Finite Group Databasebeta

← #25064320

Subgroups — #25064320

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148429C211yesmaximal, characteristic
2#19143617C211yesmaximal, characteristic, complemented
3#19137537C211yesmaximal, characteristic, complemented
4#19133169C212yesmaximal, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19133148C212yesmaximal, complemented
7#19133083C212yesmaximal, complemented
8#19133078C212yesmaximal, complemented
9C2×#14582637C211yesmaximal, characteristic, complemented
10C2×#14582633C211yesmaximal, characteristic, complemented
11C43×#1519C211yesmaximal, characteristic, complemented
12#14583601C412yescomplemented
13#14583592—22no—
14#14583584C412yescomplemented
15#14583575—22no—
16#14583555C412yescomplemented
17#14583543C412yescomplemented
18#14583494—21no—
19#14583486—21no—
20#14583458—21no—
21#14583430C2212yes—
22#14583409C2212yes—
23C2×#13063304C2211yescharacteristic
24#14583374—21no—
25C2×C4×C22⋊D43C2211yescharacteristic
26C8×C22⋊D43—22no—
27(C22⋊D43)⋊C8—22no—
28#14582949C2212yescomplemented
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C22⋊C8×D43C2212yescomplemented
31#14582789—21no—
32#14582780—21no—
33#14582776—21no—
34#14582766C2211yescharacteristic, complemented
35#14582761C2211yescharacteristic, complemented
36C22⋊C4×Dic43—21no—
37#14582746C2211yescharacteristic, complemented
38#14582744C2211yescharacteristic, complemented
39C2×C43⋊#95C2211yescharacteristic
40#14582637C2212yescomplemented
41#14582637C2212yescomplemented
42#14582635C2212yescomplemented
43#14582635C2212yescomplemented
44#14582633C2212yes—
45#14582633C2212yes—
46C2×#121×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#380C2211yescharacteristic
49C43×#327C2212yes—
50C43×#327C2212yes—
51C2×#10621900C2×C412yescomplemented
52C22×Dic86C2×C411yescharacteristic
53C22×C22⋊D43D411yescharacteristic
54C23×Dic43—21no—
55C22×C4×D43C2311yescharacteristic
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58#13063320—22no—
59#13063318—22no—
60#13063318—22no—
61#13063316C2×C412yescomplemented
62#13063315—22no—
63#13063312C2×C412yescomplemented
64#13063311—22no—
65#13063309—22no—
66#13063308—22no—
67#13063307—22no—
68#13063306—22no—
69#13063306—22no—
70#13063305C2×C412yescomplemented
71#13063304—21no—
72#13063304—21no—
73#13063304C2×C412yes—
74#13063304C2312yes—
75#13063302—22no—
76#13063297—22no—
77#13063297—22no—
78#13063297—22no—
79#13063296C2×C412yescomplemented
80#13063294—22no—
81#13063293—22no—
82#13063290C2×C412yescomplemented
83D4×Dic43—22no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43C2×C412yescomplemented
88C4×C22⋊D43C2×C412yes—
89C4×C22⋊D43C2×C412yes—
90C4×C22⋊D43D412yes—
91C4×C22⋊D43D412yes—
92(C22⋊D43)⋊C4—22no—
93#13063284—22no—
94#13063283C2×C412yescomplemented
95#13063281—22no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)C2312yes—
111(C2×D43)⋊C8—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95C2311yescharacteristic
119C43⋊#95C2311yescharacteristic
120C22×D4×C43—21no—
121C22×D4×C43C2×C411yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43C2×C412yes—
127#121×C43C2312yes—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C22⋊C8×C43—21no—
133C22⋊C8×C43C2312yes—
134#95×C43C2311yescharacteristic
135#95×C43C2311yescharacteristic
136C24×C43—21no—
137C24×C43C2×D411yescharacteristic
138C23×D43C2×D411yescharacteristic
139C2×D4×C43—21no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43—81no—
145C2×D4×C43C22×C412yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—81no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
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⋊D43C22⋊C412yes—
161C2×C22⋊D43C22⋊C412yes—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—81no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174#10621900—82no—
175C2×C4×D43—81no—
176C2×C4×D43C22×C412yes—
177C2×C4×D43C2×D412yes—
178C2×Dic86—21no—
179C2×Dic86—81no—
180C2×Dic86C22×C412yes—
181C2×C8×C43—22no—
182C2×C8×C43—81no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—42no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43C22⋊C412yes—
