Finite Group Databasebeta

← #16787669

Subgroups — #16787669

Order 3328.

452 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 88 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#13130541C211yesmaximal, characteristic
2#13130069C211yesmaximal, characteristic
3#13129820C214yesmaximal, complemented
4#13120603C211yesmaximal, characteristic
5C2×D13⋊M16—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×#88200—21no—
8C2×#88126C2211yescharacteristic
9#11719119—21no—
10#11718891—21no—
11#11718654—21no—
12#11718654C412yes—
13#11718641—21no—
14#11718641C2212yes—
15#11718597C411yescharacteristic
16#11718291—21no—
17#11718291C2212yes—
18#11718287—21no—
19#11718286C2212yes—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×#6122—22no—
23D13⋊M16—24no—
24D13⋊M16—42no—
25C2×#6118—41no—
26C2×D13⋊C8—41no—
27C13×C4⋊Q8—41no—
28C13×C4⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C42×C13C2×C411yescharacteristic
32#88200—42no—
33#88200—42no—
34C2×#6103—22no—
35C2×#6103C2×C411yescharacteristic
36C2×#6103D411yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×#6101—22no—
39C2×#6101D411yescharacteristic
40C2×#6101C2311yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42#88126—41no—
43#88126—41no—
44C22⋊#1057—22no—
45C4⋊#1057—41no—
46C4×#1057—41no—
47#88071—21no—
48#88071—22no—
49#88071—22no—
50#88071C2×C412yes—
51#11700—131nomaximal, Sylow
52C23×D13C22⋊C411yescharacteristic
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—42no—
56C2×Q8×C13—42no—
57C22×C4×C13—22no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—22no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—22no—
68C2×C4×D13D812yes—
69C2×C4×D13SD1612yes—
70#6122—24no—
71#6122—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74#6118—44no—
75D13⋊C8—44no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C42×C13—21no—
79C42×C13—21no—
80#6103—41no—
81#6103—41no—
82#6103—44no—
83C4⋊Dic13—42no—
84#6101—41no—
85#6101—41no—
86#6101—42no—
87#6101—42no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90#2621—131no—
91#1742—131no—
92#1458—131no—
93#1346—134no—
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13#10212yes—
100Q8×C13—82no—
101Q8×C13—82no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#10212yes—
112C2×C4×C13#10412yes—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13C2×D811yescharacteristic
123C2×Dic13C2×SD1611yescharacteristic
124C4×D13—22no—
125C4×D13—22no—
126C4×D13—22no—
127C4×D13—22no—
128#1057—44no—
129#1057—82no—
130C22×M16—261no—
131C2×C4⋊Q8#26111yescharacteristic
132C2×C22⋊Q8—261no—
133C2×#117—131no—
134#431—261no—
135#398—132no—
136#398—261no—
137#397—132no—
138#397—261no—
139#391—261no—
140#382—131no—
141#343—132no—
142#343—261no—
143#324—132no—
144#323—261no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13C2×#9911yescharacteristic
148C22×C13C2×#10211yescharacteristic
149C22×C13C2×#10411yescharacteristic
150C2×D13—22no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—42no—
154C2×D13—81no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—82no—
158C4×C13#32712yes—
159C4×C13#32712yes—
160Dic13—21no—
161Dic13—21no—
162Dic13—41no—
163Dic13—41no—
164Dic13—82no—
165C22×Q8—21no—
166C23×C4—131no—
167C2×M16—262no—
168C2×M16—264no—
169C2×M16—522no—
170C2×M16—521no—
171C22×C8—521no—
172C4⋊Q8—41no—
173C4⋊Q8—41no—
174C22⋊Q8—522no—
175C22⋊Q8—522no—
176#117—521no—
177#117—521no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—262no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4C2×#26112yes—
184C2×C22⋊C4—131no—
185C2×C22⋊C4—131no—
186C2×C22⋊C4—262no—
187C2×C42—131no—
188C2×C42C2×#26111yescharacteristic
189C4⋊C8—521no—
190C22⋊C8—262no—
191C4×C8—521no—
192#95—132no—
193#95—262no—
194#95—262no—
195#95—261no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13C2×#32711yescharacteristic
199C2×C13#212311yescharacteristic
200C2×C13#213511yescharacteristic
201D13—42no—
202C24—131no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×Q8—41no—
206C2×Q8—41no—
207C22×C4—22no—
208C22×C4—131no—
209C22×C4—132no—
210C22×C4—132no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—262no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4—262no—
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22⋊#26111yescharacteristic
219C22×C4C22×#26111yescharacteristic
220M16—264no—
221M16—522no—
222M16—524no—
223C2×C8—524no—
224C2×C8—522no—
225C2×C8—522no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—521no—
229C4⋊C4—521no—
230C4⋊C4—522no—
231C4⋊C4—522no—
232C4⋊C4—522no—
233C22⋊C4—521no—
234C22⋊C4—521no—
235C22⋊C4—524no—
236C42—21no—
237C42—21no—
238C42—261no—
239C42—261no—
240C13#1170011yescharacteristic, complemented, Sylow
241C23—132no—
242C23—261no—
243C23—261no—
244C23—521no—
245C23—521no—
246C23C2×C22⋊#26111yescharacteristic
247Q8—82no—
248Q8—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—131no—
257C2×C4—131no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4#8811512yes—
272C2×C4#8811612yes—
273C2×C4#8811911yescharacteristic
274C2×C4#8811911yescharacteristic
275C8—524no—
276C8—1042no—
277C22—21no—
278C22—21no—
279C22—262no—
280C22—522no—
281C22—521no—
282C22—521no—
283C22—1041no—
284C22C2×#8811511yescharacteristic
285C22C2×#8811611yescharacteristic
286C22C2×#8811911yescharacteristic
287C4—41no—
288C4—41no—
289C4—82no—
290C4—261no—
291C4—261no—
292C4—521no—
293C4—521no—
294C4—1042no—
295C4#1171829212yes—
296C4#1171829212yes—
297C2—21no—
298C2—21no—
299C2—522no—
300C2C2×#1171829211yescharacteristic
301C2#1313109811yescharacteristic
302C2#1313113811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×#6101C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11700
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129820C2semidirect
240. C13#11700semidirect

Maximal subgroups

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

subgroupindex
#131305412
#131300692
#131298202
#131206032
#1170013