Finite Group Databasebeta

← #15871930

Subgroups — #15871930

Order 3328.

1570 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×D13×C22⋊C8C211yesmaximal, characteristic
3D13×#380C211yesmaximal, characteristic
4#13115258C214yesmaximal, complemented
5#13115142C214yesmaximal, complemented
6#13114926C211yesmaximal, characteristic, complemented
7#13114772C211yesmaximal, characteristic, complemented
8#13114770C211yesmaximal, characteristic, complemented
9C13×#1824C211yesmaximal, characteristic, complemented
10C23×C4×D13C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×#6103—21no—
14C22×C4⋊Dic13—21no—
15C22×C8×D13C2212yes—
16C2×#88151—21no—
17C2×#88151—21no—
18C2×#88151—24no—
19C2×#88151C418yescomplemented
20C2×#88151C2212yes—
21C2×#88151C2212yes—
22C2×C4⋊C4×D13C2212yes—
23C2×C22⋊C4×D13—21no—
24C2×C13×C22⋊C8C2211yescharacteristic
25C13×#380C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88060C2212yes—
29C2×#88056C2214yescomplemented
30#11718648C2212yes—
31C2×#88050C2214yescomplemented
32#11718603—21no—
33D13×C22⋊C8—24no—
34#11718328—21no—
35D13×#95—21no—
36C13×#340C2214yescomplemented
37#11718121C2214yescomplemented
38C24×D13D411yescharacteristic
39C23×C4×C13—21no—
40C23×C4×C13C2311yescharacteristic
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C22×C4×D13—22no—
44C22×C4×D13—44no—
45C22×C4×D13C2×C414yes—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D414yes—
49C22×C4×D13C2311yescharacteristic
50C22×C4×D13C2311yescharacteristic
51C22×Dic26—21no—
52C22×Dic26—22no—
53C22×Dic26—44no—
54C22×Dic26C2×C414yescomplemented
55C22×Dic26C2312yes—
56C22×C8×C13C2312yes—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4C2×C414yescomplemented
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C4⋊C4C2312yes—
62C2×C13×C22⋊C4—21no—
63C2×C22⋊Dic13—21no—
64C2×#6103—28no—
65C2×#6103—22no—
66C2×#6103—22no—
67C2×#6103—22no—
68C2×C4⋊Dic13—28no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13C2312yes—
72C2×#6101—22no—
73C22×#1055C2312yes—
74C2×C8×D13—24no—
75C2×C8×D13—44no—
76#88151—28no—
77#88151—28no—
78#88151—24no—
79#88151—24no—
80#88151C2×C418yes—
81#88151C2×C418yescomplemented
82C4⋊C4×D13—44no—
83C22⋊C4×D13—44no—
84C13×C22⋊C8—22no—
85C13×#95—21no—
86#88071—21no—
87#88071—22no—
88C22⋊#1055—22no—
89#88060—24no—
90#88056—44no—
91#88050—44no—
92#21759—131nomaximal, Sylow
93C24×C13C2×D411yescharacteristic
94C23×D13—42no—
95C23×D13—42no—
96C23×D13C22⋊C414yes—
97C23×D13SD1614yes—
98C23×D13Q1614yes—
99C23×D13C2×D411yescharacteristic
100C23×D13C2×D411yescharacteristic
101C22×C4×C13—24no—
102C22×C4×C13—24no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—44no—
106C22×C4×C13C22×C412yes—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2411yescharacteristic
110C22×Dic13—24no—
111C22×Dic13—22no—
