Finite Group Databasebeta

← #15833033

Subgroups — #15833033

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124836C211yesmaximal, characteristic
2#13123914C211yesmaximal, characteristic, complemented
3#13123860C211yesmaximal, characteristic, complemented
4#13113697C212yesmaximal, complemented
5#13113662C212yesmaximal, complemented
6#13113657C212yesmaximal, complemented
7#13113628C212yesmaximal, complemented
8#13113617C211yesmaximal, characteristic, complemented
9#13113254C211yesmaximal, characteristic, complemented
10#13113133C211yesmaximal, characteristic, complemented
11C13×#1490C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13C2211yescharacteristic
13#11719182C2211yescharacteristic
14C13×#432C2211yescharacteristic
15C4×C13×M16C2211yescharacteristic
16#11718878C412yes—
17C2×C22⋊#1055—22no—
18#11718676C412yes—
19C4×#6104C2212yes—
20C4×#6104C2212yes—
21D4×#1055—22no—
22D4×#1055C2212yes—
23D4×#1055C2212yes—
24#11718668C412yes—
25#11718628C412yes—
26#11718586C2211yescharacteristic
27#11718586C2211yescharacteristic
28#11718586C2211yescharacteristic
29#11718499C2212yescomplemented
30#11718495C2212yescomplemented
31#11718388—22no—
32#11718367—22no—
33C13×D4⋊C8C2212yes—
34C13×D4⋊C8C2212yes—
35#11718072C2212yescomplemented
36#11718071C2212yescomplemented
37#11718051C2212yescomplemented
38#11718051C2212yescomplemented
39#11718047C2211yescharacteristic, complemented
40#11718046C2211yescharacteristic, complemented
41#11718046C2211yescharacteristic, complemented
42C8×#1055C2211yescharacteristic, complemented
43C22×D4×C13C2×C411yescharacteristic
44C23×C4×C13—21no—
45C2×#6127—21no—
46C2×C13×M16—21no—
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C4×D4×C13C2×C412yes—
50C4×D4×C13C2312yes—
51C2×C13×C4⋊C4C2×C411yescharacteristic
52C2×C13×C22⋊C4—21no—
53C2×C42×C13C2311yescharacteristic
54C2×#6104C2×C412yes—
55C2×#6104C2×C412yes—
56#88184—21no—
57#88184C2×C412yes—
58C22×#1055—22no—
59C22×#1055—22no—
60C2×#6094—22no—
61C2×C8×D13—22no—
62#88129—21no—
63#88128C2×C411yescharacteristic
64C4×D52—21no—
65C4×D52C2312yes—
66#88123C2×C411yescharacteristic
67C13×C4⋊C8C2312yes—
68C13×C22⋊C8—21no—
69C13×#97—21no—
70C13×#97—21no—
71C4×C8×C13C2311yescharacteristic
72C4×C8×C13C2311yescharacteristic
73#88072C2×C412yes—
74#88072C2×C412yes—
75C22⋊#1055—21no—
76C22⋊#1055—22no—
77C22⋊#1055—22no—
78C22⋊#1055C2×C412yes—
79C22⋊#1055D412yes—
80#88060—22no—
81#88060—22no—
82#88049C2×C412yes—
83#88049C2×C412yes—
84#88047C2×C412yes—
85#88047C2×C412yes—
86C4⋊#1055C2×C412yes—
87C4⋊#1055D412yes—
88C4⋊#1055C2312yes—
89C4×#1055—21no—
90C4×#1055C2311yescharacteristic
91C4×#1055C2311yescharacteristic
92C4×#1055C2311yescharacteristic
93C4×#1055C2311yescharacteristic
94#17922—131nomaximal, Sylow
95C24×C13—21no—
96C2×D4×C13—24no—
97C2×D4×C13—21no—
98C2×D4×C13C22×C412yes—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—82no—
103C22×C4×C13C22×C411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C2×C22⋊D13—22no—
107#6127—82no—
108C2×D52—21no—
109C2×D52—21no—
110C2×D52C22×C412yes—
111C2×C4×D13—22no—
112C2×Dic26—21no—
113C13×M16—42no—
114C2×C8×C13—21no—
115C2×C8×C13—22no—
