Finite Group Databasebeta

← #15765930

Subgroups — #15765930

Order 3328.

588 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#13119862C211yesmaximal, characteristic, complemented
2#13115763C211yesmaximal, characteristic
3#13115762C211yesmaximal, characteristic
4#13115642C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88142—21no—
9C2×#88128C2211yescharacteristic
10C2×#88123—21no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88061—21no—
15C2×#88061—21no—
16C2×#88061—22no—
17#11718646—21no—
18C2×#88049—21no—
19C2×#88049—21no—
20#11718596C2211yescharacteristic
21C4×C4⋊Dic13C2211yescharacteristic
22#11718589—21no—
23C2×C4⋊#1055C2211yescharacteristic
24#11718317—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52—21no—
28C22×Dic26—22no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D412yes—
41C2×#6101—22no—
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44#88142—42no—
45#88142—42no—
46#88128—21no—
47#88128—21no—
48#88128—21no—
49#88128Q812yescomplemented
50#88123—42no—
51#88123—42no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56C13×#95—21no—
57#88071—22no—
58#88071—21no—
59#88061—44no—
60#88061—42no—
61#88061—42no—
62#88049—42no—
63#88049—42no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66#10348—131nomaximal, Sylow
67C23×D13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—22no—
76C2×D52—22no—
77C2×D52—22no—
78C2×D52—22no—
79C2×D52—42no—
80C2×D52—42no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—41no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52—41no—
92C2×Dic26—44no—
93C2×Dic26—44no—
94C2×Dic26—82no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4D812yes—
104C13×C4⋊C4SD1612yes—
105C42×C13—41no—
106C42×C13—41no—
107C42×C13C2×Q811yescharacteristic
108C42×C13#4111yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13#4111yescharacteristic
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13—44no—
114C4⋊Dic13—41no—
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117C4⋊Dic13—41no—
118C4⋊Dic13—42no—
119C4⋊Dic13D812yes—
120C4⋊Dic13SD1612yes—
121#6101—44no—
122C4×Dic13—41no—
123C4×Dic13—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127#2551—131no—
128#1982—131no—
129#1982—131no—
130#1957—131no—
131#1296—131no—
132#1279—131no—
133#1279D1311yescharacteristic, complemented
134C23×C13#12011yescharacteristic
135C22×D13—42no—
136C22×D13—81no—
137C22×D13—81no—
138C22×D13—81no—
139C22×D13—81no—
140C22×D13—81no—
141C22×D13—81no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13C22⋊Q811yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×C4×C13C22⋊Q811yescharacteristic
153C2×C4×C13#12411yescharacteristic
154C2×C4×C13#12411yescharacteristic
155C2×C4×C13#12411yescharacteristic
156C2×C4×C13C2×D811yescharacteristic
157C2×C4×C13C2×D811yescharacteristic
158C2×C4×C13C2×SD1611yescharacteristic
159C2×C4×C13C2×SD1611yescharacteristic
160C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13#13711yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×Dic13—22no—
165C2×Dic13—22no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173D52—44no—
174D52—42no—
175D52—42no—
176D52—42no—
177D52—42no—
178D52—82no—
179D52—81no—
180D52—81no—
181D52—81no—
182D52—81no—
183Dic26—88no—
184C8×C13—42no—
185C8×C13—81no—
186#1055—81no—
187C2×C4⋊Q8—261no—
188C2×C4⋊Q8—261no—
189C2×#127—131no—
190C2×C4⋊C8—131no—
191C2×C4⋊C8C2×D1311yescharacteristic
192C2×#102—262no—
193C2×#102—261no—
194C2×#102—261no—
195C2×#102—261no—
196C2×#102—261no—
197C2×C4×C8C2×D1311yescharacteristic
198#395—262no—
199#389—261no—
200#389—261no—
201#384—131no—
202C4×C4⋊C4—131no—
203C4×C4⋊C4C2×D1311yescharacteristic
204C22×C13#39311yescharacteristic
205C22×C13#44711yescharacteristic
206C22×C13#44711yescharacteristic
207C22×C13#44811yescharacteristic
208C22×C13#44811yescharacteristic
209C22×C13#45311yescharacteristic
210C22×C13#45411yescharacteristic
211C2×D13—82no—
212C2×D13—82no—
213C2×D13—82no—
214C2×D13—161no—
215C2×D13—161no—
216C2×D13—161no—
217C2×D13—161no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—42no—
221C4×C13—42no—
222C4×C13#47411yescharacteristic
223C4×C13#47411yescharacteristic
224C4×C13#47611yescharacteristic
225C4×C13#47611yescharacteristic
226C4×C13#48611yescharacteristic
227C4×C13#48611yescharacteristic
228C4×C13#48911yescharacteristic
229C4×C13#48911yescharacteristic
230Dic13—42no—
231Dic13—42no—
232Dic13—82no—
233C22×Q8—262no—
234C22×D4—261no—
235C22×D4—261no—
