Finite Group Databasebeta

← #15767645

Subgroups — #15767645

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115629C211yesmaximal, characteristic
2#13114992C211yesmaximal, characteristic, complemented
3#13114837C211yesmaximal, characteristic
4#13114833C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88061—21no—
13C2×#88060—21no—
14C2×#88060—21no—
15C2×#88049—21no—
16C2×#88048—21no—
17C2×#88048—21no—
18#11718596C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718143—21no—
22#11718121—21no—
23C22×D52D411yescharacteristic
24C22×C4×D13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13C2311yescharacteristic
31C2×#6103—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D411yescharacteristic
36C22×#1055—21no—
37C22×#1055D411yescharacteristic
38C22×#1055D411yescharacteristic
39C4×D52—21no—
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47#88061—42no—
48#88060—42no—
49#88060—42no—
50#88049—42no—
51#88048—42no—
52#88048—42no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4×#1055—21no—
56C4×#1055—21no—
57#10619—131nomaximal, Sylow
58C23×D13—21no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13#4111yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—41no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52SD1612yes—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—81no—
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91C42×C13#4111yescharacteristic
92#6103—41no—
93#6103—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—81no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055D812yes—
109C2×#1055SD1612yes—
110#1954—131no—
111#1844—131no—
112#1802—131no—
113#1802—131no—
114#1296—131no—
115#1296D1311yescharacteristic, complemented
116#1277—131no—
117C23×C13#12111yescharacteristic
118C22×D13—22no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C22×D13—41no—
124C22×D13—41no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#12311yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13#12311yescharacteristic
133C2×C4×C13#12411yescharacteristic
134C2×C4×C13#12611yescharacteristic
135C2×C4×C13#12611yescharacteristic
136C2×C4×C13C2×D811yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150D52—22no—
151D52—22no—
152D52—41no—
153D52—41no—
154C4×D13—81no—
155C4×D13—81no—
156C4×D13—81no—
157C4×D13—81no—
158C8×C13—81no—
159C8×C13—81no—
160#1055—22no—
161#1055—22no—
162#1055—81no—
163C2×C4×D4—131no—
164C2×#106—261no—
165C2×#106—261no—
166C2×C4⋊C8—131no—
167C2×C4⋊C8C2×D1311yescharacteristic
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×#102—261no—
170C2×#102—261no—
171C2×C22⋊C8—261no—
172C2×C22⋊C8—261no—
173C2×C4×C8—131no—
174#384—131no—
175#384C2×D1311yescharacteristic
176#340—261no—
177#340—261no—
178C22×C13#39711yescharacteristic
179C22×C13#45911yescharacteristic
180C22×C13#46111yescharacteristic
181C22×C13#46511yescharacteristic
182C22×C13#46811yescharacteristic
183C22×C13#47111yescharacteristic
184C22×C13#47111yescharacteristic
185C2×D13—42no—
186C2×D13—42no—
187C2×D13—42no—
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C2×D13—81no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—161no—
195C4×C13#48011yescharacteristic
196C4×C13#48111yescharacteristic
197C4×C13#48111yescharacteristic
198C4×C13#48211yescharacteristic
199C4×C13#48311yescharacteristic
200C4×C13#48511yescharacteristic
201C4×C13#48611yescharacteristic
202C4×C13#48911yescharacteristic
203Dic13—81no—
204Dic13—161no—
205C22×D4—131no—
206C23×C4—261no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—261no—
212C4×D4—261no—
213C4×D4—261no—
214C4×D4—261no—
215C4×D4—261no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C42C22×D1311yescharacteristic
225#106—522no—
226#106—522no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—261no—
232C4⋊C8—261no—
233#102—522no—
234#102—522no—
235C22⋊C8—522no—
236C22⋊C8—522no—
237C4×C8—261no—
238C4×C8—261no—
239C2×C13#166511yescharacteristic
240C2×C13#167111yescharacteristic
241C2×C13#168511yescharacteristic
242C2×C13#169111yescharacteristic
243C2×C13#207111yescharacteristic
244C2×C13#207711yescharacteristic
245C2×C13#207911yescharacteristic
246D13—82no—
247C24—261no—
248C2×D4—132no—
249C2×D4—261no—
250C2×D4—261no—
251C2×D4—261no—
252C2×D4—261no—
253C2×D4—261no—
254C22×C4—41no—
255C22×C4—261no—
256C22×C4—521no—
257C22×C4—521no—
258C22×C4—521no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4#612711yescharacteristic
264C22×C4D4×D1311yescharacteristic
265C22×C4D4×D1311yescharacteristic
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—132no—
273C2×C8—132no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8—261no—
277C2×C8—261no—
278C2×C8—521no—
279C2×C8—521no—
280C2×C8—521no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—261no—
287C4⋊C4—261no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—1041no—
293C22⋊C4—521no—
294C22⋊C4—521no—
295C42#612711yescharacteristic
296C42#612711yescharacteristic
297C42#612911yescharacteristic
298C42#613111yescharacteristic
299C13#1061911yescharacteristic, complemented, Sylow
300C23—262no—
301C23—521no—
302C23—521no—
303C23—521no—
304C23—521no—
305C23—521no—
306C23—521no—
307C23#8813811yescharacteristic
308D4—262no—
309D4—262no—
310D4—521no—
311D4—521no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4—1041no—
325C2×C4—1041no—
326C2×C4—1041no—
327C2×C4#8813011yescharacteristic
328C2×C4#8813711yescharacteristic
329C2×C4#8813911yescharacteristic
330C2×C4#8814811yescharacteristic
331C2×C4#8814811yescharacteristic
332C2×C4#8815211yescharacteristic
333C2×C4D8×D1311yescharacteristic
334C2×C4#8816511yescharacteristic
335C2×C4SD16×D1311yescharacteristic
336C2×C4SD16×D1311yescharacteristic
337C2×C4#8816811yescharacteristic
338C2×C4#8816911yescharacteristic
339C2×C4#8817211yescharacteristic
340C2×C4#8817311yescharacteristic
341C8—81no—
342C8—81no—
343C8—262no—
344C8—262no—
345C8—1041no—
346C22—522no—
347C22—522no—
348C22—522no—
349C22—1041no—
350C22—1041no—
351C22—1041no—
352C22—1041no—
353C22#1171833611yescharacteristic
354C22#1171840911yescharacteristic
355C22#1171841511yescharacteristic
356C22#1171844111yescharacteristic
357C22#1171844711yescharacteristic
358C22#1171846811yescharacteristic
359C22#1171847911yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—1041no—
364C4—2081no—
365C4#1171842111yescharacteristic
366C4#1171843811yescharacteristic
367C4#1171845611yescharacteristic
368C4#1171847511yescharacteristic
369C4#1171852311yescharacteristic
370C4#1171852411yescharacteristic
371C4#1171854311yescharacteristic
372C4#1171854611yescharacteristic
373C2—1042no—
374C2#1311418011yescharacteristic
375C2#1311421411yescharacteristic
376C2#1311430011yescharacteristic
377C2#1311433411yescharacteristic
378C2#1311624311yescharacteristic
379C2#1311627511yescharacteristic
380C2#1311628511yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenter#1296D13
hypocenterC13#10619
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13114992C2semidirect
5. #13112720C2semidirect
6. #13112670C2semidirect
7. C13×#1296C2semidirect
115. #1296D13semidirect
299. C13#10619semidirect

Maximal subgroups

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

subgroupindex
#131156292
#131149922
#131148372
#131148332
#131127202
#131126702
C13×#12962
#1061913