116C2×C8×C13—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4C22×C412yes—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C42×C13C22×C411yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13#4111yescharacteristic
124C42×C13C2411yescharacteristic
125#6104—24no—
126#6104—24no—
127#6103—22no—
128#6103—22no—
129C4⋊Dic13—21no—
130C4⋊Dic13C22×C412yes—
131C2×#1055—22no—
132C2×#1055—82no—
133C2×#1055—82no—
134C2×#1055C22×C412yes—
135C2×#1055C22×C412yes—
136C2×#1055C2×D412yes—
137C2×#1055C2×D412yes—
138#6094—82no—
139C8×D13—82no—
140#3100—131no—
141#2981—131no—
142#2972—131no—
143#1586—132no—
144#1581—132no—
145#1580—132no—
146C8×D8—132no—
147#1572—131no—
148#1490D1311yescharacteristic, complemented
149#1484—131no—
150#1453—131no—
151C23×C13—24no—
152C23×C13—22no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13C4×D411yescharacteristic
156C22×D13—22no—
157D4×C13—24no—
158D4×C13—22no—
159D4×C13#13114yes—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13—22no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—82no—
167C2×C4×C13—81no—
168C2×C4×C13C4×D411yescharacteristic
169C2×C4×C13C4×D411yescharacteristic
170C2×C4×C13C4×D411yescharacteristic
171C2×C4×C13C23×C411yescharacteristic
172C2×C4×C13C22×D411yescharacteristic
173C2×C4×C13C2×#4111yescharacteristic
174C22⋊D13—82no—
175C2×Dic13—22no—
176D52—22no—
177D52—22no—
178D52—81no—
179D52—81no—
180C4×D13—42no—
181C4×D13—42no—
182Dic26—81no—
183C8×C13—22no—
184C8×C13—41no—
185C8×C13—42no—
186#1055—22no—
187#1055—22no—
188#1055—22no—
189#1055—22no—
190#1055—42no—
191#532—131no—
192C2×C4×D4C2×D1311yescharacteristic
193#480—132no—
194#474—132no—
195#459—132no—
196#447—132no—
197C4×D8—132no—
198C4×D8—132no—
199#436—132no—
200#435—262no—
201C8×D4—132no—
202C8×D4—132no—
203C8×D4—132no—
204C8×D4—262no—
205#432C2×D1311yescharacteristic
206#431—131no—
207#431—131no—
208#431—131no—
209#408—262no—
210C2×C22⋊C8—262no—
211C4×M16C2×D1311yescharacteristic
212#335—132no—
213#334—132no—
214D4⋊C8—132no—
215D4⋊C8—132no—
216D4⋊C8C2×D1312yes—
217D4⋊C8C2×D1312yes—
218#322—131no—
219#322—131no—
220#322—131no—
221C82—131no—
222C22×C13—21no—
223C22×C13—24no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—42no—
227C22×C13—42no—
228C22×C13—84no—
229C22×C13C2×C4×D411yescharacteristic
230C2×D13—42no—
231C2×D13—42no—
232C2×D13—42no—
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—42no—
238C4×C13C2×#13112yes—
239C4×C13#57612yes—
240Dic13—42no—
241C2×#41—261no—
242C22×D4C4×D1311yescharacteristic
243C23×C4—21no—
244C2×D8—132no—
245C2×D8—132no—
246C2×M16—21no—
247C2×M16—262no—
248C22×C8—262no—
249C22×C8—262no—
250C22×C8—262no—
251C4⋊Q8—131no—
252#127—131no—
253#124—261no—
254#121—132no—
255#121—261no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—132no—
259C4×D4—261no—
260C4×D4C4×D1312yes—
261C4×D4C22×D1312yes—
262C2×C4⋊C4C4×D1311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C42C22×D1311yescharacteristic
265#107—132no—
266#107—132no—
267C4⋊C8—132no—
268C4⋊C8—132no—
269C4⋊C8—132no—
270C4⋊C8C22×D1312yes—
271#102—132no—
272#102—132no—
273#102—132no—
274#102—132no—
275C22⋊C8—21no—
276C22⋊C8—132no—
277C22⋊C8—132no—
278C22⋊C8—262no—
279C22⋊C8—262no—
280C22⋊C8—262no—
281C22⋊C8—262no—
282C22⋊C8—261no—
283#97—21no—
284#97—21no—
285C4×C8—131no—
286C4×C8—131no—
