Finite Group Databasebeta

← C2×#19133139 #25063853

Subgroups — C2×#19133139 #25063853

Order 11008.

1510 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582759C211yesmaximal, characteristic, complemented
3#19133139C218yesmaximal, direct product factor
4C2×#14582637C212yesmaximal, complemented
5C2×#14582634C212yesmaximal, complemented
6C2×C43×#407C211yesmaximal, characteristic, complemented
7C22×#10621898C411yescharacteristic, complemented
8#14583410—22no—
9#14583410—22no—
10#14583410C414yescomplemented
11#14583410C2214yes—
12C2×#13063308—21no—
13C2×#13063304C411yescharacteristic, complemented
14C2×#13063304C2211yescharacteristic
15C2×#13063299C411yescharacteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×#13063294—21no—
18C2×C4×C22⋊D43—21no—
19C2×C4×C22⋊D43—21no—
20C2×#13063284C411yescharacteristic, complemented
21C22×C4⋊Dic43—21no—
22C22×C22⋊Dic43—21no—
23#14582759—22no—
24#14582759C2214yescomplemented
25C2×C43⋊#95C2212yes—
26#14582637C2218yescomplemented
27#14582634C2218yescomplemented
28C24×C4×C43C2211yescharacteristic
29C22×M16×C43—21no—
30C43×#407—22no—
31C43×#407C2214yescomplemented
32C2×C22⋊C8×C43—21no—
33C2×C22⋊C8×C43C2212yes—
34C2×#10621898—22no—
35C2×#10621898—44no—
36C2×#10621898C2×C414yescomplemented
37C22×Dic86C2×C411yescharacteristic
38C22×D172C2×C411yescharacteristic
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C23×Dic43—22no—
43C22×C4×D43—21no—
44#13063308—24no—
45#13063308—24no—
46#13063304—22no—
47#13063304—21no—
48#13063304—21no—
49#13063304C2×C412yes—
50#13063304C2×C414yescomplemented
51#13063304C2312yes—
52#13063299—22no—
53#13063299—21no—
54#13063299—21no—
55#13063299C2×C412yes—
56#13063299C2×C414yescomplemented
57#13063299C2312yes—
58#13063294—24no—
59#13063294—24no—
60C4×C22⋊D43—24no—
61C4×C22⋊D43—24no—
62C4×C22⋊D43—24no—
63C4×C22⋊D43—24no—
64#13063284—22no—
65#13063284C2×C414yescomplemented
66C2×C4⋊Dic43—24no—
67C2×C4⋊Dic43—44no—
68C2×C4⋊Dic43C2×C411yescharacteristic
69C2×C4⋊Dic43C2×C411yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—24no—
76C2×C22⋊Dic43—44no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×C4×Dic43—21no—
80C43⋊#95—22no—
81C43⋊#95C2314yes—
82C25×C43D411yescharacteristic
83C23×C4×C43—44no—
84C23×C4×C43C2×C411yescharacteristic
85C23×C4×C43C2×C411yescharacteristic
86C23×C4×C43C2×C412yes—
87C23×C4×C43D411yescharacteristic
88C23×C4×C43D412yes—
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D412yes—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C2×M16×C43—24no—
95C2×M16×C43—44no—
96C22×C8×C43—22no—
97C22⋊C8×C43—24no—
98C22⋊C8×C43—22no—
99C22⋊C8×C43C2314yes—
100C24×C43—22no—
101C24×C43—22no—
102C24×C43—42no—
103C24×C43—42no—
104C24×C43C22⋊C411yescharacteristic
105C24×C43C22⋊C411yescharacteristic
106C24×C43C22⋊C412yes—
107C24×C43C2×D411yescharacteristic
108C24×C43C2×D412yes—
109C23×D43—21no—
110C22×C4×C43—24no—
111C22×C4×C43—24no—
112C22×C4×C43—24no—
113C22×C4×C43—42no—
114C22×C4×C43—42no—
115C22×C4×C43—42no—
116C22×C4×C43—44no—
117C22×C4×C43—44no—
118C22×C4×C43—44no—
119C22×C4×C43—44no—
120C22×C4×C43C22⋊C411yescharacteristic
121C22×C4×C43C22⋊C412yes—
122C22×C4×C43C22⋊C412yes—
123C22×C4×C43C22⋊C412yes—
124C22×C4×C43C22⋊C412yes—
125C22×C4×C43C22⋊C412yes—
126C22×C4×C43C22⋊C411yescharacteristic
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C411yescharacteristic
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—22no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43—22no—
142C2×C22⋊D43—44no—
143C2×C22⋊D43—44no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—42no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—24no—
150C22×Dic43—44no—
151C22×Dic43—44no—
152C22×Dic43—44no—
153#10621898—48no—
154#10621898—48no—
155C2×D172—21no—
156C2×D172—42no—
157C2×D172C22×C412yes—
158C2×C4×D43—24no—
159C2×C4×D43—44no—
160C2×Dic86—21no—
161C2×Dic86—42no—
162C2×Dic86C22×C412yes—
163M16×C43—48no—
164C2×C8×C43—24no—
