Finite Group Databasebeta

← #25001973

Subgroups — #25001973

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147796C211yesmaximal, characteristic
2C2×#14582872C211yesmaximal, characteristic
3C2×#14582867C211yesmaximal, characteristic
4#19134311C211yesmaximal, characteristic, complemented
5#19134311C211yesmaximal, characteristic, complemented
6#19134306C211yesmaximal, characteristic, complemented
7C43×#1733C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C23×C43⋊C8C2211yescharacteristic
10#14583380—22no—
11#14583379—22no—
12#14583376C412yescomplemented
13#14583373C412yescomplemented
14#14583372—22no—
15C4×#10621898—22no—
16#14583367—22no—
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#117×D43—22no—
20#14582872—22no—
21#14582872C414yescomplemented
22C2×#13063239—22no—
23#14582867—22no—
24#14582867C414yescomplemented
25C2×(C2×D43)⋊C8—22no—
26#14582661—22no—
27#14582661—22no—
28#14582660—22no—
29C22×M16×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#339—22no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898C2×C412yes—
42C2×#10621898C2×C412yes—
43C2×#10621898D412yes—
44C2×#10621898Q812yes—
45C22×Dic86C2×C411yescharacteristic
46C22×D172C2×C411yescharacteristic
47C22×C22⋊D43D412yes—
48C22×C4×D43D412yes—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8C2×C412yescomplemented
56C4×Dic86—24no—
57#13063290—24no—
58C4×D172—24no—
59#13063287—24no—
60C4×C22⋊D43—28no—
61(C22⋊D43)⋊C4—28no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67#13063284C2×C412yes—
68#13063284C2×C412yescomplemented
69#13063284D412yes—
70#13063283—24no—
71#13063282—24no—
72#13063281—24no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43D412yes—
75C4⋊C4×D43—24no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C22⋊C4×D43—24no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C42×D43—24no—
82#13063239—28no—
83(C2×D43)⋊C8—28no—
84C23×C4×C43C2311yescharacteristic
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43C2×C412yescomplemented
91C22×C8×C43—21no—
92#117×C43—21no—
93#117×C43—21no—
94#117×C43—21no—
95#117×C43—21no—
96#117×C43—21no—
97#117×C43C2×C412yes—
98#117×C43C2×C412yescomplemented
99#117×C43D412yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D412yes—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C42×C43—21no—
105C2×C42×C43—21no—
106C24×C43C2×D411yescharacteristic
107C23×D43C22⋊C412yes—
108C22×C4×C43—22no—
109C22×C4×C43—41no—
110C22×C4×C43C22×C411yescharacteristic
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×Q811yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C2×C22⋊D43—22no—
125C2×C22⋊D43—22no—
126C2×C22⋊D43—22no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43C22⋊C414yes—
129C2×C22⋊D43C4⋊C414yes—
130C22×Dic43—22no—
131C22×Dic43—41no—
132C22×Dic43C22⋊C412yes—
133#10621898—22no—
134#10621898—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—22no—
139#10621898—22no—
140#10621898—22no—
141#10621898—22no—
142#10621898—22no—
143#10621898—22no—
144#10621898—22no—
145#10621898—22no—
146#10621898—22no—
147#10621898—22no—
148#10621898—22no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C4212yes—
154C2×D172C4⋊C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—28no—
160C2×C4×D43C22⋊C414yes—
161C2×C4×D43C4⋊C414yes—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C4212yes—
167C2×Dic86C4⋊C412yes—
168M16×C43—22no—
169M16×C43—22no—
170M16×C43—41no—
171M16×C43—41no—
172C2×C8×C43—22no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C22⋊C414yes—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—41no—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43—41no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—41no—
191(C2×D43)⋊C4—28no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—41no—
195C4⋊Dic43C22⋊C414yes—
196Dic43⋊C4—28no—
197C4×Dic43—28no—
198C4×Dic43—22no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—41no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—41no—
206C2×C43⋊C8—41no—
207C2×C43⋊C8—41no—
208C2×C43⋊C8—41no—
209C23×C43—42no—
210C23×C43C2×C22⋊C411yescharacteristic
211C23×C43C2×C22⋊C411yescharacteristic
212C23×C43C2×C4⋊C411yescharacteristic
213C23×C43#12011yescharacteristic
214C23×C43#12011yescharacteristic
215C23×C43#12311yescharacteristic
216C23×C43#12311yescharacteristic
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—44no—
220C22×D43#9514yes—
221C2×C4×C43—24no—
222C2×C4×C43—42no—
223C2×C4×C43—82no—
