Finite Group Databasebeta

← #16781897

Subgroups — #16781897

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#13130696C212yesmaximal
3#13129699C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic, complemented
6C2×C4×C22⋊D13C2211yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×#88119—22no—
9#11719136C2214yes—
10C2×#88101—22no—
11C2×C22⋊#1055C411yescharacteristic, complemented
12C8×C22⋊D13—22no—
13C8×C22⋊D13—22no—
14C2×#88060C2211yescharacteristic
15C2×#88054C411yescharacteristic, complemented
16C2×C8×Dic13C411yescharacteristic, complemented
17#11718289—22no—
18#11718265—22no—
19C23×C4×C13C2×C411yescharacteristic
20C22×C22⋊D13D411yescharacteristic
21C22×C4×D13C2311yescharacteristic
22C2×C22⋊#261—24no—
23C2×C4⋊#261—24no—
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—42no—
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C2×C22⋊Dic13Q811yescharacteristic
30C4×C22⋊D13—22no—
31C4×C22⋊D13—22no—
32C2×#6103D411yescharacteristic
33C2×#6101Q811yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C2×C8×D13—42no—
38C2×C8×D13D412yes—
39C2×C8×D13D412yes—
40#88119—44no—
41(C2×#261)⋊C4—24no—
42#88101—44no—
43C22⋊#1055—22no—
44#88060—22no—
45#88054—22no—
46C8×Dic13—21no—
47C8×Dic13—21no—
48#8608—131nomaximal, Sylow
49C24×C13C4⋊C411yescharacteristic
50C23×D13C2×D411yescharacteristic
51C22×#261—44no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C2×C22⋊D13—22no—
59C2×C22⋊D13—22no—
60C2×C22⋊D13SD1614yes—
61C22×Dic13C4⋊C411yescharacteristic
62C22×Dic13C4⋊C411yescharacteristic
63C22×Dic13C2×Q811yescharacteristic
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—42no—
75C2×C8×C13—42no—
76C2×C8×C13—41no—
77C2×C8×C13C22⋊C411yescharacteristic
78C2×C8×C13C22⋊C411yescharacteristic
79C22⋊Dic13—22no—
80#6103—22no—
81#6101—22no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C2×#1055—21no—
85C2×#1055—41no—
86C2×#1055—41no—
87C2×#1055C22⋊C412yes—
88C8×D13—24no—
89C8×D13—42no—
90C2×C8×D4—131no—
91#1807—132no—
92#1799—132no—
93#1289—132no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13#10612yescomplemented
99C23×C13C2×C4⋊C411yescharacteristic
100C22×D13—41no—
101C22×D13—41no—
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—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13#11711yescharacteristic
117C22⋊D13—28no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13#10612yescomplemented
124C2×Dic13C22⋊Q812yes—
125C4×D13—22no—
126C4×D13—22no—
127C4×D13—42no—
128C8×C13—21no—
129C8×C13—41no—
130C8×C13#9912yescomplemented
131#1055—22no—
132#1055—41no—
133C23×C8—131no—
134C23×C8#26111yescharacteristic, complemented
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—131no—
144#380—134no—
145#342—262no—
146#340—262no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13#38011yescharacteristic
155C22×C13C2×#10611yescharacteristic
156C22×C13#42711yescharacteristic
157C2×D13—22no—
158C2×D13—22no—
159C2×D13—42no—
160C2×D13—42no—
161C2×D13#46514yes—
162#261—164no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13C2×#9911yescharacteristic
166C4×C13#41011yescharacteristic
167Dic13—22no—
168Dic13—22no—
169Dic13—41no—
170C22×D4—131no—
171C23×C4—131no—
172C23×C4C2×#26111yescharacteristic
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—42no—
176C22×C8—131no—
177C22×C8—132no—
178C22×C8—132no—
179C22×C8—131no—
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×C42—131no—
191#106—524no—
192C4⋊C8—262no—
193#99—524no—
194C22⋊C8—262no—
195C22⋊C8—262no—
196C4×C8—261no—
197C4×C8—261no—
198#95—264no—
199C2×C13—21no—
200C2×C13—21no—
201C2×C13—42no—
202C2×C13#179911yescharacteristic
203C2×C13#180711yescharacteristic
204C2×C13#181211yescharacteristic
205D13—24no—
206C24—131no—
207C24C4⋊#26111yescharacteristic
208C2×D4—134no—
209C2×D4—262no—
210C2×D4—262no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—132no—
218C22×C4—132no—
219C22×C4—131no—
220C22×C4—521no—
221C22×C4—521no—
222C22×C4—524no—
223C22×C4C4⋊#26111yescharacteristic
224C22×C4C22×#26111yescharacteristic
225C2×C8—22no—
226C2×C8—21no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—41no—
230C2×C8—132no—
231C2×C8—264no—
232C2×C8—261no—
233C2×C8—522no—
234C2×C8—521no—
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—261no—
246C42—261no—
247C13#860811yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—132no—
253C23—132no—
254C23—132no—
255C23—521no—
256C23—521no—
257C23#8810112yescomplemented
258C23C2×C4⋊#26111yescharacteristic
259D4—268no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—522no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—1044no—
278C2×C4—1044no—
279C2×C4—1044no—
280C2×C4#8823711yescharacteristic
281C2×C4C2×C22⋊#26111yescharacteristic
282C8—21no—
283C8—41no—
284C8—262no—
285C8—521no—
286C8#8811912yescomplemented
287C22—21no—
288C22—21no—
289C22—22no—
290C22—42no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—134no—
295C22—262no—
296C22—262no—
297C22—522no—
298C22—522no—
299C22C2×#8810111yescharacteristic
300C22#1171909211yescharacteristic
301C22#1171913611yescharacteristic
302C4—21no—
303C4—41no—
304C4—262no—
305C4—262no—
306C4—521no—
307C4—2084no—
308C4#1171911611yescharacteristic
309C4C2×#8811911yescharacteristic
310C2—21no—
311C2—21no—
312C2—42no—
313C2—264no—
314C2#1313069611yescharacteristic
315C2#1313071211yescharacteristic
316C2#1313071811yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC22×C4×D13C23
hypercenterC23×C8#261
hypocenterC13#8608
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. #13130712C2semidirect
3. #13129699C2semidirect
5. C23×C8×C13C4semidirect
11. C2×C22⋊#1055C4semidirect
15. C2×#88054C4semidirect
16. C2×C8×Dic13C4semidirect
98. C23×C13#106semidirect
123. C2×Dic13#106semidirect
130. C8×C13#99semidirect
134. C23×C8#261semidirect
247. C13#8608semidirect
257. C23#88101semidirect
286. C8#88119semidirect

Maximal subgroups

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

subgroupindex
#131307122
#131306962
#131296992
C2×C8×C22⋊D132
#860813