Finite Group Databasebeta

← #28326762

Subgroups — #28326762

Order 13568.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291513C211yesmaximal, characteristic
2#20291511C211yesmaximal, characteristic
3#20290892C211yesmaximal, characteristic
4#20290891C211yesmaximal, characteristic
5#20290824C211yesmaximal, characteristic
6#20290822C211yesmaximal, characteristic
7#20290783C211yesmaximal, characteristic
8#20290781C211yesmaximal, characteristic
9#20290781C211yesmaximal, characteristic
10#20290780C211yesmaximal, characteristic
11#20290535C211yesmaximal, characteristic
12#20290523C211yesmaximal, characteristic
13#20290519C211yesmaximal, characteristic
14#20290513C211yesmaximal, characteristic
15#20285236C211yesmaximal, characteristic
16#16811675—21no—
17#16811675—21no—
18#16811674—21no—
19#16811674—21no—
20#16811673—21no—
21#16811673—21no—
22#16811672—21no—
23#16811672—21no—
24C2×#13133288C2211yescharacteristic
25C2×#13133287C2211yescharacteristic
26#16811630C2211yescharacteristic
27#16811630C2211yescharacteristic
28#16811630C2211yescharacteristic
29#16811630C2211yescharacteristic
30D53⋊(C4⋊C8)C2211yescharacteristic
31#16811588C2211yescharacteristic
32#16811588C2211yescharacteristic
33#16811588C2211yescharacteristic
34#16811588C2211yescharacteristic
35C4×#11719936C2211yescharacteristic
36C4×#11719936C2211yescharacteristic
37C2×#13133271C2211yescharacteristic
38C2×C8×#6157C2211yescharacteristic
39C4×C4⋊#6157C2211yescharacteristic
40#16811499C2211yescharacteristic
41#16811499C2211yescharacteristic
42#16811493C2211yescharacteristic
43#16811493C2211yescharacteristic
44#16811493C2211yescharacteristic
45#16811493C2211yescharacteristic
46#16811493C2211yescharacteristic
47#16811493C2211yescharacteristic
48#16811493C2211yescharacteristic
49#16811493C2211yescharacteristic
50(C2×#6157)⋊C8C2211yescharacteristic
51(C2×#6157)⋊C8C2211yescharacteristic
52#16811179C2211yescharacteristic
53#16811178C2211yescharacteristic
54#16811033C411yescharacteristic, complemented
55#16811032C411yescharacteristic, complemented
56#16811031C411yescharacteristic, complemented
57#16811031C411yescharacteristic, complemented
58#16811030C411yescharacteristic, complemented
59#16811030C411yescharacteristic, complemented
60#16811029C411yescharacteristic, complemented
61#16810660C2211yescharacteristic
62#16810660C2211yescharacteristic
63#16810658C2211yescharacteristic
64#16810658C2211yescharacteristic
65#97×D53C2211yescharacteristic
66C53×#501C411yescharacteristic, complemented
67C2×#11719936C2311yescharacteristic
68C2×#11719936C2311yescharacteristic
69C2×#11719936C2311yescharacteristic
70C2×#11719936C2311yescharacteristic
71C2×D53⋊C8C2311yescharacteristic
72C2×D53⋊C8C2311yescharacteristic
73C2×C4⋊#6157—21no—
74C2×C4×#6157C2311yescharacteristic
75C2×C4×#6157C2311yescharacteristic
76#13133288Q814yescomplemented
