Finite Group Databasebeta

← #29670614

Subgroups — #29670614

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458466C211yesmaximal, characteristic
2#21458245C211yesmaximal, characteristic, complemented
3#21457695C211yesmaximal, characteristic, complemented
4#21445466C211yesmaximal, characteristic, complemented
5#21445401C211yesmaximal, characteristic, complemented
6#21445268C211yesmaximal, characteristic, complemented
7#21445246C211yesmaximal, characteristic, complemented
8#21445206C211yesmaximal, characteristic, complemented
9#21445088C211yesmaximal, characteristic, complemented
10#21445082C211yesmaximal, characteristic, complemented
11#21445024C211yesmaximal, characteristic, complemented
12#21444991C211yesmaximal, characteristic, complemented
13#21444667C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic
15C61×#3367C211yesmaximal, characteristic
16#16840482C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840115—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840103—21no—
25#16840100—21no—
26#16840095—21no—
27#16840068—21no—
28#16840057C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840044C2211yescharacteristic
32#16840001—21no—
33#16840001—21no—
34#16839975—21no—
35#16839969C2211yescharacteristic
36#16839967C2211yescharacteristic
37#16839918—21no—
38C8×Dic122C2211yescharacteristic
39C4×#11758202C2211yescharacteristic
40#16839853—21no—
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839798—21no—
44C2×#14519701—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#487C2211yescharacteristic
60C61×#477—21no—
61C61×#474C2211yescharacteristic
62C61×#463—21no—
63C61×#461C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×D8×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202D411yescharacteristic
69C2×#11758200—21no—
70C22×#92418—21no—
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519770—41no—
75#14519768—21no—
76#14519764—21no—
77#14519756—21no—
78#14519756—21no—
79#14519754—41no—
80C4×Dic122C2311yescharacteristic
81#14519742—21no—
82D4×Dic61—21no—
83#14519736—21no—
84C2×C4⋊Dic61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710D411yescharacteristic
89#14519708—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—41no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—21no—
107#14519700—41no—
108#14519700D411yescharacteristic
109#14519698—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×Q8×C61—21no—
116C2×SD16×C61—21no—
117C2×D8×C61D411yescharacteristic
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#126×C61—41no—
122#124×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C22×Dic61—41no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C2×D411yescharacteristic
159SD16×C61—42no—
160D8×C61—22no—
161C2×C8×C61—21no—
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×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C42×C61—21no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182C22⋊Dic61—41no—
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185#11758202—41no—
186#11758202—81no—
187#11758200—42no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—41no—
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—42no—
204C2×#92418—81no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C23×C61—21no—
208C23×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—82no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61#13512yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—82no—
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—161no—
239Dic122—21no—
240Dic122—21no—
241Dic122—41no—
242Dic122—41no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#19839—611nomaximal, Sylow
254C22×C61—22no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61D4211yescharacteristic
261C4×C61—21no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61C2×#13511yescharacteristic
269C4×C61#57511yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272Dic61—41no—
273Dic61—41no—
274Dic61—81no—
275Dic61—81no—
276#3367D6111yescharacteristic
277#3360—611no—
278#3342—611no—
279#3299—611no—
280#1718—611no—
281#1704—611no—
282#1683—611no—
283#1680—611no—
284#1673—611no—
285#1652—611no—
286#1651—611no—
287#1643—611no—
288#1638—611no—
289#1584—611no—
290#1580—611no—
291C2×C61—42no—
292C2×C61—81no—
293C2×C61#326711yescharacteristic
294C2×C61#328511yescharacteristic
295C2×C61#328911yescharacteristic
296#556—611no—
297#556C2×D6111yescharacteristic
