Finite Group Databasebeta

← #25004159

Subgroups — #25004159

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 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
4C2×#14582881C211yesmaximal, characteristic
5C2×#14582671C211yesmaximal, 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×#13063253—22no—
20C2×#13063251—22no—
21#14582881—22no—
22#14582881—22no—
23C2×#13063243C412yescomplemented
24C2×#13063241C412yescomplemented
25#14582671—22no—
26#14582659—22no—
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C22×C42×C43C2211yescharacteristic
30C43×#336—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×#10621898D412yes—
42C2×#10621898Q812yes—
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×#10621877C2×C412yes—
56C2×#10621877D412yes—
57C2×#10621877D412yes—
58C2×#10621877D412yes—
59C22×C43⋊C8—21no—
60C22×C43⋊C8—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284D412yes—
65C2×C4⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C4×Dic43—21no—
68#13063260—28no—
69#13063253—28no—
70#13063251—28no—
71#13063243—24no—
72#13063241—24no—
73C23×C4×C43—21no—
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×C43—21no—
85C2×M16×C43C2×C412yes—
86C2×M16×C43D412yes—
87C22×C8×C43—21no—
88C22×C8×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43D412yes—
95C24×C43#4111yescharacteristic
96C23×D43—21no—
97C22×C4×C43—22no—
98C22×C4×C43—44no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
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×C43C2×D411yescharacteristic
109C22×C4×C43C2×Q811yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C2×C22⋊D43—22no—
116C2×C22⋊D43—22no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C22×Dic43—21no—
122C22×Dic43—41no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C4⋊C412yes—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C4⋊C412yes—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164M16×C43—41no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C2×C8×C43—41no—
170C2×C8×C43—41no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—41no—
174C42×C43—41no—
175C22⋊Dic43—22no—
176C22⋊Dic43—41no—
177C4⋊Dic43—22no—
178C4⋊Dic43—41no—
179C4×Dic43—22no—
180C4×Dic43—41no—
181#10621877—22no—
182#10621877—22no—
183#10621877—22no—
184#10621877—22no—
185#10621877—22no—
186#10621877—41no—
187#10621877—41no—
188#10621877C22⋊C414yes—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C23×C43—42no—
196C23×C43#11711yescharacteristic
197C23×C43#12111yescharacteristic
198C23×C43C22⋊Q811yescharacteristic
199C23×C43#12311yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12411yescharacteristic
202C23×C43#12411yescharacteristic
203C22×D43—22no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—82no—
207C2×C4×C43—24no—
208C2×C4×C43—42no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—42no—
212C2×C4×C43C2×C22⋊C411yescharacteristic
213C2×C4×C43C2×C4⋊C411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C22⋊Q811yescharacteristic
229C2×C4×C43C22⋊Q811yescharacteristic
230C2×C4×C43C22⋊Q811yescharacteristic
231C2×C4×C43C22⋊Q811yescharacteristic
232C2×C4×C43C22⋊Q811yescharacteristic
233C2×C4×C43#12311yescharacteristic
234C2×C4×C43#12311yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12411yescharacteristic
237C2×C4×C43#12611yescharacteristic
238C2×C4×C43#12611yescharacteristic
239C2×C4×C43#12711yescharacteristic
240C22⋊D43—42no—
241C22⋊D43—42no—
242C22⋊D43—42no—
243C22⋊D43—42no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—42no—
248C2×Dic43—82no—
249D172—22no—
250D172—22no—
251D172—41no—
252D172—41no—
253C4×D43—42no—
254C4×D43—42no—
255C4×D43—42no—
256C4×D43—42no—
257Dic86—22no—
258Dic86—22no—
259Dic86—41no—
260Dic86—41no—
261C8×C43—42no—
262C8×C43—42no—
263C43⋊C8—24no—
264C43⋊C8—42no—
265#11146—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43#38011yescharacteristic
274C22×C43#38811yescharacteristic
275C22×C43#38811yescharacteristic
276C22×C43#39311yescharacteristic
277C22×C43#39411yescharacteristic
278C22×C43#39411yescharacteristic
279C22×C43#39911yescharacteristic
280C2×D43—42no—
281C2×D43—82no—
282C2×D43—82no—
283C2×D43—82no—
284C4×C43—44no—
285C4×C43#38511yescharacteristic
286C4×C43#38511yescharacteristic
287C4×C43#38611yescharacteristic
288C4×C43#39011yescharacteristic
289C4×C43#39211yescharacteristic
290C4×C43#39611yescharacteristic
291C4×C43#39611yescharacteristic
292C4×C43#39711yescharacteristic
293Dic43—42no—
294Dic43—82no—
295C2×#430—431no—
296C2×#421—431no—
297C22×#104—431no—
298C2×#413—431no—
299C2×#344—431no—
300C2×#339—431no—
301#1728D4311yescharacteristic, complemented
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43#143911yescharacteristic
309C2×C43#193212yes—
310D43—82no—
311C22×#41—431no—
312C22×M16—431no—
313C22×M16—431no—
314C22×M16C2×D4311yescharacteristic
315C22×M16C2×D4311yescharacteristic
316C2×#117—431no—
317C22×C42C2×D4311yescharacteristic
318#430—862no—
319#430—862no—
320C2×#108—862no—
321#421—862no—
322#421—862no—
323C2×#104—862no—
324C2×#104—862no—
325C2×#104—862no—
326C2×#104—862no—
327#413—862no—
328#413—862no—
329C2×#101—432no—
330C2×#100—432no—
331#344—862no—
