Finite Group Databasebeta

← D13×#1546 #15831239

Subgroups — D13×#1546 #15831239

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2D13×#431C211yesmaximal, characteristic
3D13×#423C211yesmaximal, characteristic
4#13113509C211yesmaximal, characteristic, complemented
5#13113508C211yesmaximal, characteristic, complemented
6#13113507C211yesmaximal, characteristic, complemented
7#13113506C214yesmaximal, complemented
8D13×#332C214yesmaximal, complemented
9C13×#1546C211yesmaximal, characteristic, complemented
10C22×Q8×D13—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198—21no—
13C2×M16×D13—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8—21no—
16D13×C4⋊Q8—21no—
17D13×C4⋊Q8—21no—
18D13×C4⋊Q8C412yes—
19D13×C4⋊Q8C412yes—
20D13×C4⋊Q8C2212yes—
21D13×C4⋊Q8C2212yes—
22C2×C4⋊C4×D13—21no—
23C2×C4⋊C4×D13C412yes—
24C2×#88142—21no—
25C2×#88142C412yes—
26C2×C42×D13C2211yescharacteristic
27C2×#88123C2211yescharacteristic
28C13×#431C2211yescharacteristic
29C13×#423C2211yescharacteristic
30#11718779—21no—
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718498—21no—
34#11718498C2212yes—
35#11718494C2212yes—
36D13×C4⋊C8—21no—
37D13×C4⋊C8C2212yes—
38D13×C4⋊C8C2212yes—
39D13×C22⋊C8—21no—
40#11718379—21no—
41#11718346—21no—
42C4×C8×D13—21no—
43C13×#332C2214yescomplemented
44#11718139C2214yescomplemented
45#11718078C2214yescomplemented
46#11718074C2214yescomplemented
47C22×Q8×C13—21no—
48C2×Q8×D13—22no—
49C2×Q8×D13—22no—
50C2×Q8×D13—22no—
51C2×Q8×D13—22no—
52C2×Q8×D13—44no—
53C2×Q8×D13—44no—
54C22×C4×D13—22no—
55C22×C4×D13C2×C411yescharacteristic
56C22×C4×D13D411yescharacteristic
57C22×C4×D13D411yescharacteristic
58C22×Dic26—21no—
59C22×Dic26—22no—
60C2×C13×M16—21no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8C2×C412yes—
64C13×C4⋊Q8C2312yes—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2×C412yes—
67C2×C42×C13C2311yescharacteristic
68#88198—22no—
69#88198—22no—
70#88198—22no—
71#88198—22no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13C2×C412yes—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×#6099—21no—
80M16×D13—44no—
81C2×#6094—22no—
82C2×C8×D13—22no—
83C2×C8×D13—22no—
84C4⋊C4×D13—22no—
85C4⋊C4×D13—22no—
86C4⋊C4×D13—22no—
87C4⋊C4×D13—22no—
88C4⋊C4×D13—22no—
89C4⋊C4×D13—22no—
90C4⋊C4×D13C2×C414yes—
91C4⋊C4×D13C2×C414yes—
92#88142—22no—
93#88142—22no—
94#88142—22no—
95#88142—22no—
96#88142—22no—
97#88142—22no—
98#88142C2×C414yes—
99#88142C2×C414yes—
100C42×D13C2×C411yescharacteristic
101C42×D13C2×C411yescharacteristic
102C42×D13D411yescharacteristic
103C42×D13D411yescharacteristic
104C42×D13D411yescharacteristic
105C42×D13D411yescharacteristic
106C42×D13C2311yescharacteristic
107C42×D13C2311yescharacteristic
108#88123—21no—
109#88123—21no—
110#88123C2×C412yes—
111#88123C2312yes—
112C13×C4⋊C8—21no—
113C13×C4⋊C8C2312yes—
114C13×C4⋊C8C2312yes—
115C13×C22⋊C8—21no—
116C4×C8×C13—21no—
117C22⋊#1055—21no—
118#88060—22no—
119#88054—22no—
120#88054—22no—
121#88054—22no—
122C8×Dic13—22no—
123C4⋊#1055—21no—
124C4⋊#1055C2312yes—
125C4⋊#1055C2312yes—
126C4×#1055—21no—
127C2×#1546—131nomaximal, Sylow
128C23×D13C22⋊C411yescharacteristic
