Finite Group Databasebeta

← #25004383

Subgroups — #25004383

Order 11008.

830 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582917C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3#19143039C211yesmaximal, characteristic
4C2×#14582667C211yesmaximal, characteristic, complemented
5#19134316C211yesmaximal, characteristic, complemented
6C2×C43⋊#338C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12#14582917—22no—
13#14582917—22no—
14C2×#13063253—22no—
15#14582901—22no—
16#14582901—22no—
17C2×#13063250C412yescomplemented
18C2×#13063247C412yescomplemented
19#14582867—22no—
20#14582865—22no—
21#14582862—22no—
22#14582667—22no—
23#14582661—22no—
24C43⋊#338—22no—
25C22×M16×C43C2211yescharacteristic
26C22×M16×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#344—22no—
29C2×#10621898—21no—
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×#10621898D412yes—
40C2×#10621898D412yes—
41C22×Dic86C2×C411yescharacteristic
42C22×D172C2×C411yescharacteristic
43C22×C22⋊D43—21no—
44C23×Dic43—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×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877D412yes—
58C22×C43⋊C8—21no—
59C22×C43⋊C8D412yes—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2×C412yes—
66#13063253—28no—
67#13063250—24no—
68#13063247—24no—
69(C2×D43)⋊C8—28no—
70C23×C4×C43C2311yescharacteristic
71C2×M16×C43—21no—
72C2×M16×C43—21no—
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×C43D412yes—
83C22×C8×C43—21no—
84C22×C8×C43C2×C412yes—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43D412yes—
89C2×C4⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C42×C43—21no—
92C24×C43#4111yescharacteristic
93C23×D43—21no—
94C22×C4×C43—41no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C2×C22⋊D43—22no—
110C2×C22⋊D43—22no—
111C2×C22⋊D43—41no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C22×Dic43—21no—
116C22×Dic43—22no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43—82no—
120#10621898—22no—
121#10621898—22no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—41no—
129#10621898—41no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172C22⋊C412yes—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C22⋊C412yes—
154M16×C43—22no—
155M16×C43—22no—
156M16×C43—41no—
157M16×C43—41no—
158M16×C43—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—41no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—41no—
167C2×C8×C43—41no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—41no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—41no—
172C42×C43—22no—
173C42×C43—41no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—41no—
177C4⋊Dic43—41no—
178#10621877—22no—
179#10621877—22no—
180#10621877—41no—
181#10621877—41no—
182#10621877—41no—
183#10621877—41no—
184#10621877—41no—
185#10621877—41no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—41no—
191C2×C43⋊C8—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43C4×D411yescharacteristic
195C23×C43#12111yescharacteristic
196C23×C43#12311yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12411yescharacteristic
199C23×C43#12611yescharacteristic
200C23×C43#12611yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—81no—
205C22×D43—81no—
206C2×C4×C43—42no—
207C2×C4×C43—81no—
208C2×C4×C43—81no—
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43#11711yescharacteristic
211C2×C4×C43#11711yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12311yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12411yescharacteristic
234C2×C4×C43#12411yescharacteristic
235C2×C4×C43#12611yescharacteristic
236C2×C4×C43#12611yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C2×Dic43—22no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—82no—
246C2×Dic43—82no—
247C2×Dic43—82no—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—42no—
255C4×D43—42no—
256Dic86—22no—
257Dic86—22no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—42no—
261C8×C43—42no—
262C43⋊C8—42no—
263C43⋊C8—42no—
264#11185—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43#38611yescharacteristic
276C22×C43#38811yescharacteristic
277C22×C43#38811yescharacteristic
278C22×C43#39411yescharacteristic
279C22×C43#39711yescharacteristic
280C22×C43#39711yescharacteristic
281C22×C43#39711yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—82no—
286C2×D43—82no—
287C4×C43—82no—
288C4×C43#38111yescharacteristic
289C4×C43#38611yescharacteristic
290C4×C43#38811yescharacteristic
291C4×C43#38811yescharacteristic
292C4×C43#39411yescharacteristic
293C4×C43#39411yescharacteristic
294C4×C43#39411yescharacteristic
295C4×C43#39711yescharacteristic
296Dic43—42no—
297Dic43—82no—
298C2×#421—431no—
299C2×#417—431no—
300#2879—431no—
301C2×#344D4311yescharacteristic, complemented
302C2×#343—431no—
303#1736—431no—
304C2×#338—431no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43#144011yescharacteristic
312C2×C43#190211yescharacteristic
313C2×C43#190311yescharacteristic
314D43—82no—
315C22×#41—431no—
316C22×M16—431no—
317C22×M16—431no—
318C22×M16C2×D4311yescharacteristic
319C22×M16C2×D4311yescharacteristic
320C2×#117C2×D4311yescharacteristic
321C22×C4⋊C4—431no—
322#421—862no—
323#421—862no—
324C2×#104—862no—