196C22⋊Dic43C22⋊C412yes—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4C22⋊C412yes—
202(C2×D43)⋊C4C22⋊C412yes—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—22no—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—42no—
216C4×Dic43—81no—
217C4×Dic43C22×C412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—81no—
221C8×D43—82no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—42no—
226C23×C43—81no—
227C23×C43—81no—
228C23×C43C2×C22⋊C411yescharacteristic
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43#13512yes—
231C23×C43#13512yes—
232C23×C43C22×D411yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43C2×C22⋊C412yes—
238D4×C43—42no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—44no—
242D4×C43—81no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
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×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C22⋊D43—24no—
262C22⋊D43—24no—
263C22⋊D43—82no—
264C22⋊D43—82no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—82no—
278C2×Dic43—82no—
279C2×Dic43—81no—
280C2×Dic43—81no—
281C2×Dic43—84no—
282C2×Dic43C2×C22⋊C412yes—
283C2×Dic43C2×C22⋊C412yes—
284C2×Dic43C2×C22⋊C412yes—
285C4×D43—42no—
286C4×D43—42no—
287Dic86—42no—
288Dic86—81no—
289C8×C43—42no—
290C43⋊C8—42no—
291#17615—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—42no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—162no—
304C22×C43#41612yes—
305C22×C43#41612yes—
306C22×C43C22×C22⋊C411yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—42no—
319C4×C43—81no—
320C4×C43—81no—
321Dic43—22no—
322Dic43—22no—
323Dic43—22no—
324Dic43—42no—
325Dic43—42no—
326Dic43—42no—
327Dic43—81no—
328#3505—431no—
329#2972—431no—
330#2353—431no—
331#1521—432no—
332#1520—431no—
333#1519D4311yescharacteristic, complemented
334#1516—432no—
335#1501—432no—
336#1500—432no—
337C2×#328—431no—
338C2×#327—431no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—22no—
342C2×C43—22no—
343C2×C43—82no—
344C2×C43#288311yescharacteristic
345C2×C43C2×#41611yescharacteristic
346C2×C43#290111yescharacteristic
347D43—42no—
348#553—432no—
349#553—862no—
350#552—432no—
351#551—862no—
352#548—432no—
353#546—432no—
354#539—861no—
355#538—861no—
356#534—861no—
357#529—432no—
358#525—432no—
359C2×C22⋊Q8—431no—
360C2×#121C2×D4311yescharacteristic
361#518—861no—
362C2×C4×D4—431no—
363C8×D4—862no—
364C8×D4—862no—
365#431—432no—
366C2×C22⋊C8—431no—
367C2×C22⋊C8—432no—
368C2×C22⋊C8C2×D4311yescharacteristic
369#388—861no—
370#387—861no—
371#386—861no—
372#383—431no—
373#381—431no—
374#380C2×D4311yescharacteristic
375C4×C22⋊C4—431no—
376C4×C22⋊C4—861no—
377#376—431no—
378C2×#95—431no—
379#328—432no—
380#328—432no—
381#328—432no—
382#328—432no—
383#327—432no—
384#327—432no—
385#327C2×D4312yes—
386#327C2×D4312yes—
387C43#1761511yescharacteristic, complemented, Sylow
388C2×#41—432no—
389C22×Q8—431no—
390C22×D4—21no—
391C22×D4—431no—
392C22×D4C4×D4311yescharacteristic
393C23×C4—431no—
394C23×C4—861no—
395C23×C4C22×D4311yescharacteristic
396C22×C8—21no—
397C22×C8—862no—
398C22×C8—861no—
399#126—862no—
400#126—862no—
401#126—862no—
402#125—432no—
403#125—862no—
404#124—432no—
405#124—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409#123—862no—
410#123—862no—
411C22⋊Q8—432no—
412C22⋊Q8—432no—
413C22⋊Q8—432no—
414C22⋊Q8—862no—
415C22⋊Q8—861no—
416C22⋊Q8—861no—
417#121—21no—
418#121—21no—
419#121—432no—
420#121—862no—
421#121—862no—
422#121—862no—
423#121C4×D4312yes—
424#121C22×D4312yes—
425#120—862no—
426#120—862no—
427C4×Q8—432no—
428C4×D4—432no—
429C4×D4—432no—
430C4×D4—432no—
431C4×D4—432no—
432C4×D4—432no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—862no—
438#117—432no—
439#117—862no—
440#117—862no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4C4×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—862no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C42—431no—
455C2×C42—861no—
456C2×C42—861no—
457C4⋊C8—862no—
458C22⋊C8—21no—
459C22⋊C8—432no—
460C22⋊C8—862no—
461C22⋊C8—861no—
462C22⋊C8C22×D4312yes—
