Finite Group Databasebeta

← #15753984

Subgroups — #15753984

Order 3328.

482 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
1C8×C4⋊Dic13C211yesmaximal, characteristic, complemented
2#13113485C211yesmaximal, characteristic
3#13113331C211yesmaximal, characteristic
4#13113119C211yesmaximal, characteristic, complemented
5#13112737C211yesmaximal, characteristic, complemented
6#13112731C211yesmaximal, characteristic, complemented
7C13×#2931C211yesmaximal, characteristic
8C2×C13×#131—21no—
9C13×#532C2211yescharacteristic
10C13×#436—21no—
11C13×#436C412yescomplemented
12C8×D4×C13—21no—
13C8×D4×C13C412yescomplemented
14C13×#423C2211yescharacteristic
15C13×#408—21no—
16C2×C4×C8×C13C2211yescharacteristic
17C2×C8×Dic13—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718586C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22#11718142—21no—
23#11718139C412yescomplemented
24#11718136C412yescomplemented
25#11718129C414yes—
26#11718047—21no—
27C8×#1055—21no—
28C2×C13×#41—21no—
29C13×#131—42no—
30C13×#131—42no—
31C2×C13×M16—21no—
32C2×C13×M16—22no—
33C22×C8×C13—22no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C4⋊Q8C2×C411yescharacteristic
37C13×#127C2×C411yescharacteristic
38C13×#124—21no—
39C13×#121—21no—
40C13×#121C2×C412yes—
41C4×D4×C13—21no—
42C4×D4×C13C2×C412yes—
43C2×C42×C13C2311yescharacteristic
44C2×C4⋊Dic13—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8C2×C412yes—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C4×C8×C13C2×C411yescharacteristic
52C4×C8×C13C2×C411yescharacteristic
53C4×C8×C13D411yescharacteristic
54C4×C8×C13D411yescharacteristic
55#88071C2×C412yes—
56C22⋊#1055—21no—
57C22⋊#1055C2×C412yes—
58C8×Dic13—42no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055C2×C412yes—
62C4⋊#1055C2×C412yes—
63C4×#1055—21no—
64C4×#1055—21no—
65#8251—131nomaximal, Sylow
66C13×#41—41no—
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C2×Q8×C13—21no—
71C2×D4×C13—22no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13C4212yes—
75C22×C4×C13—22no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×Dic13—22no—
80C13×M16—41no—
81C13×M16—41no—
82C13×M16—44no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—22no—
86C2×C8×C13—44no—
87C2×C8×C13C22⋊C411yescharacteristic
88C2×C8×C13C22⋊C411yescharacteristic
89C2×C8×C13C22⋊C411yescharacteristic
90C2×C8×C13C22⋊C411yescharacteristic
91C2×C8×C13D812yes—
92C2×C8×C13SD1612yes—
93C13×C4⋊C4—21no—
94C13×C4⋊C4C4212yes—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C42×C13C22×C411yescharacteristic
98C42×C13C22×C411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13#4111yescharacteristic
101C4⋊Dic13—24no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C2×#1055—22no—
105C2×#1055—22no—
106C2×#1055—22no—
107C2×#1055—41no—
108C2×#1055—41no—
109#2931D1311yescharacteristic
110C8×C4⋊C4—131no—
111#1540—131no—
112#1502—131no—
113#1450—131no—
114#1303—131no—
115#1301—131no—
116C23×C13—22no—
117C23×C13C4×D411yescharacteristic
118Q8×C13—41no—
119Q8×C13—41no—
120D4×C13—42no—
121D4×C13—42no—
122D4×C13—42no—
123D4×C13—41no—
124D4×C13—41no—
125D4×C13—42no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13C2×C4211yescharacteristic
132C2×C4×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13#11711yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13C2×D811yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13#13511yescharacteristic
141C2×Dic13—24no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C8×C13—21no—
145C8×C13—21no—
146C8×C13—42no—
147C8×C13#10212yes—
148C8×C13#10212yes—
149#1055—42no—
150#1055—42no—
151#1055—42no—
152C2×#131—21no—
153#532C2×D1311yescharacteristic
154#436—21no—
155#436Dic1312yescomplemented
156C8×D4—21no—
157C8×D4Dic1312yescomplemented
158#431—131no—
159#431—131no—
160#423C2×D1311yescharacteristic
161C2×C4⋊C8—131no—
162#408—21no—
163C2×C4×C8—261no—
164C2×C4×C8C2×D1311yescharacteristic
165C4×C4⋊C4—131no—
166#336—261no—
167#332—132no—
168#331—132no—
169#327—134no—
170#322—261no—
171C82—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13C4×C22⋊C411yescharacteristic
