Finite Group Databasebeta

← C4×#14583262 #25104666

Subgroups — C4×#14583262 #25104666

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583262C211yesmaximal, characteristic
2C4×#13063321C211yesmaximal, characteristic
3C4×#13063316C211yesmaximal, characteristic, complemented
4#19135562C211yesmaximal, characteristic, complemented
5#19135417C211yesmaximal, characteristic
6#19135294C211yesmaximal, characteristic, complemented
7#19135293C211yesmaximal, characteristic, complemented
8#19135290C211yesmaximal, characteristic, complemented
9#19135289C211yesmaximal, characteristic, complemented
10#19134727C211yesmaximal, characteristic, complemented
11C4×#13063245C211yesmaximal, characteristic, complemented
12C4×#13063247C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14C4×#13063235C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C2×#13063321C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×C4×C22⋊D43—21no—
21#14583262C418yesdirect product factor
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582799—21no—
36#14582799—21no—
37#14582798C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582786—21no—
40#14582782—21no—
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×C4⋊Dic43—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46C42×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063321—22no—
67#13063321C2×C414yes—
68#13063316—22no—
69#13063316C2×C414yescomplemented
70C4×D172—22no—
71C4×D172—22no—
72C4×C22⋊D43—44no—
73C4×C22⋊D43—44no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063247—22no—
96#13063247C2×C414yescomplemented
97#13063246—22no—
98#13063246C2×C414yescomplemented
99#13063245—22no—
100#13063245C2×C414yescomplemented
101#13063235—22no—
102#13063235—22no—
103#13063235—22no—
104#13063235C2×C414yescomplemented
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43C2×C414yescomplemented
125C4×C8×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22×C412yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—24no—
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43—42no—
149C2×C22⋊D43—42no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C412yes—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C412yes—
171C2×C8×C43#4112yes—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C22×C412yes—
178C22⋊C4×C43—42no—
179C42×C43—42no—
180C42×C43#4112yes—
181C42×C43#4112yes—
182C22⋊Dic43—42no—
183C22⋊Dic43—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—24no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C4×Dic43—41no—
205C4×Dic43—42no—
206C4×Dic43C22×C412yes—
207C4×Dic43#4112yes—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C22×C412yes—
213C2×C43⋊C8#4112yes—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—84no—
245C2×C4×C43#12412yes—
246C2×C4×C43#12412yes—
247C2×C4×C43AGL(1,ℤ/8)12yes—
248C2×C4×C43AGL(1,ℤ/8)12yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C22⋊D43—48no—
256C22⋊D43—48no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43C4×D412yes—
277C2×Dic43C4×D412yes—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283C8×C43—22no—
284C8×C43—22no—
285C43⋊C8—22no—
286C43⋊C8—22no—
287C4×#490—431nomaximal, Sylow
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×C4×D411yescharacteristic
296C22×C43C2×#12411yescharacteristic
297C22×C43#53211yescharacteristic
298C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57511yescharacteristic
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43#49014yescomplemented
314C4×C43C4×#4111yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#52911yescharacteristic
318Dic43—22no—
319Dic43—22no—
320Dic43—41no—
321Dic43—41no—
322Dic43—42no—
323Dic43—81no—
324Dic43—81no—
325C2×#490—431no—
326C4×#127—431no—
327C4×#125—431no—
328#1992—431no—
329#1961—431no—
330#1936—431no—
331#1936—431no—
332#1936—431no—
333#1936—431no—
334#1836—431no—
335C4×#102—431no—
336C4×#102—431no—
337C4×#102—431no—
338C4×#102D4311yescharacteristic, complemented
339C4×#97—431no—
340C2×C43—82no—
341C2×C43C4×#12411yescharacteristic
342C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
344C2×C43C2×#49011yescharacteristic
345C2×C43#313511yescharacteristic
346C2×C43#317111yescharacteristic
347C2×C43#317111yescharacteristic
348D43—82no—
349C2×#127—431no—
350C2×#125—431no—
351C2×C4×D4—431no—
352C2×C4×D4—861no—
353C2×C4×D4—861no—
354C2×C4×D4C2×D4311yescharacteristic
355#490—438no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—431no—
362C2×#102C2×D4311yescharacteristic
363C2×#102C2×D4311yescharacteristic
364C2×#97—431no—
365C2×#97—431no—
366C2×#97—431no—
367C2×#97—431no—
