Finite Group Databasebeta

← #25062840

Subgroups — #25062840

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2#19143255C211yesmaximal, characteristic, complemented
3#19143249C211yesmaximal, characteristic, complemented
4#19132955C211yesmaximal, characteristic, complemented
5#19132945C212yesmaximal, complemented
6#19132945C212yesmaximal, complemented
7#19132931C211yesmaximal, characteristic, complemented
8#19132926C212yesmaximal, complemented
9#19132911C211yesmaximal, characteristic, complemented
10#19132906C212yesmaximal, complemented
11C43×#1471C211yesmaximal, characteristic, complemented
12#14583613—21no—
13#14583613—21no—
14#14583613—21no—
15#14583613—21no—
16#14583613—22no—
17#14583613—22no—
18C2×#13063324C411yescharacteristic
19C2×#13063312C412yes—
20C2×#13063311C2212yes—
21C2×#13063297C412yes—
22C2×#13063296C411yescharacteristic
23C2×D4×Dic43C411yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C2×#13063283C411yescharacteristic
27C2×#13063281C2212yes—
28#14582957—22no—
29#14582957—22no—
30#14582953C2212yes—
31#14582953C2212yes—
32#14582949C2212yes—
33#14582949C2212yes—
34#14582927—21no—
35#14582925—21no—
36#14582863C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38#14582857—21no—
39#14582854—21no—
40#14582624C2212yes—
41#14582624C2211yescharacteristic
42#14582624C2211yescharacteristic
43#14582623C2212yes—
44#14582623C2212yes—
45#14582622C2212yes—
46#14582622C2211yescharacteristic
47#14582622C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C43×#407C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C43×#323C2212yes—
52C43×#323C2212yes—
53C22×Dic86C2×C412yes—
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C22⋊D43C2×C412yes—
56C23×Dic43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60#13063324—22no—
61#13063324—21no—
62#13063324—21no—
63#13063312—22no—
64#13063312—22no—
65#13063312—22no—
66#13063312—22no—
67#13063311—22no—
68#13063311—22no—
69#13063311—22no—
70#13063311—22no—
71#13063297—22no—
72#13063297—22no—
73#13063297—22no—
74#13063297—22no—
75#13063296—22no—
76#13063296—21no—
77#13063296—21no—
78D4×Dic43—22no—
79D4×Dic43—21no—
80D4×Dic43—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84C4×C22⋊D43—21no—
85#13063284D411yescharacteristic
86#13063284D411yescharacteristic
87#13063284D411yescharacteristic
88#13063284D411yescharacteristic
89#13063284D412yes—
90#13063284D412yes—
91#13063283—22no—
92#13063283—21no—
93#13063283—21no—
94#13063281—22no—
95#13063281—22no—
96#13063281—22no—
97#13063281—22no—
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C412yes—
101C2×Dic43⋊C4C2311yescharacteristic
102C2×C22⋊Dic43C2×C412yes—
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C412yes—
105C2×C22⋊Dic43C2×C412yes—
106C2×(C2×D43)⋊C4C2×C412yes—
107C2×(C2×D43)⋊C4C2311yescharacteristic
108C2×C4×Dic43C2×C412yes—
109C2×C4×Dic43C2×C411yescharacteristic
110C2×C4×Dic43C2312yes—
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)C2311yescharacteristic
118C22⋊(C43⋊C8)C2311yescharacteristic
119C22⋊(C43⋊C8)C2312yes—
120#13063235—22no—
121#13063235—22no—
122C8×Dic43—22no—
123C8×Dic43—22no—
124C22×D4×C43C2×C411yescharacteristic
125C22×D4×C43C2×C412yes—
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C22×C8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2312yes—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43C2312yes—
140C24×C43C22×C412yes—
141C24×C43C22×C411yescharacteristic
142C23×D43C22×C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—42no—
148C2×D4×C43—82no—
149C22×C4×C43—42no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—21no—
161C2×C22⋊D43—21no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—82no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—24no—
167C22×Dic43—42no—
168C22×Dic43C22×C412yes—
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C412yes—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—42no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—82no—