463C4×C8—862no—
464#95—431no—
465#95—431no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95C22×D4311yescharacteristic
472#95C22×D4311yescharacteristic
473C24—21no—
474C24—431no—
475C24D4×D4311yescharacteristic
476#41—3442no—
477C2×Q8—432no—
478C2×Q8—861no—
479C2×Q8—3441no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—81no—
486C2×D4—432no—
487C2×D4—432no—
488C2×D4—862no—
489C2×D4—862no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4C2×C4×D4312yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—81no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—3441no—
509C22×C4—3441no—
510C22×C4—1722no—
511C22×C4—1722no—
512C22×C4C2×C4×D4311yescharacteristic
513C22×C4C2×C4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4D4×D4311yescharacteristic
517C22×C4C23×D4311yescharacteristic
518C2×C8—22no—
519C2×C8—81no—
520C2×C8—862no—
521C2×C8—3442no—
522C2×C8—3441no—
523C4⋊C4—21no—
524C4⋊C4—81no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—861no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—42no—
539C22⋊C4—432no—
540C22⋊C4—432no—
541C22⋊C4—432no—
542C22⋊C4—432no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—3441no—
552C22⋊C4—1722no—
553C42—432no—
554C42—432no—
555C42—862no—
556C42—862no—
557C42—3441no—
558C42—1722no—
559C23—22no—
560C23—41no—
561C23—41no—
562C23—42no—
563C23—81no—
564C23—81no—
565C23—432no—
566C23—861no—
567C23—861no—
568C23—1721no—
569C23—1721no—
570C23C22⋊C4×D4311yescharacteristic
571C23C22⋊C4×D4311yescharacteristic
572C23#1306334412yes—
573C23#1306334612yes—
574C23C2×D4×D4311yescharacteristic
575Q8—3441no—
576Q8—1722no—
577D4—42no—
578D4—44no—
579D4—42no—
580D4—42no—
581D4—81no—
582D4—864no—
583D4—864no—
584D4—3442no—
585D4—3442no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—3442no—
609C2×C4—3442no—
610C2×C4—3444no—
611C2×C4—3441no—
612C2×C4—3441no—
613C2×C4—1722no—
614C2×C4—1722no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4C22⋊C4×D4311yescharacteristic
623C2×C4C22⋊C4×D4311yescharacteristic
624C2×C4C22×C4×D4311yescharacteristic
625C2×C4C2×D4×D4311yescharacteristic
626C8—42no—
627C8—1722no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—162no—
640C22—862no—
641C22—862no—
642C22—862no—
643C22—3441no—
644C22—3441no—
645C22#1458289212yes—
646C22#1458289212yes—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22C2×#1306334411yescharacteristic
649C22C2×#1306334611yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—862no—
658C4—862no—
659C4—862no—
660C4—3441no—
661C4—1722no—
662C4—1722no—
663C4—1722no—
664C2—21no—
665C2—21no—
666C2—22no—
667C2—22no—
668C2—82no—
669C2—1722no—
670C2#1914305311yescharacteristic
671C2C2×#1458289211yescharacteristic
672C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1519C2
socleC22×C43C22×C22⋊C4
prime radical#19148429C2
cosocleC22×C4×C43C24
hypercenter#1519D43
hypocenterC43#17615
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #19143617C2semidirect
3. #19137537C2semidirect
4. #19133169C2semidirect
5. #19133166C2semidirect
6. #19133148C2semidirect
7. #19133083C2semidirect
8. #19133078C2semidirect
9. C2×#14582637C2semidirect
10. C2×#14582633C2semidirect
11. C43×#1519C2semidirect
12. #14583601C4semidirect
14. #14583584C4semidirect
16. #14583555C4semidirect
17. #14583543C4semidirect
28. #14582949C22semidirect
30. C22⋊C8×D43C22semidirect
34. #14582766C22semidirect
35. #14582761C22semidirect
37. #14582746C22semidirect
38. #14582744C22semidirect
40. #14582637C22semidirect
41. #14582637C22semidirect
42. #14582635C22semidirect
43. #14582635C22semidirect
51. C2×#10621900C2×C4semidirect
61. #13063316C2×C4semidirect
63. #13063312C2×C4semidirect
70. #13063305C2×C4semidirect
79. #13063296C2×C4semidirect
82. #13063290C2×C4semidirect
87. D4×Dic43C2×C4semidirect
94. #13063283C2×C4semidirect
333. #1519D43semidirect
387. C43#17615semidirect

Maximal subgroups

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

subgroupindex
#191484292
#191436172
#191375372
#191331692
#191331662
#191331482
#191330832
#191330782
C2×#145826372
C2×#145826332
C43×#15192
#1761543