Finite Group Databasebeta

← #24991744

Subgroups — #24991744

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583050C211yesmaximal, characteristic
2#19137328C211yesmaximal, characteristic, complemented
3#19134526C211yesmaximal, characteristic
4C2×#14582635C211yesmaximal, characteristic, complemented
5#19132474C211yesmaximal, characteristic, complemented
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1438C211yesmaximal, characteristic
8C22×#10621883—21no—
9C2×#13063304C2211yescharacteristic
10#14583050—22no—
11#14583050C414yescomplemented
12C2×#13063246—21no—
13C2×#13063246—21no—
14C2×#13063246—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582803—21no—
18#14582796—21no—
19#14582786—21no—
20#14582782—21no—
21#14582772—21no—
22#14582759C2211yescharacteristic
23C4×C22⋊Dic43—21no—
24#14582635—22no—
25C23×D4×C43C2211yescharacteristic
26C22×C22⋊C4×C43—21no—
27C22×C22⋊C4×C43—21no—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C22×Dic86D411yescharacteristic
31C2×#10621883—24no—
32C2×#10621883—42no—
33C2×#10621883—42no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304C2×C412yes—
39#13063304D412yes—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50#13063246—24no—
51#13063246—42no—
52#13063246—42no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)C2×C412yes—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C25×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—42no—
69C22×D4×C43—42no—
70C22×D4×C43C2×C412yes—
71C23×C4×C43—21no—
72C23×C4×C43D411yescharacteristic
73C23×C4×C43D411yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C2×C22⋊C4×C43—42no—
76C2×C22⋊C4×C43—42no—
77C2×C22⋊C4×C43—42no—
78C2×C22⋊C4×C43—42no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43—42no—
81#95×C43—21no—
82#95×C43—21no—
83#95×C43—21no—
84#95×C43—21no—
85C24×C43—22no—
86C24×C43—22no—
87C24×C43—22no—
88C24×C43—41no—
89C24×C43—41no—
90C24×C43—41no—
91C24×C43—41no—
92C24×C43—41no—
93C24×C43—41no—
94C24×C43—41no—
95C24×C43—41no—
96C24×C43—41no—
97C24×C43—41no—
98C24×C43—41no—
99C24×C43—41no—
100C24×C43C2×D411yescharacteristic
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—44no—
108C2×D4×C43—44no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—41no—
112C2×D4×C43—41no—
113C2×D4×C43—44no—
114C2×D4×C43—44no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43SD1612yescomplemented
136C22×C4×C43C22×C411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43#4111yescharacteristic
141C22×C4×C43#4111yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C2×Dic86—21no—
147C2×Dic86—41no—
148C2×Dic86—41no—
149C2×Dic86C22⋊C412yescomplemented
150C22⋊C4×C43—48no—
151C22⋊C4×C43—48no—
152C22⋊Dic43—22no—
153C22⋊Dic43—22no—
154C22⋊Dic43—41no—
155C22⋊Dic43—41no—
156#10621883—48no—
157C4⋊Dic43—21no—
158C4⋊Dic43—41no—
159C4⋊Dic43—41no—
160C4⋊Dic43C22⋊C412yescomplemented
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—81no—
164Dic43⋊C4—81no—
165C4×Dic43—81no—
166C4×Dic43—81no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—41no—
169C2×C43⋊C8—41no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C2×C43⋊C8—41no—
173C23×C43—21no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—24no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—81no—
197C23×C43—81no—
198C23×C43—81no—
199C23×C43—81no—
200C23×C43—81no—
201C23×C43—81no—
202C23×C43—81no—
203C23×C43—81no—
204C23×C43—81no—
205C23×C43—81no—
206C23×C43—81no—
207C23×C43—81no—
208C23×C43—81no—
209C23×C43—81no—
210C23×C43—81no—
211C23×C43—81no—
212C23×C43C4×D411yescharacteristic
213C23×C43#12011yescharacteristic
214C23×C43#12111yescharacteristic
215C23×C43C2×SD1611yescharacteristic
216C23×C43#13511yescharacteristic
217C23×C43AGL(1,ℤ/8)11yescharacteristic
218C23×C43#13711yescharacteristic
219D4×C43—24no—
220D4×C43—24no—
221D4×C43—42no—
222D4×C43—42no—
223D4×C43—42no—
224D4×C43—42no—
225D4×C43—42no—
226D4×C43—42no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—81no—
247C2×C4×C43—81no—
248C2×C4×C43—81no—
249C2×C4×C43—81no—
250C2×C4×C43—81no—
251C2×C4×C43—81no—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12311yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268Dic86—42no—
269Dic86—81no—
270C43⋊C8—42no—
271C43⋊C8—81no—
272#9042—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—44no—
286C22×C43—44no—
287C22×C43—44no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43—82no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—82no—
297C22×C43—82no—
298C22×C43—82no—
299C22×C43—82no—
300C22×C43#38611yescharacteristic
301C22×C43C4×SD1611yescharacteristic
