Finite Group Databasebeta

← #16797483

Subgroups — #16797483

Order 3328.

1314 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#261C211yesmaximal, characteristic
3#13130579C214yesmaximal, complemented
4#13130576C214yesmaximal, complemented
5#13130564C212yesmaximal, complemented
6C22⋊C8×#261C212yesmaximal, complemented
7D13×#407C211yesmaximal, characteristic
8C23×C4×D13C2211yescharacteristic
9C22×C22⋊#261C412yes—
10C22×C4×#261C2211yescharacteristic
11C22×C4×#261C2211yescharacteristic
12C2×D13⋊M16C2212yes—
13C2×M16×D13C2212yes—
14#11719169C412yescomplemented
15C4×C22⋊#261C412yes—
16C4×C22⋊#261C412yes—
17C4×C22⋊#261C2212yes—
18C4×C22⋊#261C2212yes—
19C2×(C2×#261)⋊C4C412yes—
20#11719127C412yescomplemented
21#11719127C412yescomplemented
22#11719126C412yescomplemented
23D13⋊(C22⋊C8)C2212yes—
24D13⋊(C22⋊C8)C2212yes—
25C2×#88100C2214yescomplemented
26C2×C8×#261C2214yescomplemented
27C13×#407C411yescharacteristic, complemented
28#11718868C411yescharacteristic, complemented
29#11718787C412yescomplemented
30#11718387C412yescomplemented
31#11718387C412yescomplemented
32D13×C22⋊C8C2212yes—
33D13×C22⋊C8C2212yes—
34(C2×#261)⋊C8C2214yescomplemented
35(C2×#261)⋊C8C2214yescomplemented
36C24×D13C2×C411yescharacteristic
37C23×#261C2×C412yes—
38C23×#261C2×C412yes—
39C23×C4×C13C2×C411yescharacteristic
40C23×Dic13C2×C411yescharacteristic
41C22×C4×D13—42no—
42C22×C4×D13—42no—
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×D13C2×C411yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C2×C22⋊#261—28no—
56C2×C22⋊#261C2×C414yes—
57C2×C22⋊#261C2×C414yes—
58C2×#6122C2×C414yescomplemented
59C2×C4×#261—42no—
60C2×C4×#261—42no—
61C2×C4×#261C2×C412yes—
62C2×C4×#261C2×C412yes—
63C2×C4×#261C2312yes—
64C2×C4×#261C2312yes—
65D13⋊M16—42no—
66D13⋊M16—42no—
67C2×#6118C2×C414yescomplemented
68C2×D13⋊C8C2314yes—
69C2×C13×M16C2×C412yescomplemented
70C2×#6099C2×C412yescomplemented
71M16×D13—42no—
72M16×D13—42no—
73C2×#6094C2×C414yescomplemented
74C2×C8×D13C2314yes—
75C22⋊#1057C2×C414yes—
76C22⋊#1057C2×C414yescomplemented
77(C2×#261)⋊C4C2×C414yes—
78(C2×#261)⋊C4C2×C414yes—
79#88111C2×C414yes—
80#88111C2×C414yescomplemented
81#88100—44no—
82C8×#261—44no—
83C13×C22⋊C8C2×C412yes—
84C13×C22⋊C8C2×C412yescomplemented
85C22⋊#1055C2×C412yes—
86C22⋊#1055C2×C412yescomplemented
87#88060C2×C414yes—
88#88060C2×C414yescomplemented
89#20524—131nomaximal, Sylow
90C24×C13C4211yescharacteristic
91C23×D13—24no—
92C23×D13—41no—
93C23×D13—41no—
94C23×D13—42no—
95C23×D13C4211yescharacteristic
96C23×D13C4211yescharacteristic
97C23×D13C4211yescharacteristic
98C23×D13C22×C411yescharacteristic
99C23×D13C22×C411yescharacteristic
100C23×D13C22×C411yescharacteristic
101C22×#261—24no—
102C22×#261—42no—
103C22×#261—42no—
104C22×#261—42no—
105C22×#261—42no—
106C22×#261M1618yescomplemented
107C22×#261C22×C414yes—
108C22×#261C22×C414yes—
109C22×C4×C13—42no—
110C22×C4×C13C4211yescharacteristic
111C22×C4×C13C4211yescharacteristic
112C22×C4×C13C4211yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×C4×C13C22×C411yescharacteristic
115C22×C4×C13C22×C411yescharacteristic
116C22×Dic13—42no—
117C22×Dic13C4211yescharacteristic
118C22×Dic13C4211yescharacteristic
