Finite Group Databasebeta

← D13⋊#1546 #16794634

Subgroups — D13⋊#1546 #16794634

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2D13⋊#423C211yesmaximal, characteristic
3#13130346C214yesmaximal, complemented
4#13130345C214yesmaximal, complemented
5D13⋊#332C214yesmaximal, complemented
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13—21no—
8C2×D13⋊M16—21no—
9C2×C13×C4⋊Q8C411yescharacteristic
10C2×#88198—21no—
11D13×C4⋊Q8—21no—
12D13×C4⋊Q8—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8C412yes—
16D13×C4⋊Q8C412yes—
17D13×C4⋊Q8C2212yes—
18D13×C4⋊Q8C2212yes—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13C412yes—
21C2×#88142—21no—
22C2×#88142C2212yes—
23C2×C42×D13C2211yescharacteristic
24C2×#88123C411yescharacteristic
25#11719129—21no—
26#11719129C2212yes—
27#11719125C2212yes—
28D13⋊(C22⋊C8)—21no—
29#11719119—21no—
30#11719053C2212yes—
31#11719052—21no—
32#11719051—21no—
33D13⋊(C4⋊C8)—21no—
34D13⋊(C4⋊C8)C2212yes—
35D13⋊(C4⋊C8)C2212yes—
36#11719049C2212yes—
37C4×D13⋊C8—21no—
38#11718245C22116yescomplemented
39C22×Q8×C13—21no—
40C2×Q8×D13—22no—
41C2×Q8×D13—22no—
42C2×Q8×D13—22no—
43C2×Q8×D13—22no—
44C2×Q8×D13—44no—
45C2×Q8×D13—44no—
46C22×C4×D13—22no—
47C22×C4×D13C2×C411yescharacteristic
48C22×C4×D13D411yescharacteristic
49C22×C4×D13D411yescharacteristic
50C22×Dic26—21no—
51C22×Dic26—22no—
52C2×#6122—22no—
53D13⋊M16—44no—
54C2×#6118—22no—
55C2×D13⋊C8—22no—
56C2×D13⋊C8—22no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8C2×C412yes—
60C13×C4⋊Q8C2×C412yes—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4C2×C412yes—
63C2×C42×C13C2×C411yescharacteristic
64#88198—22no—
65#88198—22no—
66#88198—22no—
67#88198—22no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2×C412yes—
70C2×#6101—22no—
71C2×#6101—22no—
72C2×C4×Dic13D411yescharacteristic
73C2×C4×Dic13D411yescharacteristic
74C2×C4×Dic13C2311yescharacteristic
75C4⋊C4×D13—22no—
76C4⋊C4×D13—22no—
77C4⋊C4×D13—22no—
78C4⋊C4×D13—22no—
79C4⋊C4×D13—22no—
80C4⋊C4×D13—22no—
81C4⋊C4×D13C2×C414yes—
82C4⋊C4×D13C2×C414yes—
83#88142—22no—
84#88142—22no—
85#88142—22no—
86#88142—22no—
87#88142—22no—
88#88142—22no—
89#88142C2×C414yes—
90#88142C2314yes—
91C42×D13C2×C411yescharacteristic
92C42×D13C2×C411yescharacteristic
93C42×D13D411yescharacteristic
94C42×D13D411yescharacteristic
95C42×D13D411yescharacteristic
96C42×D13D411yescharacteristic
97C42×D13C2311yescharacteristic
98C42×D13C2311yescharacteristic
99#88123—21no—
100#88123—21no—
101#88123C2×C412yes—
102#88123C2×C412yes—
103C22⋊#1057—22no—
104#88112—22no—
105#88112C2314yes—
106#88112C2314yes—
107#88111—22no—
108C4⋊#1057—22no—
109C4⋊#1057—22no—
110C4⋊#1057—22no—
111C4×#1057—22no—
112C4×#1057—22no—
113C2×#1546—131nomaximal, Sylow
114C23×D13C22⋊C411yescharacteristic
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—44no—
118C22×C4×C13—22no—
