Finite Group Databasebeta

← C2×#19144522 #25964379

Subgroups — C2×#19144522 #25964379

Order 11008.

2650 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583412C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#19144522C2116yesmaximal, direct product factor
4C2×#14583232C211yesmaximal, characteristic, complemented
5C2×#14583218C211yesmaximal, characteristic, complemented
6C2×#14583217C211yesmaximal, characteristic, complemented
7C2×#14583228C212yesmaximal, complemented
8C2×#14583214C212yesmaximal, complemented
9C2×#14582940C212yesmaximal, complemented
10C2×#14582899C212yesmaximal, complemented
11C2×#14582861C211yesmaximal, characteristic, complemented
12C2×C43×#484C211yesmaximal, characteristic, complemented
13C22×#10621902C2211yescharacteristic
14C23×C4×D43—21no—
15C23×C4×D43C2211yescharacteristic
16C22×#10621872C2212yes—
17#14583412—24no—
18#14583412C2218yes—
19C2×#13063310—21no—
20C2×#13063301C2211yescharacteristic
21C2×#13063300C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063295—21no—
24C2×#13063287—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊C4—21no—
29C2×C4⋊C4×D43—24no—
30C2×C4⋊C4×D43—21no—
31C2×C4⋊C4×D43—21no—
32C2×C4⋊C4×D43C2212yes—
33C2×C4⋊C4×D43C2212yes—
34C2×C4⋊C4×D43C2218yescomplemented
35#14583232C2218yescomplemented
36#14583228C22116yescomplemented
37#14583218C2218yescomplemented
38#14583217C2218yescomplemented
39#14583214C22116yescomplemented
40#14582940C22116yescomplemented
41C2×#13063258C2212yescomplemented
42C2×#13063257C2212yescomplemented
43C2×#13063256C2212yescomplemented
44#14582899C22116yescomplemented
45C2×#13063249C2212yescomplemented
46C2×#13063247C2212yescomplemented
47C2×#13063245C2212yescomplemented
48#14582861C2218yescomplemented
49C2×C22⋊(C43⋊C8)C2211yescharacteristic
50C2×(C2×D43)⋊C8C2212yes—
51C2×C22⋊Q8×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C43×#484C2218yescomplemented
54C2×#107×C43C2212yescomplemented
55C2×#103×C43C2212yescomplemented
56C2×C22⋊C8×C43C2211yescharacteristic
57C24×D43D411yescharacteristic
58C2×#10621902—22no—
59C2×#10621902—28no—
60C2×#10621902C2314yes—
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C23×Dic43D411yescharacteristic
67C22×C4×D43—28no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—28no—
71C22×C4×D43—21no—
72C22×C4×D43—48no—
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D414yes—
76C22×C4×D43C2311yescharacteristic
77C22×C4×D43C2314yes—
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—28no—
80C2×#10621872C2318yes—
81C22×C43⋊C8C2312yes—
82#13063310—28no—
83#13063301—22no—
84#13063301C2314yes—
85#13063300—22no—
86#13063300C2314yes—
87#13063299—22no—
88#13063299C2314yes—
89#13063295—28no—
90#13063287—28no—
91(C22⋊D43)⋊C4—28no—
92#13063283—22no—
93#13063283C2314yes—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43C2312yes—
97C2×C4⋊Dic43C2314yes—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—28no—
102C2×Dic43⋊C4—21no—
103C4⋊C4×D43—24no—
104C4⋊C4×D43—24no—
105C4⋊C4×D43—28no—
106C4⋊C4×D43—28no—
