Finite Group Databasebeta

← #25064412

Subgroups — #25064412

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148434C211yesmaximal, characteristic
2#19137568C211yesmaximal, characteristic, complemented
3#19133152C212yesmaximal, complemented
4#19133134C212yesmaximal, complemented
5#19133129C211yesmaximal, characteristic, complemented
6#19133125C211yesmaximal, characteristic, complemented
7#19133121C212yesmaximal, complemented
8#19133116C211yesmaximal, characteristic, complemented
9#19133112C211yesmaximal, characteristic, complemented
10#19133087C212yesmaximal, complemented
11C43×#2973C211yesmaximal, characteristic, complemented
12#14583598—22no—
13#14583595C412yescomplemented
14#14583589C412yescomplemented
15#14583578—22no—
16#14583558C412yescomplemented
17#14583545C412yescomplemented
18#14583496—21no—
19#14583487—21no—
20#14583458—21no—
21#14583433C2212yes—
22#14583410C2212yes—
23C2×#13063304C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25#14583372—21no—
26#14582802—21no—
27#14582792—21no—
28#14582792—21no—
29#14582765C2211yescharacteristic, complemented
30#14582762C2211yescharacteristic
31#14582762C2211yescharacteristic, complemented
32C4⋊C4×Dic43—21no—
33C4×C4⋊Dic43C2211yescharacteristic, complemented
34C4×C22⋊Dic43C2211yescharacteristic
35C4×C22⋊Dic43C2211yescharacteristic, complemented
36#14582637C2212yescomplemented
37#14582637C2212yescomplemented
38#14582637C2212yescomplemented
39#14582637C2212yescomplemented
40#14582634C2212yes—
41#14582634C2212yes—
42#14582634C2212yes—
43#14582634C2212yes—
44C2×C4×D4×C43C2211yescharacteristic
45C43×#435—22no—
46C43×#435—22no—
47C43×#432C2212yescomplemented
48C43×#407C2211yescharacteristic
49C43×#407C2211yescharacteristic
50C2×C22⋊C8×C43C2212yescomplemented
51C2×#10621898C2×C412yes—
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×C22⋊D43—21no—
55#13063320—22no—
56#13063319—22no—
57#13063318—22no—
58#13063317C2×C412yes—
59#13063315—22no—
60#13063313C2×C412yes—
61#13063311—22no—
62#13063310—22no—
63#13063308—22no—
64#13063308—22no—
65#13063307—22no—
66#13063306—22no—
67#13063304—21no—
68#13063304—21no—
69#13063304C2×C412yes—
70#13063304C2×C412yes—
71#13063304C2312yes—
72#13063303—22no—
73#13063299—21no—
74#13063299—21no—
75#13063299C2×C412yes—
76#13063299C2×C412yes—
77#13063299C2312yes—
78#13063298—22no—
79#13063297—22no—
80#13063297—22no—
81#13063294—22no—
82#13063293—22no—
83C4×Dic86C2×C412yes—
84C4×D172C2×C412yes—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88(C22⋊D43)⋊C4—22no—
89(C22⋊D43)⋊C4—22no—
90#13063284C2×C412yes—
91#13063282—22no—
92#13063281—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—22no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95C2311yescharacteristic
112C43⋊#95C2311yescharacteristic
113C43⋊#95C2311yescharacteristic
114C43⋊#95C2311yescharacteristic
115C22×D4×C43D411yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C22×C8×C43—22no—
121C4×D4×C43C2×C412yes—
122C4×D4×C43C2×C412yes—
123C4×D4×C43D412yes—
124C4×D4×C43D412yes—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C22⋊C8×C43—21no—
132C22⋊C8×C43—21no—
133C22⋊C8×C43C2312yes—
134C22⋊C8×C43C2312yes—
135#97×C43—22no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43C22⋊C412yes—
142C2×D4×C43C22⋊C412yes—
143C22×C4×C43—81no—
144C22×C4×C43—81no—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169#10621898—82no—
170C2×D172—21no—
171C2×D172—81no—
172C2×D172C22×C412yes—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×Dic86—21no—
176C2×Dic86—81no—
177C2×Dic86C22×C412yes—
178M16×C43—81no—
179M16×C43—81no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C2×C8×C43—82no—
183C4⋊C4×C43C22⋊C412yes—
184C4⋊C4×C43C22⋊C412yes—
185C22⋊C4×C43C22⋊C412yes—
186C22⋊C4×C43C22⋊C412yes—
187C22⋊C4×C43C22⋊C412yes—
188C22⋊C4×C43C22⋊C412yes—
189C42×C43C22×C412yes—
190C42×C43C2×D412yes—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—42no—
196C22⋊Dic43—42no—
197C22⋊Dic43—81no—
198C22⋊Dic43—81no—
199(C2×D43)⋊C4—22no—