325#417—862no—
326#417—862no—
327C2×#103—432no—
328C2×#102—432no—
329#408—862no—
330#408—862no—
331#407—862no—
332#344—22no—
333#343—862no—
334#340—862no—
335#338—862no—
336C43#1118511yescharacteristic, complemented, Sylow
337C2×#41—432no—
338C2×#41—432no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C2×#41—861no—
349C22×Q8—431no—
350C22×D4—431no—
351C22×D4—861no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4C22×D4311yescharacteristic
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—21no—
364C2×M16—21no—
365C2×M16—21no—
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×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16D17212yes—
379C22×C8—21no—
380C22×C8—432no—
381C22×C8—861no—
382C22×C8C4×D4312yes—
383#117—21no—
384#117—21no—
385#117—21no—
386#117C22⋊D4312yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—432no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396#104—868no—
397#103—864no—
398#102—864no—
399C22⋊C8—868no—
400C24—861no—
401C24#1062189811yescharacteristic
402#41—862no—
403#41—862no—
404#41—862no—
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—862no—
410#41—1721no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×D4—432no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—1721no—
433C2×D4—1721no—
434C2×D4—1721no—
435C2×D4—1721no—
436C22×C4—41no—
437C22×C4—861no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—3442no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4#1062189811yescharacteristic
452C22×C4#1062189811yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4#1062190011yescharacteristic
458C22×C4#1062190011yescharacteristic
459C22×C4#1062190211yescharacteristic
460C22×C4#1062190211yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—862no—
471M16—862no—
472M16—1721no—
473M16—1721no—
474M16—1721no—
475M16—1721no—
476M16—1721no—
477M16—1721no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C2×C8—862no—
488C2×C8—1721no—
489C2×C8—1721no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C22⋊C4—22no—
497C22⋊C4—41no—
498C42—22no—
499C42—41no—
500C23—41no—
501C23—41no—
502C23—862no—
503C23—3441no—
504C23—3441no—
505C23—1721no—
506C23—1721no—
507C23C4×D17211yescharacteristic
508C23#1306329811yescharacteristic
509C23#1306330811yescharacteristic
510C23#1306331011yescharacteristic
511C23#1306331111yescharacteristic
512C23#1306331911yescharacteristic
513C23#1306332011yescharacteristic
514Q8—862no—
515Q8—862no—
516Q8—1721no—
517Q8—1721no—
518D4—862no—
519D4—862no—
520D4—1722no—
521D4—1722no—
522D4—1722no—
523D4—1722no—
524D4—1721no—
525D4—1721no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—862no—
530C2×C4—3442no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—1722no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4C22⋊C4×D4311yescharacteristic
541C2×C4#1306328211yescharacteristic
542C2×C4#1306328311yescharacteristic
543C2×C4(C22⋊D43)⋊C411yescharacteristic
544C2×C4C4×C22⋊D4311yescharacteristic
545C2×C4#1306328711yescharacteristic
546C2×C4#1306329311yescharacteristic
547C2×C4#1306329511yescharacteristic
548C2×C4#1306329611yescharacteristic
549C2×C4#1306329711yescharacteristic
550C2×C4#1306329811yescharacteristic
551C2×C4#1306329811yescharacteristic
552C2×C4#1306329911yescharacteristic
553C2×C4#1306330011yescharacteristic
554C2×C4#1306330011yescharacteristic
555C2×C4#1306330711yescharacteristic
556C2×C4#1306330711yescharacteristic
557C2×C4#1306330711yescharacteristic
558C2×C4#1306330911yescharacteristic
559C2×C4#1306331011yescharacteristic
560C2×C4#1306331011yescharacteristic
561C2×C4#1306331011yescharacteristic
562C2×C4#1306331011yescharacteristic
563C2×C4#1306331111yescharacteristic
564C2×C4#1306331311yescharacteristic
565C2×C4#1306331411yescharacteristic
566C2×C4#1306332011yescharacteristic
567C2×C4#1306332011yescharacteristic
568C8—42no—
569C8—42no—
570C8—1722no—
571C8—1722no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—3442no—
583C22—3442no—
584C22—1722no—
585C22—1722no—
586C22—1722no—
587C22#1458277711yescharacteristic
588C22#1458279011yescharacteristic
589C22#1458279111yescharacteristic
590C22#1458281411yescharacteristic
591C22#1458282511yescharacteristic
592C22#1458282811yescharacteristic
593C22#1458282811yescharacteristic
594C4—82no—
595C4—3442no—
596C4—1722no—
597C4#1458276111yescharacteristic
598C4#1458277511yescharacteristic
599C4#1458278811yescharacteristic
600C4#1458278911yescharacteristic
601C4#1458281511yescharacteristic
602C4#1458281611yescharacteristic
603C4#1458281711yescharacteristic
604C4#1458282611yescharacteristic
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—3442no—
612C2#1913284311yescharacteristic
613C2#1913506711yescharacteristic
614C2#1913507411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#11185
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#14582667C2semidirect
5. #19134316C2semidirect
6. C2×C43⋊#338C2semidirect
7. C2×C43×#344C2semidirect
17. C2×#13063250C4semidirect
18. C2×#13063247C4semidirect
301. C2×#344D43semidirect
336. C43#11185semidirect

Maximal subgroups

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

subgroupindex
C2×#145829172
C2×#145829012
#191430392
C2×#145826672
#191343162
C2×C43⋊#3382
C2×C43×#3442
#1118543