Finite Group Databasebeta

← #25062838

Subgroups — #25062838

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×#14583612C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19132956C211yesmaximal, characteristic, complemented
4#19132954C211yesmaximal, characteristic, complemented
5#19132948C212yesmaximal, complemented
6#19132946C212yesmaximal, complemented
7#19132931C211yesmaximal, characteristic, complemented
8#19132927C212yesmaximal, complemented
9#19132911C211yesmaximal, characteristic, complemented
10#19132907C212yesmaximal, complemented
11C43×#2924C211yesmaximal, characteristic, complemented
12#14583612—21no—
13#14583612—21no—
14#14583612—22no—
15#14583612—21no—
16#14583612—21no—
17#14583612—22no—
18C2×#13063324C411yescharacteristic
19C2×#13063313C2212yes—
20C2×#13063311C412yes—
21C2×#13063300C411yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063298C412yes—
24C2×#13063287C411yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063283C411yescharacteristic
27C2×#13063282C2212yes—
28#14582960—22no—
29#14582956C2212yes—
30#14582952C2212yes—
31#14582926—21no—
32#14582863C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582855—21no—
35#14582624C2212yes—
36#14582624C2211yescharacteristic
37#14582624C2211yescharacteristic
38#14582622C2212yes—
39#14582622C2211yescharacteristic
40#14582622C2212yes—
41#14582622C2212yes—
42#14582622C2211yescharacteristic
43#14582622C2212yes—
44#14582622C2212yes—
45C2×#117×C43C2211yescharacteristic
46C43×#433—22no—
47C43×#432C2212yes—
48C43×#431C2212yes—
49C43×#424—21no—
50C43×#407C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C43×#405—21no—
53C22×Dic86C2×C412yes—
54C22×D172C2×C411yescharacteristic
55C22×D172C2×C412yes—
56C22×C22⋊D43C2×C411yescharacteristic
57C22×C22⋊D43C2×C412yes—
58C22×C4×D43C2×C412yes—
59C22×C4×D43C2×C411yescharacteristic
60C2×#10621877—21no—
61C22×C43⋊C8—21no—
62#13063324—22no—
63#13063324—21no—
64#13063324—21no—
65#13063313—22no—
66#13063313—22no—
67#13063313—22no—
68#13063313—22no—
69#13063311—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063300—22no—
74#13063300—21no—
75#13063300—21no—
76#13063299—21no—
77#13063299—21no—
78#13063299—21no—
79#13063299—21no—
80#13063298—22no—
81#13063298—22no—
82#13063298—22no—
83#13063298—22no—
84#13063287—22no—
85#13063287—21no—
86#13063287—21no—
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91#13063283—22no—
92#13063283—21no—
93#13063283—21no—
94#13063282—22no—
95#13063282—22no—
96#13063282—22no—
97#13063282—22no—
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C412yes—
100C2×Dic43⋊C4C2311yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C412yes—
103C2×(C2×D43)⋊C4C2×C412yes—
104C2×(C2×D43)⋊C4C2×C412yes—
105C2×(C2×D43)⋊C4C2312yes—
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×C4×Dic43C2×C412yes—
108C2×C4×Dic43C2×C411yescharacteristic
109C4⋊(C43⋊C8)—22no—
110C4⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)C2311yescharacteristic
114C22⋊(C43⋊C8)C2311yescharacteristic
115C22⋊(C43⋊C8)C2312yes—
116#13063236—22no—
117C4×C43⋊C8—22no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—21no—
120C22×C8×C43—21no—
121#117×C43D411yescharacteristic
122#117×C43D411yescharacteristic
123#117×C43D412yes—
124#117×C43D411yescharacteristic
125#117×C43D411yescharacteristic
126#117×C43D412yes—
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43C2×C412yes—
130C2×C42×C43C2312yes—
131C4⋊C8×C43—22no—
132C4⋊C8×C43—22no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43C2312yes—
138#97×C43—22no—
139C4×C8×C43—22no—
140C24×C43C22×C411yescharacteristic
141C23×D43C22×C412yes—
142C23×D43C22×C411yescharacteristic
143C22×C4×C43—42no—
144C22×C4×C43C22×C412yes—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—82no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C412yes—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—22no—
