Finite Group Databasebeta

← C4×#14583270 #25105014

Subgroups — C4×#14583270 #25105014

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583270C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5C4×#13063323C211yesmaximal, characteristic, complemented
6C4×#13063321C211yesmaximal, characteristic
7#19135451C211yesmaximal, characteristic, complemented
8#19135450C211yesmaximal, characteristic, complemented
9#19135447C211yesmaximal, characteristic, complemented
10#19135446C211yesmaximal, characteristic, complemented
11#19135399C211yesmaximal, characteristic
12#19135395C211yesmaximal, characteristic, complemented
13#19134750C211yesmaximal, characteristic, complemented
14C4×C8×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43—22no—
24#14583270C418yesdirect product factor
25C4×#10621873—24no—
26C4×#10621884—24no—
27C4×#10621883—24no—
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582804C2211yescharacteristic
44#14582802C2211yescharacteristic
45#14582800C2211yescharacteristic
46#14582799—22no—
47#14582794—22no—
48#14582768C2211yescharacteristic
49#14582768C2211yescharacteristic
50C4×Dic43⋊C4—22no—
51C42×Dic43C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C4×SD16×C43—24no—
56C2×#106×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—22no—
63C22×C4×D43—21no—
64C2×#10621873—22no—
65C2×#10621873—22no—
66C2×#10621873C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yescomplemented
70C2×#10621884—22no—
71C2×#10621884—22no—
72C2×#10621884C2×C414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063323—22no—
76#13063323C2×C414yescomplemented
77#13063321—22no—
78#13063321C2×C414yes—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×D172—22no—
82C4×D172—22no—
83C4×C22⋊D43—48no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×C22⋊Dic43—22no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—22no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43D412yes—
95C2×C4×Dic43D412yes—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063257—22no—
99#13063256—22no—
100#13063256—22no—
101#13063250—22no—
102#13063249—22no—
103#13063248—22no—
104#13063247—22no—
105#13063246—22no—
106#13063245—22no—
107C4×C43⋊C8D414yescomplemented
108C8×Dic43—22no—
109C8×Dic43—22no—
110C8×Dic43—22no—
111C8×Dic43C2×C414yescomplemented
112C43⋊#95—22no—
113C43⋊#95—22no—
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43C2×C414yescomplemented
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#106×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135C4×C8×C43D414yescomplemented
136C24×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—44no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—28no—
159C2×C22⋊D43—44no—
160C2×C22⋊D43—44no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43C2×D412yes—
165C22×Dic43C2×D412yes—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C22×C412yes—
172C2×C4×D43—42no—
173C2×C4×D43—44no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86C22×C412yes—
180SD16×C43—28no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43C22×C412yes—
184C2×C8×C43C2×D412yes—
185C2×C8×C43C2×D412yes—
186C2×C8×C43#4112yes—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C42×C43—42no—
194C42×C43C2×D412yes—
195C42×C43C2×D412yes—
196C22⋊Dic43—44no—
197#10621884—28no—
198#10621883—28no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—44no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205Dic43⋊C4—28no—
206Dic43⋊C4—42no—
207Dic43⋊C4—44no—
208Dic43⋊C4—44no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—24no—
212C4×Dic43—42no—
213C4×Dic43SD1618yescomplemented
214C4×Dic43C22×C412yes—
215C4×Dic43#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C2×C43⋊C8C2×D412yes—
220C2×C43⋊C8C2×D412yes—
221C2×C43⋊C8#4112yes—
222#10621873—28no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—42no—
