Finite Group Databasebeta

← C4×#11718399 #15868514

Subgroups — C4×#11718399 #15868514

Order 3328.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic, complemented
2C2×#11718399C211yesmaximal, characteristic
3C2×C4×#6095C212yesmaximal, complemented
4C4×#88184C211yesmaximal, characteristic
5#13115190C212yesmaximal, complemented
6#13115151C211yesmaximal, characteristic
7#13115107C212yesmaximal, complemented
8#13115031C211yesmaximal, characteristic, complemented
9#13114772C211yesmaximal, characteristic, complemented
10C4×#88056C212yesmaximal, complemented
11C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×Dic26C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C2×#88184C2211yescharacteristic
15C2×C4×C22⋊D13—21no—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101—21no—
18C22×C4×Dic13—21no—
19C22×#6095C2212yes—
20C2×C4×D52C2211yescharacteristic
21C2×C4×Dic26—21no—
22C2×C4×Dic26—21no—
23C2×C4×Dic26—28no—
24C2×C4×Dic26C2212yes—
25C2×C4×Dic26C2212yes—
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C13C2212yes—
29#11718874—21no—
30#11718873C2211yescharacteristic
31C2×#88061C2212yes—
32C2×#88057C2212yes—
33C2×#88056C2212yes—
34C2×#88056C2212yes—
35C2×#88056C2212yes—
36#11718601—21no—
37#11718600C2211yescharacteristic
38C4×#6103—21no—
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718399C418yesdirect product factor
42C4×#6095—28no—
43C13×#336C2212yes—
44#11718143C2212yes—
45#11718143C2212yes—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C22×C22⋊D13—21no—
50C23×Dic13—21no—
51C23×Dic13—21no—
52C22×D52C2311yescharacteristic
53C22×C4×D13—21no—
54C22×Dic26—21no—
55C22×Dic26—22no—
56C22×Dic26—24no—
57C22×Dic26—24no—
58C22×Dic26C2×C414yescomplemented
59C22×Dic26C2312yes—
60C22×C8×C13C2312yes—
61C22×C8×C13C2312yes—
62C2×C42×C13—24no—
63C2×C42×C13D411yescharacteristic
64C2×C42×C13D411yescharacteristic
65C2×C42×C13C2311yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C22⋊Dic13—21no—
68#88184—22no—
69#88184C2×C414yes—
70C4×C22⋊D13—44no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—24no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2312yes—
81C2×#6101—28no—
82C2×#6101—22no—
83C2×#6101—22no—
84C2×#6101—21no—
85C2×C4×Dic13—28no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—21no—
89C2×#6095—24no—
90C2×#6095—24no—
91C2×#6095C2×C418yescomplemented
92C4×D52—24no—
93C4×Dic26—28no—
94C4×Dic26—28no—
95C4×Dic26—24no—
96C4×Dic26—24no—
97C4×Dic26—24no—
98C4×Dic26D418yescomplemented
99C13×C22⋊C8—22no—
100C13×C22⋊C8C2×C414yescomplemented
101C4×C8×C13—24no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88061—24no—
106#88057—24no—
107#88056—24no—
108#88056—24no—
109#88056C2×C418yescomplemented
110C4×#448—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—41no—
120C22×C4×C13SD1614yescomplemented
121C22×C4×C13C22×C412yes—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13#4112yes—
128C22×C4×C13C2411yescharacteristic
129C2×C22⋊D13—24no—
130C2×C22⋊D13—42no—
131C2×C22⋊D13—42no—
132C22×Dic13—24no—
133C22×Dic13—24no—
134C22×Dic13—24no—
135C22×Dic13—22no—
136C22×Dic13—24no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—42no—
142C22×Dic13—42no—
143C2×D52—22no—
144C2×D52—22no—
145C2×D52—21no—
146C2×D52C22×C412yes—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×Dic26—24no—
151C2×Dic26—24no—
152C2×Dic26—216no—
153C2×Dic26—24no—
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26—22no—
157C2×Dic26—216no—
158C2×Dic26C22×C414yes—
159C2×Dic26C2×D414yes—
160C2×Dic26#4114yes—
161C2×C8×C13—22no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13C22×C414yes—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—22no—
170C42×C13C2×D414yes—
171C22⋊Dic13—42no—
172#6103—24no—
173#6103—42no—
174#6103—42no—
175#6103—42no—
176C4⋊Dic13—24no—
177C4⋊Dic13—22no—
178C4⋊Dic13—21no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13C22×C412yes—
182C4⋊Dic13C2×D414yes—
183#6101—28no—
184#6101—28no—
185#6101—42no—
186C4×Dic13—28no—
187C4×Dic13—28no—
