Finite Group Databasebeta

← #25098064

Subgroups — #25098064

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063347C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582898C211yesmaximal, characteristic, complemented
5#19137188C211yesmaximal, characteristic, complemented
6#19134951C212yesmaximal, complemented
7#19134944C212yesmaximal, complemented
8#19134937C212yesmaximal, complemented
9#19134930C212yesmaximal, complemented
10#19134291C211yesmaximal, characteristic, complemented
11C2×C43×#340C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621898C2211yescharacteristic
14C2×#13063347—24no—
15C2×#13063347—24no—
16C2×#13063347C418yescomplemented
17C22×Dic172C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22#14583380—24no—
23#14583380—24no—
24C2×#13063290C2212yes—
25C2×#13063287C2212yes—
26C2×C4×C22⋊D43—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063283—21no—
29C2×C4⋊C4×D43—21no—
30#14582898—24no—
31#14582898—24no—
32C2×#13063248C2212yes—
33C2×#13063248C2212yes—
34C2×#13063245C2212yes—
35C2×#13063245C2212yes—
36#14582804C2212yes—
37#14582800C2212yes—
38#14582778—22no—
39#14582756—21no—
40#14582756—21no—
41#14582653C2212yes—
42#14582653C2212yes—
43C23×C8×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#340C2212yes—
47C43×#340C2212yes—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898—22no—
55C2×#10621898—22no—
56C2×#10621898C2×C414yes—
57C2×#10621898C2×C414yescomplemented
58C2×#10621898D414yes—
59C2×#10621898D414yes—
60C22×Dic86C2311yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—22no—
69#13063347—232no—
70C2×Dic172—22no—
71C2×Dic172—22no—
72C2×Dic172C2×C414yescomplemented
73C2×#10621873—22no—
74C2×#10621873—22no—
75C2×#10621873—22no—
76C2×#10621873—22no—
77C2×#10621873C2×C414yescomplemented
78C2×#10621873C2×C414yescomplemented
79C2×D344—22no—
80C2×D344—22no—
81C2×D344C2×C414yescomplemented
82C2×#10621877—22no—
83C2×#10621877—22no—
84C2×#10621877—22no—
85C22×C43⋊C8C2312yes—
86#13063290—24no—
87#13063290—24no—
88#13063287—24no—
89#13063287—24no—
90C4×C22⋊D43—216no—
91#13063284—22no—
92#13063284—22no—
93#13063283—28no—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43D411yescharacteristic
96C2×Dic43⋊C4—22no—
97C4⋊C4×D43—28no—
98C2×C22⋊Dic43D412yes—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43C2312yes—
104#13063248—24no—
105#13063248—24no—
106#13063245—24no—
107#13063245—24no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43—22no—
114C22×C8×C43—22no—
115C22×C8×C43C2×C414yescomplemented
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43—22no—
121C2×C4⋊C4×C43—22no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43D414yes—
124C2×C4⋊C4×C43C2312yes—
125C2×C4⋊C4×C43C2312yes—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C23×D43—21no—
129C22×C4×C43—24no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—42no—
133C22×C4×C43—81no—
134C22×C4×C43—81no—
135C22×C4×C43—81no—
136C22×C4×C43—81no—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43#4112yes—
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—24no—
147C2×C22⋊D43—24no—
148C2×C22⋊D43—24no—
149C2×C22⋊D43—42no—
150C2×C22⋊D43—42no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D412yes—
154C22×Dic43C2×D412yes—
155#10621898—28no—
156#10621898—28no—
157#10621898—28no—
158#10621898—28no—
159#10621898—28no—
160#10621898—44no—
161#10621898—44no—
