Finite Group Databasebeta

← #15834623

Subgroups — #15834623

Order 3328.

668 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
1#13123926C211yesmaximal, characteristic, complemented
2#13123873C211yesmaximal, characteristic
3C2×C4×#6095C211yesmaximal, characteristic
4#13113737C212yesmaximal, complemented
5#13113678C212yesmaximal, complemented
6#13113671C212yesmaximal, complemented
7#13113647C212yesmaximal, complemented
8#13113282C211yesmaximal, characteristic, complemented
9#13113278C211yesmaximal, characteristic
10#13113125C211yesmaximal, characteristic, complemented
11C13×#1568C211yesmaximal, characteristic, complemented
12C22×#6095C411yescharacteristic
13C2×C4×D52C2211yescharacteristic
14C2×C4×Dic26C2211yescharacteristic
15C13×#432C2211yescharacteristic
16C13×#432C2211yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18C2×#88061C411yescharacteristic
19C2×#88057C411yescharacteristic
20C2×#88056C411yescharacteristic
21#11718586C2211yescharacteristic
22C4×#6099C2211yescharacteristic
23#11718499C2212yes—
24#11718495C2212yes—
25#11718492C2212yescomplemented
26#11718491C2212yescomplemented
27#11718387—21no—
28D13×C22⋊C8—21no—
29#11718380—21no—
30#11718379—21no—
31#11718367—22no—
32#11718362—22no—
33C4×#6095C411yescharacteristic
34C4×#6095C411yescharacteristic
35C4×#6095C411yescharacteristic
36C4×#6095C411yescharacteristic
37C4×#6095C2211yescharacteristic
38C4×#6095C2211yescharacteristic
39C4×#6095C2211yescharacteristic
40C4×#6095C2211yescharacteristic
41C13×#335C2212yescomplemented
42C13×#334C2212yescomplemented
43#11718076C2212yescomplemented
44#11718076C2212yescomplemented
45#11718075C2212yes—
46#11718075C2212yes—
47#11718047C2212yescomplemented
48#11718046C2212yescomplemented
49C22×D52C2×C411yescharacteristic
50C22×C4×D13—21no—
51C22×Dic26C2×C411yescharacteristic
52C22×C8×C13C2×C411yescharacteristic
53C22×C8×C13C2×C411yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C2×#6103—21no—
56C2×C4⋊Dic13C2×C411yescharacteristic
57C2×C4⋊Dic13C2×C411yescharacteristic
58C2×#6101—21no—
59C2×C4×Dic13—21no—
60C2×#6099—21no—
61C2×#6095—24no—
62C2×#6095C2×C411yescharacteristic
63C2×#6095C2×C411yescharacteristic
64C2×#6095C2×C411yescharacteristic
65C2×#6095C2×C411yescharacteristic
66C2×#6094—22no—
67C2×C8×D13—22no—
68C4×D52—21no—
69C4×D52—21no—
70C4×D52C2×C411yescharacteristic
71C4×D52C2×C411yescharacteristic
72C4×D52C2311yescharacteristic
73C4×D52C2311yescharacteristic
74C4×Dic26—21no—
75C4×Dic26—21no—
76C4×Dic26C2×C411yescharacteristic
77C4×Dic26C2×C411yescharacteristic
78C4×Dic26C2311yescharacteristic
79C4×Dic26C2311yescharacteristic
80C13×C4⋊C8C2312yes—
81C13×C4⋊C8C2312yes—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84C13×#97—21no—
85C13×#97—21no—
86C4×C8×C13C2×C411yescharacteristic
87C4×C8×C13C2×C411yescharacteristic
88C4×C8×C13C2311yescharacteristic
89C4×C8×C13C2311yescharacteristic
90C22⋊#1055D411yescharacteristic
91C22⋊#1055D411yescharacteristic
92#88061C2×C411yescharacteristic
93#88061C2×C411yescharacteristic
