Finite Group Databasebeta

← C2×#19134831 #25097462

Subgroups — C2×#19134831 #25097462

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C22×#13063251C211yesmaximal, characteristic
4C2×#14582901C211yesmaximal, characteristic
5C2×#14582764C211yesmaximal, characteristic, complemented
6#19134831C218yesmaximal, direct product factor
7C2×#14582660C211yesmaximal, characteristic, complemented
8C2×C43×#343C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583380—22no—
11#14583380—22no—
12#14583380—22no—
13#14583380C2214yes—
14C2×#13063290—21no—
15C2×#13063287—21no—
16C2×C4×C22⋊D43—22no—
17C2×#13063284C2211yescharacteristic
18C2×#13063283—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21C22×C4×Dic43C2211yescharacteristic
22#14582941—22no—
23#14582941C2214yescomplemented
24C2×#13063259—21no—
25C2×#13063257—21no—
26C2×#13063251C418yescomplemented
27C2×#13063251C2214yes—
28#14582901—22no—
29#14582901C2214yes—
30C2×#13063250—21no—
31C2×#13063247—21no—
32#14582764—22no—
33#14582764C2214yescomplemented
34C2×C43⋊#95—22no—
35#14582660C2214yescomplemented
36C22×M16×C43C2211yescharacteristic
37C22×M16×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C43×#343C2214yescomplemented
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—
51C23×Dic43—21no—
52C23×Dic43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—22no—
55#13063290—24no—
56#13063290—24no—
57#13063287—24no—
58#13063287—24no—
59C4×C22⋊D43—28no—
60C4×C22⋊D43—28no—
61#13063284—21no—
62#13063284—21no—
63#13063284D412yes—
64#13063284C2312yes—
65#13063283—24no—
66#13063283—24no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—22no—
76C4⋊C4×D43—24no—
77C4⋊C4×D43—24no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—22no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43C2×C414yescomplemented
85C2×C4×Dic43C2312yes—
86#13063259—24no—
87#13063257—24no—
88#13063251C2×C4116yescomplemented
89#13063250—24no—
90#13063247—24no—
91C43⋊#95—28no—
92C23×C4×C43D412yes—
93C23×C4×C43C2311yescharacteristic
94C2×M16×C43—21no—
95C2×M16×C43—22no—
96C2×M16×C43—21no—
97C2×M16×C43—22no—
98C2×M16×C43—22no—
99C2×M16×C43C2×C414yescomplemented
100C2×M16×C43C2312yes—
101C2×M16×C43C2312yes—
102C22×C8×C43—21no—
103C22×C8×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D412yes—
109C2×C4⋊C4×C43C2312yes—
110C24×C43C2×D411yescharacteristic
111C23×D43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—44no—
115C22×C4×C43C22×C412yes—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D414yes—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×Q812yes—
123C22×C4×C43#4112yes—
124C22×C4×C43#4112yes—
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—24no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—22no—
130C22×Dic43—24no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—42no—
137C22×Dic43—42no—
138C22×Dic43—44no—
139C22×Dic43—41no—
140C22×Dic43—41no—
141#10621898—24no—
142#10621898—24no—
143#10621898—24no—
144#10621898—24no—
145#10621898—24no—
146#10621898—22no—
147#10621898—22no—
148#10621898C4⋊C418yes—
149#10621898C22×C414yes—
150#10621898C2×Q814yes—
151C2×D172—21no—
152C2×D172—22no—
153C2×D172C4⋊C414yes—
154C2×D172C2×D412yes—
155C2×C4×D43—24no—
156C2×C4×D43—22no—
157C2×C4×D43—24no—
158C2×C4×D43—22no—
159C2×C4×D43—28no—
160C2×C4×D43—84no—
161C2×Dic86—21no—
162C2×Dic86—22no—
163C2×Dic86C4⋊C414yes—
164C2×Dic86C2×D412yes—
165M16×C43—24no—
166M16×C43—22no—
167M16×C43—22no—
168M16×C43—22no—
169M16×C43—42no—
170M16×C43C22×C414yescomplemented
171C2×C8×C43—24no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—42no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181(C2×D43)⋊C4—28no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D412yes—
189C4⋊Dic43C2×D412yes—
190Dic43⋊C4—28no—
191C4×Dic43—28no—
192C4×Dic43—24no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43C22×C414yescomplemented
197C23×C43—22no—
198C23×C43—22no—
199C23×C43C4×D412yes—
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43C22⋊Q812yes—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—24no—