119C22×Dic13C4211yescharacteristic
120C22×Dic13C22×C411yescharacteristic
121C22×Dic13C22×C411yescharacteristic
122C22×Dic13C22×C411yescharacteristic
123C2×C4×D13—22no—
124C2×C4×D13—22no—
125C2×C4×D13—22no—
126C2×C4×D13—22no—
127C2×C4×D13—22no—
128C2×C4×D13—22no—
129C2×C4×D13—42no—
130C2×C4×D13—42no—
131C2×C4×D13—42no—
132C2×C4×D13—42no—
133C2×C4×D13—42no—
134C2×C4×D13—42no—
135C2×C4×D13—41no—
136C2×C4×D13—41no—
137C2×C4×D13—41no—
138C2×C4×D13—41no—
139C2×C4×D13—41no—
140C2×C4×D13—41no—
141C2×C4×D13C4211yescharacteristic
142C2×C4×D13C4211yescharacteristic
143C2×C4×D13C4211yescharacteristic
144C2×C4×D13C4211yescharacteristic
145C2×C4×D13C4211yescharacteristic
146C2×C4×D13C4211yescharacteristic
147C2×C4×D13C22×C411yescharacteristic
148C2×C4×D13C22×C411yescharacteristic
149C2×C4×D13C22×C411yescharacteristic
150C2×C4×D13C22×C411yescharacteristic
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C22×C411yescharacteristic
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C22×C411yescharacteristic
156C2×C4×D13C2411yescharacteristic
157C22⋊#261—28no—
158C22⋊#261—28no—
159#6122—44no—
160C2×#1057C22×C418yes—
161C4×#261—24no—
162C4×#261—24no—
163C4×#261—42no—
164C4×#261—42no—
165#6118—44no—
166D13⋊C8—24no—
167D13⋊C8—24no—
168C13×M16—42no—
169C2×C8×C13C22×C414yes—
170#6099—42no—
171C2×#1055C22×C414yes—
172#6094—44no—
173C8×D13—24no—
174C8×D13—24no—
175C2×#407—131no—
176C2×#407—131no—
177C2×C4×C22⋊C4—131no—
178#1753—134no—
179#1753—134no—
180#1749—132no—
181C4×C22⋊C8—132no—
182C23×C13—22no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13C2×C4211yescharacteristic
186C23×C13C2×C4211yescharacteristic
187C23×C13C2×C4211yescharacteristic
188C22×D13—21no—
189C22×D13—21no—
190C22×D13—22no—
191C22×D13—22no—
192C22×D13—21no—
193C22×D13—21no—
194C22×D13—21no—
195C22×D13—21no—
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—22no—
201C22×D13—22no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—41no—
206C22×D13—41no—
207C22×D13—41no—
208C22×D13—48no—
209C22×D13—48no—
210C22×D13C2×C4211yescharacteristic
211C22×D13C2×C4211yescharacteristic
212C22×D13C2×C4211yescharacteristic
213C22×D13C2×M1614yes—
214C22×D13C23×C411yescharacteristic
215C2×#261—24no—
216C2×#261—24no—
217C2×#261—24no—
218C2×#261—24no—
219C2×#261—24no—
220C2×#261—48no—
221C2×#261—48no—
222C2×#261C2×M1618yes—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13C2×C4211yescharacteristic
230C2×C4×C13C2×C4211yescharacteristic
231C2×C4×C13C2×C4211yescharacteristic
232C2×C4×C13C23×C411yescharacteristic
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13C2×C4211yescharacteristic
240C2×Dic13C2×C4211yescharacteristic
241C2×Dic13C2×C4211yescharacteristic
242C2×Dic13C23×C411yescharacteristic
243C4×D13—21no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—22no—
250C4×D13—22no—
251C4×D13—22no—
252C4×D13—22no—
253C4×D13—22no—
254C4×D13—22no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—41no—
258C4×D13—41no—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13H(5,𝔽2)12yes—
262C4×D13H(5,𝔽2)12yes—
263#1057—28no—
264C8×C13—24no—
265#1055—24no—
266C24×C4—131no—
267C22×M16—132no—
268C22×M16—132no—
269C22×C22⋊C4—132no—
270C22×C42—131no—
271C22×C42—131no—
272#407—132no—
