Finite Group Databasebeta

← C4×#11718727 #15870519

Subgroups — C4×#11718727 #15870519

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic
2C42×D52C211yesmaximal, characteristic
3#13115794C211yesmaximal, characteristic, complemented
4#13115602C211yesmaximal, characteristic, complemented
5#13115425C211yesmaximal, characteristic, complemented
6#13115411C211yesmaximal, characteristic, complemented
7#13115096C211yesmaximal, characteristic
8#13115082C211yesmaximal, characteristic
9#13114843C211yesmaximal, characteristic
10C4×#88047C211yesmaximal, characteristic, complemented
11C4×#88048C211yesmaximal, characteristic, complemented
12C4×C4⋊#1055C211yesmaximal, characteristic, complemented
13C4×#88049C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C4×C13×#125C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C42×D13—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C13×#382C2211yescharacteristic
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C43×C13C2211yescharacteristic
31#11718727C418yesdirect product factor
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C4×#6103—21no—
41C4×#6103—21no—
42C4×#6103—21no—
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C13×#125—22no—
65C13×#125C2×C414yescomplemented
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13D411yescharacteristic
77C2×C42×C13D411yescharacteristic
78C2×C42×C13D411yescharacteristic
79C2×C42×C13D411yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C4×D52—22no—
97C4×D52—22no—
98C4×D52—22no—
99C4×D52—22no—
100C4×D52C2×C414yes—
101C4×D52Q814yes—
102C42×D13—44no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88049—22no—
113#88049—22no—
114#88049C2×C414yes—
115#88049C2×C414yes—
116#88048—22no—
117#88048C2×C414yescomplemented
118#88047—22no—
119#88047C2×C414yescomplemented
120C4⋊#1055—22no—
121C4⋊#1055C2×C414yescomplemented
122C4×#1055—22no—
123C4×#1055—22no—
124C4×#478—131nomaximal, Sylow
125C23×D13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52C22×C412yes—
144C2×D52C2×Q812yes—
145C2×D52#4112yes—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13—42no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4C22×C412yes—
166C13×C4⋊C4C22×C412yes—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—22no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—41no—
173C42×C13—42no—
174C42×C13—42no—
175C42×C13C22×C412yes—
176C42×C13C2×Q812yes—
177C42×C13#4112yes—
178C42×C13#4112yes—
179#6103—24no—
180#6103—24no—
181#6103—24no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C412yes—
186C4⋊Dic13C2×Q812yes—
187C4⋊Dic13#4112yes—
188C4×Dic13—42no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C22×C412yes—
202C2×#1055C22×C412yes—
203C2×#478—131no—
204C4×#125D1311yescharacteristic, complemented
205C42×D4—131no—
206#1989—131no—
207#1949—131no—
208#1921—131no—
209#1919—131no—
210#1864—131no—
211#1862—131no—
212#1804—131no—
213C4×#107—131no—
214C4×#106—131no—
215C4×C4⋊C8—131no—
216C4×#102—131no—
217C4×#102—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
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×C13C4×D412yes—
250C2×C4×C13C4×D412yes—
251C2×C4×C13C22⋊Q812yes—
252C2×C4×C13C22⋊Q812yes—
253C2×C4×C13#13512yes—
254C2×C4×C13#13512yes—
255C2×C4×C13AGL(1,ℤ/8)12yes—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271D52—22no—
272D52—22no—
273D52—22no—
274D52C4×Q814yes—
275C4×D13—48no—
276C4×D13—48no—
277C4×D13—48no—
278#1055—22no—
279#1055—22no—
280#1055—41no—
281#1055—41no—
282C2×#125C2×D1311yescharacteristic
283C2×C4×D4—131no—
284C2×C4×D4—131no—
285C2×C4×D4—131no—
286C22×C42—261no—
287#478—138no—
288C2×#107—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#389C2×D1311yescharacteristic
301#389C2×D1311yescharacteristic
302#387—21no—
303#387—21no—
304#382C2×D1311yescharacteristic
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C4⋊C4C2×D1311yescharacteristic
312C4×C22⋊C4—261no—
313C4×C22⋊C4—261no—
314C4×C22⋊C4—261no—
315C43C2×D1311yescharacteristic
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336—131no—
325#336—131no—
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13C2×#13511yescharacteristic
330C22×C13C2×#13511yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13#57511yescharacteristic
333C2×D13—24no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—81no—
348C4×C13—81no—