94#88061C2×C411yescharacteristic
95#88061C2×C411yescharacteristic
96#88060—22no—
97#88060—22no—
98#88057C2×C411yescharacteristic
99#88057C2×C411yescharacteristic
100#88057C2×C411yescharacteristic
101#88057C2×C411yescharacteristic
102#88056C2×C411yescharacteristic
103#88056C2×C411yescharacteristic
104#88056C2×C411yescharacteristic
105#88056C2×C411yescharacteristic
106#88055—22no—
107#88054—22no—
108#88054—22no—
109C8×Dic13—22no—
110C4⋊#1055D412yes—
111#88043—21no—
112C4×#1055C2312yes—
113C4×#1055C2312yes—
114#18060—131nomaximal, Sylow
115C23×D13—21no—
116C22×C4×C13C22×C411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—21no—
122C2×D52—22no—
123C2×D52—21no—
124C2×D52—41no—
125C2×D52C22×C411yescharacteristic
126C2×D52C22×C411yescharacteristic
127C2×C4×D13—21no—
128C2×C4×D13—21no—
129C2×C4×D13—21no—
130C2×C4×D13—21no—
131C2×C4×D13—82no—
132C2×Dic26—22no—
133C2×Dic26—21no—
134C2×Dic26—41no—
135C2×Dic26C22×C411yescharacteristic
136C2×Dic26C22×C411yescharacteristic
137C2×C8×C13—22no—
138C2×C8×C13—22no—
139C2×C8×C13—22no—
140C2×C8×C13—41no—
141C2×C8×C13C22×C411yescharacteristic
142C2×C8×C13C22×C411yescharacteristic
143C2×C8×C13C22×C411yescharacteristic
144C2×C8×C13C22×C411yescharacteristic
145C42×C13C22×C411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13#4111yescharacteristic
148C42×C13C2411yescharacteristic
149#6103—21no—
150#6103—21no—
151#6103—21no—
152#6103—21no—
153C4⋊Dic13—21no—
154C4⋊Dic13—21no—
155C4⋊Dic13C22×C411yescharacteristic
156C4⋊Dic13C22×C411yescharacteristic
157C4⋊Dic13C22×C411yescharacteristic
158C4⋊Dic13C22×C411yescharacteristic
159#6101—21no—
160#6101—21no—
161#6101—21no—
162#6101—21no—
163C4×Dic13—21no—
164C4×Dic13—21no—
165C4×Dic13—21no—
166C4×Dic13—21no—
167#6099—42no—
168C2×#1055—22no—
169C2×#1055C2×D412yes—
170C2×#1055C2×D412yes—
171#6095—22no—
172#6095—22no—
173#6095—22no—
174#6095M1614yescomplemented
175#6094—82no—
176C8×D13—82no—
177#2984—131no—
178#2974—131no—
179C2×C4×SD16—131no—
180#1592—132no—
181#1583—132no—
182#1582—132no—
183SD16⋊C8—132no—
184#1568D1311yescharacteristic, complemented
185#1491—131no—
186#1490—131no—
187#1451—131no—
188C23×C13C4×D411yescharacteristic
189C22×D13—21no—
190C22×D13—21no—
191C22×D13—42no—
192C22×D13—42no—
193C22×D13—81no—
194C2×C4×C13—22no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—22no—
198C2×C4×C13C4×D411yescharacteristic
199C2×C4×C13C4×D411yescharacteristic
200C2×C4×C13C4×D411yescharacteristic
201C2×C4×C13C23×C411yescharacteristic
202C2×C4×C13C22×D411yescharacteristic
203C2×C4×C13C2×#4111yescharacteristic
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13—81no—
213D52—21no—
214D52—21no—
215D52—21no—
216D52—42no—
217D52C2×M1612yes—
218C4×D13—42no—
219C4×D13—42no—
220C4×D13—81no—
221C4×D13—81no—
222Dic26—21no—
223Dic26—21no—
224Dic26—21no—
225Dic26—42no—
226Dic26C2×M1612yes—
227C8×C13—21no—
228C8×C13—21no—
229C8×C13—21no—
230C8×C13—42no—
231C8×C13—42no—
232C8×C13C2×M1612yes—
233#1055—22no—
234#1055—22no—
235#1055—42no—
236C22×SD16—131no—
