Finite Group Databasebeta

← #15757104

Subgroups — #15757104

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117736C211yesmaximal, characteristic
2#13115597C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic
4C2×#11718051C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1844C211yesmaximal, characteristic, complemented
8C2×#88147—21no—
9C2×C4⋊C4×D13—21no—
10C2×C4×D52C2211yescharacteristic
11C2×C13×#106—22no—
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C13×#384C2211yescharacteristic
15#11718650—22no—
16#11718648—21no—
17#11718634—21no—
18C2×#88049—21no—
19C2×#88048—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718121—21no—
24#11718121—21no—
25#11718051C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C4×D13—22no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D412yes—
36C2×C42×C13C2311yescharacteristic
37C2×#6103—21no—
38C2×#6103—22no—
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—22no—
43C2×C4×Dic13—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46#88147—42no—
47#88147—42no—
48C4⋊C4×D13—42no—
49C4⋊C4×D13—42no—
50C4×D52—21no—
51C4×D52—21no—
52C4×D52C2×C412yes—
53C4×D52Q812yes—
54C13×#106—44no—
55C4×C8×C13—21no—
56C4×C8×C13C2×C412yescomplemented
57#88071—22no—
58#88071—21no—
59#88049—42no—
60#88048—42no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C412yescomplemented
65#8886—131nomaximal, Sylow
66C23×D13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—41no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C4⋊C412yes—
79C2×D52SD1612yes—
80C2×D52SD1612yes—
81C2×C4×D13—22no—
82C2×C4×D13—22no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—44no—
88C2×C4×D13—44no—
89C2×C4×D13—82no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C42×C13C22×C411yescharacteristic
104C42×C13C2×Q811yescharacteristic
105C42×C13#4111yescharacteristic
106C42×C13#4111yescharacteristic
107#6103—22no—
108#6103—22no—
109#6103—44no—
110C4⋊Dic13—21no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4⋊Dic13C4⋊C412yes—
115C4⋊Dic13SD1612yes—
116#6101—44no—
117C4×Dic13—41no—
118C4×Dic13—41no—
119C2×#1055—22no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125D4×C4⋊C4—131no—
126#1948—131no—
127#1844D1311yescharacteristic, complemented
128#1802—131no—
129C2×D4⋊C8—131no—
130#1296—131no—
131#1279—131no—
132C23×C13#12011yescharacteristic
133C22×D13—22no—
134C22×D13—22no—
135C22×D13—22no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13C2×C4⋊C411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×C4×C13C22⋊Q811yescharacteristic
153C2×C4×C13#12311yescharacteristic
154C2×C4×C13C2×SD1611yescharacteristic
155C2×C4×C13C2×SD1611yescharacteristic
156C2×C4×C13C2×SD1611yescharacteristic
157C2×C4×C13#13511yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C13#13711yescharacteristic
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171D52—22no—
172D52—22no—
173D52—22no—
174D52#10614yescomplemented
175C4×D13—42no—
176C4×D13—42no—
177C4×D13—42no—
178C4×D13—42no—
179C4×D13—88no—
180C8×C13—24no—
181#1055—42no—
182#1055—81no—
183C2×C4×D4—131no—
184C2×C4×D4—261no—
185C22×C4⋊C4—261no—
186C2×#106—22no—
187C2×#106—261no—
188C2×C4⋊C8—131no—
189C2×C4⋊C8—131no—
190C2×#102—261no—
191C2×C4×C8C2×D1311yescharacteristic
192#389—261no—
193#385—262no—
194#384C2×D1311yescharacteristic
195#384C2×D1311yescharacteristic
196#380—261no—
197C4×C4⋊C4—131no—
198#340—261no—
199#340—261no—
200D4⋊C8—134no—
201C22×C13#38511yescharacteristic
202C22×C13#44811yescharacteristic
203C22×C13#44911yescharacteristic
204C22×C13#45011yescharacteristic
205C22×C13#45011yescharacteristic
206C22×C13#45311yescharacteristic
207C22×C13#45611yescharacteristic
208C2×D13—24no—
209C2×D13—42no—
210C2×D13—42no—
211C2×D13—42no—
212C2×D13—42no—
213C2×D13—42no—
214C2×D13—42no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—82no—
218C4×C13—161no—
219C4×C13C2×#10611yescharacteristic
220C4×C13#42811yescharacteristic
221C4×C13C4×SD1611yescharacteristic
222C4×C13#44211yescharacteristic
223C4×C13#47611yescharacteristic
224C4×C13#47811yescharacteristic
225C4×C13#48111yescharacteristic
226C4×C13#48311yescharacteristic
227Dic13—42no—
228Dic13—42no—
229Dic13—81no—
230C22×D4—131no—
