Finite Group Databasebeta

← C4×#11718425 #15870988

Subgroups — C4×#11718425 #15870988

Order 3328.

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×#11718425C211yesmaximal, characteristic
2C4×#88194C211yesmaximal, characteristic
3C4×#88144C211yesmaximal, characteristic, complemented
4#13115803C211yesmaximal, characteristic, complemented
5#13115658C211yesmaximal, characteristic
6#13115535C211yesmaximal, characteristic, complemented
7#13115534C211yesmaximal, characteristic, complemented
8#13115531C211yesmaximal, characteristic, complemented
9#13115530C211yesmaximal, characteristic, complemented
10#13114968C211yesmaximal, characteristic, complemented
11C4×#88049C211yesmaximal, characteristic, complemented
12C4×#88061C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14C4×#88055C211yesmaximal, characteristic, complemented
15C4×C13×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88194C2211yescharacteristic
18C2×C4×C22⋊D13—21no—
19C2×C4×C22⋊D13—21no—
20C2×#88144C2211yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26#11718882C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88061C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×#88055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35#11718649C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718638C2211yescharacteristic
38#11718637C2211yescharacteristic
39#11718634C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42#11718618—21no—
43#11718618—21no—
44C4×C4⋊Dic13—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46C4×#6101—21no—
47C42×Dic13C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718425C418yesdirect product factor
50#11718316—21no—
51#11718315—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C22×C22⋊D13—21no—
63C22×C22⋊D13—21no—
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78#88194—22no—
79#88194C2×C414yes—
80C4×C22⋊D13—44no—
81C4×C22⋊D13—44no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13D411yescharacteristic
98C2×C4×Dic13D411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103#88144—22no—
104#88144C2×C414yescomplemented
105C4×D52—22no—
106C4×D52—22no—
107C13×#102—22no—
108C13×#102C2×C414yescomplemented
109C4×C8×C13—22no—
110C13×#95—21no—
111#88072—22no—
112#88072C2×C414yescomplemented
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88061—22no—
119#88061C2×C414yescomplemented
120#88055—22no—
121#88055—22no—
122#88055—22no—
123#88055C2×C414yescomplemented
124#88049—22no—
125#88049C2×C414yescomplemented
126C4×#1055—22no—
127C4×#490—131nomaximal, Sylow
128C24×C13—21no—
129C23×D13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13C22×C412yes—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C2×C22⋊D13—24no—
146C2×C22⋊D13—24no—
147C2×C22⋊D13—42no—
148C2×C22⋊D13—42no—
149C2×C22⋊D13—42no—
150C2×C22⋊D13—42no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52C22×C412yes—
164C2×C4×D13—42no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C22×C412yes—
172C2×C8×C13#4112yes—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C412yes—
179C13×C22⋊C4—42no—
180C42×C13—42no—
181C42×C13#4112yes—
182C42×C13#4112yes—
183C22⋊Dic13—42no—
184C22⋊Dic13—42no—
185#6103—42no—
186#6103—42no—
187#6103—42no—
188C4⋊Dic13—21no—
189C4⋊Dic13—24no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—42no—
195C4⋊Dic13C22×C412yes—
196#6101—24no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—41no—
205C4×Dic13—41no—
206C4×Dic13—42no—
207C4×Dic13C22×C412yes—
208C4×Dic13#4112yes—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055C22×C412yes—
214C2×#1055#4112yes—
215C2×#490—131no—
216C4×#127—131no—
217C4×#125—131no—
218#1992—131no—
219#1961—131no—
220#1936—131no—
221#1936—131no—
222#1936—131no—
223#1936—131no—
224#1836—131no—
225C4×#102—131no—
226C4×#102—131no—
227C4×#102—131no—
228C4×#102D1311yescharacteristic, complemented
