Finite Group Databasebeta

← #25097697

Subgroups — #25097697

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147796C211yesmaximal, characteristic
2C2×#14582872C211yesmaximal, characteristic
3#19137218C211yesmaximal, characteristic, complemented
4#19137215C211yesmaximal, characteristic, complemented
5#19137183C211yesmaximal, characteristic
6#19134877C218yesmaximal, complemented
7#19134327C211yesmaximal, characteristic, complemented
8C43×#1740C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583380—21no—
11#14583380—21no—
12#14583379—21no—
13#14583379—21no—
14#14583376—21no—
15#14583373—21no—
16#14583372C2214yes—
17C4×#10621898—22no—
18#14583367—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#117×D43—22no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14582872C418yescomplemented
24C2×#13063239C2214yes—
25#14582805—21no—
26#14582801—21no—
27#14582798—22no—
28#14582797—22no—
29#14582776C2214yes—
30#14582774C2214yes—
31#14582771C2214yes—
32#14582769—21no—
33#14582768—21no—
34#14582765—21no—
35#14582764—21no—
36#14582756—22no—
37#14582665C2214yes—
38C2×#117×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#342C2214yes—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898C2×C414yes—
49C2×#10621898Q814yes—
50C22×Dic86D411yescharacteristic
51C22×D172D411yescharacteristic
52C22×C22⋊D43C2312yes—
53C23×Dic43C2312yes—
54C22×C4×D43D412yes—
55C4×Dic86—22no—
56C4×Dic86—22no—
57#13063290—22no—
58#13063290—22no—
59C4×D172—22no—
60C4×D172—22no—
61#13063287—22no—
62#13063287—22no—
63C4×C22⋊D43—24no—
64C4×C22⋊D43—24no—
65(C22⋊D43)⋊C4—24no—
66(C22⋊D43)⋊C4—24no—
67#13063284—21no—
68#13063284—21no—
69#13063284—21no—
70#13063284—21no—
71#13063284—22no—
72#13063284C2×C414yescomplemented
73#13063283—22no—
74#13063283—22no—
75#13063282—24no—
76#13063281—24no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—24no—
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43D411yescharacteristic
87C2×Dic43⋊C4—24no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C2×C22⋊Dic43C2312yes—
91C2×C22⋊Dic43C2312yes—
92C2×(C2×D43)⋊C4—24no—
93C22⋊C4×D43—24no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43D412yes—
96C42×D43—24no—
97#13063239C2×C4116yescomplemented
98C43⋊#95—24no—
99C43⋊#95—24no—
100C43⋊#95—24no—
101C23×C4×C43C2311yescharacteristic
102#117×C43—21no—
103#117×C43—21no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—22no—
107#117×C43—22no—
108#117×C43—22no—
109#117×C43C2×C414yescomplemented
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43C2312yes—
115C2×C22⋊C4×C43C2312yes—
116C2×C22⋊C4×C43C2312yes—
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43D412yes—
120C24×C43C2411yescharacteristic
121C23×D43C2×D412yes—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×Q812yes—
134C22×C4×C43#4112yes—
135C22×C4×C43#4112yes—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43C22×C414yes—
141C2×C22⋊D43C2×Q814yes—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—82no—
147C22×Dic43C2×D412yes—
148C22×Dic43C2×D412yes—
149C22×Dic43C2×D412yes—
150#10621898—24no—
151#10621898—24no—
152#10621898—24no—
153#10621898—24no—
154#10621898—24no—
155#10621898—24no—
156#10621898—24no—
157#10621898—24no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—22no—
161C2×D172C4⋊C414yescomplemented
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—24no—
165C2×C4×D43—24no—
166C2×C4×D43—24no—
167C2×C4×D43C4⋊C418yescomplemented
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—22no—
171C2×Dic86C4⋊C414yescomplemented
172C4⋊C4×C43—24no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43C22×C414yes—
184C42×C43—24no—
185C42×C43—22no—
186C42×C43—22no—
187C42×C43—42no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43C22×C414yes—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—84no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43—84no—
205Dic43⋊C4—24no—
206Dic43⋊C4—24no—
207Dic43⋊C4—84no—
208C4×Dic43—24no—
209C4×Dic43—24no—
210C4×Dic43—24no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C23×C411yescharacteristic
