Finite Group Databasebeta

← #15773812

Subgroups — #15773812

Order 3328.

382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112860C212yesmaximal
4#13112836C212yesmaximal
5C13×#2611C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#398C411yescharacteristic, complemented
11C13×#397C2211yescharacteristic
12C13×#389—21no—
13C13×#388—21no—
14C13×#387—21no—
15C13×#385—21no—
16C13×#376C411yescharacteristic, complemented
17#11718872—21no—
18#11718586—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#125—41no—
25C13×#125—41no—
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88071—41no—
52#88071—41no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55C4×#1055—41no—
56#11846—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C2×#1055—42no—
94#2611D1311yescharacteristic
95#1820—131no—
96#1458—131no—
97#1352—132no—
98#1344—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13512yes—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13#9911yescharacteristic
134C2×Dic13—82no—
135C2×Dic13—82no—
136C2×Dic13—82no—
137#1055—82no—
138C2×#125Dic1311yescharacteristic, complemented
139C2×#117C2×D1311yescharacteristic
140#431—261no—
141#400Dic1311yescharacteristic, complemented
142#399C2×D1311yescharacteristic
143#398Dic1311yescharacteristic, complemented
144#397C2×D1311yescharacteristic
145#389—21no—
146#388—21no—
147#387—21no—
148#385—21no—
149#381—261no—
150#376Dic1311yescharacteristic, complemented
151#342—132no—
152#342—261no—
153#324—261no—
154#323—132no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—42no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—81no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—81no—
174C4×C13—81no—
175C4×C13—81no—
176Dic13—162no—
177C23×C4C22⋊D1311yescharacteristic
178#125—41no—
179#125—41no—
180#117—41no—
181#117—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×Dic1311yescharacteristic
187C2×C4⋊C4C2×Dic1311yescharacteristic
188C2×C4⋊C4C2×Dic1311yescharacteristic
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4C22×D1311yescharacteristic
195C2×C42—21no—
196C2×C42C2×Dic1311yescharacteristic
197C2×C42C22⋊D1311yescharacteristic
198C4⋊C8—521no—
199C22⋊C8—262no—
200C4×C8—521no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—521no—
207#95—521no—
208#95C2×Dic1311yescharacteristic
209#95C2×Dic1311yescharacteristic
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#151611yescharacteristic
214C2×C13#212311yescharacteristic
215C2×C13#212611yescharacteristic
216C24C2×C22⋊D1311yescharacteristic
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—522no—
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22⋊Dic1311yescharacteristic
228C22×C4C22⋊Dic1311yescharacteristic
229C22×C4C22⋊Dic1311yescharacteristic
230C22×C4C22×Dic1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—522no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—522no—
247C22⋊C4—522no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—42no—
253C13#1184611yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#8820412yes—
259C23C2×C22⋊Dic1311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—1042no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8807411yescharacteristic
291C2×C4#8807411yescharacteristic
292C8—1042no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#8807411yescharacteristic
301C22#1171889411yescharacteristic
302C22#1171889711yescharacteristic
303C4—21no—
304C4—21no—
305C4—42no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—2082no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1311339211yescharacteristic
319C2#1311649011yescharacteristic
320C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2611C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2611D13
hypocenterC13#11846
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2611

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
8. C13×#400C4semidirect
10. C13×#398C4semidirect
16. C13×#376C4semidirect
138. C2×#125Dic13semidirect
141. #400Dic13semidirect
143. #398Dic13semidirect
150. #376Dic13semidirect
253. C13#11846semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131502
#131128602
#131128362
C13×#26112
#1184613