Finite Group Databasebeta

← #16798968

Subgroups — #16798968

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131295C211yesmaximal, characteristic, complemented
2C4×D4×#261C211yesmaximal, characteristic
3#13130915C212yesmaximal, complemented
4#13130899C212yesmaximal, complemented
5#13130829C212yesmaximal
6#13130801C212yesmaximal
7C4×#88101C211yesmaximal, characteristic, complemented
8C4×#88117C211yesmaximal, characteristic, complemented
9C4×#88115C211yesmaximal, characteristic
10#13130549C211yesmaximal, characteristic, complemented
11C4×SD16×D13C211yesmaximal, characteristic
12C2×D4×#261C2212yes—
13C22×C4×#261—21no—
14C2×SD16×D13C2211yescharacteristic
15C4×Q8×D13C2211yescharacteristic
16C4×D4×D13C2211yescharacteristic
17(C2×#261)⋊Q8C2212yes—
18C2×#88117C2212yes—
19C2×#88115C2212yes—
20C4×C22⋊#261—21no—
21C2×#88101C2212yes—
22#11719083C2212yes—
23#11719082—22no—
24C4⋊C4×#261C2212yes—
25C22⋊C4×#261—22no—
26C4×C4⋊#261—21no—
27C4×C4⋊#261C2211yescharacteristic
28C4×C4⋊#261C2211yescharacteristic
29#11719057—21no—
30C42×#261C2211yescharacteristic
31C4×D13⋊C8C2211yescharacteristic
32C4×C13×SD16C411yescharacteristic, complemented
33SD16×Dic13C411yescharacteristic, complemented
34C4×#6106C411yescharacteristic, complemented
35C4×#6105C411yescharacteristic, complemented
36D13×#106C2211yescharacteristic
37#11718513C411yescharacteristic, complemented
38D13×#103C2211yescharacteristic
39#11718449C411yescharacteristic, complemented
40D13×#102C2211yescharacteristic
41#11718419C411yescharacteristic, complemented
42C4×#6095C411yescharacteristic, complemented
43C4×C8×D13C2211yescharacteristic
44#11718265C2212yes—
45(C2×#261)⋊C8C2212yes—
46(C2×#261)⋊C8C2212yes—
47#11718246C2212yes—
48#11718246C2212yes—
49C23×#261—22no—
50C2×Q8×D13C2311yescharacteristic
51C2×D4×D13C2311yescharacteristic
52C22×C4×D13—21no—
53C2×C22⋊#261—22no—
54D4×#261—24no—
55D4×#261—24no—
56C2×C4⋊#261—22no—
57C2×C4⋊#261C2312yes—
58C2×C4⋊#261C2312yes—
59C2×C4×#261—22no—
60C2×C4×#261—21no—
61C2×C4×#261—21no—
62C2×C4×#261—44no—
63C2×C4×#261D411yescharacteristic
64C2×C4×#261D412yes—
65C2×C4×#261D411yescharacteristic
66C2×C4×#261C2312yes—
67C2×D13⋊C8C2312yes—
68C2×C13×SD16C2×C411yescharacteristic
69C4×Q8×C13C2×C411yescharacteristic, complemented
70C4×D4×C13C2×C411yescharacteristic
71Q8×Dic13C2×C411yescharacteristic, complemented
72C2×#6106C2×C411yescharacteristic
73D4×Dic13C2×C411yescharacteristic
74C2×#6105C2×C411yescharacteristic
75C4×C22⋊D13—21no—
76SD16×D13—24no—
77C2×#6095C2×C411yescharacteristic
78C2×C8×D13C2311yescharacteristic
79C2×C8×D13C2311yescharacteristic
80#88147C2×C411yescharacteristic
81C4⋊C4×D13—21no—
82C4⋊C4×D13C2311yescharacteristic
83C4⋊C4×D13C2311yescharacteristic
84#88141—21no—
85#88141C2×C411yescharacteristic, complemented
86#88135—21no—
87C22⋊C4×D13—21no—
88C4×D52C2×C411yescharacteristic
89C42×D13—21no—
90C42×D13C2311yescharacteristic
91C4×Dic26—21no—
92C4×Dic26C2×C411yescharacteristic, complemented
93#88117—24no—
94#88115—24no—
95(C2×#261)⋊C4—22no—
96(C2×#261)⋊C4—22no—
97(C2×#261)⋊C4—22no—
98(C2×#261)⋊C4—22no—
99(C2×#261)⋊C4—21no—
100(C2×#261)⋊C4—21no—
101C4×#1057—21no—
102C4×#1057—21no—
103#88101—24no—
104C13×#106C2×C411yescharacteristic, complemented
105C13×#103C2×C411yescharacteristic, complemented
106C13×#102C2×C411yescharacteristic
107C4×C8×C13C2×C411yescharacteristic, complemented
108#88075C2×C411yescharacteristic, complemented
109#88072C2×C411yescharacteristic
110#88061C2×C411yescharacteristic