112C22×Dic13—22no—
113C22×Dic13—42no—
114C22×Dic13—44no—
115C22×Dic13C22⋊C414yes—
116C22×Dic13C2×D411yescharacteristic
117C22×Dic13C2×D411yescharacteristic
118C2×C4×D13—24no—
119C2×C4×D13—24no—
120C2×C4×D13—48no—
121C2×C4×D13—48no—
122C2×C4×D13—42no—
123C2×C4×D13—42no—
124C2×C4×D13—44no—
125C2×C4×D13—44no—
126C2×C4×D13—44no—
127C2×C4×D13C22⋊C414yes—
128C2×C4×D13C22⋊C414yes—
129C2×C4×D13C22×C412yes—
130C2×C4×D13C22×C412yes—
131C2×C4×D13C2×D412yes—
132C2×C4×D13C2×D412yes—
133C2×Dic26—24no—
134C2×Dic26—24no—
135C2×Dic26—24no—
136C2×Dic26—22no—
137C2×Dic26—48no—
138C2×Dic26—44no—
139C2×Dic26—48no—
140C2×Dic26C22×C414yes—
141C2×C8×C13—22no—
142C2×C8×C13—24no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4C22×C414yes—
147C13×C22⋊C4—42no—
148C22⋊Dic13—42no—
149#6103—28no—
150#6103—28no—
151#6103—44no—
152C4⋊Dic13—28no—
153C4⋊Dic13—28no—
154C4⋊Dic13—24no—
155#6101—44no—
156C2×#1055—22no—
157C2×#1055—24no—
158C8×D13—48no—
159C22×C22⋊Q8—131no—
160C22×C22⋊C8—131no—
161C2×#380—131no—
162#1892—134no—
163#1872—134no—
164#1824—131no—
165#1824D1311yescharacteristic, complemented
166#1787—131no—
167#1787—131no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13C2×C22⋊C412yes—
171C23×C13C2×SD1612yes—
172C23×C13C2×Q1612yes—
173C23×C13C22×D411yescharacteristic
174C22×D13—22no—
175C22×D13—22no—
176C22×D13—22no—
177C22×D13—22no—
178C22×D13—44no—
179C22×D13—44no—
180C22×D13—48no—
181C22×D13—48no—
182C22×D13#103116yescomplemented
183C22×D13C2×C22⋊C412yes—
184C22×D13C2×C22⋊C412yes—
185C22×D13C2×SD1612yes—
186C22×D13C2×SD1612yes—
187C22×D13C2×Q1612yes—
188C22×D13C2×Q1612yes—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—24no—
193C2×C4×C13—48no—
194C2×C4×C13—44no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13C2×C22⋊C412yes—
199C2×C4×C13C23×C411yescharacteristic
200C2×C4×C13C22×D411yescharacteristic
201C2×C4×C13H(5,𝔽2)14yes—
202C2×Dic13—22no—
203C2×Dic13—22no—
204C2×Dic13—24no—
205C2×Dic13—44no—
206C2×Dic13—48no—
207C2×Dic13—44no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13C2×C22⋊C412yes—
212C2×Dic13C2×C22⋊C412yes—
213C4×D13—24no—
214C4×D13—24no—
215C4×D13—24no—
216C4×D13—24no—
217C4×D13—44no—
218C4×D13—44no—
219C4×D13—88no—
220Dic26—24no—
221Dic26—24no—
222Dic26—48no—
223Dic26—44no—
224C8×C13—42no—
225#1055—42no—
226C23×Q8—131no—
227C24×C4—131no—
228C23×C8—132no—
229C2×C22⋊Q8—138no—
230C2×C22⋊Q8—132no—
231C2×C22⋊Q8—132no—
232C2×C22⋊Q8—261no—
233C2×C22⋊Q8—261no—
234C2×C22⋊Q8—264no—
235C22×C4⋊C4—132no—
236C22×C4⋊C4—261no—
237C22×C4⋊C4C2×D1311yescharacteristic
238C22×C22⋊C4—261no—
239C22×C22⋊C4—261no—
240C2×#103—134no—
241C2×#103—134no—
242C2×C22⋊C8—131no—
243C2×C22⋊C8—132no—
244C2×C22⋊C8—264no—
245C2×C22⋊C8C2×D1311yescharacteristic
246#380—131no—
247#380—132no—
248#380—261no—
249#380—261no—