233C22×D43—42no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—84no—
251C2×C4×C43#12712yes—
252C2×C4×C43#12712yes—
253C2×C4×C43C2×SD1614yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C22⋊D43—416no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43C4×D414yes—
271C2×Dic43C2×SD1614yes—
272C2×Dic43C2×SD1614yes—
273C2×Dic43#13514yes—
274D172—22no—
275D172—22no—
276D172—41no—
277D172—41no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—22no—
284C8×C43C4×D414yescomplemented
285C43⋊C8—22no—
286C43⋊C8C4×D414yescomplemented
287C4×#492—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—44no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—82no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43C2×#12711yescharacteristic
295C22×C43#53211yescharacteristic
296C22×C43C22×SD1612yes—
297C22×C43C2×#13512yes—
298C2×D43—42no—
299C2×D43—44no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—82no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#49214yescomplemented
308C4×C43C2×C4×D411yescharacteristic
309C4×C43C2×C4×D411yescharacteristic
310C4×C43#53211yescharacteristic
311C4×C43#53211yescharacteristic
312Dic43—24no—
313Dic43—42no—
314Dic43—81no—
315Dic43—81no—
316Dic43C4×SD1618yescomplemented
317C2×#492—431no—
318C2×C4×SD16—431no—
319C2×C4×SD16—431no—
320C2×C4×SD16—431no—
321C2×C4×SD16D4311yescharacteristic, complemented
322C4×C4⋊Q8—431no—
323C4×#127—431no—
324#1968—431no—
325#1968—431no—
326#1968—431no—
327#1968—431no—
328#1957—431no—
329#1956—431no—
330#1844—431no—
331C42×C8—431no—
332C2×C43—82no—
333C2×C43C4×#12711yescharacteristic
334C2×C43C2×C4×SD1612yes—
335C2×C43C2×#49211yescharacteristic
336C2×C43#314711yescharacteristic
337C2×C43#316712yes—
338D43—82no—
339C22×SD16—431no—
340C22×SD16—431no—
341C22×SD16—431no—
342C22×SD16C2×D4311yescharacteristic
343C2×C4⋊Q8—431no—
344C2×#127—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348C2×C4×D4—862no—
349C2×C4×D4C2×D4311yescharacteristic
350#492—438no—
351C4×SD16—24no—
352C4×SD16—864no—
353C4×SD16—864no—
354C4×SD16—864no—
355C2×#106—431no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#106C2×D4311yescharacteristic
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102C2×D4311yescharacteristic
367C2×C4×C8—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371C2×C4×C8—431no—
372C2×C4×C8C2×D4311yescharacteristic
373#391—431no—
374#391—431no—
375#390—431no—
376#390—431no—
377#390—862no—
378#389—862no—
379#384—431no—
380#384—431no—
381C4×C4⋊C4—862no—
382C43—431no—
383C43C4×#49211yescharacteristic, complemented, Sylow
384C22×Q8—431no—
385C22×Q8C22×D4311yescharacteristic
386C22×D4—431no—
387C22×D4—862no—
388C22×D4C22×D4311yescharacteristic
389C23×C4—21no—
390C23×C4—861no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—434no—
394C2×SD16—434no—
395C2×SD16—434no—
396C2×SD16—862no—
397C2×SD16—862no—
398C2×SD16—862no—
399C2×SD16—862no—
400C2×SD16—862no—
401C2×SD16—862no—
402C2×SD16C4×D4314yescomplemented
403C22×C8—431no—
404C22×C8—431no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C4⋊Q8—434no—
408C4⋊Q8—862no—
409#127—434no—
410#127—862no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—1728no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—862no—
431C2×C22⋊C4—862no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—432no—
435C2×C42—431no—
436C2×C42—432no—
437C2×C42—431no—
438C2×C42—861no—
439C2×C42C22×D4311yescharacteristic
440#106—22no—
441#106—862no—
442#106—862no—
443#106—862no—
444#103—22no—
445#103—862no—
446#103—862no—
447#103—862no—
448#102—22no—
449#102—862no—
450#102—862no—
451#102—862no—
452C4×C8—434no—
453C4×C8—434no—
454C4×C8—862no—
455C4×C8—862no—
456C4×C8—862no—
457C4×C8C22⋊D4314yescomplemented
458#95—862no—
459#95—862no—
460C24—21no—
461C24—861no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8C2×C4×D4312yes—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—432no—
