Finite Group Databasebeta

← #16800804

Subgroups — #16800804

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2#13131285C211yesmaximal, characteristic
3#13131017C214yesmaximal, complemented
4#13131014C214yesmaximal, complemented
5#13130740C214yesmaximal
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13—21no—
8C2×#88237—21no—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88198—21no—
11D13×C4⋊Q8—21no—
12D13×C4⋊Q8—21no—
13D13×C4⋊Q8—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8C412yescomplemented
16D13×C4⋊Q8C412yescomplemented
17D13×C4⋊Q8C2212yes—
18D13×C4⋊Q8C2212yes—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13C2212yes—
21C2×#88142—21no—
22C2×#88142C412yescomplemented
23C2×C42×D13C2211yescharacteristic
24C2×#88123C411yescharacteristic, complemented
25#11719136—21no—
26#11719136C2212yes—
27#11719125—21no—
28D13⋊(C22⋊C8)C2212yes—
29#11719119—21no—
30#11719060—21no—
31#11719059C2212yes—
32C4×C4⋊#261—21no—
33C4×C4⋊#261C2212yes—
34#11719051—21no—
35D13⋊(C4⋊C8)C2212yes—
36#11719049—21no—
37C4×D13⋊C8C2212yes—
38#11718246C22116yes—
39C22×Q8×C13—21no—
40C2×Q8×D13—22no—
41C2×Q8×D13—22no—
42C2×Q8×D13—22no—
43C2×Q8×D13—22no—
44C2×Q8×D13—48no—
45C22×C4×D13—22no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×Dic26—21no—
50C22×Dic26—22no—
51C2×C22⋊#261—22no—
52#88237—44no—
53C2×C4⋊#261—22no—
54C2×C4⋊#261—22no—
55C2×C4⋊#261C2314yes—
56C2×C4×#261—22no—
57C2×D13⋊C8C2314yes—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8C2×C412yes—
61C13×C4⋊Q8C2×C412yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4C2×C412yes—
64C2×C42×C13C2×C411yescharacteristic
65#88198—22no—
66#88198—22no—
67#88198—22no—
68#88198—22no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13C2×C412yes—
71C2×#6101—22no—
72C2×#6101—22no—
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13D411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C4⋊C4×D13—22no—
77C4⋊C4×D13—22no—
78C4⋊C4×D13—22no—
79C4⋊C4×D13—22no—
80C4⋊C4×D13—22no—
81C4⋊C4×D13—22no—
82C4⋊C4×D13C2×C414yes—
83C4⋊C4×D13C2314yes—
84#88142—22no—
85#88142—22no—
86#88142—22no—
87#88142—22no—
88#88142—22no—
89#88142—22no—
90#88142C2×C414yes—
91#88142C2×C414yes—
92C42×D13C2×C411yescharacteristic
93C42×D13C2×C411yescharacteristic
94C42×D13D411yescharacteristic
95C42×D13D411yescharacteristic
96C42×D13D411yescharacteristic
97C42×D13D411yescharacteristic
98C42×D13C2311yescharacteristic
99C42×D13C2311yescharacteristic
100#88123—21no—
101#88123—21no—
102#88123C2×C412yes—
103#88123C2×C412yes—
104C22⋊#1057—22no—
105(C2×#261)⋊C4—22no—
106(C2×#261)⋊C4—22no—
107#88112—22no—
108#88111—22no—
109C4⋊#1057—22no—
110C4×#1057—22no—
111C4×#1057—22no—
112#21834—131nomaximal, Sylow
113C23×D13C2×D411yescharacteristic
114C22×#261—24no—
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×Dic13C22⋊C411yescharacteristic
125C22×Dic13C2×D411yescharacteristic
126Q8×D13—48no—
127Q8×D13—48no—
128Q8×D13—48no—
129Q8×D13—48no—
130C2×C4×D13—24no—
131C2×C4×D13—24no—
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—48no—
135C2×C4×D13C22⋊C411yescharacteristic
136C2×C4×D13C22⋊C411yescharacteristic
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13SD1614yes—
140C2×C4×D13Q1614yes—
141C2×C4×D13C22×C411yescharacteristic
142C2×C4×D13C2×D411yescharacteristic
143C2×C4×D13C2×D411yescharacteristic
144C2×C4×D13C2×D411yescharacteristic
145C2×C4×D13C2×D411yescharacteristic
146C2×C4×D13C2×D411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2411yescharacteristic
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—24no—
152C2×Dic26—24no—
153C2×Dic26—48no—
154C2×Dic26—44no—
155C22⋊#261—44no—
156C2×#1057—24no—
157C4⋊#261—28no—
158C4⋊#261—44no—
159C4⋊#261—44no—
160C4×#261—44no—
161D13⋊C8—28no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C22×C414yes—
166C42×C13C22⋊C411yescharacteristic
