Finite Group Databasebeta

← #16781898

Subgroups — #16781898

Order 3328.

550 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130712C212yesmaximal, complemented
2#13130697C212yesmaximal
3#13129699C212yesmaximal, complemented
4C2×C8×D52C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic, complemented
6C22×C8×D13C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8#11719136C2214yes—
9C2×#88107—22no—
10C2×#88101—22no—
11C2×C4×C8×C13C411yescharacteristic, complemented
12C2×#88060C411yescharacteristic, complemented
13C2×#88060C2211yescharacteristic
14C2×C4⋊#1055C411yescharacteristic, complemented
15C8×D52—22no—
16C8×D52—22no—
17#11718289—22no—
18#11718265—22no—
19C22×D52D411yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13C2311yescharacteristic
22C2×C22⋊#261—24no—
23C2×C4⋊#261—24no—
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×#6103D411yescharacteristic
28C2×#6103Q811yescharacteristic
29C2×C4⋊Dic13Q811yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C22×#1055C2×C411yescharacteristic
32C2×C8×D13—21no—
33C2×C8×D13—21no—
34C2×C8×D13—42no—
35C2×C8×D13—42no—
36C2×C8×D13D412yes—
37C2×C8×D13D412yes—
38C4×D52—22no—
39C4×D52—22no—
40(C2×#261)⋊C4—24no—
41#88107—44no—
42#88101—44no—
43C4×C8×C13—21no—
44C4×C8×C13—21no—
45#88060—22no—
46#88060—22no—
47C4⋊#1055—22no—
48#8608—131nomaximal, Sylow
49C23×D13C4⋊C411yescharacteristic
50C23×D13C2×D411yescharacteristic
51C22×#261—44no—
52C22×C4×C13C4⋊C411yescharacteristic
53C22×C4×C13C4⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13C4⋊C411yescharacteristic
56C22×Dic13C2×Q811yescharacteristic
57C2×D52—22no—
58C2×D52—22no—
59C2×D52SD1614yes—
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—41no—
63C2×C4×D13—41no—
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13C2×D412yes—
67C2×C4×D13#4112yes—
68C22⋊#261—44no—
69C22⋊#261—44no—
70C4⋊#261—44no—
71C4⋊#261—44no—
72C2×C8×C13—22no—
73C2×C8×C13—21no—
74C2×C8×C13—41no—
75C2×C8×C13C22⋊C411yescharacteristic
76C2×C8×C13C22⋊C411yescharacteristic
77C42×C13—21no—
78C42×C13—21no—
79#6103—22no—
80#6103—22no—
81C4⋊Dic13—22no—
82C2×#1055—21no—
83C2×#1055—41no—
84C2×#1055—41no—
85C2×#1055C22⋊C412yes—
86C8×D13—24no—
87C8×D13—42no—
88C8×D13—42no—
89C8×D13—42no—
90C2×C8×D4—131no—
91#1807—132no—
92#1799—132no—
93#1289—132no—
94C23×C13C2×C4⋊C411yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13#10612yescomplemented
102C22×D13#12112yes—
103C22×D13C2×SD1612yes—
104C22×D13#13512yes—
105C2×#261—84no—
106C2×#261—84no—
107C2×#261—84no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13#10612yescomplemented
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13#11711yescharacteristic
117C2×Dic13—21no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13C22⋊Q812yes—
121D52—28no—
122C4×D13—22no—
123C4×D13—22no—
124C4×D13—42no—
125C4×D13—42no—
126C4×D13—41no—
127C4×D13—41no—
128C8×C13—21no—
129C8×C13—41no—
130C8×C13#9912yescomplemented
131#1055—22no—
132#1055—41no—
133C23×C8—131no—
134C23×C8—131no—
135C2×C4×D4—131no—
136C8×D4—262no—
137C8×D4—262no—
138C2×#106—262no—
139C2×C4⋊C8—131no—
140C2×#99—262no—
141C2×C22⋊C8—131no—
142C2×C22⋊C8—131no—
143C2×C4×C8#26111yescharacteristic, complemented
144#380—134no—
145#342—262no—
146#340—262no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#38011yescharacteristic
150C22×C13C2×#10611yescharacteristic
151C22×C13#42711yescharacteristic
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—22no—
155C2×D13—42no—
156C2×D13—42no—
157C2×D13—42no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—42no—
