Finite Group Databasebeta

← #15832452

Subgroups — #15832452

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123802C211yesmaximal, characteristic, complemented
2C8×#6127C211yesmaximal, characteristic, complemented
3C4×#88158C211yesmaximal, characteristic
4#13113688C212yesmaximal, complemented
5#13113681C212yesmaximal, complemented
6#13113674C212yesmaximal, complemented
7#13113667C212yesmaximal, complemented
8#13113584C211yesmaximal, characteristic, complemented
9#13113219C211yesmaximal, characteristic, complemented
10#13113219C211yesmaximal, characteristic, complemented
11C2×C13×#322C211yesmaximal, characteristic, complemented
12C2×#88158C411yescharacteristic
13C4×#6127C2211yescharacteristic
14C4×#6127C2211yescharacteristic
15C2×C4×C8×C13C2211yescharacteristic
16C2×C4×C8×C13C2211yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18#11718774C411yescharacteristic
19#11718774C411yescharacteristic
20#11718772—22no—
21C8×C22⋊D13—22no—
22#11718767C411yescharacteristic
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25C4×Dic52C411yescharacteristic
26C4×Dic52C2211yescharacteristic
27C4×D104C411yescharacteristic
28C4×D104C2211yescharacteristic
29C4×#6095C411yescharacteristic
30C4×#6095C411yescharacteristic
31C4×#6095C2211yescharacteristic
32C4×#6095C2211yescharacteristic
33#11718349C2212yes—
34C4×#6094—21no—
35C8×D52C2212yes—
36#11718346—21no—
37#11718346—21no—
38C4×C8×D13—21no—
39#11718340C2212yes—
40C8×Dic26C2212yes—
41C13×#322C2212yes—
42C13×#322C2212yes—
43#11718051C2212yes—
44#11718051C2212yes—
45#11718050C2212yes—
46#11718049C2212yes—
47#11718048C2212yes—
48#11718048C2212yes—
49C2×#6127C2×C411yescharacteristic
50C2×#6127C2×C411yescharacteristic
51C22×C8×C13—21no—
52C22×C8×C13C2×C411yescharacteristic
53C22×C8×C13C2×C411yescharacteristic
54C22×C8×C13D412yes—
55C2×C42×C13C2311yescharacteristic
56C4×C22⋊D13—21no—
57C4×C22⋊D13—21no—
58C4×C22⋊D13—21no—
59C4×C22⋊D13—21no—
60#88180C2×C411yescharacteristic
61#88180C2×C411yescharacteristic
62C2×Dic52C2×C411yescharacteristic
63#88158—24no—
64C2×D104C2×C411yescharacteristic
65C2×#6095C2×C411yescharacteristic
66C2×#6095C2×C411yescharacteristic
67C2×#6094—22no—
68C2×C8×D13—22no—
69C4×D52C2×C411yescharacteristic
70C4×D52C2×C411yescharacteristic
71C4×D52C2311yescharacteristic
72C4×D52C2311yescharacteristic
73#88126—21no—
74#88126—21no—
75C42×D13—21no—
76C42×D13—21no—
77C4×Dic26C2×C411yescharacteristic
78C4×Dic26C2×C411yescharacteristic
79C4×Dic26C2311yescharacteristic
80C4×Dic26C2311yescharacteristic
81C4×C8×C13—21no—
82C4×C8×C13C2×C411yescharacteristic
83C4×C8×C13C2×C411yescharacteristic
84C4×C8×C13D411yescharacteristic
85C4×C8×C13D411yescharacteristic
86C4×C8×C13C2312yes—
87C4×C8×C13C2311yescharacteristic
88C4×C8×C13C2311yescharacteristic
89C4×C8×C13C2312yes—
90C22⋊#1055—21no—
91C22⋊#1055—21no—
92#88061C2×C411yescharacteristic