224C2×C4×C43—82no—
225C2×C4×C43C2×C4211yescharacteristic
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43C2×C4⋊C411yescharacteristic
230C2×C4×C43C2×C4⋊C411yescharacteristic
231C2×C4×C43#11711yescharacteristic
232C2×C4×C43#11711yescharacteristic
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C4×D411yescharacteristic
237C2×C4×C43C4×D411yescharacteristic
238C2×C4×C43C4×D411yescharacteristic
239C2×C4×C43C4×D411yescharacteristic
240C2×C4×C43C4×D411yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43C22⋊Q811yescharacteristic
249C2×C4×C43C22⋊Q811yescharacteristic
250C2×C4×C43C22⋊Q811yescharacteristic
251C2×C4×C43#12311yescharacteristic
252C2×C4×C43#12311yescharacteristic
253C22⋊D43—24no—
254C22⋊D43—24no—
255C22⋊D43—24no—
256C22⋊D43—24no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—42no—
261C2×Dic43—82no—
262C2×Dic43—82no—
263C2×Dic43#9514yes—
264D172—22no—
265D172—22no—
266D172—22no—
267D172—22no—
268C4×D43—24no—
269C4×D43—24no—
270C4×D43—24no—
271C4×D43—24no—
272C4×D43—88no—
273Dic86—22no—
274Dic86—22no—
275Dic86—22no—
276Dic86—22no—
277C8×C43—42no—
278C43⋊C8—42no—
279#10752—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C2×#9511yescharacteristic
288C22×C43#37911yescharacteristic
289C22×C43#38111yescharacteristic
290C22×C43#38511yescharacteristic
291C22×C43#38511yescharacteristic
292C22×C43#38611yescharacteristic
293C22×C43#38611yescharacteristic
294C2×D43—24no—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—82no—
298C4×C43—44no—
299C4×C43—82no—
300C4×C43C4×C22⋊C411yescharacteristic
301C4×C43C4×C22⋊C411yescharacteristic
302C4×C43#38011yescharacteristic
303C4×C43#38011yescharacteristic
304C4×C43#38511yescharacteristic
305C4×C43#38511yescharacteristic
306C4×C43#38611yescharacteristic
307C4×C43#38611yescharacteristic
308Dic43—24no—
309Dic43—44no—
310Dic43—82no—
311#3428—431no—
312C2×#410—431no—
313C2×#408—431no—
314#1735—431no—
315#1735—431no—
316#1733—431no—
317#1733D4311yescharacteristic, complemented
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43C22⋊#9511yescharacteristic
325C2×C43#179412yes—
326D43—44no—
327C22×#41—431no—
328C22×M16C2×D4311yescharacteristic
329C23×C8—431no—
330#520—862no—
331#520—862no—
332#519—432no—
333#518—432no—
334#518—862no—
335C4×#41—862no—
336C4×#41—862no—
337C2×#117—431no—
338C2×#117—431no—
339C2×#117—862no—
340C2×#117C2×D4311yescharacteristic
341C2×#117C2×D4311yescharacteristic
342#410—434no—
343#410—862no—
344C2×#99—862no—
345#408—434no—
346#408—862no—
347C2×C22⋊C8—862no—
348#340—862no—
349#340—862no—
350#339—22no—
351#339—862no—
352C43#1075211yescharacteristic, complemented, Sylow
353C2×#41—432no—
354C2×#41—432no—
355C2×#41—432no—
356C2×#41—432no—
357C2×#41—861no—
358C2×#41—861no—
359C2×#41—861no—
360C2×#41—861no—
361C2×#41—861no—
362C2×#41—861no—
363C2×#41—861no—
364C2×#41—861no—
365C22×Q8—431no—
366C22×D4—432no—
367C22×D4—431no—
368C23×C4—432no—
369C23×C4C22×D4311yescharacteristic
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16C4×D4312yescomplemented
376C22×C8—21no—
377C22×C8—432no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4×Q8—864no—
385C4×Q8—864no—
386C4×D4—864no—
387C4×D4—868no—
388C4×D4—868no—
389C4×D4—864no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—432no—
396#117—432no—
397#117—432no—
398#117—864no—
399#117—864no—
400#117—864no—
401#117—861no—
402#117—861no—
403#117—861no—
404#117—861no—
405#117—861no—
406#117C4×D4312yes—
407#117C4×D4312yescomplemented
408#117C22⋊D4312yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—432no—
411C2×C4⋊C4—864no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4D17212yes—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—864no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—864no—
422C2×C42—861no—
423C2×C42—861no—
424#99—868no—
425C22⋊C8—868no—
426C24—432no—
427C24D4×D4311yescharacteristic
428#41—862no—
429#41—862no—
430#41—862no—
431#41—862no—
432#41—862no—
433#41—862no—
434#41—862no—
435#41—862no—
436#41—862no—
437#41—862no—
438#41—862no—
439#41—862no—
440#41—862no—
441#41—862no—
442#41—862no—
443#41—862no—
444C2×Q8—432no—
445C2×Q8—432no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×D4—434no—
451C2×D4—434no—
452C2×D4—432no—
453C2×D4—432no—
454C2×D4—862no—
455C2×D4—862no—
456C2×D4—862no—
457C2×D4—862no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C22×C4—22no—
463C22×C4—41no—
464C22×C4—432no—
465C22×C4—434no—
466C22×C4—434no—
