Finite Group Databasebeta

← #25169851

Subgroups — #25169851

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139206C211yesmaximal, characteristic, complemented
2#19137666C211yesmaximal, characteristic
3#19136113C211yesmaximal, characteristic
4#19135914C211yesmaximal, characteristic
5#19135836C211yesmaximal, characteristic
6#19135692C211yesmaximal, characteristic
7#19135454C211yesmaximal, characteristic, complemented
8#19135229C211yesmaximal, characteristic, complemented
9#19135227C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134937C211yesmaximal, characteristic, complemented
12#19134930C211yesmaximal, characteristic
13#19134609C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic
15C43×#1921C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C43⋊#401—21no—
33#14582838—21no—
34#14582805C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582791—21no—
40#14582790—21no—
41#14582785—21no—
42#14582773—21no—
43#14582766—21no—
44#14582764C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4—21no—
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×Dic172—22no—
64C2×Dic172—22no—
65C2×Dic172—41no—
66C2×#10621873—22no—
67C2×#10621873—41no—
68C2×#10621873—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063313—22no—
72#13063313—22no—
73#13063290—22no—
74#13063290—41no—
75#13063287—22no—
76#13063287—41no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063256—41no—
91Dic43⋊C8—41no—
92#13063250—41no—
93#13063248—22no—
94#13063248—22no—
95#13063248—41no—
96#13063248—41no—
97#13063247—22no—
98#13063245—22no—
99#13063245—41no—
100C8×Dic43—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172#4112yes—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43#4112yes—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—81no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—22no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189Dic43⋊C4—42no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—44no—
203#10621873—44no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43#13512yes—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—84no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274#27070—431nomaximal, Sylow
275C22×C43#52511yescharacteristic
276C22×C43#54611yescharacteristic
277C22×C43#55011yescharacteristic
278C22×C43C2×#13511yescharacteristic
279C22×C43#57511yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#52911yescharacteristic
296C4×C43#53811yescharacteristic
297C4×C43#55111yescharacteristic
298C4×C43#55311yescharacteristic
299Dic43—22no—
300Dic43—42no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306#2514—431no—
307#2367—431no—
308#2092—431no—
309#2055—431no—
310#2042—431no—
311#2015—431no—
312#1969—431no—
313#1927—431no—
314#1927—431no—
315#1921D4311yescharacteristic, complemented
316#1916—431no—
317#1878—431no—
318#1877—431no—
319#1805—431no—
320C4×#102—431no—
321C2×C43#246711yescharacteristic
322C2×C43#310211yescharacteristic
323C2×C43#312011yescharacteristic
324C2×C43#329611yescharacteristic
325C2×C43#331311yescharacteristic
326C2×C43#339311yescharacteristic
327C2×C43#340111yescharacteristic
328D43—82no—
329C22×Q16—431no—
330C22×SD16—431no—
331C2×#124—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#107C2×D4311yescharacteristic
335C2×#106—431no—
336C2×C4⋊C8—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×C4×C8—431no—
346#401—861no—
347#400—861no—
348#391—431no—
349#391—431no—
350#391—431no—
351#391—431no—
352#390—431no—
353#389C2×D4311yescharacteristic
354#388—861no—
355#388—861no—
356#387—861no—
357#385—861no—
358#383—861no—
359#382—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4C2×D4311yescharacteristic
363C4×C22⋊C4—861no—
364#340—431no—
365#340C2×D4311yescharacteristic
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#336—431no—
369#336—431no—
370#336—431no—
371#336C2×D4311yescharacteristic
372C43#2707011yescharacteristic, complemented, Sylow
373C22×Q8—431no—
374C22×Q8—431no—
375C22×D4—431no—
376C23×C4—861no—
377C2×Q16—862no—
378C2×Q16—862no—
379C2×Q16—1721no—
380C2×SD16—862no—
381C2×SD16—1721no—
382C2×SD16—1721no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387#124—862no—
388#124—862no—
389C4×Q8—862no—
390C4×Q8—1721no—
391C4×D4—862no—
392C4×D4—1721no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C42—21no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—22no—
414#106—1721no—
415C4⋊C8—1721no—
416#103—862no—
417#103—862no—
418#103—1721no—
419#103—1721no—
420#103—1721no—
421#102—862no—
422#102—862no—
423#102—1721no—
424C4×C8—1721no—
425#95—21no—
426#95—21no—
427#95—431no—
428#95—431no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—861no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×D4—432no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—3441no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476Q16—1724no—
477SD16—1724no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8#1062189812yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—862no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—1721no—
502C4⋊C4—1722no—
503C4⋊C4#1062190212yes—
504C22⋊C4—864no—
505C22⋊C4—864no—
506C22⋊C4—3441no—
507C22⋊C4—1722no—
508C22⋊C4—1722no—
509C42—21no—
510C42—21no—
511C42—81no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—1722no—
517C42—1722no—
518C23—862no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23C2×D4×D4311yescharacteristic
526Q8—862no—
527Q8—862no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531Q8—1721no—
532Q8—1721no—
533Q8—1721no—
534D4—862no—
535D4—862no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—432no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—862no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—3444no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#41×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4C2×#1062189811yescharacteristic
581C2×C4C2×#1062190211yescharacteristic
582C2×C4#1306337111yescharacteristic
583C2×C4#1306337111yescharacteristic
584C8—22no—
585C8—41no—
586C8—1721no—
587C8—1721no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—1722no—
593C22—1722no—
594C22—1722no—
595C22#1458340711yescharacteristic
596C22#1458354011yescharacteristic
597C22#1458357011yescharacteristic
598C22#135×D4311yescharacteristic
599C22#1458369511yescharacteristic
600C22#1458370911yescharacteristic
601C22#1458371211yescharacteristic
602C4—41no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—862no—
609C4—3441no—
610C4—3441no—
611C4—1722no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4#1458343611yescharacteristic
616C4#1458348811yescharacteristic
617C4#1458357311yescharacteristic
618C4#1458360211yescharacteristic
619C2—3442no—
620C2#1913864311yescharacteristic
621C2#1914460811yescharacteristic
622C2#1914480411yescharacteristic
623C2#1914642711yescharacteristic
624C2#1914665811yescharacteristic
625C2#1914758311yescharacteristic
626C2#1914766611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1921D43
hypocenterC43#27070
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #19139206C2semidirect
7. #19135454C2semidirect
8. #19135229C2semidirect
9. #19135227C2semidirect
10. #19135151C2semidirect
11. #19134937C2semidirect
13. #19134609C2semidirect
15. C43×#1921C2semidirect
315. #1921D43semidirect
372. C43#27070semidirect

Maximal subgroups

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

subgroupindex
#191392062
#191376662
#191361132
#191359142
#191358362
#191356922
#191354542
#191352292
#191352272
#191351512
#191349372
#191349302
#191346092
#191344092
C43×#19212
#2707043