Finite Group Databasebeta

← D13⋊#1917 #16798720

Subgroups — D13⋊#1917 #16798720

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#11719047C211yesmaximal, characteristic
3#13130896C212yesmaximal, complemented
4#13130895C212yesmaximal, complemented
5#13130894C212yesmaximal, complemented
6#13130893C212yesmaximal, complemented
7#13130497C211yesmaximal, characteristic
8#13130497C211yesmaximal, characteristic
9#13130497C211yesmaximal, characteristic
10#13130497C211yesmaximal, characteristic
11C4×C4⋊C4×D13C211yesmaximal, characteristic
12C22×D13⋊C8C2211yescharacteristic
13C22×D13⋊C8C2211yescharacteristic
14C22×D13⋊C8C2211yescharacteristic
15C22×D13⋊C8C2211yescharacteristic
16C2×C4⋊C4×D13C411yescharacteristic
17C2×C4⋊C4×D13C411yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×C42×D13C2211yescharacteristic
21C2×#88112C2212yes—
22C2×#88110C2212yes—
23C2×#88110C2212yes—
24C2×C4⋊#1057C2212yes—
25D13⋊(C4⋊C8)—24no—
26#11719047—24no—
27C4×C13×C4⋊C4C411yescharacteristic
28C4⋊C4×Dic13C2211yescharacteristic
29C4⋊C4×Dic13C2211yescharacteristic
30C4×C4⋊Dic13C411yescharacteristic
31C4×#6101C411yescharacteristic
32C4×#6101C411yescharacteristic
33D13×#95C411yescharacteristic
34D13×#95C411yescharacteristic
35#11718310C2211yescharacteristic
36#11718310C2211yescharacteristic
37#11718290C2212yes—
38#11718290C2212yes—
39#11718290C2212yes—
40#11718290C2212yes—
41#11718290C2212yes—
42#11718290C2212yes—
43#11718290C2212yes—
44#11718290C2212yes—
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×D13C2311yescharacteristic
52C22×#1057C2312yes—
53C22×#1057C2312yes—
54C22×#1057C2312yes—
55C22×#1057C2312yes—
56C2×D13⋊C8—22no—
57C2×D13⋊C8—22no—
58C2×D13⋊C8—22no—
59C2×D13⋊C8—22no—
60C2×D13⋊C8—22no—
61C2×D13⋊C8—22no—
62C2×D13⋊C8—22no—
63C2×D13⋊C8—22no—
64C2×D13⋊C8—22no—
65C2×D13⋊C8—22no—
66C2×D13⋊C8D414yes—
67C2×D13⋊C8Q814yes—
68C2×C13×C4⋊C4C2×C411yescharacteristic
69C2×C13×C4⋊C4C2×C411yescharacteristic
70C2×C42×C13C2×C411yescharacteristic
71C2×C42×C13C2×C411yescharacteristic
72C2×C42×C13C2×C411yescharacteristic
73C2×C4⋊Dic13C2×C411yescharacteristic
74C2×C4⋊Dic13C2×C411yescharacteristic
75C2×#6101C2×C411yescharacteristic
76C2×#6101C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C4⋊C4×D13—24no—
89C4⋊C4×D13—24no—
90C42×D13—22no—
91C42×D13—22no—
92C42×D13—22no—
93C42×D13—22no—
94C42×D13—22no—
95C42×D13—22no—
96#88112—24no—
97#88110—24no—
98#88110—24no—
99C4⋊#1057—24no—
100C13×#95C2×C411yescharacteristic
101C13×#95C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108C2×#1917—131nomaximal, Sylow
109C23×D13C22×C411yescharacteristic
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C22×C411yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×C4×C13C22×C411yescharacteristic
115C22×C4×C13C22×C411yescharacteristic
116C22×C4×C13C22×C411yescharacteristic
117C22×Dic13C22×C411yescharacteristic
118C22×Dic13C22×C411yescharacteristic
119C22×Dic13C22×C411yescharacteristic
120C22×Dic13C22×C411yescharacteristic
121C22×Dic13C22×C411yescharacteristic
122C22×Dic13C22×C411yescharacteristic
123C22×Dic13C2411yescharacteristic
124C2×C4×D13—22no—
125C2×C4×D13—22no—
126C2×C4×D13—22no—
127C2×C4×D13—22no—
128C2×C4×D13—22no—
129C2×C4×D13—22no—
130C2×C4×D13—22no—
131C2×C4×D13—22no—
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—22no—
139C2×C4×D13—22no—
140C2×C4×D13M1614yes—
141C2×C4×D13M1614yes—
142C2×C4×D13C2×D412yes—
143C2×C4×D13C2×Q812yes—
144C2×C4×D13#4112yes—
145C2×C4×D13#4112yes—
146C2×C4×D13#4112yes—
147C2×C4×D13#4112yes—
148C2×#1057—22no—
149C2×#1057—22no—
150C2×#1057—22no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057—22no—
154C2×#1057—22no—
155C2×#1057—22no—
156C2×#1057—22no—