332#339—862no—
333#336—22no—
334C43#1114611yescharacteristic, complemented, Sylow
335C2×#41—432no—
336C2×#41—432no—
337C2×#41—861no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C22×Q8—431no—
348C22×D4—431no—
349C22×D4—861no—
350C23×C4—21no—
351C23×C4—861no—
352C23×C4C22×D4311yescharacteristic
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—21no—
362C2×M16—21no—
363C2×M16—432no—
364C2×M16—432no—
365C2×M16—432no—
366C2×M16—432no—
367C2×M16—861no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16C4×D4312yes—
376C2×M16D17212yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—861no—
380C22×C8—861no—
381#117—432no—
382#117—861no—
383#117—861no—
384#117—861no—
385C2×C4⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—861no—
393C2×C42C22⋊D4312yes—
394#108—868no—
395#104—868no—
396#104—868no—
397#101—864no—
398#100—864no—
399C24—861no—
400C24#1062189811yescharacteristic
401#41—862no—
402#41—862no—
403#41—862no—
404#41—862no—
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—1721no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417C2×Q8—432no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—432no—
424C2×D4—862no—
425C2×D4—862no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—1721no—
432C2×D4—1721no—
433C2×D4—1721no—
434C2×D4—1721no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—861no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4C2×C4×D4311yescharacteristic
448C22×C4C2×D17211yescharacteristic
449C22×C4#1062189811yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4#1062189811yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4#1062190011yescharacteristic
458C22×C4Q8×D4311yescharacteristic
459C22×C4#1062190211yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—434no—
470M16—862no—
471M16—862no—
472M16—862no—
473M16—862no—
474M16—862no—
475M16—1721no—
476M16—1721no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C2×C8—1721no—
488C2×C8—1721no—
489C4⋊C4—862no—
490C4⋊C4—1721no—
491C22⋊C4—862no—
492C22⋊C4—1721no—
493C42—22no—
494C42—22no—
495C42—41no—
496C42—41no—
497C42—862no—
498C42—1721no—
499C23—42no—
500C23—862no—
501C23—3442no—
502C23—1721no—
503C23—1721no—
504C23#1306328211yescharacteristic
505C23#1306329811yescharacteristic
506C23#1306330311yescharacteristic
507C23#1306330811yescharacteristic
508C23#1306331011yescharacteristic
509C23#1306331111yescharacteristic
510C23#1306331311yescharacteristic
511Q8—862no—
512Q8—862no—
513Q8—1721no—
514Q8—1721no—
515D4—862no—
516D4—862no—
517D4—1722no—
518D4—1722no—
519D4—1722no—
520D4—1722no—
521D4—1721no—
522D4—1721no—
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—862no—
529C2×C4—3442no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4C22⋊C4×D4311yescharacteristic
538C2×C4C4⋊C4×D4311yescharacteristic
539C2×C4(C22⋊D43)⋊C411yescharacteristic
540C2×C4C4×C22⋊D4311yescharacteristic
541C2×C4#1306328711yescharacteristic
542C2×C4C4×D17211yescharacteristic
543C2×C4#1306329311yescharacteristic
544C2×C4#1306329511yescharacteristic
545C2×C4#1306329511yescharacteristic
546C2×C4#1306329711yescharacteristic
547C2×C4#1306329811yescharacteristic
548C2×C4#1306329811yescharacteristic
549C2×C4#1306329811yescharacteristic
550C2×C4#1306329811yescharacteristic
551C2×C4#1306329911yescharacteristic
552C2×C4#1306330011yescharacteristic
553C2×C4#1306330111yescharacteristic
554C2×C4#1306330311yescharacteristic
555C2×C4#1306330311yescharacteristic
556C2×C4#1306330311yescharacteristic
557C2×C4#1306330511yescharacteristic
558C2×C4#1306330711yescharacteristic
559C2×C4#1306331011yescharacteristic
560C2×C4#1306331011yescharacteristic
561C2×C4#1306331111yescharacteristic
562C2×C4#1306331911yescharacteristic
563C2×C4#1306332011yescharacteristic
564C2×C4#1306332111yescharacteristic
565C8—42no—
566C8—42no—
567C8—864no—
568C8—1722no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—3442no—
577C22—3442no—
578C22—3442no—
579C22—1722no—
580C22#1458275811yescharacteristic
581C22#1458278811yescharacteristic
582C22#1458279011yescharacteristic
583C22#1458281211yescharacteristic
584C22#1458281411yescharacteristic
585C22#1458281711yescharacteristic
586C22#1458283411yescharacteristic
587C4—44no—
588C4—3442no—
589C4—1722no—
590C4#1458277011yescharacteristic
591C4#1458277311yescharacteristic
592C4#1458277711yescharacteristic
593C4#1458279911yescharacteristic
594C4#1458280811yescharacteristic
595C4#1458282111yescharacteristic
596C4#1458282311yescharacteristic
597C4#1458282811yescharacteristic
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—3442no—
605C2#1913283911yescharacteristic
606C2#1913526412yes—
subgroupG/H
centerC2×C4#13063299
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1728C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1728D43
hypocenterC43#11146
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×#14582671C2semidirect
6. C2×#14582659C2semidirect
7. C43×#1728C2semidirect
23. C2×#13063243C4semidirect
24. C2×#13063241C4semidirect
301. #1728D43semidirect
334. C43#11146semidirect

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
C2×#145828812
C2×#145826712
C2×#145826592
C43×#17282
#1114643