Finite Group Databasebeta

← #15778096

Subgroups — #15778096

Order 3328.

532 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117379C211yesmaximal, characteristic
2C2×#11718069C212yesmaximal
3#101×Dic13C212yesmaximal, complemented
4#13112963C211yesmaximal, characteristic, complemented
5C13×#1394C211yesmaximal, characteristic, complemented
6C2×#88201C2211yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×#88147C411yescharacteristic
9C2×C13×#101C2212yes—
10C13×#391C2211yescharacteristic
11C2×#88076C2212yes—
12M16×Dic13—22no—
13#11718638C411yescharacteristic
14#11718600C411yescharacteristic
15C42×Dic13C411yescharacteristic
16#11718331—22no—
17#11718327—22no—
18#11718146—22no—
19#11718069C418yescomplemented
20C22×Q8×C13C2311yescharacteristic
21C22×D52C2×C411yescharacteristic
22C22×C4×D13—21no—
23C2×C13×M16—22no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26#88201—21no—
27#88201—21no—
28#88201C2×C414yes—
29Q8×Dic13—41no—
30Q8×Dic13—41no—
31C2×#6103—22no—
32C2×#6103—21no—
33C2×#6103—22no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13D412yes—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D412yes—
41C2×#6099—22no—
42#88147—41no—
43#88147—41no—
44C13×#101—22no—
45C13×#101C2×C414yescomplemented
46C13×#95—22no—
47#88076—22no—
48#88076C2×C414yescomplemented
49#88071—22no—
50#88055—42no—
51C8×Dic13—42no—
52C4×#355—131nomaximal, Sylow
53C23×D13—21no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C22×C412yes—
57C2×Q8×C13#4111yescharacteristic
58C2×Q8×C13#4111yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C412yes—
66C22×Dic13C22⋊C411yescharacteristic
67C2×D52—21no—
68C2×D52—41no—
69C2×D52—41no—
70C2×D52C4212yes—
71C2×C4×D13—44no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C13×M16—24no—
75C13×M16—42no—
76C2×C8×C13—42no—
77C13×C4⋊C4—41no—
78C42×C13—41no—
79#6103—24no—
80#6103—24no—
81#6103—42no—
82#6103—44no—
83C4⋊Dic13—41no—
84C4⋊Dic13—42no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—21no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—42no—
91C4×Dic13—42no—
92C4×Dic13C4212yes—
93#6099—24no—
94#6099—42no—
95C2×#1055—42no—
96C4×#124—131no—
97C2×#355—132no—
98C4×#101—132no—
99#1394—131no—
100#1394D1311yescharacteristic, complemented
101C23×C13C2×C22⋊C411yescharacteristic
102C22×D13—22no—
103C22×D13—42no—
104C22×D13—42no—
105C22×D13—41no—
106C22×D13—41no—
107Q8×C13—42no—
108Q8×C13—41no—
109Q8×C13—41no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13C2×C4211yescharacteristic
120C2×C4×C13#11711yescharacteristic
121C2×C4×C13C4×D412yes—
122C2×C4×C13C4×D412yes—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—21no—
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131C2×Dic13#9911yescharacteristic
132C2×Dic13#9911yescharacteristic
133D52—42no—
134D52—42no—
135C4×D13—82no—
136C4×D13—82no—
137C8×C13—44no—
138#1055—44no—
139C2×#124—131no—
140C2×C4×Q8—131no—
141C2×C4×D4—131no—
142C2×#101—132no—
143C2×#101C2×D1312yes—
144C4×M16—262no—
145#391C2×D1311yescharacteristic
146#390—131no—
147#388—262no—
148#382—131no—
149C4×C22⋊C4—262no—
150C43—131no—
151#355—138no—
152#343—262no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13C4×C22⋊C411yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13#41011yescharacteristic
158C2×D13—44no—
159C2×D13—42no—
160C2×D13—82no—
161C2×D13—81no—
162C2×D13—81no—