206C22×D43—42no—
207C22×D43—42no—
208C2×C4×C43—24no—
209C2×C4×C43—44no—
210C2×C4×C43—44no—
211C2×C4×C43—82no—
212C2×C4×C43C2×C4⋊C412yes—
213C2×C4×C43C2×C4⋊C412yes—
214C2×C4×C43C4×D412yes—
215C2×C4×C43C4×D412yes—
216C2×C4×C43C4×D412yes—
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43C22⋊Q812yes—
220C2×C4×C43C22⋊Q812yes—
221C2×C4×C43C22⋊Q812yes—
222C2×C4×C43#12312yes—
223C2×C4×C43#12312yes—
224C2×C4×C43C23×C411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×Q811yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—24no—
231C22⋊D43—24no—
232C22⋊D43—28no—
233C2×Dic43—22no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—48no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—44no—
244C2×Dic43—42no—
245C2×Dic43—82no—
246C2×Dic43—82no—
247D172—22no—
248D172—24no—
249D172C2×C4⋊C414yes—
250C4×D43—24no—
251C4×D43—24no—
252C4×D43—28no—
253C4×D43—88no—
254Dic86—22no—
255Dic86—24no—
256Dic86C2×C4⋊C414yes—
257C8×C43—24no—
258C8×C43—42no—
259C2×#1860—431nomaximal, Sylow
260C22×C43—24no—
261C22×C43—24no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43#38512yes—
267C22×C43#38512yes—
268C22×C43#45412yes—
269C22×C43#45512yes—
270C22×C43C2×C4×D411yescharacteristic
271C22×C43C2×#12011yescharacteristic
272C22×C43C2×C22⋊Q811yescharacteristic
273C2×D43—24no—
274C2×D43—48no—
275C2×D43—42no—
276C2×D43—42no—
277C4×C43—44no—
278C4×C43#38512yes—
279C4×C43#38512yes—
280C4×C43C22×C4⋊C411yescharacteristic
281C4×C43C2×C4×D411yescharacteristic
282C4×C43C2×C22⋊Q811yescharacteristic
283C4×C43C2×#12311yescharacteristic
284Dic43—24no—
285Dic43—44no—
286Dic43—42no—
287Dic43—42no—
288Dic43—82no—
289C2×#520—431no—
290C2×#428—431no—
291C22×#104—431no—
292C2×#417—431no—
293C2×#382—431no—
294#1860—438no—
295C2×#343D4311yescharacteristic, complemented
296C2×#339—431no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—22no—
300C2×C43#186014yescomplemented
301C2×C43C2×#38511yescharacteristic
302C2×C43C2×#45511yescharacteristic
303C2×C43C2×#45411yescharacteristic
304D43—44no—
305C22×#41—431no—
306C22×M16C2×D4311yescharacteristic
307C22×M16C2×D4311yescharacteristic
308#520—434no—
309#520—862no—
310#520—862no—
311#520—862no—
312C2×C4×Q8—861no—
313C2×C4×D4—861no—
314C2×C4×D4—862no—
315C2×#117—431no—
316C2×#117—861no—
317C22×C4⋊C4—431no—
318C22×C4⋊C4—861no—
319C22×C4⋊C4C2×D4311yescharacteristic
320C22×C42—431no—
321#428—434no—
322#428—862no—
323C2×#107—861no—
324C2×#106—861no—
325C2×#104—434no—
326C2×#104—438no—
327#417—434no—
328#417—862no—
329C2×#103—861no—
330C2×#102—861no—
331#382—434no—
332#382—862no—
333C2×#95—862no—
334#343C2×D4314yescomplemented
335#339—434no—
336C43C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—434no—
338C2×#41—432no—
339C2×#41—434no—
340C2×#41—432no—
341C2×#41—861no—
342C2×#41—862no—
343C2×#41—861no—
344C2×#41—862no—
345C22×Q8—431no—
346C22×D4—431no—
347C22×D4—861no—
348C23×C4—862no—
349C23×C4—861no—
350C23×C4—861no—
351C23×C4—861no—
352C23×C4D17212yes—
353C23×C4C22×D4311yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16C4×D4314yescomplemented
360C2×M16C22×D4312yes—
361C2×M16C22×D4312yes—
362C22×C8—21no—
363C22×C8—21no—
364C4×Q8—864no—
365C4×Q8—864no—
366C4×D4—864no—
367C4×D4—864no—
368C4×D4—868no—
369C4×D4—868no—
370#117—432no—
371#117—432no—
372#117—864no—
373#117—864no—
374#117—861no—
375#117—861no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—864no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4D17212yes—
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—861no—
395C2×C42—434no—
396C2×C42—432no—
397C2×C42—862no—
398C2×C42—861no—
399C2×C42—862no—
400C2×C42—861no—
401#107—864no—
402#106—864no—
403#104—4316no—
404#103—864no—
405#102—864no—
406#95—868no—
407C24—861no—
408C24C2×D17211yescharacteristic
409#41—438no—
410#41—434no—
411#41—434no—
412#41—864no—
413#41—864no—
414#41—864no—
415#41—864no—
416#41—864no—
417#41—862no—
418#41—862no—
419C2×Q8—434no—
420C2×Q8—432no—
421C2×Q8—861no—
