Finite Group Databasebeta

← #28316282

Subgroups — #28316282

Order 13568.

588 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#20291411C211yesmaximal, characteristic
2#20291410C211yesmaximal, characteristic
3#20290293C211yesmaximal, characteristic, complemented
4#20290291C211yesmaximal, characteristic, complemented
5#20290290C211yesmaximal, characteristic, complemented
6#20290289C211yesmaximal, characteristic, complemented
7#20290286C211yesmaximal, characteristic, complemented
8#20290286C211yesmaximal, characteristic, complemented
9#20290280C211yesmaximal, characteristic, complemented
10#20290279C211yesmaximal, characteristic, complemented
11#20290277C211yesmaximal, characteristic, complemented
12#20290267C211yesmaximal, characteristic, complemented
13#20290266C211yesmaximal, characteristic, complemented
14#20290262C211yesmaximal, characteristic, complemented
15#20283675C211yesmaximal, characteristic
16#16811648—21no—
17#16811647—21no—
18#16811647—21no—
19#16811647—21no—
20#16811645C2211yescharacteristic
21#16811644C2211yescharacteristic
22#16811644C2211yescharacteristic
23#16811644C2211yescharacteristic
24#16811642C2211yescharacteristic
25#16811639C2211yescharacteristic
26#16811639C2211yescharacteristic
27#16811639C2211yescharacteristic
28#16811627C2211yescharacteristic
29#16811626C2211yescharacteristic
30D53⋊(C4⋊C8)C2211yescharacteristic
31C2×C4⋊#88324C2211yescharacteristic
32#16811597—21no—
33#16811596—21no—
34#16811588—21no—
35#16811587—21no—
36#16811487C2211yescharacteristic
37#16811487C2211yescharacteristic
38#16811486C2211yescharacteristic
39#16811486C2211yescharacteristic
40#16811486C2211yescharacteristic
41#16811486C2211yescharacteristic
42#16811486C2211yescharacteristic
43#16811486C2211yescharacteristic
44#16811485C2211yescharacteristic
45#16811485C2211yescharacteristic
46#16811485C2211yescharacteristic
47#16811485C2211yescharacteristic
48#16811484C2211yescharacteristic
49#16811484C2211yescharacteristic
50#16811484C2211yescharacteristic
51#16811484C2211yescharacteristic
52C4×#11719947C2211yescharacteristic
53#16810752C411yescharacteristic
54#16810751C411yescharacteristic
55#16810699C411yescharacteristic
56#16810698C411yescharacteristic
57#16810695C411yescharacteristic
58#16810694C411yescharacteristic
59#16810691C411yescharacteristic
60#16810675C2211yescharacteristic
61#16810673C2211yescharacteristic
62#16810673C2211yescharacteristic
63#16810575C2211yescharacteristic
64M16×Dic53C2211yescharacteristic
65C2×C8×Dic53C2211yescharacteristic
66C53×#435C411yescharacteristic
67C2×#11719936—21no—
68C2×#11719940—21no—
69C2×D53⋊C8—21no—
70C22×#88324—21no—
71#13133284—21no—
72#13133284—21no—
73C4⋊#88324—21no—
74C4⋊#88324—21no—
75C4⋊#88324C2311yescharacteristic
76C4⋊#88324C2311yescharacteristic
77C4⋊#88324C2311yescharacteristic
78C4⋊#88324C2311yescharacteristic
79C4⋊#88324C2311yescharacteristic
80C4⋊#88324C2311yescharacteristic