157C2×#1057—22no—
158C2×#1057C2×D414yes—
159C2×#1057C2×Q814yes—
160D13⋊C8—28no—
161D13⋊C8—28no—
162D13⋊C8—44no—
163D13⋊C8—44no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C42×C13—22no—
167C42×C13—22no—
168C42×C13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171#6101—22no—
172#6101—22no—
173#6101—22no—
174#6101—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C22×C4⋊C8—131no—
191C22×#97—131no—
192C2×C4×C4⋊C4—131no—
193#1917—132no—
194#1917—132no—
195#1917—132no—
196#1917—132no—
197C2×#336—131no—
198C2×#336—131no—
199C2×#336—131no—
200C2×#336—131no—
201C23×C13C23×C411yescharacteristic
202C22×D13#11712yes—
203C22×D13C4×D412yes—
204C22×D13C4×Q812yes—
205C22×D13C2×M1612yes—
206C22×D13C2×M1612yes—
207C22×D13#13112yes—
208C22×D13#13112yes—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13#11712yes—
226C2×C4×C13C4×D412yes—
227C2×C4×C13C4×Q812yes—
228C2×C4×C13C2×M1612yes—
229C2×C4×C13C2×M1612yes—
230C2×Dic13—21no—
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13C2×M1612yes—
247C2×Dic13C2×M1612yes—
248C2×Dic13C22×D411yescharacteristic
249C2×Dic13C22×Q811yescharacteristic
250C2×Dic13C2×#4111yescharacteristic
251C2×Dic13C2×#4111yescharacteristic
252C2×Dic13C2×#4111yescharacteristic
253C2×Dic13C2×#4111yescharacteristic
254C4×D13—28no—
255C4×D13—28no—
256C4×D13—44no—
257C4×D13—44no—
258C4×D13—44no—
259C4×D13—44no—
260C4×D13C22⋊Q814yes—
261C4×D13#12314yes—
262C4×D13#12514yes—
263C4×D13#12614yes—
264#1057—24no—
265#1057—24no—
266#1057—42no—
267#1057—42no—
268C23×C8—131no—
269C23×C8—131no—
270C23×C8—131no—
271C23×C8—131no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—131no—
274C22×C42—131no—
275C22×C42—131no—
276C22×C42—131no—
277C2×C4⋊C8—132no—
278C2×C4⋊C8—132no—
279C2×C4⋊C8—264no—
280C2×#97—132no—
281C2×#97—132no—
282C2×#97—264no—
283C4×C4⋊C4—131no—
284C4×C4⋊C4—131no—
285C4×C4⋊C4—131no—
286C4×C4⋊C4—131no—
287C4×C4⋊C4—131no—
288C4×C4⋊C4—131no—
289C4×C4⋊C4—131no—
290C4×C4⋊C4#26111yescharacteristic
291C2×#95—131no—
292C2×#95—131no—
293#336—132no—
294#336—132no—
295#336—132no—
296#336—132no—
297#336—132no—
298#336—132no—
299#336—132no—
300#336—132no—
301C22×C13C2×#11711yescharacteristic
302C22×C13C2×C4×D411yescharacteristic
303C22×C13C2×C4×Q811yescharacteristic
304C22×C13C22×M1611yescharacteristic
305C22×C13C22×M1611yescharacteristic
306C22×C13C2×#13111yescharacteristic
307C22×C13C2×#13111yescharacteristic
308C2×D13#38714yes—
309C2×D13#43214yes—
310C2×D13#43314yes—
311C2×D13#43514yes—
312C2×D13#43614yes—
313C2×D13#44614yes—
314C2×D13#44614yes—
315C4×C13—22no—
316C4×C13—22no—
317C4×C13—41no—
318C4×C13—41no—
319C4×C13—41no—
320C4×C13—41no—
321C4×C13#38714yes—
322Dic13—22no—
323Dic13—22no—
324Dic13—41no—
325Dic13—41no—
326Dic13—41no—
327Dic13—41no—
328Dic13C2×C22⋊Q811yescharacteristic
329Dic13C2×#12311yescharacteristic
330Dic13C2×#12511yescharacteristic
331Dic13C2×#12611yescharacteristic
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—131no—
339C22×C8—132no—
340C22×C8—132no—
341C22×C8—134no—
342C22×C8—134no—
343C22×C8—132no—
344C22×C8—132no—
345C22×C8—262no—
346C22×C8—262no—
347C22×C8—262no—
348C22×C8—262no—
349C22×C8—262no—
350C22×C8—262no—
351C22×C8—262no—
352C22×C8—262no—
353C22×C8—262no—
354C22×C8—262no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—131no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—264no—
362C2×C4⋊C4—264no—
363C2×C4⋊C4C2×#26111yescharacteristic
364C2×C4⋊C4C2×#26111yescharacteristic
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×C42—131no—
374C2×C42—262no—
375C2×C42—262no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42—262no—
380C2×C42C2×#26111yescharacteristic
