Finite Group Databasebeta

← #15753804

Subgroups — #15753804

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic, complemented
3C2×#11718043C212yesmaximal
4#13112715C212yesmaximal, complemented
5C13×#1434C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×C4×C22⋊D13—21no—
9C2×C4×D52C411yescharacteristic, complemented
10C2×C13×#95—21no—
11C2×C13×#95—21no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718873C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718601—21no—
17#11718600C411yescharacteristic, complemented
18C4×#6103—21no—
19C4×C4⋊Dic13C411yescharacteristic, complemented
20#11718589C411yescharacteristic, complemented
21C2×#88043—21no—
22#11718116—21no—
23#11718043C418yescomplemented
24C23×C4×C13—22no—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C22×C22⋊D13—21no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C2×C42×C13—42no—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37#88184—22no—
38#88184C2×C414yes—
39C4×C22⋊D13—44no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×C4⋊Dic13C2×C411yescharacteristic
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C22×#1055—22no—
50C4×D52—42no—
51C13×#95—22no—
52C13×#95—42no—
53C13×#95—42no—
54C13×#95C2×C414yescomplemented
55#88071—21no—
56#88071—21no—
57#88071—21no—
58C22⋊#1055—22no—
59C22⋊#1055C2×C414yescomplemented
60#88043—42no—
61#8216—131nomaximal, Sylow
62C24×C13C2×D411yescharacteristic
63C23×D13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—24no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C22×C412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4112yes—
88C2×C22⋊D13—24no—
89C2×C22⋊D13—42no—
90C2×C22⋊D13—41no—
91C2×C22⋊D13—41no—
92C22×Dic13—21no—
93C22×Dic13—21no—
94C22×Dic13—21no—
95C2×D52—21no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52C4212yes—
99C2×C4×D13—42no—
100C2×C4×D13—42no—
101C2×C4×D13—42no—
102C42×C13—22no—
103C42×C13—22no—
104C42×C13—41no—
105C42×C13—41no—
106C22⋊Dic13—42no—
107#6103—24no—
108#6103—42no—
109#6103—42no—
110#6103—42no—
111C4⋊Dic13—21no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13C4212yes—
115#6101—42no—
116C4×Dic13—42no—
117C2×#1055—24no—
118C2×#1055—42no—
119C2×#1055—42no—
120C4×#121—131no—
121#1749—131no—
122C2×#327—132no—
123#1434D1311yescharacteristic, complemented
124#1294—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13C2×C22⋊C411yescharacteristic
130C23×C13C4×D412yes—
131C23×C13AGL(1,ℤ/8)11yescharacteristic
132C23×C13AGL(1,ℤ/8)12yes—
133C23×C13#13711yescharacteristic
134C22×D13—22no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—44no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—44no—
162C2×C4×C13—44no—
163C2×C4×C13—44no—
164C2×C4×C13—82no—
165C2×C4×C13—82no—
166C2×C4×C13—82no—
167C2×C4×C13—82no—
168C2×C4×C13#9912yes—
169C2×C4×C13C2×C4211yescharacteristic
170C2×C4×C13#11711yescharacteristic
171C2×C4×C13C4×D412yes—
172C22⋊D13—44no—
173C22⋊D13—44no—
174C2×Dic13—22no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183D52—42no—
184D52—42no—
185C4×D13—84no—
186#1055—44no—
187C2×#121—131no—
188C2×C4×D4—131no—
189C2×C4×D4—261no—
190C22×C42C2×D1311yescharacteristic
191C2×C22⋊C8—132no—
192C2×#97—261no—
193#390—131no—
194#389—131no—
195#388—261no—
196#386—261no—
197#380—131no—
198C4×C4⋊C4—131no—
199C4×C22⋊C4—261no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95C2×D1312yes—
203#336—261no—
204#327—138no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—22no—
213C22×C13C4×C22⋊C411yescharacteristic
214C22×C13C2×#9911yescharacteristic
215C22×C13#41011yescharacteristic
216C22×C13#41711yescharacteristic
217C22×C13#41811yescharacteristic
218C22×C13#42111yescharacteristic
219C22×C13#42111yescharacteristic
220C22×C13#44012yes—
221C22×C13#44212yes—
222C2×D13—42no—
223C2×D13—42no—
224C2×D13—42no—
225C2×D13—81no—
226C2×D13—81no—
227C2×D13—81no—
228C2×D13—81no—
229C4×C13—22no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—22no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—84no—
237Dic13—42no—
