Finite Group Databasebeta

← #25003939

Subgroups — #25003939

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582947C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3C22×#13063253C211yesmaximal, characteristic
4#19143039C211yesmaximal, characteristic
5C2×#14582670C211yesmaximal, characteristic, complemented
6C2×#14582659C211yesmaximal, characteristic, complemented
7C43×#1728C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582947—22no—
13#14582947—22no—
14C2×#13063260—22no—
15#14582915—22no—
16#14582915—22no—
17C2×#13063253—22no—
18C2×#13063253—22no—
19C2×#13063253C414yescomplemented
20C2×#13063251—22no—
21#14582867—22no—
22#14582865—22no—
23#14582862—22no—
24#14582670—22no—
25#14582659—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C22×C42×C43C2211yescharacteristic
29C43×#336—22no—
30C2×#10621898—21no—
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×#10621898C2×C412yes—
41C2×#10621898D412yes—
42C22×Dic86Q811yescharacteristic
43C22×D172Q811yescharacteristic
44C22×C22⋊D43—21no—
45C22×C4×D43—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877C2×C412yes—
55C2×#10621877D412yes—
56C2×#10621877D412yes—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284D412yes—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67#13063260—28no—
68#13063253—28no—
69#13063251—28no—
70(C2×D43)⋊C8—28no—
71C23×C4×C43—21no—
72C23×C4×C43C2311yescharacteristic
73C2×M16×C43—21no—
74C2×M16×C43—21no—
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×C43D412yes—
85C22×C8×C43—21no—
86C22×C8×C43D412yes—
87C2×C42×C43—21no—
88C2×C42×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43C2×C412yes—
93C24×C43#4111yescharacteristic
94C23×D43—21no—
95C22×C4×C43—22no—
96C22×C4×C43—44no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×Q811yescharacteristic
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—41no—
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×D172C4⋊C412yes—
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×Dic86C4⋊C412yes—
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—41no—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—41no—
172C42×C43—41no—
173C22⋊Dic43—22no—
174C22⋊Dic43—41no—
175C4⋊Dic43—22no—
176C4⋊Dic43—41no—
177C4×Dic43—22no—
178C4×Dic43—41no—
179#10621877—22no—
180#10621877—22no—
181#10621877—22no—
182#10621877—22no—
183#10621877—22no—
184#10621877—41no—
185#10621877—41no—
186#10621877C22⋊C414yes—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C23×C43—42no—
194C23×C43C4×D411yescharacteristic
195C23×C43#12111yescharacteristic
196C23×C43C22⋊Q811yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12411yescharacteristic
199C23×C43#12411yescharacteristic
200C23×C43#12611yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—82no—
205C2×C4×C43—24no—
206C2×C4×C43—42no—
207C2×C4×C43—44no—
208C2×C4×C43—44no—
209C2×C4×C43—42no—
210C2×C4×C43C2×C22⋊C411yescharacteristic
211C2×C4×C43C2×C4⋊C411yescharacteristic
212C2×C4×C43#11711yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12311yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12411yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C2×C4×C43#12711yescharacteristic
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—82no—
247D172—22no—
248D172—22no—
249D172—41no—
250D172—41no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—42no—
255Dic86—22no—
256Dic86—22no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—42no—
260C8×C43—42no—
261C43⋊C8—24no—
262C43⋊C8—42no—
263#11114—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#38511yescharacteristic
272C22×C43#38811yescharacteristic
273C22×C43#39011yescharacteristic
274C22×C43#39311yescharacteristic
275C22×C43#39411yescharacteristic
276C22×C43#39611yescharacteristic
277C22×C43#39711yescharacteristic
278C2×D43—44no—
279C2×D43—42no—
280C2×D43—82no—
281C2×D43—82no—
282C4×C43—44no—
283C4×C43#38011yescharacteristic
284C4×C43#38511yescharacteristic
285C4×C43#38611yescharacteristic
286C4×C43#38811yescharacteristic
287C4×C43#39211yescharacteristic
288C4×C43#39411yescharacteristic
289C4×C43#39611yescharacteristic
290C4×C43#39911yescharacteristic
291Dic43—42no—
292Dic43—82no—
293C2×#430—431no—
294C2×#421—431no—
295C22×#104—431no—
296#2879—431no—
297C2×#344—431no—
298C2×#339—431no—
299#1728D4311yescharacteristic, complemented
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43#143911yescharacteristic
307C2×C43#186112yes—
308D43—82no—
309C22×#41—431no—
310C22×M16—431no—
311C22×M16—431no—
312C22×M16C2×D4311yescharacteristic
313C22×M16C2×D4311yescharacteristic
314C2×#117—431no—
315C22×C42C2×D4311yescharacteristic
316#430—862no—
317#430—862no—
318C2×#108—862no—
319#421—862no—
320#421—862no—
321C2×#104—434no—
322C2×#104—862no—
323C2×#104—862no—
324C2×#104—862no—
325#408—862no—
326#408—862no—
327#407—862no—
328#344—862no—
329#339—862no—
330#336—22no—
331C43#1111411yescharacteristic, 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—21no—
348C23×C4—861no—
349C23×C4C22×D4311yescharacteristic