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—42no—
132C2×Q8×C13—42no—
133C22×C4×C13—22no—
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×Dic13—22no—
138C22×Dic13C22⋊C411yescharacteristic
139C22×Dic13C22⋊C411yescharacteristic
140C22×Dic13C22⋊C411yescharacteristic
141Q8×D13—48no—
142Q8×D13—48no—
143Q8×D13—44no—
144Q8×D13—44no—
145Q8×D13—44no—
146Q8×D13—44no—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—24no—
150C2×C4×D13—24no—
151C2×C4×D13—48no—
152C2×C4×D13C22⋊C411yescharacteristic
153C2×C4×D13C22⋊C411yescharacteristic
154C2×C4×D13C22⋊C411yescharacteristic
155C2×C4×D13C22⋊C411yescharacteristic
156C2×C4×D13C22⋊C411yescharacteristic
157C2×C4×D13C22⋊C411yescharacteristic
158C2×C4×D13D814yes—
159C2×C4×D13SD1614yes—
160C2×C4×D13C22×C411yescharacteristic
161C2×C4×D13C22×C411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13C2×D411yescharacteristic
165C2×C4×D13C2×D411yescharacteristic
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26—24no—
169C2×Dic26—24no—
170C2×Dic26—42no—
171C2×Dic26—42no—
172C2×Dic26—48no—
173C13×M16—42no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4C22×C414yes—
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13C2411yescharacteristic
184C4⋊Dic13—22no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13C22×C414yes—
188#6101—24no—
189#6101—24no—
190#6101—24no—
191#6101—24no—
192C4×Dic13C22⋊C411yescharacteristic
193C4×Dic13C22⋊C411yescharacteristic
194C4×Dic13C22⋊C411yescharacteristic
195C4×Dic13C22⋊C411yescharacteristic
196C4×Dic13C22⋊C411yescharacteristic
197C4×Dic13C22⋊C411yescharacteristic
198C4×Dic13C22×C411yescharacteristic
199C4×Dic13C22×C411yescharacteristic
200C4×Dic13C2×D411yescharacteristic
201C4×Dic13C2×D411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13C2×D411yescharacteristic
204#6099—42no—
205C2×#1055—22no—
206C2×#1055—22no—
207#6094—44no—
208C8×D13—44no—
209C8×D13—44no—
210C22×C4⋊Q8—131no—
211C2×#431—131no—
212C2×#423—131no—
213#1546—131no—
214#1546—131no—
215#1546—134no—
216#1546—131no—
217#1546D1311yescharacteristic, direct product factor
218C2×#332—134no—
219C23×C13C2×C22⋊C411yescharacteristic
220C22×D13—22no—
221C22×D13—22no—
222C22×D13#10214yes—
223C22×D13C2×C22⋊C411yescharacteristic
224C22×D13C2×C22⋊C411yescharacteristic
225Q8×C13—42no—
226Q8×C13—42no—
227Q8×C13—44no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—44no—
232C2×C4×C13C2×C22⋊C411yescharacteristic
233C2×C4×C13C2×C22⋊C411yescharacteristic
234C2×C4×C13C2×C22⋊C411yescharacteristic
235C2×C4×C13C2×D812yes—
236C2×C4×C13C2×SD1612yes—
237C2×C4×C13C23×C411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C22×D411yescharacteristic
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—44no—
244C2×Dic13#10214yes—
245C2×Dic13C2×C22⋊C411yescharacteristic
246C2×Dic13C2×C22⋊C411yescharacteristic
247C2×Dic13C2×C22⋊C411yescharacteristic
248C2×Dic13C2×C22⋊C411yescharacteristic
249C2×Dic13C2×C22⋊C411yescharacteristic
250C2×Dic13C2×C22⋊C411yescharacteristic
251C4×D13—22no—
252C4×D13—22no—
253C4×D13—22no—
254C4×D13—22no—
255C4×D13—22no—
256C4×D13—22no—
257C4×D13—48no—
258C4×D13—48no—
259C4×D13#10114yes—
260C4×D13#10214yes—
261C4×D13#10214yes—
