Finite Group Databasebeta

← #25132294

Subgroups — #25132294

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063348C211yesmaximal, characteristic, complemented
2C2×#14583135C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
4#19137942C212yesmaximal, complemented
5#19135909C212yesmaximal, complemented
6#19135596C212yesmaximal, complemented
7#19135459C211yesmaximal, characteristic, complemented
8#19135457C211yesmaximal, characteristic, complemented
9#19134621C211yesmaximal, characteristic, complemented
10#19134534C212yesmaximal, complemented
11C2×C43×#467C211yesmaximal, characteristic, complemented
12C22×#10621902C2212yes—
13C2×#13063348—24no—
14C2×#13063348—24no—
15C2×#13063348—24no—
16C22×#10621884C2212yes—
17C22×D344C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063299C2212yes—
20C2×C4×C22⋊D43C2211yescharacteristic
21#14583135—24no—
22C8×C22⋊D43—24no—
23C2×#13063259C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063249C2212yes—
26C2×#13063247C2212yes—
27C2×#13063245C2212yes—
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582816—22no—
32#14582808—22no—
33#14582806C2212yes—
34#14582800C2212yes—
35#14582775—22no—
36#14582770—22no—
37#14582756C2212yes—
38#14582661C2212yes—
39C22×Q16×C43C2211yescharacteristic
40C23×C8×C43C2211yescharacteristic
41C2×C22⋊Q8×C43C2212yes—
42C43×#467—24no—
43C2×#107×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C2×#10621902—24no—
46C2×#10621902—24no—
47C2×#10621902—24no—
48C2×#10621902—24no—
49C2×#10621902—42no—
50C2×#10621902—42no—
51C22×D172—22no—
52C22×D172C2312yes—
53C22×C22⋊D43—22no—
54C22×C22⋊D43D411yescharacteristic
55C22×C4×D43—22no—
56C22×C4×D43C2311yescharacteristic
57#13063348—232no—
58C2×#10621884—24no—
59C2×#10621884—24no—
60C2×#10621884—24no—
61C2×D344—22no—
62C2×D344—22no—
63C2×D344D414yescomplemented
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43D414yescomplemented
69#13063299—24no—
70#13063299—42no—
71C4×C22⋊D43—22no—
72C4×C22⋊D43—22no—
73C2×C4⋊Dic43C2312yes—
74C2×Dic43⋊C4D411yescharacteristic
75C2×C22⋊Dic43D411yescharacteristic
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4D411yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063259—22no—
83Dic43⋊C8—22no—
84#13063249—42no—
85#13063247—24no—
86#13063245—42no—
87C22⋊(C43⋊C8)—22no—
88(C2×D43)⋊C8—22no—
89C8×Dic43—22no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C43⋊#95—22no—
93C22×Q8×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C2×Q16×C43—22no—
96C2×Q16×C43—22no—
97C2×Q16×C43D414yescomplemented
98C22×C8×C43—22no—
99C22×C8×C43—22no—
100C22×C8×C43—22no—
101C22×C8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22⋊Q8×C43—24no—
104C22⋊Q8×C43—42no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—22no—
108#107×C43—22no—
109#103×C43—24no—
110C24×C43C2×D411yescharacteristic
111C23×D43—22no—
112C23×D43C2×D411yescharacteristic
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43C2×D414yes—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C2×C22⋊D43—22no—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—44no—
133C2×C22⋊D43—44no—
134C2×C22⋊D43—82no—
135C22×Dic43—22no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139#10621902—216no—
140#10621902—48no—
141#10621902—48no—
142#10621902—48no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—44no—
149C2×D172—44no—
150C2×D172—44no—
151C2×D172C2×D414yes—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43C2×D412yes—
160C2×C4×D43#4112yes—
161Q16×C43—28no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—44no—
166C2×C8×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C2×C8×C43C2×D412yes—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—44no—
172C22⋊C4×C43—44no—
173C22⋊Dic43—22no—
174#10621884—216no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4—44no—
177(C2×D43)⋊C4—44no—
178(C2×D43)⋊C4—82no—
