Finite Group Databasebeta

← #15767363

Subgroups — #15767363

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115599C211yesmaximal, characteristic
2#13115594C211yesmaximal, characteristic
3#13114963C211yesmaximal, characteristic
4#13112719C211yesmaximal, characteristic
5#13112677C211yesmaximal, characteristic
6#13112677C211yesmaximal, characteristic
7C13×#2551C211yesmaximal, characteristic
8C2×C13×C4⋊Q8—21no—
9C2×C13×C4⋊Q8—21no—
10C13×#395—22no—
11C13×#389—21no—
12C13×#389—21no—
13C13×#384C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15C4×C13×C4⋊C4C2211yescharacteristic
16C2×#88048—21no—
17C2×#88047—21no—
18#11718596C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718121—22no—
23#11718121—21no—
24#11718121—21no—
25C22×Q8×C13—22no—
26C13×C4⋊Q8—42no—
27C13×C4⋊Q8—42no—
28C13×C4⋊Q8—42no—
29C13×C4⋊Q8—42no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D412yes—
39C2×C42×C13—21no—
40C2×C42×C13—21no—
41C2×C42×C13C2311yescharacteristic
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C22×#1055—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×#95—22no—
49C13×#95—21no—
50C13×#95—21no—
51#88048—42no—
52#88047—42no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055Q812yescomplemented
56C4⋊#1055Q812yescomplemented
57C4×#1055—21no—
58C4×#1055Q812yescomplemented
59#10575—131nomaximal, Sylow
60C2×Q8×C13—44no—
61C2×Q8×C13—44no—
62C2×Q8×C13—82no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—41no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—44no—
78C13×C4⋊C4—44no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4D812yes—
84C13×C4⋊C4SD1612yes—
85C13×C4⋊C4SD1612yes—
86C13×C4⋊C4Q1612yes—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13C2×Q811yescharacteristic
92C42×C13C2×Q811yescharacteristic
93C42×C13C2×Q811yescharacteristic
94C42×C13#4111yescharacteristic
95C4⋊Dic13—42no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C2×#1055—22no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109#2551D1311yescharacteristic
110#1948—131no—
111#1947—131no—
112#1834—131no—
113#1296—131no—
114#1279—131no—
115#1279—131no—
116C23×C13#12011yescharacteristic
117Q8×C13—88no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13C22⋊Q811yescharacteristic
138C2×C4×C13C4⋊Q811yescharacteristic
139C2×C4×C13C4⋊Q811yescharacteristic
140C2×C4×C13C4⋊Q811yescharacteristic
141C2×C4×C13C2×D811yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13C2×Q1611yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×C4×C13#13711yescharacteristic
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13—81no—
152#1055—42no—
153#1055—42no—
154#1055—42no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—21no—
157C2×#107—261no—
158C2×#106—261no—
159C2×C4⋊C8—131no—
160C2×C4⋊C8—131no—
161C2×C4×C8—131no—
162#395—22no—
163#389—21no—
164#389—21no—
165#384—131no—
166#384C2×D1311yescharacteristic
167C4×C4⋊C4C2×D1311yescharacteristic
168C4×C4⋊C4C2×D1311yescharacteristic
169#340—262no—
170#340—261no—
171#340—261no—
172C22×C13#39511yescharacteristic
173C22×C13#44711yescharacteristic
174C22×C13#44811yescharacteristic
175C22×C13#45011yescharacteristic
176C22×C13#45111yescharacteristic
177C22×C13#45411yescharacteristic
178C22×C13#45511yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—42no—
182C4×C13—42no—
183C4×C13—42no—
184C4×C13—42no—
185C4×C13—82no—
186C4×C13#47411yescharacteristic
187C4×C13#47511yescharacteristic
188C4×C13#47611yescharacteristic
189C4×C13#47711yescharacteristic
190C4×C13#49811yescharacteristic
191C4×C13#50011yescharacteristic
192C4×C13#50111yescharacteristic
193C4×C13#50111yescharacteristic
194Dic13—161no—
195C22×Q8—22no—