166C2×D172—22no—
167C2×D172—42no—
168C2×D172—82no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—24no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—82no—
179M16×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—22no—
182C2×C8×C43—21no—
183C2×C8×C43—42no—
184C4⋊C4×C43C22⋊C412yes—
185C4⋊C4×C43C22⋊C411yescharacteristic
186C4⋊C4×C43C22⋊C411yescharacteristic
187C4⋊C4×C43C22⋊C412yes—
188C4⋊C4×C43C22⋊C411yescharacteristic
189C4⋊C4×C43C22⋊C411yescharacteristic
190C22⋊C4×C43C22⋊C412yes—
191C22⋊C4×C43C22⋊C412yes—
192C22⋊C4×C43C22⋊C412yes—
193C22⋊C4×C43C22⋊C412yes—
194C42×C43C2×D412yes—
195C42×C43C2×D412yes—
196C42×C43C2×D412yes—
197C42×C43C2×D412yes—
198C22⋊Dic43—21no—
199C22⋊Dic43—21no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—21no—
219C4×Dic43—21no—
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—41no—
228C23×C43—41no—
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C23×C411yescharacteristic
232C22×D43—22no—
233C22×D43—21no—
234C22×D43—22no—
235C22×D43—21no—
236C22×D43—22no—
237C22×D43—21no—
238C22×D43—41no—
239C22×D43—42no—
240C22×D43—41no—
241C22×D43—42no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C2×C22⋊C412yes—
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C22⋊D43—42no—
260C22⋊D43—42no—
261C22⋊D43—82no—
262C22⋊D43—82no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—41no—
271C2×Dic43#13112yes—
272D172—42no—
273D172—42no—
274D172—82no—
275D172—82no—
276C4×D43—44no—
277C4×D43—44no—
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—81no—
298C22×C43—81no—
299C22×C43C22×C22⋊C411yescharacteristic
300C22×C43C2×#13111yescharacteristic
301C22×C43#56811yescharacteristic
302C2×D43—42no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—42no—
306C2×D43—41no—
307C2×D43—42no—
308C2×D43—82no—
309C2×D43—81no—
310C2×D43—82no—
311C2×D43—81no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43#41012yes—
320Dic43—22no—
321Dic43—41no—
322Dic43—41no—
323Dic43—42no—
324C2×#555—431no—
325#2924—431no—
326#2924D4311yescharacteristic, complemented
327#1471—431no—
328#1471—431no—
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#288011yescharacteristic
340C2×C43C2×#41011yescharacteristic
341C2×C43#288811yescharacteristic
342D43—82no—
343D43—81no—
344#555—861no—
345#555—861no—
346#555—862no—
347#555—861no—
348#555—861no—
349#555—862no—
350C2×C4⋊Q8—431no—
351C2×#124—432no—
352C2×#124—432no—
353C2×#121—431no—
354C2×#121—431no—
355C2×#121—432no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×#117—431no—
359C2×#117—432no—
360C2×#117C2×D4311yescharacteristic
361#433—22no—
362#433—862no—
363#432—432no—
364#432C2×D4312yes—
365#431—432no—
366#431C2×D4312yes—
367#424—21no—
368#424—861no—
369#407—431no—
370#407C2×D4311yescharacteristic
371C2×C22⋊C8—431no—
372C2×C22⋊C8C2×D4311yescharacteristic
373#405—21no—
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#323—432no—
384#323—432no—
385C43#1741811yescharacteristic, complemented, Sylow
386C22×Q8—432no—
387C22×D4—431no—
388C22×D4—432no—
389C22×D4—432no—
390C22×D4—431no—
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—861no—
410#121—861no—
411#121—861no—
412#121—861no—
413#121—862no—
414#121—861no—
415#121—861no—
416#121—862no—
417#121—862no—
418#121—862no—
419#121—862no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4—862no—
425C4×D4—861no—
426C4×D4—861no—
427#117—862no—
428#117—861no—
429#117—861no—
430#117—862no—
431#117—862no—
432#117—862no—
433#117—862no—
434#117D17211yescharacteristic
435#117D17211yescharacteristic
436#117D17212yes—
437#117C22⋊D4311yescharacteristic
438#117C22⋊D4311yescharacteristic
439#117C22⋊D4312yes—
440C2×C4⋊C4—432no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4C4×D4311yescharacteristic
444C2×C4⋊C4C4×D4311yescharacteristic
445C2×C22⋊C4—431no—