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—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43C22×C412yes—
210C4⋊Dic43C22×C412yes—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—42no—
220C4×Dic43—81no—
221C4×Dic43—81no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C2×C22⋊C412yes—
232C23×C43C2×C22⋊C411yescharacteristic
233C23×C43C22×D411yescharacteristic
234C22×D43—22no—
235C22×D43—42no—
236C22×D43—81no—
237C22×D43—81no—
238D4×C43—42no—
239D4×C43—42no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—41no—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C22⋊D43—44no—
260C22⋊D43—42no—
261C22⋊D43—42no—
262C22⋊D43—82no—
263C22⋊D43—82no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282D172—42no—
283D172—81no—
284C4×D43—82no—
285C4×D43—82no—
286Dic86—42no—
287Dic86—81no—
288C8×C43—42no—
289C8×C43—42no—
290#17625—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—22no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—22no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—22no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43C22×C22⋊C411yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57511yescharacteristic
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—162no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—22no—
317C4×C43—21no—
318C4×C43—22no—
319C4×C43—22no—
320Dic43—42no—
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327#3505—431no—
328#2973D4311yescharacteristic, complemented
329#2357—431no—
330#1516—432no—
331#1512—432no—
332#1511—431no—
333#1510—431no—
334#1509—432no—
335#1508—431no—
336#1507—431no—
337#1501—432no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—41no—
341C2×C43—41no—
342C2×C43—42no—
343C2×C43#288311yescharacteristic
344C2×C43#289611yescharacteristic
345C2×C43#290111yescharacteristic
346D43—82no—
347#553—432no—
348#553—862no—
349#552—432no—
350#551—862no—
351#548—432no—
352#546—432no—
353#539—861no—
354#538—861no—
355#534—861no—
356#529—432no—
357#525—432no—
358C2×C22⋊Q8—431no—
359C2×#121—431no—
360#518—861no—
361C2×C4×D4C2×D4311yescharacteristic
362#435—22no—
363#435—22no—
364#432C2×D4312yescomplemented
365#407C2×D4311yescharacteristic
366#407C2×D4311yescharacteristic
367C2×C22⋊C8C2×D4312yescomplemented
368#390—861no—
369#388—861no—
370#388—861no—
371#382—431no—
372#381—431no—
373#381—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—861no—
376C4×C22⋊C4—431no—
377C4×C22⋊C4—431no—
378#328—432no—
379#328—432no—
380#328—432no—
381#328—432no—
382#327—432no—
383#327—432no—
384#327—432no—
385#327—432no—
386C43#1762511yescharacteristic, complemented, Sylow
387C2×#41—432no—
388C22×Q8—431no—
389C22×D4—431no—
390C22×D4—861no—
391C22×D4D17211yescharacteristic
392C23×C4C22×D4311yescharacteristic
393C23×C4C22×D4311yescharacteristic
394C2×M16—21no—
395C2×M16—21no—
396C22×C8—22no—
397#126—862no—
398#126—862no—
399#126—862no—
400#125—432no—
401#125—862no—
402#124—432no—
403#124—862no—
404#123—862no—
405#123—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409C22⋊Q8—432no—
410C22⋊Q8—432no—
411C22⋊Q8—432no—
412C22⋊Q8—861no—
413C22⋊Q8—861no—
414C22⋊Q8—862no—
415#121—432no—
416#121—432no—
417#121—432no—
418#121—862no—
419#121—862no—
420#121—861no—
421#121—861no—
422#121—862no—
423#120—862no—
424#120—862no—
425C4×Q8—432no—
426C4×D4—432no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4C4×D4312yes—
433C4×D4C4×D4312yes—
434C4×D4C22⋊D4312yes—
435C4×D4C22⋊D4312yes—
436#117—432no—
437#117—862no—
438#117—862no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4D17211yescharacteristic
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—862no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4D17211yescharacteristic
453C2×C22⋊C4D17211yescharacteristic
454C2×C42—861no—
455C2×C42—861no—
456C2×C42—861no—
457C2×C42C22×D4311yescharacteristic
458C4⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C22⋊C8C22×D4312yes—
463C22⋊C8C22×D4312yes—
464#97—22no—
465#95—431no—
466#95—431no—
467#95—431no—
468#95—431no—
469#95—861no—
470#95—861no—
471#95—861no—
472C24—861no—