238Dic13—81no—
239Dic13—81no—
240C22×D4—131no—
241C22×D4—261no—
242C23×C4—22no—
243C23×C4—261no—
244C23×C4C22⋊D1311yescharacteristic
245C23×C4C22⋊D1311yescharacteristic
246C23×C4C22×D1311yescharacteristic
247C22×C8—262no—
248#121—134no—
249#121—262no—
250C4×D4—522no—
251C4×D4—524no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—261no—
256C2×C22⋊C4—261no—
257C2×C22⋊C4—261no—
258C2×C22⋊C4—261no—
259C2×C22⋊C4—261no—
260C2×C22⋊C4—261no—
261C2×C42—42no—
262C2×C42—261no—
263C2×C42C4×D1311yescharacteristic
264C2×C42C4×D1311yescharacteristic
265C2×C42D5211yescharacteristic
266C2×C42D5211yescharacteristic
267C22⋊C8—134no—
268C22⋊C8—262no—
269#97—522no—
270#95—22no—
271#95—42no—
272#95—42no—
273#95—261no—
274#95—261no—
275#95—261no—
276#95C4×D1314yescomplemented
277C2×C13—22no—
278C2×C13—22no—
279C2×C13#151011yescharacteristic
280C2×C13#151211yescharacteristic
281C2×C13#151311yescharacteristic
282C2×C13#151411yescharacteristic
283C2×C13C4×#9911yescharacteristic
284C2×C13#175911yescharacteristic
285C2×C13#176211yescharacteristic
286D13—82no—
287C24—261no—
288C24C2×C22⋊D1311yescharacteristic
289C2×D4—132no—
290C2×D4—264no—
291C2×D4—261no—
292C2×D4—521no—
293C2×D4—521no—
294C2×D4—521no—
295C2×D4—521no—
296C2×D4—522no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—261no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—522no—
317C22×C4—522no—
318C22×C4—522no—
319C22×C4#610311yescharacteristic
320C22×C4#610311yescharacteristic
321C22×C4#610311yescharacteristic
322C22×C4#610311yescharacteristic
323C22×C4C2×C4×D1311yescharacteristic
324C22×C4C2×C4×D1312yes—
325C22×C4C2×D5211yescharacteristic
326C22×C4#612712yes—
327C2×C8—264no—
328C2×C8—522no—
329C2×C8—522no—
330C4⋊C4—132no—
331C4⋊C4—261no—
332C4⋊C4—521no—
333C4⋊C4—521no—
334C4⋊C4—522no—
335C22⋊C4—264no—
336C22⋊C4—522no—
337C22⋊C4—522no—
338C22⋊C4—522no—
339C22⋊C4—522no—
340C42—22no—
341C42—22no—
342C42—41no—
343C42—41no—
344C42—522no—
345C13#821611yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—262no—
351C23—521no—
352C23—521no—
353C23—521no—
354C23—521no—
355C23—521no—
356C23—521no—
357C23C2×#610311yescharacteristic
358C23C4×C22⋊D1312yes—
359C23#8818611yescharacteristic
360C23#8819611yescharacteristic
361C23#8820312yes—
362D4—522no—
363D4—522no—
364D4—524no—
365D4—524no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—262no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4—521no—
402C2×C4—1044no—
403C2×C4#8804612yes—
404C2×C4C42×D1311yescharacteristic
405C2×C4#8812611yescharacteristic
406C2×C4C4×D5212yes—
407C8—524no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—522no—
417C22—522no—
418C22—522no—
419C22—1041no—
420C22—1041no—
421C22—1041no—
422C22—1041no—
423C22C4×#610311yescharacteristic
424C22C2×#8804611yescharacteristic
425C22#1171862711yescharacteristic
426C22#1171866211yescharacteristic
427C22#1171866611yescharacteristic
428C22#1171866611yescharacteristic
429C22#1171866711yescharacteristic
430C22#1171867512yes—
431C22#1171868712yes—
432C4—22no—
433C4—21no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—522no—
441C4—1041no—
442C4—1041no—
443C2—22no—
444C2—22no—
445C2—1042no—
446C2#1311336411yescharacteristic
447C2#1311337211yescharacteristic
448C2#1311337711yescharacteristic
449C2#1311338211yescharacteristic
450C2C4×#8804611yescharacteristic
451C2#1311464711yescharacteristic
452C2#1311466411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1434C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#1434D13
hypocenterC13#8216
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13114598C2semidirect
4. #13112715C2semidirect
5. C13×#1434C2semidirect
9. C2×C4×D52C4semidirect
17. #11718600C4semidirect
19. C4×C4⋊Dic13C4semidirect
20. #11718589C4semidirect
23. #11718043C4semidirect
54. C13×#95C2×C4semidirect
59. C22⋊#1055C2×C4semidirect
123. #1434D13semidirect
276. #95C4×D13semidirect
345. C13#8216semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
#131145982
C2×#117180432
#131127152
C13×#14342
#821613