Finite Group Databasebeta

← C4×#11718456 #15870983

Subgroups — C4×#11718456 #15870983

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718456C211yesmaximal, characteristic
2C4×#88142C211yesmaximal, characteristic, complemented
3C4×#88201C211yesmaximal, characteristic
4#13115807C211yesmaximal, characteristic, complemented
5#13115649C211yesmaximal, characteristic
6#13115534C211yesmaximal, characteristic
7#13115531C211yesmaximal, characteristic
8#13115528C211yesmaximal, characteristic, complemented
9#13115523C211yesmaximal, characteristic, complemented
10#13114968C211yesmaximal, characteristic, complemented
11C4×#88075C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic
13C4×#88061C211yesmaximal, characteristic
14C4×#88055C211yesmaximal, characteristic, complemented
15C4×C13×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88201C2211yescharacteristic
18C2×#88142C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C4×Dic26—21no—
21C2×C13×#103C2211yescharacteristic
22C2×C13×#103C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×#88055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34#11718651—21no—
35#11718651—21no—
36#11718649C2211yescharacteristic
37#11718646C2211yescharacteristic
38#11718638C2211yescharacteristic
39#11718637C2211yescharacteristic
40#11718634C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C4×#6103—21no—
44C4×#6103—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46C4×#6101—21no—
47C42×Dic13C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718456C418yesdirect product factor
50#11718308—21no—
51#11718307—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C22×Dic26—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75#88201—22no—
76#88201C2×C414yes—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13D411yescharacteristic
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88142—22no—
100#88142C2×C414yescomplemented
101C4×D52—22no—
102C4×D52—22no—
103C4×Dic26—44no—
104C13×#103—22no—
105C13×#103C2×C414yescomplemented
106C4×C8×C13—22no—
107C13×#95—21no—
108#88075—22no—
109#88075C2×C414yescomplemented
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88061—22no—
118#88061C2×C414yes—
119#88055—22no—
120#88055—22no—
121#88055—22no—
122#88055C2×C414yescomplemented
123#88049—22no—
124#88049C2×C414yes—
125C4×#1055—22no—
126C4×#489—131nomaximal, Sylow
127C23×D13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C2×D52—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52C22×C412yes—
154C2×C4×D13—42no—
155C2×C4×D13—42no—
156C2×C4×D13—42no—
157C2×Dic26—24no—
158C2×Dic26—42no—
159C2×Dic26—42no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C412yes—
165C2×C8×C13#4112yes—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4C22×C412yes—
173C42×C13—42no—
174C42×C13—42no—
175C42×C13#4112yes—
176C42×C13#4112yes—
177#6103—24no—
178#6103—24no—
179#6103—42no—
180#6103—42no—
181#6103—42no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13C22×C412yes—
189#6101—24no—
190#6101—42no—
191#6101—42no—
192#6101—42no—
193C4×Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—41no—
198C4×Dic13—41no—
199C4×Dic13—42no—
200C4×Dic13C22×C412yes—
201C4×Dic13#4112yes—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C412yes—
207C2×#1055#4112yes—
208C2×#489—131no—
209C4×C4⋊Q8—131no—
210C4×#124—131no—
211#1993—131no—
212#1959—131no—
213#1936—131no—
214#1936—131no—
215#1935—131no—
216#1935—131no—
217#1836—131no—
218C4×#103—131no—
219C4×#103D1311yescharacteristic, complemented
220C4×#102—131no—
221C4×#102—131no—
222C4×#97—131no—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—41no—
234Q8×C13—41no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13#12412yes—
250C2×C4×C13#12412yes—
251C2×C4×C13AGL(1,ℤ/8)12yes—
252C2×C4×C13#13712yes—
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—22no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13C4×D412yes—
279C2×Dic13C4×D412yes—
280D52—22no—
281D52—22no—
282D52—41no—
283D52—41no—
284C4×D13—84no—
285Dic26—48no—
286C8×C13—22no—
287C8×C13—22no—
288#1055—22no—
289#1055—22no—
290C2×C4⋊Q8—131no—
291C2×#124—131no—
292C2×C4×Q8—261no—
293C2×C4×Q8C2×D1311yescharacteristic
294C2×C4×D4—131no—
295#489—138no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103C2×D1311yescharacteristic
299C2×#103C2×D1311yescharacteristic
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#97—131no—
305C2×#97—131no—
306C2×#97—131no—
307C2×#97—131no—
308C2×C4×C8—131no—
309C2×C4×C8C2×D1311yescharacteristic
310#391—131no—
311#391—261no—
312#390—131no—
313#389—131no—
314#389—131no—
315#389—261no—
316#388—261no—
317#388—261no—
318#384—131no—
319#382—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—261no—
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C22⋊C4—261no—
324C4×C22⋊C4—261no—
325C43—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340C2×D1311yescharacteristic
333#340C2×D1311yescharacteristic
334C22×C13C2×C4×D411yescharacteristic
335C22×C13C2×#12411yescharacteristic
336C22×C13#53211yescharacteristic
337C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C13C2×#13711yescharacteristic