229C4×#97—131no—
230C23×C13—22no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13C22×D411yescharacteristic
238C22×D13—22no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245D4×C13—22no—
246D4×C13—22no—
247D4×C13—41no—
248D4×C13—41no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—84no—
261C2×C4×C13#12412yes—
262C2×C4×C13#12412yes—
263C2×C4×C13AGL(1,ℤ/8)12yes—
264C2×C4×C13AGL(1,ℤ/8)12yes—
265C2×C4×C13C23×C411yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C22⋊D13—48no—
272C22⋊D13—48no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—22no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13C4×D412yes—
293C2×Dic13C4×D412yes—
294D52—22no—
295D52—22no—
296D52—41no—
297D52—41no—
298C4×D13—84no—
299C8×C13—22no—
300C8×C13—22no—
301#1055—22no—
302#1055—22no—
303C2×#127—131no—
304C2×#125—131no—
305C2×C4×D4—131no—
306C2×C4×D4—261no—
307C2×C4×D4—261no—
308C2×C4×D4C2×D1311yescharacteristic
309#490—138no—
310C2×#102—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#102—131no—
314C2×#102—131no—
315C2×#102—131no—
316C2×#102C2×D1311yescharacteristic
317C2×#102C2×D1311yescharacteristic
318C2×#97—131no—
319C2×#97—131no—
320C2×#97—131no—
321C2×#97—131no—
322C2×C4×C8—131no—
323C2×C4×C8C2×D1311yescharacteristic
324#390—131no—
325#390—131no—
326#390—261no—
327#390—261no—
328#389—131no—
329#389—131no—
330#387—261no—
331#387—261no—
332#384—131no—
333#382—131no—
334C4×C4⋊C4—131no—
335C4×C4⋊C4—261no—
336C4×C4⋊C4—261no—
337C4×C4⋊C4C2×D1311yescharacteristic
338C43—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340C2×D1311yescharacteristic
346#340C2×D1311yescharacteristic
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13C2×C4×D411yescharacteristic
355C22×C13C2×#12411yescharacteristic
356C22×C13#53211yescharacteristic
357C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C13#57511yescharacteristic
360C22×C13#57511yescharacteristic
361C2×D13—42no—
362C2×D13—42no—
363C2×D13—42no—
364C2×D13—81no—
365C2×D13—81no—
366C2×D13—81no—
367C2×D13—81no—
368C4×C13—22no—
369C4×C13—42no—
370C4×C13—81no—
371C4×C13—81no—
372C4×C13#49014yescomplemented
373C4×C13C4×#4111yescharacteristic
374C4×C13C4×#4111yescharacteristic
375C4×C13#52911yescharacteristic
376C4×C13#52911yescharacteristic
377Dic13—22no—
378Dic13—22no—
379Dic13—41no—
380Dic13—41no—
381Dic13—42no—
382Dic13—81no—
383Dic13—81no—
384C22×D4—131no—
385C22×D4—261no—
386C22×D4—261no—
387C22×D4C22×D1311yescharacteristic
388C23×C4—21no—
389C23×C4—261no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8C22×D1311yescharacteristic
393C22×C8C22×D1311yescharacteristic
394#127—134no—
395#127—262no—
396#125—134no—
397#125—262no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4—524no—
403C4×D4—524no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—261no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4—261no—
422C2×C42—21no—
423C2×C42—131no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—261no—
430C2×C42C22×D1311yescharacteristic
431#102—22no—
432#102—134no—
433#102—134no—
434#102—134no—
435#102—262no—
436#102—262no—
437#102—262no—
438#102C4×D1314yescomplemented
439#97—134no—
440#97—262no—
441#97—262no—
442#97—262no—
443C4×C8—22no—
444C4×C8—262no—
445#95—21no—
446#95—261no—
447#95—261no—
448#95—261no—
449#95—261no—
450#95—261no—
451C2×C13—82no—
452C2×C13C4×#12411yescharacteristic
453C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
454C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C13C2×#49011yescharacteristic
456C2×C13#313511yescharacteristic
457C2×C13#317111yescharacteristic
458C2×C13#317111yescharacteristic
459D13—82no—
460C24—21no—
461C24—261no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—132no—
468C2×D4—264no—
469C2×D4—264no—
470C2×D4—261no—
471C2×D4—261no—
472C2×D4—261no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—522no—
476C2×D4—522no—
477C2×D4—522no—
