Finite Group Databasebeta

← #15767408

Subgroups — #15767408

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#13115599C211yesmaximal, characteristic
2#13115599C211yesmaximal, characteristic
3#13114963C211yesmaximal, characteristic
4#13112719C211yesmaximal, characteristic
5#13112677C211yesmaximal, characteristic
6#13112677C211yesmaximal, characteristic
7C13×#2552C211yesmaximal, characteristic
8C2×C13×#125—21no—
9C13×#398—22no—
10C13×#389—21no—
11C13×#389—21no—
12C13×#384—21no—
13C13×#384C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15C4×C13×C4⋊C4C2211yescharacteristic
16C2×#88048—21no—
17C2×#88048—21no—
18#11718596C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718121—22no—
23#11718121—21no—
24#11718121—21no—
25C13×#125—42no—
26C13×#125—42no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D412yes—
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C22×#1055—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46C13×#95—22no—
47C13×#95—21no—
48C13×#95—21no—
49#88048—42no—
50#88048—42no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055Q812yes—
54C4⋊#1055Q812yes—
55C4×#1055—21no—
56C4×#1055Q812yes—
57#10582—131nomaximal, Sylow
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—41no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—44no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—82no—
81C13×C4⋊C4SD1612yes—
82C13×C4⋊C4SD1612yes—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13—41no—
87C42×C13C2×Q811yescharacteristic
88C42×C13C2×Q811yescharacteristic
89C42×C13C2×Q811yescharacteristic
90C42×C13#4111yescharacteristic
91C4⋊Dic13—42no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C2×#1055—22no—
97C2×#1055—22no—
98C2×#1055—22no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2552D1311yescharacteristic
106#1948—131no—
107#1948—131no—
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—22no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13C22⋊Q811yescharacteristic
132C2×C4×C13C22⋊Q811yescharacteristic
133C2×C4×C13C4⋊Q811yescharacteristic
134C2×C4×C13C4⋊Q811yescharacteristic
135C2×C4×C13C4⋊Q811yescharacteristic
136C2×C4×C13C2×SD1611yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
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—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147#1055—42no—
148#1055—42no—
149#1055—42no—
150C2×#125—21no—
151C2×#106—261no—
152C2×#106—261no—
153C2×C4⋊C8—131no—
154C2×C4⋊C8—131no—
155C2×C4×C8—131no—
156#398—22no—
157#389—21no—
158#389—21no—
159#384—21no—
160#384—131no—
161#384C2×D1311yescharacteristic
162C4×C4⋊C4C2×D1311yescharacteristic
163C4×C4⋊C4C2×D1311yescharacteristic
164#340—262no—
165#340—261no—
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—42no—
177C4×C13—42no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13—82no—
181C4×C13#47511yescharacteristic
182C4×C13#47611yescharacteristic
183C4×C13#47811yescharacteristic
184C4×C13#47911yescharacteristic
185C4×C13#49811yescharacteristic
186C4×C13#49911yescharacteristic
187C4×C13#50111yescharacteristic
188C4×C13#50111yescharacteristic
189Dic13—161no—
190C22×C8—261no—
191C22×C8—261no—
192C22×C8—261no—
193#125—42no—
194#125—42no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C4⋊C4C22⋊D1311yescharacteristic
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C4⋊C4C22⋊D1312yes—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22×D1311yescharacteristic
211#106—522no—
212#106—522no—
213C4⋊C8—132no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4×C8—132no—
218C4×C8—261no—
219#95—22no—
220#95—21no—
221#95—21no—
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—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—521no—
235C22×C4C2×C22⋊D1311yescharacteristic
236C22×C4C2×C22⋊D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—262no—
239C2×C8—262no—
240C2×C8—262no—
241C2×C8—521no—
242C2×C8—521no—
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—21no—
252C4⋊C4—21no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—44no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—82no—
261C4⋊C4—522no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4#610512yes—
267C4⋊C4#610612yes—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42Q8×D1311yescharacteristic
273C42Q8×D1311yescharacteristic
274C42Q8×D1311yescharacteristic
275C42#613111yescharacteristic
276C13#1058211yescharacteristic, complemented, Sylow
277C23#8820711yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4#8818611yescharacteristic
299C2×C4C2×#610511yescharacteristic
300C2×C4C2×#610611yescharacteristic
301C2×C4#8819611yescharacteristic
302C2×C4#8819811yescharacteristic
303C2×C4#8819811yescharacteristic
304C2×C4#8819811yescharacteristic
305C2×C4#8820011yescharacteristic
306C2×C4#8820011yescharacteristic
307C2×C4#8820011yescharacteristic
308C2×C4#8820311yescharacteristic
309C2×C4#8820411yescharacteristic
310C2×C4#8820411yescharacteristic
311C2×C4#8820511yescharacteristic
312C8—522no—
313C8—522no—
314C8—522no—
315C22#1171887911yescharacteristic
316C22#1171888811yescharacteristic
317C22#1171889011yescharacteristic
318C22#1171889911yescharacteristic
319C22#1171890011yescharacteristic
320C22#1171890311yescharacteristic
321C22#1171890611yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4—82no—
329C4—2081no—
330C4#1171872411yescharacteristic
331C4#1171872511yescharacteristic
332C4#1171872611yescharacteristic
333C4#1171872711yescharacteristic
334C4#1171874011yescharacteristic
335C4#1171874111yescharacteristic
336C4#1171874511yescharacteristic
337C4#1171875511yescharacteristic
338C2#1311393211yescharacteristic
339C2#1311398711yescharacteristic
340C2#1311403611yescharacteristic
341C2#1311404311yescharacteristic
342C2#1311616611yescharacteristic
343C2#1311617111yescharacteristic
344C2#1311618311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2552C2
socle, prime radicalC23×C13#120
hypercenter#2552D13
hypocenterC13#10582
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
276. C13#10582semidirect

Maximal subgroups

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

subgroupindex
#131155992
#131149632
#131127192
#131126772
C13×#25522
#1058213