Finite Group Databasebeta

← #25106165

Subgroups — #25106165

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3#19136991C211yesmaximal, characteristic
4#19135574C214yesmaximal, complemented
5#19135540C211yesmaximal, characteristic, complemented
6#19135539C211yesmaximal, characteristic, complemented
7#19135538C211yesmaximal, characteristic, complemented
8#19134693C214yesmaximal
9C43×#1986C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455C412yescomplemented
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453—21no—
16#14583452C2212yes—
17#14583451—21no—
18#14583451—21no—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43C412yescomplemented
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43—21no—
24C4×Q8×D43—21no—
25C4×Q8×D43—21no—
26#117×D43C2212yes—
27C2×C42×D43C2211yescharacteristic
28#14582954—21no—
29#14582954—21no—
30#14582950—21no—
31#14582950—21no—
32#14582922C2212yes—
33#14582862C2212yes—
34C4×#10621877C2211yescharacteristic
35#14582766—21no—
36#14582764—21no—
37#14582761—21no—
38#14582756—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40C4×(C2×D43)⋊C4C2212yes—
41#14582745C2212yes—
42#14582660C2214yes—
43#14582659C2214yes—
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063324—21no—
58#13063324—21no—
59#13063324C2×C412yes—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323—21no—
63#13063317C2×C412yes—
64#13063316C2×C412yes—
65#13063316C2×C412yes—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305—21no—
70#13063304—21no—
71#13063304—21no—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84#13063290—21no—
85#13063290—21no—
86#13063290—22no—
87#13063290—22no—
88#13063284C2312yes—
89#13063283C2×C412yes—
90#13063283C2×C412yes—
91#13063282—22no—
92#13063281—22no—
93C2×C4⋊Dic43—21no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43C2×C412yes—
99C4⋊C4×D43C2×C412yes—
100C2×(C2×D43)⋊C4—22no—
101C22⋊C4×D43—22no—
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43C2312yes—
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—22no—
107C42×D43C2×C411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C43⋊#95—21no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C2×M16×C43C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43C2×C412yes—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133#117×C43C2312yes—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43C2312yes—
136C2×C42×C43C2311yescharacteristic
137#97×C43—21no—
138C4×C8×C43—21no—
139#95×C43—21no—
140C23×D43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—22no—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151Q8×D43—44no—
152Q8×D43—44no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22×C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175M16×C43—22no—
176M16×C43—22no—
177C2×C8×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43C22×C412yes—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C42×C43—22no—
187C42×C43—24no—
188C42×C43C22×C411yescharacteristic
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—44no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—42no—
201C4⋊Dic43C22×C412yes—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—24no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227#10621877—22no—
228#10621877—22no—
229C2×C43⋊C8—22no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—22no—
234C22×D43—41no—
235C22×D43C2×C22⋊C411yescharacteristic
236C22×D43C2×C22⋊C411yescharacteristic
237Q8×C43—42no—
238Q8×C43—42no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C432−1+412yes—
253C2×C4×C432−1+412yes—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—44no—
282C4×D43—44no—
283Dic86—44no—
284Dic86—44no—
285Dic86—42no—
286Dic86—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289#21845—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43C22×C22⋊C411yescharacteristic
293C22×C43#53611yescharacteristic
294C22×C43#53611yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—21no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43#42112yes—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43—82no—
309C4×C43#42112yes—
310C4×C43#51912yes—
311C4×C43#53612yes—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—42no—
319Dic43—42no—
320Dic43—82no—
321C2×#533—431no—
322#2920—431no—
323#2283—431no—
324#1995—434no—
325#1986—431no—
326#1986—431no—
327#1986—431no—
328#1986D4311yescharacteristic, complemented