478C2×D4—522no—
479C2×D4C2×C4×D1312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—522no—
494C22×C4—522no—
495C22×C4—522no—
496C22×C4D4×D1311yescharacteristic
497C22×C4D4×D1311yescharacteristic
498C22×C4C23×D1311yescharacteristic
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8C2×C4×D1312yes—
510C2×C8#612712yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—132no—
517C4⋊C4—264no—
518C4⋊C4—264no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—522no—
525C4⋊C4—522no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4C2×C4×D1312yes—
529C22⋊C4—42no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C22⋊C4—522no—
533C22⋊C4—522no—
534C22⋊C4—522no—
535C42—42no—
536C42—132no—
537C42—132no—
538C42—262no—
539C42—262no—
540C42—261no—
541C42—261no—
542C42—521no—
543C42—521no—
544C42—522no—
545C42#612712yes—
546C42#612912yes—
547C13C4×#49011yescharacteristic, complemented, Sylow
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—262no—
556C23—521no—
557C23—521no—
558C23—521no—
559C23—521no—
560C23—521no—
561C23—521no—
562C23C2×D4×D1311yescharacteristic
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—262no—
568D4—262no—
569D4—528no—
570D4—528no—
571D4—521no—
572D4—521no—
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—132no—
586C2×C4—132no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—262no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—1044no—
607C2×C4#8813912yes—
608C2×C4#8813912yes—
609C2×C4#8816512yes—
610C2×C4#8816812yes—
611C2×C4C22×C4×D1311yescharacteristic
612C2×C4C2×#612711yescharacteristic
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×#612911yescharacteristic
615C2×C4#41×D1311yescharacteristic
616C2×C4#41×D1311yescharacteristic
617C8—22no—
618C8—22no—
619C8—262no—
620C8—262no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—522no—
629C22—522no—
630C22—522no—
631C22—1041no—
632C22—1041no—
633C22—1041no—
634C22—1041no—
635C22C2×#8813911yescharacteristic
636C22C4×D4×D1311yescharacteristic
637C22#1171925311yescharacteristic
638C22C2×#8816511yescharacteristic
639C22C2×#8816811yescharacteristic
640C22#1171947311yescharacteristic
641C22#1171947311yescharacteristic
642C4—22no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—262no—
647C4—262no—
648C4—521no—
649C4—521no—
650C4—522no—
651C4—1041no—
652C4—1041no—
653C4#1171842514yesdirect product factor
654C4C4×#612711yescharacteristic
655C4#1171923311yescharacteristic
656C4C4×#612911yescharacteristic
657C4#1171924311yescharacteristic
658C2—82no—
659C2—1042no—
660C2C4×#8813911yescharacteristic
661C2C4×#8816511yescharacteristic
662C2C4×#8816811yescharacteristic
663C2C2×#1171842511yescharacteristic
664C2#1312517911yescharacteristic
665C2#1312542711yescharacteristic
666C2#1312542911yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#102C2
socleC23×C13C22×D4
prime radicalC2×#88194C22
cosocleC22×C4×C13C24
hypercenterC4×#102D13
hypocenterC13C4×#490
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C4×#88144C2semidirect
4. #13115803C2semidirect
6. #13115535C2semidirect
7. #13115534C2semidirect
8. #13115531C2semidirect
9. #13115530C2semidirect
10. #13114968C2semidirect
11. C4×#88049C2semidirect
12. C4×#88061C2semidirect
13. C4×#88072C2semidirect
14. C4×#88055C2semidirect
15. C4×C13×#102C2semidirect
49. #11718425C4direct (N × H)
104. #88144C2×C4semidirect
108. C13×#102C2×C4semidirect
112. #88072C2×C4semidirect
119. #88061C2×C4semidirect
123. #88055C2×C4semidirect
125. #88049C2×C4semidirect
228. C4×#102D13semidirect
372. C4×C13#490semidirect
438. #102C4×D13semidirect
547. C13C4×#490semidirect
653. C4#11718425direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117184252
C4×#881942
C4×#881442
#131158032
#131156582
#131155352
#131155342
#131155312
#131155302
#131149682
C4×#880492
C4×#880612
C4×#880722
C4×#880552
C4×C13×#1022
C4×#49013