Finite Group Databasebeta

← D13×#1997 #15867576

Subgroups — D13×#1997 #15867576

Order 3328.

1342 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×#423C211yesmaximal, characteristic
3C4×M16×D13C211yesmaximal, characteristic
4#13115826C211yesmaximal, characteristic, complemented
5#13115825C211yesmaximal, characteristic, complemented
6#13115824C211yesmaximal, characteristic, complemented
7#13115823C214yesmaximal, complemented
8D13×#343C214yesmaximal
9C13×#1997C211yesmaximal, characteristic, complemented
10C22×Q8×D13C412yes—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198C412yes—
13C2×M16×D13C2212yes—
14C2×M16×D13C2212yes—
15D13×C4⋊Q8—21no—
16D13×C4⋊Q8—21no—
17D13×C4⋊Q8—21no—
18D13×C4⋊Q8—21no—
19D13×C4⋊Q8—21no—
20D13×C4⋊Q8—21no—
21D13×C4⋊Q8—21no—
22D13×C4⋊Q8—21no—
23C2×C4⋊C4×D13C412yes—
24C2×C4⋊C4×D13C2212yes—
25C2×#88142C412yes—
26C2×#88142C2212yes—
27C2×C42×D13C2211yescharacteristic
28C2×#88123C2211yescharacteristic
29C13×#423C2211yescharacteristic
30C4×C13×M16C2211yescharacteristic
31#11718779C2212yes—
32M16×Dic13C2212yes—
33#11718585C2211yescharacteristic
34C4×#6099C2211yescharacteristic
35#11718498—21no—
36#11718498—21no—
37D13×C4⋊C8—21no—
38D13×C4⋊C8—21no—
39#11718368—21no—
40D13×#97—21no—
41C4×#6094—21no—
42C4×C8×D13—21no—
43C13×#343C2214yes—
44#11718146C2214yes—
45#11718146C2214yes—
46#11718122C2214yes—
47C22×Q8×C13C2×C412yes—
48C2×Q8×D13—22no—
49C2×Q8×D13—22no—
50C2×Q8×D13—22no—
51C2×Q8×D13—22no—
52C2×Q8×D13—48no—
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13C2×C414yes—
56C22×C4×D13C2311yescharacteristic
57C22×Dic26C2×C412yes—
58C22×Dic26C2×C414yes—
59C2×C13×M16C2312yes—
60C2×C13×M16C2312yes—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—21no—
65C2×C13×C4⋊C4C2×C412yes—
66C2×C13×C4⋊C4C2312yes—
67C2×C42×C13C2311yescharacteristic
68#88198—22no—
69#88198—22no—
70#88198—22no—
71#88198—22no—
72C2×C4⋊Dic13C2×C412yes—
73C2×C4⋊Dic13C2312yes—
74C2×#6101C2×C414yes—
75C2×#6101C2×C414yes—
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×#6099C2312yes—
80C2×#6099C2312yes—
81M16×D13—24no—
82M16×D13—28no—
83M16×D13Q818yescomplemented
84C2×#6094—22no—
85C2×#6094—22no—
86C2×C8×D13—22no—
87C2×C8×D13—22no—
88C4⋊C4×D13—22no—
89C4⋊C4×D13—22no—
90C4⋊C4×D13—22no—
91C4⋊C4×D13—22no—
92C4⋊C4×D13—22no—
93C4⋊C4×D13—22no—
94C4⋊C4×D13—22no—
95C4⋊C4×D13—22no—
96#88142—22no—
97#88142—22no—
98#88142—22no—
99#88142—22no—
100#88142—22no—
101#88142—22no—
102#88142—22no—
103#88142—22no—
104C42×D13D411yescharacteristic
105C42×D13D411yescharacteristic
106C42×D13D411yescharacteristic
107C42×D13D411yescharacteristic
108C42×D13D411yescharacteristic
109C42×D13D411yescharacteristic
110C42×D13D411yescharacteristic
111C42×D13D411yescharacteristic
112#88123—21no—
113#88123—21no—
114#88123—21no—
115#88123—21no—
116C13×C4⋊C8—21no—
117C13×C4⋊C8—21no—
118C13×#97—21no—
119C4×C8×C13—21no—
120#88055—22no—
121#88054—22no—
122#88054—22no—
123C8×Dic13—22no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126#88043—21no—
127C4×#1055—21no—
128C2×#1997—131nomaximal, Sylow
129C23×D13C22×C411yescharacteristic
130C2×Q8×C13—22no—
131C2×Q8×C13—22no—
132C2×Q8×C13—44no—
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C414yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C414yes—
140C22×Dic13C22×C411yescharacteristic
141Q8×D13—48no—
142Q8×D13—48no—
143Q8×D13—48no—
144Q8×D13—48no—
145C2×C4×D13—24no—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—48no—
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×D13C22⋊C411yescharacteristic
157C2×C4×D13C22⋊C411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×C4×D13C2×Q814yes—
163C2×C4×D13#4114yes—
164C2×Dic26—22no—
165C2×Dic26—22no—
166C2×Dic26—24no—
167C2×Dic26—24no—
168C2×Dic26—48no—
169C2×Dic26—44no—
170C13×M16—22no—
171C13×M16—24no—
172C13×M16C2×Q814yescomplemented
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C42×C13C2×D411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C4⋊Dic13—22no—
