Finite Group Databasebeta

← C2×#19134820 #25097450

Subgroups — C2×#19134820 #25097450

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C22×#13063253C211yesmaximal, characteristic
4C2×#14582898C211yesmaximal, characteristic
5#19134820C218yesmaximal, direct product factor
6C2×#14582668C211yesmaximal, characteristic, complemented
7C2×#14582659C211yesmaximal, characteristic, complemented
8C2×C43×#384C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583380—22no—
13#14583380—22no—
14#14583380—22no—
15#14583380C2214yes—
16C2×#13063290—21no—
17C2×#13063287—21no—
18C2×C4×C22⋊D43—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063283—21no—
21C2×C4⋊C4×D43—21no—
22#14582939—22no—
23#14582939C2214yescomplemented
24C2×#13063258—21no—
25C2×#13063256—21no—
26C2×#13063253C418yescomplemented
27C2×#13063253C2214yes—
28#14582898—22no—
29#14582898C2214yes—
30C2×#13063248—21no—
31C2×#13063245—21no—
32#14582668C2214yescomplemented
33#14582659C2214yescomplemented
34C22×C4⋊C4×C43—22no—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#384—22no—
39C43×#384C2214yescomplemented
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898C2×C414yes—
45C2×#10621898D412yes—
46C2×#10621898Q814yes—
47C2×#10621898C2312yes—
48C22×Dic86D411yescharacteristic
49C22×D172D411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C22×C4×D43—22no—
53C2×#10621877—21no—
54C2×#10621877—22no—
55C2×#10621877—21no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877C2×C414yescomplemented
59C2×#10621877C2312yes—
60C2×#10621877C2312yes—
61C22×C43⋊C8—21no—
62C22×C43⋊C8—21no—
63#13063290—24no—
64#13063290—24no—
65#13063287—24no—
66#13063287—24no—
67C4×C22⋊D43—28no—
68C4×C22⋊D43—28no—
69#13063284—21no—
70#13063284—21no—
71#13063284D412yes—
72#13063284C2312yes—
73#13063283—24no—
74#13063283—24no—
75C2×C4⋊Dic43D411yescharacteristic
76C2×C4⋊Dic43D411yescharacteristic
77C2×Dic43⋊C4—22no—
78C4⋊C4×D43—24no—
79C4⋊C4×D43—24no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—21no—
84#13063258—24no—
85#13063256—24no—
86#13063253C2×C4116yescomplemented
87#13063248—24no—
88#13063245—24no—
89C23×C4×C43—21no—
90C23×C4×C43—21no—
91C23×C4×C43D412yes—
92C23×C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—28no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—48no—
104C2×C4⋊C4×C43D412yes—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C42×C43—21no—
108C2×C42×C43—22no—
109C2×C42×C43C2×C414yescomplemented
110C2×C42×C43C2312yes—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C22×C4×C43—24no—
114C22×C4×C43—24no—
115C22×C4×C43—24no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—44no—
121C22×C4×C43—44no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D414yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×Q812yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142#10621898—24no—
143#10621898—24no—
144#10621898—24no—
145#10621898—24no—
146#10621898—24no—
147#10621898—22no—
148#10621898—22no—
149#10621898C4⋊C418yescomplemented
150#10621898C22×C414yes—
151#10621898C2×Q814yes—
152C2×D172—21no—
153C2×D172—22no—
154C2×D172C4⋊C414yescomplemented
155C2×D172C2×D412yes—
156C2×C4×D43—24no—
157C2×C4×D43—22no—
158C2×C4×D43—24no—
159C2×C4×D43—22no—
160C2×C4×D43—28no—
161C2×C4×D43—84no—
162C2×Dic86—21no—
163C2×Dic86—22no—
164C2×Dic86C4⋊C414yescomplemented
165C2×Dic86C2×D412yes—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—416no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C42×C43—24no—
176C42×C43—22no—
177C42×C43C22×C414yescomplemented
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180(C2×D43)⋊C4—28no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C2×D412yes—
184C4⋊Dic43C2×D412yes—
185Dic43⋊C4—28no—
186C4×Dic43—28no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189#10621877—24no—
190#10621877—22no—
191#10621877—22no—
192#10621877—22no—
193#10621877—42no—
194#10621877C22×C414yescomplemented
195C2×C43⋊C8—24no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—42no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43C4×D412yes—
202C23×C43#12011yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43C22⋊Q812yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—22no—
