Finite Group Databasebeta

← #16797497

Subgroups — #16797497

Order 3328.

1210 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#407C211yesmaximal, characteristic
2#13131280C211yesmaximal, characteristic
3#13130579C214yesmaximal, complemented
4#13130572C212yesmaximal, complemented
5C8×C22⋊#261C212yesmaximal, complemented
6#13130567C214yesmaximal, complemented
7C2×D13×C22⋊C8C211yesmaximal, characteristic
8C23×C4×D13C2211yescharacteristic
9C2×#88237C2212yes—
10C2×D13⋊M16C2212yes—
11C22×C8×D13C2211yescharacteristic
12C22×C8×D13C2211yescharacteristic
13#11719171C412yes—
14#11719169C412yescomplemented
15#11719136C412yes—
16#11719136C412yes—
17#11719135C412yes—
18C4×C22⋊#261C2212yes—
19C4×C22⋊#261C2212yes—
20#11719127C412yescomplemented
21#11719127C412yescomplemented
22#11719126C412yescomplemented
23D13⋊(C22⋊C8)C2212yes—
24D13⋊(C22⋊C8)C2212yes—
25C2×#88100C2214yescomplemented
26C2×C8×#261C2214yescomplemented
27C2×C13×C22⋊C8C411yescharacteristic, complemented
28C2×C22⋊#1055C411yescharacteristic, complemented
29C2×#88060C411yescharacteristic, complemented
30C2×#88060C411yescharacteristic, complemented
31D13×C22⋊C8C412yescomplemented
32D13×C22⋊C8C412yescomplemented
33D13×C22⋊C8C2212yes—
34D13×C22⋊C8C2212yes—
35(C2×#261)⋊C8C2214yescomplemented
36(C2×#261)⋊C8C2214yescomplemented
37C24×D13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×Dic13C2×C411yescharacteristic
40C22×C4×D13—42no—
41C22×C4×D13—42no—
42C22×C4×D13C2×C411yescharacteristic
43C22×C4×D13C2×C411yescharacteristic
44C22×C4×D13C2×C411yescharacteristic
45C22×C4×D13C2×C411yescharacteristic
46C22×C4×D13C2×C411yescharacteristic
47C22×C4×D13C2×C411yescharacteristic
48C22×C4×D13C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C2×C22⋊#261C2×C414yes—
55C2×C22⋊#261C2×C414yes—
56C2×C22⋊#261C2×C414yes—
57C2×#6122C2×C414yes—
58#88237—42no—
59#88237—42no—
60C2×C4⋊#261C2×C414yes—
61C2×C4×#261C2314yes—
62D13⋊M16—42no—
63D13⋊M16—42no—
64C2×#6118C2×C414yes—
65C2×D13⋊C8C2314yes—
66C22×C8×C13C2×C411yescharacteristic
67C22×C8×C13C2×C411yescharacteristic
68C22×#1055C2×C411yescharacteristic
69C22×#1055C2×C411yescharacteristic
70C2×C8×D13—42no—
71C2×C8×D13—42no—
72C2×C8×D13C2×C412yes—
73C2×C8×D13C2×C412yes—
74C2×C8×D13C2312yes—
75C2×C8×D13C2312yes—
76C22⋊#1057C2×C414yes—
77C22⋊#1057C2×C414yes—
78(C2×#261)⋊C4C2×C414yes—
79(C2×#261)⋊C4C2×C414yes—
80#88111C2×C414yes—
81#88111C2×C414yes—
82#88100—44no—
83C8×#261—44no—
84C13×C22⋊C8C2×C412yes—
85C13×C22⋊C8C2×C412yes—
86C22⋊#1055C2×C412yes—
87C22⋊#1055C2×C412yes—
88#88060C2×C412yes—
89#88060C2×C412yes—
90#88060C2×C412yes—
91#88060C2×C412yes—
92#20527—131nomaximal, Sylow
93C24×C13C4211yescharacteristic
94C23×D13—24no—
95C23×D13—42no—
96C23×D13—42no—
97C23×D13C4211yescharacteristic
98C23×D13C4211yescharacteristic
99C23×D13C4211yescharacteristic
100C23×D13C22×C411yescharacteristic
101C23×D13C22×C411yescharacteristic
102C23×D13C22×C411yescharacteristic
103C22×#261C22×C418yes—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13C4211yescharacteristic
107C22×C4×C13C4211yescharacteristic
