Finite Group Databasebeta

← #16788193

Subgroups — #16788193

Order 3328.

382 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 66 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#13130733C211yesmaximal, characteristic
2#13130069C211yesmaximal, characteristic
3#13129833C212yesmaximal
4#13129816C212yesmaximal
5#13120536C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C2×#88126C2211yescharacteristic
8#11719135—21no—
9#11719119—21no—
10#11718654C2211yescharacteristic
11#11718653C2211yescharacteristic
12#11718651—21no—
13#11718650—21no—
14#11718643C411yescharacteristic, complemented
15#11718641C411yescharacteristic, complemented
16#11718639—21no—
17#11718633—21no—
18#11718593C411yescharacteristic, complemented
19#11718289—21no—
20#11718289C2212yes—
21#11718287C2212yes—
22#11718286—21no—
23C22×C4×D13D411yescharacteristic
24C2×C22⋊#261—22no—
25C13×#125—41no—
26C13×#125—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103D411yescharacteristic
35C2×#6103C2311yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101C2×C411yescharacteristic
39C2×#6101D411yescharacteristic
40C2×C4×Dic13—21no—
41C2×C4×Dic13D411yescharacteristic
42#88126—41no—
43#88126—41no—
44C22⋊#1057—22no—
45(C2×#261)⋊C4—41no—
46(C2×#261)⋊C4—41no—
47C4⋊#1057—41no—
48C4×#1057—41no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56#11846—131nomaximal, Sylow
57C23×D13C2×D411yescharacteristic
58C22×#261—42no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×C4×D13—22no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—41no—
73C22⋊#261—42no—
74C22⋊#261—42no—
75C2×#1057—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C42×C13—21no—
82C42×C13—21no—
83#6103—41no—
84#6103—41no—
85#6103—42no—
86#6103—42no—
87#6101—41no—
88#6101—41no—
89#6101—42no—
90#6101—42no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—42no—
94#2611—131no—
95#1820—131no—
96#1458—131no—
97#1352—132no—
98#1344—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—41no—
103C22×D13—41no—
104C22×D13#13512yes—
105C2×#261—82no—
106C2×#261—82no—
107C2×#261—82no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×Dic13—22no—
123C2×Dic13—21no—
124C2×Dic13—21no—
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—
135C4×D13—42no—
136C4×D13—42no—
137#1057—82no—
138C2×#125#26111yescharacteristic, complemented
139C2×#117—131no—
140#431—261no—
141#400—131no—
142#399—131no—
143#398—131no—
144#397—131no—
145#389—261no—
146#388—261no—
147#387—261no—
148#385—261no—
149#381—261no—
150#376—131no—
151#342—132no—
152#342—261no—
153#324—261no—
154#323—132no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13C2×#9911yescharacteristic
158C22×C13#41611yescharacteristic
159C22×C13#42111yescharacteristic
160C2×D13—22no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—42no—
164C2×D13—81no—
165#261—162no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—81no—
171C4×C13—81no—
172Dic13—42no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—81no—
177C23×C4—131no—
178#125—41no—
179#125—41no—
180#117—521no—
181#117—521no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—261no—
193C2×C22⋊C4—261no—
194C2×C22⋊C4—262no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42C2×#26111yescharacteristic
198C4⋊C8—521no—
199C22⋊C8—262no—
200C4×C8—521no—
201#95—131no—
202#95—131no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—521no—
209#95—521no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#151611yescharacteristic
213C2×C13#212311yescharacteristic
214C2×C13#212611yescharacteristic
215D13—42no—
216C24—131no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—262no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4—521no—
228C22×C4—522no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—522no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C4⋊C4—522no—
241C4⋊C4—522no—
242C22⋊C4—521no—
243C22⋊C4—521no—
244C22⋊C4—522no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C22⋊C4—522no—
248C42—21no—
249C42—21no—
250C42—261no—
251C42—261no—
252C42—522no—
253C13#1184611yescharacteristic, complemented, Sylow
254C23—132no—
255C23—261no—
256C23—261no—
257C23—521no—
258C23—521no—
259C23C2×C22⋊#26111yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—1042no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8811911yescharacteristic
291C2×C4#8811911yescharacteristic
292C8—1042no—
293C22—21no—
294C22—21no—
295C22—262no—
296C22—522no—
297C22—521no—
298C22—521no—
299C22—1041no—
300C22#1171916511yescharacteristic
301C22#1171916611yescharacteristic
302C22C2×#8811911yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—522no—
310C4—521no—
311C4—521no—
312C4—521no—
313C4—1041no—
314C4—2082no—
315C2—21no—
316C2—21no—
317C2—522no—
318C2#1313026211yescharacteristic
319C2#1313109811yescharacteristic
320C2#1313110711yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socleC22×C13C2×#99
prime radicalC23×D13C2×D4
cosocleC2×#6103C23
hypercenterC2×#125#261
hypocenterC13#11846
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
14. #11718643C4semidirect
15. #11718641C4semidirect
18. #11718593C4semidirect
138. C2×#125#261semidirect
253. C13#11846semidirect

Maximal subgroups

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

subgroupindex
#131307332
#131300692
#131298332
#131298162
#131205362
#1184613