Finite Group Databasebeta

← #16787232

Subgroups — #16787232

Order 3328.

394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130099C211yesmaximal, characteristic
2#13130079C211yesmaximal, characteristic
3#13129767C212yesmaximal
4#13129766C212yesmaximal
5#13119822C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×#88198C411yescharacteristic
9C2×#88198C411yescharacteristic
10#11719128—21no—
11#11719119—21no—
12#11718891C2211yescharacteristic
13#11718645—21no—
14#11718645—21no—
15#11718633—21no—
16#11718633—21no—
17C4×#6101C411yescharacteristic
18#11718590C2211yescharacteristic
19#11718285—21no—
20#11718285—21no—
21#11718285C2212yes—
22#11718285C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13C2×C411yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C13×C4⋊Q8—42no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C42×C13C2×C411yescharacteristic
30Q8×Dic13—41no—
31Q8×Dic13—41no—
32#88198—41no—
33#88198—41no—
34#88198—42no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13C2311yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C22⋊#1057—22no—
48C22⋊#1057—22no—
49#88112—41no—
50#88110—41no—
51C4⋊#1057—41no—
52C4×#1057—41no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#11568—131nomaximal, Sylow
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×Dic26—22no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×#1057—42no—
80C2×#1057—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C42×C13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87#6101—24no—
88#6101—42no—
89#6101—42no—
90#6101—42no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—41no—
100#2546—131no—
101#1467—131no—
102#1461—131no—
103#1319—132no—
104#1319—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—44no—
107Q8×C13—82no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#10012yes—
122C2×C4×C13#13112yes—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13#9911yescharacteristic
137C2×Dic13#9911yescharacteristic
138Dic26—82no—
139#1057—82no—
140#1057—82no—
141C2×C4⋊Q8—131no—
142C2×C4⋊Q8—131no—
143C2×C4⋊Q8#26111yescharacteristic
144C2×C4×Q8—131no—
145#432—261no—
146#431—261no—
147#398—261no—
148#398—261no—
149#391—131no—
150#391—131no—
151#389—261no—
152#389—261no—
153C4×C4⋊C4—131no—
154#324—132no—
155#324—132no—
156#324—261no—
157#324—261no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13#40811yescharacteristic
161C22×C13C2×#9911yescharacteristic
162C22×C13C2×#10011yescharacteristic
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—81no—
168Dic13—21no—
169Dic13—42no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—81no—
174Dic13#35612yes—
175C22×Q8—131no—
176C22×Q8C2×#26111yescharacteristic
177C22×Q8C2×#26111yescharacteristic
178C4⋊Q8—42no—
179C4⋊Q8—521no—
180C4⋊Q8—521no—
181C4⋊Q8—522no—
182C4×Q8—521no—
183C4×Q8—521no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42C2×#26111yescharacteristic
199C4⋊C8—521no—
200C4⋊C8—521no—
201C22⋊C8—262no—
202C22⋊C8—262no—
203#97—521no—
204C4×C8—521no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#147111yescharacteristic
213C2×C13#212911yescharacteristic
214C2×C13C2×#35611yescharacteristic
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—262no—
222C2×Q8—521no—
223C2×Q8—521no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4C22⋊#26111yescharacteristic
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22×#26111yescharacteristic
235C2×C8—522no—
236C2×C8—522no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—264no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—522no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—522no—
247C4⋊C4—522no—
248C42—41no—
249C42—261no—
250C42—261no—
251C42—261no—
252C42—261no—
253C42—261no—
254C42—261no—
255C42—521no—
256C13#1156811yescharacteristic, complemented, Sylow
257C23C2×C22⋊#26111yescharacteristic
258Q8—44no—
259Q8—82no—
260Q8—1042no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4#8812112yes—
290C2×C4#8823812yes—
291C8—1042no—
292C8—1042no—
293C22—21no—
294C22—21no—
295C22D13⋊#9911yescharacteristic
296C22#1171914611yescharacteristic
297C22C2×#8812111yescharacteristic
298C4—22no—
299C4—22no—
300C4—42no—
301C4—41no—
302C4—81no—
303C4—132no—
304C4—261no—
305C4—522no—
306C4—521no—
307C4—521no—
308C4—521no—
309C4—1041no—
310C2—21no—
311C2—21no—
312C2#1313011211yescharacteristic
313C2#1313111911yescharacteristic
314C2D13⋊#35611yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11568
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
256. C13#11568semidirect

Maximal subgroups

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

subgroupindex
#131300992
#131300792
#131297672
#131297662
#131198222
#1156813