111#88057C2×C411yescharacteristic, complemented
112#88056C2×C411yescharacteristic, complemented
113C8×Dic13C2×C411yescharacteristic, complemented
114C8×Dic13C2×C411yescharacteristic, complemented
115#88050C2×C411yescharacteristic, complemented
116#88049C2×C411yescharacteristic
117#88048C2×C411yescharacteristic, complemented
118#88048C2×C411yescharacteristic, complemented
119C4×#1055C2×C411yescharacteristic, complemented
120#21117—131nomaximal, Sylow
121C23×D13—21no—
122C22×#261—28no—
123C22×#261—22no—
124C22×#261—22no—
125C22×#261—44no—
126C22×#261—44no—
127C22×#261C2×D412yes—
128C22×#261C2×D412yes—
129C2×Q8×C13C22×C411yescharacteristic
130C2×D4×C13C22×C411yescharacteristic
131C22×C4×C13—21no—
132C2×C22⋊D13—21no—
133C22×Dic13—21no—
134Q8×D13—22no—
135Q8×D13—22no—
136D4×D13—22no—
137D4×D13#4114yes—
138C2×D52C22×C411yescharacteristic
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—21no—
144C2×C4×D13—42no—
145C2×C4×D13—42no—
146C2×C4×D13C2×D411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2411yescharacteristic
149C2×Dic26—21no—
150C2×Dic26C22×C411yescharacteristic
151C22⋊#261—28no—
152C2×#1057—22no—
153C4⋊#261—22no—
154C4⋊#261—22no—
155C4⋊#261—22no—
156C4⋊#261—44no—
157C4⋊#261#4114yes—
158C4×#261—22no—
159C4×#261—22no—
160C4×#261—22no—
161C4×#261—42no—
162C4×#261—44no—
163C4×#261—42no—
164C4×#261—42no—
165C4×#261SD1614yescomplemented
166D13⋊C8—22no—
167D13⋊C8—22no—
168C13×SD16—22no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C13×C4⋊C4—21no—
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C22⋊C4—21no—
175C42×C13—21no—
176C42×C13C22×C411yescharacteristic
177C22⋊Dic13—21no—
178#6106—22no—
179#6105—22no—
180#6103—21no—
181#6103—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13C22×C411yescharacteristic
193C4×Dic13#4111yescharacteristic
194C4×Dic13#4111yescharacteristic
195C2×#1055C22×C411yescharacteristic
196C2×#1055C22×C411yescharacteristic
197#6095—22no—
198C8×D13—22no—
199C8×D13—22no—
200C2×C4×SD16—131no—
201#2295—131no—
202C42×D4—131no—
203#1927—132no—
204#1920—132no—
205#1877—132no—
206#1864—132no—
207C4×#106—131no—
208C4×#103—131no—
209C4×#102—131no—
210#1744—131no—
211C23×C13—21no—
212C22×D13—21no—
213C22×D13—24no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—42no—
217C22×D13C22×D411yescharacteristic
218C2×#261—22no—
219C2×#261—22no—
220C2×#261—22no—
221C2×#261—24no—
222C2×#261—22no—
223C2×#261—22no—
224C2×#261—416no—
225C2×#261—42no—
226C2×#261—42no—
227C2×#261—42no—
228C2×#261—42no—
229C2×#261—42no—
230C2×#261C2×SD1614yes—
231Q8×C13—21no—
232Q8×C13—21no—
233D4×C13—21no—
234D4×C13#11712yes—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—42no—
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C23×C411yescharacteristic
242C22⋊D13—24no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—42no—
247C2×Dic13C4×D411yescharacteristic
248C2×Dic13C4×D411yescharacteristic
249C2×Dic13C2×#4111yescharacteristic
250D52—21no—
251D52#11712yes—
252C4×D13—22no—
253C4×D13—42no—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13—42no—
257C4×D13—42no—
258C4×D13—42no—
259C4×D13C2×SD1612yes—
260C4×D13#13512yes—
261C4×D13C2×#4112yes—
262C4×D13C2×#4112yes—
263Dic26—21no—
264Dic26—21no—
265Dic26—42no—
266#1057—42no—
267C8×C13—21no—
268C8×C13—21no—
269#1055—21no—
270#1055—21no—
271C22×SD16—131no—
272C2×C4×Q8—131no—
273C2×C4×D4—131no—
274C2×C4×D4—132no—
275C22×C42—261no—
276C4×SD16—131no—
277C4×SD16—131no—
278C4×SD16—131no—
279C4×SD16—131no—
280C4×SD16—131no—
281C4×SD16—131no—
282C4×SD16—131no—
