Finite Group Databasebeta

← #25067227

Subgroups — #25067227

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145184C211yesmaximal, characteristic
2#19143746C211yesmaximal, characteristic, complemented
3#19133507C211yesmaximal, characteristic, complemented
4#19133497C211yesmaximal, characteristic, complemented
5#19133483C211yesmaximal, characteristic, complemented
6#19133478C211yesmaximal, characteristic, complemented
7#19133417C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9C8×#10621883C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133363C211yesmaximal, characteristic, complemented
12#19133053C211yesmaximal, characteristic, complemented
13#19133046C211yesmaximal, characteristic, complemented
14#19132876C211yesmaximal, characteristic, complemented
15C43×#2981C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305C411yescharacteristic
18#14583286C411yescharacteristic
19#14583263C411yescharacteristic
20#14583261C411yescharacteristic
21#14583150C411yescharacteristic
22#14583150C411yescharacteristic
23#14583143C411yescharacteristic
24#14583143C411yescharacteristic
25#14583029C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582974—21no—
33#14582973—21no—
34C8×D172C2211yescharacteristic
35#14582959—21no—
36#14582924—21no—
37#14582923C2211yescharacteristic
38C4×#10621877C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44#14582629C2211yescharacteristic
45#14582629C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#436C2211yescharacteristic
58C43×#436C2211yescharacteristic
59C43×#435—21no—
60C43×#435—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#432C2211yescharacteristic
64C43×#431C2211yescharacteristic
65C43×#408—21no—
66C43×#408—21no—
67C2×#10621883C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621877C2×C411yescharacteristic
73C2×#10621877C2×C411yescharacteristic
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063319—21no—
78#13063317C2×C411yescharacteristic
79#13063313C2×C411yescharacteristic
80#13063308—21no—
81#13063304C2×C411yescharacteristic
82#13063299C2×C411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85C4×C22⋊D43—21no—
86#13063282—21no—
87#13063258C2×C411yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104(C2×D43)⋊C8—21no—
105(C2×D43)⋊C8—21no—
106#13063236C2×C411yescharacteristic
107#13063236C2×C411yescharacteristic
108#13063235—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43—21no—
120C4⋊Q8×C43C2×C411yescharacteristic
121#127×C43C2×C411yescharacteristic
122#124×C43—21no—
123#121×C43—21no—
124#121×C43C2×C411yescharacteristic
125#121×C43C2×C411yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C411yescharacteristic
152C2×D4×C43C22×C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C2×C22⋊D43—21no—
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×Dic86C22×C411yescharacteristic
162M16×C43—81no—
163M16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43—81no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C42×C43C22×C411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621883—22no—
185#10621883—22no—
186#10621882—22no—
187#10621882—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199#10621877—22no—
200#10621877—22no—
201#10621877—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C22×C411yescharacteristic
211#10621872—81no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43C4×D411yescharacteristic
216C22×D43—21no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—81no—
223D4×C43—81no—
224D4×C43—81no—
225D4×C43—81no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—81no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247D172—21no—
248D172—21no—
249C4×D43—41no—
250C4×D43—41no—
251Dic86—21no—
252Dic86—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—22no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8#13112yes—
266C43⋊C8#13112yes—
267#17968—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43C2×C4×D411yescharacteristic
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43C2×#13111yescharacteristic
288C4×C43C2×#13111yescharacteristic
289C4×C43#57611yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294#3171—431no—
295#2993—431no—
296#2981D4311yescharacteristic, complemented
297#1594—431no—
298#1592—431no—
299#1590—431no—
300#1589—431no—
301#1580—431no—
302SD16⋊C8—431no—
303C8×SD16—431no—
304C8×D8—431no—
305#1569—431no—
306#1494—431no—
307#1492—431no—
308C8×M16—431no—
309C2×C43—41no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43#293111yescharacteristic
313C2×C43#294611yescharacteristic
314C2×C43#295611yescharacteristic
315D43—81no—
316#532C2×D4311yescharacteristic
317#529—431no—