216C23×C43C22×D411yescharacteristic
217C23×C43C22×D411yescharacteristic
218C23×C43C22×D411yescharacteristic
219C23×C43C22×Q811yescharacteristic
220C23×C43C2×#4111yescharacteristic
221C23×C43C2×#4111yescharacteristic
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43C2×C4⋊C414yes—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43C2×C4⋊C412yes—
238C2×C4×C43C2×C4⋊C412yes—
239C2×C4×C43C4×D412yes—
240C2×C4×C43C4×D412yes—
241C2×C4×C43C4×D412yes—
242C2×C4×C43C4×D412yes—
243C2×C4×C43#12011yescharacteristic
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43C22⋊Q812yes—
248C2×C4×C43C22⋊Q812yes—
249C2×C4×C43C22⋊Q812yes—
250C2×C4×C43C22⋊Q812yes—
251C2×C4×C43#12312yes—
252C2×C4×C43#12312yes—
253C22⋊D43—24no—
254C22⋊D43—24no—
255C22⋊D43—24no—
256C22⋊D43—24no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—44no—
267C2×Dic43—44no—
268C2×Dic43—44no—
269C2×Dic43—42no—
270C2×Dic43C2×C4⋊C414yes—
271D172—24no—
272D172—24no—
273C4×D43—28no—
274C4×D43—28no—
275C4×D43—84no—
276C4×D43—84no—
277Dic86—24no—
278Dic86—24no—
279#20890—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C22×C4⋊C411yescharacteristic
291C22×C43C2×C4×D411yescharacteristic
292C22×C43C2×C4×D411yescharacteristic
293C22×C43C2×#12011yescharacteristic
294C22×C43C2×C22⋊Q811yescharacteristic
295C22×C43C2×C22⋊Q811yescharacteristic
296C22×C43C2×#12311yescharacteristic
297C2×D43—24no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—44no—
301C2×D43—82no—
302C4×C43—44no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43—82no—
306C4×C43#38512yes—
307C4×C43#38512yes—
308C4×C43#38512yes—
309C4×C43#38512yes—
310Dic43—24no—
311Dic43—44no—
312Dic43—42no—
313Dic43—42no—
314Dic43—82no—
315#3428—431no—
316C2×#410—431no—
317#2317—431no—
318#2317—431no—
319#2311—431no—
320#1867—438no—
321#1740—431no—
322#1740D4311yescharacteristic, complemented
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43C2×#38511yescharacteristic
330C2×C43#302711yescharacteristic
331C2×C43#302811yescharacteristic
332D43—44no—
333C22×#41—431no—
334#520—861no—
335#520—861no—
336#520—861no—
337#520—861no—
338#519—861no—
339#518—434no—
340#518—861no—
341C4×#41—862no—
342C4×#41—862no—
343C2×#117—431no—
344C2×#117—431no—
345C2×#117—862no—
346C2×#117C2×D4311yescharacteristic
347C2×#117C2×D4311yescharacteristic
348C2×#117C2×D4311yescharacteristic
349C22×C4⋊C4—431no—
350#410—438no—
351C2×#99—434no—
352#391—861no—
353#390—861no—
354#389—862no—
355#389—862no—
356#386—434no—
357#385—434no—
358#385—434no—
359#384—861no—
360#384—861no—
361#382—861no—
362#382—861no—
363#380—862no—
364#342—434no—
365#342C2×D4314yes—
366C43#2089011yescharacteristic, complemented, Sylow
367C2×#41—434no—
368C2×#41—434no—
369C2×#41—861no—
370C2×#41—861no—
371C2×#41—862no—
372C2×#41—861no—
373C2×#41—861no—
374C2×#41—862no—
375C22×Q8—431no—
376C22×D4—432no—
377C22×D4—431no—
378C23×C4—432no—
379C23×C4—432no—
380C23×C4C22×D4311yescharacteristic
381C4×Q8—862no—
382C4×Q8—862no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×D4—862no—
386C4×D4—862no—
387C4×D4—864no—
388C4×D4—864no—
389C4×D4—862no—
390C4×D4—862no—
391C4×D4—864no—
392C4×D4—864no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—434no—
401#117—864no—
402#117—864no—
403#117—862no—
404#117—862no—
405#117—861no—
406#117—861no—
407#117—862no—
408#117—861no—
409#117—861no—
410#117C4×D4314yescomplemented
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—864no—
419C2×C4⋊C4—864no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4D17211yescharacteristic
427C2×C4⋊C4D17211yescharacteristic
428C2×C22⋊C4—432no—
429C2×C22⋊C4—432no—
430C2×C22⋊C4—864no—
431C2×C22⋊C4—864no—
432C2×C22⋊C4C22×D4312yes—
433C2×C22⋊C4C22×D4312yes—
434C2×C22⋊C4C22×D4312yes—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—432no—
438C2×C42—864no—
439C2×C42—861no—
440C2×C42D17212yes—
441#99—4316no—
442#95—864no—
443#95—864no—
444#95—864no—
445C24—432no—
446C24C23×D4311yescharacteristic
447#41—864no—
448#41—864no—
449#41—864no—
450#41—864no—