262C4×D13C2×D812yes—
263C4×D13C2×D812yes—
264C4×D13C2×SD1612yes—
265C4×D13C2×SD1612yes—
266C4×D13#13714yes—
267Dic26—42no—
268Dic26—42no—
269Dic26—44no—
270Dic26—48no—
271Dic26—48no—
272C8×C13—42no—
273C8×C13—42no—
274#1055—42no—
275#1055—42no—
276C23×Q8—261no—
277C22×M16—261no—
278C2×C4⋊Q8—132no—
279C2×C4⋊Q8—132no—
280C2×C4⋊Q8—132no—
281C2×C4⋊Q8—132no—
282C2×C4⋊Q8—132no—
283C2×C4⋊Q8—131no—
284C2×C4⋊Q8—261no—
285C2×C4⋊Q8—261no—
286C2×C4⋊Q8—261no—
287C2×C4⋊Q8—261no—
288C2×C4⋊Q8—261no—
289C2×C4⋊Q8—261no—
290C2×C4⋊Q8C2×D1311yescharacteristic
291C22×C4⋊C4—132no—
292C22×C4⋊C4—261no—
293C22×C42—131no—
294#431—131no—
295#431—132no—
296#431—261no—
297#431—261no—
298#431C2×D1311yescharacteristic
299#423—131no—
300#423—132no—
301#423—261no—
302#423—261no—
303#423C2×D1311yescharacteristic
304C2×C4⋊C8—132no—
305C2×C4⋊C8—132no—
306C2×C4⋊C8—261no—
307C2×C22⋊C8—261no—
308C2×C4×C8—261no—
309#332—134no—
310#332—134no—
311#332—134no—
312#332C2×D1314yescomplemented
313C22×C13—21no—
314C22×C13—21no—
315C22×C13C2×#10212yes—
316C22×C13C22×C22⋊C411yescharacteristic
317C2×D13—21no—
318C2×D13—21no—
319C2×D13—28no—
320C2×D13C2×#10112yes—
321C2×D13C2×#10212yes—
322C2×D13C2×#10212yes—
323C2×D13#41912yes—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—44no—
327C4×C13C2×#10112yes—
328C4×C13C2×#10212yes—
329C4×C13C22×D811yescharacteristic
330C4×C13C22×SD1611yescharacteristic
331C4×C13C2×#13712yes—
332Dic13—21no—
333Dic13—21no—
334Dic13—44no—
335Dic13C2×#10112yes—
336Dic13C2×#10212yes—
337Dic13C2×#10212yes—
338Dic13#41912yes—
339C22×Q8—21no—
340C22×Q8—262no—
341C22×Q8—262no—
342C22×Q8—262no—
343C22×Q8—262no—
344C22×Q8—262no—
345C22×Q8—261no—
346C22×Q8—524no—
347C22×Q8—524no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—262no—
352C2×M16—21no—
353C2×M16—262no—
354C2×M16—261no—
355C2×M16—524no—
356C22×C8—262no—
357C22×C8—262no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—134no—
361C4⋊Q8—134no—
362C4⋊Q8—132no—
363C4⋊Q8—132no—
364C4⋊Q8—262no—
365C4⋊Q8—262no—
366C4⋊Q8—262no—
367C4⋊Q8—262no—
368C4⋊Q8—262no—
369C4⋊Q8—262no—
370C4⋊Q8—262no—
371C4⋊Q8—262no—
372C4⋊Q8—262no—
373C4⋊Q8—262no—
374C4⋊Q8—261no—
375C4⋊Q8—261no—
376C4⋊Q8C4×D1312yes—
377C4⋊Q8C22×D1312yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—132no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C4×D1312yes—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42C22×D1311yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—132no—
406C4⋊C8—132no—
407C4⋊C8—262no—
408C4⋊C8—262no—
409C4⋊C8—262no—
410C4⋊C8—261no—
411C4⋊C8C22×D1312yes—
412C4⋊C8C22×D1312yes—
413C22⋊C8—21no—
414C22⋊C8—262no—
415C22⋊C8—261no—
416C4×C8—21no—
417C4×C8—262no—
418C4×C8—261no—
419C2×C13—22no—
420C2×C13C22×#10111yescharacteristic
421C2×C13C22×#10211yescharacteristic
422C2×C13C2×#41911yescharacteristic
423D13—22no—
424D13#154614yesdirect product factor
425C24—131no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—264no—
431C2×Q8—264no—
432C2×Q8—262no—
433C2×Q8—262no—
434C2×Q8—528no—
435C2×Q8—528no—
436C2×Q8—528no—
437C2×Q8—524no—
438C2×Q8—524no—
439C2×Q8—524no—
440C2×Q8—524no—
441C2×Q8—522no—
442C2×Q8—522no—
