Finite Group Databasebeta

← #16800733

Subgroups — #16800733

Order 3328.

1366 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2#13131285C211yesmaximal, characteristic
3#13131002C214yesmaximal, complemented
4#13130963C214yesmaximal, complemented
5#13130675C214yesmaximal
6C2×D13×C4⋊Q8C211yesmaximal, characteristic
7C22×Q8×D13C2212yes—
8C2×#88237—21no—
9C2×C13×C4⋊Q8C411yescharacteristic, complemented
10C2×#88198C412yescomplemented
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×D13—21no—
21C2×#88142—21no—
22C2×#88142—21no—
23C2×C42×D13C2211yescharacteristic
24C2×#88123C411yescharacteristic, complemented
25C2×#88117C22116yes—
26#11719136—21no—
27#11719136C2212yes—
28#11719125—21no—
29D13⋊(C22⋊C8)C2212yes—
30#11719119—21no—
31#11719060—21no—
32#11719059C2212yes—
33C4×C4⋊#261—21no—
34C4×C4⋊#261C2212yes—
35#11719051—21no—
36D13⋊(C4⋊C8)C2212yes—
37#11719049—21no—
38C4×D13⋊C8C2212yes—
39C22×Q8×C13C2×C412yes—
40C2×Q8×D13—22no—
41C2×Q8×D13—22no—
42C2×Q8×D13—48no—
43C2×Q8×D13C2×C414yes—
44C2×Q8×D13C2314yes—
45C22×C4×D13—22no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×Dic26—22no—
50C22×Dic26C2×C412yes—
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⋊C4—21no—
64C2×C42×C13C2×C411yescharacteristic
65#88198—22no—
66#88198—22no—
67#88198C2×C414yes—
68#88198C2×C414yes—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
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×D13—22no—
83C4⋊C4×D13—22no—
84#88142—22no—
85#88142—22no—
86#88142—22no—
87#88142—22no—
88#88142—22no—
89#88142—22no—
90#88142—22no—
91#88142—22no—
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#88117—416no—
106(C2×#261)⋊C4—22no—
107(C2×#261)⋊C4—22no—
108#88112—22no—
109#88111—22no—
110C4⋊#1057—22no—
111C4×#1057—22no—
112C4×#1057—22no—
113#21804—131nomaximal, Sylow
114C23×D13C2×D411yescharacteristic
115C22×#261—24no—
116C2×Q8×C13—22no—
117C2×Q8×C13—44no—
118C2×Q8×C13C22×C414yes—
119C22×C4×C13—22no—
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22⋊C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×Dic13—22no—
124C22×Dic13C22⋊C411yescharacteristic
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C2×D411yescharacteristic
127Q8×D13—216no—
128Q8×D13—48no—
129Q8×D13—48no—
130Q8×D13—48no—
131C2×C4×D13—24no—
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—24no—
135C2×C4×D13—48no—
136C2×C4×D13C22⋊C411yescharacteristic
137C2×C4×D13C22⋊C411yescharacteristic
138C2×C4×D13C22⋊C411yescharacteristic
139C2×C4×D13C22⋊C411yescharacteristic
140C2×C4×D13SD1614yes—
141C2×C4×D13Q1614yes—
142C2×C4×D13C22×C411yescharacteristic
143C2×C4×D13C2×D411yescharacteristic
144C2×C4×D13C2×D411yescharacteristic
145C2×C4×D13C2×D411yescharacteristic
146C2×C4×D13C2×D411yescharacteristic
147C2×C4×D13C2×D411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13C2411yescharacteristic
150C2×Dic26—22no—
151C2×Dic26—24no—
152C2×Dic26—24no—
153C2×Dic26—44no—
154C2×Dic26—48no—
155C2×Dic26C22×C414yes—
156C22⋊#261—44no—
157C2×#1057—24no—
158C4⋊#261—28no—
159C4⋊#261—44no—
160C4⋊#261—44no—
161C4×#261—44no—
162D13⋊C8—28no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C42×C13C22⋊C411yescharacteristic
168C42×C13C22⋊C411yescharacteristic
169C42×C13C22×C411yescharacteristic
170C42×C13C22×C411yescharacteristic
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175#6101—24no—
176#6101—24no—
177#6101—24no—
178#6101—24no—
179C4×Dic13C22⋊C411yescharacteristic
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22×C411yescharacteristic
186C4×Dic13C22×C411yescharacteristic
187C4×Dic13C2×D411yescharacteristic