165C2×C8×C43—44no—
166C22⋊Dic43—24no—
167C22⋊Dic43—22no—
168C22⋊Dic43—24no—
169C22⋊Dic43—22no—
170C22⋊Dic43—48no—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—48no—
177C4⋊Dic43C22×C412yes—
178C4⋊Dic43C22×C412yes—
179Dic43⋊C4—22no—
180Dic43⋊C4—24no—
181Dic43⋊C4—22no—
182C4×Dic43—24no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—24no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—48no—
199C23×C43—48no—
200C23×C43C2×C22⋊C412yes—
201C23×C43C2×C22⋊C412yes—
202C23×C43C2×C22⋊C411yescharacteristic
203C23×C43C2×C22⋊C411yescharacteristic
204C23×C43AGL(1,ℤ/8)12yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43#9914yes—
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43C2×C22⋊C412yes—
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C412yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C22⋊D43—48no—
236C22⋊D43—48no—
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—44no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—44no—
249C2×Dic43—88no—
250D172—42no—
251D172—42no—
252C4×D43—48no—
253Dic86—42no—
254Dic86—42no—
255C8×C43—44no—
256C2×#1513—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—24no—
262C22×C43—24no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—48no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43C2×#9912yes—
275C22×C43#41712yes—
276C22×C43#41712yes—
277C22×C43#42112yes—
278C22×C43C22×C22⋊C411yescharacteristic
279C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C43C2×#13711yescharacteristic
281C2×D43—42no—
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—84no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—22no—
290C4×C43C2×#9914yes—
291Dic43—42no—
292Dic43—42no—
293Dic43—42no—
294Dic43—84no—
295C2×#525—431no—
296C2×#407D4311yescharacteristic, complemented
297C2×#380—431no—
298#1513—438no—
299C2×#328—432no—
300C2×#327—432no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—22no—
304C2×C43—42no—
305C2×C43—42no—
306C2×C43#151314yescomplemented
307C2×C43C22×#9911yescharacteristic
308C2×C43C2×#41711yescharacteristic
309C2×C43C2×#42111yescharacteristic
310D43—82no—
311C22×#41—431no—
312C24×C4C2×D4311yescharacteristic
313C22×M16—21no—
314#525—434no—
315#525—434no—
316#525—862no—
317#525—862no—
318C2×#123—861no—
319C2×C22⋊Q8—431no—
320C2×C22⋊Q8—431no—
321C2×#121—431no—
322C2×#121—431no—
323C2×#120—861no—
324C2×C4×D4—861no—
325C2×C4×D4—861no—
326C2×#117—431no—
327C22×C4⋊C4—861no—
328C22×C22⋊C4—861no—
329#407—22no—
330#407C2×D4314yescomplemented
331C2×C22⋊C8—21no—
332C2×C22⋊C8C2×D4312yes—
333#380—434no—
334#380—862no—
335C2×#95—432no—
336#328—438no—
337#327—438no—
338C43C2×#151311yescharacteristic, complemented, Sylow
339C25D17211yescharacteristic
340C2×#41—434no—
341C2×#41—862no—
342C2×#41—1724no—
343C22×Q8—431no—
344C22×D4—431no—
345C22×D4—861no—
346C22×D4—861no—
347C22×D4—861no—
348C23×C4—44no—
349C23×C4—861no—
350C23×C4—862no—
351C23×C4C4×D4311yescharacteristic
352C23×C4C4×D4311yescharacteristic
353C23×C4C4×D4312yes—
354C23×C4D17211yescharacteristic
355C23×C4D17212yes—
356C23×C4C22⋊D4311yescharacteristic
357C23×C4C22⋊D4311yescharacteristic
358C23×C4C22⋊D4312yes—
359C23×C4C22×D4311yescharacteristic
360C23×C4C22×D4312yes—
361C2×M16—24no—
362C2×M16—44no—
363C22×C8—22no—
364#123—864no—
365#123—864no—
366C22⋊Q8—432no—
367C22⋊Q8—434no—
368C22⋊Q8—432no—
369C22⋊Q8—862no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—432no—
373#121—434no—
374#121—432no—
375#121—862no—
376#121—861no—
377#121—861no—
378#120—864no—
379#120—864no—
380C4×D4—864no—
381C4×D4—864no—
382C4×D4—864no—
383C4×D4—864no—
384#117—434no—
385#117—862no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—1724no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—864no—
398C2×C22⋊C4—1724no—
399C2×C42—861no—
400C22⋊C8—24no—
401C22⋊C8—22no—
402C22⋊C8C22×D4314yes—
403#95—434no—
404#95—862no—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—861no—