108C22×C4×C13C4211yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×Dic13—42no—
113C22×Dic13C4211yescharacteristic
114C22×Dic13C4211yescharacteristic
115C22×Dic13C4211yescharacteristic
116C22×Dic13C22×C411yescharacteristic
117C22×Dic13C22×C411yescharacteristic
118C22×Dic13C22×C411yescharacteristic
119C2×C4×D13—22no—
120C2×C4×D13—22no—
121C2×C4×D13—22no—
122C2×C4×D13—22no—
123C2×C4×D13—22no—
124C2×C4×D13—22no—
125C2×C4×D13—42no—
126C2×C4×D13—42no—
127C2×C4×D13—42no—
128C2×C4×D13—41no—
129C2×C4×D13—41no—
130C2×C4×D13—41no—
131C2×C4×D13—41no—
132C2×C4×D13—41no—
133C2×C4×D13—41no—
134C2×C4×D13—42no—
135C2×C4×D13—42no—
136C2×C4×D13—42no—
137C2×C4×D13C4211yescharacteristic
138C2×C4×D13C4211yescharacteristic
139C2×C4×D13C4211yescharacteristic
140C2×C4×D13C4211yescharacteristic
141C2×C4×D13C4211yescharacteristic
142C2×C4×D13C4211yescharacteristic
143C2×C4×D13C22×C411yescharacteristic
144C2×C4×D13C22×C411yescharacteristic
145C2×C4×D13C22×C411yescharacteristic
146C2×C4×D13C22×C411yescharacteristic
147C2×C4×D13C22×C411yescharacteristic
148C2×C4×D13C22×C411yescharacteristic
149C2×C4×D13C22×C411yescharacteristic
150C2×C4×D13C22×C411yescharacteristic
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C2411yescharacteristic
153C22⋊#261—28no—
154C22⋊#261—44no—
155C22⋊#261—44no—
156#6122—44no—
157C2×#1057C22×C418yes—
158C4⋊#261—44no—
159C4×#261—24no—
160C4×#261—24no—
161#6118—44no—
162D13⋊C8—24no—
163D13⋊C8—24no—
164C2×C8×C13—41no—
165C2×C8×C13—41no—
166C2×C8×C13C22×C412yes—
167C2×C8×C13C22×C412yes—
168C2×#1055—41no—
169C2×#1055—41no—
170C2×#1055C22×C412yes—
171C2×#1055C22×C412yes—
172C8×D13—24no—
173C8×D13—24no—
174C8×D13—42no—
175C8×D13—42no—
176C2×#407—131no—
177C22×C22⋊C8—131no—
178#2280—131no—
179#1753—134no—
180#1752—132no—
181C8×C22⋊C4—132no—
182#1750—134no—
183C23×C13—22no—
184C23×C13—41no—
185C23×C13—41no—
186C23×C13C2×C4211yescharacteristic
187C23×C13C2×C4211yescharacteristic
188C23×C13C2×C4211yescharacteristic
189C22×D13—22no—
190C22×D13—22no—
191C22×D13—22no—
192C22×D13—22no—
193C22×D13—22no—
194C22×D13—22no—
195C22×D13—22no—
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—41no—
201C22×D13—41no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—41no—
206C22×D13—416no—
207C22×D13C2×C4211yescharacteristic
208C22×D13C2×C4211yescharacteristic
209C22×D13C2×C4211yescharacteristic
210C22×D13#13114yes—
211C22×D13C23×C411yescharacteristic
212C2×#261—28no—
213C2×#261—28no—
214C2×#261—28no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13C2×C4211yescharacteristic
225C2×C4×C13C2×C4211yescharacteristic
226C2×C4×C13C2×C4211yescharacteristic
227C2×C4×C13C23×C411yescharacteristic
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—41no—
232C2×Dic13—41no—
233C2×Dic13—41no—
234C2×Dic13C2×C4211yescharacteristic
235C2×Dic13C2×C4211yescharacteristic
236C2×Dic13C2×C4211yescharacteristic
237C2×Dic13C23×C411yescharacteristic
238C4×D13—22no—
239C4×D13—22no—
240C4×D13—22no—
241C4×D13—21no—
242C4×D13—21no—
243C4×D13—21no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—22no—
248C4×D13—22no—
249C4×D13—22no—
250C4×D13—41no—
251C4×D13—41no—
252C4×D13—41no—
