Finite Group Databasebeta

← #15765960

Subgroups — #15765960

Order 3328.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115763C211yesmaximal, characteristic
2#13115763C211yesmaximal, characteristic
3#13115641C211yesmaximal, characteristic
4#13112719C211yesmaximal, characteristic, complemented
5#13112677C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#2552C211yesmaximal, characteristic, complemented
8C2×C13×#125—21no—
9C2×#88128C2211yescharacteristic
10C13×#398—22no—
11C13×#389—21no—
12C13×#389—21no—
13C13×#384—21no—
14C13×#384C2211yescharacteristic
15C4×C13×C4⋊C4C2211yescharacteristic
16C4×C13×C4⋊C4C2211yescharacteristic
17C2×#88049—21no—
18C2×#88049—21no—
19C2×#88049—21no—
20C2×#88049—21no—
21C2×#88049—22no—
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25C22×D52—21no—
26C22×D52—21no—
27C22×D52—21no—
28C13×#125—42no—
29C13×#125—42no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D412yes—
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2311yescharacteristic
43C22×#1055—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46#88128—21no—
47#88128—21no—
48#88128—21no—
49#88128Q812yes—
50C13×#95—22no—
51C13×#95—21no—
52C13×#95—21no—
53#88049—44no—
54#88049—42no—
55#88049—42no—
56#88049—42no—
57#88049—42no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4×#1055—21no—
63C4×#1055—21no—
64#10354—131nomaximal, Sylow
65C23×D13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C2×D52—22no—
75C2×D52—22no—
76C2×D52—22no—
77C2×D52—42no—
78C2×D52—42no—
79C2×D52—41no—
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—41no—
89C2×D52—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—44no—
98C13×C4⋊C4—44no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—82no—
104C13×C4⋊C4D812yes—
105C13×C4⋊C4SD1612yes—
106C42×C13—41no—
107C42×C13—41no—
108C42×C13—41no—
109C42×C13—41no—
110C42×C13C2×Q811yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13#4111yescharacteristic
113C42×C13#4111yescharacteristic
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123#2552D1311yescharacteristic, complemented
124#1982—131no—
125#1982—131no—
126#1957—131no—
127#1296—131no—
128#1279—131no—
129#1279—131no—
130C23×C13#12011yescharacteristic
131C22×D13—42no—
132C22×D13—81no—
133C22×D13—81no—
134C22×D13—81no—
135C22×D13—81no—
136C22×D13—81no—
137C22×D13—81no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13C22⋊Q811yescharacteristic
156C2×C4×C13C22⋊Q811yescharacteristic
157C2×C4×C13C22⋊Q811yescharacteristic
158C2×C4×C13#12411yescharacteristic
159C2×C4×C13#12411yescharacteristic
160C2×C4×C13#12411yescharacteristic
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C2×SD1611yescharacteristic
163C2×C4×C13#13511yescharacteristic
164C2×C4×C13#13511yescharacteristic
165C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C13#13711yescharacteristic
169D52—44no—
170D52—42no—
171D52—42no—
172D52—42no—
173D52—42no—
174D52—82no—
175D52—81no—
176D52—81no—
177D52—81no—
178D52—81no—
179#1055—42no—
180#1055—81no—
181#1055—81no—
182C2×#127—131no—
183C2×#125—21no—
184C2×C4⋊C8—131no—
185C2×C4⋊C8—131no—
186C2×#102—262no—
187C2×#102—261no—
188C2×#102—261no—
189C2×#102—261no—
190C2×#102—261no—
191C2×C4×C8—131no—
192#398—22no—
193#389—21no—
194#389—21no—
195#384—21no—
196#384C2×D1311yescharacteristic
197C4×C4⋊C4C2×D1311yescharacteristic
198C4×C4⋊C4C2×D1311yescharacteristic
199C22×C13#39311yescharacteristic
200C22×C13#44711yescharacteristic
201C22×C13#44811yescharacteristic
202C22×C13#44911yescharacteristic
203C22×C13#44911yescharacteristic
204C22×C13#45311yescharacteristic
205C22×C13#45411yescharacteristic
206C2×D13—82no—
207C2×D13—82no—
208C2×D13—82no—
209C2×D13—161no—
210C2×D13—161no—
211C2×D13—161no—
212C2×D13—161no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—42no—
216C4×C13—42no—
217C4×C13—81no—
218C4×C13—82no—
219C4×C13—81no—
220C4×C13#47411yescharacteristic
221C4×C13#47611yescharacteristic
222C4×C13#47811yescharacteristic
223C4×C13#47811yescharacteristic
224C4×C13#48611yescharacteristic
225C4×C13#48811yescharacteristic
226C4×C13#48911yescharacteristic
227C4×C13#49011yescharacteristic
228C22×D4—261no—
229C22×D4—261no—
230C22×D4—261no—
231C22×C8—261no—
232C22×C8—261no—
233C22×C8—261no—
