Finite Group Databasebeta

← #15767400

Subgroups — #15767400

Order 3328.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119871C211yesmaximal, characteristic
2#13115599C211yesmaximal, characteristic
3#13115595C211yesmaximal, characteristic
4#13114993C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic
8C2×#88124—21no—
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88058—21no—
13C2×#88057—22no—
14#11718637—21no—
15#11718634—21no—
16C2×#88048—21no—
17#11718596C2211yescharacteristic
18#11718596C2211yescharacteristic
19C4×C4⋊Dic13C2211yescharacteristic
20#11718589—21no—
21C2×C4⋊#1055C2211yescharacteristic
22#11718318—22no—
23#11718143—21no—
24#11718121—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D412yes—
39C2×#6101—22no—
40C2×#6101—22no—
41C2×#6101—22no—
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44#88124—42no—
45#88124—42no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8Q812yes—
48C4×C8×C13—21no—
49C4×C8×C13Q812yes—
50C13×#95—21no—
51#88071—22no—
52#88071—21no—
53#88058—42no—
54#88057—44no—
55#88048—42no—
56C4⋊#1055—21no—
57C4⋊#1055Q812yes—
58#10580—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C2×C8×C13—22no—
69C2×C8×C13—22no—
70C2×C8×C13—22no—
71C2×C8×C13—22no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C42×C13—41no—
79C42×C13—41no—
80C42×C13C2×Q811yescharacteristic
81C42×C13C2×Q811yescharacteristic
82C42×C13C2×Q811yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—42no—
91C4⋊Dic13—42no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13SD1612yes—
97C4⋊Dic13SD1612yes—
98#6101—44no—
99#6101—44no—
100#6101—82no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103C2×#1055—22no—
104C2×#1055—41no—
105C2×#1055—41no—
106#2552—131no—
107#1948—131no—
108#1947—131no—
109#1844—131no—
110#1296—131no—
111#1279—131no—
112#1279D1311yescharacteristic
113C23×C13#12011yescharacteristic
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13C22⋊Q811yescharacteristic
125C2×C4×C13C4⋊Q811yescharacteristic
126C2×C4×C13C4⋊Q811yescharacteristic
127C2×C4×C13C4⋊Q811yescharacteristic
128C2×C4×C13C2×SD1611yescharacteristic
129C2×C4×C13C2×SD1611yescharacteristic
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C8×C13—24no—
149C8×C13—42no—
150#1055—42no—
151C2×#125—261no—
152C2×#107—261no—
153C2×#106—262no—
154C2×#106—261no—
155C2×C4⋊C8—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×C4×C8C2×D1311yescharacteristic
158#398—262no—
159#389—261no—
160#389—261no—
161#384—131no—
162#384—131no—
163#384—261no—
164C4×C4⋊C4—131no—
165C4×C4⋊C4C2×D1311yescharacteristic
166#340—261no—
167#340—261no—
168C22×C13#39511yescharacteristic
169C22×C13#44811yescharacteristic
170C22×C13#44911yescharacteristic
171C22×C13#45011yescharacteristic
172C22×C13#45211yescharacteristic
173C22×C13#45311yescharacteristic
174C22×C13#45611yescharacteristic
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13#47511yescharacteristic
180C4×C13#47611yescharacteristic
181C4×C13#47811yescharacteristic
182C4×C13#47911yescharacteristic
183C4×C13#49811yescharacteristic
184C4×C13#49911yescharacteristic
185C4×C13#50111yescharacteristic
186C4×C13#50111yescharacteristic
187Dic13—42no—
188Dic13—42no—
189Dic13—82no—
190Dic13—161no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—261no—
194#125—522no—
195#125—522no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—132no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—262no—
207C2×C4⋊C4D5211yescharacteristic
208C2×C4⋊C4D5211yescharacteristic
209C2×C42—21no—
210C2×C42—261no—
211C2×C42C22×D1311yescharacteristic
212#107—522no—
213#106—522no—
214#106—524no—
215C4⋊C8—21no—
216C4⋊C8—132no—
217C4⋊C8—261no—
218C4⋊C8Dic2612yes—
219C4×C8—21no—
220C4×C8Dic2612yes—
221#95—21no—
222#95—262no—
223#95—261no—
224C2×C13#162211yescharacteristic
225C2×C13#163111yescharacteristic
226C2×C13#165311yescharacteristic
227C2×C13#165411yescharacteristic
228C2×C13#205811yescharacteristic
229C2×C13#205911yescharacteristic
230C2×C13#206011yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—262no—
236C22×C4—521no—
237C22×C4C2×D5211yescharacteristic
238C22×C4D4×D1311yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—262no—
247C2×C8—521no—
248C2×C8—521no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—132no—
254C4⋊C4—132no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—522no—
258C4⋊C4—522no—
259C4⋊C4—524no—
260C4⋊C4—524no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—1042no—
270C42—41no—
271C42—41no—
272C42—521no—
273C42—521no—
274C42C2×Dic2611yescharacteristic
275C42C2×Dic2611yescharacteristic
276C42#612911yescharacteristic
277C42Q8×D1311yescharacteristic
278C13#1058011yescharacteristic, complemented, Sylow
279C23#8813611yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—262no—
289C2×C4—262no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4#8812311yescharacteristic
301C2×C4#8813211yescharacteristic
302C2×C4#8813211yescharacteristic
303C2×C4#8814211yescharacteristic
304C2×C4#8814211yescharacteristic
305C2×C4#8815111yescharacteristic
306C2×C4#8815811yescharacteristic
307C2×C4#8815811yescharacteristic
308C2×C4#8816211yescharacteristic
309C2×C4#8816311yescharacteristic
310C2×C4#8816511yescharacteristic
311C2×C4SD16×D1311yescharacteristic
312C2×C4SD16×D1311yescharacteristic
313C2×C4#8817211yescharacteristic
314C8—24no—
315C8—42no—
316C8—522no—
317C22#1171831711yescharacteristic
318C22#1171839411yescharacteristic
319C22#1171839511yescharacteristic
320C22#1171843711yescharacteristic
321C22#1171846711yescharacteristic
322C22#1171848311yescharacteristic
323C22#1171848711yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—522no—
329C4—522no—
330C4—1042no—
331C4—2081no—
332C4#1171834411yescharacteristic
333C4#1171836311yescharacteristic
334C4#1171842211yescharacteristic
335C4#1171845211yescharacteristic
336C4#1171849011yescharacteristic
337C4#1171850811yescharacteristic
338C4#1171851611yescharacteristic
339C4#1171853711yescharacteristic
340C2#1311391111yescharacteristic
341C2#1311396611yescharacteristic
342C2#1311411611yescharacteristic
343C2#1311412211yescharacteristic
344C2#1311616811yescharacteristic
345C2#1311617511yescharacteristic
346C2#1311618011yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socle, prime radicalC23×C13#120
hypercenter#1279D13
hypocenterC13#10580
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
278. C13#10580semidirect

Maximal subgroups

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

subgroupindex
#131198712
#131155992
#131155952
#131149932
#131127202
#131126762
C13×#12792
#1058013