93#88061C2×C411yescharacteristic
94#88061C2×C411yescharacteristic
95#88061C2×C411yescharacteristic
96#88060—22no—
97#88060—22no—
98#88058C2×C411yescharacteristic
99#88058C2×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⋊#1055C2312yes—
111C4⋊#1055C2312yes—
112C4×#1055—21no—
113C4×#1055—21no—
114#17863—131nomaximal, Sylow
115C22×C4×C13C22×C411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C2×C22⋊D13—21no—
119C2×C22⋊D13—21no—
120#6127—22no—
121#6127—22no—
122#6127—22no—
123#6127M1614yescomplemented
124C2×D52C22×C411yescharacteristic
125C2×D52C22×C411yescharacteristic
126C2×C4×D13—21no—
127C2×C4×D13—21no—
128C2×C4×D13—21no—
129C2×C4×D13—21no—
130C2×C4×D13—21no—
131C2×C4×D13—21no—
132C2×Dic26C22×C411yescharacteristic
133C2×Dic26C22×C411yescharacteristic
134C2×C8×C13—22no—
135C2×C8×C13—22no—
136C2×C8×C13—24no—
137C2×C8×C13—22no—
138C2×C8×C13—42no—
139C2×C8×C13C22×C411yescharacteristic
140C2×C8×C13C22×C411yescharacteristic
141C2×C8×C13C22×C411yescharacteristic
142C2×C8×C13C22×C411yescharacteristic
143C2×C8×C13C2×D412yes—
144C2×C8×C13C2×D412yes—
145C42×C13C22×C411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13#4111yescharacteristic
148C42×C13C2411yescharacteristic
149C22⋊Dic13—21no—
150C22⋊Dic13—21no—
151#6103—21no—
152#6103—21no—
153#6103—21no—
154#6103—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—
167C4×Dic13—21no—
168C4×Dic13—21no—
169C2×#1055—22no—
170C2×#1055—22no—
171Dic52—22no—
172D104—22no—
173#6095—22no—
174#6095—22no—
175#6094—44no—
176C8×D13—44no—
177#2965—131no—
178C8×#41—131no—
179C4×#135—131no—
180#1584—132no—
181#1583—132no—
182#1582—132no—
183#1581—132no—
184#1564—131no—
185#1476—131no—
186#1476—131no—
187C2×#322D1311yescharacteristic, complemented
188C23×C13C4×D411yescharacteristic
189C22×D13—21no—
190C22×D13—21no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13C4×D411yescharacteristic
194C2×C4×C13C4×D411yescharacteristic
195C2×C4×C13C4×D411yescharacteristic
196C2×C4×C13C2×M1612yes—
197C2×C4×C13#13112yes—
198C2×C4×C13C23×C411yescharacteristic
199C2×C4×C13C22×D411yescharacteristic
200C2×C4×C13C2×#4111yescharacteristic
201C22⋊D13—24no—
202C22⋊D13—42no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209D52—21no—
210D52—21no—
211D52—21no—
212D52C2×M1612yes—
213C4×D13—24no—
214C4×D13—42no—
215C4×D13—42no—
216C4×D13—42no—
217C4×D13—42no—
218C4×D13—42no—
219Dic26—21no—
220Dic26—21no—
221Dic26—21no—
222Dic26C2×M1612yes—
223C8×C13—21no—
224C8×C13—21no—
225C8×C13—21no—
226C8×C13—21no—
227C8×C13—22no—
228C8×C13—42no—
229C8×C13#13514yescomplemented
230#1055—42no—
231#1055—42no—
232C2×#135—131no—
233C4×#41—131no—
234C4×#41—131no—
235#446—132no—
236C8×Q8—132no—
237C4×Q16—131no—
238C4×Q16—131no—
239C4×SD16—131no—
240C4×SD16—131no—
241C4×SD16—131no—
242C4×SD16—131no—
243C4×D8—131no—
244C4×D8—131no—
245#436—132no—
246#435—262no—
247C8×D4—132no—
248C8×D4—262no—