184C4⋊Dic13—22no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187#6101—24no—
188#6101—24no—
189#6101—24no—
190#6101—24no—
191C4×Dic13C22⋊C411yescharacteristic
192C4×Dic13C22⋊C411yescharacteristic
193C4×Dic13C22⋊C411yescharacteristic
194C4×Dic13C22⋊C411yescharacteristic
195C4×Dic13C22⋊C411yescharacteristic
196C4×Dic13C22⋊C411yescharacteristic
197C4×Dic13C22⋊C411yescharacteristic
198C4×Dic13C22⋊C411yescharacteristic
199C4×Dic13C2×D411yescharacteristic
200C4×Dic13C2×D411yescharacteristic
201C4×Dic13C2×D411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203#6099—22no—
204#6099—24no—
205#6099C2×Q814yescomplemented
206C2×#1055—22no—
207C2×#1055—22no—
208#6094—28no—
209#6094—44no—
210C8×D13—28no—
211C8×D13—44no—
212C22×C4⋊Q8—131no—
213C2×#423—131no—
214C2×C4×M16—131no—
215#1997—131no—
216#1997—131no—
217#1997—134no—
218#1997—131no—
219#1997D1311yescharacteristic, direct product factor
220C2×#343—134no—
221C23×C13C23×C411yescharacteristic
222C22×D13—22no—
223C22×D13—22no—
224C22×D13C2×C22⋊C411yescharacteristic
225C22×D13C2×C22⋊C411yescharacteristic
226C22×D13C4×Q814yes—
227Q8×C13—44no—
228Q8×C13—44no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—44no—
233C2×C4×C13C2×C22⋊C411yescharacteristic
234C2×C4×C13C2×C22⋊C411yescharacteristic
235C2×C4×C13C2×C22⋊C411yescharacteristic
236C2×C4×C13C2×C22⋊C411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C22×Q812yes—
240C2×C4×C13C2×#4112yes—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—24no—
244C2×Dic13—44no—
245C2×Dic13C2×C22⋊C411yescharacteristic
246C2×Dic13C2×C22⋊C411yescharacteristic
247C2×Dic13C2×C22⋊C411yescharacteristic
248C2×Dic13C2×C22⋊C411yescharacteristic
249C2×Dic13C2×C22⋊C411yescharacteristic
250C2×Dic13C2×C22⋊C411yescharacteristic
251C2×Dic13C4×Q814yes—
252C4×D13—22no—
253C4×D13—22no—
254C4×D13—22no—
255C4×D13—22no—
256C4×D13—22no—
257C4×D13—22no—
258C4×D13—48no—
259C4×D13—48no—
260C4×D13#10014yes—
261C4×D13#10114yes—
262C4×D13C22⋊Q814yes—
263C4×D13C22⋊Q814yes—
264C4×D13#12412yes—
265C4×D13#12412yes—
266C4×D13C4⋊Q812yes—
267C4×D13C4⋊Q812yes—
268Dic26—48no—
269Dic26—44no—
270Dic26—44no—
271Dic26—48no—
272C8×C13—24no—
273C8×C13—42no—
274#1055—24no—
275#1055—42no—
276C23×Q8—132no—
277C22×M16—132no—
278C22×M16—132no—
279C2×C4⋊Q8—132no—
280C2×C4⋊Q8—132no—
281C2×C4⋊Q8—132no—
282C2×C4⋊Q8—131no—
283C2×C4⋊Q8—261no—
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⋊Q8—261no—
291C2×C4⋊Q8C2×D1311yescharacteristic
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C42—131no—
295#423—132no—
296#423—131no—
297#423—261no—
298#423—261no—
299#423C2×D1311yescharacteristic
300C2×C4⋊C8—261no—
301C2×C4⋊C8—261no—
302C4×M16—132no—
303C4×M16—131no—
304C4×M16—261no—
305C4×M16—261no—
306C4×M16C2×D1311yescharacteristic
307C2×#97—261no—
308C2×C4×C8—261no—
309#343—134no—
310#343—134no—
311#343—134no—
312#343C2×D1314yes—
313C22×C13—21no—
314C22×C13—21no—
315C22×C13C22×C22⋊C411yescharacteristic
316C22×C13C2×C4×Q812yes—
317C2×D13—21no—
318C2×D13—21no—
319C2×D13—28no—
320C2×D13#39112yes—
321C2×D13#39112yes—
322C2×D13C2×#10012yes—
323C2×D13C2×#10112yes—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—44no—
327C4×C13C2×#10012yes—
328C4×C13C2×#10112yes—
329C4×C13C2×C22⋊Q812yes—
330C4×C13C2×#12411yescharacteristic
331C4×C13C2×C4⋊Q811yescharacteristic
332Dic13—21no—
333Dic13—21no—
334Dic13—44no—
335Dic13#39112yes—
336Dic13#39112yes—
337Dic13C2×#10012yes—
338Dic13C2×#10112yes—
339C22×Q8—134no—
340C22×Q8—132no—
341C22×Q8—262no—
342C22×Q8—262no—
343C22×Q8—262no—
344C22×Q8—262no—
345C22×Q8—528no—
346C22×Q8C4×D1312yes—
347C23×C4—131no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—134no—
351C2×M16—132no—
352C2×M16—138no—
353C2×M16—132no—
354C2×M16—262no—
355C2×M16—262no—
356C2×M16—264no—
357C2×M16—268no—
358C2×M16C22×D1312yes—
359C2×M16C22×D1312yes—
360C22×C8—262no—
361C22×C8—262no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