196C22×C8—261no—
197C22×C8—261no—
198C22×C8—261no—
199C4⋊Q8—42no—
200C4⋊Q8—42no—
201C4⋊Q8—42no—
202C4⋊Q8—42no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4C22⋊D1311yescharacteristic
211C2×C4⋊C4C22⋊D1311yescharacteristic
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C4⋊C4C22⋊D1311yescharacteristic
214C2×C4⋊C4C22⋊D1312yes—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42C22×D1311yescharacteristic
218#107—522no—
219#106—522no—
220C4⋊C8—132no—
221C4⋊C8—132no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4×C8—132no—
225C4×C8—261no—
226#95—22no—
227#95—21no—
228#95—21no—
229C2×C13#162711yescharacteristic
230C2×C13#163711yescharacteristic
231C2×C13#163911yescharacteristic
232C2×C13#164511yescharacteristic
233C2×C13#205711yescharacteristic
234C2×C13#205811yescharacteristic
235C2×C13#206111yescharacteristic
236C2×Q8—44no—
237C2×Q8—44no—
238C2×Q8—82no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—521no—
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—262no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8—521no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C2×C8—521no—
256C2×C8—521no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—42no—
262C4⋊C4—44no—
263C4⋊C4—44no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—522no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4#610412yes—
274C4⋊C4#610512yes—
275C4⋊C4#610612yes—
276C4⋊C4#610712yes—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C42Q8×D1311yescharacteristic
282C42Q8×D1311yescharacteristic
283C42Q8×D1311yescharacteristic
284C42#613111yescharacteristic
285C13#1057511yescharacteristic, complemented, Sylow
286C23#8820711yescharacteristic
287Q8—88no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4C2×#610411yescharacteristic
309C2×C4#8818611yescharacteristic
310C2×C4#8818611yescharacteristic
311C2×C4C2×#610511yescharacteristic
312C2×C4C2×#610611yescharacteristic
313C2×C4#8819611yescharacteristic
314C2×C4#8819611yescharacteristic
315C2×C4C2×#610711yescharacteristic
316C2×C4#8819811yescharacteristic
317C2×C4#8819811yescharacteristic
318C2×C4#8819811yescharacteristic
319C2×C4#8820011yescharacteristic
320C2×C4#8820011yescharacteristic
321C2×C4#8820011yescharacteristic
322C8—522no—
323C8—522no—
324C8—522no—
325C22#1171887811yescharacteristic
326C22#1171887911yescharacteristic
327C22#1171888811yescharacteristic
328C22#1171888911yescharacteristic
329C22#1171889011yescharacteristic
330C22#1171890311yescharacteristic
331C22#1171890611yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—42no—
338C4—82no—
339C4—2081no—
340C4#1171873911yescharacteristic
341C4#1171874011yescharacteristic
342C4#1171874111yescharacteristic
343C4#1171874111yescharacteristic
344C4#1171874511yescharacteristic
345C4#1171874811yescharacteristic
346C4#1171875211yescharacteristic
347C4#1171875511yescharacteristic
348C2#1311393911yescharacteristic
349C2#1311400111yescharacteristic
350C2#1311401511yescharacteristic
351C2#1311405711yescharacteristic
352C2#1311616111yescharacteristic
353C2#1311616611yescharacteristic
354C2#1311618311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2551C2
socle, prime radicalC23×C13#120
hypercenter#2551D13
hypocenterC13#10575
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2551

Complements

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

NH ≅ G/Ntype
55. C4⋊#1055Q8semidirect
56. C4⋊#1055Q8semidirect
58. C4×#1055Q8semidirect
285. C13#10575semidirect

Maximal subgroups

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

subgroupindex
#131155992
#131155942
#131149632
#131127192
#131126772
C13×#25512
#1057513