Finite Group Databasebeta

← #25105634

Subgroups — #25105634

Order 11008.

1590 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
3#380×D43C211yesmaximal, characteristic, complemented
4#19135024C211yesmaximal, characteristic, complemented
5#19135018C211yesmaximal, characteristic, complemented
6#19135016C211yesmaximal, characteristic, complemented
7#19134909C212yesmaximal, complemented
8#19134901C212yesmaximal, complemented
9#19134689C212yesmaximal, complemented
10#19134532C212yesmaximal, complemented
11C43×#1893C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15#14583409—24no—
16#14583409C418yescomplemented
17C2×#13063307—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×#13063293—21no—
22C2×D4×Dic43—21no—
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063283C2211yescharacteristic
25C2×C4⋊C4×D43C2212yes—
26C2×C22⋊C4×D43—21no—
27C2×#13063250C2212yescomplemented
28C2×#13063248C2212yescomplemented
29C2×#13063246C2212yescomplemented
30C2×(C2×D43)⋊C8—24no—
31C2×(C2×D43)⋊C8C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582759C2211yescharacteristic
34#14582758—21no—
35#14582757—21no—
36#14582756C2212yes—
37#95×D43—21no—
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C23×C8×C43C2211yescharacteristic
42C2×#121×C43C2211yescharacteristic
43C2×#102×C43C2212yescomplemented
44C43×#380C2211yescharacteristic
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C2×#10621900—22no—
48C2×#10621900—42no—
49C2×#10621900—42no—
50C2×#10621900C2×C414yescomplemented
51C22×Dic86C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C22×C4×D43—22no—
57C22×C4×D43—42no—
58C22×C4×D43—42no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D414yes—
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8—22no—
66C22×C43⋊C8—42no—
67C22×C43⋊C8C2312yes—
68#13063307—28no—
69#13063305—22no—
70#13063305C2×C414yes—
71#13063304—22no—
72#13063304C2×C414yescomplemented
73#13063296—22no—
74#13063296C2×C414yes—
75#13063293—28no—
76D4×Dic43—28no—
77(C22⋊D43)⋊C4—28no—
78#13063283—22no—
79#13063283C2×C414yescomplemented
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2312yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—22no—
85C4⋊C4×D43—42no—
86C4⋊C4×D43—42no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C22⋊C4×D43—44no—
94C2×C4×Dic43—21no—
95#13063250—42no—
96#13063248—42no—
97#13063246—42no—
98(C2×D43)⋊C8—24no—
99(C2×D43)⋊C8—24no—
100C43⋊#95—21no—
101C43⋊#95—22no—
102C22×D4×C43—21no—
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43—22no—
106C22×C8×C43—42no—
107C22×C8×C43C2312yes—
108#121×C43—22no—
109#121×C43C2×C414yescomplemented
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114#102×C43—42no—
115#95×C43—21no—
116C24×C43—21no—
117C24×C43C2×D411yescharacteristic
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—24no—
121C23×D43—42no—
122C23×D43C22⋊C414yes—
123C23×D43C2×D411yescharacteristic
124C23×D43C2×D411yescharacteristic
125C2×D4×C43—21no—
126C2×D4×C43—24no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—24no—
142C2×C22⋊D43—44no—
143C2×C22⋊D43—44no—
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—44no—
150C22×Dic43C22⋊C414yes—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153#10621900—48no—
154#10621900—44no—
155#10621900—44no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43—48no—
165C2×C4×D43—44no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43C22⋊C414yes—
169C2×C4×D43C22⋊C414yes—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C22×C412yes—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—21no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—44no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—24no—
187C22⋊C4×C43—42no—
188C22⋊Dic43—24no—
189C22⋊Dic43—24no—
190C22⋊Dic43—42no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—44no—
194C4⋊Dic43—21no—
195C4⋊Dic43—24no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43C22×C412yes—
199Dic43⋊C4—24no—
200Dic43⋊C4—44no—
