Finite Group Databasebeta

← #25003801

Subgroups — #25003801

Order 11008.

852 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×#14582881C211yesmaximal, characteristic
2C2×#14582881C211yesmaximal, characteristic
3C2×#14582872C211yesmaximal, characteristic
4C2×#14582671C211yesmaximal, characteristic, complemented
5C2×#14582669C211yesmaximal, characteristic, complemented
6#19134333C211yesmaximal, characteristic, complemented
7C43×#2905C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582881—22no—
13#14582881—22no—
14#14582881—22no—
15#14582881—22no—
16C2×#13063243—21no—
17C2×#13063243—21no—
18C2×#13063241—21no—
19C2×#13063241—21no—
20#14582872—22no—
21#14582872—22no—
22C2×#13063239C414yes—
23#14582671—22no—
24#14582669—22no—
25#14582667—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C43×#424—22no—
30C43×#424—22no—
31C43×#423—22no—
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×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C22×Dic86D411yescharacteristic
45C22×D172D411yescharacteristic
46C22×C22⋊D43C2×C412yes—
47C22×C4×D43Q812yes—
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×#10621877—21no—
58C2×#10621877D412yes—
59C2×#10621877D412yes—
60C22×C43⋊C8—21no—
61C22×C43⋊C8—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66C2×C4⋊Dic43—21no—
67C2×C22⋊Dic43C2×C412yes—
68C2×C4×Dic43—21no—
69#13063243—24no—
70#13063243—24no—
71#13063241—24no—
72#13063241—24no—
73#13063239—28no—
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×C43D412yes—
86C2×M16×C43D412yes—
87C22×C8×C43—21no—
88C22×C8×C43—21no—
89#117×C43—21no—
90#117×C43—21no—
91#117×C43D412yes—
92#117×C43D412yes—
93C2×C4⋊C4×C43—21no—
94C2×C22⋊C4×C43C2×C412yes—
95C2×C42×C43—21no—
96C4⋊C8×C43—28no—
97C24×C43C22×C411yescharacteristic
98C23×D43C4⋊C412yes—
99C22×C4×C43—22no—
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
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—22no—
115C2×C22⋊D43—22no—
116C2×C22⋊D43—22no—
117C2×C22⋊D43—22no—
118C2×C22⋊D43—22no—
119C2×C22⋊D43—22no—
120C22×Dic43—22no—
121C22×Dic43C4⋊C412yes—
122#10621898—41no—
123#10621898—41no—
124#10621898—41no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129#10621898—41no—
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×D172—21no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—41no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—41no—
167C2×C8×C43—41no—
168C2×C8×C43—41no—
169C2×C8×C43—41no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43C22⋊C414yes—
174C42×C43—22no—
175C42×C43—22no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C4⋊Dic43—41no—
179C4⋊Dic43—41no—
180C4×Dic43—41no—
181C4×Dic43—41no—
182#10621877—22no—
183#10621877—22no—
184#10621877—22no—
185#10621877—22no—
186#10621877—41no—
187#10621877—41no—
188#10621877—41no—
189#10621877—41no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C23×C43—81no—
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43C2×C4⋊C411yescharacteristic
199C23×C43#11711yescharacteristic
200C23×C43C4×D411yescharacteristic
201C23×C43C4×D411yescharacteristic
202C23×C43C4×D411yescharacteristic
203C23×C43C4×D411yescharacteristic
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—82no—
208C2×C4×C43—24no—
209C2×C4×C43—82no—
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12111yescharacteristic
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×C43C22⋊Q811yescharacteristic
222C2×C4×C43C22⋊Q811yescharacteristic
223C2×C4×C43C22⋊Q811yescharacteristic
224C2×C4×C43C22⋊Q811yescharacteristic
225C2×C4×C43C22⋊Q811yescharacteristic
226C2×C4×C43C22⋊Q811yescharacteristic
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
237C2×C4×C43#12711yescharacteristic
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—42no—
246C2×Dic43—82no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—42no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—42no—
260C8×C43—42no—
261C43⋊C8—42no—
262C43⋊C8—42no—
263#11090—431nomaximal, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#38011yescharacteristic
272C22×C43#38511yescharacteristic
273C22×C43#38511yescharacteristic
274C22×C43#38611yescharacteristic
275C22×C43#38811yescharacteristic
276C22×C43#38811yescharacteristic
277C22×C43#39011yescharacteristic
278C2×D43—42no—
279C2×D43—82no—
280C2×D43—82no—
281C2×D43—82no—
282C4×C43—44no—
283C4×C43#39211yescharacteristic
284C4×C43#39311yescharacteristic
285C4×C43#39411yescharacteristic
286C4×C43#39411yescharacteristic
287C4×C43#39611yescharacteristic
288C4×C43#39611yescharacteristic
289C4×C43#39711yescharacteristic
290C4×C43#39911yescharacteristic
291Dic43—42no—
292Dic43—82no—
293#2905D4311yescharacteristic, complemented
294C2×#413—431no—
295C2×#413—431no—
296C2×#410—431no—
297C2×#344—431no—
298C2×#344—431no—
299#1742—431no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43#143911yescharacteristic
308D43—82no—
309C22×#41—431no—
310C22×M16—431no—
311C22×M16—431no—
312C22×M16C2×D4311yescharacteristic
313C22×M16C2×D4311yescharacteristic
314C2×#117—431no—
315C2×#117C2×D4311yescharacteristic
316#424—22no—
317#424—22no—
318#423—22no—
319#413—862no—
320#413—862no—
321#413—862no—
322#413—862no—
323C2×#101—861no—
324C2×#101—861no—
325C2×#100—861no—
326C2×#100—861no—
327#410—862no—
328#410—862no—
329C2×#99—434no—
330#344—862no—
