Finite Group Databasebeta

← #25004185

Subgroups — #25004185

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063251C211yesmaximal, characteristic
2#19143115C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4#19134333C211yesmaximal, characteristic, complemented
5C2×#14582660C211yesmaximal, characteristic, complemented
6#19134288C211yesmaximal, characteristic, complemented
7C2×C43×#338C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12C2×#13063251—22no—
13C2×#13063251—22no—
14C2×#13063251—22no—
15#14582909—21no—
16#14582905—21no—
17#14582901—22no—
18#14582896—22no—
19#14582881—22no—
20#14582881C414yescomplemented
21C2×#13063243—21no—
22C2×#13063241—21no—
23#14582667—22no—
24#14582660—22no—
25#14582653—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C22×M16×C43C2211yescharacteristic
29C43×#338—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×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C22×C4×D43—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877C2×C412yes—
53C22×C43⋊C8—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58C2×C4⋊Dic43D412yes—
59C2×C22⋊Dic43—21no—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43D412yes—
67#13063251—28no—
68#13063250—24no—
69#13063247—24no—
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×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43C2×C412yes—
90C2×M16×C43D412yes—
91C22×C8×C43—21no—
92C22×C8×C43—21no—
93C22×C8×C43D412yes—
94C24×C43#4111yescharacteristic
95C23×D43—21no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C2×C22⋊D43—22no—
111C2×C22⋊D43—22no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C22×Dic43—22no—
117C22×Dic43—21no—
118C22×Dic43—22no—
119C22×Dic43—44no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122#10621898—22no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—41no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172C22⋊C412yes—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—41no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22⋊C412yes—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4×Dic43—22no—
182C4×Dic43—22no—
183C4×Dic43—41no—
184C4×Dic43—41no—
185C4×Dic43—41no—
186C4×Dic43—41no—
187#10621877—22no—
188#10621877—22no—
189#10621877—41no—
190#10621877—41no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C23×C43—42no—
195C23×C43#11711yescharacteristic
196C23×C43#12111yescharacteristic
197C23×C43#12311yescharacteristic
198C23×C43#12311yescharacteristic
199C23×C43#12311yescharacteristic
200C23×C43#12411yescharacteristic
201C23×C43#12611yescharacteristic
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—82no—
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43#11711yescharacteristic
208C2×C4×C43C4×D411yescharacteristic
209C2×C4×C43C4×D411yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12311yescharacteristic
222C2×C4×C43#12311yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12411yescharacteristic
229C2×C4×C43#12411yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12611yescharacteristic
232C2×C4×C43#12611yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—42no—
237C22⋊D43—42no—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—42no—
241C2×Dic43—44no—
242C2×Dic43—44no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—42no—
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—
262C8×C43—42no—
263C43⋊C8—42no—
264#11151—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43#38111yescharacteristic
273C22×C43#38811yescharacteristic
274C22×C43#38811yescharacteristic
275C22×C43#39411yescharacteristic
276C22×C43#39411yescharacteristic
277C22×C43#39711yescharacteristic
278C22×C43#39711yescharacteristic
279C2×D43—42no—
280C2×D43—82no—
281C2×D43—82no—
282C2×D43—82no—
283C4×C43#38611yescharacteristic
284C4×C43#38611yescharacteristic
285C4×C43#38811yescharacteristic
286C4×C43#38811yescharacteristic
287C4×C43#39411yescharacteristic
288C4×C43#39411yescharacteristic
289C4×C43#39711yescharacteristic
290C4×C43#39711yescharacteristic
291Dic43—44no—
292Dic43—42no—
293Dic43—82no—
294C22×#104—431no—
295#2896—431no—
296C2×#413—431no—
297#1742—431no—
298C2×#339—431no—
299C2×#338D4311yescharacteristic, complemented
300#1728—431no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43#144011yescharacteristic
308C2×C43#205012yes—
309D43—82no—
310C22×#41—431no—
311C22×M16—431no—
312C22×M16C2×D4311yescharacteristic
313C22×M16C2×D4311yescharacteristic
314C22×M16C2×D4311yescharacteristic
315C2×#117—431no—
316C22×C42—431no—
317C2×#104—862no—
318C2×#104—862no—
319C2×#104—862no—
320#419—861no—
321#418—861no—
322#417—862no—
323#416—862no—
324#413—434no—
325#413—862no—
326C2×#101—861no—
327C2×#100—861no—
328#343—862no—
329#339—862no—
330#338—22no—
331#336—862no—
332C43#1115111yescharacteristic, complemented, Sylow