162#10621898C22⋊C4116yescomplemented
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C22×C412yes—
172C2×D172C22×C412yes—
173C2×D172C2×D412yes—
174C2×D172C2×D412yes—
175C2×C4×D43—24no—
176C2×C4×D43—24no—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—28no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—82no—
183C2×C4×D43—82no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C22×C412yes—
193C2×Dic86C22×C412yes—
194C2×Dic86C2×D412yes—
195C2×Dic86C2×D412yes—
196C2×C8×C43—28no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C22×C412yes—
202C2×C8×C43C22×C412yes—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—22no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43C2×D414yes—
209C22⋊Dic43—24no—
210(C2×D43)⋊C4—28no—
211(C2×D43)⋊C4—82no—
212(C2×D43)⋊C4—82no—
213C4⋊Dic43—22no—
214C4⋊Dic43—22no—
215Dic43⋊C4—28no—
216C4×Dic43—28no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219#10621877—44no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223Dic172—28no—
224D344—28no—
225#10621873—28no—
226#10621873—28no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43C4×D412yes—
232C23×C43#12012yes—
233C23×C43#12112yes—
234C23×C43C22×D411yescharacteristic
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C2×C4×C43—24no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—84no—
256C2×C4×C43—84no—
257C2×C4×C43C2×C22⋊C414yes—
258C2×C4×C43C4×D412yes—
259C2×C4×C43C4×D414yes—
260C2×C4×C43#12012yes—
261C2×C4×C43#12112yes—
262C2×C4×C43#12114yes—
263C2×C4×C43#12314yes—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C22⋊D43—216no—
271C22⋊D43—48no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284D172—22no—
285D172—22no—
286D172—22no—
287D172—22no—
288D172—22no—
289D172—41no—
290D172—41no—
291D172C2×C22⋊C414yes—
292C4×D43—216no—
293C4×D43—48no—
294C4×D43—88no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86—22no—
299Dic86—22no—
300Dic86—41no—
301Dic86—41no—
302Dic86C2×C22⋊C414yes—
303C8×C43—22no—
304C8×C43—22no—
305C43⋊C8—42no—
306#20937—431nomaximal, Sylow
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43#38614yes—
314C22×C43C2×C4×D411yescharacteristic
315C22×C43C2×#12011yescharacteristic
316C22×C43C2×#12111yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57711yescharacteristic
319C22×C43#57711yescharacteristic
320C22×C43#57811yescharacteristic
321C2×D43—24no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—42no—
329C2×D43—42no—
330C2×D43—42no—
331C2×D43—81no—
332C2×D43—81no—
333C2×D43—81no—
334C2×D43—81no—
335C4×C43—44no—
336C4×C43—82no—
337C4×C43#38614yes—
338C4×C43C22×C22⋊C411yescharacteristic
339C4×C43C2×C4×D411yescharacteristic
340C4×C43C2×#12111yescharacteristic
341C4×C43C2×#12311yescharacteristic
342Dic43—24no—
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346C22×#135—431no—
347C2×#520—431no—
348C2×#417—431no—
349C2×#417—431no—
350#2311—431no—
351#1880—432no—
352#1879—432no—
353#1878—432no—
354#1877—432no—
355C2×#340D4311yescharacteristic, complemented
356#1729—431no—
357C2×C43—24no—
358C2×C43C2×#38611yescharacteristic
359C2×C43#295111yescharacteristic
360C2×C43#295211yescharacteristic
361C2×C43#301211yescharacteristic
362C2×C43#301311yescharacteristic
363C2×C43#304511yescharacteristic
364C2×C43#304611yescharacteristic
365D43—44no—
366D43—82no—
367C22×#41—431no—
368C22×#41—431no—
369C2×#135—438no—
370C2×#135—864no—
371C2×#135—864no—