253C4×D13—41no—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13H(5,𝔽2)12yes—
257C4×D13H(5,𝔽2)12yes—
258#1057—28no—
259C8×C13—22no—
260C8×C13—22no—
261#1055—22no—
262#1055—22no—
263C24×C4—131no—
264C22×M16—132no—
265C23×C8—131no—
266C23×C8—131no—
267C2×#117—132no—
268#407—132no—
269#407—132no—
270#407—132no—
271#407—132no—
272C2×C22⋊C8—132no—
273C2×C22⋊C8—132no—
274C2×C22⋊C8—131no—
275C2×C22⋊C8—131no—
276C2×C22⋊C8—131no—
277C2×C22⋊C8—132no—
278C2×C22⋊C8—132no—
279C2×C22⋊C8—132no—
280C2×C22⋊C8—132no—
281C2×C22⋊C8#26111yescharacteristic, complemented
282C2×#97—134no—
283C2×C4×C8—134no—
284#381—132no—
285#380—132no—
286#380—132no—
287#379—132no—
288C4×C22⋊C4—132no—
289C4×C22⋊C4—132no—
290#336—134no—
291#336—134no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—44no—
301C22×C13#40512yes—
302C22×C13C22×C4211yescharacteristic
303C2×D13—21no—
304C2×D13—21no—
305C2×D13—28no—
306C2×D13—21no—
307C2×D13—21no—
308C2×D13—21no—
309C2×D13—21no—
310C2×D13—21no—
311C2×D13—21no—
312C2×D13—44no—
313C2×D13—44no—
314C2×D13—44no—
315C2×D13—44no—
316C2×D13—44no—
317C2×D13#40512yes—
318C2×D13#51812yes—
319C2×D13C2×#13112yes—
320C2×D13#56812yes—
321#261—48no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13#51811yescharacteristic
326C4×C13#51811yescharacteristic
327Dic13—21no—
328Dic13—21no—
329Dic13—21no—
330Dic13#51812yes—
331C25—131no—
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—522no—
346C23×C4—522no—
347C23×C4C2×#26111yescharacteristic
348C2×M16—134no—
349C2×M16—134no—
350C2×M16—522no—
351C2×M16—522no—
352C22×C8—134no—
353C22×C8—131no—
354C22×C8—131no—
355C22×C8—132no—
356C22×C8—132no—
357C22×C8—132no—
358C22×C8—132no—
359C22×C8—522no—
360C22×C8—522no—
361C22×C8C2×#26111yescharacteristic
362C22×C8C2×#26111yescharacteristic
363#117—522no—
364#117—522no—
365C2×C4⋊C4—134no—
366C2×C22⋊C4—134no—
367C2×C22⋊C4—134no—
368C2×C22⋊C4—134no—
369C2×C42—134no—
370C22⋊C8—134no—
371C22⋊C8—134no—
372C22⋊C8—134no—
373C22⋊C8—134no—
374C22⋊C8—132no—
375C22⋊C8—132no—
376C22⋊C8—132no—
377C22⋊C8—132no—
378C22⋊C8—132no—
379C22⋊C8—132no—
380C22⋊C8C2×#26112yes—
381C22⋊C8C2×#26112yes—
382#97—524no—
383C4×C8—524no—
384#95—134no—
385#95—134no—
386C2×C13—22no—
387C2×C13—41no—
388C2×C13—41no—
389C2×C13#227311yescharacteristic
390C2×C13C2×#40511yescharacteristic
391C2×C13#287311yescharacteristic
392D13—22no—
393D13—41no—
394D13—41no—
395D13#297614yes—
396C24—131no—
397C24—131no—
398C24—131no—
399C24—131no—
400C24—131no—
401C24—131no—
402C24—264no—
403C24—522no—
404C24—522no—
405C24C4×#26111yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—131no—
409C22×C4—131no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—131no—
413C22×C4—131no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—138no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—521no—
438C22×C4—521no—
439C22×C4—521no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—522no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4C4×#26111yescharacteristic
451C22×C4C4×#26111yescharacteristic
452C22×C4C4×#26111yescharacteristic
453C22×C4C22×#26111yescharacteristic
