Finite Group Databasebeta

← D13×#1556 #15831435

Subgroups — D13×#1556 #15831435

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2D13×#432C211yesmaximal, characteristic
3D13×#432C211yesmaximal, characteristic
4#13113554C211yesmaximal, characteristic, complemented
5#13113553C211yesmaximal, characteristic, complemented
6#13113552C211yesmaximal, characteristic, complemented
7#13113551C214yesmaximal, complemented
8D13×#332C214yesmaximal, complemented
9C13×#1556C211yesmaximal, characteristic, complemented
10C22×Q8×D13—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8—21no—
16D13×C4⋊Q8—21no—
17D13×C4⋊Q8C412yes—
18D13×C4⋊Q8C412yes—
19D13×C4⋊Q8C2212yes—
20D13×C4⋊Q8C2212yes—
21C2×C4⋊C4×D13—21no—
22C2×C4⋊C4×D13C412yes—
23C2×#88142—21no—
24C2×#88142C412yes—
25C2×C42×D13C2211yescharacteristic
26C2×#88123C2211yescharacteristic
27C13×#432C2211yescharacteristic
28C13×#432C2211yescharacteristic
29#11718587C2211yescharacteristic
30#11718587C2211yescharacteristic
31#11718496C2212yes—
32#11718496C2212yes—
33D13×C4⋊C8C2212yes—
34D13×C4⋊C8C2212yes—
35D13×C22⋊C8—21no—
36D13×C22⋊C8—21no—
37#11718380—21no—
38#11718380—21no—
39#11718366—21no—
40#11718366—21no—
41D13×#97—21no—
42D13×#97—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—48no—
53C22×C4×D13—22no—
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13D411yescharacteristic
56C22×C4×D13D411yescharacteristic
57C22×Dic26—21no—
58C22×Dic26—22no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8C2×C412yes—
62C13×C4⋊Q8C2312yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2×C412yes—
65C2×C42×C13C2311yescharacteristic
66#88198—22no—
67#88198—22no—
68#88198—22no—
69#88198—22no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13C2×C412yes—
72C2×#6101—22no—
73C2×#6101—22no—
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C8×D13—22no—
78C2×C8×D13—22no—
79C4⋊C4×D13—22no—
80C4⋊C4×D13—22no—
81C4⋊C4×D13—22no—
82C4⋊C4×D13—22no—
83C4⋊C4×D13—22no—
84C4⋊C4×D13—22no—
85C4⋊C4×D13C2×C414yes—
86C4⋊C4×D13C2×C414yes—
87#88142—22no—
88#88142—22no—
89#88142—22no—
90#88142—22no—
91#88142—22no—
92#88142—22no—
93#88142C2×C414yes—
94#88142C2×C414yes—
95C42×D13C2×C411yescharacteristic
96C42×D13C2×C411yescharacteristic
97C42×D13D411yescharacteristic
98C42×D13D411yescharacteristic
99C42×D13D411yescharacteristic
100C42×D13D411yescharacteristic
101C42×D13C2311yescharacteristic
102C42×D13C2311yescharacteristic
103#88123—21no—
104#88123—21no—
105#88123C2×C412yes—
106#88123C2312yes—
107C13×C4⋊C8C2312yes—
108C13×C4⋊C8C2312yes—
109C13×C22⋊C8—21no—
110C13×C22⋊C8—21no—
111C13×#97—21no—
112C13×#97—21no—
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115#88060—22no—
116#88060—22no—
117#88055—22no—
118#88055—22no—
119#88054—22no—
120#88054—22no—
121C4⋊#1055C2312yes—
122C4⋊#1055C2312yes—
123#88043—21no—
124#88043—21no—
125C2×#1556—131nomaximal, Sylow
126C23×D13C22⋊C411yescharacteristic
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—44no—
130C22×C4×C13—22no—
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×Dic13—22no—
135C22×Dic13C22⋊C411yescharacteristic
136C22×Dic13C22⋊C411yescharacteristic
137C22×Dic13C22⋊C411yescharacteristic
138Q8×D13—48no—
139Q8×D13—48no—
140Q8×D13—48no—
141Q8×D13—48no—
142C2×C4×D13—24no—
143C2×C4×D13—24no—
144C2×C4×D13—24no—
145C2×C4×D13—24no—
146C2×C4×D13—24no—
147C2×C4×D13—48no—
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×D13C2×D411yescharacteristic
157C2×C4×D13C2×D411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×Dic26—22no—
161C2×Dic26—22no—
162C2×Dic26—24no—
163C2×Dic26—24no—
164C2×Dic26—48no—
165C2×Dic26—44no—
166C2×C8×C13—22no—
167C2×C8×C13—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4C22×C414yes—
172C42×C13C22×C411yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13C2411yescharacteristic