422C2×Q8—862no—
423C2×D4—434no—
424C2×D4—432no—
425C2×D4—864no—
426C2×D4—862no—
427C2×D4—864no—
428C2×D4—862no—
429C2×D4—861no—
430C2×D4—862no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—868no—
435C22×C4—861no—
436C22×C4—864no—
437C22×C4—862no—
438C22×C4—864no—
439C22×C4—862no—
440C22×C4—864no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—3444no—
446C22×C4—1724no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4C2×C4×D4312yes—
452C22×C4C2×D17214yes—
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189812yes—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4#1062190012yes—
460C22×C4Q8×D4312yes—
461C22×C4C23×D4311yescharacteristic
462M16—24no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—42no—
467M16C2×C4×D4314yescomplemented
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—42no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—432no—
477C4⋊C4—432no—
478C4⋊C4—868no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C22⋊C4—868no—
486C22⋊C4—862no—
487C22⋊C4—862no—
488C42—434no—
489C42—868no—
490C42—864no—
491C42—862no—
492C42—862no—
493C42—862no—
494C23—22no—
495C23—22no—
496C23—862no—
497C23—864no—
498C23—1722no—
499C23—1722no—
500C23C4×D17212yes—
501C23#1306329511yescharacteristic
502C23#1306329511yescharacteristic
503C23#1306330512yes—
504C23C22×D17211yescharacteristic
505Q8—434no—
506Q8—862no—
507Q8—864no—
508D4—434no—
509D4—864no—
510D4—864no—
511D4—868no—
512D4—862no—
513D4—864no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—82no—
518C2×C4—862no—
519C2×C4—864no—
520C2×C4—864no—
521C2×C4—864no—
522C2×C4—868no—
523C2×C4—864no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—3448no—
527C2×C4—3442no—
528C2×C4—3442no—
529C2×C4—1724no—
530C2×C4—1722no—
531C2×C4—1728no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4C4⋊C4×D4312yes—
537C2×C4C4⋊C4×D4312yes—
538C2×C4(C22⋊D43)⋊C412yes—
539C2×C4(C22⋊D43)⋊C412yes—
540C2×C4C4×D17212yes—
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4#1306330312yes—
544C2×C4#1306330312yes—
545C2×C4#1306330512yes—
546C2×C4#1306330712yes—
547C2×C4#1306330712yes—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×D4×D4311yescharacteristic
551C2×C4C2×Q8×D4311yescharacteristic
552C2×C4C2×#1062190011yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C8—24no—
555C8—42no—
556C22—24no—
557C22—24no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—864no—
563C22—1728no—
564C22—1722no—
565C22—1722no—
566C22#1458277312yes—
567C22#1458277312yes—
568C22#1458307412yes—
569C22#1458307912yes—
570C22C2×C4×D17211yescharacteristic
571C22C2×#1306329511yescharacteristic
572C22C2×#1306330511yescharacteristic
573C4—44no—
574C4—864no—
575C4—3442no—
576C4—1724no—
577C4—1722no—
578C4—1722no—
579C4#1458277312yes—
580C4#1458277312yes—
581C4C2×C4⋊C4×D4311yescharacteristic
582C4C2×(C22⋊D43)⋊C411yescharacteristic
583C4C2×#1306330311yescharacteristic
584C4C2×#1306330711yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—1724no—
589C2#1913483114yesdirect product factor
590C2C2×#1458277311yescharacteristic
591C2C2×#1458307911yescharacteristic
592C2C2×#1458307411yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#343D43
hypocenterC43C2×#1860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
5. C2×#14582764C2semidirect
6. #19134831C2direct (N × H)
7. C2×#14582660C2semidirect
8. C2×C43×#343C2semidirect
23. #14582941C22semidirect
26. C2×#13063251C4semidirect
33. #14582764C22semidirect
35. #14582660C22semidirect
39. C43×#343C22semidirect
84. C2×C4×Dic43C2×C4semidirect
88. #13063251C2×C4semidirect
99. C2×M16×C43C2×C4semidirect
170. M16×C43C22×C4semidirect
196. C4×Dic43C22×C4semidirect
295. C2×#343D43semidirect
300. C2×C43#1860semidirect
334. #343C2×D43semidirect
336. C43C2×#1860semidirect
359. C2×M16C4×D43semidirect
467. M16C2×C4×D43semidirect
589. C2#19134831direct (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×#145829412
C22×#130632512
C2×#145829012
C2×#145827642
#191348312
C2×#145826602
C2×C43×#3432
C2×#186043