Finite Group Databasebeta

← #15767413

Subgroups — #15767413

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119871C211yesmaximal, characteristic
2#13115597C211yesmaximal, characteristic
3#13114963C211yesmaximal, characteristic
4#13112720C211yesmaximal, characteristic
5#13112677C211yesmaximal, characteristic
6#13112675C211yesmaximal, characteristic
7C13×#1948C211yesmaximal, characteristic
8C2×#88124—21no—
9C2×C13×#106—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13#11718637—21no—
14#11718634—21no—
15C2×#88048—21no—
16#11718596C2211yescharacteristic
17C4×C4⋊Dic13C2211yescharacteristic
18#11718589—21no—
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718318—22no—
22C13×#340—21no—
23#11718121—22no—
24#11718121—21no—
25C22×C8×C13—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D412yes—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×#6101—22no—
41C2×C4×Dic13—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44#88124—42no—
45#88124—42no—
46C13×#106—42no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8Q812yes—
49C13×#95—21no—
50#88071—22no—
51#88071—21no—
52#88048—42no—
53C4⋊#1055—21no—
54C4⋊#1055Q812yes—
55C4×#1055—21no—
56C4×#1055Q812yes—
57#10582—131nomaximal, Sylow
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—41no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—22no—
67C2×C8×C13—22no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13C2×Q811yescharacteristic
82C42×C13C2×Q811yescharacteristic
83C42×C13C2×Q811yescharacteristic
84C42×C13#4111yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—42no—
92C4⋊Dic13SD1612yes—
93C4⋊Dic13SD1612yes—
94#6101—44no—
95#6101—44no—
96#6101—82no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C2×#1055—22no—
100C2×#1055—22no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2552—131no—
106#1948—131no—
107#1948D1311yescharacteristic
108#1834—131no—
109#1296—131no—
110#1279—131no—
111#1279—131no—
112C23×C13#12011yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13C22⋊Q811yescharacteristic
125C2×C4×C13C22⋊Q811yescharacteristic
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13C4⋊Q811yescharacteristic
128C2×C4×C13C4⋊Q811yescharacteristic
129C2×C4×C13C4⋊Q811yescharacteristic
130C2×C4×C13C2×SD1611yescharacteristic
131C2×C4×C13C2×SD1611yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×Dic13—22no—
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C8×C13—42no—
148#1055—42no—
149#1055—42no—
150C2×#125—261no—
151C2×#106—21no—
152C2×#106—261no—
153C2×C4⋊C8—131no—
154C2×C4⋊C8C2×D1311yescharacteristic
155C2×C4×C8—131no—
156#398—262no—
157#389—261no—
158#389—261no—
159#384—131no—
160#384—261no—
161#384C2×D1311yescharacteristic
162C4×C4⋊C4—131no—
163C4×C4⋊C4C2×D1311yescharacteristic
164#340—21no—
165#340—262no—
166#340—261no—
167C22×C13#39511yescharacteristic
168C22×C13#44811yescharacteristic
169C22×C13#44911yescharacteristic
170C22×C13#45011yescharacteristic
171C22×C13#45211yescharacteristic
172C22×C13#45411yescharacteristic
173C22×C13#45511yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—161no—
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—
190C22×C8—21no—
191C22×C8—261no—
192C22×C8—261no—
193#125—522no—
194#125—522no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—132no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—262no—
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C4⋊C4C22⋊D1311yescharacteristic
208C2×C42—21no—
209C2×C42—261no—
210C2×C42C22×D1311yescharacteristic
211#106—42no—
212#106—522no—
213C4⋊C8—21no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8Dic2612yes—
217C4×C8—132no—
218C4×C8—261no—
219#95—21no—
220#95—262no—
221#95—261no—
222C2×C13#162611yescharacteristic
223C2×C13#163511yescharacteristic
224C2×C13#164211yescharacteristic
225C2×C13#164311yescharacteristic
226C2×C13#205811yescharacteristic
227C2×C13#205911yescharacteristic
228C2×C13#206111yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—262no—
235C22×C4D4×D1311yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—262no—
242C2×C8—262no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8—521no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—132no—
257C4⋊C4—132no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—522no—
261C4⋊C4—524no—
262C4⋊C4—524no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—1042no—
268C42—41no—
269C42—41no—
270C42—521no—
271C42—521no—
272C42C2×Dic2611yescharacteristic
273C42#612711yescharacteristic
274C42Q8×D1311yescharacteristic
275C42Q8×D1311yescharacteristic
276C13#1058211yescharacteristic, complemented, Sylow
277C23#8819111yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—262no—
290C2×C4—262no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4#8814211yescharacteristic
299C2×C4#8814211yescharacteristic
300C2×C4#8815011yescharacteristic
301C2×C4#8815011yescharacteristic
302C2×C4SD16×D1311yescharacteristic
303C2×C4SD16×D1311yescharacteristic
304C2×C4#8816811yescharacteristic
305C2×C4#8816911yescharacteristic
306C2×C4#8817811yescharacteristic
307C2×C4#8818611yescharacteristic
308C2×C4#8819611yescharacteristic
309C2×C4#8819811yescharacteristic
310C2×C4#8820411yescharacteristic
311C2×C4#8820411yescharacteristic
312C8—42no—
313C8—522no—
314C8—522no—
315C22#1171864011yescharacteristic
316C22#1171869811yescharacteristic
317C22#1171870811yescharacteristic
318C22#1171883011yescharacteristic
319C22#1171883111yescharacteristic
320C22#1171886211yescharacteristic
321C22#1171886311yescharacteristic
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—161no—
327C4—522no—
328C4—522no—
329C4—1042no—
330C4#1171851511yescharacteristic
331C4#1171851611yescharacteristic
332C4#1171851711yescharacteristic
333C4#1171853111yescharacteristic
334C4#1171867011yescharacteristic
335C4#1171868311yescharacteristic
336C4#1171872511yescharacteristic
337C4#1171874111yescharacteristic
338C2#1311393011yescharacteristic
339C2#1311398611yescharacteristic
340C2#1311403411yescharacteristic
341C2#1311404211yescharacteristic
342C2#1311616711yescharacteristic
343C2#1311617411yescharacteristic
344C2#1311618411yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1948C2
socle, prime radicalC23×C13#120
hypercenter#1948D13
hypocenterC13#10582
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
276. C13#10582semidirect

Maximal subgroups

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

subgroupindex
#131198712
#131155972
#131149632
#131127202
#131126772
#131126752
C13×#19482
#1058213