Finite Group Databasebeta

← #29663772

Subgroups — #29663772

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457139C211yesmaximal, characteristic
2#21456998C211yesmaximal, characteristic, complemented
3#21454823C211yesmaximal, characteristic, complemented
4#21445398C211yesmaximal, characteristic, complemented
5#21445356C211yesmaximal, characteristic, complemented
6#21445339C211yesmaximal, characteristic, complemented
7#21445281C211yesmaximal, characteristic, complemented
8#21445267C211yesmaximal, characteristic, complemented
9#21445225C211yesmaximal, characteristic, complemented
10#21445220C211yesmaximal, characteristic, complemented
11#21445164C211yesmaximal, characteristic, complemented
12#21444571C211yesmaximal, characteristic, complemented
13#21444481C211yesmaximal, characteristic, complemented
14#21444476C211yesmaximal, characteristic, complemented
15C61×#3182C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840161—21no—
18#16840119—21no—
19#16840103—21no—
20#16840086—21no—
21#16840062—21no—
22#16840054C2211yescharacteristic
23#16840054C2211yescharacteristic
24#16840049C2211yescharacteristic
25#16840049C2211yescharacteristic
26#16840044C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16839996—21no—
29#16839989—21no—
30#16839977—21no—
31#16839959C2211yescharacteristic
32#16839954C2211yescharacteristic
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839838—21no—
37#16839831—21no—
38C8×D244C2211yescharacteristic
39#16839824—21no—
40#16839815C2211yescharacteristic
41#16839815C2211yescharacteristic
42C2×C4⋊#92418C2211yescharacteristic
43#16839719—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#532C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#468—21no—
63C61×#468—21no—
64C61×#440—21no—
65C61×#440—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758199—21no—
69C2×#11758189—21no—
70C22×#92418—21no—
71C2×C8×D61—21no—
72#14519771—21no—
73#14519769D411yescharacteristic
74#14519765D411yescharacteristic
75#14519760—21no—
76#14519756D411yescharacteristic
77#14519751D411yescharacteristic
78C4×Dic122C2311yescharacteristic
79C4×D244C2311yescharacteristic
80C4×C22⋊D61—21no—
81#14519734—21no—
82#14519710—21no—
83#14519710—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519698—21no—
101#14519698—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519687—21no—
110C4×#92418—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C2×SD16×C61—21no—
115C2×SD16×C61—21no—
116C2×M16×C61D411yescharacteristic
117C2×M16×C61D411yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#125×C61—21no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#107×C61—21no—
135#107×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—82no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C22×C4×C61—41no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C2×C22⋊D61—21no—
157C2×D244C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×Dic122C2×D411yescharacteristic
160SD16×C61—42no—
161SD16×C61—42no—
162M16×C61—22no—
163M16×C61—41no—
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×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C42×C61—41no—
180C42×C61C2×D411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61#4111yescharacteristic
183C42×C61C2411yescharacteristic
184C22⋊Dic61—21no—
185#11758200—81no—
186#11758199—81no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61C2×D411yescharacteristic
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—81no—
205#11758189—42no—
206C8×D61—42no—
207C23×C61—41no—
208C23×C61#12111yescharacteristic
209C22×D61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213Q8×C61—81no—
214D4×C61—41no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—81no—
219D4×C61—82no—
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—82no—
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C22⋊D61—81no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239D244—21no—
240D244—21no—
241C4×D61—41no—
242C4×D61—41no—
243Dic122—21no—
244Dic122—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61#13512yes—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#19253—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61C2×#12111yescharacteristic
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61C2×#13511yescharacteristic
274C4×C61#57511yescharacteristic
275C4×C61#57711yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280#3247—611no—
281#3233—611no—
282#3182D6111yescharacteristic, complemented
283#2969—611no—
284#1704—611no—
285#1698—611no—
286#1695—611no—
287#1685—611no—
288#1683—611no—
289#1677—611no—
290#1676—611no—
291#1666—611no—
292#1565—611no—
293#1543—611no—
294#1542—611no—
295C2×C61—41no—
296C2×C61—161no—
297C2×C61#303511yescharacteristic
298C2×C61#306311yescharacteristic