298#554—611no—
299D4×Q8C2×D6111yescharacteristic
300#500—611no—
301#498—611no—
302#489—21no—
303#488—1221no—
304#487—611no—
305#487—611no—
306#487—611no—
307#487C2×D6111yescharacteristic
308#485—1221no—
309#485—1221no—
310#484—1221no—
311#479—1221no—
312#477—21no—
313#477—611no—
314#476—611no—
315#475—611no—
316#475—611no—
317#474C2×D6111yescharacteristic
318#467—1221no—
319#467—1221no—
320#463—21no—
321#463—1221no—
322#462—611no—
323#461—611no—
324#461C2×D6111yescharacteristic
325#451—1221no—
326#446C2×D6111yescharacteristic
327C8×Q8—611no—
328#440—21no—
329C4×Q16—611no—
330C4×SD16—1221no—
331C4×D8C2×D6111yescharacteristic
332C8×D4—611no—
333C8×D4—611no—
334#427—1221no—
335C2×#103—1221no—
336#335—611no—
337#334—611no—
338#333—611no—
339#332—611no—
340#332—611no—
341#332—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344D4⋊C8—611no—
345D4⋊C8—611no—
346#322—611no—
347C61#1983911yescharacteristic, complemented, Sylow
348C22×Q8—21no—
349C2×Q16—611no—
350C2×Q16—1221no—
351C2×SD16—21no—
352C2×SD16—1221no—
353C2×D8C22⋊D6111yescharacteristic
354C22×C8—1221no—
355C22×C8—1221no—
356C4⋊Q8—21no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359C4⋊Q8C22×D6111yescharacteristic
360C4⋊Q8C22×D6111yescharacteristic
361#126—41no—
362#126—2441no—
363#125—1221no—
364#124—21no—
365#124—1221no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369C22⋊Q8—1221no—
370C22⋊Q8—1221no—
371C22⋊Q8—2441no—
372C4×Q8—21no—
373C4×Q8—611no—
374C4×Q8—1221no—
375C4×Q8C22×D6111yescharacteristic
376C4×D4—21no—
377C4×D4—1221no—
378C4×D4C22×D6111yescharacteristic
379C4×D4C22×D6111yescharacteristic
380#117—21no—
381#117—1221no—
382C2×C4⋊C4—1221no—
383#107—21no—
384#107—611no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107C22⋊D6111yescharacteristic
389#106—1221no—
390#106—1221no—
391#106—1221no—
392#106—2441no—
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—611no—
403#103—611no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—2441no—
414#102—21no—
415#102—1221no—
416#102C22⋊D6111yescharacteristic
417#102C22⋊D6111yescharacteristic
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—21no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—42no—
429C2×Q8—81no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8D4×D6111yescharacteristic
434C2×D4C2×C22⋊D6111yescharacteristic
435C2×D4C2×C22⋊D6111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—2441no—
440Q16—4881no—
441Q16—2441no—
442SD16—42no—
443SD16—2442no—
444D8—22no—
445C2×C8—21no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—4881no—
453C2×C8—2442no—
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4D4×D6111yescharacteristic
473C4⋊C4C2×C22⋊D6111yescharacteristic
474C4⋊C4C2×C22⋊D6111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—2441no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C42—21no—
484C42—41no—
485C42—1221no—
486C42—2441no—
487C42C23×D6111yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—82no—
497Q8—1221no—
498Q8—1221no—
499Q8—4881no—
500Q8—2441no—
501Q8—2441no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4#1451979712yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—9761no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4#1451982211yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D4×C22⋊D6111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—4881no—
549C4—4881no—
550C4—2441no—
551C4—2441no—
552C4C2×#1451979711yescharacteristic
553C4#1684055811yescharacteristic
554C4#1684057211yescharacteristic
555C4#1684057711yescharacteristic
556C2—42no—
557C2—81no—
558C2#2145733811yescharacteristic
559C2#2145755611yescharacteristic
560C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3367C2
socleC22×C61D42
prime radicalC2×D8×C61D4
hypercenter#3367D61
hypocenterC61#19839
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
2. #21458245C2semidirect
3. #21457695C2semidirect
4. #21445466C2semidirect
5. #21445401C2semidirect
6. #21445268C2semidirect
7. #21445246C2semidirect
8. #21445206C2semidirect
9. #21445088C2semidirect
10. #21445082C2semidirect
11. #21445024C2semidirect
12. #21444991C2semidirect
13. #21444667C2semidirect
347. C61#19839semidirect

Maximal subgroups

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

subgroupindex
#214584662
#214582452
#214576952
#214454662
#214454012
#214452682
#214452462
#214452062
#214450882
#214450822
#214450242
#214449912
#214446672
#214446432
C61×#33672
#1983961