Finite Group Databasebeta

← #25097813

Subgroups — #25097813

Order 11008.

1986 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
1C2×#14583412C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582894C212yesmaximal, complemented
4C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
5#19134917C211yesmaximal, characteristic, complemented
6#19134915C211yesmaximal, characteristic, complemented
7#19134911C212yesmaximal, complemented
8#19134908C211yesmaximal, characteristic, complemented
9#19134899C212yesmaximal, complemented
10#19134310C212yesmaximal, complemented
11C43×#1873C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×C8×D43C2212yes—
15#14583412—24no—
16#14583412C418yescomplemented
17C2×#13063310—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063295—21no—
22C2×#13063287—21no—
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063284C2211yescharacteristic
25C2×#13063283C2211yescharacteristic
26C2×#13063283C2212yes—
27C2×#13063282—21no—
28C2×#13063281—21no—
29#117×D43—28no—
30C2×C4⋊C4×D43C2212yes—
31C2×C22⋊C4×D43—21no—
32C2×C42×D43—21no—
33#14582894—28no—
34C2×#13063249C2212yescomplemented
35C2×#13063247C2212yescomplemented
36C2×#13063245C2212yescomplemented
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2212yes—
39C22⋊C8×D43—24no—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C2×C22⋊Q8×C43C2211yescharacteristic
44C2×#117×C43C2211yescharacteristic
45C2×#103×C43C2212yescomplemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#340C2212yescomplemented
48C24×D43D411yescharacteristic
49C2×#10621902—22no—
50C2×#10621902—24no—
51C2×#10621902—24no—
52C2×#10621902C2×C414yescomplemented
53C22×D172—21no—
54C22×D172—21no—
55C22×D172C2311yescharacteristic
56C22×C22⋊D43—21no—
57C23×Dic43D411yescharacteristic
58C22×C4×D43—24no—
59C22×C4×D43—24no—
60C22×C4×D43—22no—
61C22×C4×D43—21no—
62C22×C4×D43C2×C414yes—
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D414yes—
66C22×C4×D43C2311yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2312yes—
69C2×C8×D43—24no—
70C2×C8×D43—24no—
71C2×C8×D43—24no—
72#13063310—28no—
73#13063301—22no—
74#13063301C2×C414yes—
75#13063300—22no—
76#13063300C2×C414yes—
77#13063299—22no—
78#13063299C2×C414yescomplemented
79#13063295—28no—
80#13063287—28no—
81(C22⋊D43)⋊C4—28no—
82#13063284—24no—
83#13063283—24no—
84#13063283—22no—
85#13063283C2×C414yescomplemented
86#13063283D418yescomplemented
87#13063282—28no—
88#13063281—28no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2312yes—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—21no—
93C4⋊C4×D43—24no—
94C4⋊C4×D43—24no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C22⋊C4×D43—28no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—21no—
105C42×D43—28no—
106#13063249—24no—
107#13063247—24no—
108#13063245—24no—
109C22⋊(C43⋊C8)—22no—
110(C2×D43)⋊C8—24no—
111C22×Q8×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2312yes—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43C2×C414yescomplemented
116#117×C43—24no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2312yes—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123#103×C43—24no—
124C22⋊C8×C43—22no—
125C24×C43C2×D411yescharacteristic
126C23×D43—22no—
127C23×D43—22no—
128C23×D43—24no—
129C23×D43—21no—
130C23×D43—42no—
131C23×D43C22⋊C414yes—
132C23×D43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C2×Q8×C43—21no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43C22×C412yes—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C22×C412yes—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—24no—