331#344—862no—
332#343—862no—
333C43#1109011yescharacteristic, complemented, Sylow
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—
344C2×#41—861no—
345C2×#41—861no—
346C22×Q8—431no—
347C22×D4—432no—
348C22×D4—431no—
349C23×C4—432no—
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—432no—
362C2×M16—432no—
363C2×M16—861no—
364C2×M16—861no—
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×M16C22⋊D4312yes—
374C2×M16C22⋊D4312yes—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—861no—
378C22×C8—861no—
379#117—21no—
380#117—21no—
381#117—861no—
382#117—861no—
383#117—861no—
384#117—861no—
385#117D17212yes—
386#117C22⋊D4312yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—861no—
389C2×C22⋊C4—432no—
390C2×C22⋊C4C4×D4312yes—
391C2×C42—21no—
392C2×C42—861no—
393C4⋊C8—28no—
394#101—864no—
395#101—864no—
396#100—864no—
397#100—864no—
398#99—868no—
399C24—432no—
400C24C2×C4×D4311yescharacteristic
401#41—1721no—
402#41—1721no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407#41—1721no—
408#41—1721no—
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—861no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—862no—
424C2×D4—862no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—862no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C22×C4—22no—
436C22×C4—432no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4C2×D17211yescharacteristic
445C22×C4#1062189811yescharacteristic
446C22×C4#1062189811yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4Q8×D4311yescharacteristic
452C22×C4#1062190211yescharacteristic
453C22×C4#1062190211yescharacteristic
454C22×C4#1062190211yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—862no—
467M16—862no—
468M16—862no—
469M16—862no—
470M16—1721no—
471M16—1721no—
472M16—1721no—
473M16—1721no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—862no—
481C2×C8—862no—
482C2×C8—1721no—
483C2×C8—1721no—
484C2×C8—1721no—
485C2×C8—1721no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C22⋊C4—22no—
491C22⋊C4—862no—
492C22⋊C4—862no—
493C22⋊C4(C2×D43)⋊C414yes—
494C42—22no—
495C42—22no—
496C42—1721no—
497C42—1721no—
498C23—81no—
499C23—862no—
500C23—862no—
501C23—862no—
502C23—3442no—
503C23C2×(C2×D43)⋊C411yescharacteristic
504C23C4⋊C4×D4311yescharacteristic
505C23#1306328311yescharacteristic
506C23C4×C22⋊D4311yescharacteristic
507C23C4×C22⋊D4311yescharacteristic
508C23#1306328711yescharacteristic
509C23#1306328711yescharacteristic
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514D4—1722no—
515D4—1722no—
516D4—1722no—
517D4—1722no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—24no—
523C2×C4—82no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—3442no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4#1306329311yescharacteristic
534C2×C4#1306329311yescharacteristic
535C2×C4#1306329411yescharacteristic
536C2×C4#1306329611yescharacteristic
537C2×C4#1306329711yescharacteristic
538C2×C4#1306329711yescharacteristic
539C2×C4#1306329911yescharacteristic
540C2×C4#1306329911yescharacteristic
541C2×C4#1306330011yescharacteristic
542C2×C4#1306330011yescharacteristic
543C2×C4#1306330011yescharacteristic
544C2×C4#1306330111yescharacteristic
545C2×C4#1306330111yescharacteristic
546C2×C4#1306330111yescharacteristic
547C2×C4#1306330311yescharacteristic
548C2×C4#1306330311yescharacteristic
549C2×C4#1306330511yescharacteristic
550C2×C4#1306330811yescharacteristic
551C2×C4#1306331011yescharacteristic
552C2×C4#1306331011yescharacteristic
553C2×C4#1306331011yescharacteristic
554C2×C4#1306331011yescharacteristic
555C2×C4#1306331411yescharacteristic
556C2×C4#1306331411yescharacteristic
557C2×C4#1306331411yescharacteristic
558C2×C4#1306332011yescharacteristic
559C2×C4#1306332011yescharacteristic
560C2×C4#1306332111yescharacteristic
561C8—42no—
562C8—42no—
563C8—1722no—
564C8—1722no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—3442no—
573C22—3442no—
574C22—3442no—
575C22—1722no—
576C22#1458275611yescharacteristic
577C22#1458277011yescharacteristic
578C22#1458277011yescharacteristic
579C22#1458277811yescharacteristic
580C22#1458278911yescharacteristic
581C22#1458278911yescharacteristic
582C22#1458280011yescharacteristic
583C4—44no—
584C4—3442no—
585C4—1722no—
586C4#1458280711yescharacteristic
587C4#1458281011yescharacteristic
588C4#1458281611yescharacteristic
589C4#1458281611yescharacteristic
590C4#1458282111yescharacteristic
591C4#1458282111yescharacteristic
592C4#1458282511yescharacteristic
593C4#1458283411yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—3442no—
602C2#1913283711yescharacteristic
subgroupG/H
centerC4#14582810
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2905C2
socleC2×C43#1439
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#2905D43
hypocenterC43#11090
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2905

Complements

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

NH ≅ G/Ntype
4. C2×#14582671C2semidirect
5. C2×#14582669C2semidirect
6. #19134333C2semidirect
7. C43×#2905C2semidirect
293. #2905D43semidirect
333. C43#11090semidirect

Maximal subgroups

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

subgroupindex
C2×#145828812
C2×#145828722
C2×#145826712
C2×#145826692
#191343332
C43×#29052
#1109043