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—262no—
375C4⋊Q8—262no—
376C4⋊Q8—262no—
377C4⋊Q8—262no—
378C4⋊Q8—261no—
379C4⋊Q8—261no—
380C4⋊Q8—261no—
381C4⋊Q8—261no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—132no—
385C2×C4⋊C4—132no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—262no—
394C2×C4⋊C4C4×D1312yes—
395C2×C4⋊C4C22×D1312yes—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42C22×D1311yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—262no—
411C4⋊C8—262no—
412C4⋊C8—261no—
413C4⋊C8—261no—
414#97—21no—
415#97—262no—
416#97—261no—
417C4×C8—21no—
418C4×C8—262no—
419C4×C8—261no—
420C2×C13—22no—
421C2×C13C2×#39111yescharacteristic
422C2×C13C22×#10011yescharacteristic
423C2×C13C22×#10111yescharacteristic
424D13—22no—
425D13#199714yesdirect product factor
426C24—131no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—44no—
430C2×Q8—264no—
431C2×Q8—264no—
432C2×Q8—262no—
433C2×Q8—262no—
434C2×Q8—524no—
435C2×Q8—528no—
436C2×Q8—528no—
437C2×Q8—528no—
438C2×Q8—528no—
439C2×Q8—528no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—134no—
448C22×C4—134no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—134no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—264no—
461C22×C4—264no—
462C22×C4—528no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×C4×D1314yes—
466C22×C4C23×D1311yescharacteristic
467M16—22no—
468M16—24no—
469M16—134no—
470M16—268no—
471M16—262no—
472M16—264no—
473M16—524no—
474M16Q8×D1314yescomplemented
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—268no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—524no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4—264no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—262no—
493C42—131no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—131no—
499C42—131no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42—131no—
504C42—131no—
505C42D4×D1311yescharacteristic
506C42D4×D1311yescharacteristic
507C42D4×D1311yescharacteristic
508C42D4×D1311yescharacteristic
509C13C2×#199711yescharacteristic, complemented, Sylow
510C23—131no—
511C23—131no—
512C23—134no—
513C23—262no—
514C23—262no—
515C23C22×C4×D1311yescharacteristic
516Q8—44no—
517Q8—44no—
518Q8—524no—
519Q8—528no—
520Q8—528no—
521Q8—524no—
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—132no—
532C2×C4—132no—
533C2×C4—134no—
534C2×C4—134no—
535C2×C4—134no—
536C2×C4—134no—
537C2×C4—132no—
538C2×C4—132no—
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×C4C22⋊C4×D1311yescharacteristic
557C2×C4C2×D4×D1311yescharacteristic
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4C2×Q8×D1312yes—
560C2×C4#41×D1312yes—
561C8—24no—
562C8—42no—
563C8—264no—
564C8—522no—
565C22—21no—
566C22—21no—
567C22—132no—
568C22—132no—
569C22—132no—
570C22—132no—
571C22—268no—
572C22—261no—
573C22—261no—
574C22C2×C22⋊C4×D1311yescharacteristic
575C22C4×Q8×D1312yes—
576C4—21no—
577C4—21no—
578C4—44no—
579C4—132no—
580C4—132no—
581C4—132no—
582C4—132no—
583C4—261no—
584C4—261no—
585C4—524no—
586C4D13×#10012yes—
587C4D13×#10112yes—
588C4D13×C22⋊Q812yes—
589C4D13×#12411yescharacteristic
590C4D13×C4⋊Q811yescharacteristic
591C2—22no—
592C2—134no—
593C2—262no—
594C2D13×#39111yescharacteristic
595C2C2×D13×#10011yescharacteristic
596C2C2×D13×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1997C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1997D13
hypocenterC13C2×#1997
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #13115826C2semidirect
5. #13115825C2semidirect
6. #13115824C2semidirect
7. #13115823C2semidirect
9. C13×#1997C2semidirect
83. M16×D13Q8semidirect
172. C13×M16C2×Q8semidirect
205. #6099C2×Q8semidirect
219. #1997D13direct (N × H)
425. D13#1997direct (N × H)
474. M16Q8×D13semidirect
509. C13C2×#1997semidirect

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×#4232
C4×M16×D132
#131158262
#131158252
#131158242
#131158232
D13×#3432
C13×#19972
C2×#199713