339C22×C13#57511yescharacteristic
340C22×C13#57511yescharacteristic
341C2×D13—42no—
342C2×D13—42no—
343C2×D13—42no—
344C2×D13—81no—
345C2×D13—81no—
346C2×D13—81no—
347C2×D13—81no—
348C4×C13—22no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13#48914yescomplemented
354C4×C13C4×#4111yescharacteristic
355C4×C13C4×#4111yescharacteristic
356C4×C13#52911yescharacteristic
357C4×C13#52911yescharacteristic
358Dic13—22no—
359Dic13—22no—
360Dic13—41no—
361Dic13—41no—
362Dic13—42no—
363Dic13—81no—
364Dic13—81no—
365C22×Q8—261no—
366C22×Q8C22×D1311yescharacteristic
367C22×D4—131no—
368C23×C4—261no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8C22×D1311yescharacteristic
372C22×C8C22×D1311yescharacteristic
373C4⋊Q8—134no—
374C4⋊Q8—262no—
375#124—134no—
376#124—262no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—524no—
380C4×D4—262no—
381C4×D4—262no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—261no—
408C2×C42C22×D1311yescharacteristic
409#103—22no—
410#103—134no—
411#103—262no—
412#103C4×D1314yescomplemented
413#102—134no—
414#102—134no—
415#102—262no—
416#102—262no—
417#97—134no—
418#97—262no—
419#97—262no—
420#97—262no—
421C4×C8—22no—
422C4×C8—262no—
423#95—21no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431C2×C13C4×#12411yescharacteristic
432C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
433C2×C13C4×#13711yescharacteristic
434C2×C13C2×#48911yescharacteristic
435C2×C13#313511yescharacteristic
436C2×C13#317111yescharacteristic
437C2×C13#317211yescharacteristic
438D13—82no—
439C24—261no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—264no—
446C2×Q8—522no—
447C2×Q8—522no—
448C2×Q8C2×C4×D1312yes—
449C2×D4—132no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4—261no—
454C2×D4—261no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—522no—
467C22×C4—522no—
468C22×C4—522no—
469C22×C4D4×D1311yescharacteristic
470C22×C4D4×D1311yescharacteristic
471C22×C4C23×D1311yescharacteristic
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—132no—
477C2×C8—132no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8C2×C4×D1312yes—
483C2×C8#612712yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—132no—
491C4⋊C4—264no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4C2×C4×D1312yes—
502C22⋊C4—264no—
503C22⋊C4—264no—
504C22⋊C4—522no—
505C22⋊C4—522no—
506C22⋊C4—522no—
507C42—42no—
508C42—42no—
509C42—132no—
510C42—132no—
511C42—262no—
512C42—262no—
513C42—261no—
514C42—261no—
515C42—521no—
516C42—521no—
517C42—522no—
518C42#612712yes—
519C42#612912yes—
520C13C4×#48911yescharacteristic, complemented, Sylow
521C23—262no—
522C23—521no—
523C23—521no—
524C23—521no—
525C23—521no—
526C23—521no—
527C23—521no—
528C23C2×D4×D1311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—528no—
534D4—262no—
535D4—262no—
536D4—521no—
537D4—521no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—262no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—1044no—
574C2×C4#8813912yes—
575C2×C4#8813912yes—
576C2×C4#8816812yes—
577C2×C4#8817212yes—
578C2×C4C22×C4×D1311yescharacteristic
579C2×C4C2×#612711yescharacteristic
580C2×C4C2×#612711yescharacteristic
581C2×C4C2×#612911yescharacteristic
582C2×C4#41×D1311yescharacteristic
583C2×C4#41×D1311yescharacteristic
584C8—22no—
585C8—22no—
586C8—262no—
587C8—262no—
588C22—522no—
589C22—522no—
590C22—522no—
591C22—1041no—
592C22—1041no—
593C22—1041no—
594C22—1041no—
595C22C2×#8813911yescharacteristic
596C22C4×D4×D1311yescharacteristic
597C22#1171925311yescharacteristic
598C22C2×#8816811yescharacteristic
599C22C2×#8817211yescharacteristic
600C22#1171947311yescharacteristic
601C22#1171947311yescharacteristic
602C4—22no—
603C4—42no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—262no—
608C4—262no—
609C4—521no—
610C4—522no—
611C4—521no—
612C4—1041no—
613C4—1041no—
614C4#1171845614yesdirect product factor
615C4C4×#612711yescharacteristic
616C4#1171923311yescharacteristic
617C4C4×#612911yescharacteristic
618C4#1171924311yescharacteristic
619C2—1042no—
620C2C4×#8813911yescharacteristic
621C2C4×#8816811yescharacteristic
622C2C4×#8817211yescharacteristic
623C2C2×#1171845611yescharacteristic
624C2#1312517911yescharacteristic
625C2#1312542711yescharacteristic
626C2#1312544011yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#103C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#103D13
hypocenterC13C4×#489
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C4×#88142C2semidirect
4. #13115807C2semidirect
8. #13115528C2semidirect
9. #13115523C2semidirect
10. #13114968C2semidirect
11. C4×#88075C2semidirect
14. C4×#88055C2semidirect
15. C4×C13×#103C2semidirect
49. #11718456C4direct (N × H)
100. #88142C2×C4semidirect
105. C13×#103C2×C4semidirect
109. #88075C2×C4semidirect
122. #88055C2×C4semidirect
219. C4×#103D13semidirect
353. C4×C13#489semidirect
412. #103C4×D13semidirect
520. C13C4×#489semidirect
614. C4#11718456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117184562
C4×#881422
C4×#882012
#131158072
#131156492
#131155342
#131155312
#131155282
#131155232
#131149682
C4×#880752
C4×#880492
C4×#880612
C4×#880552
C4×C13×#1032
C4×#48913