Finite Group Databasebeta

← #25004157

Subgroups — #25004157

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×#14582915C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C2×#14582670C211yesmaximal, characteristic, complemented
5C2×#14582660C211yesmaximal, characteristic, complemented
6#19134288C211yesmaximal, characteristic, complemented
7C2×C43×#430C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582915—22no—
13#14582915—22no—
14C2×#13063251—22no—
15C2×#13063251—22no—
16C2×#13063251—22no—
17C2×#13063251—22no—
18#14582881—22no—
19#14582881—22no—
20C2×#13063243C412yescomplemented
21C2×#13063241C412yescomplemented
22#14582670—22no—
23#14582660—22no—
24#14582653—22no—
25C22×M16×C43C2211yescharacteristic
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C43×#430—22no—
29C43×#430—22no—
30C2×#108×C43—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—
46C23×Dic43—21no—
47C22×C4×D43—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877C2×C412yes—
54C22×C43⋊C8—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284D412yes—
59C2×C4⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43D412yes—
68#13063251—28no—
69#13063251—28no—
70#13063243—24no—
71#13063241—24no—
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×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43C2×C412yes—
87C2×M16×C43D412yes—
88C2×M16×C43D412yes—
89C2×M16×C43D412yes—
90C2×M16×C43D412yes—
91C22×C8×C43—21no—
92C22×C8×C43—21no—
93C22×C8×C43—21no—
94#108×C43—28no—
95C24×C43#4111yescharacteristic
96C23×D43—21no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×Q811yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—22no—
112C2×C22⋊D43—22no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—21no—
118C22×Dic43—22no—
119C22×Dic43—44no—
120C22×Dic43—41no—
121C22×Dic43—41no—
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—22no—
162M16×C43—22no—
163M16×C43—22no—
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168M16×C43C22⋊C414yes—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C2×C8×C43—41no—
178C22⋊Dic43—22no—
179C22⋊Dic43—41no—
180C4⋊Dic43—22no—
181C4⋊Dic43—41no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43—22no—
185C4×Dic43—41no—
186C4×Dic43—41no—
187C4×Dic43—41no—
188#10621877—22no—
189#10621877—22no—
190#10621877—41no—
191#10621877—41no—
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×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43C2×C4⋊C411yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
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×C43C22⋊Q811yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
227C2×C4×C43C22⋊Q811yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12711yescharacteristic
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C2×Dic43—24no—
240C2×Dic43—22no—
241C2×Dic43—42no—
242C2×Dic43—44no—
243C2×Dic43—44no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—42no—
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—24no—
262C8×C43—42no—
263C8×C43—42no—
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#38511yescharacteristic
285C4×C43#38511yescharacteristic
286C4×C43#38611yescharacteristic
287C4×C43#39011yescharacteristic
288C4×C43#39211yescharacteristic
289C4×C43#39611yescharacteristic
290C4×C43#39611yescharacteristic
291C4×C43#39711yescharacteristic
292Dic43—44no—
293Dic43—42no—
294Dic43—82no—
295C2×#430D4311yescharacteristic, complemented
296C2×#421—431no—
297C22×#104—431no—
298C2×#413—431no—
299C2×#344—431no—
300C2×#339—431no—
301#1728—431no—
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×M16C2×D4311yescharacteristic
314C22×M16C2×D4311yescharacteristic
315C22×M16C2×D4311yescharacteristic
316C2×#117—431no—
317C22×C42—431no—
318#430—22no—
319#430—22no—
320C2×#108—22no—
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—862no—
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—861no—
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—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×M16C4×D4312yes—
373C2×M16D17212yes—
374C2×M16C22⋊D4312yes—
375C2×M16C22⋊D4312yes—