454C22×C4C22×#26111yescharacteristic
455C22×C4C22×#26111yescharacteristic
456M16—524no—
457M16—524no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—138no—
461C2×C8—132no—
462C2×C8—132no—
463C2×C8—264no—
464C2×C8—264no—
465C2×C8—264no—
466C2×C8—264no—
467C2×C8—522no—
468C2×C8—522no—
469C2×C8—521no—
470C2×C8—521no—
471C2×C8C22×#26112yes—
472C2×C8C22×#26112yes—
473C4⋊C4—524no—
474C22⋊C4—268no—
475C22⋊C4—524no—
476C22⋊C4—524no—
477C42—264no—
478C42—264no—
479C13#2052711yescharacteristic, complemented, Sylow
480C23—22no—
481C23—41no—
482C23—41no—
483C23—131no—
484C23—134no—
485C23—131no—
486C23—131no—
487C23—131no—
488C23—262no—
489C23—262no—
490C23—262no—
491C23—262no—
492C23—262no—
493C23—262no—
494C23—262no—
495C23—262no—
496C23—262no—
497C23—262no—
498C23—262no—
499C23—521no—
500C23—521no—
501C23—521no—
502C23—521no—
503C23—521no—
504C23—521no—
505C23—5216no—
506C23C2×C4×#26111yescharacteristic
507C23C2×C4×#26111yescharacteristic
508C23C2×C4×#26111yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—131no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—131no—
522C2×C4—131no—
523C2×C4—131no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—268no—
540C2×C4—268no—
541C2×C4—268no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4C2×C4×#26111yescharacteristic
552C2×C4C2×C4×#26111yescharacteristic
553C2×C4C2×C4×#26111yescharacteristic
554C2×C4C23×#26111yescharacteristic
555C8—22no—
556C8—22no—
557C8—268no—
558C8—262no—
559C8—262no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—44no—
569C22—132no—
570C22—132no—
571C22—132no—
572C22—132no—
573C22—268no—
574C22—261no—
575C22—261no—
576C22—261no—
577C22—261no—
578C22—261no—
579C22—261no—
580C22—261no—
581C22—261no—
582C22—524no—
583C22—524no—
584C22—524no—
585C22—524no—
586C22—524no—
587C22#1171908912yes—
588C22C22×C4×#26111yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—132no—
593C4—261no—
594C4—261no—
595C4—261no—
596C4—528no—
597C4#1171962311yescharacteristic
598C4#1171962311yescharacteristic
599C2—22no—
600C2—41no—
601C2—41no—
602C2—134no—
603C2—262no—
604C2—521no—
605C2—521no—
606C2#1313127211yescharacteristic
607C2C2×#1171908911yescharacteristic
608C2#1313139911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC2×C13×C22⋊C8C4
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC2×C22⋊C8#261
hypocenterC13#20527
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #13130579C2semidirect
4. #13130572C2semidirect
5. C8×C22⋊#261C2semidirect
6. #13130567C2semidirect
14. #11719169C4semidirect
20. #11719127C4semidirect
21. #11719127C4semidirect
22. #11719126C4semidirect
25. C2×#88100C22semidirect
26. C2×C8×#261C22semidirect
27. C2×C13×C22⋊C8C4semidirect
28. C2×C22⋊#1055C4semidirect
29. C2×#88060C4semidirect
30. C2×#88060C4semidirect
31. D13×C22⋊C8C4semidirect
32. D13×C22⋊C8C4semidirect
35. (C2×#261)⋊C8C22semidirect
36. (C2×#261)⋊C8C22semidirect
281. C2×C22⋊C8#261semidirect
479. C13#20527semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4072
#131312802
#131305792
#131305722
C8×C22⋊#2612
#131305672
C2×D13×C22⋊C82
#2052713