81C4⋊#88324C2311yescharacteristic
82C4⋊#88324C2311yescharacteristic
83#13133274—21no—
84#13133274—21no—
85C22⋊#88324—21no—
86C22⋊#88324—21no—
87C22⋊#88324—21no—
88C22⋊#88324—21no—
89C22⋊#88324—21no—
90C22⋊#88324—21no—
91#13133272—21no—
92#13133272—21no—
93#13133272—21no—
94#13133272—21no—
95C4×#88324—21no—
96C4×#88324—21no—
97C4×#88324—21no—
98C4×#88324—21no—
99C2×#11719947D411yescharacteristic
100C2×#11719917C2×C411yescharacteristic
101C2×#11719912C2×C411yescharacteristic
102C2×#11719912C2×C411yescharacteristic
103C22×#88322C2×C411yescharacteristic
104C4×Dic106C2×C411yescharacteristic
105#13133182Q811yescharacteristic
106D4×Dic53Q811yescharacteristic
107C4×C22⋊D53C2×C411yescharacteristic
108C4×C22⋊D53C2×C411yescharacteristic
109#13133177Q811yescharacteristic
110#13133177Q811yescharacteristic
111#13133175D411yescharacteristic
112#13133173D411yescharacteristic
113#13133173D411yescharacteristic
114C2×C4×Dic53C2311yescharacteristic
115C2×C4×Dic53C2311yescharacteristic
116C42×D53C2311yescharacteristic
117C4⋊#88322C2×C411yescharacteristic
118#13133146C2×C411yescharacteristic
119#13133146C2×C411yescharacteristic
120#13133146C2×C411yescharacteristic
121#13133146C2×C411yescharacteristic
122C22⋊#88322C2×C411yescharacteristic
123C22⋊#88322C2×C411yescharacteristic
124#13133129C2×C411yescharacteristic
125#13133129C2×C411yescharacteristic
126#13133128C2×C411yescharacteristic
127#13133127C2×C411yescharacteristic
128#13133127C2×C411yescharacteristic
129C8×Dic53C2×C411yescharacteristic
130C8×Dic53C2×C411yescharacteristic
131C8×Dic53C2311yescharacteristic
132C8×Dic53C2311yescharacteristic
133C8×Dic53C2311yescharacteristic
134C8×Dic53C2311yescharacteristic
135C2×M16×C53C2×C411yescharacteristic
136C22×C8×C53C2×C411yescharacteristic
137C4×D4×C53C2×C411yescharacteristic
138C4⋊C8×C53C2×C411yescharacteristic
139C22⋊C8×C53C2×C411yescharacteristic
140C22⋊C8×C53C2×C411yescharacteristic
141#97×C53C2×C411yescharacteristic
142C2×D4×C53C4⋊C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C22×C4×C53C22×C411yescharacteristic
145C2×C22⋊D53C4⋊C411yescharacteristic
146C2×C22⋊D53C4⋊C411yescharacteristic
147C22×Dic53C2×D411yescharacteristic
148C22×Dic53C2×D411yescharacteristic
149C22×Dic53C2×Q811yescharacteristic
150C22×Dic53C2×Q811yescharacteristic
151#11719947—41no—
152#11719947—41no—
153C2×C4×D53C22×C411yescharacteristic
154C2×C4×D53C2×D411yescharacteristic
155C2×C4×D53C2×Q811yescharacteristic
156C2×Dic106C4⋊C411yescharacteristic
157#11719940—42no—
158C2×#88324—21no—
159C2×#88324—21no—
160C2×#88324—21no—
161C2×#88324—21no—
162C2×#88324—21no—
163C2×#88324—21no—
164C2×#88324—21no—
165C2×#88324—21no—
166C2×#88324—42no—
167#11719936—42no—
168D53⋊C8—42no—
169M16×C53—22no—
170C2×C8×C53—22no—
171C2×C8×C53C22×C411yescharacteristic
172C2×C8×C53C22×C411yescharacteristic
173C2×C8×C53C22×C411yescharacteristic
174C2×C8×C53C22×C411yescharacteristic
175C4⋊C4×C53C4⋊C411yescharacteristic