372C22×Q16—431no—
373C22×SD16—431no—
374C22×SD16—431no—
375C22×D8—431no—
376C22×M16—431no—
377C23×C8C2×D4311yescharacteristic
378#520—864no—
379#520—864no—
380C2×C4×Q8—432no—
381C2×C4×D4—432no—
382C2×C4×D4—862no—
383C2×#117—431no—
384C2×#117—861no—
385C22×C4⋊C4—861no—
386C22×C4⋊C4C2×D4311yescharacteristic
387C22×C4⋊C4C2×D4311yescharacteristic
388#417—864no—
389#417—864no—
390C2×#103—432no—
391C2×#103—432no—
392C2×#102—432no—
393C2×#102—432no—
394#391—432no—
395#390—432no—
396#386—862no—
397#380—861no—
398#380—861no—
399#340C2×D4312yes—
400#340C2×D4312yes—
401#336—432no—
402#336—432no—
403C43#2093711yescharacteristic, complemented, Sylow
404C2×#41—434no—
405C2×#41—434no—
406C2×#41—434no—
407C2×#41—434no—
408C2×#41—862no—
409C2×#41—862no—
410C2×#41—862no—
411C2×#41—862no—
412C2×#41—862no—
413C2×#41—862no—
414C2×#41—862no—
415C2×#41—862no—
416C22×Q8—431no—
417C22×Q8—431no—
418C22×D4—431no—
419C22×D4—431no—
420C22×D4—861no—
421C22×D4—861no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—862no—
425C23×C4—861no—
426C23×C4—861no—
427C23×C4C22×D4311yescharacteristic
428#135—8632no—
429C2×Q16—434no—
430C2×Q16—862no—
431C2×Q16—862no—
432C2×SD16—434no—
433C2×SD16—434no—
434C2×SD16—862no—
435C2×SD16—862no—
436C2×SD16—862no—
437C2×SD16—862no—
438C2×D8—434no—
439C2×D8—862no—
440C2×D8—862no—
441C2×M16—862no—
442C2×M16—862no—
443C2×M16—862no—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—432no—
447C22×C8C4×D4314yescomplemented
448C22×C8C22×D4311yescharacteristic
449C22×C8C22×D4311yescharacteristic
450C4×Q8—864no—
451C4×Q8—864no—
452C4×D4—864no—
453C4×D4—8616no—
454C4×D4—864no—
455#117—868no—
456#117—862no—
457#117—862no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—868no—
466C2×C4⋊C4—862no—
467C2×C4⋊C4D17214yes—
468C2×C4⋊C4C22×D4312yes—
469C2×C4⋊C4C22×D4312yes—
470C2×C22⋊C4—432no—
471C2×C22⋊C4—862no—
472C2×C22⋊C4—862no—
473C2×C22⋊C4—862no—
474C2×C42—432no—
475C2×C42—862no—
476#103—864no—
477#103—864no—
478#102—864no—
479#102—864no—
480#95—862no—
481#95—862no—
482C24—861no—
483C24—861no—
484C24D4×D4311yescharacteristic
485#41—4316no—
486#41—868no—
487#41—868no—
488#41—868no—
489#41—868no—
490#41—868no—
491#41—1724no—
492#41—1724no—
493C2×Q8—432no—
494C2×Q8—432no—
495C2×Q8—432no—
496C2×Q8—432no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×D4—432no—
506C2×D4—432no—
507C2×D4—432no—
508C2×D4—432no—
509C2×D4—864no—
510C2×D4—864no—
511C2×D4—864no—
512C2×D4—864no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4—861no—
520C2×D4—861no—
521C2×D4—1722no—
522C2×D4—1722no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—432no—
532C22×C4—432no—
533C22×C4—868no—
534C22×C4—861no—
535C22×C4—864no—
536C22×C4—864no—
537C22×C4—864no—
538C22×C4—861no—
539C22×C4—864no—
540C22×C4—3442no—
541C22×C4—3442no—
542C22×C4—1722no—
543C22×C4—1722no—
544C22×C4C2×C4×D4312yes—
545C22×C4C2×D17212yes—
546C22×C4#1062189812yes—
547C22×C4D4×D4312yes—
548C22×C4D4×D4312yes—
549C22×C4D4×D4311yescharacteristic
550C22×C4#1062190212yes—
551C22×C4C23×D4311yescharacteristic
552Q16—868no—
553SD16—868no—
554SD16—868no—
555D8—868no—
556M16—1724no—
557C2×C8—28no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—862no—
563C2×C8—862no—
564C2×C8—862no—
565C2×C8C2×C4×D4312yes—
566C2×C8C2×C4×D4312yes—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—42no—
572C4⋊C4—868no—
573C4⋊C4—862no—
574C4⋊C4—862no—
575C4⋊C4C2×D17214yes—
