Finite Group Databasebeta

← C2×#19134824 #25097454

Subgroups — C2×#19134824 #25097454

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×#14582941C211yesmaximal, characteristic, complemented
3C22×#13063251C211yesmaximal, characteristic
4C2×#14582901C211yesmaximal, characteristic
5C2×#14582768C211yesmaximal, characteristic, complemented
6#19134824C218yesmaximal, 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
20C22×Dic43⋊C4—22no—
21C2×C4⋊C4×D43—21no—
22C22×C4×Dic43C2211yescharacteristic
23#14582941—22no—
24#14582941C2214yescomplemented
25C2×#13063259—21no—
26C2×#13063257—21no—
27C2×#13063251C418yescomplemented
28C2×#13063251C2214yes—
29#14582901—22no—
30#14582901C2214yes—
31C2×#13063250—21no—
32C2×#13063247—21no—
33#14582768—22no—
34#14582768C2214yescomplemented
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—
76C2×Dic43⋊C4—28no—
77C2×Dic43⋊C4—48no—
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—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43C2×C414yescomplemented
87C2×C4×Dic43C2312yes—
88#13063259—24no—
89#13063257—24no—
90#13063251C2×C4116yescomplemented
91#13063250—24no—
92#13063247—24no—
93C23×C4×C43D412yes—
94C23×C4×C43C2311yescharacteristic
95C2×M16×C43—21no—
96C2×M16×C43—22no—
97C2×M16×C43—21no—
98C2×M16×C43—22no—
99C2×M16×C43—22no—
100C2×M16×C43C2×C414yescomplemented
101C2×M16×C43C2312yes—
102C2×M16×C43C2312yes—
103C22×C8×C43—21no—
104C22×C8×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43D412yes—
110C2×C4⋊C4×C43C2312yes—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—44no—
116C22×C4×C43C22×C412yes—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D414yes—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×Q812yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—24no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—22no—
131C22×Dic43—24no—
132C22×Dic43—24no—
133C22×Dic43—24no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—44no—
140C22×Dic43—41no—
141C22×Dic43—41no—
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—
166M16×C43—24no—
167M16×C43—22no—
168M16×C43—22no—
169M16×C43—22no—
170M16×C43—42no—
171M16×C43C22×C414yescomplemented
172C2×C8×C43—24no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—42no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182(C2×D43)⋊C4—28no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D412yes—
190C4⋊Dic43C2×D412yes—
191Dic43⋊C4—28no—
192Dic43⋊C4—416no—
193C4×Dic43—28no—
194C4×Dic43—24no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43C22×C414yescomplemented
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—44no—
212C2×C4×C43—44no—
213C2×C4×C43—82no—
214C2×C4×C43C2×C4⋊C412yes—
215C2×C4×C43C2×C4⋊C412yes—
216C2×C4×C43C4×D412yes—
217C2×C4×C43C4×D412yes—
218C2×C4×C43C4×D412yes—
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43C22⋊Q812yes—
222C2×C4×C43C22⋊Q812yes—
223C2×C4×C43C22⋊Q812yes—
224C2×C4×C43#12312yes—
225C2×C4×C43#12312yes—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—24no—
233C22⋊D43—24no—
234C22⋊D43—28no—
235C2×Dic43—24no—
236C2×Dic43—216no—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—44no—
246C2×Dic43—42no—
247C2×Dic43—82no—
248C2×Dic43—82no—
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
259C8×C43—24no—
260C8×C43—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—44no—
280C4×C43#38512yes—
281C4×C43#38512yes—
282C4×C43C22×C4⋊C411yescharacteristic
283C4×C43C2×C4×D411yescharacteristic
284C4×C43C2×C22⋊Q811yescharacteristic
285C4×C43C2×#12311yescharacteristic
286Dic43—28no—
287Dic43—24no—
288Dic43—42no—
289Dic43—42no—
290Dic43—82no—
291C2×#520—431no—
292C2×#428—431no—
293C22×#104—431no—
294C2×#417—431no—
295C2×#384—431no—
296#1859—438no—
297C2×#343D4311yescharacteristic, complemented
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×M16C2×D4311yescharacteristic
309C22×M16C2×D4311yescharacteristic
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—431no—
320C22×C4⋊C4—861no—
321C22×C4⋊C4—862no—
322C22×C4⋊C4C2×D4311yescharacteristic
323C22×C42—431no—
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—434no—
335#384—862no—
336#343C2×D4314yescomplemented
337#339—434no—
338C43C2×#185911yescharacteristic, complemented, Sylow
339C2×#41—434no—
340C2×#41—432no—
341C2×#41—434no—
342C2×#41—432no—
343C2×#41—861no—
344C2×#41—862no—
345C2×#41—861no—
346C2×#41—862no—
347C22×Q8—431no—
348C22×D4—431no—
349C22×D4—861no—
350C23×C4—862no—
351C23×C4—861no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4D17212yes—
355C23×C4C22×D4311yescharacteristic
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16C4×D4314yescomplemented
362C2×M16C22×D4312yes—
363C2×M16C22×D4312yes—
364C22×C8—21no—
365C22×C8—21no—