176C22⋊C4×C53C4⋊C411yescharacteristic
177C22⋊C4×C53C4⋊C411yescharacteristic
178C42×C53C22×C411yescharacteristic
179C22⋊Dic53C4⋊C411yescharacteristic
180C22⋊Dic53C4⋊C411yescharacteristic
181#11719921C4⋊C411yescharacteristic
182#11719921C4⋊C411yescharacteristic
183C4⋊Dic53C4⋊C411yescharacteristic
184#11719919C4⋊C411yescharacteristic
185#11719919C4⋊C411yescharacteristic
186#11719919C4⋊C411yescharacteristic
187#11719919C4⋊C411yescharacteristic
188C4×Dic53C22×C411yescharacteristic
189C4×Dic53C22×C411yescharacteristic
190C4×Dic53C2×D411yescharacteristic
191C4×Dic53C2×D411yescharacteristic
192C4×Dic53C2×D411yescharacteristic
193C4×Dic53C2×Q811yescharacteristic
194C4×Dic53C2×Q811yescharacteristic
195C4×Dic53C2×Q811yescharacteristic
196C4×Dic53C2411yescharacteristic
197#11719917—41no—
198C2×#88322—41no—
199C2×#88322C22×C411yescharacteristic
200C2×#88322C22×C411yescharacteristic
201C2×#88322C22×C411yescharacteristic
202C2×#88322C22×C411yescharacteristic
203#11719912—22no—
204#11719912—41no—
205C23×C53C2×C4⋊C411yescharacteristic
206C23×C53C2×C4⋊C411yescharacteristic
207C22×D53C2×C4⋊C411yescharacteristic
208D4×C53—41no—
209C2×C4×C53—21no—
210C2×C4×C53—21no—
211C2×C4×C53—21no—
212C2×C4×C53—21no—
213C2×C4×C53C2×C4⋊C411yescharacteristic
214C2×C4×C53C2×C4⋊C411yescharacteristic
215C2×C4×C53C2×C4⋊C411yescharacteristic
216C2×C4×C53C2×C4⋊C411yescharacteristic
217C2×C4×C53C23×C411yescharacteristic
218C22⋊D53—41no—
219C22⋊D53—41no—
220C2×Dic53—21no—
221C2×Dic53—21no—
222C2×Dic53—21no—
223C2×Dic53—21no—
224C2×Dic53—41no—
225C2×Dic53—41no—
226C2×Dic53C2×C4⋊C411yescharacteristic
227C2×Dic53C2×C4⋊C411yescharacteristic
228C2×Dic53C2×C4⋊C411yescharacteristic
229C2×Dic53C2×C4⋊C411yescharacteristic
230C2×Dic53C2×C4⋊C411yescharacteristic
231C2×Dic53C22×D411yescharacteristic
232C2×Dic53C22×Q811yescharacteristic
233C4×D53—21no—
234C4×D53—21no—
235C4×D53—21no—
236C4×D53—21no—
237C4×D53—41no—
238Dic106—41no—
239#88324—41no—
240#88324—41no—
241#88324—41no—
242#88324—41no—
243#88324—41no—
244#88324—41no—
245#88324—41no—
246#88324—41no—
247C8×C53—21no—
248C8×C53—21no—
249C8×C53—21no—
250C8×C53#13112yes—
251#88322—21no—
252#88322—21no—
253#88322—21no—
254#88322—21no—
255#17831—531nomaximal, Sylow
256C22×C53—21no—
257C22×C53—21no—
258C22×C53—21no—
259C22×C53—21no—
260C22×C53—21no—
261C22×C53—21no—
262C22×C53C22×C4⋊C411yescharacteristic
263C2×D53—21no—
264C2×D53—21no—
265C2×D53—21no—
266C4×C53—21no—
267C4×C53—21no—
268C4×C53—21no—
269C4×C53—21no—
270C4×C53C2×#13111yescharacteristic
271C4×C53#56811yescharacteristic
272Dic53—21no—
273Dic53—21no—
274Dic53—21no—
275Dic53—21no—
276Dic53—21no—
277Dic53—21no—
278Dic53#57511yescharacteristic
279Dic53#57511yescharacteristic
280#2965—531no—
281#2925—531no—
282#2925—531no—
283#1574—531no—
284#1574—531no—
285#1573—531no—
286#1573—531no—
287#1572—531no—
288#1572—531no—
289#1569—531no—
290#1569—531no—
291#1568—531no—
292#1565—531no—
293#1565—531no—
