Finite Group Databasebeta

← #16787649

Subgroups — #16787649

Order 3328.

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

normal subgroups only

This group has 468 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#13130535C211yesmaximal, characteristic
2#13130069C211yesmaximal, characteristic
3#13129816C214yesmaximal
4#13120603C211yesmaximal, characteristic
5C2×#88237—21no—
6C2×C13×C4⋊Q8C411yescharacteristic, complemented
7C2×#88200—21no—
8C2×#88126C2211yescharacteristic
9#11719119—21no—
10#11718891—21no—
11#11718654—21no—
12#11718654C2212yes—
13#11718641—21no—
14#11718641C412yescomplemented
15#11718597C411yescharacteristic, complemented
16#11718289—21no—
17#11718289C2212yes—
18#11718287C2212yes—
19#11718286—21no—
20C22×Q8×C13—21no—
21C22×C4×D13D411yescharacteristic
22C2×C22⋊#261—22no—
23#88237—24no—
24#88237—42no—
25C2×C4⋊#261—41no—
26C2×C4×#261—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×#6103D411yescharacteristic
36C2×#6103C2311yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×#6101—22no—
39C2×#6101C2×C411yescharacteristic
40C2×#6101D411yescharacteristic
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#11694—131nomaximal, Sylow
52C23×D13C2×D411yescharacteristic
53C22×#261—42no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13—42no—
57C2×Q8×C13—42no—
58C22×C4×C13—22no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—22no—
69C2×C4×D13D812yes—
70C2×C4×D13SD1612yes—
71C22⋊#261—24no—
72C22⋊#261—42no—
73C2×#1057—42no—
74C4⋊#261—44no—
75C4×#261—44no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C42×C13—21no—
79C42×C13—21no—
80#6103—41no—
81#6103—41no—
82#6103—42no—
83#6103—42no—
84C4⋊Dic13—42no—
85#6101—41no—
86#6101—41no—
87#6101—44no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90#2621—131no—
91#1740—131no—
92#1458—131no—
93#1344—134no—
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13C2×D811yescharacteristic
100C22×D13C2×SD1611yescharacteristic
101C2×#261—44no—
102C2×#261—82no—
103C2×#261—82no—
104Q8×C13—82no—
105Q8×C13—82no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#10212yes—
116C2×C4×C13#10412yes—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13#10212yes—
127C4×D13—22no—
128C4×D13—22no—
129C4×D13—22no—
130C4×D13—22no—
131#1057—82no—
132C2×C4⋊Q8#26111yescharacteristic, complemented
133C2×C22⋊Q8—261no—
134C2×#117—131no—
135C2×#117—261no—
136#431—261no—
137#398—132no—
138#398—261no—
139#397—132no—
140#397—261no—
141#391—261no—
142#382—131no—
143#342—132no—
144#342—261no—
145#324—261no—
146#323—132no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C2×#9911yescharacteristic
150C22×C13C2×#10211yescharacteristic
151C22×C13C2×#10411yescharacteristic
152C2×D13—21no—
153C2×D13—21no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C2×D13—81no—
159#261—84no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—82no—
163C4×C13#32712yes—
164C4×C13#32712yes—
165Dic13—22no—
166Dic13—41no—
167Dic13—41no—
168Dic13—82no—
169C22×Q8—21no—
170C23×C4—131no—
171C4⋊Q8—41no—
172C4⋊Q8—41no—
173C22⋊Q8—522no—
174C22⋊Q8—522no—
175#117—264no—
176#117—521no—
177#117—521no—
178#117—522no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—262no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—521no—
185C2×C4⋊C4C2×#26112yes—
186C2×C22⋊C4—131no—
187C2×C22⋊C4—131no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—262no—
190C2×C42—131no—
191C2×C42—521no—
192C2×C42C2×#26111yescharacteristic
193C4⋊C8—521no—
194C22⋊C8—262no—
195C4×C8—521no—
196#95—132no—
197#95—262no—
198#95—262no—
199#95—261no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13C2×#32711yescharacteristic
203C2×C13#212311yescharacteristic
204C2×C13#212911yescharacteristic
205D13—41no—
206D13—41no—
207C24—131no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—41no—
211C2×Q8—41no—
212C22×C4—22no—
213C22×C4—131no—
214C22×C4—132no—
215C22×C4—132no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—262no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—262no—
222C22×C4—522no—
223C22×C4C22⋊#26111yescharacteristic
224C22×C4C22⋊#26111yescharacteristic
225C22×C4C22×#26111yescharacteristic
226C2×C8—522no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—521no—
230C4⋊C4—521no—
231C4⋊C4—524no—
232C4⋊C4—524no—
233C4⋊C4—522no—
234C22⋊C4—264no—
235C22⋊C4—521no—
236C22⋊C4—521no—
237C22⋊C4—522no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C42—21no—
241C42—21no—
242C42—261no—
243C42—261no—
244C42—524no—
245C13#1169411yescharacteristic, complemented, Sylow
246C23—131no—
247C23—131no—
248C23—261no—
249C23—261no—
250C23—521no—
251C23—521no—
252C23C2×C22⋊#26111yescharacteristic
253Q8—82no—
254Q8—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—132no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—524no—
276C2×C4—522no—
277C2×C4—1042no—
278C2×C4—1042no—
279C2×C4#8811512yes—
280C2×C4#8811612yes—
281C2×C4#8811911yescharacteristic
282C2×C4#8811911yescharacteristic
283C8—1042no—
284C22—21no—
285C22—21no—
286C22—261no—
287C22—261no—
288C22—521no—
289C22—521no—
290C22—521no—
291C22—521no—
292C22—1041no—
293C22C2×#8811511yescharacteristic
294C22C2×#8811611yescharacteristic
295C22C2×#8811911yescharacteristic
296C4—41no—
297C4—41no—
298C4—82no—
299C4—262no—
300C4—521no—
301C4—521no—
302C4—1042no—
303C4—1044no—
304C4#1171829212yes—
305C4#1171829212yes—
306C2—21no—
307C2—21no—
308C2—521no—
309C2—521no—
310C2C2×#1171829211yescharacteristic
311C2#1313109811yescharacteristic
312C2#1313111811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×D13C2×D4
cosocleC2×#6103C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11694
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
6. C2×C13×C4⋊Q8C4semidirect
14. #11718641C4semidirect
15. #11718597C4semidirect
132. C2×C4⋊Q8#261semidirect
245. C13#11694semidirect

Maximal subgroups

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

subgroupindex
#131305352
#131300692
#131298162
#131206032
#1169413