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—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—432no—
362C2×M16—432no—
363C2×M16—432no—
364C2×M16—432no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16D17212yes—
374C22×C8—21no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8C22⋊D4312yes—
378#117—432no—
379#117—861no—
380#117—861no—
381#117—861no—
382C2×C4⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—861no—
390C2×C42C4×D4312yes—
391#108—868no—
392#104—868no—
393#104—868no—
394C22⋊C8—868no—
395C24—861no—
396C24#1062189811yescharacteristic
397#41—862no—
398#41—862no—
399#41—862no—
400#41—862no—
401#41—862no—
402#41—862no—
403#41—862no—
404#41—862no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413C2×Q8—432no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—861no—
419C2×D4—432no—
420C2×D4—862no—
421C2×D4—862no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—1721no—
428C2×D4—1721no—
429C2×D4—1721no—
430C2×D4—1721no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—861no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4C2×C4×D4311yescharacteristic
444C22×C4C2×D17211yescharacteristic
445C22×C4#1062189811yescharacteristic
446C22×C4#1062189811yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4#1062190011yescharacteristic
454C22×C4Q8×D4311yescharacteristic
455C22×C4#1062190211yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457M16—22no—
458M16—22no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—434no—
466M16—862no—
467M16—862no—
468M16—862no—
469M16—862no—
470M16—862no—
471M16—1721no—
472M16—1721no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—862no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—862no—
483C2×C8—1721no—
484C2×C8—1721no—
485C4⋊C4—862no—
486C4⋊C4—1721no—
487C22⋊C4—862no—
488C22⋊C4—1721no—
489C42—22no—
490C42—22no—
491C42—41no—
492C42—41no—
493C42—862no—
494C42—1721no—
495C23—42no—
496C23—862no—
497C23—3442no—
498C23—1721no—
499C23—1721no—
500C23C4×C22⋊D4311yescharacteristic
501C23#1306329811yescharacteristic
502C23#1306330311yescharacteristic
503C23#1306331011yescharacteristic
504C23#1306331111yescharacteristic
505C23#1306331311yescharacteristic
506C23#1306331911yescharacteristic
507Q8—862no—
508Q8—862no—
509Q8—1721no—
510Q8—1721no—
511D4—862no—
512D4—862no—
513D4—1722no—
514D4—1722no—
515D4—1722no—
516D4—1722no—
517D4—1721no—
518D4—1721no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—862no—
525C2×C4—3442no—
526C2×C4—1722no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4C22⋊C4×D4311yescharacteristic
534C2×C4C4⋊C4×D4311yescharacteristic
535C2×C4#1306328211yescharacteristic
536C2×C4(C22⋊D43)⋊C411yescharacteristic
537C2×C4#1306328711yescharacteristic
538C2×C4C4×D17211yescharacteristic
539C2×C4#1306329311yescharacteristic
540C2×C4#1306329511yescharacteristic
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329711yescharacteristic
543C2×C4#1306329811yescharacteristic
544C2×C4#1306329811yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4#1306329811yescharacteristic
547C2×C4#1306329911yescharacteristic
548C2×C4#1306330011yescharacteristic
549C2×C4#1306330111yescharacteristic
550C2×C4#1306330311yescharacteristic
551C2×C4#1306330311yescharacteristic
552C2×C4#1306330311yescharacteristic
553C2×C4#1306330511yescharacteristic
554C2×C4#1306330711yescharacteristic
555C2×C4#1306330811yescharacteristic
556C2×C4#1306331011yescharacteristic
557C2×C4#1306331011yescharacteristic
558C2×C4#1306331111yescharacteristic
559C2×C4#1306332011yescharacteristic
560C2×C4#1306332111yescharacteristic
561C8—42no—
562C8—42no—
563C8—864no—
564C8—1722no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—3442no—
573C22—3442no—
574C22—1724no—
575C22—1722no—
576C22#1458277011yescharacteristic
577C22#1458279011yescharacteristic
578C22#1458279911yescharacteristic
579C22#1458281211yescharacteristic
580C22#1458281711yescharacteristic
581C22#1458282311yescharacteristic
582C22#1458282811yescharacteristic
583C4—44no—
584C4—3442no—
585C4—1722no—
586C4#1458275811yescharacteristic
587C4#1458277311yescharacteristic
588C4#1458277711yescharacteristic
589C4#1458278811yescharacteristic
590C4#1458280811yescharacteristic
591C4#1458281411yescharacteristic
592C4#1458282111yescharacteristic
593C4#1458283411yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—3442no—
601C2#1913283911yescharacteristic
602C2#1913483412yes—
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1728C2
socleC22×C43#385
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1728D43
hypocenterC43#11114
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
1. C2×#14582947C2semidirect
5. C2×#14582670C2semidirect
6. C2×#14582659C2semidirect
7. C43×#1728C2semidirect
19. C2×#13063253C4semidirect
299. #1728D43semidirect
331. C43#11114semidirect

Maximal subgroups

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

subgroupindex
C2×#145829472
C2×#145829152
C22×#130632532
#191430392
C2×#145826702
C2×#145826592
C43×#17282
#1111443