Finite Group Databasebeta

← #15753468

Subgroups — #15753468

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#1055C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13114615C212yesmaximal, complemented
4#13112682C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C23×#1055C411yescharacteristic, complemented
8C23×#1055C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C2×#88074C412yes—
11C4×C22⋊Dic13C2212yes—
12C2×C22⋊#1055C411yescharacteristic, complemented
13C2×C22⋊#1055C2211yescharacteristic
14C2×#88055—22no—
15D4×#1055—22no—
16D4×#1055—22no—
17C2×C4⋊#1055C411yescharacteristic, complemented
18C2×C4×#1055C411yescharacteristic, complemented
19C13×#324C412yescomplemented
20C13×#323C412yescomplemented
21#11718142—22no—
22#11718118C412yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C22×C8×C13—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C22⋊Dic13C2×C414yes—
34C2×C4×Dic13—22no—
35C22×#1055—21no—
36C22×#1055—21no—
37C22×#1055—42no—
38C22×#1055—42no—
39C22×#1055C2×C411yescharacteristic
40C22×#1055C2×C411yescharacteristic
41C22×#1055C2×C411yescharacteristic
42C22×#1055C2×C411yescharacteristic
43C22×#1055D412yes—
44C22×#1055D412yes—
45C13×C22⋊C8—22no—
46C13×C22⋊C8C2×C414yes—
47#88074—24no—
48#88071—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#88055—44no—
52C4⋊#1055—22no—
53C4×#1055—21no—
54C4×#1055—21no—
55#8160—131nomaximal, Sylow
56C24×C13C4211yescharacteristic
57C24×C13C22×C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13M1614yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C4211yescharacteristic
68C22×C4×C13C4211yescharacteristic
69C22×C4×C13C4211yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13#4112yes—
74C22×Dic13—24no—
75C2×C8×C13—24no—
76C2×C8×C13—42no—
77C2×C8×C13—42no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—22no—
81C42×C13—21no—
82C42×C13—21no—
83C22⋊Dic13—24no—
84C22⋊Dic13—24no—
85C4×Dic13—42no—
86C4×Dic13—42no—
87C2×#1055—22no—
88C2×#1055—24no—
89C2×#1055—21no—
90C2×#1055—21no—
91C2×#1055—41no—
92C2×#1055—42no—
93C2×#1055—42no—
94C2×#1055—42no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055C22⋊C412yes—
98C2×#1055C22⋊C411yescharacteristic
99C2×#1055C22⋊C411yescharacteristic
100C2×C8×D4—131no—
101C4×#99—131no—
102#1752—132no—
103#1459D1311yescharacteristic
104#1282—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13#9712yescomplemented
112C23×C13C2×C4211yescharacteristic
113C23×C13C4×D412yes—
114C23×C13C2×M1612yes—
115C23×C13#13112yes—
116D4×C13—28no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#9712yescomplemented
133C2×C4×C13C2×C22⋊C411yescharacteristic
134C2×C4×C13#11711yescharacteristic
135C2×C4×C13C4×D412yes—
136C2×Dic13—44no—
137C2×Dic13—44no—
138C2×Dic13—44no—
139C8×C13—44no—
140#1055—21no—
141#1055—22no—
142#1055—41no—
143#1055—41no—
144#1055#9912yescomplemented
145C23×C8—131no—
146C23×C8—131no—
147C2×C4×D4C2×D1311yescharacteristic
148C8×D4—262no—
149C8×D4—262no—
150C2×C4⋊C8—131no—
151C2×#99—132no—
152C2×C22⋊C8—131no—
153C2×C22⋊C8—131no—
154C2×C22⋊C8C2×D1312yes—
155C2×#97—262no—
156C2×C4×C8—131no—
157C4×C22⋊C4—132no—
158#342—132no—
159#336—262no—
160#324Dic1312yescomplemented
161#323Dic1312yescomplemented
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C4×C22⋊C411yescharacteristic
174C22×C13C2×#9711yescharacteristic
175C22×C13#40511yescharacteristic
176C22×C13#43514yes—
177C4×C13—22no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#9911yescharacteristic
