Finite Group Databasebeta

← C2×#19134911 #25097796

Subgroups — C2×#19134911 #25097796

Order 11008.

2614 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063300C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4C22×#13063245C211yesmaximal, characteristic, complemented
5C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
6#19134911C218yesmaximal, direct product factor
7C2×#14582661C211yesmaximal, characteristic, complemented
8C2×C43×#340C211yesmaximal, characteristic, complemented
9C23×D172—21no—
10C23×D172C2211yescharacteristic
11C23×C4×D43—21no—
12C23×C4×D43C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063300—24no—
15C2×#13063300—22no—
16C2×#13063300C418yescomplemented
17C2×#13063300C2214yes—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4—21no—
20C2×C4⋊C4×D43—22no—
21C2×C4⋊C4×D43—24no—
22C2×C4⋊C4×D43—24no—
23C2×C4⋊C4×D43C2214yescomplemented
24C22×(C2×D43)⋊C4—21no—
25C2×#13063247—24no—
26C2×#13063247C2214yescomplemented
27C2×#13063245—24no—
28C2×#13063245C2214yescomplemented
29C2×(C2×D43)⋊C8—24no—
30C2×(C2×D43)⋊C8C2214yescomplemented
31#14582661C2214yescomplemented
32C23×C8×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#340C2214yescomplemented
36C24×D43—21no—
37C24×D43D411yescharacteristic
38C22×D172—22no—
39C22×D172—22no—
40C22×D172—22no—
41C22×D172—22no—
42C22×D172—28no—
43C22×D172—24no—
44C22×D172—21no—
45C22×D172—22no—
46C22×D172—44no—
47C22×D172—44no—
48C22×D172C2×C414yescomplemented
49C22×D172C2312yes—
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43—28no—
57C22×C4×D43—24no—
58C22×C4×D43—44no—
59C22×C4×D43—44no—
60C22×C4×D43C2×C414yes—
61C22×C4×D43D412yes—
62C22×C4×D43D414yes—
63C22×C4×D43C2312yes—
64C22×C43⋊C8—22no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8C2312yes—
68#13063300—216no—
69#13063300—28no—
70#13063300C2×C4116yescomplemented
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D414yescomplemented
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—28no—
76C2×Dic43⋊C4—24no—
77C4⋊C4×D43—216no—
78C4⋊C4×D43—28no—
79C4⋊C4×D43—28no—
80C2×(C2×D43)⋊C4—28no—
81C2×(C2×D43)⋊C4—24no—
82#13063247—28no—
83#13063245—28no—
84(C2×D43)⋊C8—28no—
85C23×C4×C43—21no—
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C22×C8×C43—22no—
89C22×C8×C43—22no—
90C22×C8×C43—22no—
91C22×C8×C43C2312yes—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43C2×C414yescomplemented
97C2×C4⋊C4×C43D414yescomplemented
98C2×C4⋊C4×C43C2312yes—
99C2×C4⋊C4×C43C2312yes—
100C24×C43C2×D411yescharacteristic
101C23×D43—22no—
102C23×D43—22no—
103C23×D43—22no—
104C23×D43—22no—
105C23×D43—24no—
106C23×D43—22no—
107C23×D43—42no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43—42no—
111C23×D43—42no—
112C23×D43—42no—
113C23×D43C22⋊C414yes—
114C23×D43D814yes—
115C23×D43SD1614yes—
116C23×D43C2×D412yes—
117C22×C4×C43—24no—
118C22×C4×C43—24no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—22no—
134C22×Dic43—24no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43C22⋊C414yes—
140C22×Dic43C2×D412yes—
141C2×D172—24no—
142C2×D172—22no—
143C2×D172—216no—
144C2×D172—28no—
145C2×D172—28no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—22no—
150C2×D172—42no—
151C2×D172—44no—
152C2×D172—44no—
153C2×D172—42no—
154C2×D172—432no—
155C2×D172—48no—
156C2×D172—48no—
157C2×D172C22×C414yescomplemented
158C2×C4×D43—28no—
159C2×C4×D43—28no—
160C2×C4×D43—24no—
161C2×C4×D43—28no—
162C2×C4×D43—28no—
163C2×C4×D43—24no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—216no—