368C2×C4×C8—431no—
369C2×C4×C8C2×D4311yescharacteristic
370#390—431no—
371#390—431no—
372#390—861no—
373#390—861no—
374#389—431no—
375#389—431no—
376#387—861no—
377#387—861no—
378#384—431no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4C2×D4311yescharacteristic
384C43—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#340C2×D4311yescharacteristic
393C43C4×#49011yescharacteristic, complemented, Sylow
394C22×D4—431no—
395C22×D4—861no—
396C22×D4—861no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—21no—
399C23×C4—861no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#127—434no—
405#127—862no—
406#125—434no—
407#125—862no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—1724no—
413C4×D4—1724no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—21no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441#102—22no—
442#102—434no—
443#102—434no—
444#102—434no—
445#102—862no—
446#102—862no—
447#102—862no—
448#102C4×D4314yescomplemented
449#97—434no—
450#97—862no—
451#97—862no—
452#97—862no—
453C4×C8—22no—
454C4×C8—862no—
455#95—21no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461C24—21no—
462C24—861no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—864no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4C2×C4×D4312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8C2×C4×D4312yes—
511C2×C8#1062189812yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—432no—
518C4⋊C4—864no—
519C4⋊C4—864no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4—1722no—
529C4⋊C4C2×C4×D4312yes—
530C22⋊C4—42no—
531C22⋊C4—1722no—
532C22⋊C4—1722no—
533C22⋊C4—1722no—
534C22⋊C4—1722no—
535C22⋊C4—1722no—
536C42—42no—
537C42—432no—
538C42—432no—
539C42—862no—
540C42—862no—
541C42—861no—
542C42—861no—
543C42—1721no—
544C42—1721no—
545C42—1722no—
546C42#1062189812yes—
547C42#1062190012yes—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—862no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23C2×D4×D4311yescharacteristic
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—862no—
568D4—862no—
569D4—1728no—
570D4—1728no—
571D4—1721no—
572D4—1721no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—84no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—3444no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4#1306331112yes—
608C2×C4#1306331112yes—
609C2×C4#1306334912yes—
610C2×C4#1306335212yes—
611C2×C4C22×C4×D4311yescharacteristic
612C2×C4#41×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4C2×#1062190011yescharacteristic
615C2×C4C2×#1062189811yescharacteristic
616C2×C4C2×#1062189811yescharacteristic
617C8—22no—
618C8—22no—
619C8—862no—
620C8—862no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22—1722no—
633C22—1722no—
634C22—1722no—
635C22C4×D4×D4311yescharacteristic
636C22C2×#1306331111yescharacteristic
637C22#1458344611yescharacteristic
638C22C2×#1306334911yescharacteristic
639C22C2×#1306335211yescharacteristic
640C22#1458369611yescharacteristic
641C22#1458369611yescharacteristic
642C4—22no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—3441no—
650C4—1721no—
651C4—1721no—
652C4—1722no—
653C4#1458326214yesdirect product factor
654C4C4×#1062190011yescharacteristic
655C4C4×#1062189811yescharacteristic
656C4#1458342711yescharacteristic
657C4#1458342911yescharacteristic
658C2—82no—
659C2—3442no—
660C2C4×#1306331111yescharacteristic
661C2C4×#1306334911yescharacteristic
662C2C4×#1306335211yescharacteristic
663C2C2×#1458326211yescharacteristic
664C2#1914493811yescharacteristic
665C2#1914518611yescharacteristic
666C2#1914518811yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43C4×#490
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C4×#13063316C2semidirect
4. #19135562C2semidirect
6. #19135294C2semidirect
7. #19135293C2semidirect
8. #19135290C2semidirect
9. #19135289C2semidirect
10. #19134727C2semidirect
11. C4×#13063245C2semidirect
12. C4×#13063247C2semidirect
13. C4×#13063246C2semidirect
14. C4×#13063235C2semidirect
15. C4×#102×C43C2semidirect
21. #14583262C4direct (N × H)
69. #13063316C2×C4semidirect
96. #13063247C2×C4semidirect
98. #13063246C2×C4semidirect
100. #13063245C2×C4semidirect
104. #13063235C2×C4semidirect
124. #102×C43C2×C4semidirect
313. C4×C43#490semidirect
338. C4×#102D43semidirect
393. C43C4×#490semidirect
448. #102C4×D43semidirect
653. C4#14583262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832622
C4×#130633212
C4×#130633162
#191355622
#191354172
#191352942
#191352932
#191352902
#191352892
#191347272
C4×#130632452
C4×#130632472
C4×#130632462
C4×#130632352
C4×#102×C432
C4×#49043