107C4⋊C4×D43C2318yes—
108C4⋊C4×D43C2318yes—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114#13063258C2318yescomplemented
115#13063257C2318yescomplemented
116#13063256C2318yescomplemented
117#13063249C2318yescomplemented
118#13063247C2318yescomplemented
119#13063245C2318yescomplemented
120C22⋊(C43⋊C8)C2314yes—
121(C2×D43)⋊C8C2318yes—
122C22×Q8×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C22×C8×C43C2312yes—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43C2314yes—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2312yes—
132C2×C4⋊C4×C43C2314yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135#107×C43C2318yescomplemented
136#103×C43C2318yescomplemented
137C22⋊C8×C43C2314yes—
138C24×C43C2×D411yescharacteristic
139C23×D43—24no—
140C23×D43—24no—
141C23×D43—24no—
142C23×D43—21no—
143C23×D43C2×D414yes—
144C23×D43C2×D411yescharacteristic
145C23×D43C2×D411yescharacteristic
146C2×Q8×C43—21no—
147C2×Q8×C43—24no—
148C2×Q8×C43C2412yes—
149C22×C4×C43—24no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—24no—
153C22×C4×C43—22no—
154C22×C4×C43—44no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2412yes—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—44no—
161C22×Dic43—24no—
162C22×Dic43—21no—
163C22×Dic43—24no—
164C22×Dic43—22no—
165C22×Dic43—44no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D414yes—
168C22×Dic43C2×D411yescharacteristic
169#10621902—216no—
170#10621902—48no—
171C2×D172—21no—
172C2×D172—24no—
173C2×D172—24no—
174C2×D172—24no—
175C2×D172—44no—
176C2×D172—44no—
177C2×D172C2412yes—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—216no—
181C2×C4×D43—216no—
182C2×C4×D43—24no—
183C2×C4×D43—24no—
184C2×C4×D43—28no—
185C2×C4×D43—28no—
186C2×C4×D43—48no—
187C2×C4×D43—432no—
188C2×C4×D43—44no—
189C2×C4×D43—48no—
190C2×C4×D43C2×D414yes—
191C2×C4×D43C2×D412yes—
192C2×C4×D43C2×D414yes—
193C2×C4×D43C2×D412yes—
194C2×C4×D43#4118yes—
195C2×C4×D43C2412yes—
196C2×C4×D43C2412yes—
197C2×C8×C43—24no—
198C2×C8×C43C2414yes—
199C4⋊C4×C43—24no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43C2414yes—
204C4⋊C4×C43C2412yes—
205C22⋊C4×C43—24no—
206(C2×D43)⋊C4—24no—
207(C2×D43)⋊C4—24no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—24no—
210C4⋊Dic43—24no—
211C4⋊Dic43—22no—
212C4⋊Dic43—21no—
213C4⋊Dic43C2414yes—
214C4⋊Dic43C2412yes—
215Dic43⋊C4—28no—
216Dic43⋊C4—28no—
217Dic43⋊C4—24no—
218C4×Dic43—24no—
219C2×C43⋊C8—24no—
220C2×C43⋊C8C2414yes—
221#10621872—216no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43#13714yes—
225C23×C43C22×D412yes—
226C23×C43C22×D411yescharacteristic
227C22×D43—232no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—28no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—28no—
234C22×D43—28no—
235C22×D43—22no—
236C22×D43—42no—
237C22×D43—42no—
238C22×D43—42no—
239C22×D43#12314yes—
240C22×D43AGL(1,ℤ/8)14yes—
241C22×D43C22×D412yes—
242C22×D43C22×D412yes—
243Q8×C43—24no—
244Q8×C43—42no—
245C2×C4×C43—22no—
246C2×C4×C43—24no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—24no—