161C2×D13#46514yes—
162#261—164no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—41no—
166C4×C13C2×#9911yescharacteristic
167C4×C13#41011yescharacteristic
168Dic13—22no—
169Dic13—41no—
170C22×D4—131no—
171C23×C4—131no—
172C23×C4—131no—
173C22×C8—131no—
174C22×C8—132no—
175C22×C8—132no—
176C22×C8—131no—
177C22×C8—261no—
178C22×C8—261no—
179C22×C8—522no—
180C22×C8—522no—
181C22×C8C2×#26111yescharacteristic
182C22×C8C2×#26111yescharacteristic
183C4×D4—262no—
184C4×D4—262no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—264no—
187C2×C22⋊C4—131no—
188C2×C22⋊C4—131no—
189C2×C22⋊C4—264no—
190C2×C42C2×#26111yescharacteristic
191#106—524no—
192C4⋊C8—262no—
193#99—524no—
194C22⋊C8—262no—
195C22⋊C8—262no—
196C4×C8—21no—
197C4×C8—21no—
198#95—264no—
199C2×C13—21no—
200C2×C13—21no—
201C2×C13#179911yescharacteristic
202C2×C13#180711yescharacteristic
203C2×C13#181211yescharacteristic
204D13—24no—
205D13—42no—
206C24—131no—
207C24—131no—
208C2×D4—134no—
209C2×D4—262no—
210C2×D4—262no—
211C22×C4—131no—
212C22×C4—132no—
213C22×C4—132no—
214C22×C4—131no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—521no—
218C22×C4—521no—
219C22×C4—521no—
220C22×C4—521no—
221C22×C4—524no—
222C22×C4C4⋊#26111yescharacteristic
223C22×C4C4⋊#26111yescharacteristic
224C22×C4C22×#26111yescharacteristic
225C2×C8—22no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8—132no—
229C2×C8—264no—
230C2×C8—261no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—521no—
234C2×C8—522no—
235C2×C8—521no—
236C2×C8C22⋊#26111yescharacteristic
237C2×C8C22⋊#26111yescharacteristic
238C4⋊C4—262no—
239C4⋊C4—524no—
240C4⋊C4—524no—
241C22⋊C4—262no—
242C22⋊C4—262no—
243C22⋊C4—524no—
244C22⋊C4—524no—
245C42—21no—
246C42—21no—
247C13#860811yescharacteristic, complemented, Sylow
248C23—132no—
249C23—132no—
250C23—132no—
251C23—132no—
252C23—261no—
253C23—261no—
254C23—521no—
255C23—521no—
256C23—521no—
257C23—521no—
258C23C2×C4⋊#26111yescharacteristic
259D4—268no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—132no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—1044no—
277C2×C4—1044no—
278C2×C4—1044no—
279C2×C4#8810112yescomplemented
280C2×C4#8823711yescharacteristic
281C2×C4C2×C22⋊#26111yescharacteristic
282C8—21no—
283C8—41no—
284C8—262no—
285C8—521no—
286C8#8810712yescomplemented
287C22—21no—
288C22—21no—
289C22—134no—
290C22—262no—
291C22—262no—
292C22—262no—
293C22—522no—
294C22—522no—
295C22—522no—
296C22—522no—
297C22—521no—
298C22—521no—
299C22C2×#8810111yescharacteristic
300C22#1171909211yescharacteristic
301C22#1171913611yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—262no—
306C4—521no—
307C4—2084no—
308C4C2×#8810711yescharacteristic
309C4#1171911611yescharacteristic
310C2—21no—
311C2—21no—
312C2—264no—
313C2—522no—
314C2#1313069711yescharacteristic
315C2#1313071211yescharacteristic
316C2#1313071811yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13#380
prime radicalC22×D52D4
cosocleC22×C4×D13C23
hypercenterC2×C4×C8#261
hypocenterC13#8608
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. #13130712C2semidirect
3. #13129699C2semidirect
5. C22×C8×D13C4semidirect
11. C2×C4×C8×C13C4semidirect
12. C2×#88060C4semidirect
14. C2×C4⋊#1055C4semidirect
101. C22×D13#106semidirect
114. C2×C4×C13#106semidirect
130. C8×C13#99semidirect
143. C2×C4×C8#261semidirect
247. C13#8608semidirect
279. C2×C4#88101semidirect
286. C8#88107semidirect

Maximal subgroups

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

subgroupindex
#131307122
#131306972
#131296992
C2×C8×D522
#860813