Finite Group Databasebeta

← #15834372

Subgroups — #15834372

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123854C211yesmaximal, characteristic, complemented
2#13123851C211yesmaximal, characteristic, complemented
3C4×#88158C211yesmaximal, characteristic
4#13113728C212yesmaximal, complemented
5#13113688C212yesmaximal, complemented
6#13113667C212yesmaximal, complemented
7C8×#6095C212yesmaximal, complemented
8#13113599C211yesmaximal, characteristic, complemented
9#13113271C211yesmaximal, characteristic, complemented
10#13113271C211yesmaximal, characteristic, complemented
11C8×C13×M16C211yesmaximal, characteristic, complemented
12C2×#88158C411yescharacteristic
13C4×#6127C2211yescharacteristic
14C4×#6127C2211yescharacteristic
15C13×#431C2211yescharacteristic
16C4×C13×M16C2211yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18#11718789—22no—
19#11718788—22no—
20#11718774C411yescharacteristic
21#11718774C411yescharacteristic
22#11718767C411yescharacteristic
23#11718587C2211yescharacteristic
24#11718587C2211yescharacteristic
25#11718368—21no—
26#11718366—21no—
27#11718366—21no—
28D13×#97—21no—
29C4×Dic52C411yescharacteristic
30C4×Dic52C2211yescharacteristic
31C4×D104C411yescharacteristic
32C4×D104C2211yescharacteristic
33C4×#6095C411yescharacteristic
34C4×#6095C411yescharacteristic
35C4×#6095C2211yescharacteristic
36C4×#6095C2211yescharacteristic
37#11718349C2212yes—
38C8×D52C2212yes—
39#11718340C2212yes—
40C8×Dic26C2212yes—
41C13×#322C2212yes—
42C82×C13C2212yes—
43#11718051C2212yes—
44#11718051C2212yes—
45#11718050C2212yes—
46#11718049C2212yes—
47#11718048C2212yes—
48#11718048C2212yes—
49C2×#6127C2×C411yescharacteristic
50C2×#6127C2×C411yescharacteristic
51C2×C13×M16D412yes—
52C22×C8×C13C2×C411yescharacteristic
53C22×C8×C13C2×C411yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C4×C22⋊D13—21no—
56C4×C22⋊D13—21no—
57C4×C22⋊D13—21no—
58C4×C22⋊D13—21no—
59#88180C2×C411yescharacteristic
60#88180C2×C411yescharacteristic
61C2×Dic52C2×C411yescharacteristic
62#88158—24no—
63C2×D104C2×C411yescharacteristic
64C2×#6095C2×C411yescharacteristic
65C2×#6095C2×C411yescharacteristic
66C2×#6094—22no—
67C2×C8×D13—22no—
68C4×D52C2×C411yescharacteristic
69C4×D52C2×C411yescharacteristic
70C4×D52C2311yescharacteristic
71C4×D52C2311yescharacteristic
72#88126—21no—
73#88126—21no—
74C42×D13—21no—
75C42×D13—21no—
76C4×Dic26C2×C411yescharacteristic
77C4×Dic26C2×C411yescharacteristic
78C4×Dic26C2311yescharacteristic
79C4×Dic26C2311yescharacteristic
80C13×C4⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×#97D411yescharacteristic
83C13×#97D411yescharacteristic
84C4×C8×C13C2×C411yescharacteristic
85C4×C8×C13C2×C411yescharacteristic
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—
112#88043—21no—
113#88043—21no—
114#18037—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—41no—
123#6127—41no—
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
134C13×M16—24no—
135C2×C8×C13—22no—
136C2×C8×C13—22no—
137C2×C8×C13—41no—
138C2×C8×C13C22×C411yescharacteristic
139C2×C8×C13C22×C411yescharacteristic
140C2×C8×C13C22×C411yescharacteristic
141C2×C8×C13C22×C411yescharacteristic
142C2×C8×C13C2×D412yes—
143C2×C8×C13C2×D412yes—
144C42×C13C22×C411yescharacteristic
145C42×C13C2×D411yescharacteristic
146C42×C13#4111yescharacteristic
147C42×C13C2411yescharacteristic
148C22⋊Dic13—21no—
149C22⋊Dic13—21no—
150#6103—21no—
151#6103—21no—
152#6103—21no—
153#6103—21no—
154C4⋊Dic13C22×C411yescharacteristic
155C4⋊Dic13C22×C411yescharacteristic
156C4⋊Dic13C22×C411yescharacteristic
157C4⋊Dic13C22×C411yescharacteristic