234#127—132no—
235#127—261no—
236#127—261no—
237#127—261no—
238#125—42no—
239#125—42no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4C22⋊D1311yescharacteristic
246C2×C4⋊C4C22⋊D1311yescharacteristic
247C2×C4⋊C4C22⋊D1311yescharacteristic
248C2×C4⋊C4C22⋊D1311yescharacteristic
249C2×C4⋊C4C22⋊D1312yes—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C22×D1311yescharacteristic
253C4⋊C8—261no—
254C4⋊C8—261no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257#102—522no—
258#102—522no—
259#102—524no—
260#102—522no—
261#102—522no—
262C4×C8—261no—
263C4×C8—261no—
264#95—22no—
265#95—21no—
266#95—21no—
267C2×C13#162111yescharacteristic
268C2×C13#162211yescharacteristic
269C2×C13#162511yescharacteristic
270C2×C13#162611yescharacteristic
271C2×C13#202311yescharacteristic
272C2×C13#202511yescharacteristic
273C2×C13#202711yescharacteristic
274D13—162no—
275C24—521no—
276C2×D4—262no—
277C2×D4—262no—
278C2×D4—262no—
279C2×D4—522no—
280C2×D4—522no—
281C2×D4—521no—
282C2×D4—521no—
283C2×D4—521no—
284C2×D4—521no—
285C2×D4—521no—
286C2×D4—521no—
287C2×D4—521no—
288C2×D4—521no—
289C2×D4—521no—
290C2×D4—521no—
291C2×D4—521no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4C2×C22⋊D1311yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299C22×C4C2×C22⋊D1311yescharacteristic
300C2×C8—262no—
301C2×C8—521no—
302C2×C8—521no—
303C2×C8—521no—
304C2×C8—521no—
305C2×C8—521no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—521no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—42no—
316C4⋊C4—44no—
317C4⋊C4—44no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—82no—
323C4⋊C4#610412yes—
324C4⋊C4#610612yes—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42Q8×D1311yescharacteristic
330C42#613111yescharacteristic
331C42#613111yescharacteristic
332C42#613111yescharacteristic
333C13#1035411yescharacteristic, complemented, Sylow
334C23—522no—
335C23—1041no—
336C23—1041no—
337C23—1041no—
338C23—1041no—
339C23—1041no—
340C23—1041no—
341C23#8820711yescharacteristic
342D4—524no—
343D4—522no—
344D4—522no—
345D4—522no—
346D4—522no—
347D4—1042no—
348D4—1041no—
349D4—1041no—
350D4—1041no—
351D4—1041no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4C2×#610411yescharacteristic
370C2×C4#8818611yescharacteristic
371C2×C4C2×#610611yescharacteristic
372C2×C4#8819611yescharacteristic
373C2×C4#8820011yescharacteristic
374C2×C4#8820011yescharacteristic
375C2×C4#8820011yescharacteristic
376C2×C4#8820111yescharacteristic
377C2×C4#8820111yescharacteristic
378C2×C4#8820111yescharacteristic
379C2×C4#8820311yescharacteristic
380C2×C4#8820311yescharacteristic
381C2×C4#8820411yescharacteristic
382C2×C4#8820411yescharacteristic
383C8—522no—
384C8—1041no—
385C8—1041no—
386C22—1042no—
387C22—1042no—
388C22—1042no—
389C22—2081no—
390C22—2081no—
391C22—2081no—
392C22—2081no—
393C22#1171887811yescharacteristic
394C22#1171888811yescharacteristic
395C22#1171889211yescharacteristic
396C22#1171889911yescharacteristic
397C22#1171889911yescharacteristic
398C22#1171890211yescharacteristic
399C22#1171890611yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4#1171872711yescharacteristic
408C4#1171872711yescharacteristic
409C4#1171872811yescharacteristic
410C4#1171872911yescharacteristic
411C4#1171874511yescharacteristic
412C4#1171874811yescharacteristic
413C4#1171874911yescharacteristic
414C4#1171875011yescharacteristic
415C2—2082no—
416C2#1311390111yescharacteristic
417C2#1311390811yescharacteristic
418C2#1311392511yescharacteristic
419C2#1311393211yescharacteristic
420C2#1311596911yescharacteristic
421C2#1311597911yescharacteristic
422C2#1311598911yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2552C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#2552D13
hypocenterC13#10354
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2552

Complements

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

NH ≅ G/Ntype
4. #13112719C2semidirect
5. #13112677C2semidirect
6. #13112677C2semidirect
7. C13×#2552C2semidirect
123. #2552D13semidirect
333. C13#10354semidirect

Maximal subgroups

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

subgroupindex
#131157632
#131156412
#131127192
#131126772
C13×#25522
#1035413