179M16×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—22no—
183C2×C8×C43—42no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43C22⋊C412yes—
195C22⋊Dic43C22⋊C412yes—
196C22⋊Dic43C22⋊C412yes—
197C22⋊Dic43C22⋊C412yes—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202C4⋊Dic43C22⋊C412yes—
203C4⋊Dic43C22⋊C411yescharacteristic
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C412yes—
206C4⋊Dic43C22⋊C411yescharacteristic
207C4⋊Dic43C22⋊C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220#10621877—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—42no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C23×C411yescharacteristic
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—41no—
241C22×D43—41no—
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—82no—
245D4×C43—82no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—42no—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C22⋊D43—42no—
259C22⋊D43—42no—
260C22⋊D43—82no—
261C22⋊D43—82no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—42no—
269C2×Dic43—44no—
270C2×Dic43—44no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275C2×Dic43C2×C22⋊C412yes—
276C2×Dic43C2×C22⋊C412yes—
277C2×Dic43#13112yes—
278C4×D43—42no—
279C4×D43—42no—
280Dic86—82no—
281Dic86—82no—
282C8×C43—41no—
283C8×C43—41no—
284C8×C43—42no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—42no—
288#17418—431nomaximal, Sylow
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—82no—
303C22×C43—82no—
304C22×C43C22×C22⋊C411yescharacteristic
305C22×C43C2×#13111yescharacteristic
306C22×C43#56811yescharacteristic
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—81no—
311C2×D43—81no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—42no—
316C4×C43#41012yes—
317Dic43—22no—
318Dic43—22no—
319Dic43—22no—
320Dic43—22no—
321Dic43—22no—
322Dic43—41no—
323Dic43—41no—
324C2×#555—431no—
325#2924—431no—
326#2924—431no—
327#1471—431no—
328#1471D4311yescharacteristic, complemented
329#1469—432no—
330#1469—432no—
331#1465—431no—
332#1464—432no—
333#1459—431no—
334#1458—432no—
335C2×C43—21no—
336C2×C43—21no—
337C2×C43—41no—
338C2×C43—41no—
339C2×C43—82no—
340C2×C43#288011yescharacteristic
341C2×C43C2×#41011yescharacteristic
342C2×C43#288811yescharacteristic
343D43—81no—
344#555—861no—
345#555—861no—
346#555—861no—
347#555—861no—
348#555—862no—
349#555—862no—
350C2×C4⋊Q8—431no—
351C2×#124—432no—
352C2×#124—432no—
353C2×#121—431no—
354C2×#121—432no—
355C2×#121C2×D4311yescharacteristic
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×#117—431no—
359C2×#117—431no—
360C2×#117—432no—
361#433—862no—
362#433—862no—
363#432—432no—
364#432—432no—
365#431—432no—
366#431—432no—
367#424—861no—
368#424—861no—
369#407—431no—
370#407C2×D4311yescharacteristic
371C2×C22⋊C8—431no—
372C2×C22⋊C8C2×D4311yescharacteristic
373#405—861no—
374#405—861no—
375#324—431no—
376#324—432no—
377#324—431no—
378#323—432no—
379#323—432no—
380#323—431no—
381#323—431no—
382#323—432no—
383#323C2×D4312yes—
384#323C2×D4312yes—
385C43#1741811yescharacteristic, complemented, Sylow
386C22×Q8—432no—
387C22×D4—431no—
388C22×D4—432no—
389C22×D4C4×D4311yescharacteristic
390C22×D4C4×D4312yes—
391C23×C4—432no—
392C23×C4—431no—
393C23×C4C22×D4311yescharacteristic
394C2×M16—21no—
395C2×M16—861no—
396C22×C8—21no—
397C22×C8—861no—
398C4⋊Q8—862no—
399C4⋊Q8—861no—
400C4⋊Q8—861no—
401#124—862no—
402#124—862no—
403#124—862no—
404#124—862no—
405#124—862no—
406#124—862no—
407#124—862no—
408#124—862no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—862no—
414#121—862no—
415#121—862no—
416#121—862no—
417#121—862no—
418#121—861no—
419#121—861no—
420C4×D4—862no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4—861no—
427#117—431no—
428#117—431no—
429#117—431no—
430#117—431no—
431#117—432no—
432#117—432no—
433#117—862no—
434#117—862no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—861no—
