Finite Group Databasebeta

← #29667601

Subgroups — #29667601

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#21457157C211yesmaximal, characteristic
2#21457040C211yesmaximal, characteristic
3#21456963C211yesmaximal, characteristic, complemented
4#21454975C211yesmaximal, characteristic
5#21445404C211yesmaximal, characteristic, complemented
6#21445397C211yesmaximal, characteristic, complemented
7#21445328C211yesmaximal, characteristic, complemented
8#21445321C211yesmaximal, characteristic, complemented
9#21445280C211yesmaximal, characteristic, complemented
10#21445273C211yesmaximal, characteristic, complemented
11#21445204C211yesmaximal, characteristic, complemented
12#21445197C211yesmaximal, characteristic, complemented
13#21444602C211yesmaximal, characteristic, complemented
14#21444517C211yesmaximal, characteristic, complemented
15C2×C61×#333C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840168—21no—
19#16840158C2211yescharacteristic
20#16840158C2211yescharacteristic
21#16840124—21no—
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840092—21no—
25#16840092—21no—
26#16840092—21no—
27#16840075—21no—
28#16840070—21no—
29#16840054C2211yescharacteristic
30#16840054C2211yescharacteristic
31#16840049C2211yescharacteristic
32#16840049C2211yescharacteristic
33#16840048C2211yescharacteristic
34#16840044—21no—
35#16840044—21no—
36#16840043C2211yescharacteristic
37#16840003—21no—
38#16839991—21no—
39#16839985—21no—
40#16839973C2211yescharacteristic
41#16839968C2211yescharacteristic
42#16839889C2211yescharacteristic
43#16839886C2211yescharacteristic
44#16839839C2211yescharacteristic
45#16839833—21no—
46#16839827C2211yescharacteristic
47C8×C22⋊D61—21no—
48#16839822—21no—
49#16839819C2211yescharacteristic
50#16839815C2211yescharacteristic
51#16839787—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C2×C4⋊Q8×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#333C2211yescharacteristic
64C61×#333C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#333C2211yescharacteristic
67C2×Dic244—21no—
68C2×#11758190—21no—
69C2×#11758189—21no—
70C2×C8×D61—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519771—21no—
74#14519769—21no—
75#14519769D411yescharacteristic
76#14519765D411yescharacteristic
77#14519760—21no—
78#14519756—21no—
79#14519756—21no—
80#14519756D411yescharacteristic
81#14519751D411yescharacteristic
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85C4×D244C2311yescharacteristic
86C4×C22⋊D61—21no—
87#14519736—21no—
88#14519734—21no—
89#14519711—21no—
90#14519710—21no—
91#14519710—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519702—21no—
107#14519702—21no—
108#14519700—21no—
109#14519700—21no—
110#14519700—21no—
111#14519700—21no—
112#14519700—21no—
113#14519700—21no—
114#14519699—21no—
115#14519697—21no—
116#14519697—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122#14519688—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×Q8×C61—21no—
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61—21no—
131C4⋊Q8×C61—21no—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134C4⋊Q8×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C4⋊C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—82no—
148C22×C4×C61—41no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C2×C22⋊D61—21no—
153C2×D244C2×D411yescharacteristic
154C2×C4×D61—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C2×D411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
163C2×C8×C61—81no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61#4111yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—41no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C2×D411yescharacteristic
185C4⋊Dic61C2×D411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—41no—
191#11758196—41no—
192C4×Dic61—21no—
193C4×Dic61—41no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C2×D411yescharacteristic
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200Dic244—81no—
201#11758190—81no—
202#11758189—81no—
203C8×D61—81no—
204C23×C61#12111yescharacteristic
205C22×D61—21no—
206Q8×C61—82no—
207Q8×C61—81no—
208Q8×C61—81no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—82no—
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C22⋊D61—42no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229D244—21no—
230D244—21no—
231C4×D61—41no—
232C4×D61—41no—
233Dic122—21no—
234Dic122—21no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239C8×C61—41no—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#19588—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61#47112yes—
253C22×C61C2×#12111yescharacteristic