201C4×Dic43—24no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—44no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C2×C22⋊C412yes—
214C23×C43AGL(1,ℤ/8)12yes—
215C23×C43#13712yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—28no—
225C22×D43—28no—
226C22×D43—44no—
227C22×D43—48no—
228C22×D43—48no—
229C22×D43C2×C22⋊C412yes—
230C22×D43C2×C22⋊C412yes—
231C22×D43#13514yes—
232D4×C43—24no—
233D4×C43—48no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—22no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43C2×C22⋊C412yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)12yes—
250C2×C4×C43H(5,𝔽2)12yes—
251C22⋊D43—48no—
252C22⋊D43—48no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—44no—
258C2×Dic43—48no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C4×D43—24no—
267C4×D43—24no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—44no—
273C4×D43—44no—
274C4×D43—88no—
275Dic86—24no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—42no—
279C43⋊C8—42no—
280#21763—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—24no—
284C22×C43—24no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43#41714yes—
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43#53412yes—
293C22×C43C2×#13512yes—
294C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—24no—
299C2×D43—24no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—416no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43#41614yes—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—82no—
310C4×C43#51812yes—
311C4×C43#53411yescharacteristic
312C4×C43#53411yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—42no—
317Dic43—82no—
318C2×#525—431no—
319C22×C22⋊C8—431no—
320C2×#380—431no—
321#1893—431no—
322#1893D4311yescharacteristic, complemented
323#1892—431no—
324#1892—431no—
325#1874—432no—
326#1872—432no—
327#1825—432no—
328#1788—432no—
329C2×C43—24no—
330C2×C43—82no—
331C2×C43#230811yescharacteristic
332C2×C43C2×#41611yescharacteristic
333C2×C43C2×#41711yescharacteristic
334C2×C43#318812yes—
335C2×C43#319012yes—
336D43—24no—
337D43—42no—
338C22×#41—431no—
339C24×C4—431no—
340C23×C8—431no—
341C23×C8C2×D4311yescharacteristic
342#525—438no—
343#525—864no—
344C2×#123—861no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8—431no—
347C2×#121—431no—
348C2×#121C2×D4311yescharacteristic
349C2×#120—861no—
350C2×C4×D4—861no—
351C2×C4×D4—861no—
352C2×#117—431no—
353C22×C4⋊C4—432no—
354C22×C22⋊C4—861no—
355C2×#103—432no—
356C2×#103—432no—
357C2×#102—432no—
358C2×#102C2×D4312yescomplemented
359C2×C22⋊C8—432no—
360C2×C22⋊C8—432no—
361C2×C22⋊C8—864no—
362#380—431no—
363#380—432no—
364#380—861no—
365#380—861no—
366#380C2×D4311yescharacteristic
367C2×#95—861no—
368#340—432no—
369#340—432no—
370#340—432no—
371#340C2×D4312yescomplemented
372C43#2176311yescharacteristic, complemented, Sylow
373C25—431no—
374C2×#41—434no—
375C2×#41—862no—
376C2×#41—1722no—
377C2×#41—1722no—
378C22×Q8—431no—
379C22×D4—21no—
380C22×D4—861no—
381C22×D4—861no—
382C22×D4C22×D4311yescharacteristic
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—434no—
387C23×C4—431no—
388C23×C4—431no—
389C23×C4—434no—
390C23×C4—862no—
391C23×C4—861no—
392C23×C4—1722no—
393C23×C4—1722no—
394C23×C4C22×D4311yescharacteristic
395C22×C8—22no—
396C22×C8—42no—
397C22×C8—432no—
398C22×C8—862no—
399C22×C8—1722no—
400C22×C8C22×D4312yes—
401#123—868no—
402C22⋊Q8—434no—
403C22⋊Q8—434no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406#121—22no—
407#121—434no—
408#121—862no—
409#121C4×D4314yescomplemented
410#120—868no—
411C4×D4—868no—
412C4×D4—868no—
413#117—434no—
414#117—862no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—1722no—
421C2×C4⋊C4—1722no—
422C2×C4⋊C4C22×D4312yes—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—862no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—1724no—
433C2×C42—861no—
434#103—1722no—
435#103—1722no—
436#102—42no—
437#102—1722no—
438C22⋊C8—864no—
439C22⋊C8—864no—
440#95—21no—
441#95—862no—
