Finite Group Databasebeta

← #25002997

Subgroups — #25002997

Order 11008.

904 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
1C2×#14582915C211yesmaximal, characteristic
2#19143112C211yesmaximal, characteristic
3#19143039C211yesmaximal, characteristic
4#19143013C211yesmaximal, characteristic, complemented
5C2×C43⋊#338C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582915—22no—
13#14582915C414yescomplemented
14C2×#13063251—22no—
15#14582907C412yescomplemented
16#14582903C412yescomplemented
17#14582898—22no—
18#14582893—22no—
19#14582867C414yescomplemented
20#14582865—22no—
21#14582862—22no—
22#14582857—22no—
23#14582854—22no—
24M16×Dic43—22no—
25C43⋊#338—22no—
26#14582655—22no—
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C43×#344—22no—
31C2×#10621898—21no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898C2×C412yes—
42C2×#10621898C2×C412yes—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43—21no—
46C22×C4×D43—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877C2×C412yes—
58C2×#10621877D412yes—
59C22×C43⋊C8C2×C412yes—
60C22×C43⋊C8D412yes—
61#13063284—21no—
62#13063284—21no—
63#13063284C2×C412yes—
64#13063284D412yes—
65C2×C4⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C4×Dic43D412yes—
68#13063251—28no—
69#13063248—24no—
70#13063245—24no—
71(C2×D43)⋊C8—28no—
72#13063235—24no—
73C8×Dic43—24no—
74C23×C4×C43C2311yescharacteristic
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43C2×C412yes—
85C2×M16×C43C2×C412yes—
86C2×M16×C43D412yes—
87C22×C8×C43—21no—
88C22×C8×C43D412yes—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92#117×C43C2×C412yes—
93C2×C4⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43—21no—
96C24×C43#4111yescharacteristic
97C23×D43—21no—
98C22×C4×C43—41no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C2×C22⋊D43—22no—
114C2×C22⋊D43—22no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C22×Dic43—21no—
120C22×Dic43—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172C4212yes—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C4212yes—
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—41no—
162M16×C43—41no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—41no—
167C2×C8×C43—41no—
168C2×C8×C43C22⋊C414yes—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—41no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—41no—
173C42×C43—22no—
174C42×C43—41no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43C22⋊C414yes—
181#10621877—22no—
182#10621877—22no—
183#10621877—22no—
184#10621877—22no—
185#10621877—41no—
186#10621877—41no—
187#10621877—41no—
188#10621877—41no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8C22⋊C414yes—
195C23×C43—81no—
196C23×C43#11711yescharacteristic
197C23×C43C4×D411yescharacteristic
198C23×C43C4×D411yescharacteristic
199C23×C43#12111yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12411yescharacteristic
202C23×C43#12611yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—82no—
207C2×C4×C43—42no—
208C2×C4×C43—82no—
209C2×C4×C43C2×C4211yescharacteristic
210C2×C4×C43C2×C22⋊C411yescharacteristic
211C2×C4×C43C2×C22⋊C411yescharacteristic
212C2×C4×C43C2×C22⋊C411yescharacteristic
213C2×C4×C43#11711yescharacteristic
214C2×C4×C43#11711yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C4×D411yescharacteristic
219C2×C4×C43C4×D411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12411yescharacteristic
234C2×C4×C43#12411yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43#12711yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C2×Dic43—22no—
242C2×Dic43—24no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246D172—22no—
247D172—22no—
248D172—41no—
249D172—41no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254Dic86—22no—
255Dic86—22no—
256Dic86—41no—
257Dic86—41no—
258C8×C43—24no—
259C8×C43—42no—
260C43⋊C8—24no—
261C43⋊C8—42no—
262#10950—431nomaximal, Sylow
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C4×C22⋊C411yescharacteristic
271C22×C43#38611yescharacteristic
272C22×C43#38811yescharacteristic
273C22×C43#38811yescharacteristic
274C22×C43#38811yescharacteristic
275C22×C43#38811yescharacteristic
276C22×C43#39011yescharacteristic
277C2×D43—44no—
278C2×D43—42no—
279C2×D43—82no—
280C2×D43—82no—
281C4×C43—82no—
282C4×C43C4×C22⋊C411yescharacteristic
283C4×C43C4×C22⋊C411yescharacteristic
284C4×C43#38611yescharacteristic
285C4×C43#38611yescharacteristic
286C4×C43#38811yescharacteristic
287C4×C43#38811yescharacteristic
288C4×C43#39011yescharacteristic
289C4×C43#39011yescharacteristic
290Dic43—44no—
291Dic43—42no—
292C2×#421—431no—
293#2896—431no—
294#2879—431no—
295#2873—431no—
296C2×#344D4311yescharacteristic, complemented
297C2×#338—431no—
298C2×H(3,ℤ/4)—431no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43#143711yescharacteristic
307D43—82no—
308C22×#41—431no—
309C22×M16—431no—
310C22×M16—431no—
311C22×M16C2×D4311yescharacteristic
312C22×M16C2×D4311yescharacteristic
313C2×#117—431no—
314C2×#117C2×D4311yescharacteristic
315#421—434no—
316#421—862no—
317C2×#104—862no—
318#419—432no—
319#418—432no—
320#417—862no—
321#416—862no—
322#408—434no—
323#408—862no—
324#407—862no—
325#405—862no—
326#405—862no—
327C4×M16—862no—
328#344—22no—
329#338—862no—
330H(3,ℤ/4)—862no—
331C43#1095011yescharacteristic, complemented, Sylow