283C4×SD16#26111yescharacteristic, complemented
284C2×#106—131no—
285C2×#106—132no—
286C2×#103—131no—
287C2×#103—132no—
288C2×#102—131no—
289C2×#102—132no—
290C2×C4×C8—131no—
291C2×C4×C8—131no—
292#391—132no—
293#389—132no—
294#387—262no—
295C4×C4⋊C4—132no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—261no—
299C4×C22⋊C4—262no—
300C4×C22⋊C4—261no—
301#376—261no—
302C43—131no—
303#340—132no—
304#340—132no—
305#340—132no—
306#336—132no—
307#336—132no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13C2×C4×D411yescharacteristic
312C2×D13—22no—
313C2×D13—41no—
314C2×D13—41no—
315C2×D13—44no—
316C2×D13—44no—
317C2×D13#52512yes—
318C2×D13C22×SD1611yescharacteristic
319C2×D13C2×#13511yescharacteristic
320C2×D13#57512yes—
321#261—24no—
322#261—44no—
323#261—42no—
324#261—82no—
325C4×C13—21no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13C4×SD1612yes—
330C4×C13C2×#11711yescharacteristic
331C4×C13C4×#4111yescharacteristic
332Dic13—21no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336Dic13C4×SD1612yes—
337Dic13#52912yes—
338C22×Q8—131no—
339C22×D4—131no—
340C23×C4—261no—
341C23×C4—262no—
342C2×SD16—131no—
343C2×SD16—131no—
344C2×SD16—131no—
345C2×SD16—264no—
346C2×SD16C2×#26111yescharacteristic
347C22×C8—131no—
348C22×C8—131no—
349C22×C8—132no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—131no—
353C4×Q8—261no—
354C4×Q8—261no—
355C4×Q8C2×#26111yescharacteristic, complemented
356C4×D4—131no—
357C4×D4—131no—
358C4×D4—131no—
359C4×D4—261no—
360C4×D4—261no—
361C4×D4—264no—
362C4×D4—264no—
363C4×D4C2×#26111yescharacteristic
364C2×C4⋊C4—132no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—132no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—262no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—262no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—132no—
375C2×C42—131no—
376C2×C42—132no—
377C2×C42—261no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—262no—
381C2×C42—524no—
382#106—131no—
383#106—131no—
384#106—131no—
385#106—264no—
386#106C2×#26111yescharacteristic, complemented
387#103—131no—
388#103—131no—
389#103—131no—
390#103—264no—
391#103C2×#26111yescharacteristic, complemented
392#102—131no—
393#102—131no—
394#102—131no—
395#102—264no—
396#102C2×#26111yescharacteristic
397C4×C8—131no—
398C4×C8—131no—
399C4×C8—131no—
400C4×C8—261no—
401C4×C8—261no—
402C4×C8C2×#26111yescharacteristic, complemented
403#95—262no—
404#95—262no—
405#95—261no—
406#95—262no—
407#95—261no—
408#95—262no—
409C2×C13—42no—
410C2×C13#229011yescharacteristic
411C2×C13C2×C4×SD1611yescharacteristic
412C2×C13#294311yescharacteristic
413D13—42no—
414D13#310112yes—
415D13#310212yes—
416C24—261no—
417C2×Q8—131no—
418C2×Q8—261no—
419C2×Q8—262no—
420C2×Q8—262no—
421C2×Q8C22×#26111yescharacteristic
422C2×D4—134no—
423C2×D4—131no—
424C2×D4—262no—
425C2×D4—261no—
426C2×D4C22×#26111yescharacteristic
427C22×C4—21no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—132no—
431C22×C4—131no—
432C22×C4—132no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—268no—
440C22×C4—261no—
441C22×C4—262no—
442C22×C4—522no—
443C22×C4—522no—
444C22×C4—524no—
445C22×C4—524no—
446SD16—22no—
447SD16—262no—
448SD16—262no—
449SD16—262no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—262no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—262no—
457C2×C8C22×#26111yescharacteristic
458C2×C8C22×#26111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—134no—
461C4⋊C4—131no—