302C22×C43#44011yescharacteristic
303C22×C43#44811yescharacteristic
304C22×C43#44911yescharacteristic
305C22×C43#45311yescharacteristic
306C22×C43#45411yescharacteristic
307C22×C43B(4,𝔽2)11yescharacteristic
308C22×C43B(4,𝔽2)11yescharacteristic
309C22×C43#46011yescharacteristic
310C22×C43#46411yescharacteristic
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—42no—
316C4×C43—82no—
317C4×C43—81no—
318Dic43—42no—
319Dic43—42no—
320Dic43—81no—
321Dic43—81no—
322C2×#450—431no—
323#2329—431no—
324#1786—431no—
325C2×#328—431no—
326#1438D4311yescharacteristic
327#1294—431no—
328#1280—431no—
329C2×C43—21no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—84no—
334C2×C43#159611yescharacteristic
335C2×C43#159711yescharacteristic
336C2×C43#159911yescharacteristic
337C2×C43#160011yescharacteristic
338C2×C43#188011yescharacteristic
339C2×C43#188311yescharacteristic
340C2×C43#188911yescharacteristic
341C23×D4C2×D4311yescharacteristic
342C22×SD16—861no—
343C2×C22⋊Q8—431no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4—21no—
346#450—434no—
347#450—862no—
348C2×#102—861no—
349C2×#102—861no—
350C2×#102—861no—
351C2×C22⋊C8—431no—
352C2×C22⋊C8—431no—
353#391—861no—
354#389—861no—
355#387—861no—
356#387—861no—
357#385—861no—
358#380—431no—
359C4×C22⋊C4—861no—
360C2×#95C2×D4311yescharacteristic
361C2×#95C2×D4311yescharacteristic
362#328—862no—
363C43#904211yescharacteristic, complemented, Sylow
364C25—21no—
365C22×Q8—431no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C4×D4312yes—
374C23×C4—21no—
375C23×C4C22⋊D4311yescharacteristic
376C23×C4C22⋊D4311yescharacteristic
377C23×C4C22×D4311yescharacteristic
378C2×SD16—864no—
379C2×SD16—1722no—
380C2×SD16—1722no—
381C22×C8—861no—
382C22×C8—861no—
383C22⋊Q8—432no—
384C22⋊Q8—432no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—861no—
402C2×C42—861no—
403#102—864no—
404#102—1722no—
405#102—1722no—
406C22⋊C8—432no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×C22⋊D4311yescharacteristic
435C2×Q8—432no—
436C2×Q8—861no—
437C2×Q8—1721no—
438C2×Q8—1721no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4#1062188312yescomplemented
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4#1062189811yescharacteristic
480C22×C4D4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4#1062190011yescharacteristic
484SD16—1728no—
485C2×C8—862no—
486C2×C8—1721no—
487C2×C8—1721no—
488C2×C8—1721no—
489C2×C8—1721no—
490C2×C8—1721no—
491C4⋊C4—432no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—861no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C42—3441no—
506C42—3441no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×C22⋊D4311yescharacteristic
547C23#1306329311yescharacteristic
548C23#1306329611yescharacteristic
549C23C2×#1062188311yescharacteristic
550C23#1306334511yescharacteristic
551C23#1306335111yescharacteristic
552C23#1306335511yescharacteristic
553Q8—3441no—
554Q8—1722no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4(C22⋊D43)⋊C411yescharacteristic
602C2×C4#1306329811yescharacteristic
603C2×C4#1306330711yescharacteristic
604C8—3441no—
605C8—1722no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22#1458277511yescharacteristic
634C22C4×#1062188311yescharacteristic
635C22#1458299911yescharacteristic
636C22#1458303711yescharacteristic
637C22#1458304211yescharacteristic
638C22#1458306611yescharacteristic
639C22#1458307111yescharacteristic
640C22#1458308511yescharacteristic
641C22#1458308511yescharacteristic
642C22#1458309611yescharacteristic
643C22#1458311811yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—82no—
650C4—81no—
651C4—3441no—
652C4—3441no—
653C4—1722no—
654C4—1722no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2#1913351711yescharacteristic
661C2#1913352211yescharacteristic
662C2#1913353411yescharacteristic
663C2#1913353911yescharacteristic
664C2#1913495311yescharacteristic
665C2#1913497411yescharacteristic
666C2#1913500011yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1438C2
socleC23×C43#120
prime radicalC23×D4×C43C22
cosocleC23×C4×C43C23
hypercenter#1438D43
hypocenterC43#9042
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #19137328C2semidirect
4. C2×#14582635C2semidirect
5. #19132474C2semidirect
6. #19132438C2semidirect
11. #14583050C4semidirect
135. C22×C4×C43SD16semidirect
149. C2×Dic86C22⋊C4semidirect
160. C4⋊Dic43C22⋊C4semidirect
363. C43#9042semidirect
477. C22×C4#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
#191373282
#191345262
C2×#145826352
#191324742
#191324382
C43×#14382
#904243