249#431—131no—
250#431—131no—
251#431—261no—
252#431—261no—
253#427—131no—
254#416—131no—
255#416—131no—
256C4×M16—261no—
257C2×C4×C8—261no—
258C2×C4×C8C2×D1311yescharacteristic
259C2×C4×C8C2×D1311yescharacteristic
260C2×C4×C8C2×D1311yescharacteristic
261#335—132no—
262#334—132no—
263Q8⋊C8—132no—
264Q8⋊C8—132no—
265D4⋊C8—132no—
266D4⋊C8—132no—
267#322C2×D1312yes—
268#322C2×D1312yes—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13#43512yes—
272C22×C13C2×C4×D411yescharacteristic
273C2×D13—22no—
274C2×D13—41no—
275C2×D13—41no—
276C2×D13—41no—
277C2×D13—41no—
278C2×D13—41no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13#43512yes—
282C4×C13#44412yes—
283C4×C13C22×M1611yescharacteristic
284C4×C13C2×#13111yescharacteristic
285C4×C13C2×#13512yes—
286Dic13—22no—
287Dic13—41no—
288Dic13—41no—
289Dic13—41no—
290Dic13—41no—
291Dic13—41no—
292C2×#41—131no—
293C2×#41—131no—
294#135—264no—
295C2×Q16—131no—
296C2×SD16—131no—
297C2×SD16—131no—
298C2×D8—131no—
299C2×M16—262no—
300C22×C8—21no—
301C22×C8—262no—
302C22×C8C4×D1311yescharacteristic
303C22×C8C4×D1311yescharacteristic
304C22×C8D5212yes—
305C4×Q8—131no—
306C4×Q8—131no—
307C4×Q8—131no—
308C4×Q8—131no—
309C4×D4—131no—
310C4×D4—131no—
311C4×D4—131no—
312C4×D4—131no—
313C4×D4—261no—
314C4×D4—261no—
315C4×D4—261no—
316C4×D4—261no—
317#117—131no—
318#117—131no—
319#117—261no—
320#117—261no—
321C2×C42—261no—
322C2×C42—261no—
323C2×C42C22×D1311yescharacteristic
324#107—131no—
325#107—131no—
326#106—131no—
327#106—131no—
328C4⋊C8—132no—
329C4⋊C8—132no—
330C4⋊C8—262no—
331C4⋊C8—262no—
332#103—131no—
333#103—131no—
334#103—131no—
335#103—131no—
336#102—131no—
337#102—131no—
338#102—131no—
339#102—131no—
340C22⋊C8—261no—
341C22⋊C8—261no—
342C22⋊C8—262no—
343C22⋊C8—262no—
344#97—262no—
345C4×C8—21no—
346C4×C8—262no—
347C4×C8—261no—
348C4×C8—261no—
349C4×C8C4×D1311yescharacteristic
350C4×C8C4×D1311yescharacteristic
351C4×C8D5211yescharacteristic
352C4×C8D5211yescharacteristic
353C4×C8C22×D1312yes—
354C4×C8C22×D1311yescharacteristic
355C4×C8C22×D1311yescharacteristic
356C4×C8C22×D1312yes—
357C2×C13—22no—
358C2×C13C2×#43511yescharacteristic
359C2×C13C4×#13511yescharacteristic
360C2×C13C2×#44411yescharacteristic
361D13—42no—
362D13—81no—
363#41—134no—
364#41—262no—
365#41—262no—
366#41—262no—
367C2×Q8—131no—
368C2×Q8—131no—
369C2×D4—131no—
370C2×D4—131no—
371C2×D4—261no—
372C2×D4—261no—
373C22×C4—261no—
374C22×C4—261no—
375C22×C4—261no—
376C22×C4—261no—
377C22×C4—261no—
378C22×C4—261no—
379C22×C4C2×C4×D1311yescharacteristic
380C22×C4C2×D5211yescharacteristic
381C22×C4#612711yescharacteristic
382Q16—262no—
383SD16—262no—
384SD16—262no—
385D8—262no—
386M16—524no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—24no—
390C2×C8—22no—
391C2×C8—42no—
392C2×C8—262no—
393C2×C8—262no—
394C2×C8—524no—
395C2×C8C2×C4×D1311yescharacteristic