179(C2×D43)⋊C4—82no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182Dic43⋊C4—22no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8C2×D412yes—
191D344—28no—
192C8×D43—28no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43#13512yescomplemented
200C23×C43C22×D411yescharacteristic
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—24no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43#12112yes—
215Q8×C43—24no—
216Q8×C43—24no—
217Q8×C43—42no—
218Q8×C43—42no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—24no—
222C2×C4×C43—21no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C22⋊D43—28no—
239C22⋊D43—88no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43#12112yes—
251C2×Dic43#13512yescomplemented
252D172—24no—
253D172—24no—
254D172—416no—
255D172—42no—
256D172—42no—
257C4×D43—22no—
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—416no—
262C8×C43—41no—
263C8×C43#12014yes—
264C43⋊C8—22no—
265C43⋊C8—41no—
266#24266—431nomaximal, Sylow
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×#12111yescharacteristic
275C22×C43D4211yescharacteristic
276C22×C43D4211yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43C2×#13511yescharacteristic
279C22×C43#57611yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—44no—
289C2×D43—44no—
290C2×D43—44no—
291C2×D43—82no—
292C2×D43—82no—
293C2×D43—82no—
294C2×D43—82no—
295C4×C43—44no—
296C4×C43—41no—
297C4×C43—82no—
298C4×C43C2×#12011yescharacteristic
299C4×C43#53511yescharacteristic
300C4×C43#54611yescharacteristic
301C4×C43#54611yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—41no—
305Dic43—82no—
306C22×#135—431no—
307C2×#467D4311yescharacteristic, complemented
308C2×#466—431no—
309C2×C8×D4—431no—
310#2407—432no—
311#2055—432no—
312#2000—432no—
313#1970—431no—
314#1969—431no—
315#1808—431no—
316#1788—432no—
317C2×C43—42no—
318C2×C43#240811yescharacteristic
319C2×C43#305011yescharacteristic
320C2×C43#306111yescharacteristic
321C2×C43#328011yescharacteristic
322C2×C43#328311yescharacteristic
323C2×C43#328511yescharacteristic
324C2×C43#328711yescharacteristic
325D43—42no—
326D43—84no—
327C22×#41—432no—
328C2×#135—864no—
329C2×#135—864no—
330C2×#135—864no—
331C22×Q16C2×D4311yescharacteristic
332C22×SD16—432no—
333C22×D8—431no—
334C23×C8—431no—
335C23×C8C2×D4311yescharacteristic
336C2×C22⋊Q8C2×D4312yes—
337C2×#121—432no—
338C2×C4×D4—431no—
339#467—24no—
340#466—864no—
341C8×D4—864no—
342C2×#107—431no—
343C2×#107C2×D4311yescharacteristic
344C2×C4⋊C8—431no—
345C2×#103—432no—
346C2×#103C2×D4312yes—
347C2×#102—432no—
348C2×#102—432no—
349C2×C22⋊C8—431no—
350C2×C22⋊C8—431no—
351C2×C4×C8—431no—
352#394—862no—
353#392—862no—
354#391—432no—
355#390—432no—
356#386—862no—
357#385—862no—
358#380—432no—
359#340—432no—
360C43#2426611yescharacteristic, complemented, Sylow
361C2×#41—864no—
362C2×#41—864no—
363C2×#41—864no—
364C2×#41—864no—
365C2×#41—1722no—
366C2×#41—1722no—
367C22×Q8C22×D4312yes—
368C22×D4—431no—
369C22×D4—432no—
370C22×D4—862no—
371C22×D4—862no—
372C23×C4—431no—
373C23×C4—862no—
374C23×C4C22×D4311yescharacteristic
375#135—8632no—
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16C22⋊D4314yescomplemented
379C2×SD16—864no—
380C2×SD16—864no—
381C2×SD16—864no—
382C2×D8—434no—
383C2×D8—862no—
384C2×D8—862no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—431no—
389C22×C8—434no—
390C22×C8—431no—
391C22×C8—862no—
392C22×C8—862no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C22⋊Q8—24no—
396C22⋊Q8—42no—
397#121—864no—
398#121—1722no—
399C4×D4—862no—
400C4×D4—862no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—432no—
404C2×C4⋊C4C22×D4312yes—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—431no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C42—431no—
413#107—22no—
414#107—862no—
415C4⋊C8—862no—
416#103—24no—
417#103—1722no—
418#102—864no—
419#102—1722no—
420C22⋊C8—862no—