250#380C2×D1311yescharacteristic
251C2×#95—261no—
252#340—134no—
253#340C2×D1314yescomplemented
254C22×C13—22no—
255C22×C13—22no—
256C22×C13—24no—
257C22×C13—24no—
258C22×C13C2×#10314yes—
259C22×C13C22×C22⋊C411yescharacteristic
260C22×C13#53412yes—
261C22×C13C22×SD1611yescharacteristic
262C22×C13C22×Q1611yescharacteristic
263C22×C13#57512yes—
264C2×D13—22no—
265C2×D13—22no—
266C2×D13—22no—
267C2×D13—22no—
268C2×D13—24no—
269C2×D13—24no—
270C2×D13—24no—
271C2×D13—24no—
272C2×D13—416no—
273C2×D13C2×#10314yes—
274C2×D13C2×#10314yes—
275C4×C13—22no—
276C4×C13—44no—
277C4×C13—82no—
278C4×C13#51812yes—
279C4×C13#53412yes—
280Dic13—22no—
281Dic13—22no—
282Dic13—44no—
283Dic13—82no—
284C25—131no—
285C22×Q8—134no—
286C22×Q8—132no—
287C22×Q8—262no—
288C22×Q8—261no—
289C22×Q8—524no—
290C23×C4—21no—
291C23×C4—131no—
292C23×C4—131no—
293C23×C4—131no—
294C23×C4—134no—
295C23×C4—131no—
296C23×C4—131no—
297C23×C4—134no—
298C23×C4—262no—
299C23×C4—261no—
300C23×C4—524no—
301C23×C4C22×D1311yescharacteristic
302C22×C8—132no—
303C22×C8—264no—
304C22×C8—524no—
305C22×C8C22×D1312yes—
306C22⋊Q8—138no—
307C22⋊Q8—138no—
308C22⋊Q8—268no—
309C22⋊Q8—268no—
310C22⋊Q8—264no—
311C22⋊Q8—264no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—132no—
315C2×C4⋊C4—268no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4—262no—
318C2×C4⋊C4—262no—
319C2×C4⋊C4—524no—
320C2×C4⋊C4C4×D1314yescomplemented
321C2×C4⋊C4C22×D1312yes—
322C2×C4⋊C4C22×D1312yes—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—268no—
325C2×C22⋊C4—262no—
326C2×C22⋊C4—262no—
327C2×C22⋊C4—262no—
328C2×C22⋊C4—261no—
329C2×C22⋊C4—524no—
330#103—524no—
331#103—524no—
332C22⋊C8—22no—
333C22⋊C8—264no—
334C22⋊C8—262no—
335#95—21no—
336#95—262no—
337#95—261no—
338C2×C13—24no—
339C2×C13#230811yescharacteristic
340C2×C13C22×#10311yescharacteristic
341C2×C13#289611yescharacteristic
342C2×C13#318712yes—
343C2×C13#318912yes—
344D13—24no—
345D13—24no—
346C24—131no—
347C24—131no—
348C24—134no—
349C24—134no—
350C24—134no—
351C24—522no—
352C24—522no—
353C24D4×D1311yescharacteristic
354C2×Q8—134no—
355C2×Q8—264no—
356C2×Q8—262no—
357C2×Q8—264no—
358C2×Q8—264no—
359C2×Q8—528no—
360C2×Q8—524no—
361C2×Q8—528no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—44no—
367C22×C4—131no—
368C22×C4—131no—
369C22×C4—134no—
370C22×C4—132no—
371C22×C4—132no—
372C22×C4—132no—
373C22×C4—132no—
374C22×C4—134no—
375C22×C4—134no—
376C22×C4—264no—
377C22×C4—264no—
378C22×C4—264no—
379C22×C4—262no—
380C22×C4—262no—
381C22×C4—528no—
382C22×C4—528no—
383C22×C4—522no—
384C22×C4—522no—
385C22×C4—524no—
386C22×C4—524no—
387C22×C4—524no—
388C22×C4—522no—
389C22×C4—524no—
390C22×C4C2×C4×D1312yes—
391C22×C4D4×D1311yescharacteristic
392C22×C4D4×D1312yes—
393C22×C4C23×D1311yescharacteristic
394C2×C8—22no—
395C2×C8—24no—