410C24(C2×D43)⋊C411yescharacteristic
411C24(C2×D43)⋊C411yescharacteristic
412C24(C2×D43)⋊C412yes—
413C24C2×D17211yescharacteristic
414C24C2×D17212yes—
415#41—1728no—
416#41—1728no—
417C2×Q8—432no—
418C2×Q8—861no—
419C2×Q8—1722no—
420C2×D4—432no—
421C2×D4—864no—
422C2×D4—862no—
423C2×D4—864no—
424C2×D4—862no—
425C2×D4—861no—
426C2×D4—1722no—
427C2×D4—1724no—
428C2×D4—1724no—
429C2×D4—1722no—
430C2×D4—1722no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—864no—
445C22×C4—864no—
446C22×C4—1724no—
447C22×C4—1724no—
448C22×C4—1724no—
449C22×C4—1724no—
450C22×C4(C2×D43)⋊C412yes—
451C22×C4(C2×D43)⋊C412yes—
452C22×C4(C2×D43)⋊C412yes—
453C22×C4(C2×D43)⋊C411yescharacteristic
454C22×C4(C2×D43)⋊C412yes—
455C22×C4(C2×D43)⋊C412yes—
456C22×C4(C2×D43)⋊C411yescharacteristic
457C22×C4C2×C4×D4312yes—
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4C2×C4×D4312yes—
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4C2×D17212yes—
462C22×C4C2×D17211yescharacteristic
463C22×C4C2×C22⋊D4312yes—
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4312yes—
467C22×C4C23×D4311yescharacteristic
468M16—48no—
469C2×C8—24no—
470C2×C8—44no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—864no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—1728no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—862no—
482C22⋊C4—862no—
483C22⋊C4—864no—
484C22⋊C4—862no—
485C22⋊C4—862no—
486C22⋊C4—1728no—
487C42—864no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—862no—
506C23—1722no—
507C23—1722no—
508C23—1722no—
509C23C2×(C2×D43)⋊C412yes—
510C23C2×(C2×D43)⋊C412yes—
511C23C2×(C2×D43)⋊C411yescharacteristic
512C23C2×(C2×D43)⋊C411yescharacteristic
513C23#1306335312yes—
514C23#1306335812yes—
515C23C22×D17211yescharacteristic
516Q8—1722no—
517Q8—1722no—
518D4—1722no—
519D4—1722no—
520D4—1728no—
521D4—1728no—
522D4—1724no—
523D4—1722no—
524D4—1722no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—3448no—
546C2×C4—1724no—
547C2×C4—1724no—
548C2×C4—1724no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1728no—
553C2×C4#1306323914yes—
554C2×C4C2×(C2×D43)⋊C411yescharacteristic
555C2×C4C2×(C2×D43)⋊C412yes—
556C2×C4C2×(C2×D43)⋊C411yescharacteristic
557C2×C4C2×(C2×D43)⋊C412yes—
558C2×C4C22×C4×D4311yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C8—44no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—44no—
574C22—48no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—3444no—
579C22—1722no—
580C22—1722no—
581C22—1722no—
582C22C2×#1306323912yes—
583C22#1458290112yes—
584C22#1458290112yes—
585C22#1458291512yes—
586C22C22×(C2×D43)⋊C411yescharacteristic
587C22C2×#1306335311yescharacteristic
588C22C2×#1306335811yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—3444no—
595C4—1722no—
596C4—1722no—
597C4—1722no—
598C4C2×#1306323914yes—
599C2—21no—
600C2—22no—
601C2—21no—
602C2—42no—
603C2—42no—
604C2—3442no—
605C2#1913313914yesdirect product factor
606C2C22×#1306323911yescharacteristic
607C2C2×#1458290111yescharacteristic
608C2C2×#1458291511yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43C2×#1513
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582759C2semidirect
3. #19133139C2direct (N × H)
4. C2×#14582637C2semidirect
5. C2×#14582634C2semidirect
6. C2×C43×#407C2semidirect
7. C22×#10621898C4semidirect
10. #14583410C4semidirect
13. C2×#13063304C4semidirect
15. C2×#13063299C4semidirect
20. C2×#13063284C4semidirect
24. #14582759C22semidirect
26. #14582637C22semidirect
27. #14582634C22semidirect
31. C43×#407C22semidirect
36. C2×#10621898C2×C4semidirect
50. #13063304C2×C4semidirect
56. #13063299C2×C4semidirect
65. #13063284C2×C4semidirect
296. C2×#407D43semidirect
306. C2×C43#1513semidirect
330. #407C2×D43semidirect
338. C43C2×#1513semidirect
605. C2#19133139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145827592
#191331392
C2×#145826372
C2×#145826342
C2×C43×#4072
C2×#151343