250C2×C4×C43—22no—
251C2×C4×C43—48no—
252C2×C4×C43—42no—
253C2×C4×C43—44no—
254C2×C4×C43—42no—
255C2×C4×C43C22×D412yes—
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4114yes—
258C2×C4×C43C2511yescharacteristic
259C22⋊D43—48no—
260C2×Dic43—22no—
261C2×Dic43—28no—
262C2×Dic43—22no—
263C2×Dic43—24no—
264C2×Dic43—48no—
265C2×Dic43—44no—
266C2×Dic43—42no—
267C2×Dic43#12314yes—
268C2×Dic43C22×D412yes—
269C2×Dic43C22×D412yes—
270D172—24no—
271D172—48no—
272D172—48no—
273D172—42no—
274C4×D43—28no—
275C4×D43—24no—
276C4×D43—24no—
277C4×D43—28no—
278C4×D43—416no—
279C4×D43—416no—
280C4×D43—48no—
281C4×D43#12318yes—
282C4×D43C2×#4118yes—
283C8×C43—24no—
284C43⋊C8—24no—
285C2×#3092—431nomaximal, Sylow
286C22×C43—28no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43C2×#12312yes—
290C22×C43C2×AGL(1,ℤ/8)12yes—
291C22×C43C2×#13714yes—
292C22×C43C2×#13712yes—
293C22×C43C23×D411yescharacteristic
294C2×D43—232no—
295C2×D43—28no—
296C2×D43—28no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—84no—
305C2×D43C2×#12314yes—
306C2×D43C2×AGL(1,ℤ/8)14yes—
307C4×C43—22no—
308C4×C43—42no—
309C4×C43—44no—
310C4×C43—42no—
311C4×C43C2×#12312yes—
312C4×C43C22×#4112yes—
313Dic43—22no—
314Dic43—44no—
315Dic43—42no—
316Dic43C2×#12314yes—
317C2×#525—431no—
318C23×C4⋊C4—431no—
319#3092—4316no—
320C2×#484—431no—
321C2×#484D4311yescharacteristic, complemented
322C2×#481—431no—
323C2×#481—431no—
324C2×#483—432no—
325C2×#480—432no—
326C2×#428—432no—
327C2×#417—432no—
328C2×#407—431no—
329C2×C43—24no—
330C2×C43#309214yescomplemented
331C2×C43C22×#12311yescharacteristic
332C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
333C2×C43C22×#13711yescharacteristic
334D43—24no—
335D43—24no—
336D43—82no—
337C22×#41—431no—
338C24×C4—431no—
339C24×C4—861no—
340C22×M16—432no—
341#525—438no—
342#525—864no—
343C2×#123—861no—
344C2×C22⋊Q8—431no—
345C2×C22⋊Q8C2×D4311yescharacteristic
346C2×#121—431no—
347C2×#121—431no—
348C2×#120—861no—
349C2×C4×D4—861no—
350C2×C4×D4—861no—
351C2×#117—431no—
352C22×C4⋊C4—431no—
353C22×C4⋊C4—432no—
354C22×C4⋊C4—438no—
355C22×C4⋊C4—432no—
356C22×C4⋊C4—861no—
357C22×C4⋊C4—861no—
358C22×C4⋊C4—864no—
359C22×C4⋊C4—861no—
360C22×C4⋊C4C2×D4311yescharacteristic
361#484—438no—
362#484C2×D4318yescomplemented
363#483—4316no—
364#481—438no—
365#481—438no—
366#480—4316no—
367#428—4316no—
368C2×#107—432no—
369C2×#107C2×D4312yescomplemented
370C2×#106—432no—
371C2×#106—432no—
372#417—4316no—
373C2×#103—432no—
374C2×#103C2×D4312yescomplemented
375C2×#102—432no—
376C2×#102—432no—
377#407—438no—
378C2×C22⋊C8—431no—
379C2×C22⋊C8—432no—
380C2×C22⋊C8C2×D4311yescharacteristic
381C43C2×#309211yescharacteristic, complemented, Sylow
382C25—431no—
383C2×#41—434no—
384C2×#41—862no—
385C2×#41—868no—
386C22×Q8C22×D4311yescharacteristic
387C22×D4—431no—
388C22×D4—861no—
389C22×D4—861no—
390C22×D4—861no—
391C23×C4—21no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C23×C4—431no—
396C23×C4—434no—
397C23×C4—431no—