299C2×C61#306811yescharacteristic
300D61—81no—
301#533C2×D6111yescharacteristic
302#532C2×D6111yescharacteristic
303#529—611no—
304#500C2×D6111yescharacteristic
305#499—1221no—
306#492C2×D6111yescharacteristic
307#488—1221no—
308#487C2×D6111yescharacteristic
309#486C2×D6111yescharacteristic
310#485—1221no—
311#482—1221no—
312#478—1221no—
313#477—611no—
314#477—611no—
315#476—611no—
316#476—611no—
317#475—611no—
318#474—611no—
319#468—21no—
320#468—21no—
321#466—1221no—
322#465—1221no—
323#463—1221no—
324#460—611no—
325#459—611no—
326#446—611no—
327C8×Q8—611no—
328#440—21no—
329#440—21no—
330#436—611no—
331#436—1221no—
332#435—1221no—
333C8×D4—611no—
334#433—1221no—
335#431—611no—
336#431—611no—
337C2×C4⋊C8—611no—
338#405—1221no—
339C4×M16C2×D6111yescharacteristic
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344#333—611no—
345#333—611no—
346#333—611no—
347#333—611no—
348#332—611no—
349#332—611no—
350#331—611no—
351#331—611no—
352C61#1925311yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—1221no—
357C2×D8—1221no—
358C2×M16—1221no—
359C2×M16C22⋊D6111yescharacteristic
360C2×M16C22⋊D6111yescharacteristic
361C22×C8—1221no—
362C22×C8—1221no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365C4⋊Q8C22×D6111yescharacteristic
366#127C22×D6111yescharacteristic
367#126—1221no—
368#125—21no—
369#125—611no—
370#124—21no—
371#124—611no—
372#123—1221no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—611no—
376#121—21no—
377#121—21no—
378#121—611no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—611no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—611no—
385C4×D4—1221no—
386#117—21no—
387#117—1221no—
388C2×C42C22×D6111yescharacteristic
389#107—21no—
390#107—21no—
391#107—1221no—
392#107—1221no—
393#107—1221no—
394#106—1221no—
395#106—1221no—
396#106—1221no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406#103—21no—
407#103—21no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—21no—
412#102—21no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422#97—1221no—
423#97C22⋊D6111yescharacteristic
424#97C22⋊D6111yescharacteristic
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429C4×C8C22×D6111yescharacteristic
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—611no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—611no—
440C2×D4—1221no—
441C22×C4—41no—
442C22×C4—1221no—
443C22×C4D4×D6111yescharacteristic
444C22×C4#1175822411yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446SD16—42no—
447SD16—42no—
448SD16—4881no—
449D8—4881no—
450M16—22no—
451M16—41no—
452M16—2442no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—4881no—
460C2×C8—2442no—
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C42—41no—
488C42—1221no—
489C42D4×D6111yescharacteristic
490C42#1175822411yescharacteristic
491C42C2×C22⋊D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—41no—
494C23—1221no—
495C23#1451974811yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—1221no—
501Q8—1221no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508D4—1221no—
509D4—1221no—
510D4—4881no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4#1451974811yescharacteristic
526C2×C4#1451974811yescharacteristic
527C2×C4#1451974811yescharacteristic
528C2×C4C2×D4×D6111yescharacteristic
529C2×C4C22×C22⋊D6111yescharacteristic
530C2×C4C2×#1175822411yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8#1451979712yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—2441no—
548C22—2441no—
549C22—2441no—
550C22C2×#1451974811yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—2441no—
559C4—2441no—
560C4—2441no—
561C4C2×#1451979711yescharacteristic
562C4#1684056011yescharacteristic
563C4#1684057111yescharacteristic
564C4#1684057811yescharacteristic
565C2—41no—
566C2—161no—
567C2—4881no—
568C2#2145526811yescharacteristic
569C2#2145550411yescharacteristic
570C2#2145554311yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3182C2
socleC22×C61C2×#121
prime radical#21457139C2
hypercenter#3182D61
hypocenterC61#19253
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
2. #21456998C2semidirect
3. #21454823C2semidirect
4. #21445398C2semidirect
5. #21445356C2semidirect
6. #21445339C2semidirect
7. #21445281C2semidirect
8. #21445267C2semidirect
9. #21445225C2semidirect
10. #21445220C2semidirect
11. #21445164C2semidirect
12. #21444571C2semidirect
13. #21444481C2semidirect
14. #21444476C2semidirect
15. C61×#3182C2semidirect
282. #3182D61semidirect
352. C61#19253semidirect

Maximal subgroups

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

subgroupindex
#214571392
#214569982
#214548232
#214453982
#214453562
#214453392
#214452812
#214452672
#214452252
#214452202
#214451642
#214445712
#214444812
#214444762
C61×#31822
#1925361