Finite Group Databasebeta

← #15757341

Subgroups — #15757341

Order 3328.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117900C211yesmaximal, characteristic
2#13115642C211yesmaximal, characteristic
3#13115600C211yesmaximal, characteristic, complemented
4#13115594C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88147—21no—
9C2×#88128C2211yescharacteristic
10C2×C4×D52—21no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88061—22no—
15C2×#88057—21no—
16#11718649—21no—
17C2×#88047—21no—
18#11718600—21no—
19#11718596C2211yescharacteristic
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22#11718326—22no—
23#11718143—21no—
24#11718121—21no—
25#11718077C414yescomplemented
26C22×D52—21no—
27C22×D52—21no—
28C22×D52D412yes—
29C22×C4×D13—22no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×C4×Dic13—21no—
45C22×#1055—21no—
46#88147—42no—
47#88147—42no—
48#88128—21no—
49#88128—21no—
50#88128C2×C412yes—
51#88128Q812yes—
52C4×D52—42no—
53C4×D52—42no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8C2×C412yescomplemented
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58C13×#95—21no—
59#88071—21no—
60#88061—44no—
61#88057—42no—
62#88047—42no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C412yescomplemented
65#8921—131nomaximal, Sylow
66C23×D13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—41no—
75C2×D52—22no—
76C2×D52—22no—
77C2×D52—22no—
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—42no—
89C2×D52—42no—
90C2×D52C4⋊C414yes—
91C2×C4×D13—44no—
92C2×C4×D13—44no—
93C2×C4×D13—82no—
94C2×C8×C13—22no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4SD1612yes—
104C42×C13—41no—
105C42×C13—41no—
106C42×C13C22×C411yescharacteristic
107C42×C13C2×Q811yescharacteristic
108C42×C13#4111yescharacteristic
109C42×C13#4111yescharacteristic
110#6103—44no—
111#6103—44no—
112#6103—82no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—42no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13D812yes—
122C4×Dic13—41no—
123C4×Dic13—41no—
124C2×#1055—22no—
125C2×#1055—41no—
126C2×#1055—41no—
127#2366—131no—
128#1957—131no—
129#1948—131no—
130#1947—131no—
131C2×#331—131no—
132#1279—131no—
133#1279D1311yescharacteristic, complemented
134C23×C13#12011yescharacteristic
135C22×D13—24no—
136C22×D13—42no—
137C22×D13—42no—
138C22×D13—42no—
139C22×D13—42no—
140C22×D13—42no—
141C22×D13—42no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13C2×C4⋊C411yescharacteristic
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13C4×D411yescharacteristic
153C2×C4×C13C22⋊Q811yescharacteristic
154C2×C4×C13C22⋊Q811yescharacteristic
155C2×C4×C13#12311yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×SD1611yescharacteristic
158C2×C4×C13#13511yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×Dic13—22no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—81no—
171C2×Dic13—81no—
172C2×Dic13—81no—
173D52—44no—
174D52—42no—
175D52—42no—
176D52—42no—
177D52—42no—
178D52—42no—
179D52—42no—
180D52—42no—
181D52—42no—
182D52—82no—
183C4×D13—88no—
184C8×C13—42no—
185C8×C13—42no—
186#1055—42no—
187C2×#127—131no—
188C2×C4×D4—261no—
189C2×C4×D4—261no—
190C2×#107—261no—
191C2×#106—261no—
192C2×C4⋊C8—131no—
193C2×C4⋊C8C2×D1311yescharacteristic
194C2×#102—262no—
195C2×C4×C8C2×D1311yescharacteristic
196#390—261no—
197#390—261no—
198#386—262no—
199#384—131no—
200C4×C4⋊C4—131no—
201C4×C4⋊C4C2×D1311yescharacteristic
202#340—261no—
203#340—261no—
204#331—134no—
205C22×C13#38511yescharacteristic
206C22×C13#44711yescharacteristic
207C22×C13#44911yescharacteristic
208C22×C13#45011yescharacteristic
209C22×C13#45211yescharacteristic
210C22×C13#45311yescharacteristic
211C22×C13#45511yescharacteristic
212C2×D13—44no—
213C2×D13—44no—
214C2×D13—44no—
215C2×D13—82no—
216C2×D13—82no—
217C2×D13—82no—
218C2×D13—82no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—42no—
222C4×C13—81no—
223C4×C13C4×D811yescharacteristic
224C4×C13C4×SD1611yescharacteristic
225C4×C13#44011yescharacteristic
226C4×C13#44211yescharacteristic
227C4×C13#47411yescharacteristic
228C4×C13#47611yescharacteristic
229C4×C13#47811yescharacteristic
230C4×C13#47811yescharacteristic
231Dic13—42no—
232Dic13—81no—
233Dic13—161no—
234C22×D4—132no—
235C22×D4—261no—
236C22×D4—261no—
237C23×C4—262no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—261no—
241#127—132no—
242#127—132no—