381C2×C42C2×#26111yescharacteristic
382C2×C42C2×#26111yescharacteristic
383C4⋊C8—264no—
384C4⋊C8—264no—
385#97—264no—
386#97—264no—
387#95—131no—
388#95—131no—
389#95—131no—
390#95—131no—
391#95—131no—
392#95—131no—
393#95C2×#26111yescharacteristic
394#95C2×#26111yescharacteristic
395C2×C13C2×#38711yescharacteristic
396C2×C13C2×#43211yescharacteristic
397C2×C13C2×#43311yescharacteristic
398C2×C13C2×#43511yescharacteristic
399C2×C13C2×#43611yescharacteristic
400C2×C13C2×#44611yescharacteristic
401C2×C13C2×#44611yescharacteristic
402D13#191718yescomplemented
403C24—131no—
404C22×C4—131no—
405C22×C4—132no—
406C22×C4—132no—
407C22×C4—132no—
408C22×C4—132no—
409C22×C4—132no—
410C22×C4—132no—
411C22×C4—131no—
412C22×C4—131no—
413C22×C4—134no—
414C22×C4—134no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4C22×#26111yescharacteristic
436C22×C4C22×#26111yescharacteristic
437C22×C4C22×#26111yescharacteristic
438C22×C4C22×#26111yescharacteristic
439C22×C4C22×#26111yescharacteristic
440C22×C4C22×#26111yescharacteristic
441C22×C4C22×#26111yescharacteristic
442C2×C8—134no—
443C2×C8—134no—
444C2×C8—262no—
445C2×C8—268no—
446C2×C8—268no—
447C2×C8—262no—
448C2×C8—262no—
449C2×C8—262no—
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—262no—
456C2×C8—524no—
457C2×C8—524no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C4⋊C4—262no—
463C4⋊C4—262no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—261no—
470C42—261no—
471C42—261no—
472C42—261no—
473C42—261no—
474C42—261no—
475C42—261no—
476C42—261no—
477C42—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—262no—
482C42—262no—
483C42—262no—
484C13C2×#191711yescharacteristic, complemented, Sylow
485C23—132no—
486C23—132no—
487C23—132no—
488C23—132no—
489C23—132no—
490C23—132no—
491C23—132no—
492C23C23×#26111yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—131no—
512C2×C4—131no—
513C2×C4—131no—
514C2×C4—131no—
515C2×C4—134no—
516C2×C4—134no—
517C2×C4—134no—
518C2×C4—134no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—268no—
522C2×C4—268no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—524no—
540C2×C4—524no—
541C2×C4—524no—
542C2×C4—524no—
543C2×C4D13⋊M1612yes—
544C2×C4D13⋊M1612yes—
545C2×C4#8823712yes—
546C2×C4D4×#26112yes—
547C2×C4Q8×#26112yes—
548C8—264no—
549C8—264no—
550C8—522no—
551C8—522no—
552C22—134no—
553C22—134no—
554C22—134no—
555C22—134no—
556C22—134no—
557C22—134no—
558C22—134no—
559C22C2×D13⋊M1611yescharacteristic
560C22C2×D13⋊M1611yescharacteristic
561C22C2×#8823711yescharacteristic
562C22C2×D4×#26111yescharacteristic
563C22C2×Q8×#26111yescharacteristic
564C22D13⋊#13111yescharacteristic
565C22D13⋊#13111yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—131no—
573C4—131no—
574C4—131no—
575C4—131no—
576C4—262no—
577C4—262no—
578C4—521no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4#1171908214yes—
583C2—138no—
584C2C2×#1171908211yescharacteristic
585C2D13⋊#43211yescharacteristic
586C2D13⋊#43311yescharacteristic
587C2D13⋊#43511yescharacteristic
588C2D13⋊#43611yescharacteristic
589C2D13⋊#44611yescharacteristic
590C2D13⋊#44611yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutator, socleC23×C13C23×C4
FrattiniC23C23×#261
FittingC4×C13×C4⋊C4C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenterC4×C4⋊C4#261
hypocenterC13C2×#1917
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130896C2semidirect
4. #13130895C2semidirect
5. #13130894C2semidirect
6. #13130893C2semidirect
402. D13#1917semidirect
484. C13C2×#1917semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊(C4⋊C8)2
C2×#117190472
#131308962
#131308952
#131308942
#131308932
#131304972
C4×C4⋊C4×D132
C2×#191713