207C22×D43—24no—
208C22×D43—42no—
209C22×D43—42no—
210C2×C4×C43—24no—
211C2×C4×C43—216no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—44no—
216C2×C4×C43—44no—
217C2×C4×C43—44no—
218C2×C4×C43—42no—
219C2×C4×C43—82no—
220C2×C4×C43—82no—
221C2×C4×C43—82no—
222C2×C4×C43C2×C4⋊C412yes—
223C2×C4×C43C2×C4⋊C412yes—
224C2×C4×C43C4×D412yes—
225C2×C4×C43C4×D412yes—
226C2×C4×C43C4×D412yes—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C22⋊Q812yes—
230C2×C4×C43C22⋊Q812yes—
231C2×C4×C43C22⋊Q812yes—
232C2×C4×C43#12312yes—
233C2×C4×C43#12312yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×Q811yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—24no—
241C22⋊D43—24no—
242C22⋊D43—28no—
243C2×Dic43—22no—
244C2×Dic43—24no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249D172—22no—
250D172—24no—
251D172C2×C4⋊C414yescomplemented
252C4×D43—24no—
253C4×D43—24no—
254C4×D43—28no—
255C4×D43—88no—
256Dic86—22no—
257Dic86—24no—
258Dic86C2×C4⋊C414yescomplemented
259C43⋊C8—24no—
260C43⋊C8—42no—
261C2×#1859—431nomaximal, Sylow
262C22×C43—24no—
263C22×C43—24no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43#38512yes—
269C22×C43#38512yes—
270C22×C43#45312yes—
271C22×C43#45612yes—
272C22×C43C2×C4×D411yescharacteristic
273C22×C43C2×#12011yescharacteristic
274C22×C43C2×C22⋊Q811yescharacteristic
275C2×D43—24no—
276C2×D43—48no—
277C2×D43—42no—
278C2×D43—42no—
279C4×C43—28no—
280C4×C43—44no—
281C4×C43—82no—
282C4×C43#38512yes—
283C4×C43#38512yes—
284C4×C43C22×C4⋊C411yescharacteristic
285C4×C43C2×C4×D411yescharacteristic
286C4×C43C2×C22⋊Q811yescharacteristic
287C4×C43C2×#12311yescharacteristic
288Dic43—24no—
289Dic43—42no—
290Dic43—42no—
291C2×#520—431no—
292C2×#428—431no—
293C22×#104—431no—
294C2×#417—431no—
295C2×#384D4311yescharacteristic, complemented
296#1859—438no—
297C2×#343—431no—
298C2×#339—431no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—22no—
302C2×C43#185914yescomplemented
303C2×C43C2×#38511yescharacteristic
304C2×C43C2×#45311yescharacteristic
305C2×C43C2×#45611yescharacteristic
306D43—44no—
307C22×#41—431no—
308C22×M16—431no—
309C22×M16—431no—
310#520—434no—
311#520—862no—
312#520—862no—
313#520—862no—
314C2×C4×Q8—861no—
315C2×C4×D4—861no—
316C2×C4×D4—862no—
317C2×#117—431no—
318C2×#117—861no—
319C22×C4⋊C4—22no—
320C22×C4⋊C4—861no—
321C22×C4⋊C4C2×D4311yescharacteristic
322C22×C4⋊C4C2×D4311yescharacteristic
323C22×C42C2×D4311yescharacteristic
324#428—434no—
325#428—862no—
326C2×#107—861no—
327C2×#106—861no—
328C2×#104—434no—
329C2×#104—438no—
330#417—434no—
331#417—862no—
332C2×#103—861no—
333C2×#102—861no—
334#384—22no—
335#384C2×D4314yescomplemented
336#343—434no—
337#339—434no—
338C43C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—434no—
340C2×#41—432no—
341C2×#41—434no—
342C2×#41—432no—
343C2×#41—862no—
344C2×#41—861no—
345C2×#41—862no—
346C2×#41—861no—
347C22×Q8—431no—
348C22×D4—431no—
349C22×D4—861no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—862no—
353C23×C4—861no—
354C23×C4C22⋊D4312yes—
355C23×C4C22×D4311yescharacteristic
356C2×M16—434no—
357C2×M16—432no—
358C2×M16—432no—
359C2×M16—861no—
360C2×M16—862no—
361C2×M16—861no—
362C2×M16—862no—
363C2×M16—862no—
364C22×C8—861no—
365C22×C8—861no—
366C4×Q8—864no—
367C4×Q8—864no—
368C4×D4—864no—
369C4×D4—864no—
370C4×D4—868no—
371C4×D4—868no—
372#117—432no—
373#117—432no—
374#117—864no—
375#117—864no—
376#117—861no—
377#117—861no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—48no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4C22⋊D4312yes—
395C2×C4⋊C4C22×D4312yes—
396C2×C4⋊C4C22×D4312yes—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—861no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—862no—
402C2×C42—861no—
403C2×C42C4×D4314yescomplemented
404C2×C42C22×D4312yes—
405#107—864no—
406#106—864no—
407#104—4316no—
408#103—864no—
409#102—864no—
410C24—861no—
411C24C2×C22⋊D4311yescharacteristic
412#41—438no—
413#41—434no—
414#41—434no—
415#41—864no—
416#41—864no—
417#41—864no—
418#41—864no—
419#41—864no—
420#41—862no—
421#41—862no—
422C2×Q8—434no—
423C2×Q8—432no—
424C2×Q8—861no—
425C2×Q8—862no—