421C22⋊C8—862no—
422C4×C8—862no—
423#95—862no—
424#95—862no—
425#95—862no—
426C24—431no—
427C24—862no—
428C24D4×D4311yescharacteristic
429#41—8616no—
430#41—1728no—
431#41—1728no—
432#41—1728no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8C2×C22⋊D4314yes—
439C2×D4—434no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—862no—
443C2×D4—862no—
444C2×D4—862no—
445C2×D4—862no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4—3442no—
449C2×D4—1724no—
450C2×D4—1724no—
451C2×D4—1724no—
452C2×D4—1724no—
453C2×D4—1724no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—862no—
472C22×C4—1724no—
473C22×C4—1724no—
474C22×C4—1724no—
475C22×C4D4×D4311yescharacteristic
476C22×C4C23×D4311yescharacteristic
477Q16—28no—
478SD16—8616no—
479D8—868no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—44no—
484C2×C8—432no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—868no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8D4×D4312yes—
492C2×C8D4×D4312yes—
493C2×C8C2×C22⋊D4312yes—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—44no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C22⋊C4—44no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C22⋊C4—3442no—
504C22⋊C4—3442no—
505C22⋊C4—1724no—
506C22⋊C4—1724no—
507C42—861no—
508C42—861no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—432no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—864no—
523C23—1722no—
524C23—1722no—
525C23—1722no—
526C23—1722no—
527C23—1722no—
528C23—1722no—
529C23#1306334812yescomplemented
530C23C2×D4×D4311yescharacteristic
531Q8—24no—
532Q8—24no—
533Q8—42no—
534Q8—42no—
535D4—868no—
536D4—864no—
537D4—864no—
538D4—3448no—
539D4—17216no—
540D4—1722no—
541D4—1722no—
542C2×C4—21no—
543C2×C4—24no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—17216no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C22×C22⋊D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337111yescharacteristic
578C8—41no—
579C8—862no—
580C8—1721no—
581C8#1306329314yes—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—3442no—
593C22—3442no—
594C22—3442no—
595C22—3442no—
596C22—1724no—
597C22—1724no—
598C22—1724no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22—1721no—
603C22#121×D4311yescharacteristic
604C22D4×C22⋊D4311yescharacteristic
605C22#1458353311yescharacteristic
606C22#135×D4311yescharacteristic
607C22C2×#1306334811yescharacteristic
608C22#1458370111yescharacteristic
609C22#1458371211yescharacteristic
610C4—41no—
611C4—44no—
612C4—82no—
613C4—862no—
614C4—862no—
615C4—3442no—
616C4—1721no—
617C4C2×#1306329311yescharacteristic
618C4#1458346511yescharacteristic
619C4#1458353711yescharacteristic
620C4#1458354611yescharacteristic
621C2—42no—
622C2—3444no—
623C2—1722no—
624C2#1913794711yescharacteristic
625C2#1914417811yescharacteristic
626C2#1914426611yescharacteristic
627C2#1914627711yescharacteristic
628C2#1914631411yescharacteristic
629C2#1914633611yescharacteristic
630C2#1914634911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
hypercenterC2×#467D43
hypocenterC43#24266
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13063348C2semidirect
2. C2×#14583135C2semidirect
3. C2×C8×C22⋊D43C2semidirect
4. #19137942C2semidirect
5. #19135909C2semidirect
6. #19135596C2semidirect
7. #19135459C2semidirect
8. #19135457C2semidirect
9. #19134621C2semidirect
10. #19134534C2semidirect
11. C2×C43×#467C2semidirect
63. C2×D344D4semidirect
68. C2×C8×D43D4semidirect
97. C2×Q16×C43D4semidirect
199. C23×C43#135semidirect
251. C2×Dic43#135semidirect
307. C2×#467D43semidirect
360. C43#24266semidirect
378. C2×Q16C22⋊D43semidirect
529. C23#13063348semidirect

Maximal subgroups

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

subgroupindex
C22×#130633482
C2×#145831352
C2×C8×C22⋊D432
#191379422
#191359092
#191355962
#191354592
#191354572
#191346212
#191345342
C2×C43×#4672
#2426643