169C2×C4×D43—48no—
170C2×C4×D43—432no—
171C2×C4×D43—48no—
172C2×C4×D43C22⋊C418yes—
173C2×C4×D43C22×C414yes—
174C2×C4×D43C2×D414yes—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—44no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—24no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C414yescomplemented
184C4⋊C4×C43C2×D414yescomplemented
185(C2×D43)⋊C4—216no—
186C4⋊Dic43—24no—
187C4⋊Dic43—22no—
188C4⋊Dic43C2×D414yescomplemented
189Dic43⋊C4—216no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—44no—
194C23×C43C2×C22⋊C412yes—
195C23×C43#12012yes—
196C23×C43#12312yes—
197C23×C43C2×D812yes—
198C23×C43C2×SD1612yes—
199C23×C43AGL(1,ℤ/8)12yes—
200C23×C43#13712yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—28no—
207C22×D43—28no—
208C22×D43—28no—
209C22×D43—28no—
210C22×D43—28no—
211C22×D43—28no—
212C22×D43—24no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—48no—
220C22×D43—48no—
221C22×D43—48no—
222C22×D43—84no—
223C22×D43—84no—
224C22×D43—84no—
225C22×D43—84no—
226C22×D43#102116yescomplemented
227C22×D43C2×C22⋊C414yes—
228C22×D43C2×D814yes—
229C22×D43C2×SD1614yes—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—48no—
237C2×C4×C43—48no—
238C2×C4×C43C2×C22⋊C412yes—
239C2×C4×C43C4×D414yes—
240C2×C4×C43C4×D414yes—
241C2×C4×C43#12012yes—
242C2×C4×C43#12114yes—
243C2×C4×C43#12114yes—
244C2×C4×C43#12312yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—28no—
254C2×Dic43—24no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—48no—
258C2×Dic43C2×C22⋊C414yes—
259D172—24no—
260D172—24no—
261D172—432no—
262D172—42no—
263D172—42no—
264D172—48no—
265C4×D43—24no—
266C4×D43—24no—
267C4×D43—24no—
268C4×D43—24no—
269C4×D43—216no—
270C4×D43—432no—
271C8×C43—42no—
272C43⋊C8—42no—
273C2×#1874—431nomaximal, Sylow
274C22×C43#38614yes—
275C22×C43C2×#10214yes—
276C22×C43#41714yes—
277C22×C43#44714yes—
278C22×C43#44814yes—
279C22×C43#48014yes—
280C22×C43#48114yes—
281C22×C43C22×C22⋊C411yescharacteristic
282C22×C43C2×#12011yescharacteristic
283C22×C43C2×#12311yescharacteristic
284C22×C43C22×D811yescharacteristic
285C22×C43C22×SD1611yescharacteristic
286C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C2×D43—24no—
289C2×D43—24no—
290C2×D43—24no—
291C2×D43—232no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—44no—
296C2×D43—44no—
297C2×D43—44no—
298C2×D43—82no—
299C2×D43—82no—
300C2×D43—816no—
301C2×D43—82no—
302C2×D43—82no—
303C2×D43C2×#10218yescomplemented
304C4×C43—44no—
305C4×C43—44no—
306C4×C43#38614yes—
307C4×C43C2×C4×D411yescharacteristic
308C4×C43C2×C4×D411yescharacteristic
309C4×C43C2×#12111yescharacteristic
310C4×C43C2×#12111yescharacteristic
311Dic43—24no—
312Dic43—44no—
313C22×#121—431no—
314C23×C4⋊C4—431no—
315C22×#102—431no—
316C22×#102—431no—
317C22×C22⋊C8—431no—
318#1874—438no—
319C2×#340—431no—
320C2×#340D4311yescharacteristic, complemented
321C2×C43#187418yescomplemented
322C2×C43C2×#38611yescharacteristic
323C2×C43C22×#10211yescharacteristic
324C2×C43C2×#41711yescharacteristic
325C2×C43C2×#44711yescharacteristic
326C2×C43C2×#44811yescharacteristic
327C2×C43C2×#48011yescharacteristic
328C2×C43C2×#48111yescharacteristic
329D43—28no—
330D43—84no—
331C23×D4—431no—
332C23×D4—861no—
333C24×C4—431no—
334C24×C4—861no—
335C23×C8—431no—
336C23×C8C2×D4311yescharacteristic
337C2×#121—434no—
338C2×#121—438no—
339C2×#121—862no—
340C2×#121—864no—
341C22×C4⋊C4—431no—
342C22×C4⋊C4—434no—
343C22×C4⋊C4—864no—
344C22×C4⋊C4—862no—
345C22×C4⋊C4—861no—