398C23×C4—434no—
399C23×C4—868no—
400C23×C4—861no—
401C23×C4—868no—
402C23×C4—862no—
403C23×C4—862no—
404C23×C4—861no—
405C23×C4—1728no—
406C23×C4C22×D4311yescharacteristic
407C2×M16—438no—
408C2×M16—868no—
409C22×C8—432no—
410C22×C8C22×D4312yes—
411#123—868no—
412C22⋊Q8—22no—
413C22⋊Q8—434no—
414C22⋊Q8—862no—
415C22⋊Q8C22×D4314yes—
416#121—434no—
417#121—434no—
418#121—862no—
419#121—862no—
420#120—868no—
421C4×D4—868no—
422C4×D4—868no—
423#117—434no—
424#117—862no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—432no—
429C2×C4⋊C4—434no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—438no—
432C2×C4⋊C4—438no—
433C2×C4⋊C4—864no—
434C2×C4⋊C4—868no—
435C2×C4⋊C4—864no—
436C2×C4⋊C4—868no—
437C2×C4⋊C4—868no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—862no—
440C2×C4⋊C4—861no—
441C2×C4⋊C4—862no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4312yes—
444C2×C4⋊C4C22×D4314yes—
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C42—861no—
452#107—438no—
453#107C22×D4318yescomplemented
454#106—438no—
455#106—438no—
456#103—438no—
457#103C22×D4318yescomplemented
458#102—438no—
459#102—438no—
460C22⋊C8—434no—
461C22⋊C8—438no—
462C22⋊C8C22×D4314yes—
463C24—431no—
464C24—431no—
465C24—434no—
466C24—864no—
467C24—864no—
468C24—864no—
469C24—861no—
470C24D4×D4311yescharacteristic
471#41—8616no—
472#41—1728no—
473C2×Q8—21no—
474C2×Q8—24no—
475C2×Q8C23×D4312yes—
476C2×D4—432no—
477C2×D4—864no—
478C2×D4—864no—
479C2×D4—864no—
480C2×D4—861no—
481C2×D4—864no—
482C2×D4—1724no—
483C2×D4—1724no—
484C2×D4—1724no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—44no—
491C22×C4—431no—
492C22×C4—432no—
493C22×C4—438no—
494C22×C4—432no—
495C22×C4—434no—
496C22×C4—431no—
497C22×C4—434no—
498C22×C4—432no—
499C22×C4—434no—
500C22×C4—432no—
501C22×C4—864no—
502C22×C4—8616no—
503C22×C4—8616no—
504C22×C4—864no—
505C22×C4—864no—
506C22×C4—868no—
507C22×C4—868no—
508C22×C4—864no—
509C22×C4—864no—
510C22×C4—864no—
511C22×C4—861no—
512C22×C4—862no—
513C22×C4—1724no—
514C22×C4—1728no—
515C22×C4—17232no—
516C22×C4—1728no—
517C22×C4—1724no—
518C22×C4D4×D4312yes—
519C22×C4D4×D4311yescharacteristic
520C22×C4C23×D4312yes—
521C22×C4C23×D4311yescharacteristic
522M16—8616no—
523C2×C8—24no—
524C2×C8—434no—
525C2×C8—864no—
526C2×C8C23×D4314yes—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—434no—
532C4⋊C4—432no—
533C4⋊C4—868no—
534C4⋊C4—868no—
535C4⋊C4—864no—
536C4⋊C4—864no—
537C4⋊C4—862no—
538C4⋊C4—861no—
539C4⋊C4C23×D4314yes—
540C4⋊C4C23×D4312yes—
541C22⋊C4—24no—
542C22⋊C4—864no—
543C22⋊C4—864no—
544C22⋊C4—864no—
545C22⋊C4—864no—
546C42—864no—
547C23—22no—
548C23—22no—
549C23—434no—
550C23—434no—
551C23—432no—
552C23—432no—
553C23—868no—
554C23—868no—
555C23—8632no—
556C23—862no—
557C23—862no—
558C23—868no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1722no—
563C23—1722no—
564C23—1722no—
565C23#1306335714yes—
566C23C2×D4×D4312yes—
567C23C2×D4×D4311yescharacteristic
568Q8—24no—
569Q8—42no—
570D4—864no—
571D4—1728no—
572D4—1728no—