188C4×Dic13C2×D411yescharacteristic
189C4×Dic13C2×D411yescharacteristic
190C4×Dic13C2×D411yescharacteristic
191C22×C4⋊Q8—131no—
192C2×#431—131no—
193#2285—131no—
194#1981—134no—
195#1956—134no—
196#1787—134no—
197C23×C13C2×C22⋊C411yescharacteristic
198C22×D13—22no—
199C22×D13—22no—
200C22×D13C2×C22⋊C411yescharacteristic
201C22×D13C2×SD1612yes—
202C22×D13C2×Q1612yes—
203C22×D13C22×D411yescharacteristic
204C2×#261—44no—
205C2×#261—44no—
206C2×#261—44no—
207Q8×C13—28no—
208Q8×C13—44no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—24no—
212C2×C4×C13—44no—
213C2×C4×C13#10314yescomplemented
214C2×C4×C13C2×C22⋊C411yescharacteristic
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C2×C22⋊C411yescharacteristic
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C23×C411yescharacteristic
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—24no—
223C2×Dic13—44no—
224C2×Dic13#10314yescomplemented
225C2×Dic13C2×C22⋊C411yescharacteristic
226C2×Dic13C2×C22⋊C411yescharacteristic
227C2×Dic13C2×C22⋊C411yescharacteristic
228C2×Dic13C2×C22⋊C411yescharacteristic
229C2×Dic13C2×C22⋊C411yescharacteristic
230C2×Dic13C22×D411yescharacteristic
231C4×D13—22no—
232C4×D13—22no—
233C4×D13—22no—
234C4×D13—22no—
235C4×D13—22no—
236C4×D13—22no—
237C4×D13—48no—
238C4×D13—48no—
239C4×D13#10314yescomplemented
240C4×D13#10314yescomplemented
241C4×D13C2×SD1612yes—
242C4×D13C2×SD1612yes—
243C4×D13C2×Q1612yes—
244C4×D13C2×Q1612yes—
245C4×D13#13714yes—
246C4×D13H(5,𝔽2)14yes—
247Dic26—28no—
248Dic26—48no—
249Dic26—44no—
250Dic26—48no—
251#1057—44no—
252C23×Q8—132no—
253C2×C4⋊Q8—132no—
254C2×C4⋊Q8—132no—
255C2×C4⋊Q8—132no—
256C2×C4⋊Q8—132no—
257C2×C4⋊Q8—132no—
258C2×C4⋊Q8—131no—
259C2×C4⋊Q8—261no—
260C2×C4⋊Q8—261no—
261C2×C4⋊Q8—261no—
262C2×C4⋊Q8—261no—
263C2×C4⋊Q8—261no—
264C2×C4⋊Q8—261no—
265C2×C4⋊Q8#26111yescharacteristic, complemented
266C2×#117—261no—
267C22×C4⋊C4—261no—
268C22×C4⋊C4—261no—
269C22×C42—131no—
270#431—261no—
271#431—261no—
272#431—261no—
273#431—261no—
274C2×C4⋊C8—132no—
275C2×#103—1316no—
276C2×C22⋊C8—132no—
277C2×C4×C8—132no—
278#384—132no—
279#382—261no—
280#380—132no—
281#380—261no—
282C4×C4⋊C4—132no—
283C4×C4⋊C4—261no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13C2×#10312yes—
287C22×C13C22×C22⋊C411yescharacteristic
288C2×D13—21no—
289C2×D13—21no—
290C2×D13—24no—
291C2×D13—24no—
292C2×D13C2×#10312yes—
293C2×D13#53512yes—
294C2×D13C22×SD1611yescharacteristic
295C2×D13C22×Q1611yescharacteristic
296C2×D13C2×#13712yes—
297#261—84no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—44no—
301C4×C13C2×#10312yes—
302C4×C13C2×#10312yes—
303C4×C13#41912yes—
304C4×C13#51812yes—
305Dic13—21no—
306Dic13—21no—
307Dic13—44no—
308Dic13C2×#10312yes—
309Dic13C2×#10312yes—
310Dic13#41912yes—
311Dic13#53512yes—
312C22×Q8—134no—
313C22×Q8—134no—
314C22×Q8—132no—
315C22×Q8—262no—
316C22×Q8—262no—
317C22×Q8—262no—
318C22×Q8—528no—
319C22×Q8C2×#26112yes—
320C23×C4—131no—
321C23×C4—131no—
322C23×C4—131no—
323C23×C4—262no—
324C22×C8—134no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—134no—
328C4⋊Q8—134no—
329C4⋊Q8—132no—
330C4⋊Q8—132no—
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—262no—
341C4⋊Q8—261no—
342C4⋊Q8—261no—
343C4⋊Q8C2×#26112yes—
344C4⋊Q8C2×#26112yes—
345#117—524no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—134no—
349C2×C4⋊C4—262no—
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—262no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C22⋊C4—262no—
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—131no—
375C2×C42—262no—
376C2×C42C2×#26111yescharacteristic
