Finite Group Databasebeta

← #25070240

Subgroups — #25070240

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144515C211yesmaximal, characteristic, complemented
2C2×#14583232C211yesmaximal, characteristic, complemented
3#19139067C211yesmaximal, characteristic, complemented
4#19133643C214yesmaximal, complemented
5#19133620C214yesmaximal, complemented
6#19133115C211yesmaximal, characteristic, complemented
7#19133086C211yesmaximal, characteristic, complemented
8#19132955C211yesmaximal, characteristic, complemented
9C43×#3536C211yesmaximal, characteristic
10C2×#13063306—22no—
11C22×C4⋊Dic43C2211yescharacteristic
12#14583232—22no—
13#14583232C2214yes—
14#14583232C2212yes—
15#14583227—21no—
16#14583215C2212yes—
17#14583210—21no—
18#14582942—21no—
19C2×#13063258—21no—
20#14582900—21no—
21C2×#13063249—21no—
22#14582863C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24#14582835C2214yes—
25#14582802—21no—
26#14582768—21no—
27C4×C22⋊Dic43C2211yescharacteristic
28#14582636C2212yes—
29#14582636C2214yes—
30#14582633C2212yes—
31#14582623C2214yes—
32C43×#562—22no—
33C43×#554—21no—
34C43×#548—21no—
35C43×#547—21no—
36C43×#546—22no—
37C43×#546—21no—
38C43×#543C2212yes—
39C43×#542—21no—
40C43×#539—21no—
41C43×#538C2212yes—
42C43×#537—21no—
43C43×#537—21no—
44C43×#525C2211yescharacteristic
45C2×C22⋊Q8×C43C2211yescharacteristic
46C2×#121×C43C2211yescharacteristic
47C23×Dic43—21no—
48C2×#10621877—21no—
49C22×C43⋊C8—21no—
50#13063306—48no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4—24no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—24no—
60C2×C4×Dic43—21no—
61#13063258—24no—
62#13063258—22no—
63#13063256—22no—
64#13063249—24no—
65#13063249—22no—
66#13063246—22no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)C2312yes—
70C22⋊(C43⋊C8)C2312yes—
71C43⋊#95C2312yes—
72C2×#41×C43—22no—
73C2×#41×C43—21no—
74C2×#41×C43D411yescharacteristic
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43D411yescharacteristic
77C22×D4×C43D412yes—
78C23×C4×C43C2311yescharacteristic
79C4⋊Q8×C43—21no—
80#126×C43—22no—
81#125×C43—22no—
82#124×C43—21no—
83#124×C43—22no—
84#124×C43—22no—
85#123×C43—22no—
86#123×C43—22no—
87#123×C43—22no—
88#123×C43—21no—
89#123×C43—22no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43D412yes—
100C22⋊Q8×C43D411yescharacteristic
101C22⋊Q8×C43C2312yes—
102C22⋊Q8×C43C2311yescharacteristic
103#121×C43—21no—
104#121×C43—22no—
105#121×C43—22no—
106#121×C43—22no—
107#121×C43—22no—
108#121×C43—22no—
109#121×C43—21no—
110#121×C43—21no—
111#121×C43—21no—
112#121×C43—21no—
113#121×C43D411yescharacteristic
114#121×C43C2311yescharacteristic
115#120×C43—21no—
116#120×C43—22no—
117C4×Q8×C43—21no—
118C4×D4×C43—22no—
119C4×D4×C43—21no—
120C4×D4×C43—21no—
121C4×D4×C43—21no—
122C4×D4×C43—22no—
123#117×C43D411yescharacteristic
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43C2312yes—
131C24×C43C2×D411yescharacteristic
132C24×C43C2×D412yes—
133#41×C43—42no—
134#41×C43—84no—
135#41×C43—82no—
136C2×Q8×C43—22no—
137C2×Q8×C43—21no—
138C2×Q8×C43—42no—
139C2×Q8×C43C2×D411yescharacteristic
140C2×Q8×C43C2×D412yes—
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43—21no—
148C2×D4×C43—22no—
149C2×D4×C43—21no—
150C2×D4×C43—44no—
151C2×D4×C43—42no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—42no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—44no—
170C22×Dic43—41no—
171C22×Dic43—41no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D412yes—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—21no—
200C42×C43—22no—
201C42×C43—21no—
202C22⋊Dic43—24no—
203C22⋊Dic43—48no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43—41no—
207C4⋊Dic43—41no—
208Dic43⋊C4—48no—
209C4×Dic43—42no—
210#10621877—42no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—42no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—21no—
218C23×C43—24no—
219C23×C43—41no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43#12011yescharacteristic
223C23×C43#12011yescharacteristic
224C23×C43C22×D411yescharacteristic
225Q8×C43—42no—
226Q8×C43—41no—
227Q8×C43—42no—
228Q8×C43—82no—
229D4×C43—41no—
230D4×C43—42no—
231D4×C43—44no—
232D4×C43—42no—
233D4×C43—42no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—81no—
237D4×C43—82no—
238D4×C43—82no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—81no—
255C2×C4×C43—82no—
256C2×C4×C43—82no—
257C2×C4×C43—82no—
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12011yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×Dic43—24no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—44no—
266C2×Dic43—42no—
267C2×Dic43—82no—
268C2×Dic43—82no—
269C43⋊C8—42no—
270C43⋊C8—42no—
271#18267—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—44no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—42no—
283C22×C43—41no—
284C22×C43—42no—
285C22×C43—41no—
286C22×C43—84no—
287C22×C43#45312yes—
288C22×C43C2×#12011yescharacteristic
289C22×C43#57812yes—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—42no—
299C4×C43#45812yes—
300Dic43—44no—
301Dic43—82no—
302#3536D4311yescharacteristic