346C22×C4⋊C4—864no—
347C22×C4⋊C4C2×D4311yescharacteristic
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C22⋊C4—861no—
350C2×#102—434no—
351C2×#102—434no—
352C2×#102—864no—
353C2×#102—864no—
354C2×C22⋊C8—434no—
355C2×C22⋊C8—864no—
356#340—434no—
357#340C2×D4314yescomplemented
358C43C2×#187411yescharacteristic, complemented, Sylow
359C25—431no—
360C25—861no—
361C22×D4—434no—
362C22×D4—432no—
363C22×D4—868no—
364C22×D4—864no—
365C22×D4—862no—
366C22×D4—862no—
367C22×D4—862no—
368C22×D4—861no—
369C22×D4—862no—
370C22×D4—862no—
371C22×D4—1724no—
372C22×D4—1724no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—431no—
376C23×C4—434no—
377C23×C4—432no—
378C23×C4—434no—
379C23×C4—432no—
380C23×C4—864no—
381C23×C4—868no—
382C23×C4—862no—
383C23×C4—862no—
384C23×C4—862no—
385C23×C4—862no—
386C23×C4—861no—
387C23×C4—1724no—
388C23×C4—1724no—
389C23×C4C22×D4311yescharacteristic
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—432no—
394C22×C8—862no—
395C22×C8—862no—
396C22×C8—862no—
397C22×C8C22×D4312yes—
398#121—4316no—
399#121—8616no—
400#121—868no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—434no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—868no—
408C2×C4⋊C4—8616no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—868no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—868no—
414C2×C4⋊C4C4×D4314yescomplemented
415C2×C4⋊C4D17214yescomplemented
416C2×C4⋊C4C22×D4312yes—
417C2×C4⋊C4C22×D4312yes—
418C2×C22⋊C4—868no—
419C2×C22⋊C4—864no—
420#102—868no—
421#102—868no—
422C22⋊C8—868no—
423C24—434no—
424C24—434no—
425C24—434no—
426C24—432no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—864no—
432C24—862no—
433C24—1722no—
434C24—1722no—
435C24—1722no—
436C24—1722no—
437C24—1722no—
438C24—1722no—
439C24D4×D4311yescharacteristic
440C2×D4—434no—
441C2×D4—8616no—
442C2×D4—864no—
443C2×D4—868no—
444C2×D4—868no—
445C2×D4—862no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—862no—
450C2×D4—17232no—
451C2×D4—1728no—
452C2×D4—1728no—
453C2×D4—1722no—
454C2×D4—1724no—
455C2×D4—1724no—
456C2×D4—1722no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—434no—
466C22×C4—432no—
467C22×C4—438no—
468C22×C4—434no—
469C22×C4—434no—
470C22×C4—8616no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—868no—
474C22×C4—868no—
475C22×C4—864no—
476C22×C4—868no—
477C22×C4—868no—
478C22×C4—864no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—864no—
484C22×C4—862no—
485C22×C4—1728no—
486C22×C4—1728no—
487C22×C4—17232no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4C2×C4×D4312yes—
491C22×C4C2×D17212yes—
492C22×C4#1062189812yes—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4312yes—
495C22×C4D4×D4312yes—
496C22×C4#1062190212yes—
497C22×C4C23×D4311yescharacteristic
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—44no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—1724no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—434no—
511C4⋊C4—8616no—
512C4⋊C4—864no—
513C4⋊C4—862no—
514C4⋊C4C2×C4×D4314yescomplemented
515C4⋊C4C2×D17214yescomplemented
516C22⋊C4—8616no—
517C23—434no—
518C23—4316no—
519C23—434no—
520C23—434no—
521C23—862no—
522C23—862no—
523C23—868no—
524C23—862no—
525C23—862no—
526C23—868no—
527C23—868no—
528C23—868no—
529C23—868no—
530C23—868no—
531C23—864no—
532C23—3444no—
533C23—3444no—
534C23—3444no—
535C23—3444no—
536C23—1722no—
537C23—1728no—
538C23—1722no—
539C23—1728no—
540C23—1722no—
541C23—1722no—
542C23—1722no—