158#6101—21no—
159#6101—21no—
160#6101—21no—
161#6101—21no—
162C4×Dic13—21no—
163C4×Dic13—21no—
164C4×Dic13—21no—
165C4×Dic13—21no—
166C4×Dic13—21no—
167C4×Dic13—21no—
168C2×#1055—22no—
169C2×#1055—22no—
170Dic52—22no—
171D104—22no—
172#6095—22no—
173#6095M1614yescomplemented
174#6094—44no—
175C8×D13—44no—
176#2971—131no—
177#2970—131no—
178C4×#135—131no—
179#1590—132no—
180#1584—132no—
181#1581—132no—
182C8×SD16—132no—
183#1568—131no—
184#1488—131no—
185#1488—131no—
186C8×M16D1311yescharacteristic, complemented
187C23×C13C4×D411yescharacteristic
188C22×D13—21no—
189C22×D13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—41no—
194C2×C4×C13C4×D411yescharacteristic
195C2×C4×C13C4×D411yescharacteristic
196C2×C4×C13C4×D411yescharacteristic
197C2×C4×C13C23×C411yescharacteristic
198C2×C4×C13C22×D411yescharacteristic
199C2×C4×C13C2×#4111yescharacteristic
200C22⋊D13—42no—
201C22⋊D13—42no—
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208D52—21no—
209D52—21no—
210D52—21no—
211D52C2×M1612yes—
212C4×D13—42no—
213C4×D13—42no—
214C4×D13—42no—
215C4×D13—42no—
216C4×D13—81no—
217C4×D13—81no—
218Dic26—21no—
219Dic26—21no—
220Dic26—21no—
221Dic26C2×M1612yes—
222C8×C13—21no—
223C8×C13—21no—
224C8×C13—21no—
225C8×C13—22no—
226C8×C13—42no—
227C8×C13C2×M1612yes—
228C8×C13#13514yescomplemented
229#1055—42no—
230#1055—42no—
231C2×#135—131no—
232C4×#41—131no—
233C4×#41—131no—
234#446—132no—
235C8×Q8—132no—
236C4×Q16—131no—
237C4×Q16—131no—
238C4×SD16—131no—
239C4×SD16—131no—
240C4×SD16—131no—
241C4×SD16—131no—
242C4×D8—131no—
243C4×D8—131no—
244#436—132no—
245#436—262no—
246#435—262no—
247C8×D4—132no—
248#432—131no—
249#432—131no—
250#432—261no—
251#432—261no—
252#431C2×D1311yescharacteristic
253#427—131no—
254#416—131no—
255#416—131no—
256C4×M16—261no—
257C4×M16C2×D1311yescharacteristic
258C2×#97—261no—
259C2×C4×C8C2×D1311yescharacteristic
260#335—132no—
261#334—132no—
262Q8⋊C8—132no—
263Q8⋊C8—132no—
264D4⋊C8—132no—
265D4⋊C8—132no—
266#322C2×D1312yes—
267C82C2×D1312yes—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13C2×C4×D411yescharacteristic
272C2×D13—22no—
273C2×D13—41no—
274C2×D13—41no—
275C2×D13—41no—
276C2×D13—41no—
277C2×D13—41no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13C22×M1611yescharacteristic
283C4×C13#56811yescharacteristic
284C4×C13C2×#13512yes—
285Dic13—22no—
286Dic13—41no—
287Dic13—41no—
288Dic13—41no—
289Dic13—41no—
290Dic13—41no—
291C2×#41—131no—
292C2×#41—131no—
293#135—264no—
294C2×Q16—131no—
295C2×SD16—131no—
296C2×SD16—131no—
297C2×D8—131no—
298C2×M16—262no—
299C2×M16D5212yes—
300C22×C8—262no—
301C22×C8C4×D1311yescharacteristic
302C22×C8C4×D1311yescharacteristic
303C4×Q8—131no—
304C4×Q8—131no—
305C4×Q8—131no—
306C4×Q8—131no—
307C4×D4—131no—
308C4×D4—131no—
309C4×D4—131no—
310C4×D4—131no—
311C4×D4—261no—
312C4×D4—261no—
313C4×D4—261no—
314C4×D4—261no—
315#117—131no—
316#117—131no—
317#117—261no—
318#117—261no—
319C2×C42—261no—
320C2×C42—261no—
321C2×C42C22×D1311yescharacteristic
322#107—131no—
323#107—131no—
324#106—131no—
325#106—131no—
326C4⋊C8—21no—
327C4⋊C8—132no—
328C4⋊C8—132no—
329C4⋊C8—262no—
330C4⋊C8—262no—
331#103—131no—
332#103—131no—
333#103—131no—
334#103—131no—
335#102—131no—
336#102—131no—
337#102—131no—
338#102—131no—
339C22⋊C8—21no—
340C22⋊C8—261no—
341C22⋊C8—261no—
342C22⋊C8—262no—
343C22⋊C8—262no—
344#97—262no—
345#97—261no—
346#97—261no—
347#97D5211yescharacteristic
348#97D5211yescharacteristic
349C4×C8—262no—
350C4×C8C4×D1311yescharacteristic
351C4×C8C4×D1311yescharacteristic
352C4×C8C22×D1312yes—