376C2×M16C22⋊D4312yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
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—432no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—861no—
393C2×C42—861no—
394#108—28no—
395#104—868no—
396#104—868no—
397#101—864no—
398#100—864no—
399C24—861no—
400C24#1062190211yescharacteristic
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—861no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—1724no—
440C22×C4—1721no—
441C22×C4—1721no—
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×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4Q8×D4311yescharacteristic
456C22×C4#1062190211yescharacteristic
457C22×C4#1062190211yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—862no—
473M16—862no—
474M16—1721no—
475M16—1721no—
476M16(C2×D43)⋊C414yes—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—862no—
487C2×C8—1721no—
488C2×C8—1721no—
489C4⋊C4—862no—
490C4⋊C4—1721no—
491C22⋊C4—862no—
492C22⋊C4—1721no—
493C42—862no—
494C42—862no—
495C42—862no—
496C42—1721no—
497C42—1721no—
498C42—1721no—
499C23—42no—
500C23—862no—
501C23—3442no—
502C23—1721no—
503C23—1721no—
504C23#1306328311yescharacteristic
505C23#1306330011yescharacteristic
506C23#1306330111yescharacteristic
507C23#1306331011yescharacteristic
508C23#1306331011yescharacteristic
509C23#1306331411yescharacteristic
510C23#1306331411yescharacteristic
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—864no—
524C2×C4—862no—
525C2×C4—3442no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1724no—
529C2×C4—1724no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4C2×(C2×D43)⋊C411yescharacteristic
538C2×C4C4⋊C4×D4311yescharacteristic
539C2×C4C4×C22⋊D4311yescharacteristic
540C2×C4C4×C22⋊D4311yescharacteristic
541C2×C4#1306328711yescharacteristic
542C2×C4#1306328711yescharacteristic
543C2×C4#1306329311yescharacteristic
544C2×C4#1306329311yescharacteristic
545C2×C4#1306329411yescharacteristic
546C2×C4#1306329611yescharacteristic
547C2×C4#1306329711yescharacteristic
548C2×C4#1306329711yescharacteristic
549C2×C4#1306329911yescharacteristic
550C2×C4#1306329911yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4#1306330011yescharacteristic
553C2×C4#1306330111yescharacteristic
554C2×C4#1306330111yescharacteristic
555C2×C4#1306330311yescharacteristic
556C2×C4#1306330311yescharacteristic
557C2×C4#1306330511yescharacteristic
558C2×C4#1306330811yescharacteristic
559C2×C4#1306331011yescharacteristic
560C2×C4#1306331011yescharacteristic
561C2×C4#1306331411yescharacteristic
562C2×C4#1306332011yescharacteristic
563C2×C4#1306332011yescharacteristic
564C2×C4#1306332111yescharacteristic
565C8—24no—
566C8—42no—
567C8—42no—
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#1458275611yescharacteristic
581C22#1458278911yescharacteristic
582C22#1458278911yescharacteristic
583C22#1458281011yescharacteristic
584C22#1458281611yescharacteristic
585C22#1458281611yescharacteristic
586C22#1458283411yescharacteristic
587C4—3442no—
588C4—1724no—
589C4—1722no—
590C4#1458277011yescharacteristic
591C4#1458277011yescharacteristic
592C4#1458277811yescharacteristic
593C4#1458280011yescharacteristic
594C4#1458280711yescharacteristic
595C4#1458282111yescharacteristic
596C4#1458282111yescharacteristic
597C4#1458282511yescharacteristic
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—3442no—
605C2#1913283711yescharacteristic
606C2#1913526312yes—
subgroupG/H
centerC2×C4#13063297
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#430C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#430D43
hypocenterC43#11146
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×#14582670C2semidirect
5. C2×#14582660C2semidirect
6. #19134288C2semidirect
7. C2×C43×#430C2semidirect
20. C2×#13063243C4semidirect
21. C2×#13063241C4semidirect
295. C2×#430D43semidirect
334. C43#11146semidirect

Maximal subgroups

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

subgroupindex
C2×#145829152
C22×#130632512
C2×#145828812
C2×#145826702
C2×#145826602
#191342882
C2×C43×#4302
#1114643