Finite Group Databasebeta

← #25064391

Subgroups — #25064391

Order 11008.

1014 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#19148436C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19137532C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal, complemented
5#19133137C212yesmaximal, complemented
6#19133123C211yesmaximal, characteristic, complemented
7#19133115C211yesmaximal, characteristic, complemented
8#19133112C211yesmaximal, characteristic, complemented
9#19133098C212yesmaximal, complemented
10#19133080C212yesmaximal, complemented
11C43×#1511C211yesmaximal, characteristic, complemented
12#14583597—22no—
13#14583597C412yescomplemented
14#14583591C412yescomplemented
15#14583576—22no—
16#14583560C412yescomplemented
17#14583540C412yescomplemented
18#14583498—21no—
19#14583489—21no—
20#14583461—21no—
21#14583435C2212yes—
22#14583412C2212yes—
23C2×#13063299C2211yescharacteristic
24#14583372—21no—
25C2×C4×C22⋊D43C2211yescharacteristic
26#14582975—22no—
27#14582974—22no—
28#14582949C2212yescomplemented
29#14582863C2211yescharacteristic
30#14582861C2212yescomplemented
31#14582793—21no—
32#14582781—21no—
33#14582775—21no—
34#14582766C2211yescharacteristic, complemented
35#14582758C2211yescharacteristic, complemented
36C4×C22⋊Dic43C2211yescharacteristic
37#14582746—21no—
38#14582744C2211yescharacteristic, complemented
39#95×D43C2211yescharacteristic, complemented
40#14582636C2212yescomplemented
41#14582636C2212yescomplemented
42#14582634C2212yes—
43#14582634C2212yes—
44#14582632C2212yes—
45#14582632C2212yes—
46C2×C22⋊Q8×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C43×#381C2211yescharacteristic
49C43×#328C2212yescomplemented
50C43×#328C2212yescomplemented
51C2×#10621902C2×C412yes—
52C22×D172C2×C411yescharacteristic, complemented
53C22×C22⋊D43—21no—
54C22×C22⋊D43D411yescharacteristic
55C22×C4×D43—21no—
56C22×C4×D43C2311yescharacteristic
57C2×#10621877—21no—
58C2×#10621872—22no—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063316—22no—
63#13063316C2×C412yescomplemented
64#13063314—22no—
65#13063314C2×C412yescomplemented
66#13063310—22no—
67#13063310—22no—
68#13063310—22no—
69#13063309—22no—
70#13063309—22no—
71#13063301—22no—
72#13063301C2×C412yes—
73#13063300—22no—
74#13063300C2×C412yes—
75#13063299—21no—
76#13063299—21no—
77#13063299—22no—
78#13063299—22no—
79#13063299C2×C412yescomplemented
80#13063299C2312yes—
81#13063295—22no—
82#13063295—22no—
83Q8×Dic43C2×C412yescomplemented
84#13063287—22no—
85#13063287C2×C412yescomplemented
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43C2×C412yes—
89C4×C22⋊D43C2×C412yes—
90C4×C22⋊D43D412yes—
91C4×C22⋊D43D412yes—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94#13063283—22no—
95#13063283C2×C412yes—
96#13063281—22no—
97C2×C4⋊Dic43C2×C411yescharacteristic, complemented
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C22⋊C4×D43—22no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—22no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2312yes—
112(C2×D43)⋊C8—22no—
113C8×Dic43—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95C2311yescharacteristic
119C43⋊#95C2311yescharacteristic
120C22×Q8×C43C2×C411yescharacteristic, complemented
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43C2×C412yescomplemented
126C22⋊Q8×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C22⋊C8×C43—21no—
132C22⋊C8×C43C2312yes—
133#95×C43—21no—
134#95×C43C2311yescharacteristic
135#95×C43C2311yescharacteristic
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C23×D43C2×D411yescharacteristic
139C2×Q8×C43—21no—
140C2×Q8×C43—81no—
141C2×Q8×C43C22×C412yes—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—81no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43C22⋊C412yes—
160C2×C22⋊D43C22⋊C412yes—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167#10621902—82no—