167C42×C13C22⋊C411yescharacteristic
168C42×C13C22×C411yescharacteristic
169C42×C13C22×C411yescharacteristic
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13C22×C414yes—
174#6101—24no—
175#6101—24no—
176#6101—24no—
177#6101—24no—
178C4×Dic13C22⋊C411yescharacteristic
179C4×Dic13C22⋊C411yescharacteristic
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22×C411yescharacteristic
185C4×Dic13C22×C411yescharacteristic
186C4×Dic13C2×D411yescharacteristic
187C4×Dic13C2×D411yescharacteristic
188C4×Dic13C2×D411yescharacteristic
189C4×Dic13C2×D411yescharacteristic
190C22×C4⋊Q8—131no—
191C2×#431—131no—
192#2285—131no—
193#1990—134no—
194#1987—134no—
195#1824—134no—
196C23×C13C2×C22⋊C411yescharacteristic
197C22×D13—22no—
198C22×D13—22no—
199C22×D13C2×C22⋊C411yescharacteristic
200C22×D13C2×SD1612yes—
201C22×D13C2×Q1612yes—
202C22×D13C22×D411yescharacteristic
203C2×#261—44no—
204C2×#261—44no—
205C2×#261—44no—
206Q8×C13—44no—
207Q8×C13—44no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—44no—
212C2×C4×C13#10314yes—
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C2×C22⋊C411yescharacteristic
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C23×C411yescharacteristic
219C2×Dic13—22no—
220C2×Dic13—22no—
221C2×Dic13—24no—
222C2×Dic13—44no—
223C2×Dic13#10314yes—
224C2×Dic13C2×C22⋊C411yescharacteristic
225C2×Dic13C2×C22⋊C411yescharacteristic
226C2×Dic13C2×C22⋊C411yescharacteristic
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C22×D411yescharacteristic
230C4×D13—22no—
231C4×D13—22no—
232C4×D13—22no—
233C4×D13—22no—
234C4×D13—22no—
235C4×D13—22no—
236C4×D13—48no—
237C4×D13—48no—
238C4×D13#10314yes—
239C4×D13#10314yes—
240C4×D13C2×SD1612yes—
241C4×D13C2×SD1612yes—
242C4×D13C2×Q1612yes—
243C4×D13C2×Q1612yes—
244C4×D13AGL(1,ℤ/8)14yes—
245C4×D132−1+414yes—
246Dic26—48no—
247Dic26—44no—
248Dic26—44no—
249Dic26—48no—
250#1057—44no—
251C23×Q8—261no—
252C2×C4⋊Q8—132no—
253C2×C4⋊Q8—132no—
254C2×C4⋊Q8—132no—
255C2×C4⋊Q8—132no—
256C2×C4⋊Q8—132no—
257C2×C4⋊Q8—131no—
258C2×C4⋊Q8—261no—
259C2×C4⋊Q8—261no—
260C2×C4⋊Q8—261no—
261C2×C4⋊Q8—261no—
262C2×C4⋊Q8—261no—
263C2×C4⋊Q8—261no—
264C2×C4⋊Q8#26111yescharacteristic, complemented
265C2×#117—261no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4—261no—
268C22×C42—131no—
269#431—261no—
270#431—261no—
271#431—261no—
272#431—261no—
273C2×C4⋊C8—132no—
274C2×C22⋊C8—132no—
275C2×C4×C8—132no—
276#384—132no—
277#382—261no—
278#380—132no—
279#380—261no—
280C4×C4⋊C4—132no—
281C4×C4⋊C4—261no—
282#340—1316no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13C2×#10312yes—
286C22×C13C22×C22⋊C411yescharacteristic
287C2×D13—21no—
288C2×D13—21no—
289C2×D13—24no—
290C2×D13—24no—
291C2×D13C2×#10312yes—
292C2×D13#53612yes—
293C2×D13C22×SD1611yescharacteristic
294C2×D13C22×Q1611yescharacteristic
295C2×D13C2×AGL(1,ℤ/8)12yes—
296#261—84no—
297C4×C13—21no—
298C4×C13—21no—
299C4×C13—44no—
300C4×C13C2×#10312yes—
301C4×C13C2×#10312yes—
302C4×C13#41812yes—
303C4×C13#51912yes—
304Dic13—21no—
305Dic13—21no—
306Dic13—44no—
307Dic13C2×#10312yes—
308Dic13C2×#10312yes—
309Dic13#41812yes—
310Dic13#53612yes—
311C22×Q8—21no—
312C22×Q8—262no—
313C22×Q8—262no—
314C22×Q8—262no—
315C22×Q8—262no—
316C22×Q8—262no—
317C22×Q8—261no—
318C22×Q8—528no—
319C23×C4—131no—
320C23×C4—131no—
321C23×C4—131no—
322C23×C4—262no—
323C22×C8—134no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—134no—
327C4⋊Q8—134no—
328C4⋊Q8—132no—
329C4⋊Q8—132no—
330C4⋊Q8—262no—
331C4⋊Q8—262no—
332C4⋊Q8—262no—
333C4⋊Q8—262no—
334C4⋊Q8—262no—
335C4⋊Q8—262no—
336C4⋊Q8—262no—
337C4⋊Q8—262no—
338C4⋊Q8—262no—
339C4⋊Q8—262no—
340C4⋊Q8—261no—
341C4⋊Q8—261no—
342C4⋊Q8C2×#26112yes—
343C4⋊Q8C2×#26112yes—
344#117—524no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—132no—
347C2×C4⋊C4—134no—
348C2×C4⋊C4—134no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—262no—