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—42no—
168C4×C13—81no—
169Dic13—21no—
170Dic13—42no—
171Dic13—41no—
172Dic13—42no—
173Dic13#35512yescomplemented
174C22×Q8C22×D1311yescharacteristic
175C22×D4—131no—
176C23×C4—261no—
177C2×M16—22no—
178C2×M16—262no—
179#124—134no—
180#124—261no—
181#124—261no—
182C4×Q8—521no—
183C4×Q8—521no—
184C4×D4—521no—
185C4×D4—521no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—132no—
188C2×C4⋊C4C4×D1311yescharacteristic
189C2×C22⋊C4—262no—
190C2×C22⋊C4—261no—
191C2×C22⋊C4—262no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—132no—
195C2×C42—261no—
196C2×C42—261no—
197C2×C42C4×D1311yescharacteristic
198#101—22no—
199#101—134no—
200#101—262no—
201#101C4×D1314yescomplemented
202#97—522no—
203C4×C8—522no—
204#95—22no—
205#95—262no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13C4×#9911yescharacteristic
209C2×C13C2×#35511yescharacteristic
210C2×C13#213211yescharacteristic
211D13—82no—
212C24—261no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8C2×C4×D1312yes—
216C2×Q8#612911yescharacteristic
217C2×Q8#613111yescharacteristic
218C2×D4—132no—
219C2×D4—261no—
220C2×D4—521no—
221C2×D4—521no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—131no—
225C22×C4—132no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—521no—
229C22×C4—521no—
230C22×C4—524no—
231C22×C4C2×C4×D1311yescharacteristic
232C22×C4D4×D1312yes—
233M16—24no—
234M16—42no—
235M16—264no—
236M16—522no—
237C2×C8—42no—
238C2×C8—522no—
239C4⋊C4—41no—
240C4⋊C4—521no—
241C4⋊C4—522no—
242C22⋊C4—264no—
243C22⋊C4—264no—
244C22⋊C4—524no—
245C22⋊C4—522no—
246C42—41no—
247C42—132no—
248C42—262no—
249C42—262no—
250C42—261no—
251C42—261no—
252C42—261no—
253C42—522no—
254C42—522no—
255C13C4×#35511yescharacteristic, complemented, Sylow
256C23—262no—
257C23—522no—
258C23—522no—
259C23—521no—
260C23—521no—
261C23C22⋊C4×D1311yescharacteristic
262Q8—42no—
263Q8—41no—
264Q8—41no—
265D4—522no—
266D4—522no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—262no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4—1042no—
287C2×C4—1042no—
288C2×C4C42×D1311yescharacteristic
289C2×C4#8813512yes—
290C2×C4#8814611yescharacteristic
291C2×C4#8814712yes—
292C8—44no—
293C8—524no—
294C22—21no—
295C22—21no—
296C22—524no—
297C22—522no—
298C22—1042no—
299C22—1041no—
300C22—1041no—
301C22#1171832711yescharacteristic
302C22#1171840111yescharacteristic
303C22D13×#9911yescharacteristic
304C4—22no—
305C4—22no—
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—132no—
311C4—261no—
312C4—522no—
313C4—521no—
314C4—522no—
315C2—21no—
316C2—21no—
317C2—1042no—
318C2#1311462311yescharacteristic
319C2D13×#35511yescharacteristic
320C2#1311652011yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC13×#1394C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC22×Q8×C13C23
hypercenter#1394D13
hypocenterC13C4×#355
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #101×Dic13C2semidirect
4. #13112963C2semidirect
5. C13×#1394C2semidirect
19. #11718069C4semidirect
45. C13×#101C2×C4semidirect
48. #88076C2×C4semidirect
100. #1394D13semidirect
173. Dic13#355semidirect
201. #101C4×D13semidirect
255. C13C4×#355semidirect

Maximal subgroups

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

subgroupindex
#131173792
C2×#117180692
#101×Dic132
#131129632
C13×#13942
C4×#35513