426C2×D4—434no—
427C2×D4—432no—
428C2×D4—864no—
429C2×D4—862no—
430C2×D4—864no—
431C2×D4—862no—
432C2×D4—861no—
433C2×D4—862no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—868no—
446C22×C4—861no—
447C22×C4—864no—
448C22×C4—862no—
449C22×C4—864no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—3444no—
454C22×C4C2×C4×D4312yes—
455C22×C4#1062189812yes—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4Q8×D4312yes—
461C22×C4#1062190212yes—
462C22×C4C2×C22⋊D4314yes—
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C23×D4311yescharacteristic
465M16—434no—
466M16—864no—
467M16—862no—
468M16—862no—
469M16—862no—
470M16—1722no—
471C2×C8—864no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—1722no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—416no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—432no—
485C4⋊C4—432no—
486C4⋊C4—868no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C22⋊C4—868no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C42—24no—
493C42—22no—
494C42—868no—
495C42—862no—
496C42—862no—
497C42C2×C4×D4314yescomplemented
498C23—22no—
499C23—22no—
500C23—862no—
501C23—864no—
502C23—1722no—
503C23—1722no—
504C23C4×C22⋊D4312yes—
505C23#1306329311yescharacteristic
506C23#1306329311yescharacteristic
507C23#1306330112yes—
508C23C22×C22⋊D4311yescharacteristic
509Q8—434no—
510Q8—862no—
511Q8—864no—
512D4—434no—
513D4—864no—
514D4—864no—
515D4—868no—
516D4—862no—
517D4—864no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—216no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—862no—
531C2×C4—864no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—868no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3448no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4C4⋊C4×D4312yes—
541C2×C4C4⋊C4×D4312yes—
542C2×C4C4×C22⋊D4312yes—
543C2×C4#1306328712yes—
544C2×C4#1306328712yes—
545C2×C4#1306329311yescharacteristic
546C2×C4#1306329311yescharacteristic
547C2×C4#1306330112yes—
548C2×C4#1306330312yes—
549C2×C4#1306330312yes—
550C2×C4#1306331012yes—
551C2×C4#1306331012yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×Q8×D4311yescharacteristic
556C2×C4C2×#1062189811yescharacteristic
557C2×C4C2×#1062190211yescharacteristic
558C8—864no—
559C8—1722no—
560C22—21no—
561C22—21no—
562C22—24no—
563C22—24no—
564C22—21no—
565C22—21no—
566C22—864no—
567C22—1722no—
568C22—1728no—
569C22—1722no—
570C22#1458277012yes—
571C22#1458277012yes—
572C22#1458306612yes—
573C22#1458308112yes—
574C22C2×C4×C22⋊D4311yescharacteristic
575C22C2×#1306329311yescharacteristic
576C22C2×#1306330111yescharacteristic
577C4—28no—
578C4—44no—
579C4—82no—
580C4—864no—
581C4—1722no—
582C4—1722no—
583C4#1458277012yes—
584C4#1458277012yes—
585C4C2×C4⋊C4×D4311yescharacteristic
586C4C2×#1306328711yescharacteristic
587C4C2×#1306330311yescharacteristic
588C4C2×#1306331011yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—1724no—
593C2#1913482014yesdirect product factor
594C2C2×#1458277011yescharacteristic
595C2C2×#1458306611yescharacteristic
596C2C2×#1458308111yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#384C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#384D43
hypocenterC43C2×#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
5. #19134820C2direct (N × H)
6. C2×#14582668C2semidirect
7. C2×#14582659C2semidirect
8. C2×C43×#384C2semidirect
23. #14582939C22semidirect
26. C2×#13063253C4semidirect
32. #14582668C22semidirect
33. #14582659C22semidirect
39. C43×#384C22semidirect
58. C2×#10621877C2×C4semidirect
86. #13063253C2×C4semidirect
109. C2×C42×C43C2×C4semidirect
149. #10621898C4⋊C4semidirect
154. C2×D172C4⋊C4semidirect
164. C2×Dic86C4⋊C4semidirect
177. C42×C43C22×C4semidirect
194. #10621877C22×C4semidirect
251. D172C2×C4⋊C4semidirect
258. Dic86C2×C4⋊C4semidirect
295. C2×#384D43semidirect
302. C2×C43#1859semidirect
335. #384C2×D43semidirect
338. C43C2×#1859semidirect
403. C2×C42C4×D43semidirect
497. C42C2×C4×D43semidirect
593. C2#19134820direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833802
C2×#145829392
C22×#130632532
C2×#145828982
#191348202
C2×#145826682
C2×#145826592
C2×C43×#3842
C2×#185943