396C2×C8C2×C4×D1311yescharacteristic
397C2×C8C2×C4×D1311yescharacteristic
398C2×C8C2×C4×D1311yescharacteristic
399C2×C8C2×D5212yes—
400C2×C8C2×D5212yes—
401C4⋊C4—131no—
402C4⋊C4—131no—
403C4⋊C4—131no—
404C4⋊C4—131no—
405C4⋊C4—261no—
406C4⋊C4—261no—
407C4⋊C4—261no—
408C4⋊C4—261no—
409C22⋊C4—261no—
410C22⋊C4—261no—
411C22⋊C4—261no—
412C22⋊C4—261no—
413C22⋊C4—261no—
414C22⋊C4—261no—
415C42—261no—
416C42—261no—
417C42—261no—
418C42—261no—
419C42—261no—
420C42—261no—
421C42C2×C4×D1311yescharacteristic
422C42C2×D5211yescharacteristic
423C42#612711yescharacteristic
424C42C23×D1311yescharacteristic
425C13#1786311yescharacteristic, complemented, Sylow
426C23—261no—
427C23—261no—
428C23C4×D5211yescharacteristic
429Q8—132no—
430Q8—261no—
431Q8—261no—
432Q8—261no—
433D4—132no—
434D4—264no—
435D4—261no—
436D4—261no—
437D4—261no—
438D4—522no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—261no—
442C2×C4—264no—
443C2×C4—261no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—261no—
447C2×C4—261no—
448C2×C4—522no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—522no—
453C2×C4C4×D5211yescharacteristic
454C2×C4C4×D5211yescharacteristic
455C2×C4C4×D5211yescharacteristic
456C2×C4M16×D1312yes—
457C2×C4#8816112yes—
458C2×C4C22×C4×D1311yescharacteristic
459C2×C4C22×D5211yescharacteristic
460C2×C4C2×#612711yescharacteristic
461C8—22no—
462C8—21no—
463C8—21no—
464C8—21no—
465C8—21no—
466C8—42no—
467C8—522no—
468C8—522no—
469C8#8815814yescomplemented
470C22—21no—
471C22—21no—
472C22—262no—
473C22—521no—
474C22—521no—
475C22—521no—
476C22—521no—
477C22—521no—
478C22#1171836712yes—
479C22C2×C4×D5211yescharacteristic
480C4—21no—
481C4—21no—
482C4—262no—
483C4—521no—
484C4—521no—
485C4—521no—
486C4—521no—
487C4—521no—
488C4#1171836712yes—
489C4#1171837812yes—
490C4C2×#8815812yes—
491C4C2×M16×D1311yescharacteristic
492C4C2×#8816111yescharacteristic
493C2—22no—
494C2—522no—
495C2—1041no—
496C2C2×#1171836711yescharacteristic
497C2C4×#8815811yescharacteristic
498C2C2×#1171837811yescharacteristic
subgroupG/H
centerC42C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#322C2
socleC22×C13C2×C4×D4
prime radicalC2×#88158C4
cosocleC42×C13C24
hypercenterC2×#322D13
hypocenterC13#17863
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
1. #13123802C2semidirect
2. C8×#6127C2semidirect
4. #13113688C2semidirect
5. #13113681C2semidirect
6. #13113674C2semidirect
7. #13113667C2semidirect
8. #13113584C2semidirect
9. #13113219C2semidirect
10. #13113219C2semidirect
11. C2×C13×#322C2semidirect
123. #6127M16semidirect
187. C2×#322D13semidirect
229. C8×C13#135semidirect
425. C13#17863semidirect
469. C8#88158semidirect

Maximal subgroups

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

subgroupindex
#131238022
C8×#61272
C4×#881582
#131136882
#131136812
#131136742
#131136672
#131135842
#131132192
C2×C13×#3222
#1786313