439#117—861no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—432no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4C4×D4311yescharacteristic
445C2×C22⋊C4—432no—
446C2×C22⋊C4—432no—
447C2×C22⋊C4—432no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—432no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4C22×D4312yes—
452C2×C42—432no—
453C2×C42—432no—
454C2×C42—431no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C4⋊C8—862no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—431no—
462C22⋊C8—431no—
463C22⋊C8—432no—
464C22⋊C8—861no—
465C22⋊C8—861no—
466C22⋊C8C22×D4311yescharacteristic
467C22⋊C8C22×D4311yescharacteristic
468C22⋊C8C22×D4312yes—
469#97—862no—
470#97—862no—
471C4×C8—862no—
472C4×C8—862no—
473C24—431no—
474C24C2×C4×D4312yes—
475C24C2×C4×D4311yescharacteristic
476C2×Q8—862no—
477C2×Q8—862no—
478C2×Q8—3442no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—82no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—862no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—3442no—
491C2×D4—1721no—
492C22×C4—42no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—432no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—864no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4C2×C4×D4312yes—
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512M16—42no—
513M16—1722no—
514C2×C8—21no—
515C2×C8—22no—
516C2×C8—21no—
517C2×C8—42no—
518C2×C8—861no—
519C2×C8—862no—
520C2×C8—861no—
521C2×C8—1722no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—432no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—432no—
528C4⋊C4—431no—
529C4⋊C4—431no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—432no—
537C22⋊C4—432no—
538C22⋊C4—432no—
539C22⋊C4—432no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—861no—
547C22⋊C4—861no—
548C22⋊C4—861no—
549C22⋊C4—861no—
550C42—432no—
551C42—432no—
552C42—432no—
553C42—432no—
554C42—862no—
555C42—862no—
556C42—861no—
557C42—861no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—42no—
566C23—42no—
567C23—861no—
568C23—861no—
569C23—861no—
570C23—1721no—
571C23—1721no—
572C23C22⋊C4×D4311yescharacteristic
573C23C22⋊C4×D4311yescharacteristic
574C23C22×C4×D4311yescharacteristic
575Q8—3442no—
576Q8—3442no—
577D4—42no—
578D4—42no—
579D4—82no—
580D4—82no—
581D4—3442no—
582D4—3442no—
583D4—1722no—
584D4—1722no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—432no—
596C2×C4—432no—
597C2×C4—432no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1724no—
607C2×C4—1724no—
608C2×C4—1722no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C8—41no—
616C8—41no—
617C8—42no—
618C8—1721no—
619C8—1721no—
620C8—1722no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—82no—
635C22—82no—
636C22—3441no—
637C22—3441no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22C2×C22⋊C4×D4311yescharacteristic
642C22#131×D4311yescharacteristic
643C22#1458366411yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—42no—
648C4—862no—
649C4—862no—
650C4—862no—
651C4—862no—
652C4—862no—
653C4—1721no—
654C4—1721no—
655C4#1458287112yes—
656C2—21no—
657C2—21no—
658C2—41no—
659C2—41no—
660C2—82no—
661C2—3441no—
662C2#1914304311yescharacteristic
663C2C2×#1458287111yescharacteristic
664C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1471C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583613C2
cosocleC22×C4×C43C24
hypercenter#1471D43
hypocenterC43#17418
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #19143255C2semidirect
3. #19143249C2semidirect
4. #19132955C2semidirect
5. #19132945C2semidirect
6. #19132945C2semidirect
7. #19132931C2semidirect
8. #19132926C2semidirect
9. #19132911C2semidirect
10. #19132906C2semidirect
11. C43×#1471C2semidirect
328. #1471D43semidirect
385. C43#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#145836132
#191432552
#191432492
#191329552
#191329452
#191329312
#191329262
#191329112
#191329062
C43×#14712
#1741843