318#501—431no—
319#496—431no—
320#490—431no—
321#489—431no—
322#469—431no—
323#469—431no—
324#468—431no—
325#468—431no—
326#446—431no—
327C8×Q8—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×D8—431no—
331C4×D8—431no—
332#436—431no—
333#436—861no—
334#436C2×D4311yescharacteristic
335#436C2×D4311yescharacteristic
336#435—21no—
337#435—21no—
338#435—861no—
339C8×D4—431no—
340C8×D4C2×D4311yescharacteristic
341C8×D4C2×D4311yescharacteristic
342#433—861no—
343#432C2×D4311yescharacteristic
344#431C2×D4311yescharacteristic
345#424—861no—
346#423—431no—
347#408—21no—
348#408—21no—
349C4×M16—431no—
350C2×C4×C8—431no—
351#335—431no—
352#335—431no—
353#334—431no—
354#334—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363#322—431no—
364#322—431no—
365C82—431no—
366C82—431no—
367C43#1796811yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×SD16—431no—
370C2×SD16—431no—
371C2×D8—431no—
372C2×D8—431no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—431no—
376C2×M16—431no—
377C2×M16—861no—
378C2×M16—861no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8C4×D4311yescharacteristic
384#127C4×D4311yescharacteristic
385#126—861no—
386#125—431no—
387#124—21no—
388#124—431no—
389#123—861no—
390C22⋊Q8—431no—
391#121—21no—
392#121—431no—
393#121C4×D4311yescharacteristic
394#121C4×D4311yescharacteristic
395C4×Q8—431no—
396C4×D4—21no—
397C4×D4—431no—
398C4×D4—861no—
399C4×D4C22×D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401#117—861no—
402C2×C42C22×D4311yescharacteristic
403#107—431no—
404#107—431no—
405#106—431no—
406#106—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22⋊D4311yescharacteristic
413C4⋊C8C22⋊D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416#103—431no—
417#103—431no—
418#102—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8C22⋊D4311yescharacteristic
432C22⋊C8C22⋊D4311yescharacteristic
433#97—21no—
434#97—431no—
435#97—431no—
436#97—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—431no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—431no—
454C2×D4—861no—
455C2×D4C2×C4×D4311yescharacteristic
456C2×D4C2×C4×D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—861no—
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4#1062189811yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463SD16—862no—
464SD16—862no—
465D8—862no—
466D8—862no—
467M16—81no—
468M16—81no—
469M16—862no—
470M16—862no—
471M16—3441no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—431no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—3441no—
486C2×C8—1722no—
487C2×C8C2×C22⋊D4311yescharacteristic
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C2×C8C2×C22⋊D4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—861no—
510C42C2×C4×D4311yescharacteristic
511C42#1062189811yescharacteristic
512C42C2×C22⋊D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—861no—
517C23C4×C22⋊D4311yescharacteristic
518Q8—81no—
519Q8—861no—
520Q8—861no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—861no—
530D4—861no—
531D4—3441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4C4×C22⋊D4311yescharacteristic
549C2×C4C4×C22⋊D4311yescharacteristic
550C2×C4C4×C22⋊D4311yescharacteristic
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C22×C22⋊D4311yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—432no—
561C8—432no—
562C8—862no—
563C8—861no—
564C8—861no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22C2×C4×C22⋊D4311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4#131×D4311yescharacteristic
591C4#131×D4311yescharacteristic
592C4#1458370211yescharacteristic
593C4#1458371011yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—3441no—
598C2#1914330511yescharacteristic
599C2#1914342711yescharacteristic
600C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2981C2
socleC22×C43C2×C4×D4
prime radical#19145184C2
cosocleC42×C43C24
hypercenter#2981D43
hypocenterC43#17968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #19143746C2semidirect
3. #19133507C2semidirect
4. #19133497C2semidirect
5. #19133483C2semidirect
6. #19133478C2semidirect
7. #19133417C2semidirect
8. #19133407C2semidirect
9. C8×#10621883C2semidirect
10. C8×#10621882C2semidirect
11. #19133363C2semidirect
12. #19133053C2semidirect
13. #19133046C2semidirect
14. #19132876C2semidirect
15. C43×#2981C2semidirect
296. #2981D43semidirect
367. C43#17968semidirect

Maximal subgroups

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

subgroupindex
#191451842
#191437462
#191335072
#191334972
#191334832
#191334782
#191334172
#191334072
C8×#106218832
C8×#106218822
#191333632
#191330532
#191330462
#191328762
C43×#29812
#1796843