332C2×#41—432no—
333C2×#41—432no—
334C2×#41—861no—
335C2×#41—861no—
336C2×#41—861no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C22×Q8—431no—
345C22×D4—431no—
346C22×D4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—432no—
359C2×M16—432no—
360C2×M16—861no—
361C2×M16—861no—
362C2×M16—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16C4×D4312yes—
371C2×M16C4×D4312yes—
372C2×M16C22⋊D4312yes—
373C22×C8—21no—
374C22×C8—432no—
375C22×C8—432no—
376C22×C8D17212yes—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—432no—
381#117—432no—
382#117—861no—
383#117—861no—
384#117C4×D4312yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—861no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—861no—
389C2×C42—21no—
390C2×C42—432no—
391#104—868no—
392#103—864no—
393#102—864no—
394C22⋊C8—868no—
395#97—864no—
396C4×C8—864no—
397C24—861no—
398C24#1062189811yescharacteristic
399#41—862no—
400#41—862no—
401#41—862no—
402#41—862no—
403#41—862no—
404#41—862no—
405#41—862no—
406#41—862no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415C2×Q8—432no—
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×D4—432no—
422C2×D4—862no—
423C2×D4—862no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—1721no—
430C2×D4—1721no—
431C2×D4—1721no—
432C2×D4—1721no—
433C22×C4—41no—
434C22×C4—862no—
435C22×C4—861no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4C2×C4×D4311yescharacteristic
443C22×C4C2×C4×D4311yescharacteristic
444C22×C4C2×C4×D4311yescharacteristic
445C22×C4C2×D17211yescharacteristic
446C22×C4#1062189811yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4#1062190011yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4#1062190211yescharacteristic
454C22×C4#1062190211yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—862no—
465M16—862no—
466M16—862no—
467M16—862no—
468M16—1721no—
469M16—1721no—
470M16—1721no—
471M16—1721no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—434no—
478C2×C8—862no—
479C2×C8—862no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—862no—
483C2×C8(C2×D43)⋊C414yes—
484C4⋊C4—22no—
485C4⋊C4—41no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C42—22no—
493C42—41no—
494C42—434no—
495C42—862no—
496C23—81no—
497C23—862no—
498C23—3442no—
499C23—1721no—
500C23—1721no—
501C23#1306328211yescharacteristic
502C23C4×C22⋊D4311yescharacteristic
503C23C4×D17211yescharacteristic
504C23#1306329811yescharacteristic
505C23#1306331011yescharacteristic
506C23#1306331111yescharacteristic
507C23#1306332011yescharacteristic
508Q8—862no—
509Q8—862no—
510Q8—1721no—
511Q8—1721no—
512D4—862no—
513D4—862no—
514D4—1722no—
515D4—1722no—
516D4—1722no—
517D4—1722no—
518D4—1721no—
519D4—1721no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—862no—
523C2×C4—864no—
524C2×C4—3442no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4C42×D4311yescharacteristic
532C2×C4C22⋊C4×D4311yescharacteristic
533C2×C4C22⋊C4×D4311yescharacteristic
534C2×C4C2×(C2×D43)⋊C411yescharacteristic
535C2×C4#1306328311yescharacteristic
536C2×C4#1306328311yescharacteristic
537C2×C4(C22⋊D43)⋊C411yescharacteristic
538C2×C4(C22⋊D43)⋊C411yescharacteristic
539C2×C4(C22⋊D43)⋊C411yescharacteristic
540C2×C4(C22⋊D43)⋊C411yescharacteristic
541C2×C4C4×C22⋊D4311yescharacteristic
542C2×C4#1306328711yescharacteristic
543C2×C4#1306328711yescharacteristic
544C2×C4#1306328711yescharacteristic
545C2×C4#1306328711yescharacteristic
546C2×C4C4×D17211yescharacteristic
547C2×C4#1306329511yescharacteristic
548C2×C4#1306329711yescharacteristic
549C2×C4#1306329711yescharacteristic
550C2×C4#1306329811yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4#1306330011yescharacteristic
553C2×C4#1306330911yescharacteristic
554C2×C4#1306331011yescharacteristic
555C2×C4#1306331111yescharacteristic
556C2×C4#1306331411yescharacteristic
557C2×C4#1306332011yescharacteristic
558C2×C4#1306332111yescharacteristic
559C8—24no—
560C8—42no—
561C8—864no—
562C8—1722no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—3442no—
571C22—3442no—
572C22—1724no—
573C22—1722no—
574C22C4×(C2×D43)⋊C411yescharacteristic
575C22#1458277711yescharacteristic
576C22#1458278811yescharacteristic
577C22#1458278811yescharacteristic
578C22#1458278911yescharacteristic
579C22#1458279111yescharacteristic
580C22#1458279911yescharacteristic
581C4—82no—
582C4—1724no—
583C4—1722no—
584C4#1458274611yescharacteristic
585C4#1458274611yescharacteristic
586C4#1458277611yescharacteristic
587C4#1458277711yescharacteristic
588C4#1458278911yescharacteristic
589C4#1458279111yescharacteristic
590C4#1458279911yescharacteristic
591C4#1458280011yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—3442no—
600C2#1913283111yescharacteristic
subgroupG/H
centerC4#14582776
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC2×C43#1437
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#10950
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #19143013C2semidirect
5. C2×C43⋊#338C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×#344C2semidirect
13. #14582915C4semidirect
15. #14582907C4semidirect
16. #14582903C4semidirect
19. #14582867C4semidirect
296. C2×#344D43semidirect
331. C43#10950semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
#191431122
#191430392
#191430132
C2×C43⋊#3382
C2×#145826552
C2×C43×#3442
#1095043