237C2×C4×Q8—131no—
238C2×C4×D4—131no—
239#446—132no—
240#446—262no—
241C8×Q8—132no—
242C4×SD16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16—131no—
246C4×SD16—131no—
247C4×SD16—131no—
248C4×SD16—131no—
249C4×SD16—131no—
250#436—132no—
251#435—262no—
252C8×D4—132no—
253#432—261no—
254#432C2×D1311yescharacteristic
255#432C2×D1311yescharacteristic
256#431—131no—
257#431—261no—
258C2×#106—131no—
259C2×#103—131no—
260C2×#102—131no—
261#407—261no—
262C2×C22⋊C8—261no—
263C4×M16—131no—
264C2×C4×C8C2×D1311yescharacteristic
265#335C2×D1312yescomplemented
266#334C2×D1312yescomplemented
267Q8⋊C8—132no—
268Q8⋊C8—132no—
269D4⋊C8—132no—
270D4⋊C8—132no—
271#322—132no—
272#322—132no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13#44412yes—
276C22×C13C2×C4×D411yescharacteristic
277C2×D13—22no—
278C2×D13—41no—
279C2×D13—41no—
280C2×D13—41no—
281C2×D13—41no—
282C2×D13—41no—
283C2×D13—84no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13C22×M1611yescharacteristic
289C4×C13#56811yescharacteristic
290C4×C13#57712yes—
291Dic13—22no—
292Dic13—41no—
293Dic13—41no—
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297C22×Q8—131no—
298C22×D4—131no—
299C23×C4—261no—
300C2×SD16—131no—
301C2×SD16—131no—
302C2×SD16—131no—
303C2×SD16—131no—
304C2×SD16—264no—
305C2×M16—262no—
306C2×M16—261no—
307C22×C8—262no—
308C22×C8C4×D1311yescharacteristic
309C22×C8C4×D1311yescharacteristic
310C4×Q8—131no—
311C4×Q8—131no—
312C4×Q8—131no—
313C4×Q8—131no—
314C4×Q8—261no—
315C4×Q8—261no—
316C4×D4—131no—
317C4×D4—131no—
318C4×D4—131no—
319C4×D4—131no—
320C4×D4—261no—
321C4×D4—261no—
322C2×C4⋊C4—131no—
323C2×C4⋊C4—131no—
324C2×C4⋊C4—261no—
325C2×C22⋊C4—261no—
326C2×C42—261no—
327C2×C42C22×D1311yescharacteristic
328#106—131no—
329#106—131no—
330#106—131no—
331#106—131no—
332C4⋊C8—132no—
333C4⋊C8—262no—
334C4⋊C8—262no—
335C4⋊C8C22×D1312yes—
336C4⋊C8C22×D1312yes—
337#103—131no—
338#103—131no—
339#103—131no—
340#103—131no—
341#102—131no—
342#102—131no—
343#102—131no—
344#102—131no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—131no—
348C22⋊C8—131no—
349C22⋊C8—262no—
350C22⋊C8—262no—
351#97—21no—
352#97—21no—
353#97—262no—
354#97—261no—
355C4×C8—132no—
356C4×C8—132no—
357C4×C8—262no—
358C4×C8C4×D1311yescharacteristic
359C4×C8C4×D1311yescharacteristic
360C4×C8C22×D1311yescharacteristic
361C4×C8C22×D1311yescharacteristic
362C2×C13—22no—
363C2×C13D4×M1611yescharacteristic
364C2×C13#294911yescharacteristic
365C2×C13C2×#44411yescharacteristic
366D13—42no—
367D13—81no—
368C24—261no—
369C2×Q8—131no—
370C2×Q8—131no—
371C2×Q8—262no—
372C2×Q8—261no—
373C2×Q8—521no—
374C2×D4—131no—
375C2×D4—131no—
376C2×D4—262no—
377C2×D4—261no—
378C2×D4—521no—
379C22×C4—261no—
380C22×C4—261no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4—261no—
385C22×C4—261no—
386C22×C4—1042no—
387C22×C4C2×C4×D1311yescharacteristic
388C22×C4D4×D1311yescharacteristic
389C22×C4#613111yescharacteristic
390SD16—134no—
391SD16—262no—
392SD16—262no—
393SD16—262no—
394M16—522no—