273#407—132no—
274#407—132no—
275#407—132no—
276#407—131no—
277#407—132no—
278#407—132no—
279#407—132no—
280#407#26111yescharacteristic, complemented
281C2×C22⋊C8—132no—
282C2×C22⋊C8—132no—
283C2×C22⋊C8—132no—
284C2×C22⋊C8—132no—
285C2×#97—134no—
286C2×C4×C8—134no—
287C4×C22⋊C4—132no—
288C4×C22⋊C4—132no—
289C4×C22⋊C4—132no—
290C4×C22⋊C4—132no—
291C2×#95—132no—
292#336—134no—
293#336—134no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—44no—
303C22×C13C4×M1612yes—
304C22×C13C22×C4211yescharacteristic
305C2×D13—21no—
306C2×D13—21no—
307C2×D13—24no—
308C2×D13—24no—
309C2×D13—21no—
310C2×D13—21no—
311C2×D13—21no—
312C2×D13—21no—
313C2×D13—21no—
314C2×D13—21no—
315C2×D13—44no—
316C2×D13—44no—
317C2×D13—44no—
318C2×D13—42no—
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—42no—
322C2×D13C4×M1612yes—
323C2×D13#51811yescharacteristic
324C2×D13#51811yescharacteristic
325C2×D13C22×M1612yes—
326C2×D13#56812yes—
327#261—28no—
328#261—44no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13#51812yes—
333Dic13—21no—
334Dic13—21no—
335Dic13—21no—
336Dic13#51812yes—
337C25—131no—
338C23×C4—132no—
339C23×C4—131no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—132no—
353C23×C4—522no—
354C23×C4—522no—
355C23×C4C2×#26111yescharacteristic
356C2×M16—134no—
357C2×M16—134no—
358C2×M16—132no—
359C2×M16—134no—
360C2×M16—522no—
361C2×M16—522no—
362C2×M16—522no—
363C2×M16—522no—
364C2×M16C2×#26112yescomplemented
365C22×C8—134no—
366C22×C8—134no—
367C2×C22⋊C4—134no—
368C2×C22⋊C4—134no—
369C2×C22⋊C4—268no—
370C2×C42—132no—
371C2×C42—132no—
372C2×C42—132no—
373C2×C42—132no—
374C2×C42—522no—
375C2×C42—522no—
376C22⋊C8—134no—
377C22⋊C8—134no—
378C22⋊C8—134no—
379C22⋊C8—134no—
380C22⋊C8—132no—
381C22⋊C8—132no—
382C22⋊C8—134no—
383C22⋊C8—134no—
384C22⋊C8C2×#26112yes—
385C22⋊C8C2×#26112yescomplemented
386#97—524no—
387C4×C8—524no—
388#95—134no—
389#95—134no—
390C2×C13—22no—
391C2×C13—41no—
392C2×C13—41no—
393C2×C13#227311yescharacteristic
394C2×C13C2×C4×M1611yescharacteristic
395C2×C13#287311yescharacteristic
396D13—22no—
397D13—41no—
398D13—41no—
399D13#297312yes—
400D13#297512yes—
401C24—131no—
402C24—131no—
403C24—131no—
404C24—131no—
405C24—131no—
406C24—131no—
407C24—264no—
408C24—521no—
409C24—521no—
410C24—522no—
411C24C4×#26111yescharacteristic
412C22×C4—42no—
413C22×C4—131no—
414C22×C4—134no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—138no—
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—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—134no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—264no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4—522no—
451C22×C4—521no—
452C22×C4—521no—
453C22×C4—521no—
454C22×C4—521no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—522no—
458C22×C4—522no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4C4×#26111yescharacteristic
463C22×C4C4×#26111yescharacteristic
464C22×C4C4×#26111yescharacteristic
465C22×C4C22×#26111yescharacteristic
466C22×C4C22×#26111yescharacteristic
467C22×C4C22×#26111yescharacteristic
468M16—42no—
469M16—524no—
470M16—522no—
471M16—524no—
472M16—524no—
473C2×C8—138no—
474C2×C8—134no—
475C2×C8—264no—
476C2×C8—264no—