77#13133287—22no—
78#13133284—21no—
79#13133284—21no—
80#13133284—21no—
81#13133284—21no—
82#13133284D411yescharacteristic
83#13133284D411yescharacteristic
84C4⋊#88324—21no—
85C4⋊#88324—21no—
86C4⋊#88324—21no—
87C4⋊#88324—21no—
88C4⋊#88324D411yescharacteristic
89C4⋊#88324D411yescharacteristic
90#13133272—21no—
91#13133272—21no—
92#13133272—21no—
93#13133272—21no—
94#13133272—21no—
95#13133272—21no—
96#13133271—22no—
97C4×#88324—21no—
98C4×#88324—21no—
99C4×#88324—21no—
100C4×#88324—21no—
101C4×#88324—21no—
102C4×#88324—21no—
103C8×#6157—22no—
104(C2×#6157)⋊C4—21no—
105C2×C8×D53C2311yescharacteristic
106C2×C8×D53C2311yescharacteristic
107#13133217C2×C411yescharacteristic
108#13133216C2×C411yescharacteristic
109#13133216C2×C411yescharacteristic
110#13133209C2×C411yescharacteristic
111#13133208C2×C411yescharacteristic
112#13133208C2×C411yescharacteristic
113#13133197—21no—
114#13133195—21no—
115#13133195—21no—
116#13133193—21no—
117Q8×Dic53—21no—
118#13133182—21no—
119#13133182—21no—
120#13133182—21no—
121#13133175C2311yescharacteristic
122#13133175C2311yescharacteristic
123#13133175C2311yescharacteristic
124#13133175C2311yescharacteristic
125C42×D53C2311yescharacteristic
126#13133151C2×C411yescharacteristic
127#13133151C2×C411yescharacteristic
128#13133150C2×C411yescharacteristic
129#13133150C2×C411yescharacteristic
130#13133150C2×C411yescharacteristic
131#13133150C2×C411yescharacteristic
132#13133149C2×C411yescharacteristic
133#13133149C2×C411yescharacteristic
134#13133148C2×C411yescharacteristic
135#13133148C2×C411yescharacteristic
136#13133148C2×C411yescharacteristic
137#13133148C2×C411yescharacteristic
138#13133128C2×C411yescharacteristic
139#13133127C2×C411yescharacteristic
140#13133127C2×C411yescharacteristic
141C4⋊Q8×C53C2×C411yescharacteristic
142#125×C53C2×C411yescharacteristic
143#107×C53C2×C411yescharacteristic
144#107×C53C2×C411yescharacteristic
145#106×C53C2×C411yescharacteristic
146#106×C53C2×C411yescharacteristic
147#97×C53C2×C411yescharacteristic
148C22×#6157—21no—
149C22×#6157—21no—
150C2×Q8×C53—21no—
151C2×C4×D53#4111yescharacteristic
152C2×C4×D53#4111yescharacteristic
153C2×C4×D53C2411yescharacteristic
154C2×Dic106—21no—
155C2×Dic106—21no—
156C2×Dic106—21no—
157C2×#88324—21no—
158C2×#88324—21no—
159C2×#88324—21no—
160C2×#88324—21no—
161C2×#88324C2×D411yescharacteristic
162C2×#88324C2×D411yescharacteristic
163C2×#88324C2×D411yescharacteristic
164C2×#88324C2×D411yescharacteristic
165C4⋊#6157—42no—
166C4×#6157—21no—
167C4×#6157—21no—
168C4×#6157—21no—
169C4×#6157—21no—
170#11719936—21no—
171#11719936—21no—
172#11719936—21no—
173#11719936—21no—
174#11719936—21no—
175#11719936—21no—
176#11719936C2×Q812yes—
177#11719936C2×Q812yes—
178D53⋊C8—21no—
179D53⋊C8—21no—
180D53⋊C8—21no—
181D53⋊C8—21no—
182C2×C8×C53C22×C411yescharacteristic
183C2×C8×C53C22×C411yescharacteristic