395M16—1042no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—132no—
401C2×C8—132no—
402C2×C8—262no—
403C2×C8—1042no—
404C2×C8C2×C4×D1311yescharacteristic
405C2×C8C2×C4×D1311yescharacteristic
406C2×C8C2×C4×D1311yescharacteristic
407C2×C8C2×C4×D1311yescharacteristic
408C4⋊C4—131no—
409C4⋊C4—131no—
410C4⋊C4—131no—
411C4⋊C4—131no—
412C4⋊C4—261no—
413C4⋊C4—261no—
414C4⋊C4—261no—
415C4⋊C4—261no—
416C4⋊C4—261no—
417C4⋊C4—261no—
418C22⋊C4—261no—
419C22⋊C4—261no—
420C22⋊C4—261no—
421C22⋊C4—261no—
422C42—261no—
423C42—261no—
424C42—261no—
425C42—261no—
426C42C2×C4×D1311yescharacteristic
427C42D4×D1311yescharacteristic
428C42#613111yescharacteristic
429C42C23×D1311yescharacteristic
430C13#1806011yescharacteristic, complemented, Sylow
431C23—261no—
432C23—261no—
433C23—522no—
434C23—522no—
435C23—1041no—
436C23#8814711yescharacteristic
437Q8—132no—
438Q8—261no—
439Q8—261no—
440Q8—261no—
441Q8—522no—
442D4—132no—
443D4—261no—
444D4—261no—
445D4—261no—
446D4—522no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—261no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—522no—
458C2×C4—522no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—1041no—
462C2×C4—1041no—
463C2×C4—1041no—
464C2×C4#8814711yescharacteristic
465C2×C4#8814711yescharacteristic
466C2×C4#8814711yescharacteristic
467C2×C4C22×C4×D1311yescharacteristic
468C2×C4C2×D4×D1311yescharacteristic
469C2×C4C2×#613111yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—42no—
474C8—42no—
475C8—262no—
476C8—262no—
477C8—522no—
478C8M16×D1312yes—
479C22—21no—
480C22—21no—
481C22—262no—
482C22—521no—
483C22—521no—
484C22—521no—
485C22—521no—
486C22—521no—
487C22—1044no—
488C22#1171855512yes—
489C22C2×#8814711yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—262no—
495C4—521no—
496C4—521no—
497C4—521no—
498C4—521no—
499C4—521no—
500C4C2×M16×D1311yescharacteristic
501C4#1171945011yescharacteristic
502C4#1171947512yes—
503C2—22no—
504C2—522no—
505C2—1041no—
506C2#1312357111yescharacteristic
507C2#1312369411yescharacteristic
508C2C2×#1171855511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1568C2
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenter#1568D13
hypocenterC13#18060
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #13123926C2semidirect
4. #13113737C2semidirect
5. #13113678C2semidirect
6. #13113671C2semidirect
7. #13113647C2semidirect
8. #13113282C2semidirect
10. #13113125C2semidirect
11. C13×#1568C2semidirect
25. #11718492C22semidirect
26. #11718491C22semidirect
41. C13×#335C22semidirect
42. C13×#334C22semidirect
43. #11718076C22semidirect
44. #11718076C22semidirect
47. #11718047C22semidirect
48. #11718046C22semidirect
174. #6095M16semidirect
184. #1568D13semidirect
265. #335C2×D13semidirect
266. #334C2×D13semidirect
430. C13#18060semidirect

Maximal subgroups

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

subgroupindex
#131239262
#131238732
C2×C4×#60952
#131137372
#131136782
#131136712
#131136472
#131132822
#131132782
#131131252
C13×#15682
#1806013