168C2×D172—21no—
169C2×D172—22no—
170C2×D172—22no—
171C2×D172—81no—
172C2×D172C22×C412yes—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—81no—
178C2×C4×D43—81no—
179C2×C4×D43C22×C412yes—
180C2×C4×D43C2×D412yes—
181M16×C43—81no—
182C2×C8×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—81no—
190C22⋊Dic43—42no—
191C22⋊Dic43C22⋊C412yes—
192C22⋊Dic43C22⋊C412yes—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—42no—
202(C2×D43)⋊C4C22⋊C412yes—
203(C2×D43)⋊C4C22⋊C412yes—
204C4⋊Dic43—21no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—81no—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—42no—
216C4×Dic43—81no—
217C4×Dic43C22×C412yes—
218C4×Dic43C2×D412yes—
219#10621877—81no—
220C2×C43⋊C8—22no—
221#10621872—82no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43C2×C22⋊C411yescharacteristic
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43C22×D411yescharacteristic
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—42no—
235C22×D43—81no—
236C22×D43—81no—
237C22×D43C2×C22⋊C412yes—
238Q8×C43—42no—
239Q8×C43—81no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
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—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—81no—
255C2×C4×C43—81no—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C22⋊D43—42no—
261C22⋊D43—42no—
262C22⋊D43—44no—
263C22⋊D43—42no—
264C22⋊D43—42no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43C2×C22⋊C412yes—
278C2×Dic43C2×C22⋊C412yes—
279C2×Dic43C2×C22⋊C412yes—
280D172—42no—
281D172—81no—
282D172—82no—
283D172—82no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—82no—
287C4×D43—82no—
288C4×D43—84no—
289C8×C43—42no—
290C43⋊C8—42no—
291#17623—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43C22×C22⋊C411yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57511yescharacteristic
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—162no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—42no—
319C4×C43—42no—
320C4×C43—81no—
321C4×C43—81no—
322Dic43—22no—
323Dic43—22no—
324Dic43—22no—
325Dic43—42no—
326Dic43—42no—
327Dic43—81no—
328#3505—431no—
329#2975—431no—
330#2353—431no—
331#1521—432no—
332#1513—432no—
333#1511D4311yescharacteristic, complemented
334#1510—431no—
335#1508—431no—
336#1507—431no—
337#1504—432no—
338#1500—432no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—41no—
342C2×C43—41no—
343C2×C43#288311yescharacteristic
344C2×C43#289611yescharacteristic
345C2×C43#290111yescharacteristic
346D43—42no—
347D43—82no—
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⋊Q8C2×D4311yescharacteristic
360C2×#121—431no—
361#518—861no—
362C2×C4×D4—431no—
363#436—862no—
364#436—862no—
365#431—432no—
366#407—431no—
367#407—432no—
368#407C2×D4311yescharacteristic
369#388—861no—
370#387—861no—
371#386—861no—
372#383—431no—
373#381C2×D4311yescharacteristic
374#380—431no—
375C4×C22⋊C4—431no—
376C4×C22⋊C4—861no—
377#376—431no—
378C2×#95—431no—
379#328—432no—
380#328—432no—
381#328C2×D4312yescomplemented
382#328C2×D4312yescomplemented
383#327—432no—
384#327—432no—
385#327—432no—
386#327—432no—
387C43#1762311yescharacteristic, complemented, Sylow
388C2×#41—432no—
389C22×Q8C4×D4311yescharacteristic, complemented
390C22×D4—431no—
391C22×D4—431no—
392C22×D4—861no—
393C23×C4—431no—
394C23×C4—861no—
395C23×C4C22×D4311yescharacteristic
396C2×M16—21no—
397C2×M16—862no—
398C2×M16—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—21no—
412C22⋊Q8—21no—
413C22⋊Q8—432no—
414C22⋊Q8—862no—
415C22⋊Q8C4×D4312yescomplemented
416C22⋊Q8C22×D4312yes—
417#121—432no—
418#121—432no—
419#121—432no—
420#121—862no—
421#121—862no—
422#121—862no—
423#121—861no—
424#121—861no—
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, complemented
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—21no—