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—22no—
179C4⋊Dic13C22×C414yes—
180#6101—24no—
181#6101—24no—
182#6101—24no—
183#6101—24no—
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22⋊C411yescharacteristic
186C4×Dic13C22⋊C411yescharacteristic
187C4×Dic13C22⋊C411yescharacteristic
188C4×Dic13C22⋊C411yescharacteristic
189C4×Dic13C22⋊C411yescharacteristic
190C4×Dic13C22×C411yescharacteristic
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13C2×D411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13C2×D411yescharacteristic
196C2×#1055—22no—
197C2×#1055—22no—
198C8×D13—44no—
199C8×D13—44no—
200C22×C4⋊Q8—131no—
201C2×#432—131no—
202C2×#432—131no—
203#1556—131no—
204#1556—131no—
205#1556—134no—
206#1556—131no—
207#1556D1311yescharacteristic, direct product factor
208C2×#332—134no—
209C23×C13C2×C22⋊C411yescharacteristic
210C22×D13—22no—
211C22×D13—22no—
212C22×D13#10114yes—
213C22×D13C2×C22⋊C411yescharacteristic
214C22×D13C2×C22⋊C411yescharacteristic
215Q8×C13—44no—
216Q8×C13—44no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—24no—
221C2×C4×C13—44no—
222C2×C4×C13C2×C22⋊C411yescharacteristic
223C2×C4×C13C2×C22⋊C411yescharacteristic
224C2×C4×C13C2×C22⋊C411yescharacteristic
225C2×C4×C13C23×C411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—24no—
232C2×Dic13—44no—
233C2×Dic13C2×C22⋊C411yescharacteristic
234C2×Dic13C2×C22⋊C411yescharacteristic
235C2×Dic13C2×C22⋊C411yescharacteristic
236C2×Dic13C2×C22⋊C411yescharacteristic
237C2×Dic13C2×C22⋊C411yescharacteristic
238C2×Dic13C2×C22⋊C411yescharacteristic
239C4×D13—22no—
240C4×D13—22no—
241C4×D13—22no—
242C4×D13—22no—
243C4×D13—22no—
244C4×D13—22no—
245C4×D13—22no—
246C4×D13—22no—
247C4×D13—22no—
248C4×D13—22no—
249C4×D13—48no—
250C4×D13—48no—
251C4×D13AGL(1,ℤ/8)14yes—
252C4×D13#13714yes—
253Dic26—48no—
254Dic26—44no—
255Dic26—44no—
256Dic26—48no—
257C8×C13—42no—
258C8×C13—42no—
259#1055—42no—
260#1055—42no—
261C23×Q8—261no—
262C2×C4⋊Q8—132no—
263C2×C4⋊Q8—132no—
264C2×C4⋊Q8—132no—
265C2×C4⋊Q8—132no—
266C2×C4⋊Q8—132no—
267C2×C4⋊Q8—131no—
268C2×C4⋊Q8—261no—
269C2×C4⋊Q8—261no—
270C2×C4⋊Q8—261no—
271C2×C4⋊Q8—261no—
272C2×C4⋊Q8—261no—
273C2×C4⋊Q8—261no—
274C2×C4⋊Q8C2×D1311yescharacteristic
275C22×C4⋊C4—132no—
276C22×C4⋊C4—261no—
277C22×C42—131no—
278#432—131no—
279#432—131no—
280#432—132no—
281#432—132no—
282#432—261no—
283#432—261no—
284#432—261no—
285#432—261no—
286#432C2×D1311yescharacteristic
287#432C2×D1311yescharacteristic
288C2×C4⋊C8—132no—
289C2×C4⋊C8—132no—
290C2×C22⋊C8—261no—
291C2×C22⋊C8—261no—
292C2×#97—261no—
293C2×#97—261no—
294#332—134no—
295#332—134no—
296#332—134no—
297#332C2×D1314yescomplemented
298C22×C13—21no—
299C22×C13—21no—
300C22×C13C2×#10112yes—
301C22×C13C22×C22⋊C411yescharacteristic
302C2×D13—21no—
303C2×D13—21no—
304C2×D13—28no—
305C2×D13C2×#10112yes—
306C2×D13C2×#10112yes—
307C2×D13#41812yes—
308C2×D13#41912yes—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—44no—
314C4×C13C2×AGL(1,ℤ/8)12yes—
315C4×C13C2×#13712yes—
316Dic13—21no—
317Dic13—21no—
318Dic13—21no—
319Dic13—21no—
320Dic13—44no—
321Dic13#41812yes—
322Dic13#41912yes—
323C22×Q8—21no—
324C22×Q8—262no—
325C22×Q8—262no—
326C22×Q8—262no—
327C22×Q8—262no—
328C22×Q8—262no—
329C22×Q8—261no—
330C22×Q8—528no—
331C23×C4—131no—
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—262no—
335C22×C8—262no—
336C22×C8—262no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—134no—
340C4⋊Q8—134no—
341C4⋊Q8—132no—
342C4⋊Q8—132no—
343C4⋊Q8—262no—
344C4⋊Q8—262no—
345C4⋊Q8—262no—
346C4⋊Q8—262no—
347C4⋊Q8—262no—
348C4⋊Q8—262no—
349C4⋊Q8—262no—
350C4⋊Q8—262no—
351C4⋊Q8—262no—
352C4⋊Q8—262no—
353C4⋊Q8—261no—
354C4⋊Q8—261no—
355C4⋊Q8C4×D1312yes—
356C4⋊Q8C22×D1312yes—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—132no—