351C2×C4⋊C4—262no—
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—261no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4C2×#26112yes—
362C2×C22⋊C4—262no—
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×C42—131no—
374C2×C42—262no—
375C2×C42C2×#26111yescharacteristic
376C4⋊C8—262no—
377C4⋊C8—262no—
378C22⋊C8—262no—
379C22⋊C8—262no—
380C4×C8—262no—
381C4×C8—262no—
382#95—262no—
383#95—262no—
384C2×C13—22no—
385C2×C13#231011yescharacteristic
386C2×C13C22×#10311yescharacteristic
387C2×C13C2×#41811yescharacteristic
388D13—22no—
389D13#322712yes—
390D13#323012yes—
391C24—131no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—264no—
396C2×Q8—264no—
397C2×Q8—262no—
398C2×Q8—262no—
399C2×Q8—524no—
400C2×Q8—528no—
401C2×Q8—528no—
402C2×Q8—528no—
403C2×Q8—528no—
404C2×Q8—528no—
405C22×C4—22no—
406C22×C4—131no—
407C22×C4—134no—
408C22×C4—134no—
409C22×C4—131no—
410C22×C4—131no—
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—264no—
424C22×C4—264no—
425C22×C4—264no—
426C22×C4—264no—
427C22×C4—262no—
428C22×C4—264no—
429C22×C4—528no—
430C22×C4C22⋊#26111yescharacteristic
431C22×C4C22⋊#26111yescharacteristic
432C22×C4C22×#26111yescharacteristic
433C2×C8—264no—
434C2×C8—268no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—134no—
439C4⋊C4—264no—
440C4⋊C4—264no—
441C4⋊C4—264no—
442C4⋊C4—264no—
443C4⋊C4—268no—
444C4⋊C4—262no—
445C4⋊C4—262no—
446C4⋊C4—262no—
447C4⋊C4—524no—
448C4⋊C4—524no—
449C4⋊C4C22×#26114yes—
450C22⋊C4—524no—
451C42—131no—
452C42—131no—
453C42—131no—
454C42—131no—
455C42—131no—
456C42—131no—
457C42—131no—
458C42—131no—
459C42—131no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—524no—
464C42C22⋊#26111yescharacteristic
465C42C22⋊#26111yescharacteristic
466C42C22×#26111yescharacteristic
467C42C22×#26111yescharacteristic
468C13#2183411yescharacteristic, complemented, Sylow
469C23—131no—
470C23—131no—
471C23—132no—
472C23—132no—
473C23—262no—
474C23—262no—
475C23C2×C22⋊#26111yescharacteristic
476Q8—44no—
477Q8—44no—
478Q8—524no—
479Q8—528no—
480Q8—528no—
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—134no—
491C2×C4—134no—
492C2×C4—134no—
493C2×C4—132no—
494C2×C4—132no—
495C2×C4—134no—
496C2×C4—134no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—131no—
500C2×C4—131no—
501C2×C4—262no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—264no—
510C2×C4—528no—
511C2×C4—528no—
512C2×C4—524no—
513C2×C4—524no—
514C2×C4—524no—
515C2×C4—524no—
516C2×C4#8811714yes—
517C2×C4C2×C22⋊#26111yescharacteristic
518C2×C4C2×C22⋊#26111yescharacteristic
519C2×C4C2×C22⋊#26111yescharacteristic
520C2×C4C2×C22⋊#26111yescharacteristic
521C2×C4C2×C22⋊#26111yescharacteristic
522C2×C4C23×#26111yescharacteristic
523C8—524no—
524C22—21no—
525C22—21no—
526C22—132no—
527C22—131no—
528C22—131no—
529C22—132no—
530C22—132no—
531C22—264no—
532C22—264no—
533C22—261no—
534C22—261no—
535C22C2×#8811712yes—
536C22C22×C22⋊#26111yescharacteristic
537C4—21no—
538C4—21no—
539C4—44no—
540C4—132no—
541C4—132no—
542C4—132no—
543C4—132no—
544C4—261no—
545C4—261no—
546C4—524no—
547C4—1044no—
548C4#1171913812yes—
549C4C2×#8811712yes—
550C4C2×#8811712yes—
551C4#1171962712yes—
552C2—22no—
553C2—132no—
554C2—132no—
555C2—262no—
556C2#1313131011yescharacteristic
557C2C22×#8811711yescharacteristic
558C2C2×#1171913811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenterC2×C4⋊Q8#261
hypocenterC13#21834
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13131017C2semidirect
4. #13131014C2semidirect
9. C2×C13×C4⋊Q8C4semidirect
15. D13×C4⋊Q8C4semidirect
16. D13×C4⋊Q8C4semidirect
22. C2×#88142C4semidirect
24. C2×#88123C4semidirect
264. C2×C4⋊Q8#261semidirect
468. C13#21834semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131312852
#131310172
#131310142
#131307402
C2×D13×C4⋊Q82
#2183413