573D4—1728no—
574D4—1722no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—48no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—434no—
586C2×C4—432no—
587C2×C4—438no—
588C2×C4—438no—
589C2×C4—432no—
590C2×C4—868no—
591C2×C4—868no—
592C2×C4—868no—
593C2×C4—862no—
594C2×C4—864no—
595C2×C4—864no—
596C2×C4—862no—
597C2×C4—864no—
598C2×C4—1728no—
599C2×C4—17216no—
600C2×C4—17216no—
601C2×C4—1728no—
602C2×C4—1724no—
603C2×C4—1722no—
604C2×C4C2×D4×D4312yes—
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4#41×D4314yes—
607C2×C4C24×D4311yescharacteristic
608C8—24no—
609C8—864no—
610C22—22no—
611C22—22no—
612C22—28no—
613C22—434no—
614C22—434no—
615C22—8632no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—862no—
620C22—868no—
621C22—868no—
622C22—3444no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22#123×D4312yes—
627C22AGL(1,ℤ/8)×D4312yes—
628C22C2×#1306335714yes—
629C22C2×#1306335712yes—
630C22C22×D4×D4311yescharacteristic
631C4—22no—
632C4—44no—
633C4—42no—
634C4—42no—
635C4—434no—
636C4—862no—
637C4—1724no—
638C4—1722no—
639C4#123×D4312yes—
640C4C2×#41×D4312yes—
641C2—24no—
642C2—864no—
643C2—864no—
644C2—3442no—
645C2#1914452214yesdirect product factor
646C2C2×#123×D4311yescharacteristic
647C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
648C2C22×#1306335711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#484C2
socleC23×C43C22×D4
prime radicalC2×#14583412C2
hypercenterC2×#484D43
hypocenterC43C2×#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. #19144522C2direct (N × H)
4. C2×#14583232C2semidirect
5. C2×#14583218C2semidirect
6. C2×#14583217C2semidirect
7. C2×#14583228C2semidirect
8. C2×#14583214C2semidirect
9. C2×#14582940C2semidirect
10. C2×#14582899C2semidirect
11. C2×#14582861C2semidirect
12. C2×C43×#484C2semidirect
34. C2×C4⋊C4×D43C22semidirect
35. #14583232C22semidirect
36. #14583228C22semidirect
37. #14583218C22semidirect
38. #14583217C22semidirect
39. #14583214C22semidirect
40. #14582940C22semidirect
41. C2×#13063258C22semidirect
42. C2×#13063257C22semidirect
43. C2×#13063256C22semidirect
44. #14582899C22semidirect
45. C2×#13063249C22semidirect
46. C2×#13063247C22semidirect
47. C2×#13063245C22semidirect
48. #14582861C22semidirect
53. C43×#484C22semidirect
54. C2×#107×C43C22semidirect
55. C2×#103×C43C22semidirect
114. #13063258C23semidirect
115. #13063257C23semidirect
116. #13063256C23semidirect
117. #13063249C23semidirect
118. #13063247C23semidirect
119. #13063245C23semidirect
135. #107×C43C23semidirect
136. #103×C43C23semidirect
321. C2×#484D43semidirect
330. C2×C43#3092semidirect
362. #484C2×D43semidirect
369. C2×#107C2×D43semidirect
374. C2×#103C2×D43semidirect
381. C43C2×#3092semidirect
453. #107C22×D43semidirect
457. #103C22×D43semidirect
645. C2#19144522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834122
C22×C4⋊C4×D432
#191445222
C2×#145832322
C2×#145832182
C2×#145832172
C2×#145832282
C2×#145832142
C2×#145829402
C2×#145828992
C2×#145828612
C2×C43×#4842
C2×#309243