294#1564—531no—
295C2×C53—41no—
296C2×C53—41no—
297C2×C53#290611yescharacteristic
298C2×C53#291111yescharacteristic
299C2×C53#291611yescharacteristic
300D53—41no—
301C4×#41—531no—
302#446—531no—
303#446—531no—
304#436—531no—
305#436—531no—
306#435—531no—
307#435—531no—
308#435—531no—
309#435#615711yescharacteristic
310#433—1061no—
311#433—1061no—
312#433—1061no—
313#433—1061no—
314#432—531no—
315#432—531no—
316#432—531no—
317#432—531no—
318#431—531no—
319#431—531no—
320#431—531no—
321#431—531no—
322#431—531no—
323#431—531no—
324#431—531no—
325#423—531no—
326#423—531no—
327C2×C4⋊C8—531no—
328C2×C4⋊C8—531no—
329#408—1061no—
330#408—1061no—
331#405—1061no—
332#405—1061no—
333C4×M16—531no—
334C4×M16—531no—
335C2×C4×C8—531no—
336#335—531no—
337#335—531no—
338#335—531no—
339#335—531no—
340#335—531no—
341#335—531no—
342#335—531no—
343#335—531no—
344#334—531no—
345#334—531no—
346#334—531no—
347#334—531no—
348#334—531no—
349#334—531no—
350#334—531no—
351#334—531no—
352C53#1783111yescharacteristic, complemented, Sylow
353C2×#41—531no—
354C2×M16—531no—
355C2×M16—531no—
356C2×M16—531no—
357C2×M16—1061no—
358C2×M16—1061no—
359C2×M16C2×#615711yescharacteristic
360C22×C8—531no—
361C22×C8—1061no—
362C22×C8—1061no—
363C22×C8C2×#615711yescharacteristic
364C4×Q8—531no—
365C4×Q8—531no—
366C4×D4—531no—
367C4×D4—531no—
368C4×D4—531no—
369C4×D4—531no—
370C4×D4—531no—
371C4×D4C2×#615711yescharacteristic
372#117—531no—
373#117—531no—
374#117—531no—
375C2×C42—531no—
376C2×C42—531no—
377C2×C42—531no—
378C4⋊C8—531no—
379C4⋊C8—531no—
380C4⋊C8—531no—
381C4⋊C8—531no—
382C4⋊C8—531no—
383C4⋊C8—531no—
384C4⋊C8—531no—
385C4⋊C8—531no—
386C4⋊C8—531no—
387C4⋊C8—531no—
388C4⋊C8—531no—
389C4⋊C8—531no—
390C4⋊C8—531no—
391C4⋊C8—1061no—
392C4⋊C8—1061no—
393C4⋊C8—1061no—
394C4⋊C8—1061no—
395C4⋊C8C2×#615711yescharacteristic
396C22⋊C8—531no—
397C22⋊C8—531no—
398C22⋊C8—531no—
399C22⋊C8—531no—
400C22⋊C8—1061no—
401C22⋊C8—1061no—
402C22⋊C8—1061no—
403C22⋊C8—1061no—
404C22⋊C8—1061no—
405C22⋊C8—1061no—
406C22⋊C8—1061no—
407C22⋊C8—1061no—
408C22⋊C8C2×#615711yescharacteristic
409C22⋊C8C2×#615711yescharacteristic
410#97—531no—
411#97—531no—
412#97—531no—
413#97—1061no—
414#97—1061no—
415#97—1061no—
416#97—1061no—
417#97C2×#615711yescharacteristic
418C4×C8—531no—
419C4×C8—531no—
420C4×C8—531no—
421C4×C8—531no—
422C4×C8—531no—
423C4×C8—531no—
424C4×C8—1061no—
425C4×C8—1061no—
426C4×C8—1061no—
427C4×C8—1061no—
428#41—2121no—
429#41—2121no—
430C2×Q8—531no—
431C2×D4—531no—
432C2×D4—531no—
433C2×D4C4⋊#615711yescharacteristic
434C22×C4—531no—
435C22×C4—531no—
436C22×C4—531no—
437C22×C4—531no—
438C22×C4—531no—
439C22×C4—531no—
440C22×C4—531no—
441C22×C4C22×#615711yescharacteristic
442C22×C4C22×#615711yescharacteristic
443M16—22no—
444M16—1062no—
445M16—2121no—
446M16—2121no—
447M16—2122no—
448M16—2122no—
449C2×C8—22no—
450C2×C8—531no—
451C2×C8—531no—
452C2×C8—531no—
453C2×C8—531no—
454C2×C8—1061no—