287C4×C8—131no—
288C4×C8—131no—
289C4×C8—261no—
290C4×C8C22×D1311yescharacteristic
291C4×C8C22×D1311yescharacteristic
292C2×C13—41no—
293C2×C13—44no—
294C2×C13#292911yescharacteristic
295C2×C13#294811yescharacteristic
296C2×C13#295611yescharacteristic
297D13—82no—
298C24—21no—
299#41—1042no—
300C2×Q8—261no—
301C2×D4—24no—
302C2×D4—21no—
303C2×D4—132no—
304C2×D4—262no—
305C2×D4—261no—
306C2×D4—261no—
307C2×D4C2×C4×D1312yes—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—82no—
312C22×C4—262no—
313C22×C4C2×C4×D1311yescharacteristic
314C22×C4D4×D1311yescharacteristic
315C22×C4#612911yescharacteristic
316D8—264no—
317D8—264no—
318M16—42no—
319M16—1042no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8—21no—
323C2×C8—132no—
324C2×C8—132no—
325C2×C8—132no—
326C2×C8—132no—
327C2×C8—262no—
328C2×C8—1042no—
329C2×C8—1042no—
330C2×C8—1042no—
331C4⋊C4—21no—
332C4⋊C4—132no—
333C4⋊C4—261no—
334C4⋊C4C2×C4×D1312yes—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—262no—
338C22⋊C4—262no—
339C42C2×C4×D1311yescharacteristic
340C42D4×D1311yescharacteristic
341C42#612911yescharacteristic
342C42C23×D1311yescharacteristic
343C13#1792211yescharacteristic, complemented, Sylow
344C23—24no—
345C23—22no—
346C23—81no—
347C23—81no—
348C23—262no—
349C23#8813511yescharacteristic
350Q8—1041no—
351D4—24no—
352D4—22no—
353D4—262no—
354D4—262no—
355D4—1041no—
356D4—1041no—
357D4—1042no—
358D4#8816114yes—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—262no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4#8813511yescharacteristic
371C2×C4#8813511yescharacteristic
372C2×C4#8813511yescharacteristic
373C2×C4C22×C4×D1311yescharacteristic
374C2×C4C2×D4×D1311yescharacteristic
375C2×C4C2×#612911yescharacteristic
376C8—22no—
377C8—41no—
378C8—42no—
379C8—262no—
380C8—262no—
381C8—262no—
382C8—262no—
383C8—522no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—42no—
389C22—42no—
390C22—84no—
391C22—522no—
392C22—522no—
393C22—522no—
394C22C2×#8813511yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—522no—
401C4C2×#8816112yes—
402C4#1171947912yes—
403C2—41no—
404C2—44no—
405C2—1042no—
406C2#1312352611yescharacteristic
407C2#1312368411yescharacteristic
408C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1490C2
socleC22×C13C2×C4×D4
prime radical#13124836C2
cosocleC42×C13C24
hypercenter#1490D13
hypocenterC13#17922
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #13123914C2semidirect
3. #13123860C2semidirect
4. #13113697C2semidirect
5. #13113662C2semidirect
6. #13113657C2semidirect
7. #13113628C2semidirect
8. #13113617C2semidirect
9. #13113254C2semidirect
10. #13113133C2semidirect
11. C13×#1490C2semidirect
29. #11718499C22semidirect
30. #11718495C22semidirect
35. #11718072C22semidirect
36. #11718071C22semidirect
37. #11718051C22semidirect
38. #11718051C22semidirect
39. #11718047C22semidirect
40. #11718046C22semidirect
41. #11718046C22semidirect
42. C8×#1055C22semidirect
148. #1490D13semidirect
343. C13#17922semidirect

Maximal subgroups

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

subgroupindex
#131248362
#131239142
#131238602
#131136972
#131136622
#131136572
#131136282
#131136172
#131132542
#131131332
C13×#14902
#1792213