Finite Group Databasebeta

← #15751420

Subgroups — #15751420

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114598C211yesmaximal, characteristic
2C2×#11718116C211yesmaximal, characteristic
3#13112659C212yesmaximal, complemented
4#13112659C212yesmaximal, complemented
5C13×#2851C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C23×#1055—21no—
9C13×#389C2211yescharacteristic
10C13×#389C2211yescharacteristic
11C13×#387—21no—
12C13×#387—21no—
13C13×#385—21no—
14C13×#385—21no—
15C13×#382C411yescharacteristic
16C13×#380C411yescharacteristic
17C13×#380C411yescharacteristic
18C2×C22⋊#1055—21no—
19C2×#88043—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#125—42no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13—42no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13C2311yescharacteristic
42C22×#1055—24no—
43C22×#1055—22no—
44C22×#1055—22no—
45C22×#1055—42no—
46C22×#1055—42no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C22⋊#1055—24no—
54#88043—42no—
55#7691—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—22no—
89C42×C13—22no—
90C42×C13—41no—
91C42×C13—41no—
92C2×#1055—24no—
93C2×#1055—24no—
94C2×#1055—48no—
95C2×#1055—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99#2851D1311yescharacteristic
100#1749—131no—
101C2×#336—131no—
102#1271—132no—
103#1271—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13#10112yes—
109C23×C13#10412yes—
110C23×C13#10412yes—
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—24no—
113C2×C4×C13—24no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13#9912yes—
143C2×C4×C13#13112yes—
144C2×C4×C13#13512yes—
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147#1055—44no—
148#1055—44no—
149C23×C8—261no—
150C2×#125Dic1311yescharacteristic
151C22×C42C2×D1311yescharacteristic
152C2×C22⋊C8—261no—
153C2×#97—261no—
154#389C2×D1311yescharacteristic
155#389C2×D1311yescharacteristic
156#387—21no—
157#387—21no—
158#385—21no—
159#385—21no—
160#382Dic1311yescharacteristic
161#380Dic1311yescharacteristic
162#380Dic1311yescharacteristic
163#336—132no—
164#336—132no—
165#336—261no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13#33014yes—
173C22×C13#40811yescharacteristic
174C22×C13C2×#9911yescharacteristic
175C22×C13C2×#10111yescharacteristic
176C22×C13#41611yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C23×C4C2×Dic1311yescharacteristic
192C23×C4C22⋊D1311yescharacteristic
193C23×C4C22⋊D1311yescharacteristic
194C22×C8—264no—
195C22×C8—262no—
196C22×C8—262no—
197C22×C8—522no—
198C22×C8—522no—
199#125—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C4⋊C4C2×Dic1311yescharacteristic
206C2×C4⋊C4C2×Dic1311yescharacteristic
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—42no—
211C2×C42C2×Dic1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C2×C42C22⋊D1311yescharacteristic
214C2×C42C22×D1311yescharacteristic
215C22⋊C8—264no—
216#97—522no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223C2×C13—24no—
224C2×C13#147211yescharacteristic
225C2×C13#148311yescharacteristic
226C2×C13#149411yescharacteristic
227C2×C13#150111yescharacteristic
228C2×C13#150411yescharacteristic
229C2×C13C2×#33011yescharacteristic
230C2×C13#155211yescharacteristic
231C24C22⋊Dic1311yescharacteristic
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22⋊Dic1311yescharacteristic
249C22×C4C22×Dic1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252C2×C8—264no—
253C2×C8—264no—
254C2×C8—522no—
255C2×C8—528no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C13#769111yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#8807612yes—
280C23#8807712yes—
281C23#8807712yes—
282C23C2×C22⋊Dic1311yescharacteristic
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4#8807412yes—
314C2×C4#8820212yes—
315C2×C4#8820311yescharacteristic
316C2×C4#8820412yes—
317C2×C4#8820511yescharacteristic
318C8—524no—
319C8—524no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1171813514yes—
327C22C2×#8807411yescharacteristic
328C22C2×#8807611yescharacteristic
329C22#1171889311yescharacteristic
330C22#1171889411yescharacteristic
331C22#1171889511yescharacteristic
332C22C2×#8807711yescharacteristic
333C22C2×#8807711yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C2—24no—
346C2#1311320011yescharacteristic
347C2#1311324911yescharacteristic
348C2#1311329611yescharacteristic
349C2#1311332711yescharacteristic
350C2#1311334011yescharacteristic
351C2C2×#1171813511yescharacteristic
352C2#1311353611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2851C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2851D13
hypocenterC13#7691
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. #13112659C2semidirect
4. #13112659C2semidirect
274. C13#7691semidirect

Maximal subgroups

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

subgroupindex
#131145982
C2×#117181162
#131126592
C13×#28512
#769113