178C22×C13C4×D811yescharacteristic
179C22×C13C4×SD1611yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—42no—
184C4×C13C2×#10211yescharacteristic
185C4×C13#41611yescharacteristic
186C4×C13C4×D811yescharacteristic
187C4×C13C4×SD1611yescharacteristic
188C4×C13#44312yes—
189Dic13—44no—
190C2×#41—21no—
191#131—42no—
192#131—42no—
193C2×M16—21no—
194C2×M16—22no—
195C22×C8—22no—
196C22×C8—261no—
197C22×C8C22⋊D1311yescharacteristic
198C22×C8C22⋊D1311yescharacteristic
199C4⋊Q8C4×D1311yescharacteristic
200#127C4×D1311yescharacteristic
201#124—21no—
202#121—21no—
203#121C4×D1312yes—
204C4×D4—21no—
205C4×D4C2×Dic1312yes—
206C2×C4⋊C4—261no—
207C2×C42—261no—
208C2×C42C22×D1311yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—132no—
211C4⋊C8—132no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214C4⋊C8C2×Dic1312yes—
215C22⋊C8—22no—
216C22⋊C8—22no—
217C22⋊C8—132no—
218C22⋊C8—261no—
219C4×C8—261no—
220C4×C8—261no—
221C4×C8—522no—
222C4×C8C2×Dic1311yescharacteristic
223C4×C8C2×Dic1311yescharacteristic
224C4×C8C22⋊D1311yescharacteristic
225C4×C8C22⋊D1311yescharacteristic
226#95—132no—
227C2×C13—21no—
228C2×C13—21no—
229C2×C13—82no—
230C2×C13#175711yescharacteristic
231C2×C13C4×#10211yescharacteristic
232C2×C13#176411yescharacteristic
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C4×Dic1312yes—
242C22×C4—22no—
243C22×C4—262no—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4#612711yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—41no—
248M16—41no—
249M16—44no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—22no—
253C2×C8—44no—
254C2×C8—262no—
255C2×C8—262no—
256C2×C8—262no—
257C2×C8—521no—
258C2×C8—521no—
259C2×C8#610412yes—
260C2×C8#610512yes—
261C2×C8C22⋊Dic1311yescharacteristic
262C2×C8C22⋊Dic1311yescharacteristic
263C2×C8C22⋊Dic1311yescharacteristic
264C2×C8C22⋊Dic1311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—264no—
267C4⋊C4C4×Dic1312yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—521no—
271C42—521no—
272C42C2×C4×D1311yescharacteristic
273C42#612711yescharacteristic
274C42C22×Dic1311yescharacteristic
275C42C2×C22⋊D1311yescharacteristic
276C13#825111yescharacteristic, complemented, Sylow
277C23—22no—
278C23C4×C22⋊D1311yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—41no—
285D4—41no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—264no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4C2×C4×Dic1311yescharacteristic
296C2×C4#8818011yescharacteristic
297C2×C4C4×C22⋊D1311yescharacteristic
298C2×C4C4×C22⋊D1311yescharacteristic
299C2×C4C4×C22⋊D1311yescharacteristic
300C2×C4C2×#610411yescharacteristic
301C2×C4C2×#610511yescharacteristic
302C2×C4#8820411yescharacteristic
303C2×C4#8820411yescharacteristic
304C2×C4C2×C22⋊Dic1311yescharacteristic
305C8—21no—
306C8—21no—
307C8—42no—
308C8—522no—
309C8—522no—
310C8—522no—
311C8#8807212yes—
312C8#8807212yes—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C4×#610411yescharacteristic
319C22C4×#610511yescharacteristic
320C22C4×C22⋊Dic1311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—524no—
326C4C4×#610411yescharacteristic
327C4C4×#610511yescharacteristic
328C4#1171880512yes—
329C4C2×#8807211yescharacteristic
330C4#1171889411yescharacteristic
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1311463611yescharacteristic
335C2C4×#8807211yescharacteristic
336C2#1311467111yescharacteristic
subgroupG/H
centerC2×C8C22⋊Dic13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#2931C2
socleC22×C13C4×C22⋊C4
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#2931D13
hypocenterC13#8251
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. C8×C4⋊Dic13C2semidirect
4. #13113119C2semidirect
5. #13112737C2semidirect
6. #13112731C2semidirect
11. C13×#436C4semidirect
13. C8×D4×C13C4semidirect
23. #11718139C4semidirect
24. #11718136C4semidirect
155. #436Dic13semidirect
157. C8×D4Dic13semidirect
276. C13#8251semidirect

Maximal subgroups

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

subgroupindex
C8×C4⋊Dic132
#131134852
#131133312
#131131192
#131127372
#131127312
C13×#29312
#825113