184C4⋊C4×C53—21no—
185C4⋊C4×C53—21no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53C22×C411yescharacteristic
188C4⋊C4×C53C22×C411yescharacteristic
189C4⋊C4×C53C22×C411yescharacteristic
190C4⋊C4×C53C22×C411yescharacteristic
191C42×C53C22×C411yescharacteristic
192#11719921—21no—
193#11719921—21no—
194#11719921—21no—
195#11719921—21no—
196C4⋊Dic53—21no—
197C4⋊Dic53—21no—
198C4⋊Dic53—21no—
199C4⋊Dic53C22×C411yescharacteristic
200C4⋊Dic53C22×C411yescharacteristic
201C4⋊Dic53C22×C411yescharacteristic
202C4⋊Dic53C22×C411yescharacteristic
203#11719919—21no—
204#11719919—21no—
205#11719919—21no—
206#11719919—21no—
207#11719919—21no—
208#11719919—21no—
209C4×Dic53—21no—
210C4×Dic53—21no—
211C4×Dic53—21no—
212C4×Dic53—21no—
213C4×Dic53C22×C411yescharacteristic
214C4×Dic53C2×D411yescharacteristic
215C4×Dic53C2×D411yescharacteristic
216C2×#88322C22×C411yescharacteristic
217C2×#88322C22×C411yescharacteristic
218C8×D53—21no—
219C8×D53—21no—
220C8×D53C2×Q812yes—
221C8×D53#4112yes—
222C22×D53C2×#4111yescharacteristic
223C2×#6157—22no—
224C2×#6157—41no—
225C2×#6157—41no—
226C2×#6157—41no—
227C2×#6157—41no—
228C2×#6157—41no—
229Q8×C53—81no—
230C2×C4×C53—21no—
231C2×C4×C53—21no—
232C2×C4×C53—21no—
233C2×C4×C53—21no—
234C2×C4×C53C4×D411yescharacteristic
235C2×C4×C53C4×D411yescharacteristic
236C2×C4×C53C23×C411yescharacteristic
237C2×Dic53—21no—
238C2×Dic53—21no—
239C2×Dic53—21no—
240C2×Dic53—21no—
241C2×Dic53C4×D411yescharacteristic
242C2×Dic53C4×D411yescharacteristic
243C2×Dic53C22×D411yescharacteristic
244C4×D53—41no—
245C4×D53—41no—
246C4×D53C22×Q811yescharacteristic
247C4×D53C2×#4111yescharacteristic
248C4×D532−1+411yescharacteristic
249C4×D532−1+411yescharacteristic
250Dic106—42no—
251Dic106—42no—
252Dic106—81no—
253#88324—21no—
254#88324—21no—
255#88324—21no—
256#88324—21no—
257#88324—22no—
258#88324—22no—
259#88324—41no—
260#88324—41no—
261C8×C53—21no—
262C8×C53C4×Q812yes—
263#88322—21no—
264#88322C4×Q812yes—
265#23172—531nomaximal, Sylow
266C22×C53C2×C4×D411yescharacteristic
267C2×D53—21no—
268C2×D53—21no—
269C2×D53#55611yescharacteristic
270C2×D53#55711yescharacteristic
271#6157—42no—
272#6157—81no—
273C4×C53—21no—
274C4×C53—21no—
275C4×C53—41no—
276C4×C53—41no—
277C4×C53—41no—
278C4×C53—41no—
279C4×C53C2×C4×Q811yescharacteristic
280C4×C53#51911yescharacteristic
281Dic53—21no—
282Dic53—21no—
283Dic53—41no—
284Dic53—41no—
285Dic53—41no—
286Dic53—41no—
287Dic53#54711yescharacteristic
288Dic53D4×Q811yescharacteristic
289#3162—531no—
290#2962—531no—
291#2962—531no—
292#1986—531no—
293#1986—531no—
294#1946—531no—
295#1945—531no—
296#1922—531no—
297#1922—531no—
298#1922—531no—
299#1922—531no—
300#1778—531no—
301#1773—531no—
302#1772—531no—
303#1771—531no—
304C2×C53#236511yescharacteristic
305C2×C53#295511yescharacteristic
306C2×C53#295611yescharacteristic
307D53—21no—
308D53—21no—
309#533—531no—