396C2×C8—262no—
397C2×C8—264no—
398C2×C8—528no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4—268no—
403C4⋊C4—268no—
404C4⋊C4—264no—
405C4⋊C4—524no—
406C4⋊C4C2×C4×D1314yes—
407C22⋊C4—42no—
408C22⋊C4—268no—
409C22⋊C4—268no—
410C22⋊C4—524no—
411C22⋊C4—522no—
412C13#2175911yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—132no—
416C23—132no—
417C23—132no—
418C23—132no—
419C23—132no—
420C23—132no—
421C23—1316no—
422C23—262no—
423C23—262no—
424C23—262no—
425C23—262no—
426C23—524no—
427C23—524no—
428C23—528no—
429C23—528no—
430C23C22⋊C4×D1312yes—
431C23SD16×D1312yes—
432C23Q16×D1312yes—
433C23C2×D4×D1311yescharacteristic
434Q8—264no—
435Q8—264no—
436Q8—528no—
437Q8—524no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—48no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—132no—
448C2×C4—132no—
449C2×C4—262no—
450C2×C4—262no—
451C2×C4—264no—
452C2×C4—264no—
453C2×C4—264no—
454C2×C4—264no—
455C2×C4—264no—
456C2×C4—524no—
457C2×C4—524no—
458C2×C4—524no—
459C2×C4—528no—
460C2×C4—524no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—522no—
464C2×C4—1048no—
465C2×C4C22⋊C4×D1312yes—
466C2×C4C22×C4×D1311yescharacteristic
467C2×C4C2×D4×D1311yescharacteristic
468C2×C4#8825614yes—
469C8—42no—
470C8—522no—
471C22—22no—
472C22—24no—
473C22—22no—
474C22—24no—
475C22—134no—
476C22—134no—
477C22—262no—
478C22—262no—
479C22—264no—
480C22—264no—
481C22—262no—
482C22—262no—
483C22—264no—
484C22—264no—
485C22—5216no—
486C22D13×#10314yes—
487C22C2×C22⋊C4×D1311yescharacteristic
488C22#1171935812yes—
489C22C2×SD16×D1311yescharacteristic
490C22C2×Q16×D1311yescharacteristic
491C22#1171947812yes—
492C4—22no—
493C4—44no—
494C4—82no—
495C4—262no—
496C4—262no—
497C4—524no—
498C4—1042no—
499C4#1171922612yes—
500C4#1171935812yes—
501C2—24no—
502C2—264no—
503C2—264no—
504C2#1311741311yescharacteristic
505C2C2×D13×#10311yescharacteristic
506C2#1312335011yescharacteristic
507C2#1312559512yes—
508C2#1312561012yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1824C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1824D13
hypocenterC13#21759
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13115258C2semidirect
5. #13115142C2semidirect
6. #13114926C2semidirect
7. #13114772C2semidirect
8. #13114770C2semidirect
9. C13×#1824C2semidirect
19. C2×#88151C4semidirect
29. C2×#88056C22semidirect
31. C2×#88050C22semidirect
36. C13×#340C22semidirect
37. #11718121C22semidirect
54. C22×Dic26C2×C4semidirect
59. C2×C13×C4⋊C4C2×C4semidirect
81. #88151C2×C4semidirect
165. #1824D13semidirect
182. C22×D13#103semidirect
253. #340C2×D13semidirect
320. C2×C4⋊C4C4×D13semidirect
412. C13#21759semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C2×D13×C22⋊C82
D13×#3802
#131152582
#131151422
#131149262
#131147722
#131147702
C13×#18242
#2175913