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×Dic13—22no—
123C22×Dic13C22⋊C411yescharacteristic
124C22×Dic13C2×D411yescharacteristic
125C22×Dic13C2×D411yescharacteristic
126Q8×D13—48no—
127Q8×D13—48no—
128Q8×D13—44no—
129Q8×D13—44no—
130Q8×D13—44no—
131Q8×D13—44no—
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—24no—
135C2×C4×D13—24no—
136C2×C4×D13—48no—
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13C22⋊C411yescharacteristic
140C2×C4×D13C22⋊C411yescharacteristic
141C2×C4×D13C22⋊C411yescharacteristic
142C2×C4×D13C22⋊C411yescharacteristic
143C2×C4×D13D814yes—
144C2×C4×D13SD1614yes—
145C2×C4×D13C22×C411yescharacteristic
146C2×C4×D13C22×C411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13C2×D411yescharacteristic
150C2×C4×D13C2×D411yescharacteristic
151C2×Dic26—22no—
152C2×Dic26—22no—
153C2×Dic26—24no—
154C2×Dic26—24no—
155C2×Dic26—44no—
156C2×Dic26—44no—
157C2×Dic26—44no—
158#6122—44no—
159C2×#1057—24no—
160C2×#1057—24no—
161#6118—44no—
162D13⋊C8—44no—
163D13⋊C8—44no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4C22×C414yes—
168C42×C13C22⋊C411yescharacteristic
169C42×C13C22⋊C411yescharacteristic
170C42×C13C22×C411yescharacteristic
171C42×C13C22×C411yescharacteristic
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13C22×C414yes—
176#6101—24no—
177#6101—24no—
178#6101—24no—
179#6101—24no—
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22×C411yescharacteristic
185C4×Dic13C2×D411yescharacteristic
186C4×Dic13C2×D411yescharacteristic
187C4×Dic13C2×D411yescharacteristic
188C4×Dic13C2×D411yescharacteristic
189C4×Dic13C2×D411yescharacteristic
190C4×Dic13C2×D411yescharacteristic
191C4×Dic13C2411yescharacteristic
192C22×C4⋊Q8—131no—
193C2×#431—131no—
194C2×#423—131no—
195#1546—134no—
196#1546—134no—
197C2×#332—134no—
198C23×C13C2×C22⋊C411yescharacteristic
199C22×D13—22no—
200C22×D13—22no—
201C22×D13#10214yes—
202C22×D13C2×C22⋊C411yescharacteristic
203C22×D13C2×C22⋊C411yescharacteristic
204Q8×C13—44no—
205Q8×C13—44no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—44no—
210C2×C4×C13#10214yes—
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C23×C411yescharacteristic
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—24no—
220C2×Dic13—44no—
221C2×Dic13C2×C22⋊C411yescharacteristic
222C2×Dic13C2×C22⋊C411yescharacteristic
223C2×Dic13C2×C22⋊C411yescharacteristic
224C2×Dic13C2×C22⋊C411yescharacteristic
225C2×Dic13C2×D812yes—
226C2×Dic13C2×SD1612yes—
227C2×Dic13C22×D411yescharacteristic
228C2×Dic13C22×D411yescharacteristic
229C4×D13—22no—
230C4×D13—22no—
231C4×D13—22no—
232C4×D13—22no—
233C4×D13—22no—
234C4×D13—22no—
235C4×D13—48no—
236C4×D13—48no—
237C4×D13#10114yes—
238C4×D13#10214yes—
239C4×D13#10214yes—
240C4×D13C2×D812yes—
241C4×D13C2×D812yes—
242C4×D13C2×SD1612yes—
243C4×D13C2×SD1612yes—
244C4×D13#13714yes—
245Dic26—44no—
246Dic26—44no—
247Dic26—44no—