310#533—531no—
311#501—531no—
312#501—531no—
313#501—531no—
314#501—531no—
315#501—531no—
316#501—531no—
317#501—531no—
318#501#615711yescharacteristic, complemented
319#446—1061no—
320#446—1061no—
321#446—1061no—
322#446—1061no—
323#446—1061no—
324#446—1061no—
325C8×Q8—1061no—
326C8×Q8—1061no—
327C2×#108—531no—
328C2×#108—531no—
329#427—531no—
330#427—531no—
331#427—531no—
332#427—531no—
333#424—531no—
334#424—531no—
335#424—531no—
336#424—531no—
337C2×C4⋊C8—531no—
338#405—531no—
339#405—531no—
340#405—531no—
341#405—531no—
342C4×M16—531no—
343C4×M16—531no—
344C2×#97—531no—
345C2×#97—531no—
346C2×C4×C8—531no—
347C4×C4⋊C4—531no—
348#341—531no—
349#341—531no—
350#339—531no—
351#339—531no—
352#339—531no—
353#339—531no—
354#339—531no—
355#339—531no—
356#339—531no—
357#339—531no—
358#336—531no—
359#336—531no—
360C53#2317211yescharacteristic, complemented, Sylow
361C2×M16—531no—
362C2×M16—531no—
363C2×M16—531no—
364C2×M16—531no—
365C22×C8—531no—
366C22×C8—531no—
367C22×C8—531no—
368C22×C8—531no—
369C4⋊Q8—531no—
370C4⋊Q8—531no—
371C4⋊Q8—531no—
372C4⋊Q8C2×#615711yescharacteristic
373#125—531no—
374#125—531no—
375#125—531no—
376#125C2×#615711yescharacteristic
377C22⋊Q8—1061no—
378C22⋊Q8—1061no—
379C22⋊Q8—1061no—
380C22⋊Q8—1061no—
381C4×Q8—1061no—
382C4×Q8—1061no—
383C4×Q8—1061no—
384C4×Q8—1061no—
385#117—531no—
386#117—531no—
387#117—531no—
388#117—531no—
389C2×C4⋊C4—1061no—
390C2×C42—531no—
391C2×C42—531no—
392C2×C42—531no—
393#108—534no—
394#108—1062no—
395#107—531no—
396#107—531no—
397#107—531no—
398#107—531no—
399#107—531no—
400#107—531no—
401#107C2×#615711yescharacteristic
402#107C2×#615711yescharacteristic
403#106—531no—
404#106—531no—
405#106—531no—
406#106—531no—
407#106—531no—
408#106—531no—
409#106C2×#615711yescharacteristic
410#106C2×#615711yescharacteristic
411C4⋊C8—531no—
412C4⋊C8—531no—
413C4⋊C8—531no—
414C4⋊C8—531no—
415C4⋊C8—1061no—
416C4⋊C8—1061no—
417C4⋊C8—1061no—
418C4⋊C8—1061no—
419C4⋊C8—1061no—
420C4⋊C8—1061no—
421C4⋊C8—1061no—
422C4⋊C8—1061no—
423#97—531no—
424#97—531no—
425#97—531no—
426#97—1061no—
427#97—1061no—
428#97—1062no—
429#97—1061no—
430#97—1061no—
431#97—1061no—
432#97—1061no—
433#97C2×#615711yescharacteristic
434C4×C8—1061no—
435C4×C8—1061no—
436C4×C8—1062no—
437C4×C8—1061no—
438C4×C8—1061no—
439C4×C8—1061no—
440C4×C8—1061no—
441#95—1061no—
442C2×Q8—21no—
443C2×Q8—1061no—
444C2×Q8—1061no—
445C2×Q8—1061no—
446C22×C4—531no—
447C22×C4—531no—
448C22×C4—531no—
449C22×C4—1061no—
450C22×C4—1061no—
451M16—532no—
452M16—532no—
453M16—1061no—
454M16—1061no—
455M16—1061no—
456M16—1061no—
457M16—1061no—
458M16—1061no—
459C2×C8—531no—
460C2×C8—532no—
461C2×C8—532no—
462C2×C8—531no—
463C2×C8—531no—
464C2×C8—531no—
465C2×C8—531no—
466C2×C8—531no—
467C2×C8—1061no—
468C2×C8—1061no—
469C2×C8—1061no—
470C2×C8—1061no—
471C2×C8—1061no—
472C2×C8—1061no—
473C2×C8—1061no—