377C4⋊C8—262no—
378C4⋊C8—262no—
379#103—5216no—
380C22⋊C8—262no—
381C22⋊C8—262no—
382C4×C8—262no—
383C4×C8—262no—
384#95—262no—
385#95—262no—
386C2×C13—22no—
387C2×C13#230911yescharacteristic
388C2×C13C22×#10311yescharacteristic
389C2×C13C2×#41911yescharacteristic
390D13—22no—
391D13#320612yes—
392D13#320912yes—
393C24—131no—
394C2×Q8—22no—
395C2×Q8—44no—
396C2×Q8—134no—
397C2×Q8—264no—
398C2×Q8—264no—
399C2×Q8—2616no—
400C2×Q8—262no—
401C2×Q8—524no—
402C2×Q8—528no—
403C2×Q8—528no—
404C2×Q8—528no—
405C2×Q8—528no—
406C2×Q8C22×#26114yes—
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—264no—
431C22×C4—528no—
432C22×C4C22⋊#26111yescharacteristic
433C22×C4C22⋊#26111yescharacteristic
434C22×C4C22×#26111yescharacteristic
435C2×C8—264no—
436C2×C8—268no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—264no—
442C4⋊C4—264no—
443C4⋊C4—264no—
444C4⋊C4—264no—
445C4⋊C4—268no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C4⋊C4—262no—
449C4⋊C4—262no—
450C4⋊C4—524no—
451C4⋊C4—524no—
452C22⋊C4—524no—
453C42—131no—
454C42—131no—
455C42—131no—
456C42—131no—
457C42—131no—
458C42—131no—
459C42—131no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—131no—
464C42—131no—
465C42—524no—
466C42C22⋊#26111yescharacteristic
467C42C22⋊#26111yescharacteristic
468C42C22×#26111yescharacteristic
469C42C22×#26111yescharacteristic
470C13#2180411yescharacteristic, complemented, Sylow
471C23—131no—
472C23—131no—
473C23—132no—
474C23—132no—
475C23—262no—
476C23—262no—
477C23C2×C22⋊#26111yescharacteristic
478Q8—28no—
479Q8—44no—
480Q8—268no—
481Q8—524no—
482Q8—528no—
483Q8—528no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—44no—
488C2×C4—131no—
489C2×C4—131no—
490C2×C4—131no—
491C2×C4—131no—
492C2×C4—134no—
493C2×C4—134no—
494C2×C4—132no—
495C2×C4—132no—
496C2×C4—134no—
497C2×C4—134no—
498C2×C4—132no—
499C2×C4—132no—
500C2×C4—134no—
501C2×C4—131no—
502C2×C4—131no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—262no—
511C2×C4—264no—
512C2×C4—528no—
513C2×C4—528no—
514C2×C4—524no—
515C2×C4—524no—
516C2×C4—524no—
517C2×C4—524no—
518C2×C4#8811714yescomplemented
519C2×C4C2×C22⋊#26111yescharacteristic
520C2×C4C2×C22⋊#26111yescharacteristic
521C2×C4C2×C22⋊#26111yescharacteristic
522C2×C4C2×C22⋊#26111yescharacteristic
523C2×C4C2×C22⋊#26111yescharacteristic
524C2×C4C23×#26111yescharacteristic
525C8—524no—
526C22—21no—
527C22—21no—
528C22—132no—
529C22—131no—
530C22—131no—
531C22—132no—
532C22—132no—
533C22—264no—
534C22—264no—
535C22—261no—
536C22—261no—
537C22C2×#8811712yes—
538C22C22×C22⋊#26111yescharacteristic
539C4—21no—
540C4—21no—
541C4—44no—
542C4—132no—
543C4—132no—
544C4—132no—
545C4—132no—
546C4—261no—
547C4—261no—
548C4—524no—
549C4—1044no—
550C4C2×#8811712yes—
551C4C2×#8811712yes—
552C4#1171915312yes—
553C4#1171962312yes—
554C2—22no—
555C2—132no—
556C2—132no—
557C2—262no—
558C2#1313130911yescharacteristic
559C2C22×#8811711yescharacteristic
560C2C2×#1171915311yescharacteristic
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#21804
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. #13131002C2semidirect
4. #13130963C2semidirect
9. C2×C13×C4⋊Q8C4semidirect
10. C2×#88198C4semidirect
15. D13×C4⋊Q8C4semidirect
16. D13×C4⋊Q8C4semidirect
24. C2×#88123C4semidirect
213. C2×C4×C13#103semidirect
224. C2×Dic13#103semidirect
239. C4×D13#103semidirect
240. C4×D13#103semidirect
265. C2×C4⋊Q8#261semidirect
470. C13#21804semidirect
518. C2×C4#88117semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131312852
#131310022
#131309632
#131306752
C2×D13×C4⋊Q82
#2180413