Finite Group Databasebeta

← #16781933

Subgroups — #16781933

Order 3328.

450 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 96 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#13130396C212yesmaximal, complemented
2#13130095C212yesmaximal
3#13129701C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic
6C2×C4×C22⋊D13C2211yescharacteristic
7C22×C8×D13C411yescharacteristic
8#11719130C2214yes—
9C2×C22⋊#1055C411yescharacteristic
10C8×C22⋊D13—22no—
11C8×C22⋊D13—22no—
12C2×#88060C411yescharacteristic
13C2×#88054C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15#11718305—22no—
16#11718287—22no—
17#11718256—22no—
18#11718253—22no—
19C23×C4×C13C2×C411yescharacteristic
20C22×C22⋊D13Q811yescharacteristic
21C22×C4×D13C2×C411yescharacteristic
22C22×C8×C13—21no—
23C22×C8×C13—21no—
24C22×C8×C13—42no—
25C22×C8×C13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C2×C22⋊Dic13D411yescharacteristic
28C4×C22⋊D13—22no—
29C4×C22⋊D13—22no—
30C2×#6103D411yescharacteristic
31C2×#6101Q811yescharacteristic
32C2×C4×Dic13C2311yescharacteristic
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—42no—
38C22⋊#1057—24no—
39#88110—24no—
40C4⋊#1057—24no—
41C22⋊#1055—22no—
42#88060—22no—
43#88054—22no—
44C8×Dic13D412yes—
45C8×Dic13D412yes—
46#8620—131nomaximal, Sylow
47C24×C13C4⋊C411yescharacteristic
48C23×D13C4⋊C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13C4⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C2×C22⋊D13—22no—
56C2×C22⋊D13—22no—
57C2×C22⋊D13—22no—
58C22×Dic13C4⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×Q811yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—41no—
64C2×C4×D13—41no—
65C2×#1057—44no—
66C2×C8×C13—22no—
67C2×C8×C13—21no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C2×C8×C13—41no—
71C2×C8×C13C22⋊C411yescharacteristic
72C2×C8×C13C22⋊C411yescharacteristic
73C22⋊Dic13—22no—
74#6103—22no—
75#6101—22no—
76C4×Dic13C2×D412yes—
77C4×Dic13#4112yes—
78C2×#1055—21no—
79C2×#1055—41no—
80C2×#1055—41no—
81C2×#1055C22⋊C412yes—
82C8×D13—42no—
83C8×D13—42no—
84C2×C8×D4—131no—
85#1568—132no—
86#1466—132no—
87#1290—132no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13#10812yes—
93C23×C13C2×C4⋊C411yescharacteristic
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13#10812yes—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13#11711yescharacteristic
108C22⋊D13—28no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13#12112yes—
115C2×Dic13C22⋊Q812yes—
116C4×D13—42no—
117C4×D13—41no—
118C4×D13—41no—
119#1057—84no—
120C8×C13—21no—
121C8×C13—41no—
122C8×C13#10012yes—
123#1055—22no—
124#1055—41no—
125C23×C8—131no—
126C23×C8#26111yescharacteristic
127C2×C4×D4—131no—
128C8×D4—262no—
129C8×D4—262no—
130#432—134no—
131C2×C4⋊C8—131no—
132C2×C22⋊C8—131no—
133C2×C22⋊C8—131no—
134C2×C4×C8—131no—
135#335—262no—
136#334—262no—
137#323—262no—
138#323—262no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—42no—
143C22×C13—42no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13#38011yescharacteristic
147C22×C13C2×#10811yescharacteristic
148C22×C13C2×#10811yescharacteristic
149C2×D13—22no—
150C2×D13—42no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—42no—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13C2×#10011yescharacteristic
157C4×C13#41311yescharacteristic
158Dic13—22no—
159Dic13—22no—
160Dic13—41no—
161C22×D4—131no—
162C23×C4—131no—
163C23×C4C2×#26111yescharacteristic
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—42no—
167C22×C8—131no—
168C22×C8—131no—
169C22×C8—261no—
170C22×C8—261no—
171C22×C8—522no—
172C22×C8C2×#26111yescharacteristic
173C22×C8C2×#26111yescharacteristic
174C4×D4—262no—
175C4×D4—262no—
176C2×C4⋊C4—131no—
177C2×C22⋊C4—131no—
178C2×C22⋊C4—131no—
179C2×C42—131no—
180C4⋊C8—262no—
181C4⋊C8—264no—
182C22⋊C8—262no—
183C22⋊C8—262no—
184C22⋊C8—264no—
185#97—264no—
186C4×C8—132no—
187C4×C8—132no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13#180011yescharacteristic
192C2×C13#181011yescharacteristic
193C2×C13#181211yescharacteristic
194D13—42no—
195C24—131no—
196C24C4⋊#26111yescharacteristic
197C2×D4—262no—
198C2×D4—262no—
199C2×D4—262no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4—521no—
210C22×C4—521no—
211C22×C4C4⋊#26111yescharacteristic
212C22×C4C22×#26111yescharacteristic
213C2×C8—22no—
214C2×C8—21no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—41no—
218C2×C8—132no—
219C2×C8—261no—
220C2×C8—522no—
221C2×C8—521no—
222C2×C8—522no—
223C2×C8—521no—
224C2×C8—524no—
225C2×C8C22⋊#26111yescharacteristic
226C2×C8C22⋊#26111yescharacteristic
227C4⋊C4—262no—
228C22⋊C4—262no—
229C22⋊C4—262no—
230C42—132no—
231C42—132no—
232C13#862011yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—41no—
236C23—41no—
237C23—132no—
238C23—261no—
239C23—261no—
240C23—521no—
241C23—521no—
242C23#8810312yes—
243C23C2×C4⋊#26111yescharacteristic
244D4—268no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—132no—
253C2×C4—132no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4#8823711yescharacteristic
263C2×C4C2×C22⋊#26111yescharacteristic
264C8—21no—
265C8—41no—
266C8—262no—
267C8—521no—
268C8—1044no—
269C8#8812112yes—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—262no—
278C22—522no—
279C22—522no—
280C22—521no—
281C22—521no—
282C22C2×#8810311yescharacteristic
283C22D13⋊#10811yescharacteristic
284C22#1171913611yescharacteristic
285C4—21no—
286C4—41no—
287C4—262no—
288C4—262no—
289C4—521no—
290C4#1171913211yescharacteristic
291C4C2×#8812111yescharacteristic
292C2—21no—
293C2—21no—
294C2—42no—
295C2—522no—
296C2#1313070011yescharacteristic
297C2#1313071511yescharacteristic
298C2#1313071811yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13#380
prime radicalC22×C22⋊D13Q8
cosocleC2×C4×Dic13C23
hypercenterC23×C8#261
hypocenterC13#8620
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #13130396C2semidirect
3. #13129701C2semidirect
232. C13#8620semidirect

Maximal subgroups

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

subgroupindex
#131303962
#131300952
#131297012
C2×C8×C22⋊D132
#862013