474C2×C8—1061no—
475C2×C8—1061no—
476C2×C8—1061no—
477C2×C8C22×#615711yescharacteristic
478C2×C8C22×#615711yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—531no—
483C4⋊C4—531no—
484C4⋊C4—531no—
485C4⋊C4—531no—
486C4⋊C4—1061no—
487C4⋊C4—1061no—
488C4⋊C4—1061no—
489C4⋊C4—1061no—
490C4⋊C4—1061no—
491C4⋊C4—1061no—
492C4⋊C4—1061no—
493C4⋊C4—1061no—
494C4⋊C4—1061no—
495C4⋊C4—2122no—
496C4⋊C4C22×#615711yescharacteristic
497C4⋊C4C22×#615711yescharacteristic
498C4⋊C4C22×#615711yescharacteristic
499C4⋊C4C22×#615711yescharacteristic
500C22⋊C4—1061no—
501C22⋊C4—1061no—
502C22⋊C4—1061no—
503C22⋊C4—1061no—
504C42—531no—
505C42—531no—
506C42—531no—
507C42—1061no—
508C42—1061no—
509C42—1061no—
510C42—1061no—
511C42—1061no—
512C42—1061no—
513C42—1061no—
514C42—1061no—
515C42C22×#615711yescharacteristic
516C23—531no—
517Q8—81no—
518Q8—4241no—
519Q8—2122no—
520Q8—2122no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—531no—
526C2×C4—531no—
527C2×C4—531no—
528C2×C4—531no—
529C2×C4—531no—
530C2×C4—531no—
531C2×C4—531no—
532C2×C4—1062no—
533C2×C4—1061no—
534C2×C4—1061no—
535C2×C4—1061no—
536C2×C4—1061no—
537C2×C4—2121no—
538C2×C4—2121no—
539C2×C4—2121no—
540C2×C4—2121no—
541C2×C4—2121no—
542C2×C4—2121no—
543C2×C4—2121no—
544C2×C4D4×#615711yescharacteristic
545C2×C4D4×#615711yescharacteristic
546C2×C4C23×#615711yescharacteristic
547C8—21no—
548C8—532no—
549C8—1061no—
550C8—1061no—
551C8—1061no—
552C8—1061no—
553C8—1062no—
554C8—1062no—
555C8—1061no—
556C8—2121no—
557C8—2121no—
558C8Q8×#615712yes—
559C22—531no—
560C22—531no—
561C22—1061no—
562C22—1061no—
563C22C2×D4×#615711yescharacteristic
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—531no—
571C4—531no—
572C4—1061no—
573C4—1061no—
574C4—4241no—
575C4—2122no—
576C4—2121no—
577C4—2121no—
578C4—2121no—
579C4—2121no—
580C4C2×Q8×#615711yescharacteristic
581C4#1681169111yescharacteristic
582C2—1061no—
583C2—1061no—
584C2#2029124411yescharacteristic
585C2#2029148811yescharacteristic
586C2#2029148911yescharacteristic
subgroupG/H
centerC22C2×D4×#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC53×#501C4
socleC22×C53C2×C4×D4
prime radicalC22×D53C2×#41
cosocleC2×C4×D53C24
hypercenter#501#6157
hypocenterC53#23172
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
54. #16811033C4semidirect
55. #16811032C4semidirect
56. #16811031C4semidirect
57. #16811031C4semidirect
58. #16811030C4semidirect
59. #16811030C4semidirect
60. #16811029C4semidirect
66. C53×#501C4semidirect
76. #13133288Q8semidirect
318. #501#6157semidirect
360. C53#23172semidirect

Maximal subgroups

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

subgroupindex
#202915132
#202915112
#202908922
#202908912
#202908242
#202908222
#202907832
#202907812
#202907802
#202905352
#202905232
#202905192
#202905132
#202852362
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