148C2×C22⋊D43—44no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43C22⋊C414yes—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156#10621902—216no—
157#10621902—48no—
158C2×D172—21no—
159C2×D172—24no—
160C2×D172—24no—
161C2×D172—22no—
162C2×D172—22no—
163C2×D172—42no—
164C2×D172—42no—
165C2×D172—44no—
166C2×D172C22×C412yes—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—216no—
172C2×C4×D43—216no—
173C2×C4×D43—28no—
174C2×C4×D43—24no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—44no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—44no—
181C2×C4×D43C22⋊C414yes—
182C2×C4×D43C22⋊C414yes—
183C2×C4×D43C22×C412yes—
184C2×C4×D43C22×C412yes—
185C2×C4×D43C2×D412yes—
186C2×C4×D43C2×D412yes—
187C2×C4×D43C2×D414yes—
188C2×C4×D43#4114yes—
189C2×C8×C43—22no—
190C2×C8×C43—22no—
191C2×C8×C43—22no—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C22×C412yes—
196C4⋊C4×C43C2×D414yes—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—24no—
199C42×C43—24no—
200C22⋊Dic43—24no—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—24no—
205(C2×D43)⋊C4—28no—
206C4⋊Dic43—22no—
207C4⋊Dic43—21no—
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C2×D414yes—
210Dic43⋊C4—28no—
211Dic43⋊C4—24no—
212C4×Dic43—24no—
213C4×Dic43—24no—
214C4×Dic43—28no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—22no—
218C8×D43—48no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43C2×C22⋊C412yes—
224C23×C43C22×D411yescharacteristic
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—28no—
231C22×D43—28no—
232C22×D43—22no—
233C22×D43—44no—
234C22×D43—48no—
235C22×D43—48no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—42no—
239C22×D43—42no—
240C22×D43C2×C22⋊C412yes—
241C22×D43C2×C22⋊C412yes—
242C22×D43#12012yes—
243C22×D43#12312yes—
244C22×D43#13514yes—
245Q8×C43—24no—
246Q8×C43—42no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—24no—
250C2×C4×C43—24no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—24no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43C2×C22⋊C412yes—
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D412yes—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4112yes—
264C22⋊D43—48no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—28no—
268C2×Dic43—22no—
269C2×Dic43—24no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275C2×Dic43#12012yes—
276C2×Dic43#12312yes—
277D172—24no—
278D172—48no—
279D172—48no—
280D172—42no—
281C4×D43—28no—
282C4×D43—24no—
283C4×D43—24no—
284C4×D43—28no—
285C4×D43—416no—
286C4×D43—48no—
287C4×D43C4×D418yes—
288C4×D43#12118yes—
289C8×C43—42no—
290C43⋊C8—42no—
291#20908—431nomaximal, Sylow
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43C22×C22⋊C411yescharacteristic
298C22×C43C2×#12011yescharacteristic
299C22×C43C2×#12311yescharacteristic
300C22×C43C2×#13512yes—
301C22×C43#57512yes—
302C2×D43—24no—
303C2×D43—24no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—24no—
308C2×D43—24no—
309C2×D43—22no—
310C2×D43—416no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—82no—
315C2×D43—82no—
316C2×D43#38614yes—
317C2×D43#41614yescomplemented
318C4×C43—22no—
319C4×C43—42no—
320C4×C43—44no—
321C4×C43—42no—
322C4×C43C2×C4×D412yes—
323C4×C43C2×#12112yes—
324Dic43—22no—
325Dic43—42no—
326Dic43—44no—
327Dic43#38614yes—
328C2×#525—431no—
329C22×#117—431no—
330C2×#416—432no—
331C22×C22⋊C8—431no—
332#1875—431no—
333#1875—431no—