188C4×Dic13—42no—
189#6095—216no—
190C22×C4×Q8—131no—
191C2×#448—131no—
192C2×C4×SD16—132no—
193C4×#121—131no—
194#1880—132no—
195#1874—131no—
196#1865—132no—
197#1853—131no—
198#1787—131no—
199C4×#103—132no—
200C4×C22⋊C8D1311yescharacteristic, complemented
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13C4×D412yes—
206C23×C13C2×SD1612yes—
207C23×C13#13512yes—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—28no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—44no—
229C2×C4×C13C4×D412yes—
230C2×C4×C13#12012yes—
231C2×C4×C13#12012yes—
232C2×C4×C13C2×SD1612yes—
233C2×C4×C13C2×SD1612yes—
234C2×C4×C13#13712yes—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D412yes—
237C2×C4×C13C2×#4112yes—
238C2×C4×C13C2×#4111yescharacteristic
239C22⋊D13—48no—
240C2×Dic13—216no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—48no—
247C2×Dic13—41no—
248C2×Dic13—42no—
249C2×Dic13—41no—
250C2×Dic13—42no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257D52—24no—
258D52—42no—
259C4×D13—84no—
260Dic26—216no—
261Dic26—24no—
262Dic26—24no—
263Dic26—24no—
264Dic26C4×D418yescomplemented
265C8×C13—24no—
266C8×C13—42no—
267C23×Q8—131no—
268C22×SD16—132no—
269C2×#121—131no—
270C2×C4×Q8—132no—
271C2×C4×Q8—132no—
272C2×C4×Q8—268no—
273C2×C4×Q8—261no—
274C2×C4×Q8—261no—
275C2×C4×D4—131no—
276C2×C4×D4—261no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—261no—
279C22×C42—261no—
280C22×C42C2×D1311yescharacteristic
281#448—138no—
282C4×SD16—268no—
283C2×#106—132no—
284C2×#103—132no—
285C2×#103—132no—
286C2×#103—132no—
287C2×#102—132no—
288C2×C22⋊C8C2×D1311yescharacteristic
289C2×C22⋊C8C2×D1311yescharacteristic
290C2×C4×C8C2×D1312yes—
291#390—131no—
292#389—131no—
293#388—261no—
294#386—261no—
295#380—131no—
296C4×C4⋊C4—131no—
297C4×C22⋊C4—261no—
298#340—132no—
299#340—132no—
300#336C2×D1312yes—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13C4×SD1614yescomplemented
308C22×C13C2×C4×D411yescharacteristic
309C22×C13C2×#12011yescharacteristic
310C22×C13#52511yescharacteristic
311C22×C13C22×SD1611yescharacteristic
312C22×C13C2×#13511yescharacteristic
313C22×C13C2×#13711yescharacteristic
314C22×C13#57511yescharacteristic
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—81no—
319C2×D13—81no—
320C2×D13—81no—
321C2×D13—81no—
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—41no—
326C4×C13#44814yescomplemented
327C4×C13C2×C4×D412yes—
328C4×C13#52512yes—
329Dic13—28no—
330Dic13—42no—
331Dic13—44no—
332Dic13—81no—
333Dic13—81no—
334C22×Q8—134no—
335C22×Q8—132no—
336C22×Q8—264no—
337C22×Q8—264no—
338C22×Q8—261no—
339C22×Q8—262no—
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—261no—
343C23×C4—261no—
344C23×C4—261no—
345C23×C4D5211yescharacteristic
346C23×C4D5211yescharacteristic
347C23×C4C22×D1311yescharacteristic
348C2×SD16—138no—
349C2×SD16—264no—
350C2×SD16—264no—
351C22×C8C22×D1312yes—
352C22×C8C22×D1312yes—
353#121—134no—
354#121—262no—
355C4×Q8—138no—
356C4×Q8—264no—
357C4×Q8—264no—
358C4×Q8—268no—
359C4×Q8—268no—
360C4×Q8—264no—
361C4×D4—264no—
362C4×D4—524no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—264no—
368C2×C4⋊C4—268no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—261no—
373C2×C22⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C42—24no—
379C2×C42—268no—
380C2×C42—262no—
381C2×C42—262no—
382C2×C42—261no—
383C2×C42D5211yescharacteristic
384C2×C42D5211yescharacteristic
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#106—264no—
388#103—138no—
389#103—264no—
390#103—264no—
391#102—264no—
392C22⋊C8—22no—
393C22⋊C8C4×D1314yescomplemented
394C4×C8—24no—
395#95—261no—
396#95—261no—
397#95—261no—
398C2×C13—24no—
399C2×C13C4×#12011yescharacteristic
400C2×C13C2×C4×SD1611yescharacteristic
401C2×C13C4×#13711yescharacteristic
402C2×C13C2×#44811yescharacteristic
403C2×C13#300211yescharacteristic
404C2×C13#310311yescharacteristic
405C2×C13#310811yescharacteristic
406D13—82no—
407C24—261no—
408C24C2×D5211yescharacteristic