455C2×C8—1061no—
456C2×C8—1061no—
457C2×C8—1061no—
458C2×C8—1061no—
459C2×C8—1061no—
460C2×C8—1061no—
461C2×C8—1061no—
462C2×C8—2121no—
463C2×C8—2122no—
464C2×C8—2122no—
465C2×C8C22×#615711yescharacteristic
466C2×C8C22×#615711yescharacteristic
467C2×C8C22×#615711yescharacteristic
468C2×C8C22×#615711yescharacteristic
469C4⋊C4—531no—
470C4⋊C4—531no—
471C4⋊C4—531no—
472C4⋊C4—531no—
473C4⋊C4—531no—
474C4⋊C4C4⋊#615711yescharacteristic
475C22⋊C4—531no—
476C22⋊C4—531no—
477C22⋊C4—531no—
478C22⋊C4—531no—
479C22⋊C4C4⋊#615711yescharacteristic
480C22⋊C4C4⋊#615711yescharacteristic
481C42—531no—
482C42—531no—
483C42—531no—
484C42—531no—
485C42—531no—
486C42—531no—
487C42—531no—
488C42—531no—
489C42—531no—
490C42C22×#615711yescharacteristic
491C23—531no—
492C23C2×C4⋊#615711yescharacteristic
493C23C2×C4⋊#615711yescharacteristic
494Q8—2121no—
495D4—41no—
496D4—2121no—
497D4—2121no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—531no—
503C2×C4—531no—
504C2×C4—531no—
505C2×C4—531no—
506C2×C4—531no—
507C2×C4—531no—
508C2×C4—531no—
509C2×C4—1061no—
510C2×C4—1061no—
511C2×C4—1061no—
512C2×C4—1061no—
513C2×C4—1061no—
514C2×C4—1061no—
515C2×C4—1061no—
516C2×C4—1061no—
517C2×C4—2121no—
518C2×C4—2121no—
519C2×C4—2121no—
520C2×C4C2×C4⋊#615711yescharacteristic
521C2×C4C2×C4⋊#615711yescharacteristic
522C2×C4C2×C4⋊#615711yescharacteristic
523C2×C4C2×C4⋊#615711yescharacteristic
524C2×C4C23×#615711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—1061no—
529C8—1061no—
530C8—1061no—
531C8—1061no—
532C8—2121no—
533C8—2121no—
534C8—2121no—
535C8—2121no—
536C8—2121no—
537C8—2121no—
538C8—2121no—
539C8—2121no—
540C8#1313330412yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—1061no—
548C22—1061no—
549C22—1061no—
550C22C22×C4⋊#615711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—531no—
556C4—531no—
557C4—1061no—
558C4—1061no—
559C4—1061no—
560C4—1061no—
561C4—1061no—
562C4—1061no—
563C4C2×#1313330411yescharacteristic
564C4#1681170211yescharacteristic
565C2—41no—
566C2—41no—
567C2—2121no—
568C2#2029136011yescharacteristic
569C2#2029136811yescharacteristic
570C2#2029137711yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC53×#435C4
socleC22×C53C22×C4⋊C4
prime radicalC2×#11719947D4
cosocleC4×Dic53C24
hypercenter#435#6157
hypocenterC53#17831
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #20290293C2semidirect
4. #20290291C2semidirect
5. #20290290C2semidirect
6. #20290289C2semidirect
7. #20290286C2semidirect
8. #20290286C2semidirect
9. #20290280C2semidirect
10. #20290279C2semidirect
11. #20290277C2semidirect
12. #20290267C2semidirect
13. #20290266C2semidirect
14. #20290262C2semidirect
352. C53#17831semidirect

Maximal subgroups

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

subgroupindex
#202914112
#202914102
#202902932
#202902912
#202902902
#202902892
#202902862
#202902802
#202902792
#202902772
#202902672
#202902662
#202902622
#202836752
#1783153