231C23×C4—262no—
232C23×C4—261no—
233C22×C8—21no—
234C22×C8—261no—
235C22×C8—261no—
236C4×D4—132no—
237C4×D4—132no—
238C4×D4—261no—
239C4×D4—261no—
240C4×D4—522no—
241C4×D4—522no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—131no—
248C2×C4⋊C4—131no—
249C2×C4⋊C4—131no—
250C2×C4⋊C4—262no—
251C2×C4⋊C4—522no—
252C2×C4⋊C4—522no—
253C2×C4⋊C4C22⋊D1312yes—
254C2×C22⋊C4—261no—
255C2×C22⋊C4—262no—
256C2×C42—261no—
257C2×C42C22×D1311yescharacteristic
258#106—44no—
259#106—522no—
260C4⋊C8—132no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8—261no—
264#102—522no—
265C4×C8—21no—
266C4×C8C4×D1312yescomplemented
267#95—262no—
268#95—261no—
269C2×C13#162211yescharacteristic
270C2×C13#162911yescharacteristic
271C2×C13#165111yescharacteristic
272C2×C13#165411yescharacteristic
273C2×C13#185311yescharacteristic
274C2×C13#185911yescharacteristic
275C2×C13#186411yescharacteristic
276D13—44no—
277C24—261no—
278C2×D4—132no—
279C2×D4—132no—
280C2×D4—132no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—261no—
291C22×C4—524no—
292C22×C4—524no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4—1042no—
298C22×C4D4×D1311yescharacteristic
299C22×C4D4×D1311yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—262no—
305C2×C8—521no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—521no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—132no—
321C4⋊C4—132no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—261no—
326C4⋊C4—524no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—524no—
330C42—521no—
331C42—521no—
332C42C2×C4×D1311yescharacteristic
333C42#612711yescharacteristic
334C42Q8×D1311yescharacteristic
335C42#613111yescharacteristic
336C13#888611yescharacteristic, complemented, Sylow
337C23—262no—
338C23—262no—
339C23—262no—
340C23—521no—
341C23—521no—
342C23—521no—
343C23—521no—
344C23#8819111yescharacteristic
345D4—134no—
346D4—262no—
347D4—262no—
348D4—262no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—1048no—
371C2×C4C4⋊C4×D1311yescharacteristic
372C2×C4#8814711yescharacteristic
373C2×C4#8814811yescharacteristic
374C2×C4#8815011yescharacteristic
375C2×C4SD16×D1311yescharacteristic
376C2×C4SD16×D1311yescharacteristic
377C2×C4SD16×D1311yescharacteristic
378C2×C4#8816811yescharacteristic
379C2×C4#8816811yescharacteristic
380C2×C4#8816811yescharacteristic
381C2×C4#8816911yescharacteristic
382C2×C4#8817011yescharacteristic
383C2×C4C4×C22⋊D1311yescharacteristic
384C2×C4#8820011yescharacteristic
385C8—24no—
386C8—522no—
387C8—1041no—
388C22—264no—
389C22—522no—
390C22—522no—
391C22—522no—
392C22—522no—
393C22—522no—
394C22—522no—
395C22#1171865011yescharacteristic
396C22#1171873811yescharacteristic
397C22#1171875611yescharacteristic
398C22#1171883011yescharacteristic
399C22#1171883011yescharacteristic
400C22#1171883111yescharacteristic
401C22#1171883311yescharacteristic
402C4—21no—
403C4—21no—
404C4—82no—
405C4—161no—
406C4—522no—
407C4—522no—
408C4—1041no—
409C4#1171851311yescharacteristic
410C4D13×#10611yescharacteristic
411C4#1171852211yescharacteristic
412C4#1171852311yescharacteristic
413C4#1171852411yescharacteristic
414C4#1171853011yescharacteristic
415C4#1171853111yescharacteristic
416C4#1171853211yescharacteristic
417C2—524no—
418C2#1311390511yescharacteristic
419C2#1311395011yescharacteristic
420C2#1311409611yescharacteristic
421C2#1311411711yescharacteristic
422C2#1311502711yescharacteristic
423C2#1311506111yescharacteristic
424C2#1311509411yescharacteristic
subgroupG/H
centerC23#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1844C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1844D13
hypocenterC13#8886
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
2. #13115597C2semidirect
5. #13112719C2semidirect
6. #13112676C2semidirect
7. C13×#1844C2semidirect
25. #11718051C4semidirect
56. C4×C8×C13C2×C4semidirect
64. C4⋊#1055C2×C4semidirect
127. #1844D13semidirect
174. D52#106semidirect
266. C4×C8C4×D13semidirect
336. C13#8886semidirect

Maximal subgroups

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

subgroupindex
#131177362
#131155972
#131148332
C2×#117180512
#131127192
#131126762
C13×#18442
#888613