473C24C2×D17211yescharacteristic
474C24C2×D17211yescharacteristic
475#41—3442no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—3441no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—432no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—861no—
487C2×D4—3441no—
488C2×D4—1722no—
489C2×D4—1722no—
490C2×D4(C2×D43)⋊C412yes—
491C2×D4(C2×D43)⋊C412yes—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4C2×C4×D4311yescharacteristic
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4312yes—
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×D17211yescharacteristic
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4312yes—
513C22×C4C23×D4311yescharacteristic
514M16—81no—
515M16—81no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—82no—
519C4⋊C4—432no—
520C4⋊C4—432no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—1722no—
530C4⋊C4—1722no—
531C4⋊C4(C2×D43)⋊C412yes—
532C4⋊C4(C2×D43)⋊C412yes—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—3441no—
544C22⋊C4—3441no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4(C2×D43)⋊C412yes—
548C22⋊C4(C2×D43)⋊C412yes—
549C22⋊C4(C2×D43)⋊C412yes—
550C22⋊C4(C2×D43)⋊C412yes—
551C42—862no—
552C42—862no—
553C42—3441no—
554C42—3441no—
555C42—1722no—
556C42C2×C4×D4312yes—
557C42C2×C22⋊D4312yes—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—862no—
567C23—3441no—
568C23—3441no—
569C23—1722no—
570C23C2×(C2×D43)⋊C411yescharacteristic
571C23C2×(C2×D43)⋊C412yes—
572C23C2×(C2×D43)⋊C411yescharacteristic
573C23C22×D17211yescharacteristic
574Q8—3441no—
575Q8—1722no—
576D4—42no—
577D4—42no—
578D4—3441no—
579D4—3442no—
580D4—3442no—
581D4—1722no—
582D4—1724no—
583D4—1722no—
584D4—1722no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—3442no—
602C2×C4—3442no—
603C2×C4—3441no—
604C2×C4—3441no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1722no—
616C2×C4—1721no—
617C2×C4C2×(C2×D43)⋊C412yes—
618C2×C4C2×(C2×D43)⋊C412yes—
619C2×C4C2×(C2×D43)⋊C412yes—
620C2×C4C2×(C2×D43)⋊C411yescharacteristic
621C2×C4C2×(C2×D43)⋊C411yescharacteristic
622C2×C4C22×C4×D4311yescharacteristic
623C2×C4C22×C22⋊D4311yescharacteristic
624C8—42no—
625C8—42no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—22no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—22no—
634C22—21no—
635C22—22no—
636C22—21no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—6882no—
645C22C22×(C2×D43)⋊C411yescharacteristic
646C22#1458369911yescharacteristic
647C22#1458369911yescharacteristic
648C4—21no—
649C4—21no—
650C4—22no—
651C4—21no—
652C4—21no—
653C4—22no—
654C4—22no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—1722no—
659C4—1722no—
660C4—1722no—
661C4—1722no—
662C2—21no—
663C2—21no—
664C2—41no—
665C2—41no—
666C2—42no—
667C2—3442no—
668C2#1914305511yescharacteristic
669C2#1914311511yescharacteristic
670C2#1914314011yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2973C2
socleC22×C43C22×C22⋊C4
prime radical#19148434C2
cosocleC22×C4×C43C24
hypercenter#2973D43
hypocenterC43#17625
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19137568C2semidirect
3. #19133152C2semidirect
4. #19133134C2semidirect
5. #19133129C2semidirect
6. #19133125C2semidirect
7. #19133121C2semidirect
8. #19133116C2semidirect
9. #19133112C2semidirect
10. #19133087C2semidirect
11. C43×#2973C2semidirect
13. #14583595C4semidirect
14. #14583589C4semidirect
16. #14583558C4semidirect
17. #14583545C4semidirect
29. #14582765C22semidirect
31. #14582762C22semidirect
33. C4×C4⋊Dic43C22semidirect
35. C4×C22⋊Dic43C22semidirect
36. #14582637C22semidirect
37. #14582637C22semidirect
38. #14582637C22semidirect
39. #14582637C22semidirect
47. C43×#432C22semidirect
50. C2×C22⋊C8×C43C22semidirect
328. #2973D43semidirect
364. #432C2×D43semidirect
367. C2×C22⋊C8C2×D43semidirect
386. C43#17625semidirect

Maximal subgroups

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

subgroupindex
#191484342
#191375682
#191331522
#191331342
#191331292
#191331252
#191331212
#191331162
#191331122
#191330872
C43×#29732
#1762543