Finite Group Databasebeta

← #15773792

Subgroups — #15773792

Order 3328.

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

normal subgroups only

This group has 390 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#13112857C212yesmaximal
4#13112836C212yesmaximal
5C13×#2599C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C13×#398C411yescharacteristic, complemented
9C13×#397C2211yescharacteristic
10C13×#395C411yescharacteristic, complemented
11C13×#393C2211yescharacteristic
12C13×#388—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#385—21no—
16C13×#383C411yescharacteristic, complemented
17#11718872—21no—
18#11718586—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C13×#117—41no—
28C13×#117—41no—
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⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4C2311yescharacteristic
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C22⋊Dic13—22no—
43C13×#95—21no—
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#11842—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C2×Q8×C13—42no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
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#2599D1311yescharacteristic
95#1820—131no—
96#1458—131no—
97#1351—132no—
98#1344—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13512yes—
105Q8×C13—42no—
106Q8×C13—42no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
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—41no—
133C2×C4×C13—41no—
134C2×C4×C13#9911yescharacteristic
135C2×C4×C13#9911yescharacteristic
136C2×Dic13—82no—
137C2×Dic13—82no—
138C2×Dic13—82no—
139#1055—82no—
140C2×C4×Q8Dic1311yescharacteristic, complemented
141C2×#117C2×D1311yescharacteristic
142#431—261no—
143#398Dic1311yescharacteristic, complemented
144#397C2×D1311yescharacteristic
145#395Dic1311yescharacteristic, complemented
146#393C2×D1311yescharacteristic
147#388—21no—
148#387—21no—
149#387—21no—
150#385—21no—
151#383Dic1311yescharacteristic, complemented
152#381—261no—
153#342—132no—
154#342—261no—
155#324—261no—
156#323—132no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—81no—
164C22×C13C2×#9911yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13—81no—
178Dic13—162no—
179C22×Q8C2×Dic1311yescharacteristic
180C23×C4C22⋊D1311yescharacteristic
181C4×Q8—41no—
182C4×Q8—41no—
183#117—41no—
184#117—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×Dic1311yescharacteristic
189C2×C4⋊C4C2×Dic1311yescharacteristic
190C2×C4⋊C4C22⋊D1311yescharacteristic
191C2×C22⋊C4—21no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—262no—
194C2×C22⋊C4C22⋊D1311yescharacteristic
195C2×C22⋊C4C22×D1311yescharacteristic
196C2×C42—21no—
197C2×C42C2×Dic1311yescharacteristic
198C2×C42C22⋊D1311yescharacteristic
199C4⋊C8—521no—
200C22⋊C8—262no—
201C4×C8—521no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—521no—
209#95—521no—
210#95C2×Dic1311yescharacteristic
211#95C2×Dic1311yescharacteristic
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—42no—
215C2×C13#151611yescharacteristic
216C2×C13#212011yescharacteristic
217C2×C13#212911yescharacteristic
218C24C2×C22⋊D1311yescharacteristic
219C2×Q8—42no—
220C2×Q8—41no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—522no—
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C22×Dic1311yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236C2×C8—522no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—522no—
249C22⋊C4—522no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—42no—
255C13#1184211yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23#8820412yes—
261C23C2×C22⋊Dic1311yescharacteristic
262Q8—42no—
263Q8—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
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—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—1042no—
292C2×C4—1042no—
293C2×C4—1042no—
294C2×C4#8807411yescharacteristic
295C2×C4#8807411yescharacteristic
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22C2×#8807411yescharacteristic
305C22#1171889411yescharacteristic
306C22#1171889711yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—42no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—2082no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2#1311339211yescharacteristic
323C2#1311647711yescharacteristic
324C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2599C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2599D13
hypocenterC13#11842
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2599

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
8. C13×#398C4semidirect
10. C13×#395C4semidirect
16. C13×#383C4semidirect
140. C2×C4×Q8Dic13semidirect
143. #398Dic13semidirect
145. #395Dic13semidirect
151. #383Dic13semidirect
255. C13#11842semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131502
#131128572
#131128362
C13×#25992
#1184213