576C22⋊C4—868no—
577C22⋊C4—864no—
578C22⋊C4—3442no—
579C22⋊C4—3442no—
580C42—868no—
581C42—862no—
582C42—862no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—862no—
588C23—862no—
589C23—862no—
590C23—862no—
591C23—1721no—
592C23—1721no—
593C23—1721no—
594C23—1721no—
595C23—1721no—
596C23—1721no—
597C23—1721no—
598C23—1721no—
599C23—1721no—
600C23—1721no—
601C23#1306328712yes—
602C23#1306329512yes—
603C23#1306329812yes—
604C23C2×D4×D4311yescharacteristic
605Q8—434no—
606Q8—862no—
607Q8—862no—
608Q8—862no—
609Q8—862no—
610Q8—862no—
611Q8—1721no—
612Q8—1721no—
613D4—434no—
614D4—8616no—
615D4—862no—
616D4—862no—
617D4—862no—
618D4—862no—
619D4—862no—
620D4—1728no—
621D4—1721no—
622D4—1721no—
623C2×C4—24no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—84no—
630C2×C4—84no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—8616no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—3448no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1728no—
646C2×C4C22⋊C4×D4314yes—
647C2×C4#1306328712yes—
648C2×C4C4×D17214yes—
649C2×C4#1306329512yes—
650C2×C4#1306329812yes—
651C2×C4#1306330014yes—
652C2×C4#1306331014yes—
653C2×C4C22×C4×D4311yescharacteristic
654C2×C4C2×D4×D4311yescharacteristic
655C2×C4C2×D4×D4311yescharacteristic
656C2×C4C22×D17211yescharacteristic
657C2×C4C2×#1062189811yescharacteristic
658C2×C4C2×#1062190211yescharacteristic
659C8—22no—
660C8—22no—
661C8—1722no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—864no—
669C22—3441no—
670C22—3441no—
671C22—3441no—
672C22—3441no—
673C22—1722no—
674C22—1722no—
675C22—1722no—
676C22—1722no—
677C22—1722no—
678C22—1722no—
679C22—1722no—
680C22—1722no—
681C22—1722no—
682C22#1458277714yes—
683C22C2×#1306328711yescharacteristic
684C22C2×#1306329511yescharacteristic
685C22C2×#1306329811yescharacteristic
686C22#1458370011yescharacteristic
687C22#1458370511yescharacteristic
688C22#1458370511yescharacteristic
689C22#1458371211yescharacteristic
690C4—44no—
691C4—82no—
692C4—864no—
693C4—1722no—
694C4—1722no—
695C4—1722no—
696C4#1458277714yes—
697C4C2×C22⋊C4×D4311yescharacteristic
698C4C2×C4×D17211yescharacteristic
699C4C2×#1306330011yescharacteristic
700C4C2×#1306331011yescharacteristic
701C2—24no—
702C2—3442no—
703C2—1724no—
704C2C2×#1458277711yescharacteristic
705C2#1914346911yescharacteristic
706C2#1914347811yescharacteristic
707C2#1914390411yescharacteristic
708C2#1914391511yescharacteristic
709C2#1914413911yescharacteristic
710C2#1914415011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC23×C43C22×D4
prime radicalC22×#13063347C2
cosocleC22×C4×C43C24
hypercenterC2×#340D43
hypocenterC43#20937
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582898C2semidirect
5. #19137188C2semidirect
6. #19134951C2semidirect
7. #19134944C2semidirect
8. #19134937C2semidirect
9. #19134930C2semidirect
10. #19134291C2semidirect
11. C2×C43×#340C2semidirect
16. C2×#13063347C4semidirect
57. C2×#10621898C2×C4semidirect
72. C2×Dic172C2×C4semidirect
77. C2×#10621873C2×C4semidirect
78. C2×#10621873C2×C4semidirect
81. C2×D344C2×C4semidirect
115. C22×C8×C43C2×C4semidirect
162. #10621898C22⋊C4semidirect
355. C2×#340D43semidirect
403. C43#20937semidirect
447. C22×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633472
C2×#145833802
C2×#145828982
#191371882
#191349512
#191349442
#191349372
#191349302
#191342912
C2×C43×#3402
#2093743