236C22×D4—261no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—261no—
240C4⋊Q8—522no—
241C4⋊Q8—522no—
242C4⋊Q8—522no—
243C4⋊Q8—522no—
244#127—132no—
245#127—261no—
246#127—261no—
247#127—261no—
248C2×C4⋊C4—131no—
249C2×C4⋊C4—131no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—262no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4—261no—
255C2×C4⋊C4D5211yescharacteristic
256C2×C4⋊C4D5211yescharacteristic
257C2×C42—21no—
258C2×C42—261no—
259C2×C42C22×D1311yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—261no—
263C4⋊C8—261no—
264#102—522no—
265#102—522no—
266#102—524no—
267#102—522no—
268#102—522no—
269C4×C8—21no—
270C4×C8—21no—
271#95—21no—
272#95—262no—
273#95—261no—
274C2×C13#161911yescharacteristic
275C2×C13#162311yescharacteristic
276C2×C13#162711yescharacteristic
277C2×C13#162711yescharacteristic
278C2×C13#202311yescharacteristic
279C2×C13#202311yescharacteristic
280C2×C13#202711yescharacteristic
281D13—162no—
282C24—521no—
283C2×Q8—524no—
284C2×Q8—524no—
285C2×Q8—1042no—
286C2×D4—262no—
287C2×D4—262no—
288C2×D4—262no—
289C2×D4—522no—
290C2×D4—522no—
291C2×D4—521no—
292C2×D4—521no—
293C2×D4—521no—
294C2×D4—521no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C2×D4—521no—
299C2×D4—521no—
300C2×D4—521no—
301C2×D4—521no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—261no—
305C22×C4—261no—
306C22×C4—262no—
307C22×C4C2×D5211yescharacteristic
308C22×C4D4×D1311yescharacteristic
309C22×C4D4×D1311yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—521no—
317C2×C8—521no—
318C2×C8—521no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—132no—
322C4⋊C4—132no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—522no—
326C4⋊C4—524no—
327C4⋊C4—524no—
328C4⋊C4—521no—
329C4⋊C4—521no—
330C4⋊C4—521no—
331C4⋊C4—521no—
332C4⋊C4#609512yes—
333C4⋊C4D10412yes—
334C42—41no—
335C42—41no—
336C42—521no—
337C42—521no—
338C42#612711yescharacteristic
339C42#612711yescharacteristic
340C42#612911yescharacteristic
341C42Q8×D1311yescharacteristic
342C13#1034811yescharacteristic, complemented, Sylow
343C23—522no—
344C23—1041no—
345C23—1041no—
346C23—1041no—
347C23—1041no—
348C23—1041no—
349C23—1041no—
350C23#8813611yescharacteristic
351Q8—1048no—
352D4—524no—
353D4—522no—
354D4—522no—
355D4—522no—
356D4—522no—
357D4—1042no—
358D4—1041no—
359D4—1041no—
360D4—1041no—
361D4—1041no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—262no—
371C2×C4—262no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—522no—
377C2×C4—522no—
378C2×C4—522no—
379C2×C4#8812911yescharacteristic
380C2×C4#8813911yescharacteristic
381C2×C4#8813911yescharacteristic
382C2×C4#8815011yescharacteristic
383C2×C4#8815011yescharacteristic
384C2×C4#8815111yescharacteristic
385C2×C4C2×#609511yescharacteristic
386C2×C4C2×D10411yescharacteristic
387C2×C4#8816211yescharacteristic
388C2×C4#8816311yescharacteristic
389C2×C4D8×D1311yescharacteristic
390C2×C4SD16×D1311yescharacteristic
391C2×C4#8816811yescharacteristic
392C2×C4#8817211yescharacteristic
393C8—42no—
394C8—81no—
395C8—1041no—
396C22—1042no—
397C22—1042no—
398C22—1042no—
399C22—2081no—
400C22—2081no—
401C22—2081no—
402C22—2081no—
403C22#1171833411yescharacteristic
404C22#1171839311yescharacteristic
405C22#1171839911yescharacteristic
406C22#1171843411yescharacteristic
407C22#1171846711yescharacteristic
408C22#1171848311yescharacteristic
409C22#1171848811yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—42no—
414C4—522no—
415C4—522no—
416C4—1042no—
417C4#1171835511yescharacteristic
418C4#1171837511yescharacteristic
419C4#1171842111yescharacteristic
420C4#1171845611yescharacteristic
421C4#1171850311yescharacteristic
422C4#1171850711yescharacteristic
423C4#1171853111yescharacteristic
424C4#1171855111yescharacteristic
425C2—2082no—
426C2#1311389211yescharacteristic
427C2#1311391611yescharacteristic
428C2#1311394111yescharacteristic
429C2#1311394211yescharacteristic
430C2#1311597111yescharacteristic
431C2#1311597311yescharacteristic
432C2#1311599111yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#1279D13
hypocenterC13#10348
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #13119862C2semidirect
5. #13112720C2semidirect
6. #13112676C2semidirect
7. C13×#1279C2semidirect
49. #88128Q8semidirect
133. #1279D13semidirect
342. C13#10348semidirect

Maximal subgroups

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

subgroupindex
#131198622
#131157632
#131157622
#131156422
#131127202
#131126762
C13×#12792
#1034813