329#1826—434no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43#231011yescharacteristic
333C2×C43C2×#42111yescharacteristic
334C2×C43C2×#42111yescharacteristic
335D43—22no—
336D43—41no—
337#533—431no—
338#533—431no—
339#533—432no—
340#533—432no—
341#533—431no—
342#533—861no—
343#533—861no—
344#533—861no—
345#533—861no—
346#533C2×D4311yescharacteristic
347C2×C4⋊Q8—431no—
348C2×C4⋊Q8—431no—
349C2×#125—432no—
350C2×C22⋊Q8—861no—
351C2×C22⋊Q8—861no—
352C2×C4×Q8—861no—
353C2×C4×Q8—861no—
354C2×#117—432no—
355C22×C42—431no—
356#432—861no—
357#432—861no—
358#431—861no—
359#431—861no—
360#423—432no—
361#407—432no—
362C4×M16—431no—
363C4×M16C2×D4311yescharacteristic
364#383—861no—
365#382—861no—
366#381—861no—
367#380—861no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4C2×D4311yescharacteristic
370C4×C22⋊C4—432no—
371#376—432no—
372#339—434no—
373#339—434no—
374#339—434no—
375#339C2×D4314yes—
376C43#2184511yescharacteristic, complemented, Sylow
377C22×Q8—861no—
378C22×Q8—861no—
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—431no—
382C2×M16—432no—
383C2×M16C22×D4312yes—
384C4⋊Q8—432no—
385C4⋊Q8—432no—
386C4⋊Q8—431no—
387C4⋊Q8—431no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8—861no—
391C4⋊Q8—861no—
392C4⋊Q8C4×D4311yescharacteristic
393C4⋊Q8C4×D4311yescharacteristic
394#125—432no—
395#125—432no—
396#125—432no—
397#125—862no—
398#125—862no—
399#125C4×D4312yes—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8—861no—
411C22⋊Q8—861no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8—861no—
424#117—432no—
425#117—432no—
426#117—432no—
427#117—862no—
428#117—862no—
429#117C22×D4312yes—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C22⋊C4—862no—
439C2×C22⋊C4—862no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—432no—
452C2×C42—862no—
453C2×C42C22×D4312yes—
454C2×C42C22×D4311yescharacteristic
455C4⋊C8—862no—
456C4⋊C8—862no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459#97—21no—
460#97—861no—
461C4×C8—21no—
462C4×C8—861no—
463#95—21no—
464#95—862no—
465#95—862no—
466#95—862no—
467#95—861no—
468C24—431no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—1724no—
476C2×Q8—1724no—
477C22×C4—22no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—22no—
504M16—22no—
505M16—862no—
506M16—862no—
507C2×C8—22no—
508C2×C8—862no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—1722no—
529C4⋊C4C2×C4×D4312yes—
530C4⋊C4C2×C4×D4312yes—
531C22⋊C4—22no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—1724no—
536C42—22no—
537C42—24no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—862no—
551C42—862no—
552C42—862no—
553C42—864no—
554C42C2×C4×D4311yescharacteristic
555C42C2×C4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C42D4×D4311yescharacteristic
558C23—431no—
559C23—431no—
560C23—862no—
561C23—861no—
562C23—861no—
563C23—1721no—
564C23C2×D4×D4311yescharacteristic
565Q8—42no—
566Q8—42no—
567Q8—1722no—
568Q8—1724no—
569Q8—1724no—
570Q8—1722no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1724no—
601C2×C4—1724no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C22×C4×D4311yescharacteristic
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4#1306337212yes—
614C2×C4#1306337312yes—
615C8—42no—
616C8—1722no—
617C22—21no—
618C22—21no—
619C22—432no—
620C22—861no—
621C22—861no—
622C22—861no—
623C22—861no—
624C22—861no—
625C22—1722no—
626C22—1722no—
627C22C2×C22⋊C4×D4311yescharacteristic
628C22#1458346911yescharacteristic
629C22#1458347411yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—42no—
634C4—42no—
635C4—82no—
636C4—861no—
637C4—861no—
638C4—861no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—3442no—
643C4—1722no—
644C4—1722no—
645C4#1458291412yes—
646C4#1458337512yes—
647C4#1458347212yes—
648C2—21no—
649C2—21no—
650C2—862no—
651C2—1721no—
652C2#1913717811yescharacteristic
653C2#421×D4311yescharacteristic
654C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21845
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #19135574C2semidirect
5. #19135540C2semidirect
6. #19135539C2semidirect
7. #19135538C2semidirect
9. C43×#1986C2semidirect
11. #14583455C4semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
21. #125×D43C4semidirect
328. #1986D43semidirect
376. C43#21845semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432262
#191369912
#191355742
#191355402
#191355392
#191355382
#191346932
C43×#19862
#2184543