465#95—431no—
466#95—431no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95C22×D4311yescharacteristic
472#95C22×D4311yescharacteristic
473C24—431no—
474C24—861no—
475C24D4×D4311yescharacteristic
476#41—3442no—
477C2×Q8—21no—
478C2×Q8—81no—
479C2×Q8C2×C4×D4312yes—
480C2×D4—432no—
481C2×D4—432no—
482C2×D4—432no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—861no—
488C2×D4—3441no—
489C2×D4—1721no—
490C2×D4—1721no—
491C2×D4—1722no—
492C2×D4—1722no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—81no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—862no—
504C22×C4—862no—
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
518M16—81no—
519M16—3442no—
520M16—3441no—
521C2×C8—22no—
522C2×C8—862no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—432no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—861no—
534C4⋊C4—3441no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—81no—
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—1722no—
552C22⋊C4—1722no—
553C42—432no—
554C42—432no—
555C42—862no—
556C42—862no—
557C42—3441no—
558C42—1722no—
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—432no—
564C23—861no—
565C23—861no—
566C23—862no—
567C23—3441no—
568C23—3441no—
569C23—1721no—
570C23—1721no—
571C23—1722no—
572C23C22⋊C4×D4311yescharacteristic
573C23C22⋊C4×D4311yescharacteristic
574C23C2×D4×D4311yescharacteristic
575Q8—42no—
576Q8—81no—
577D4—3441no—
578D4—3442no—
579D4—3442no—
580D4—1722no—
581D4—1722no—
582D4—1722no—
583D4—1724no—
584D4—1722no—
585D4—1722no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—3442no—
610C2×C4—3442no—
611C2×C4—3444no—
612C2×C4—1722no—
613C2×C4—1722no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1722no—
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—21no—
635C22—21no—
636C22—81no—
637C22—81no—
638C22—862no—
639C22—862no—
640C22—862no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22—1722no—
646C22—6882no—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22#1458369811yescharacteristic
649C22#1458369811yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—862no—
659C4—862no—
660C4—862no—
661C4—3441no—
662C4—1722no—
663C4—1722no—
664C2—21no—
665C2—21no—
666C2—41no—
667C2—41no—
668C2—3442no—
669C2—1722no—
670C2#1914305311yescharacteristic
671C2#1914311311yescharacteristic
672C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1511C2
socleC22×C43C22×C22⋊C4
prime radical#19148436C2
cosocleC22×C4×C43C24
hypercenter#1511D43
hypocenterC43#17623
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19137532C2semidirect
4. #19133171C2semidirect
5. #19133137C2semidirect
6. #19133123C2semidirect
7. #19133115C2semidirect
8. #19133112C2semidirect
9. #19133098C2semidirect
10. #19133080C2semidirect
11. C43×#1511C2semidirect
13. #14583597C4semidirect
14. #14583591C4semidirect
16. #14583560C4semidirect
17. #14583540C4semidirect
28. #14582949C22semidirect
30. #14582861C22semidirect
34. #14582766C22semidirect
35. #14582758C22semidirect
38. #14582744C22semidirect
39. #95×D43C22semidirect
40. #14582636C22semidirect
41. #14582636C22semidirect
49. C43×#328C22semidirect
50. C43×#328C22semidirect
52. C22×D172C2×C4semidirect
63. #13063316C2×C4semidirect
65. #13063314C2×C4semidirect
79. #13063299C2×C4semidirect
83. Q8×Dic43C2×C4semidirect
85. #13063287C2×C4semidirect
97. C2×C4⋊Dic43C2×C4semidirect
120. C22×Q8×C43C2×C4semidirect
125. C22⋊Q8×C43C2×C4semidirect
128. C2×C4⋊C4×C43C2×C4semidirect
333. #1511D43semidirect
381. #328C2×D43semidirect
382. #328C2×D43semidirect
387. C43#17623semidirect
389. C22×Q8C4×D43semidirect
415. C22⋊Q8C4×D43semidirect
445. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484362
#191436342
#191375322
#191331712
#191331372
#191331232
#191331152
#191331122
#191330982
#191330802
C43×#15112
#1762343