442#95—861no—
443C24—21no—
444C24—431no—
445C24—431no—
446C24—434no—
447C24—864no—
448C24—862no—
449C24—862no—
450C24—1722no—
451C24D4×D4311yescharacteristic
452#41—1728no—
453#41—1724no—
454#41—1724no—
455C2×Q8—432no—
456C2×Q8—861no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—864no—
466C2×D4—864no—
467C2×D4—1724no—
468C2×D4—1724no—
469C2×D4C2×C4×D4312yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—434no—
482C22×C4—434no—
483C22×C4—864no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—1728no—
492C22×C4—1724no—
493C22×C4—1724no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1724no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4—1722no—
500C22×C4—1724no—
501C22×C4C2×C4×D4312yes—
502C22×C4D4×D4311yescharacteristic
503C22×C4D4×D4312yes—
504C22×C4C23×D4311yescharacteristic
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—44no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—1724no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—432no—
517C4⋊C4—864no—
518C4⋊C4—864no—
519C4⋊C4—861no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—1724no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—24no—
525C22⋊C4—42no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C22⋊C4—864no—
529C22⋊C4—864no—
530C22⋊C4—1724no—
531C22⋊C4—1722no—
532C42—864no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—432no—
541C23—434no—
542C23—432no—
543C23—868no—
544C23—861no—
545C23—861no—
546C23—862no—
547C23—868no—
548C23—862no—
549C23—861no—
550C23—861no—
551C23—862no—
552C23—1724no—
553C23—1728no—
554C23—1728no—
555C23C22⋊C4×D4312yes—
556C23#1306334912yes—
557C23#1306335412yes—
558C23C2×D4×D4311yescharacteristic
559Q8—864no—
560Q8—1721no—
561Q8—1721no—
562D4—24no—
563D4—48no—
564D4—41no—
565D4—41no—
566D4—1728no—
567D4—1728no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—3448no—
591C2×C4—1724no—
592C2×C4—1724no—
593C2×C4—1724no—
594C2×C4—1728no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4C22⋊C4×D4312yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4#1306337012yes—
604C2×C4#1306337112yes—
605C8—42no—
606C8—1722no—
607C22—24no—
608C22—22no—
609C22—24no—
610C22—22no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—82no—
615C22—82no—
616C22—434no—
617C22—864no—
618C22—862no—
619C22—864no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22—862no—
624C22—17216no—
625C22—1722no—
626C22—1722no—
627C22#1458289714yes—
628C22C2×C22⋊C4×D4311yescharacteristic
629C22#1458345712yes—
630C22#135×D4312yes—
631C22C2×#1306334911yescharacteristic
632C22C2×#1306335411yescharacteristic
633C4—22no—
634C4—42no—
635C4—82no—
636C4—862no—
637C4—862no—
638C4—3442no—
639C4—1722no—
640C4—1722no—
641C4#1458337112yes—
642C4#1458345911yescharacteristic
643C4#1458346011yescharacteristic
644C2—24no—
645C2—82no—
646C2—864no—
647C2—1722no—
648C2#1913716911yescharacteristic
649C2#416×D4311yescharacteristic
650C2C2×#1458289711yescharacteristic
651C2#1914535512yes—
652C2#1914537112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#21763
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C22×(C2×D43)⋊C8C2semidirect
3. #380×D43C2semidirect
4. #19135024C2semidirect
5. #19135018C2semidirect
6. #19135016C2semidirect
7. #19134909C2semidirect
8. #19134901C2semidirect
9. #19134689C2semidirect
10. #19134532C2semidirect
11. C43×#1893C2semidirect
16. #14583409C4semidirect
27. C2×#13063250C22semidirect
28. C2×#13063248C22semidirect
29. C2×#13063246C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
43. C2×#102×C43C22semidirect
45. C43×#340C22semidirect
50. C2×#10621900C2×C4semidirect
72. #13063304C2×C4semidirect
79. #13063283C2×C4semidirect
109. #121×C43C2×C4semidirect
322. #1893D43semidirect
358. C2×#102C2×D43semidirect
371. #340C2×D43semidirect
372. C43#21763semidirect
409. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
C22×(C2×D43)⋊C82
#380×D432
#191350242
#191350182
#191350162
#191349092
#191349012
#191346892
#191345322
C43×#18932
#2176343