443C22×C4—22no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—134no—
449C22×C4—134no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—262no—
466C22×C4—528no—
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4D4×D1311yescharacteristic
469C22×C4D4×D1311yescharacteristic
470M16—42no—
471M16—524no—
472M16—522no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—262no—
476C2×C8—262no—
477C2×C8—524no—
478C2×C8—524no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—134no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—262no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4C2×C4×D1314yes—
491C42—131no—
492C42—131no—
493C42—131no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—131no—
499C42—131no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42C2×C4×D1311yescharacteristic
504C42D4×D1311yescharacteristic
505C42D4×D1311yescharacteristic
506C42C23×D1311yescharacteristic
507C13C2×#154611yescharacteristic, complemented, Sylow
508C23—131no—
509C23—131no—
510C23—134no—
511C23—262no—
512C23—262no—
513C23C22⋊C4×D1311yescharacteristic
514Q8—44no—
515Q8—42no—
516Q8—42no—
517Q8—528no—
518Q8—528no—
519Q8—524no—
520Q8—522no—
521Q8—522no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—131no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—131no—
530C2×C4—134no—
531C2×C4—134no—
532C2×C4—134no—
533C2×C4—134no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—134no—
539C2×C4—131no—
540C2×C4—131no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—264no—
550C2×C4—528no—
551C2×C4—528no—
552C2×C4—524no—
553C2×C4C22⋊C4×D1311yescharacteristic
554C2×C4C22⋊C4×D1311yescharacteristic
555C2×C4C22⋊C4×D1311yescharacteristic
556C2×C4D8×D1312yes—
557C2×C4SD16×D1312yes—
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4C2×D4×D1311yescharacteristic
560C2×C4C2×D4×D1311yescharacteristic
561C8—42no—
562C8—42no—
563C8—522no—
564C8—522no—
565C22—21no—
566C22—21no—
567C22—132no—
568C22—132no—
569C22—132no—
570C22—132no—
571C22—268no—
572C22—261no—
573C22—261no—
574C22D13×#10212yes—
575C22C2×C22⋊C4×D1311yescharacteristic
576C4—21no—
577C4—21no—
578C4—44no—
579C4—132no—
580C4—132no—
581C4—132no—
582C4—132no—
583C4—261no—
584C4—261no—
585C4—524no—
586C4D13×#10112yes—
587C4D13×#10212yes—
588C4C2×D8×D1311yescharacteristic
589C4C2×SD16×D1311yescharacteristic
590C4D13×#13712yes—
591C2—22no—
592C2—134no—
593C2—262no—
594C2C2×D13×#10111yescharacteristic
595C2C2×D13×#10211yescharacteristic
596C2D13×#41911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1546C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenter#1546D13
hypocenterC13C2×#1546
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #13113509C2semidirect
5. #13113508C2semidirect
6. #13113507C2semidirect
7. #13113506C2semidirect
8. D13×#332C2semidirect
9. C13×#1546C2semidirect
43. C13×#332C22semidirect
44. #11718139C22semidirect
45. #11718078C22semidirect
46. #11718074C22semidirect
217. #1546D13direct (N × H)
312. #332C2×D13semidirect
424. D13#1546direct (N × H)
507. C13C2×#1546semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
D13×#4312
D13×#4232
#131135092
#131135082
#131135072
#131135062
D13×#3322
C13×#15462
C2×#154613