543C23—1722no—
544C23—1728no—
545C23C22⋊C4×D4312yes—
546C23#1306329512yes—
547C23#1306331012yes—
548C23D8×D4312yes—
549C23SD16×D4312yes—
550C23#1306335212yes—
551C23#1306335712yes—
552C23C2×D4×D4311yescharacteristic
553D4—864no—
554D4—864no—
555D4—17232no—
556D4—1722no—
557D4—1722no—
558D4—1728no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—48no—
567C2×C4—434no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—868no—
571C2×C4—864no—
572C2×C4—864no—
573C2×C4—864no—
574C2×C4—864no—
575C2×C4—8616no—
576C2×C4—864no—
577C2×C4—17232no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1728no—
581C2×C4C22⋊C4×D4312yes—
582C2×C4#1306328714yes—
583C2×C4C4×D17214yes—
584C2×C4#1306329512yes—
585C2×C4#1306329814yes—
586C2×C4#1306330014yes—
587C2×C4#1306331012yes—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C22×D17211yescharacteristic
592C2×C4C2×#1062189811yescharacteristic
593C2×C4C2×#1062190211yescharacteristic
594C8—42no—
595C8—1722no—
596C22—438no—
597C22—864no—
598C22—864no—
599C22—864no—
600C22—864no—
601C22—8632no—
602C22—864no—
603C22—864no—
604C22—3442no—
605C22—3442no—
606C22—3442no—
607C22—3442no—
608C22—34416no—
609C22—1724no—
610C22—1724no—
611C22—1724no—
612C22#1458277714yes—
613C22#102×D4314yes—
614C22#1458289914yes—
615C22#1458303414yes—
616C22#1458303914yes—
617C22#1458321414yes—
618C22#1458321914yes—
619C22C2×C22⋊C4×D4311yescharacteristic
620C22C2×#1306329511yescharacteristic
621C22C2×#1306331011yescharacteristic
622C22C2×D8×D4311yescharacteristic
623C22C2×SD16×D4311yescharacteristic
624C22C2×#1306335211yescharacteristic
625C22C2×#1306335711yescharacteristic
626C4—44no—
627C4—44no—
628C4—864no—
629C4—1724no—
630C4#1458277714yes—
631C4C2×#1306328711yescharacteristic
632C4C2×C4×D17211yescharacteristic
633C4C2×#1306329811yescharacteristic
634C4C2×#1306330011yescharacteristic
635C2—868no—
636C2—3444no—
637C2#1913491118yesdirect product factor
638C2C2×#1458277711yescharacteristic
639C2C2×#102×D4311yescharacteristic
640C2C2×#1458289911yescharacteristic
641C2C2×#1458303411yescharacteristic
642C2C2×#1458303911yescharacteristic
643C2C2×#1458321411yescharacteristic
644C2C2×#1458321911yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
prime radicalC22×#13063300C2
cosocleC22×C4×C43C24
hypercenterC2×#340D43
hypocenterC43C2×#1874
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. C22×#13063247C2semidirect
4. C22×#13063245C2semidirect
5. C22×(C2×D43)⋊C8C2semidirect
6. #19134911C2direct (N × H)
7. C2×#14582661C2semidirect
8. C2×C43×#340C2semidirect
16. C2×#13063300C4semidirect
23. C2×C4⋊C4×D43C22semidirect
26. C2×#13063247C22semidirect
28. C2×#13063245C22semidirect
30. C2×(C2×D43)⋊C8C22semidirect
31. #14582661C22semidirect
35. C43×#340C22semidirect
48. C22×D172C2×C4semidirect
70. #13063300C2×C4semidirect
73. C2×C4⋊Dic43D4semidirect
96. C2×C4⋊C4×C43C2×C4semidirect
97. C2×C4⋊C4×C43D4semidirect
157. C2×D172C22×C4semidirect
183. C4⋊C4×C43C22×C4semidirect
184. C4⋊C4×C43C2×D4semidirect
188. C4⋊Dic43C2×D4semidirect
226. C22×D43#102semidirect
303. C2×D43C2×#102semidirect
320. C2×#340D43semidirect
321. C2×C43#1874semidirect
357. #340C2×D43semidirect
358. C43C2×#1874semidirect
414. C2×C4⋊C4C4×D43semidirect
415. C2×C4⋊C4D172semidirect
514. C4⋊C4C2×C4×D43semidirect
515. C4⋊C4C2×D172semidirect
637. C2#19134911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633002
C22×C4⋊C4×D432
C22×#130632472
C22×#130632452
C22×(C2×D43)⋊C82
#191349112
C2×#145826612
C2×C43×#3402
C2×#187443