334#1874—432no—
335#1873—431no—
336#1873D4311yescharacteristic, complemented
337#1872—432no—
338#1735—432no—
339C2×C43—42no—
340C2×C43C2×#38611yescharacteristic
341C2×C43C2×#41611yescharacteristic
342C2×C43#289611yescharacteristic
343C2×C43#300212yes—
344C2×C43#309112yes—
345D43—24no—
346D43—24no—
347D43—82no—
348C22×#41—431no—
349C24×C4—431no—
350C23×C8—432no—
351#525—438no—
352#525—864no—
353C2×#123—861no—
354C2×C22⋊Q8—431no—
355C2×C22⋊Q8C2×D4311yescharacteristic
356C2×#121—431no—
357C2×#121—431no—
358C2×#120—861no—
359C2×C4×D4—861no—
360C2×C4×D4—861no—
361C2×#117—431no—
362C2×#117—432no—
363C2×#117—431no—
364C2×#117—861no—
365C2×#117—861no—
366C2×#117—868no—
367C2×#117C2×D4311yescharacteristic
368C22×C4⋊C4—432no—
369C22×C22⋊C4—861no—
370C22×C42—861no—
371#416—868no—
372C2×#103—432no—
373C2×#103C2×D4312yescomplemented
374C2×#102—432no—
375C2×#102—432no—
376C2×C22⋊C8—431no—
377C2×C22⋊C8—432no—
378C2×C22⋊C8—864no—
379C2×C22⋊C8C2×D4311yescharacteristic
380#340—432no—
381#340—432no—
382#340—432no—
383#340C2×D4312yescomplemented
384C43#2090811yescharacteristic, complemented, Sylow
385C25—431no—
386C2×#41—434no—
387C2×#41—862no—
388C2×#41—864no—
389C2×#41—864no—
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C22×D4—861no—
393C22×D4—861no—
394C22×D4—861no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—434no—
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—434no—
401C23×C4—431no—
402C23×C4—864no—
403C23×C4—864no—
404C23×C4—861no—
405C23×C4—862no—
406C23×C4C22×D4311yescharacteristic
407C22×C8—432no—
408C22×C8—864no—
409C22×C8—864no—
410C22×C8—864no—
411C22×C8C22×D4312yes—
412#123—868no—
413C22⋊Q8—22no—
414C22⋊Q8—434no—
415C22⋊Q8—862no—
416C22⋊Q8C4×D4314yescomplemented
417#121—434no—
418#121—434no—
419#121—862no—
420#121—862no—
421#120—868no—
422C4×D4—868no—
423C4×D4—868no—
424#117—24no—
425#117—434no—
426#117—438no—
427#117—868no—
428#117—868no—
429#117—864no—
430#117—862no—
431#117—864no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—432no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—864no—
436C2×C4⋊C4—862no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—864no—
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4312yes—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—868no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—862no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—21no—
451C2×C42—868no—
452C2×C42—862no—
453C2×C42—861no—
454C2×C42—861no—
455#103—24no—
456#103—864no—
457#102—864no—
458#102—864no—
459C22⋊C8—22no—
460C22⋊C8—864no—
461C22⋊C8—862no—
462C24—431no—
463C24—431no—
464C24—434no—
465C24—862no—
466C24—862no—
467C24—864no—
468C24—861no—
469C24—1722no—
470C24D4×D4311yescharacteristic
471#41—8616no—
472#41—1728no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8C2×C4×D4312yes—
477C2×D4—432no—
478C2×D4—864no—
479C2×D4—864no—
480C2×D4—864no—
481C2×D4—862no—
482C2×D4—861no—
483C2×D4—862no—
484C2×D4—1722no—
485C2×D4—1722no—
486C2×D4—1724no—
487C2×D4—1724no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—432no—
495C22×C4—434no—
496C22×C4—432no—
497C22×C4—434no—
498C22×C4—434no—
499C22×C4—431no—
500C22×C4—434no—
501C22×C4—434no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—8616no—
507C22×C4—8616no—
508C22×C4—864no—
509C22×C4—862no—
510C22×C4—862no—
511C22×C4—868no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—861no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4—1724no—
521C22×C4—1724no—
522C22×C4C2×C4×D4312yes—
