Finite Group Databasebeta

← #15767380

Subgroups — #15767380

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 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×#2571C211yesmaximal, characteristic
8C13×#400—22no—
9C13×#389—21no—
10C13×#389—21no—
11C13×#384C2211yescharacteristic
12C13×#382—21no—
13C13×#382—21no—
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—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D412yes—
33C2×C42×C13—21no—
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C22×#1055—21no—
40C22×#1055—21no—
41C22×#1055—21no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95—21no—
47#88048—42no—
48#88047—42no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4⋊#1055Q812yes—
52C4⋊#1055Q812yes—
53C4×#1055—21no—
54C4×#1055Q812yes—
55#10578—131nomaximal, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—41no—
65C13×C4⋊C4—21no—
66C13×C4⋊C4—21no—
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—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—82no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13—41no—
82C42×C13—41no—
83C42×C13C2×Q811yescharacteristic
84C42×C13C2×Q811yescharacteristic
85C42×C13C2×Q811yescharacteristic
86C42×C13#4111yescharacteristic
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C2×#1055—22no—
93C2×#1055—22no—
94C2×#1055—22no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101#2571D1311yescharacteristic
102#1948—131no—
103#1947—131no—
104#1834—131no—
105#1296—131no—
106#1279—131no—
107#1279—131no—
108C23×C13#12011yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13C22⋊Q811yescharacteristic
128C2×C4×C13C22⋊Q811yescharacteristic
129C2×C4×C13C4⋊Q811yescharacteristic
130C2×C4×C13C4⋊Q811yescharacteristic
131C2×C4×C13C4⋊Q811yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143#1055—42no—
144#1055—42no—
145#1055—42no—
146C2×#107—261no—
147C2×#106—261no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8—131no—
150C2×C4×C8—131no—
151#400—22no—
152#389—21no—
153#389—21no—
154#384—131no—
155#384C2×D1311yescharacteristic
156#382—21no—
157#382—21no—
158C4×C4⋊C4C2×D1311yescharacteristic
159C4×C4⋊C4C2×D1311yescharacteristic
160#340—262no—
161#340—261no—
162#340—261no—
163C22×C13#39511yescharacteristic
164C22×C13#44911yescharacteristic
165C22×C13#44911yescharacteristic
166C22×C13#45211yescharacteristic
167C22×C13#45211yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45511yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13—82no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13#47811yescharacteristic
178C4×C13#47811yescharacteristic
179C4×C13#47911yescharacteristic
180C4×C13#47911yescharacteristic
181C4×C13#49911yescharacteristic
182C4×C13#49911yescharacteristic
183C4×C13#50111yescharacteristic
184C4×C13#50111yescharacteristic
185Dic13—161no—
186C22×C8—261no—
187C22×C8—261no—
188C22×C8—261no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C4⋊C4C22⋊D1311yescharacteristic
197C2×C4⋊C4C22⋊D1311yescharacteristic
198C2×C4⋊C4C22⋊D1311yescharacteristic
199C2×C4⋊C4C22⋊D1312yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42C22×D1311yescharacteristic
203#107—522no—
204#106—522no—
205C4⋊C8—132no—
206C4⋊C8—132no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4×C8—132no—
210C4×C8—261no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215#95—21no—
216C2×C13#162811yescharacteristic
217C2×C13#163811yescharacteristic
218C2×C13#164011yescharacteristic
219C2×C13#164611yescharacteristic
220C2×C13#205911yescharacteristic
221C2×C13#205911yescharacteristic
222C2×C13#206111yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—521no—
229C22×C4C2×C22⋊D1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—262no—
233C2×C8—262no—
234C2×C8—262no—
235C2×C8—521no—
236C2×C8—521no—
237C2×C8—521no—
238C2×C8—521no—
239C2×C8—521no—
240C2×C8—521no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—82no—
255C4⋊C4—522no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42Q8×D1311yescharacteristic
265C42Q8×D1311yescharacteristic
266C42Q8×D1311yescharacteristic
267C42#613111yescharacteristic
268C13#1057811yescharacteristic, complemented, Sylow
269C23#8820711yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—1041no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4#8819811yescharacteristic
291C2×C4#8819811yescharacteristic
292C2×C4#8819811yescharacteristic
293C2×C4#8820011yescharacteristic
294C2×C4#8820011yescharacteristic
295C2×C4#8820011yescharacteristic
296C2×C4#8820311yescharacteristic
297C2×C4#8820311yescharacteristic
298C2×C4#8820411yescharacteristic
299C2×C4#8820411yescharacteristic
300C2×C4#8820411yescharacteristic
301C2×C4#8820411yescharacteristic
302C2×C4#8820511yescharacteristic
303C2×C4#8820511yescharacteristic
304C8—522no—
305C8—522no—
306C8—522no—
307C22#1171889011yescharacteristic
308C22#1171889911yescharacteristic
309C22#1171889911yescharacteristic
310C22#1171890011yescharacteristic
311C22#1171890011yescharacteristic
312C22#1171890311yescharacteristic
313C22#1171890611yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—2081no—
322C4#1171872411yescharacteristic
323C4#1171872411yescharacteristic
324C4#1171872511yescharacteristic
325C4#1171872511yescharacteristic
326C4#1171872611yescharacteristic
327C4#1171872611yescharacteristic
328C4#1171872711yescharacteristic
329C4#1171872711yescharacteristic
330C2#1311394611yescharacteristic
331C2#1311400811yescharacteristic
332C2#1311402211yescharacteristic
333C2#1311406411yescharacteristic
334C2#1311617111yescharacteristic
335C2#1311617111yescharacteristic
336C2#1311618311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2571C2
socle, prime radicalC23×C13#120
hypercenter#2571D13
hypocenterC13#10578
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
268. C13#10578semidirect

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×#25712
#1057813