248Dic26—44no—
249Dic26—48no—
250#1057—44no—
251#1057—44no—
252C23×Q8—261no—
253C22×M16—261no—
254C2×C4⋊Q8—132no—
255C2×C4⋊Q8—132no—
256C2×C4⋊Q8—132no—
257C2×C4⋊Q8—132no—
258C2×C4⋊Q8—132no—
259C2×C4⋊Q8—131no—
260C2×C4⋊Q8—261no—
261C2×C4⋊Q8—261no—
262C2×C4⋊Q8—261no—
263C2×C4⋊Q8—261no—
264C2×C4⋊Q8—261no—
265C2×C4⋊Q8—261no—
266C2×C4⋊Q8#26111yescharacteristic
267C22×C4⋊C4—132no—
268C22×C4⋊C4—261no—
269C22×C42—131no—
270#431—132no—
271#431—132no—
272#431—261no—
273#431—261no—
274#423—132no—
275#423—132no—
276#423—261no—
277#423—261no—
278C2×C4⋊C8—132no—
279C2×C4⋊C8—132no—
280C2×C4⋊C8—261no—
281C2×C22⋊C8—261no—
282C2×C4×C8—261no—
283#332—1316no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13C2×#10212yes—
287C22×C13C22×C22⋊C411yescharacteristic
288C2×D13—21no—
289C2×D13—21no—
290C2×D13—28no—
291C2×D13C2×#10112yes—
292C2×D13C2×#10212yes—
293C2×D13C2×#10212yes—
294C2×D13#41912yes—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—44no—
298C4×C13C2×#10112yes—
299C4×C13C2×#10212yes—
300C4×C13C2×#10212yes—
301C4×C13#41912yes—
302Dic13—21no—
303Dic13—21no—
304Dic13—44no—
305Dic13C2×#10112yes—
306Dic13C2×#10212yes—
307Dic13C22×D811yescharacteristic
308Dic13C22×SD1611yescharacteristic
309Dic13C2×#13712yes—
310C22×Q8—21no—
311C22×Q8—262no—
312C22×Q8—262no—
313C22×Q8—262no—
314C22×Q8—262no—
315C22×Q8—262no—
316C22×Q8—261no—
317C22×Q8—524no—
318C22×Q8—524no—
319C23×C4—131no—
320C23×C4—131no—
321C23×C4—131no—
322C23×C4—262no—
323C2×M16—262no—
324C2×M16—262no—
325C2×M16—524no—
326C22×C8—262no—
327C22×C8—262no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—134no—
331C4⋊Q8—134no—
332C4⋊Q8—132no—
333C4⋊Q8—132no—
334C4⋊Q8—262no—
335C4⋊Q8—262no—
336C4⋊Q8—262no—
337C4⋊Q8—262no—
338C4⋊Q8—262no—
339C4⋊Q8—262no—
340C4⋊Q8—262no—
341C4⋊Q8—262no—
342C4⋊Q8—262no—
343C4⋊Q8—262no—
344C4⋊Q8—261no—
345C4⋊Q8—261no—
346C4⋊Q8C2×#26112yes—
347C4⋊Q8C2×#26112yes—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—132no—
350C2×C4⋊C4—134no—
351C2×C4⋊C4—134no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4C2×#26112yes—
362C2×C42—131no—
363C2×C42—131no—
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—131no—
367C2×C42—131no—
368C2×C42—131no—
369C2×C42—131no—
370C2×C42—131no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42C2×#26111yescharacteristic
374C4⋊C8—134no—
375C4⋊C8—134no—
376C4⋊C8—262no—
377C4⋊C8—262no—
378C4⋊C8—262no—
379C4⋊C8—262no—
380C22⋊C8—262no—
381C22⋊C8—262no—
382C4×C8—262no—
383C4×C8—262no—
384C2×C13—22no—
385C2×C13C22×#10111yescharacteristic
386C2×C13C22×#10211yescharacteristic
387C2×C13C2×#41911yescharacteristic
388D13—22no—
389D13#154614yescomplemented
390C24—131no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—44no—
394C2×Q8—264no—
395C2×Q8—264no—
396C2×Q8—262no—
397C2×Q8—262no—
398C2×Q8—524no—
399C2×Q8—524no—
400C2×Q8—524no—
401C2×Q8—524no—
402C2×Q8—528no—