333C2×#41—432no—
334C2×#41—432no—
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—
344C2×#41—861no—
345C22×Q8—431no—
346C22×D4—431no—
347C22×D4—861no—
348C23×C4—861no—
349C23×C4—861no—
350C23×C4C22×D4311yescharacteristic
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—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—432no—
368C2×M16—861no—
369C2×M16—861no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16C4×D4312yes—
374C2×M16C22⋊D4312yes—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—861no—
378C22×C8D17212yes—
379#117—861no—
380#117—861no—
381#117—861no—
382#117—861no—
383C2×C4⋊C4—432no—
384C2×C22⋊C4—861no—
385C2×C42—432no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392#104—868no—
393#103—864no—
394#102—864no—
395#101—864no—
396#100—864no—
397C24—861no—
398C24#1062190211yescharacteristic
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—862no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—1724no—
439C22×C4—1721no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4C2×C4×D4311yescharacteristic
446C22×C4C2×D17211yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4#1062189811yescharacteristic
449C22×C4#1062189811yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4#1062190011yescharacteristic
456C22×C4#1062190011yescharacteristic
457C22×C4#1062190211yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—862no—
472M16—862no—
473M16—1721no—
474M16—1721no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—862no—
485C2×C8—1721no—
486C2×C8—1721no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—862no—
492C42—862no—
493C42—1721no—
494C42—1721no—
495C42—1721no—
496C42—1721no—
497C23—42no—
498C23—862no—
499C23—3442no—
500C23—1721no—
501C23—1721no—
502C23#1306328311yescharacteristic
503C23#1306330011yescharacteristic
504C23#1306331011yescharacteristic
505C23#1306331011yescharacteristic
506C23#1306331011yescharacteristic
507C23#1306331411yescharacteristic
508C23#1306332011yescharacteristic
509Q8—862no—
510Q8—862no—
511Q8—1721no—
512Q8—1721no—
513D4—862no—
514D4—862no—
515D4—1722no—
516D4—1722no—
517D4—1722no—
518D4—1722no—
519D4—1721no—
520D4—1721no—
521C2×C4—864no—
522C2×C4—862no—
523C2×C4—3442no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4—1724no—
527C2×C4—1724no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4C22⋊C4×D4311yescharacteristic
536C2×C4#1306328211yescharacteristic
537C2×C4(C22⋊D43)⋊C411yescharacteristic
538C2×C4C4×C22⋊D4311yescharacteristic
539C2×C4#1306328711yescharacteristic
540C2×C4C4×D17211yescharacteristic
541C2×C4#1306329311yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4#1306329611yescharacteristic
544C2×C4#1306329711yescharacteristic
545C2×C4#1306329811yescharacteristic
546C2×C4#1306329811yescharacteristic
547C2×C4#1306329811yescharacteristic
548C2×C4#1306329911yescharacteristic
549C2×C4#1306330011yescharacteristic
550C2×C4#1306330711yescharacteristic
551C2×C4#1306330711yescharacteristic
552C2×C4#1306330711yescharacteristic
553C2×C4#1306330811yescharacteristic
554C2×C4#1306330911yescharacteristic
555C2×C4#1306331011yescharacteristic
556C2×C4#1306331011yescharacteristic
557C2×C4#1306331111yescharacteristic
558C2×C4#1306331111yescharacteristic
559C2×C4#1306331311yescharacteristic
560C2×C4#1306331911yescharacteristic
561C2×C4#1306332011yescharacteristic
562C2×C4#1306332011yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—1722no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3442no—
575C22—3442no—
576C22—3442no—
577C22—1722no—
578C22#1458276111yescharacteristic
579C22#1458278911yescharacteristic
580C22#1458279111yescharacteristic
581C22#1458281611yescharacteristic
582C22#1458281711yescharacteristic
583C22#1458282511yescharacteristic
584C22#1458282811yescharacteristic
585C4—3442no—
586C4—1724no—
587C4—1722no—
588C4#1458277511yescharacteristic
589C4#1458277711yescharacteristic
590C4#1458278811yescharacteristic
591C4#1458279011yescharacteristic
592C4#1458281411yescharacteristic
593C4#1458281511yescharacteristic
594C4#1458282611yescharacteristic
595C4#1458282811yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—3442no—
603C2#1913284311yescharacteristic
604C2#1913588312yes—
subgroupG/H
centerC2×C4#13063313
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#338C2
socleC22×C43#394
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#338D43
hypocenterC43#11151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
4. #19134333C2semidirect
5. C2×#14582660C2semidirect
6. #19134288C2semidirect
7. C2×C43×#338C2semidirect
20. #14582881C4semidirect
299. C2×#338D43semidirect
332. C43#11151semidirect

Maximal subgroups

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

subgroupindex
C22×#130632512
#191431152
C2×#145828812
#191343332
C2×#145826602
#191342882
C2×C43×#3382
#1115143