467C22×C4—868no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—1721no—
474C22×C4C2×C4×D4311yescharacteristic
475C22×C4C2×C4×D4311yescharacteristic
476C22×C4C2×C4×D4311yescharacteristic
477C22×C4C2×D17211yescharacteristic
478C22×C4#1062189811yescharacteristic
479C22×C4#1062189811yescharacteristic
480C22×C4D4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4#1062190011yescharacteristic
485C22×C4Q8×D4311yescharacteristic
486C22×C4#1062190211yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—862no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—1721no—
499C2×C8—1721no—
500C2×C8—1721no—
501C2×C8—1721no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—434no—
506C4⋊C4—868no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—1721no—
510C4⋊C4(C2×D43)⋊C414yes—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—41no—
515C22⋊C4—868no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—1721no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—41no—
524C42—868no—
525C42—862no—
526C42—862no—
527C42—862no—
528C42—1721no—
529C23—42no—
530C23—434no—
531C23—862no—
532C23—862no—
533C23—1724no—
534C23C22⋊C4×D4311yescharacteristic
535C23C22⋊C4×D4311yescharacteristic
536C23C4⋊C4×D4311yescharacteristic
537C23#1306329311yescharacteristic
538C23#1306329511yescharacteristic
539C23#1306330711yescharacteristic
540C23#1306331011yescharacteristic
541Q8—862no—
542Q8—862no—
543Q8—862no—
544Q8—862no—
545D4—864no—
546D4—864no—
547D4—864no—
548D4—864no—
549D4—862no—
550D4—862no—
551D4—862no—
552D4—862no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—434no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—864no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—3448no—
566C2×C4—3442no—
567C2×C4—3442no—
568C2×C4—1722no—
569C2×C4C42×D4311yescharacteristic
570C2×C4C22⋊C4×D4311yescharacteristic
571C2×C4C22⋊C4×D4311yescharacteristic
572C2×C4C2×(C2×D43)⋊C411yescharacteristic
573C2×C4C4⋊C4×D4311yescharacteristic
574C2×C4C4⋊C4×D4311yescharacteristic
575C2×C4#1306328211yescharacteristic
576C2×C4#1306328311yescharacteristic
577C2×C4(C22⋊D43)⋊C411yescharacteristic
578C2×C4(C22⋊D43)⋊C411yescharacteristic
579C2×C4C4×C22⋊D4311yescharacteristic
580C2×C4C4×C22⋊D4311yescharacteristic
581C2×C4#1306328711yescharacteristic
582C2×C4#1306328711yescharacteristic
583C2×C4C4×D17211yescharacteristic
584C2×C4C4×D17211yescharacteristic
585C2×C4#1306329311yescharacteristic
586C2×C4#1306329511yescharacteristic
587C2×C4#1306329611yescharacteristic
588C2×C4#1306329811yescharacteristic
589C2×C4#1306329811yescharacteristic
590C2×C4#1306330011yescharacteristic
591C2×C4#1306330111yescharacteristic
592C2×C4#1306330311yescharacteristic
593C2×C4#1306330311yescharacteristic
594C2×C4#1306330511yescharacteristic
595C2×C4#1306330711yescharacteristic
596C2×C4#1306331011yescharacteristic
597C8—42no—
598C8—1722no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—864no—
607C22—3442no—
608C22—1724no—
609C22—1724no—
610C22#95×D4311yescharacteristic
611C22#1458275411yescharacteristic
612C22#1458276111yescharacteristic
613C22#1458277011yescharacteristic
614C22#1458277311yescharacteristic
615C22#1458277511yescharacteristic
616C22#1458277711yescharacteristic
617C4—44no—
618C4—82no—
619C4—864no—
620C4—3442no—
621C4—1724no—
622C4#1458274611yescharacteristic
623C4C4×(C2×D43)⋊C411yescharacteristic
624C4#1458275611yescharacteristic
625C4#1458275811yescharacteristic
626C4#1458277011yescharacteristic
627C4#1458277311yescharacteristic
628C4#1458277511yescharacteristic
629C4#1458277711yescharacteristic
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—1724no—
637C2(C2×D43)⋊#9511yescharacteristic
638C2#1913455712yes—
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#1733C2
socleC22×C43#379
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1733D43
hypocenterC43#10752
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #19134311C2semidirect
5. #19134311C2semidirect
6. #19134306C2semidirect
7. C43×#1733C2semidirect
12. #14583376C4semidirect
13. #14583373C4semidirect
21. #14582872C4semidirect
24. #14582867C4semidirect
55. C22×C43⋊C8C2×C4semidirect
68. #13063284C2×C4semidirect
90. C2×M16×C43C2×C4semidirect
98. #117×C43C2×C4semidirect
317. #1733D43semidirect
352. C43#10752semidirect
375. C2×M16C4×D43semidirect
407. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477962
C2×#145828722
C2×#145828672
#191343112
#191343062
C43×#17332
#1075243