409C2×Q8—134no—
410C2×Q8—134no—
411C2×Q8—134no—
412C2×Q8—2616no—
413C2×Q8—264no—
414C2×Q8—264no—
415C2×Q8—2616no—
416C2×Q8—264no—
417C2×Q8—262no—
418C2×Q8—262no—
419C2×Q8—262no—
420C2×D4—132no—
421C2×D4—264no—
422C2×D4—261no—
423C2×D4—262no—
424C2×D4—262no—
425C2×D4—522no—
426C2×D4—522no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—264no—
435C22×C4—264no—
436C22×C4—264no—
437C22×C4—262no—
438C22×C4—264no—
439C22×C4—261no—
440C22×C4—262no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—522no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4#609514yescomplemented
449C22×C4C2×C4×D1312yes—
450C22×C4C2×D5211yescharacteristic
451C22×C4C2×D5211yescharacteristic
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×D5211yescharacteristic
455C22×C4#612712yes—
456C22×C4C23×D1311yescharacteristic
457SD16—2616no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8C2×C4×D1314yes—
464C4⋊C4—132no—
465C4⋊C4—134no—
466C4⋊C4—268no—
467C4⋊C4—264no—
468C4⋊C4—268no—
469C4⋊C4—261no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—262no—
473C4⋊C4—522no—
474C22⋊C4—264no—
475C22⋊C4—522no—
476C22⋊C4—522no—
477C22⋊C4—522no—
478C22⋊C4—522no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—268no—
483C42—268no—
484C42—522no—
485C42D4×D1314yes—
486C13C4×#44811yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—262no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23—521no—
498C23C4×D5212yes—
499C23C2×#609512yes—
500C23#8815812yes—
501C23C22×D5211yescharacteristic
502Q8—138no—
503Q8—2616no—
504Q8—264no—
505Q8—264no—
506Q8—264no—
507D4—264no—
508D4—528no—
509D4—522no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—2616no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—262no—
528C2×C4—264no—
529C2×C4—528no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—521no—
533C2×C4—522no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1044no—
541C2×C4C4×D5212yes—
542C2×C4#8813612yes—
543C2×C4#8813612yes—
544C2×C4C2×#609512yes—
545C2×C4C2×#609512yes—
546C2×C4#8816312yes—
547C2×C4C22×C4×D1311yescharacteristic
548C2×C4C2×#612711yescharacteristic
549C2×C4C2×D4×D1312yes—
550C2×C4#41×D1312yes—
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—522no—
560C22—522no—
561C22—522no—
562C22—1041no—
563C22—1041no—
564C22—1041no—
565C22—1041no—
566C22C4×#609514yescomplemented
567C22C2×C4×D5211yescharacteristic
568C22C2×#8813611yescharacteristic
569C22#1171922911yescharacteristic
570C22C22×#609511yescharacteristic
571C22C2×#8815811yescharacteristic
572C22C2×#8816311yescharacteristic
573C22#1171945311yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—268no—
579C4—522no—
580C4—524no—
581C4—1041no—
582C4—1041no—
583C4#1171839914yesdirect product factor
584C4C4×D4×D1312yes—
585C4#1171925212yes—
586C2—24no—
587C2—1042no—
588C2C4×#8813611yescharacteristic
589C2C2×C4×#609511yescharacteristic
590C2C4×#8816311yescharacteristic
591C2C2×#1171839911yescharacteristic
592C2#1312405811yescharacteristic
593C2#1312486811yescharacteristic
594C2#1312491811yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC4×C22⋊C8D13
hypocenterC13C4×#448
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic26C2semidirect
3. C2×C4×#6095C2semidirect
5. #13115190C2semidirect
7. #13115107C2semidirect
8. #13115031C2semidirect
9. #13114772C2semidirect
10. C4×#88056C2semidirect
11. C4×C13×C22⋊C8C2semidirect
41. #11718399C4direct (N × H)
58. C22×Dic26C2×C4semidirect
91. C2×#6095C2×C4semidirect
98. C4×Dic26D4semidirect
100. C13×C22⋊C8C2×C4semidirect
109. #88056C2×C4semidirect
120. C22×C4×C13SD16semidirect
200. C4×C22⋊C8D13semidirect
264. Dic26C4×D4semidirect
307. C22×C13C4×SD16semidirect
326. C4×C13#448semidirect
393. C22⋊C8C4×D13semidirect
448. C22×C4#6095semidirect
486. C13C4×#448semidirect
566. C22C4×#6095semidirect
583. C4#11718399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117183992
C2×C4×#60952
C4×#881842
#131151902
#131151512
#131151072
#131150312
#131147722
C4×#880562
C4×C13×C22⋊C82
C4×#44813