183C4×C13#41011yescharacteristic
184Dic13—84no—
185C22×D4C4×D1311yescharacteristic
186C23×C4C4×D1311yescharacteristic
187C23×C4C22×D1311yescharacteristic
188C22×C8—22no—
189C22×C8—131no—
190C22×C8—132no—
191C22×C8—131no—
192C22×C8—132no—
193C22×C8—131no—
194C22×C8—131no—
195C22×C8—261no—
196C22×C8—261no—
197C22×C8—522no—
198C22×C8—522no—
199C4×D4—22no—
200C4×D4—22no—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C22⋊C4—134no—
203C2×C22⋊C4C4×D1311yescharacteristic
204C2×C22⋊C4C2×Dic1311yescharacteristic
205C2×C42—262no—
206C2×C42C4×D1311yescharacteristic
207C4⋊C8—262no—
208#99—264no—
209C22⋊C8—22no—
210C22⋊C8—262no—
211C22⋊C8—262no—
212C22⋊C8C2×Dic1314yes—
213#97—524no—
214C4×C8—261no—
215C4×C8—261no—
216#95—262no—
217C2×C13—24no—
218C2×C13—21no—
219C2×C13—21no—
220C2×C13—42no—
221C2×C13#175211yescharacteristic
222C2×C13C4×#9911yescharacteristic
223C2×C13#175711yescharacteristic
224C24C4×Dic1311yescharacteristic
225C24C2×C4×D1311yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4#609414yes—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—264no—
236C22×C4C4×Dic1311yescharacteristic
237C22×C4C4×Dic1311yescharacteristic
238C22×C4C4×Dic1311yescharacteristic
239C22×C4C2×C4×D1311yescharacteristic
240C22×C4D4×D1312yes—
241C22×C4#612912yes—
242C22×C4C22×Dic1311yescharacteristic
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—132no—
249C2×C8—264no—
250C2×C8—262no—
251C2×C8—261no—
252C2×C8—261no—
253C2×C8—522no—
254C2×C8—521no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—521no—
258C2×C8—521no—
259C4⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—264no—
263C22⋊C4—264no—
264C42—21no—
265C42—21no—
266C42—522no—
267C42—522no—
268C13#816011yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#8805512yescomplemented
276C23#8813512yes—
277C23C2×#609412yes—
278C23#8816112yes—
279C23C2×C4×Dic1311yescharacteristic
280D4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—524no—
297C2×C4—524no—
298C2×C4—524no—
299C2×C4#8805512yescomplemented
300C2×C4#8813111yescharacteristic
301C2×C4C22⋊C4×D1311yescharacteristic
302C2×C4D4×Dic1312yes—
303C8—44no—
304C8—132no—
305C8—262no—
306C8—261no—
307C8—521no—
308C8—521no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22#1171839114yes—
321C22C22⋊C4×Dic1311yescharacteristic
322C22C2×#8805511yescharacteristic
323C22#1171878311yescharacteristic
324C4—22no—
325C4—21no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—1044no—
330C4#1171840111yescharacteristic
331C4D13×#9911yescharacteristic
332C2—24no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1311461511yescharacteristic
337C2#99×Dic1311yescharacteristic
338C2#1311463911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC23×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1459C2
socleC22×C13C4×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#1459D13
hypocenterC13#8160
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13114615C2semidirect
4. #13112682C2semidirect
7. C23×#1055C4semidirect
12. C2×C22⋊#1055C4semidirect
17. C2×C4⋊#1055C4semidirect
18. C2×C4×#1055C4semidirect
19. C13×#324C4semidirect
20. C13×#323C4semidirect
111. C23×C13#97semidirect
132. C2×C4×C13#97semidirect
144. #1055#99semidirect
160. #324Dic13semidirect
161. #323Dic13semidirect
268. C13#8160semidirect
275. C23#88055semidirect
299. C2×C4#88055semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#10552
C4×#880742
#131146152
#131126822
C13×#14592
#816013