523C22×C4D4×D4311yescharacteristic
524C22×C4D4×D4312yes—
525C22×C4C23×D4311yescharacteristic
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—862no—
530C2×C8—862no—
531C2×C8—862no—
532C2×C8—1728no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—432no—
537C4⋊C4—434no—
538C4⋊C4—864no—
539C4⋊C4—868no—
540C4⋊C4—862no—
541C4⋊C4—861no—
542C4⋊C4C2×C4×D4312yes—
543C4⋊C4D4×D4314yes—
544C22⋊C4—24no—
545C22⋊C4—24no—
546C22⋊C4—864no—
547C22⋊C4—868no—
548C22⋊C4—864no—
549C22⋊C4—864no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C42—24no—
553C42—868no—
554C42—864no—
555C42—864no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—22no—
560C23—432no—
561C23—432no—
562C23—432no—
563C23—432no—
564C23—434no—
565C23—868no—
566C23—868no—
567C23—861no—
568C23—861no—
569C23—862no—
570C23—862no—
571C23—862no—
572C23—862no—
573C23—1724no—
574C23—1728no—
575C23—1728no—
576C23—1721no—
577C23—1721no—
578C23—1722no—
579C23—1722no—
580C23C22⋊C4×D4312yes—
581C23C2×D4×D4311yescharacteristic
582Q8—24no—
583Q8—42no—
584D4—864no—
585D4—1728no—
586D4—1728no—
587D4—1728no—
588D4—1722no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—438no—
605C2×C4—438no—
606C2×C4—432no—
607C2×C4—868no—
608C2×C4—868no—
609C2×C4—868no—
610C2×C4—861no—
611C2×C4—861no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—862no—
615C2×C4—864no—
616C2×C4—1728no—
617C2×C4—17216no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4C22⋊C4×D4312yes—
622C2×C4C22×C4×D4311yescharacteristic
623C2×C4C2×D4×D4312yes—
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4#41×D4312yes—
626C8—42no—
627C8—1722no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—434no—
634C22—434no—
635C22—864no—
636C22—864no—
637C22—864no—
638C22—864no—
639C22—862no—
640C22—862no—
641C22—862no—
642C22—862no—
643C22—3442no—
644C22—3442no—
645C22—17216no—
646C22—1722no—
647C22—1722no—
648C22—1722no—
649C22C2×C22⋊C4×D4311yescharacteristic
650C22#120×D4311yescharacteristic
651C22#123×D4311yescharacteristic
652C22#135×D4312yes—
653C22#1458369812yes—
654C4—22no—
655C4—44no—
656C4—42no—
657C4—42no—
658C4—434no—
659C4—862no—
660C4—1724no—
661C4—1722no—
662C4C4×D4×D4312yes—
663C4#121×D4312yes—
664C2—42no—
665C2—864no—
666C2—864no—
667C2—3442no—
668C2#386×D4311yescharacteristic
669C2#416×D4311yescharacteristic
670C2#1914311311yescharacteristic
671C2#1914381612yes—
672C2#1914451312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1873C2
socleC23×C43C22×D4
prime radicalC2×#14583412C2
cosocleC22×C4×C43C24
hypercenter#1873D43
hypocenterC43#20908
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582894C2semidirect
4. C2×C22⋊C8×D43C2semidirect
5. #19134917C2semidirect
6. #19134915C2semidirect
7. #19134911C2semidirect
8. #19134908C2semidirect
9. #19134899C2semidirect
10. #19134310C2semidirect
11. C43×#1873C2semidirect
16. #14583412C4semidirect
34. C2×#13063249C22semidirect
35. C2×#13063247C22semidirect
36. C2×#13063245C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#103×C43C22semidirect
47. C43×#340C22semidirect
52. C2×#10621902C2×C4semidirect
78. #13063299C2×C4semidirect
85. #13063283C2×C4semidirect
86. #13063283D4semidirect
115. C22⋊Q8×C43C2×C4semidirect
317. C2×D43#416semidirect
336. #1873D43semidirect
373. C2×#103C2×D43semidirect
383. #340C2×D43semidirect
384. C43#20908semidirect
416. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834122
C2×#117×D432
C2×#145828942
C2×C22⋊C8×D432
#191349172
#191349152
#191349112
#191349082
#191348992
#191343102
C43×#18732
#2090843