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—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—432no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—868no—
394C2×C4⋊C4—1728no—
395C2×C4⋊C4D17212yes—
396C2×C4⋊C4C22×D4312yes—
397C2×C22⋊C4—862no—
398C2×C22⋊C4—861no—
399C2×C42—434no—
400C2×C42—432no—
401C2×C42—862no—
402C2×C42—861no—
403C2×C42—862no—
404C2×C42—861no—
405#107—864no—
406#106—864no—
407#104—4316no—
408#103—864no—
409#102—864no—
410C24—861no—
411C24C2×D17211yescharacteristic
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—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—868no—
438C22×C4—864no—
439C22×C4—864no—
440C22×C4—864no—
441C22×C4—861no—
442C22×C4—862no—
443C22×C4—864no—
444C22×C4—862no—
445C22×C4—864no—
446C22×C4—862no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—862no—
450C22×C4—3444no—
451C22×C4—1724no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4C2×C4×D4312yes—
455C22×C4C2×D17214yes—
456C22×C4C2×D17211yescharacteristic
457C22×C4#1062189812yes—
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4#1062190012yes—
463C22×C4Q8×D4312yes—
464C22×C4C23×D4311yescharacteristic
465M16—24no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—42no—
470M16C2×C4×D4314yescomplemented
471C2×C8—24no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—42no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—432no—
480C4⋊C4—432no—
481C4⋊C4—868no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—17216no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C22⋊C4—868no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C42—434no—
493C42—868no—
494C42—864no—
495C42—862no—
496C42—862no—
497C42—862no—
498C23—22no—
499C23—22no—
500C23—862no—
501C23—864no—
502C23—1722no—
503C23—1722no—
504C23C4×D17212yes—
505C23#1306329511yescharacteristic
506C23#1306329511yescharacteristic
507C23#1306330512yes—
508C23C22×D17211yescharacteristic
509Q8—434no—
510Q8—862no—
511Q8—864no—
512D4—434no—
513D4—864no—
514D4—864no—
515D4—868no—
516D4—862no—
517D4—864no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—82no—
522C2×C4—864no—
523C2×C4—864no—
524C2×C4—8616no—
525C2×C4—864no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—864no—
529C2×C4—864no—
530C2×C4—868no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—3448no—
534C2×C4—3442no—
535C2×C4—3442no—
536C2×C4—1724no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4C4⋊C4×D4312yes—
541C2×C4C4⋊C4×D4312yes—
542C2×C4(C22⋊D43)⋊C412yes—
543C2×C4(C22⋊D43)⋊C412yes—
544C2×C4C4×D17212yes—
545C2×C4#1306329511yescharacteristic
546C2×C4#1306329511yescharacteristic
547C2×C4#1306330312yes—
548C2×C4#1306330312yes—
549C2×C4#1306330512yes—
550C2×C4#1306330712yes—
551C2×C4#1306330712yes—
552C2×C4C22×C4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×Q8×D4311yescharacteristic
556C2×C4C2×#1062190011yescharacteristic
557C2×C4C2×#1062189811yescharacteristic
558C8—24no—
559C8—42no—
560C22—21no—
561C22—21no—
562C22—24no—
563C22—24no—
564C22—21no—
565C22—21no—
566C22—864no—
567C22—1722no—
568C22—1728no—
569C22—1722no—
570C22#1458277312yes—
571C22#1458277312yes—
572C22#1458306912yes—
573C22#1458308412yes—
574C22C2×C4×D17211yescharacteristic
575C22C2×#1306329511yescharacteristic
576C22C2×#1306330511yescharacteristic
577C4—44no—
578C4—868no—
579C4—864no—
580C4—3442no—
581C4—1722no—
582C4—1722no—
583C4#1458277312yes—
584C4#1458277312yes—
585C4C2×C4⋊C4×D4311yescharacteristic
586C4C2×(C22⋊D43)⋊C411yescharacteristic
587C4C2×#1306330311yescharacteristic
588C4C2×#1306330711yescharacteristic
589C2—21no—
590C2—21no—
591C2—22no—
592C2—1724no—
593C2#1913482414yesdirect product factor
594C2C2×#1458277311yescharacteristic
595C2C2×#1458306911yescharacteristic
596C2C2×#1458308411yescharacteristic
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×#1859
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×#14582768C2semidirect
6. #19134824C2direct (N × H)
7. C2×#14582660C2semidirect
8. C2×C43×#343C2semidirect
24. #14582941C22semidirect
27. C2×#13063251C4semidirect
34. #14582768C22semidirect
35. #14582660C22semidirect
39. C43×#343C22semidirect
86. C2×C4×Dic43C2×C4semidirect
90. #13063251C2×C4semidirect
100. C2×M16×C43C2×C4semidirect
149. #10621898C4⋊C4semidirect
154. C2×D172C4⋊C4semidirect
164. C2×Dic86C4⋊C4semidirect
171. M16×C43C22×C4semidirect
198. C4×Dic43C22×C4semidirect
251. D172C2×C4⋊C4semidirect
258. Dic86C2×C4⋊C4semidirect
297. C2×#343D43semidirect
302. C2×C43#1859semidirect
336. #343C2×D43semidirect
338. C43C2×#1859semidirect
361. C2×M16C4×D43semidirect
470. M16C2×C4×D43semidirect
593. C2#19134824direct (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×#145827682
#191348242
C2×#145826602
C2×C43×#3432
C2×#185943