462C4⋊C4—131no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—262no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—261no—
471C4⋊C4—524no—
472C4⋊C4C22×#26111yescharacteristic
473C4⋊C4C22×#26111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—268no—
478C22⋊C4—261no—
479C42—21no—
480C42—134no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—261no—
485C42—261no—
486C42—262no—
487C42—262no—
488C42—262no—
489C42—261no—
490C42—522no—
491C42—524no—
492C42—522no—
493C42—522no—
494C42C22×#26111yescharacteristic
495C13#2111711yescharacteristic, complemented, Sylow
496C23—21no—
497C23—131no—
498C23—264no—
499C23—261no—
500C23—521no—
501C23—521no—
502C23—522no—
503Q8—21no—
504Q8—21no—
505Q8—261no—
506Q8—261no—
507Q8—522no—
508D4—21no—
509D4—132no—
510D4—264no—
511D4—261no—
512D4#8823712yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—131no—
518C2×C4—131no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—134no—
524C2×C4—131no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—264no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—522no—
536C2×C4—521no—
537C2×C4—522no—
538C2×C4—521no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—5216no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4D4×#26111yescharacteristic
549C2×C4D4×#26111yescharacteristic
550C2×C4C23×#26111yescharacteristic
551C8—21no—
552C8—21no—
553C8—261no—
554C8—261no—
555C8—522no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—132no—
560C22—131no—
561C22—131no—
562C22—132no—
563C22—262no—
564C22—524no—
565C22—524no—
566C22—521no—
567C22—521no—
568C22C2×D4×#26111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—132no—
574C4—132no—
575C4—264no—
576C4—261no—
577C4—522no—
578C4—524no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4—1042no—
583C4SD16×#26112yes—
584C4C2×#8823711yescharacteristic
585C4#41×#26111yescharacteristic
586C2—42no—
587C2—132no—
588C2—132no—
589C2—522no—
590C2#1313129011yescharacteristic
591C2C2×SD16×#26111yescharacteristic
592C2#1313159011yescharacteristic
subgroupG/H
centerC2×C4D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC4×C13×SD16C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenterC4×SD16#261
hypocenterC13#21117
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #13131295C2semidirect
3. #13130915C2semidirect
4. #13130899C2semidirect
7. C4×#88101C2semidirect
8. C4×#88117C2semidirect
10. #13130549C2semidirect
32. C4×C13×SD16C4semidirect
33. SD16×Dic13C4semidirect
34. C4×#6106C4semidirect
35. C4×#6105C4semidirect
37. #11718513C4semidirect
39. #11718449C4semidirect
41. #11718419C4semidirect
42. C4×#6095C4semidirect
69. C4×Q8×C13C2×C4semidirect
71. Q8×Dic13C2×C4semidirect
85. #88141C2×C4semidirect
92. C4×Dic26C2×C4semidirect
104. C13×#106C2×C4semidirect
105. C13×#103C2×C4semidirect
107. C4×C8×C13C2×C4semidirect
108. #88075C2×C4semidirect
111. #88057C2×C4semidirect
112. #88056C2×C4semidirect
113. C8×Dic13C2×C4semidirect
114. C8×Dic13C2×C4semidirect
115. #88050C2×C4semidirect
117. #88048C2×C4semidirect
118. #88048C2×C4semidirect
119. C4×#1055C2×C4semidirect
165. C4×#261SD16semidirect
283. C4×SD16#261semidirect
355. C4×Q8C2×#261semidirect
386. #106C2×#261semidirect
391. #103C2×#261semidirect
402. C4×C8C2×#261semidirect
495. C13#21117semidirect

Maximal subgroups

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

subgroupindex
#131312952
C4×D4×#2612
#131309152
#131308992
#131308292
#131308012
C4×#881012
C4×#881172
C4×#881152
#131305492
C4×SD16×D132
#2111713