303#3092—431no—
304C2×#484—431no—
305#2501—431no—
306#1618—434no—
307#1614—434no—
308#1508—431no—
309#1501—431no—
310#1471—431no—
311C2×C43—22no—
312C2×C43—22no—
313C2×C43—41no—
314C2×C43—81no—
315C2×C43—82no—
316C2×C43#301111yescharacteristic
317C2×C43C2×#45311yescharacteristic
318C2×C43C2×#45811yescharacteristic
319#562—22no—
320#554—21no—
321#548—21no—
322#547—21no—
323#546—22no—
324#546—21no—
325#543C2×D4312yes—
326#542—21no—
327#539—21no—
328#538C2×D4312yes—
329#537—21no—
330#537—21no—
331#525C2×D4311yescharacteristic
332C2×#123—862no—
333C2×C22⋊Q8C2×D4311yescharacteristic
334C2×#121C2×D4311yescharacteristic
335C22×C4⋊C4—431no—
336#484—434no—
337#484—432no—
338#484—862no—
339#483—861no—
340#481—432no—
341#480—861no—
342#428—861no—
343C2×#107—861no—
344#417—861no—
345C2×#103—861no—
346#407—431no—
347C2×C22⋊C8—431no—
348#399—434no—
349#390—861no—
350#384—861no—
351C4×C22⋊C4—431no—
352#328—432no—
353#328—434no—
354#327—432no—
355#323—434no—
356C43#1826711yescharacteristic, complemented, Sylow
357C2×#41—22no—
358C2×#41—21no—
359C2×#41C22⋊D4311yescharacteristic
360C22×Q8C22⋊D4311yescharacteristic
361C22×D4C22⋊D4312yes—
362C22×D4C22⋊D4311yescharacteristic
363C23×C4—861no—
364C23×C4C22×D4311yescharacteristic
365C2×M16—861no—
366C22×C8—861no—
367C4⋊Q8—21no—
368#126—22no—
369#125—22no—
370#124—21no—
371#124—22no—
372#124—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376#123—21no—
377#123—22no—
378#123—1728no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8C22⋊D4312yes—
389C22⋊Q8C22⋊D4311yescharacteristic
390C22⋊Q8C22×D4312yes—
391C22⋊Q8C22×D4311yescharacteristic
392#121—21no—
393#121—22no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—22no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121C22⋊D4311yescharacteristic
403#121C22×D4311yescharacteristic
404#120—21no—
405#120—22no—
406C4×Q8—21no—
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—22no—
412#117C22⋊D4311yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—432no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4C22⋊D4311yescharacteristic
423C2×C4⋊C4C22⋊D4311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—864no—
428C2×C22⋊C4C22×D4312yes—
429C2×C42—861no—
430#107—864no—
431#107—862no—
432#106—862no—
433#103—864no—
434#103—862no—
435#102—862no—
436C22⋊C8—432no—
437C22⋊C8—432no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#95—432no—
441C24C2×C22⋊D4311yescharacteristic
442C24C2×C22⋊D4312yes—
443#41—42no—
444#41—84no—
445#41—82no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—42no—
449C2×Q8C2×C22⋊D4311yescharacteristic
450C2×Q8C2×C22⋊D4312yes—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—44no—
462C2×D4C2×C22⋊D4311yescharacteristic
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—1724no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4312yes—
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C23×D4311yescharacteristic
482M16—1722no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8—1722no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—1728no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4C2×C22⋊D4311yescharacteristic
503C4⋊C4C2×C22⋊D4312yes—
504C4⋊C4C2×C22⋊D4311yescharacteristic
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—864no—
520C22⋊C4—1728no—
521C42—22no—
522C42—21no—
523C42—1722no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—21no—
528C23—24no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23#1306329411yescharacteristic
533C23#1306329411yescharacteristic
534C23C22×C22⋊D4311yescharacteristic
535Q8—42no—
536Q8—41no—
537Q8—42no—
538Q8—82no—
539D4—41no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—81no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—864no—
569C2×C4—3442no—
570C2×C4—3442no—
571C2×C4—1724no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4#1306329411yescharacteristic
576C2×C4#1306329411yescharacteristic
577C2×C4C22×C22⋊D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C8—1722no—
580C8—1722no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—84no—
596C22#1458306712yes—
597C22C2×#1306329411yescharacteristic
598C22#1458371412yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—42no—
604C4—41no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—3442no—
609C4—1724no—
610C4#1458308912yes—
611C2—22no—
612C2—22no—
613C2—41no—
614C2—82no—
615C2—81no—
616C2#1914389011yescharacteristic
617C2C2×#1458306711yescharacteristic
618C2C2×#1458308911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3536C2
socleC22×C43C2×#120
hypercenter#3536D43
hypocenterC43#18267
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #19144515C2semidirect
2. C2×#14583232C2semidirect
3. #19139067C2semidirect
4. #19133643C2semidirect
5. #19133620C2semidirect
6. #19133115C2semidirect
7. #19133086C2semidirect
8. #19132955C2semidirect
356. C43#18267semidirect

Maximal subgroups

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

subgroupindex
#191445152
C2×#145832322
#191390672
#191336432
#191336202
#191331152
#191330862
#191329552
C43×#35362
#1826743