no—
490Q8—2441no—
491Q8—2441no—
492Q8—2441no—
493Q8—2441no—
494Q8—2441no—
495Q8—2441no—
496Q8#1451979912yes—
497D4—24no—
498D4—21no—
499D4#1451979912yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451975111yescharacteristic
517C2×C4#1451975111yescharacteristic
518C2×C4#1451975111yescharacteristic
519C2×C4C22×C22⋊D6111yescharacteristic
520C2×C4C22×D24411yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22C2×#1451975111yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—4881no—
547C4—4881no—
548C4—4881no—
549C4—4881no—
550C4C2×#1451979911yescharacteristic
551C4C2×#1451979911yescharacteristic
552C4#1684057311yescharacteristic
553C4#1684057711yescharacteristic
554C2—41no—
555C2—42no—
556C2#2145536911yescharacteristic
557C2#2145540011yescharacteristic
558C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2988C2
socleC22×C61C2×#121
prime radicalC2×#41×C61D4
hypercenter#2988D61
hypocenterC61#19418
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #21456980C2semidirect
4. #21445277C2semidirect
5. #21445270C2semidirect
6. #21445249C2semidirect
7. #21445242C2semidirect
8. #21445213C2semidirect
9. #21445208C2semidirect
10. #21445201C2semidirect
11. #21445194C2semidirect
12. #21444599C2semidirect
13. #21444517C2semidirect
14. #21444477C2semidirect
346. C61#19418semidirect

Maximal subgroups

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

subgroupindex
#214569802
#214559812
#214558902
#214452772
#214452702
#214452492
#214452422
#214452132
#214452082
#214452012
#214451942
#214445992
#214445172
#214444772
C61×#29882
#1941861