243#127—261no—
244#127—261no—
245C4×D4—522no—
246C4×D4—522no—
247C4×D4—522no—
248C4×D4—522no—
249C2×C4⋊C4—131no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4—261no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4D5211yescharacteristic
255C2×C4⋊C4D5211yescharacteristic
256C2×C22⋊C4—262no—
257C2×C22⋊C4—262no—
258C2×C22⋊C4—262no—
259C2×C42—21no—
260C2×C42—261no—
261C2×C42C22×D1311yescharacteristic
262#107—522no—
263#106—522no—
264C4⋊C8—21no—
265C4⋊C8—132no—
266C4⋊C8—261no—
267C4⋊C8C4×D1312yescomplemented
268#102—524no—
269C4×C8—21no—
270C4×C8—21no—
271#95—21no—
272#95—261no—
273C2×C13#162111yescharacteristic
274C2×C13#163111yescharacteristic
275C2×C13#163911yescharacteristic
276C2×C13#164011yescharacteristic
277C2×C13#185611yescharacteristic
278C2×C13#186211yescharacteristic
279C2×C13#186411yescharacteristic
280D13—84no—
281C24—262no—
282C2×D4—134no—
283C2×D4—262no—
284C2×D4—262no—
285C2×D4—262no—
286C2×D4—262no—
287C2×D4—262no—
288C2×D4—522no—
289C2×D4—522no—
290C2×D4—521no—
291C2×D4—521no—
292C2×D4—521no—
293C2×D4—521no—
294C2×D4—521no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4—524no—
303C22×C4—524no—
304C22×C4—521no—
305C22×C4—1042no—
306C22×C4C2×D5211yescharacteristic
307C22×C4D4×D1311yescharacteristic
308C22×C4D4×D1311yescharacteristic
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—262no—
316C2×C8—521no—
317C2×C8—521no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—132no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—522no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C4⋊C4—521no—
329C4⋊C4—521no—
330C4⋊C4#609512yes—
331C22⋊C4—524no—
332C22⋊C4—524no—
333C22⋊C4—1042no—
334C42—41no—
335C42—41no—
336C42—521no—
337C42—521no—
338C42C2×C4×D1311yescharacteristic
339C42#612711yescharacteristic
340C42#612911yescharacteristic
341C42Q8×D1311yescharacteristic
342C13#892111yescharacteristic, complemented, Sylow
343C23—264no—
344C23—522no—
345C23—522no—
346C23—522no—
347C23—522no—
348C23—522no—
349C23—522no—
350C23#8813611yescharacteristic
351D4—524no—
352D4—522no—
353D4—522no—
354D4—522no—
355D4—522no—
356D4—522no—
357D4—522no—
358D4—522no—
359D4—522no—
360D4—1042no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—262no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—1048no—
376C2×C4—1041no—
377C2×C4—1041no—
378C2×C4—1041no—
379C2×C4C4×D5211yescharacteristic
380C2×C4#8813511yescharacteristic
381C2×C4#8813711yescharacteristic
382C2×C4C4⋊C4×D1311yescharacteristic
383C2×C4#8815011yescharacteristic
384C2×C4#8815111yescharacteristic
385C2×C4C2×#609511yescharacteristic
386C2×C4#8815811yescharacteristic
387C2×C4#8816211yescharacteristic
388C2×C4#8816211yescharacteristic
389C2×C4D8×D1311yescharacteristic
390C2×C4#8816811yescharacteristic
391C2×C4#8817011yescharacteristic
392C2×C4#8817211yescharacteristic
393C8—42no—
394C8—42no—
395C8—522no—
396C22—524no—
397C22—524no—
398C22—524no—
399C22—1042no—
400C22—1042no—
401C22—1042no—
402C22—1042no—
403C22#1171832911yescharacteristic
404C22#1171839211yescharacteristic
405C22#1171839511yescharacteristic
406C22#1171843411yescharacteristic
407C22#1171847111yescharacteristic
408C22#1171848311yescharacteristic
409C22#1171848611yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—522no—
415C4—1041no—
416C4—2081no—
417C4C4×#609511yescharacteristic
418C4#1171837211yescharacteristic
419C4#1171841711yescharacteristic
420C4#1171847811yescharacteristic
421C4#1171850311yescharacteristic
422C4#1171850811yescharacteristic
423C4#1171853211yescharacteristic
424C4#1171855111yescharacteristic
425C2—1044no—
426C2#1311390411yescharacteristic
427C2#1311396511yescharacteristic
428C2#1311401811yescharacteristic
429C2#1311402411yescharacteristic
430C2#1311504711yescharacteristic
431C2#1311508411yescharacteristic
432C2#1311510011yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8921
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #13115600C2semidirect
4. #13115594C2semidirect
6. #13112676C2semidirect
7. C13×#1279C2semidirect
25. #11718077C4semidirect
55. C13×C4⋊C8C2×C4semidirect
64. C4⋊#1055C2×C4semidirect
133. #1279D13semidirect
267. C4⋊C8C4×D13semidirect
342. C13#8921semidirect

Maximal subgroups

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

subgroupindex
#131179002
#131156422
#131156002
#131155942
C2×#117180772
#131126762
C13×#12792
#892113