451#41—864no—
452#41—864no—
453#41—864no—
454#41—864no—
455C2×Q8—434no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—862no—
459C2×D4—434no—
460C2×D4—434no—
461C2×D4—434no—
462C2×D4—862no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—862no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—862no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—432no—
472C22×C4—438no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—864no—
476C22×C4—864no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—864no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—3442no—
485C22×C4C2×C4×D4312yes—
486C22×C4C2×D17212yes—
487C22×C4C2×D17212yes—
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4#1062189812yes—
491C22×C4D4×D4311yescharacteristic
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4#1062190012yes—
496C22×C4Q8×D4312yes—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—864no—
504C4⋊C4—864no—
505C4⋊C4—864no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3444no—
511C4⋊C4—3444no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—434no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—3444no—
528C22⋊C4C2×C4×D4314yes—
529C42—24no—
530C42—22no—
531C42—22no—
532C42—42no—
533C42—864no—
534C42—864no—
535C42—864no—
536C42—862no—
537C42—862no—
538C23—41no—
539C23—41no—
540C23—434no—
541C23—862no—
542C23—862no—
543C23—1722no—
544C23—1722no—
545C23C22×C4×D4311yescharacteristic
546C23C2×D4×D4311yescharacteristic
547C23C2×D4×D4311yescharacteristic
548C23C22×D17211yescharacteristic
549C23C2×Q8×D4311yescharacteristic
550C23C2×#1062190011yescharacteristic
551C23C2×#1062189811yescharacteristic
552Q8—864no—
553Q8—864no—
554D4—864no—
555D4—864no—
556D4—864no—
557D4—864no—
558D4—864no—
559D4—864no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—434no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—868no—
574C2×C4—868no—
575C2×C4—864no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—3444no—
579C2×C4—3444no—
580C2×C4—1724no—
581C2×C4—1724no—
582C2×C4—1724no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4C4⋊C4×D4312yes—
589C2×C4C4⋊C4×D4312yes—
590C2×C4(C22⋊D43)⋊C412yes—
591C2×C4(C22⋊D43)⋊C412yes—
592C2×C4C4×D17212yes—
593C2×C4C4×D17212yes—
594C2×C4#1306329511yescharacteristic
595C2×C4#1306329511yescharacteristic
596C2×C4#1306329511yescharacteristic
597C2×C4#1306329511yescharacteristic
598C2×C4#1306330312yes—
599C2×C4#1306330312yes—
600C2×C4#1306330512yes—
601C2×C4#1306330512yes—
602C2×C4#1306330712yes—
603C2×C4#1306330712yes—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—864no—
615C22—3442no—
616C22—1724no—
617C22—1722no—
618C22—1722no—
619C22C2×C4⋊C4×D4311yescharacteristic
620C22C2×(C22⋊D43)⋊C411yescharacteristic
621C22C2×C4×D17211yescharacteristic
622C22C2×#1306329511yescharacteristic
623C22C2×#1306330311yescharacteristic
624C22C2×#1306330511yescharacteristic
625C22C2×#1306330711yescharacteristic
626C4—44no—
627C4—42no—
628C4—42no—
629C4—82no—
630C4—864no—
631C4—3442no—
632C4—1724no—
633C4—1722no—
634C4—1722no—
635C4#1458277312yes—
636C4#1458277312yes—
637C4#1458277312yes—
638C4#1458277312yes—
639C2—21no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—1724no—
646C2C2×#1458277311yescharacteristic
647C2#1914399811yescharacteristic
648C2#1914400211yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1740C2
socleC22×C43C2×#120
prime radicalC22×#10621898C22
cosocleC24×C43C24
hypercenter#1740D43
hypocenterC43#20890
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
3. #19137218C2semidirect
4. #19137215C2semidirect
6. #19134877C2semidirect
7. #19134327C2semidirect
8. C43×#1740C2semidirect
23. #14582872C4semidirect
72. #13063284C2×C4semidirect
97. #13063239C2×C4semidirect
109. #117×C43C2×C4semidirect
161. C2×D172C4⋊C4semidirect
167. C2×C4×D43C4⋊C4semidirect
171. C2×Dic86C4⋊C4semidirect
322. #1740D43semidirect
366. C43#20890semidirect
410. #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
#191372182
#191372152
#191371832
#191348772
#191343272
C43×#17402
#2089043