359C2×C4⋊C4—134no—
360C2×C4⋊C4—134no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4C4×D1312yes—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42C22×D1311yescharacteristic
383C4⋊C8—132no—
384C4⋊C8—132no—
385C4⋊C8—262no—
386C4⋊C8—262no—
387C4⋊C8C22×D1312yes—
388C4⋊C8C22×D1312yes—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—262no—
392C22⋊C8—262no—
393C22⋊C8—261no—
394C22⋊C8—261no—
395#97—21no—
396#97—21no—
397#97—262no—
398#97—262no—
399#97—261no—
400#97—261no—
401C2×C13—22no—
402C2×C13C22×#10111yescharacteristic
403C2×C13C2×#41811yescharacteristic
404C2×C13C2×#41911yescharacteristic
405D13—22no—
406D13#155614yesdirect product factor
407C24—131no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—264no—
412C2×Q8—264no—
413C2×Q8—262no—
414C2×Q8—262no—
415C2×Q8—524no—
416C2×Q8—528no—
417C2×Q8—528no—
418C2×Q8—528no—
419C2×Q8—528no—
420C2×Q8—528no—
421C22×C4—22no—
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—264no—
438C22×C4—264no—
439C22×C4—264no—
440C22×C4—264no—
441C22×C4—264no—
442C22×C4—262no—
443C22×C4—528no—
444C22×C4C2×C4×D1311yescharacteristic
445C22×C4D4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—262no—
450C2×C8—262no—
451C2×C8—524no—
452C2×C8—524no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—134no—
457C4⋊C4—264no—
458C4⋊C4—264no—
459C4⋊C4—264no—
460C4⋊C4—264no—
461C4⋊C4—262no—
462C4⋊C4—262no—
463C4⋊C4—262no—
464C4⋊C4C2×C4×D1314yes—
465C42—131no—
466C42—131no—
467C42—131no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—131no—
472C42—131no—
473C42—131no—
474C42—131no—
475C42—131no—
476C42—131no—
477C42C2×C4×D1311yescharacteristic
478C42D4×D1311yescharacteristic
479C42D4×D1311yescharacteristic
480C42C23×D1311yescharacteristic
481C13C2×#155611yescharacteristic, complemented, Sylow
482C23—131no—
483C23—134no—
484C23—131no—
485C23—262no—
486C23—262no—
487C23C22⋊C4×D1311yescharacteristic
488Q8—44no—
489Q8—44no—
490Q8—524no—
491Q8—528no—
492Q8—528no—
493Q8—524no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—44no—
499C2×C4—131no—
500C2×C4—131no—
501C2×C4—134no—
502C2×C4—134no—
503C2×C4—131no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—262no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—528no—
522C2×C4—528no—
523C2×C4—524no—
524C2×C4C22⋊C4×D1311yescharacteristic
525C2×C4C22⋊C4×D1311yescharacteristic
526C2×C4C22⋊C4×D1311yescharacteristic
527C2×C4C22×C4×D1311yescharacteristic
528C2×C4C2×D4×D1311yescharacteristic
529C2×C4C2×D4×D1311yescharacteristic
530C8—42no—
531C8—42no—
532C8—522no—
533C8—522no—
534C22—21no—
535C22—21no—
536C22—132no—
537C22—132no—
538C22—132no—
539C22—132no—
540C22—268no—
541C22—261no—
542C22—261no—
543C22D13×#10112yes—
544C22C2×C22⋊C4×D1311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—44no—
550C4—132no—
551C4—132no—
552C4—261no—
553C4—261no—
554C4—261no—
555C4—261no—
556C4—524no—
557C4D13×AGL(1,ℤ/8)12yes—
558C4D13×#13712yes—
559C2—22no—
560C2—134no—
561C2—262no—
562C2C2×D13×#10111yescharacteristic
563C2D13×#41811yescharacteristic
564C2D13×#41911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1556C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenter#1556D13
hypocenterC13C2×#1556
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
4. #13113554C2semidirect
5. #13113553C2semidirect
6. #13113552C2semidirect
7. #13113551C2semidirect
8. D13×#332C2semidirect
9. C13×#1556C2semidirect
43. C13×#332C22semidirect
44. #11718139C22semidirect
45. #11718078C22semidirect
46. #11718074C22semidirect
207. #1556D13direct (N × H)
297. #332C2×D13semidirect
406. D13#1556direct (N × H)
481. C13C2×#1556semidirect

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×#4322
#131135542
#131135532
#131135522
#131135512
D13×#3322
C13×#15562
C2×#155613