349C4×C13#47814yescomplemented
350C4×C13C2×C4×Q811yescharacteristic
351C4×C13C4×#4111yescharacteristic
352C4×C13#52911yescharacteristic
353C4×C13#53311yescharacteristic
354Dic13—42no—
355Dic13—42no—
356Dic13—42no—
357C22×D4—131no—
358C23×C4—261no—
359C23×C4—261no—
360C23×C4—261no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365#125—22no—
366#125C4×D1314yescomplemented
367C4×D4—134no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C4×D4—262no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—524no—
393C2×C42C22⋊D1311yescharacteristic
394C2×C42C22⋊D1311yescharacteristic
395C2×C42C22⋊D1311yescharacteristic
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—134no—
401#107—262no—
402#106—134no—
403#106—262no—
404C4⋊C8—134no—
405C4⋊C8—262no—
406#102—134no—
407#102—134no—
408#102—262no—
409#102—262no—
410C4×C8—262no—
411C4×C8—262no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13C4×C22⋊Q811yescharacteristic
422C2×C13C4×#13511yescharacteristic
423C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C13C2×#47811yescharacteristic
425C2×C13#307611yescharacteristic
426C2×C13#310211yescharacteristic
427C2×C13#310511yescharacteristic
428D13—44no—
429C24—261no—
430C2×D4—132no—
431C2×D4—132no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—264no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—264no—
445C22×C4—264no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4—522no—
451C22×C4—522no—
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—132no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—132no—
482C4⋊C4—132no—
483C4⋊C4—132no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4C2×C4×D1312yes—
488C4⋊C4C2×C4×D1312yes—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—42no—
499C42—42no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42C2×C4×D1312yes—
504C42#612712yes—
505C42Q8×D1312yes—
506C42#613112yes—
507C13C4×#47811yescharacteristic, complemented, Sylow
508C23—262no—
509C23—262no—
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23C22×C22⋊D1311yescharacteristic
516D4—134no—
517D4—262no—
518D4—262no—
519D4—262no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—528no—
547C2×C4—528no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—528no—
555C2×C4C4×C22⋊D1312yes—
556C2×C4C4×C22⋊D1312yes—
557C2×C4#8820012yes—
558C2×C4#8820012yes—
559C2×C4#8820312yes—
560C2×C4#8820412yes—
561C2×C4#8820412yes—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C2×C4C2×Q8×D1311yescharacteristic
565C2×C4C2×#613111yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—262no—
569C8—262no—
570C8—521no—
571C8—521no—
572C22—264no—
573C22—522no—
574C22—522no—
575C22—522no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22C2×C4×C22⋊D1311yescharacteristic
580C22C2×#8820011yescharacteristic
581C22C2×#8820311yescharacteristic
582C22C2×#8820411yescharacteristic
583C22C2×#8820411yescharacteristic
584C22#1171952711yescharacteristic
585C22#1171953311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—522no—
596C4—522no—
597C4—522no—
598C4#1171872714yesdirect product factor
599C4C4×Q8×D1311yescharacteristic
600C4C4×#613111yescharacteristic
601C4#1171928311yescharacteristic
602C4#1171928511yescharacteristic
603C2—524no—
604C2C4×#8820011yescharacteristic
605C2C4×#8820411yescharacteristic
606C2C4×#8820311yescharacteristic
607C2C2×#1171872711yescharacteristic
608C2#1312461811yescharacteristic
609C2#1312484811yescharacteristic
610C2#1312487911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#125C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×#125D13
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
3. #13115794C2semidirect
4. #13115602C2semidirect
5. #13115425C2semidirect
6. #13115411C2semidirect
10. C4×#88047C2semidirect
11. C4×#88048C2semidirect
12. C4×C4⋊#1055C2semidirect
15. C4×C13×#125C2semidirect
31. #11718727C4direct (N × H)
65. C13×#125C2×C4semidirect
117. #88048C2×C4semidirect
119. #88047C2×C4semidirect
121. C4⋊#1055C2×C4semidirect
204. C4×#125D13semidirect
349. C4×C13#478semidirect
366. #125C4×D13semidirect
507. C13C4×#478semidirect
598. C4#11718727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117187272
C42×D522
#131157942
#131156022
#131154252
#131154112
#131150962
#131150822
#131148432
C4×#880472
C4×#880482
C4×C4⋊#10552
C4×#880492
C4×C13×#1252
C4×#47813