477C2×C8—264no—
478C2×C8—264no—
479C2×C8C22×#26114yes—
480C22⋊C4—268no—
481C22⋊C4—268no—
482C42—264no—
483C42—264no—
484C42—522no—
485C42—522no—
486C13#2052411yescharacteristic, complemented, Sylow
487C23—22no—
488C23—41no—
489C23—41no—
490C23—131no—
491C23—134no—
492C23—131no—
493C23—131no—
494C23—131no—
495C23—261no—
496C23—261no—
497C23—262no—
498C23—262no—
499C23—262no—
500C23—261no—
501C23—261no—
502C23—261no—
503C23—261no—
504C23—262no—
505C23—262no—
506C23—262no—
507C23—262no—
508C23—262no—
509C23—521no—
510C23—521no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—528no—
516C23—528no—
517C23C2×C4×#26111yescharacteristic
518C23C2×C4×#26111yescharacteristic
519C23C2×C4×#26111yescharacteristic
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—131no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—138no—
530C2×C4—131no—
531C2×C4—131no—
532C2×C4—131no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—264no—
551C2×C4—264no—
552C2×C4—264no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—528no—
563C2×C4—528no—
564C2×C4C2×C4×#26111yescharacteristic
565C2×C4C2×C4×#26111yescharacteristic
566C2×C4C2×C4×#26111yescharacteristic
567C2×C4C23×#26111yescharacteristic
568C8—24no—
569C8—268no—
570C8—264no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—44no—
580C22—131no—
581C22—131no—
582C22—132no—
583C22—132no—
584C22—132no—
585C22—264no—
586C22—264no—
587C22—261no—
588C22—261no—
589C22—261no—
590C22—261no—
591C22—261no—
592C22—261no—
593C22—261no—
594C22—261no—
595C22—524no—
596C22—522no—
597C22—522no—
598C22—522no—
599C22—522no—
600C22—524no—
601C22—524no—
602C22M16×#26112yes—
603C22C22×C4×#26111yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—132no—
608C4—268no—
609C4—261no—
610C4—261no—
611C4—261no—
612C4—524no—
613C4#1171962312yes—
614C2—22no—
615C2—41no—
616C2—41no—
617C2—132no—
618C2—132no—
619C2—262no—
620C2—521no—
621C2—521no—
622C2#1313127211yescharacteristic
623C2C2×M16×#26111yescharacteristic
624C2#1313139911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#407C4
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenter#407#261
hypocenterC13#20524
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #13130579C2semidirect
4. #13130576C2semidirect
5. #13130564C2semidirect
6. C22⋊C8×#261C2semidirect
14. #11719169C4semidirect
20. #11719127C4semidirect
21. #11719127C4semidirect
22. #11719126C4semidirect
25. C2×#88100C22semidirect
26. C2×C8×#261C22semidirect
27. C13×#407C4semidirect
28. #11718868C4semidirect
29. #11718787C4semidirect
30. #11718387C4semidirect
31. #11718387C4semidirect
34. (C2×#261)⋊C8C22semidirect
35. (C2×#261)⋊C8C22semidirect
58. C2×#6122C2×C4semidirect
67. C2×#6118C2×C4semidirect
69. C2×C13×M16C2×C4semidirect
70. C2×#6099C2×C4semidirect
73. C2×#6094C2×C4semidirect
76. C22⋊#1057C2×C4semidirect
80. #88111C2×C4semidirect
84. C13×C22⋊C8C2×C4semidirect
86. C22⋊#1055C2×C4semidirect
88. #88060C2×C4semidirect
106. C22×#261M16semidirect
280. #407#261semidirect
364. C2×M16C2×#261semidirect
385. C22⋊C8C2×#261semidirect
486. C13#20524semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4072
C2×C4×C22⋊#2612
#131305792
#131305762
#131305642
C22⋊C8×#2612
D13×#4072
#2052413