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61#57711yescharacteristic
264C4×C61#57711yescharacteristic
265C4×C61#57811yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—41no—
268Dic61—41no—
269Dic61—41no—
270Dic61—81no—
271Dic61—81no—
272#3248—611no—
273#3238—611no—
274#3229—611no—
275#2994—611no—
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×#333D6111yescharacteristic, complemented
287C2×C61—22no—
288C2×C61#304611yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61C2×#47111yescharacteristic
291D61—81no—
292#533—611no—
293C2×C4⋊Q8C2×D6111yescharacteristic
294#529—611no—
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#446—611no—
320C8×Q8—611no—
321#436—611no—
322#435—1221no—
323C8×D4—611no—
324C8×D4—1221no—
325#433—1221no—
326#432—611no—
327#431—611no—
328#424—1221no—
329C2×C4⋊C8C2×D6111yescharacteristic
330C2×C4⋊C8C2×D6111yescharacteristic
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335#333C2×D6111yescharacteristic
336#333C2×D6111yescharacteristic
337#333C2×D6111yescharacteristic
338#333C2×D6111yescharacteristic
339#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343C61#1958811yescharacteristic, complemented, Sylow
344C22×Q8—21no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—1221no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—1221no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356C4⋊Q8C22×D6111yescharacteristic
357C4⋊Q8C22×D6111yescharacteristic
358#126—1221no—
359#125—611no—
360#125—1221no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364C22⋊Q8—1221no—
365C22⋊Q8—1221no—
366#121—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×D4—611no—
371C4×D4—1221no—
372#117—1221no—
373#117—1221no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
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—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—1221no—
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—611no—
412C22⋊C8—611no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—1221no—
417#97—1221no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—611no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×D4—611no—
429C2×D4—1221no—
430C22×C4—41no—
431C22×C4—1221no—
432C22×C4#1175822211yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435Q16—4881no—
436SD16—4881no—
437M16—4881no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—81no—
443C2×C8—81no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—4881no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—611no—
458C4⋊C4—611no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—2441no—
475C42—1221no—
476C42—2441no—
477C42#1175822211yescharacteristic
478C42D4×D6111yescharacteristic
479C42D4×D6111yescharacteristic
480C42C23×D6111yescharacteristic
481C23—1221no—
482C23#1451975011yescharacteristic
483Q8—81no—
484Q8—81no—
485Q8—82no—
486Q8—1221no—
487Q8—1221no—
488Q8—2441no—
489Q8—2441no—
490Q8—2441no—
491Q8—2441no—
492D4—1221no—
493D4—1221no—
494D4—2442no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—82no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4#1451975011yescharacteristic
511C2×C4#1451975011yescharacteristic
512C2×C4#1451975011yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C2×D4×D6111yescharacteristic
515C2×C4C2×#1175822211yescharacteristic
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—1221no—
521C8—1221no—
522C8—1221no—
523C8—1221no—
524C8—2441no—
525C8—2441no—
526C22—21no—
527C22—21no—
528C22—2441no—
529C22—2441no—
530C22—2441no—
531C22#1684002412yes—
532C22C2×#1451975011yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—4881no—
540C4—4881no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4#1684056811yescharacteristic
545C4#1684056811yescharacteristic
546C4#1684057511yescharacteristic
547C4#1684057511yescharacteristic
548C2—22no—
549C2—4881no—
550C2#2145537411yescharacteristic
551C2#2145550811yescharacteristic
552C2C2×#1684002411yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenterC2×#333D61
hypocenterC61#19588
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #21456963C2semidirect
5. #21445404C2semidirect
6. #21445397C2semidirect
7. #21445328C2semidirect
8. #21445321C2semidirect
9. #21445280C2semidirect
10. #21445273C2semidirect
11. #21445204C2semidirect
12. #21445197C2semidirect
13. #21444602C2semidirect
14. #21444517C2semidirect
15. C2×C61×#333C2semidirect
286. C2×#333D61semidirect
343. C61#19588semidirect

Maximal subgroups

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

subgroupindex
#214571572
#214570402
#214569632
#214549752
#214454042
#214453972
#214453282
#214453212
#214452802
#214452732
#214452042
#214451972
#214446022
#214445172
C2×C61×#3332
#1958861