353C4×C8C22×D1311yescharacteristic
354C4×C8C22×D1311yescharacteristic
355C4×C8C22×D1312yes—
356C2×C13—41no—
357C2×C13D4×M1611yescharacteristic
358C2×C13C4×#13511yescharacteristic
359C2×C13#295711yescharacteristic
360D13—42no—
361D13—81no—
362#41—262no—
363#41—262no—
364#41—521no—
365#41—521no—
366C2×Q8—131no—
367C2×Q8—131no—
368C2×D4—131no—
369C2×D4—131no—
370C2×D4—261no—
371C2×D4—261no—
372C22×C4—261no—
373C22×C4—261no—
374C22×C4—261no—
375C22×C4—261no—
376C22×C4—261no—
377C22×C4—261no—
378C22×C4C2×C4×D1311yescharacteristic
379C22×C4C2×D5211yescharacteristic
380C22×C4#612711yescharacteristic
381Q16—262no—
382SD16—134no—
383SD16—262no—
384D8—262no—
385M16—24no—
386M16—524no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—41no—
390C2×C8—262no—
391C2×C8—262no—
392C2×C8—524no—
393C2×C8C2×C4×D1311yescharacteristic
394C2×C8C2×C4×D1311yescharacteristic
395C2×C8C2×C4×D1311yescharacteristic
396C2×C8C2×C4×D1311yescharacteristic
397C2×C8C2×D5212yes—
398C2×C8C2×D5212yes—
399C4⋊C4—131no—
400C4⋊C4—131no—
401C4⋊C4—131no—
402C4⋊C4—131no—
403C4⋊C4—261no—
404C4⋊C4—261no—
405C4⋊C4—261no—
406C4⋊C4—261no—
407C22⋊C4—261no—
408C22⋊C4—261no—
409C22⋊C4—261no—
410C22⋊C4—261no—
411C22⋊C4—261no—
412C22⋊C4—261no—
413C42—261no—
414C42—261no—
415C42—261no—
416C42—261no—
417C42—261no—
418C42—261no—
419C42C2×C4×D1311yescharacteristic
420C42C2×D5211yescharacteristic
421C42#612711yescharacteristic
422C42C23×D1311yescharacteristic
423C13#1803711yescharacteristic, complemented, Sylow
424C23—261no—
425C23—261no—
426C23C4×D5211yescharacteristic
427Q8—132no—
428Q8—261no—
429Q8—261no—
430Q8—261no—
431D4—132no—
432D4—261no—
433D4—261no—
434D4—261no—
435D4—522no—
436D4—522no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—261no—
442C2×C4—261no—
443C2×C4—261no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—261no—
447C2×C4—522no—
448C2×C4—522no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—1041no—
452C2×C4—1041no—
453C2×C4C4×D5211yescharacteristic
454C2×C4C4×D5211yescharacteristic
455C2×C4C4×D5211yescharacteristic
456C2×C4C22×C4×D1311yescharacteristic
457C2×C4C22×D5211yescharacteristic
458C2×C4C2×#612711yescharacteristic
459C8—22no—
460C8—21no—
461C8—21no—
462C8—21no—
463C8—42no—
464C8—522no—
465C8—522no—
466C8#8815814yescomplemented
467C8M16×D1312yes—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—262no—
472C22—521no—
473C22—521no—
474C22—521no—
475C22—521no—
476C22—521no—
477C22C2×C4×D5211yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—262no—
483C4—521no—
484C4—521no—
485C4—521no—
486C4—521no—
487C4—521no—
488C4C2×#8815812yes—
489C4C2×M16×D1311yescharacteristic
490C4#1171945011yescharacteristic
491C2—41no—
492C2—522no—
493C2—1041no—
494C2M16×D5211yescharacteristic
495C2C4×#8815811yescharacteristic
496C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×M16C2
socleC22×C13C2×C4×D4
prime radicalC2×#88158C4
cosocleC42×C13C24
hypercenterC8×M16D13
hypocenterC13#18037
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
1. #13123854C2semidirect
2. #13123851C2semidirect
4. #13113728C2semidirect
5. #13113688C2semidirect
6. #13113667C2semidirect
7. C8×#6095C2semidirect
8. #13113599C2semidirect
9. #13113271C2semidirect
10. #13113271C2semidirect
11. C8×C13×M16C2semidirect
173. #6095M16semidirect
186. C8×M16D13semidirect
228. C8×C13#135semidirect
423. C13#18037semidirect
466. C8#88158semidirect

Maximal subgroups

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

subgroupindex
#131238542
#131238512
C4×#881582
#131137282
#131136882
#131136672
C8×#60952
#131135992
#131132712
C8×C13×M162
#1803713