446C2×C22⋊C4—432no—
447C2×C22⋊C4—432no—
448C2×C22⋊C4—432no—
449C2×C22⋊C4—432no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4C4×D4312yes—
452C2×C42—432no—
453C2×C42—431no—
454C2×C42C22×D4312yes—
455C4⋊C8—22no—
456C4⋊C8—22no—
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—22no—
470#97—862no—
471C4×C8—22no—
472C4×C8—862no—
473C24—432no—
474C24—431no—
475C24C2×C4×D4311yescharacteristic
476C2×Q8—862no—
477C2×Q8—862no—
478C2×Q8—3442no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—3442no—
489C2×D4—3442no—
490C2×D4—1722no—
491C2×D4—1721no—
492C22×C4—42no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—432no—
497C22×C4—864no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4C2×C4×D4312yes—
505C22×C4C2×C4×D4311yescharacteristic
506C22×C4C2×C4×D4312yes—
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×C22⋊D4311yescharacteristic
510C22×C4C2×C22⋊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—862no—
523C4⋊C4—862no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4(C2×D43)⋊C412yes—
529C4⋊C4(C2×D43)⋊C411yescharacteristic
530C4⋊C4(C2×D43)⋊C411yescharacteristic
531C4⋊C4(C2×D43)⋊C412yes—
532C4⋊C4(C2×D43)⋊C411yescharacteristic
533C4⋊C4(C2×D43)⋊C411yescharacteristic
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—861no—
544C22⋊C4—862no—
545C22⋊C4—861no—
546C22⋊C4(C2×D43)⋊C412yes—
547C22⋊C4(C2×D43)⋊C412yes—
548C22⋊C4(C2×D43)⋊C412yes—
549C22⋊C4(C2×D43)⋊C412yes—
550C42—862no—
551C42—862no—
552C42—861no—
553C42—861no—
554C42C2×D17212yes—
555C42C2×D17212yes—
556C42C2×C22⋊D4312yes—
557C42C2×C22⋊D4312yes—
558C23—21no—
559C23—21no—
560C23—41no—
561C23—41no—
562C23—862no—
563C23—861no—
564C23—862no—
565C23—861no—
566C23—862no—
567C23—861no—
568C23—1721no—
569C23—1721no—
570C23—1722no—
571C23—1722no—
572C23C2×(C2×D43)⋊C411yescharacteristic
573C23C2×(C2×D43)⋊C411yescharacteristic
574C23C22×C4×D4311yescharacteristic
575Q8—3442no—
576Q8—3442no—
577D4—3442no—
578D4—3442no—
579D4—3442no—
580D4—3442no—
581D4—1722no—
582D4—1722no—
583D4—1722no—
584D4—1722no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—432no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—1724no—
601C2×C4—1724no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1721no—
605C2×C4—1722no—
606C2×C4—1721no—
607C2×C4C2×(C2×D43)⋊C412yes—
608C2×C4C2×(C2×D43)⋊C412yes—
609C2×C4C2×(C2×D43)⋊C411yescharacteristic
610C2×C4C2×(C2×D43)⋊C412yes—
611C2×C4C2×(C2×D43)⋊C412yes—
612C2×C4C2×(C2×D43)⋊C411yescharacteristic
613C2×C4C22×C22⋊D4311yescharacteristic
614C2×C4C22×D17211yescharacteristic
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—81no—
630C22—81no—
631C22—3442no—
632C22—3441no—
633C22—3442no—
634C22—3441no—
635C22—1722no—
636C22—1721no—
637C22—1721no—
638C22—1722no—
639C22—1721no—
640C22—1722no—
641C22C22×(C2×D43)⋊C411yescharacteristic
642C22#131×D4311yescharacteristic
643C22#1458366411yescharacteristic
644C4—22no—
645C4—22no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—22no—
650C4—22no—
651C4—862no—
652C4—1721no—
653C4—1722no—
654C4—1721no—
655C4#1458287212yes—
656C2—21no—
657C2—21no—
658C2—41no—
659C2—41no—
660C2—3442no—
661C2—3441no—
662C2#1914304211yescharacteristic
663C2C2×#1458287211yescharacteristic
664C2#1914307311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583612C2
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#17418
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19132956C2semidirect
4. #19132954C2semidirect
5. #19132948C2semidirect
6. #19132946C2semidirect
7. #19132931C2semidirect
8. #19132927C2semidirect
9. #19132911C2semidirect
10. #19132907C2semidirect
11. C43×#2924C2semidirect
326. #2924D43semidirect
385. C43#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#145836122
#191432532
#191329562
#191329542
#191329482
#191329462
#191329312
#191329272
#191329112
#191329072
C43×#29242
#1741843