480C2×D4—868no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—1724no—
487C2×D4—1724no—
488C2×D4C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—44no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—1722no—
500C22×C4—1724no—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504SD16—28no—
505SD16—868no—
506SD16—868no—
507SD16—868no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—432no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8C2×C4×D4312yes—
517C2×C8#1062189812yes—
518C2×C8C2×C22⋊D4312yes—
519C2×C8C2×C22⋊D4312yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—868no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—1724no—
531C4⋊C4—1724no—
532C4⋊C4—1722no—
533C22⋊C4—42no—
534C22⋊C4—1724no—
535C22⋊C4—1724no—
536C22⋊C4—1722no—
537C42—42no—
538C42—438no—
539C42—432no—
540C42—432no—
541C42—864no—
542C42—861no—
543C42—861no—
544C42—1722no—
545C42D4×D4312yes—
546C42C2×C22⋊D4312yes—
547C23—22no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23—41no—
552C23—862no—
553C23—1722no—
554C23—1722no—
555C23—1721no—
556C23—1721no—
557C23C2×D4×D4311yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—862no—
563Q8—862no—
564Q8—1721no—
565Q8—1721no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—862no—
571D4—862no—
572D4—17216no—
573D4—1721no—
574D4—1721no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4—434no—
585C2×C4—434no—
586C2×C4—434no—
587C2×C4—434no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3444no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4#1306332112yes—
599C2×C4#1306332112yes—
600C2×C4SD16×D4314yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C2×C4C22×C22⋊D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C8—22no—
608C8—434no—
609C8—862no—
610C8C4×C22⋊D4314yescomplemented
611C22—42no—
612C22—44no—
613C22—81no—
614C22—81no—
615C22—82no—
616C22—3441no—
617C22—3441no—
618C22—3442no—
619C22—1722no—
620C22—1724no—
621C22C4×D4×D4311yescharacteristic
622C22C2×#1306332111yescharacteristic
623C22#1458344611yescharacteristic
624C22C2×SD16×D4312yes—
625C22#135×D4312yes—
626C4—22no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—438no—
631C4—864no—
632C4—3441no—
633C4—3441no—
634C4—1722no—
635C4#1458327014yesdirect product factor
636C4C4×D4×D4311yescharacteristic
637C4C2×C4×C22⋊D4311yescharacteristic
638C4#1458344511yescharacteristic
639C4#1458344611yescharacteristic
640C2—82no—
641C2—3442no—
642C2C4×#1306332111yescharacteristic
643C2C4×SD16×D4312yes—
644C2C2×#1458327011yescharacteristic
645C2#1914501911yescharacteristic
646C2#1914515112yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43C4×#492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621873C2semidirect
3. C2×C4×#10621884C2semidirect
4. C2×C4×#10621883C2semidirect
5. C4×#13063323C2semidirect
7. #19135451C2semidirect
8. #19135450C2semidirect
9. #19135447C2semidirect
10. #19135446C2semidirect
12. #19135395C2semidirect
13. #19134750C2semidirect
14. C4×C8×Dic43C2semidirect
15. C2×C4×SD16×C43C2semidirect
24. #14583270C4direct (N × H)
66. C2×#10621873C2×C4semidirect
69. C2×#10621883C2×C4semidirect
72. C2×#10621884C2×C4semidirect
76. #13063323C2×C4semidirect
107. C4×C43⋊C8D4semidirect
111. C8×Dic43C2×C4semidirect
119. C2×SD16×C43C2×C4semidirect
135. C4×C8×C43D4semidirect
213. C4×Dic43SD16semidirect
284. C8×C43C4×D4semidirect
286. C43⋊C8C4×D4semidirect
307. C4×C43#492semidirect
316. Dic43C4×SD16semidirect
321. C2×C4×SD16D43semidirect
383. C43C4×#492semidirect
402. C2×SD16C4×D43semidirect
457. C4×C8C22⋊D43semidirect
610. C8C4×C22⋊D43semidirect
635. C4#14583270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832702
C2×C4×#106218732
C2×C4×#106218842
C2×C4×#106218832
C4×#130633232
C4×#130633212
#191354512
#191354502
#191354472
#191354462
#191353992
#191353952
#191347502
C4×C8×Dic432
C2×C4×SD16×C432
C4×#49243