403C2×Q8—528no—
404C2×Q8—524no—
405C2×Q8—524no—
406C2×Q8—524no—
407C22×C4—22no—
408C22×C4—131no—
409C22×C4—134no—
410C22×C4—134no—
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—264no—
426C22×C4—264no—
427C22×C4—264no—
428C22×C4—264no—
429C22×C4—262no—
430C22×C4—528no—
431C22×C4C22⋊#26111yescharacteristic
432C22×C4C22⋊#26111yescharacteristic
433C22×C4C22×#26111yescharacteristic
434M16—524no—
435M16—524no—
436C2×C8—264no—
437C2×C8—264no—
438C2×C8—524no—
439C2×C8—524no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—134no—
444C4⋊C4—264no—
445C4⋊C4—264no—
446C4⋊C4—264no—
447C4⋊C4—264no—
448C4⋊C4—262no—
449C4⋊C4—262no—
450C4⋊C4—262no—
451C4⋊C4C22×#26114yes—
452C42—131no—
453C42—131no—
454C42—131no—
455C42—131no—
456C42—131no—
457C42—131no—
458C42—131no—
459C42—131no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—131no—
464C42C22⋊#26111yescharacteristic
465C42C22⋊#26111yescharacteristic
466C42C22×#26111yescharacteristic
467C42C22×#26111yescharacteristic
468C13C2×#154611yescharacteristic, complemented, Sylow
469C23—131no—
470C23—131no—
471C23—134no—
472C23—262no—
473C23—262no—
474C23C2×C22⋊#26111yescharacteristic
475Q8—44no—
476Q8—44no—
477Q8—524no—
478Q8—524no—
479Q8—528no—
480Q8—524no—
481Q8—524no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—131no—
487C2×C4—131no—
488C2×C4—131no—
489C2×C4—131no—
490C2×C4—132no—
491C2×C4—132no—
492C2×C4—132no—
493C2×C4—132no—
494C2×C4—134no—
495C2×C4—134no—
496C2×C4—132no—
497C2×C4—132no—
498C2×C4—134no—
499C2×C4—134no—
500C2×C4—131no—
501C2×C4—131no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—264no—
511C2×C4—528no—
512C2×C4—528no—
513C2×C4—524no—
514C2×C4#8811514yes—
515C2×C4C2×C22⋊#26111yescharacteristic
516C2×C4C2×C22⋊#26111yescharacteristic
517C2×C4C2×C22⋊#26111yescharacteristic
518C2×C4C2×C22⋊#26111yescharacteristic
519C2×C4C2×C22⋊#26111yescharacteristic
520C2×C4C23×#26111yescharacteristic
521C8—524no—
522C8—524no—
523C22—21no—
524C22—21no—
525C22—132no—
526C22—132no—
527C22—132no—
528C22—132no—
529C22—268no—
530C22—261no—
531C22—261no—
532C22C2×#8811512yes—
533C22C22×C22⋊#26111yescharacteristic
534C4—21no—
535C4—21no—
536C4—44no—
537C4—132no—
538C4—131no—
539C4—131no—
540C4—132no—
541C4—132no—
542C4—261no—
543C4—261no—
544C4—524no—
545C4C2×#8811512yes—
546C4C2×#8811512yes—
547C4#1171915312yes—
548C4D13⋊#10112yes—
549C2—22no—
550C2—134no—
551C2—262no—
552C2C2×D13⋊#10111yescharacteristic
553C2C22×#8811511yescharacteristic
554C2C2×#1171915311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#1546
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13130346C2semidirect
4. #13130345C2semidirect
5. D13⋊#332C2semidirect
38. #11718245C22semidirect
389. D13#1546semidirect
468. C13C2×#1546semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
D13⋊#4232
#131303462
#131303452
D13⋊#3322
C2×D13×C4⋊Q82
C2×#154613