Finite Group Databasebeta

← #25067221

Subgroups — #25067221

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#19143740C211yesmaximal, characteristic, complemented
3#19143671C211yesmaximal, characteristic, complemented
4#19133506C211yesmaximal, characteristic, complemented
5#19133494C211yesmaximal, characteristic, complemented
6#19133488C211yesmaximal, characteristic, complemented
7#19133477C211yesmaximal, characteristic, complemented
8#19133416C211yesmaximal, characteristic, complemented
9#19133404C211yesmaximal, characteristic, complemented
10#19133398C211yesmaximal, characteristic, complemented
11#19133387C211yesmaximal, characteristic, complemented
12#19133360C211yesmaximal, characteristic, complemented
13#19133056C211yesmaximal, characteristic, complemented
14C8×#10621877C211yesmaximal, characteristic, complemented
15C43×#1492C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305C411yescharacteristic
18#14583286C411yescharacteristic
19#14583263C411yescharacteristic
20#14583261C411yescharacteristic
21#14583150C411yescharacteristic
22#14583150C411yescharacteristic
23#14583143C411yescharacteristic
24#14583143C411yescharacteristic
25#14583026C2211yescharacteristic
26#14583023C2211yescharacteristic
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582977C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582975—21no—
35#14582971—21no—
36#14582971—21no—
37#14582968—21no—
38D4×C43⋊C8C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic
41#14582959—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582924—21no—
45#14582866—21no—
46#14582866—21no—
47C4×#10621877C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621883C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2×C411yescharacteristic
74C2×#10621877C2×C411yescharacteristic
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063319—21no—
80#13063317C2×C411yescharacteristic
81#13063313C2×C411yescharacteristic
82#13063308—21no—
83#13063304C2×C411yescharacteristic
84#13063299C2×C411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×D172C2311yescharacteristic
87C4×C22⋊D43—21no—
88#13063282—21no—
89#13063258C2×C411yescharacteristic
90#13063258C2×C411yescharacteristic
91#13063256C2×C411yescharacteristic
92#13063256C2×C411yescharacteristic
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063248C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102#13063246C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)—21no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)D411yescharacteristic
113C22⋊(C43⋊C8)D411yescharacteristic
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116#13063236—21no—
117#13063236C2×C411yescharacteristic
118#13063236C2×C411yescharacteristic
119#13063235—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C2×#41×C43—21no—
126C2×M16×C43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129#127×C43C2×C411yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43C2×C411yescharacteristic
133#121×C43C2×C411yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4×C8×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—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—42no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621883—22no—
181#10621883—22no—
182#10621882—22no—
183#10621882—22no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195#10621877—22no—
196#10621877—22no—
197#10621877—81no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
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—22no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
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#2981—431no—
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#1492D4311yescharacteristic, complemented
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—431no—
334#436—431no—
335#436—861no—
336#435—861no—
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342#433—861no—
343#432—431no—
344#431—431no—
345#424—861no—
346#423C2×D4311yescharacteristic
347#408—861no—
348#408—861no—
349C4×M16—431no—
350C2×C4×C8C2×D4311yescharacteristic
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⋊C8C2×D4311yescharacteristic
360D4⋊C8C2×D4311yescharacteristic
361D4⋊C8C2×D4311yescharacteristic
362D4⋊C8C2×D4311yescharacteristic
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—431no—
375C2×M16—431no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C22×C8—21no—
380C22×C8—861no—
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—21no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
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—431no—
425C22⋊C8—431no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—431no—
434#97—431no—
435#97—861no—
436#97—861no—
437C4×C8—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
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×C4D4×D4311yescharacteristic
462C22×C4#1062190011yescharacteristic
463SD16—862no—
464SD16—862no—
465D8—862no—
466D8—862no—
467M16—81no—
468M16—862no—
469M16—862no—
470M16—3441no—
471M16—3441no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8—3441no—
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
511C42D4×D4311yescharacteristic
512C42#1062190011yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—861no—
517C23(C22⋊D43)⋊C411yescharacteristic
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×C4(C22⋊D43)⋊C411yescharacteristic
549C2×C4(C22⋊D43)⋊C411yescharacteristic
550C2×C4(C22⋊D43)⋊C411yescharacteristic
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—432no—
559C8—432no—
560C8—861no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
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×(C22⋊D43)⋊C411yescharacteristic
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#1458370011yescharacteristic
593C4#1458370511yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—3441no—
598C2#1914330311yescharacteristic
599C2#1914342111yescharacteristic
600C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1492C2
socleC22×C43C2×C4×D4
prime radical#19145184C2
cosocleC42×C43C24
hypercenter#1492D43
hypocenterC43#17968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #19143740C2semidirect
3. #19143671C2semidirect
4. #19133506C2semidirect
5. #19133494C2semidirect
6. #19133488C2semidirect
7. #19133477C2semidirect
8. #19133416C2semidirect
9. #19133404C2semidirect
10. #19133398C2semidirect
11. #19133387C2semidirect
12. #19133360C2semidirect
13. #19133056C2semidirect
14. C8×#10621877C2semidirect
15. C43×#1492C2semidirect
307. #1492D43semidirect
367. C43#17968semidirect

Maximal subgroups

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

subgroupindex
#191451842
#191437402
#191436712
#191335062
#191334942
#191334882
#191334772
#191334162
#191334042
#191333982
#191333872
#191333602
#191330562
C8×#106218772
C43×#14922
#1796843