Finite Group Databasebeta

← #16789441

Subgroups — #16789441

Order 3328.

584 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#11718226C212yesmaximal
2#13130581C212yesmaximal
3#13129931C212yesmaximal
4#13117375C211yesmaximal, characteristic
5C2×#88147C2211yescharacteristic
6C2×#88141C411yescharacteristic, complemented
7C2×#88129C2211yescharacteristic
8C4×C22⋊#261—22no—
9C2×#88107C2214yes—
10C13×#382C411yescharacteristic, complemented
11#11718649C2211yescharacteristic
12#11718635C411yescharacteristic, complemented
13C42×Dic13C411yescharacteristic, complemented
14#11718330—22no—
15#11718327—22no—
16#11718289—22no—
17#11718226C418yescomplemented
18C22×D52C2311yescharacteristic
19C22×C4×D13D412yes—
20C22×Dic26C2×C411yescharacteristic
21C2×C22⋊#261—24no—
22C2×C4×#261—42no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×#6103—22no—
27C2×#6103—22no—
28C2×#6103D412yes—
29C2×#6101—21no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35#88147—41no—
36#88147—41no—
37#88141—41no—
38#88141—41no—
39#88129—22no—
40#88129C2×C414yes—
41(C2×#261)⋊C4—42no—
42#88107—24no—
43#88107C2×C418yes—
44C13×#95—22no—
45#88071—22no—
46C4×#354—131nomaximal, Sylow
47C23×D13C2×D412yes—
48C22×#261—44no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C22⋊C411yescharacteristic
57C2×D52—41no—
58C2×D52—41no—
59C2×D52C22×C412yes—
60C2×D52#4112yes—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—44no—
64C2×Dic26—21no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26C4212yescomplemented
68C22⋊#261—28no—
69C22⋊#261—44no—
70C4×#261—84no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C42×C13—21no—
74C42×C13C4212yescomplemented
75#6103—28no—
76#6103—42no—
77#6103—44no—
78#6101—42no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—42no—
82C4×Dic13—42no—
83C4×Dic13—41no—
84C4×Dic13—41no—
85C4×Dic13—41no—
86C4×#124—131no—
87C2×#354—132no—
88C4×#99—132no—
89#1393—132no—
90C23×C13C2×C22⋊C411yescharacteristic
91C22×D13—22no—
92C22×D13—22no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13C4×D414yes—
96C2×#261—48no—
97C2×#261—84no—
98C2×#261—84no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13C2×C4211yescharacteristic
109C2×C4×C13#11711yescharacteristic
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13#9911yescharacteristic
120C2×Dic13#9911yescharacteristic
121D52—42no—
122D52—42no—
123C4×D13—44no—
124C4×D13—82no—
125Dic26—42no—
126Dic26—42no—
127C2×#124—131no—
128C2×C4×Q8—131no—
129C2×C4×D4—131no—
130C2×#99—134no—
131#391—131no—
132#390—131no—
133#388—262no—
134#382#26111yescharacteristic, complemented
135C4×C22⋊C4—262no—
136C4×C22⋊C4—262no—
137C43—131no—
138#354—138no—
139#342—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13C4×C22⋊C411yescharacteristic
143C22×C13C2×#9911yescharacteristic
144C22×C13#41011yescharacteristic
145C2×D13—24no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—44no—
149C2×D13—82no—
150#261—88no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—42no—
154C4×C13—42no—
155C4×C13—81no—
156Dic13—21no—
157Dic13—42no—
158Dic13—41no—
159Dic13—42no—
160Dic13#35412yescomplemented
161C22×Q8—131no—
162C22×D4—131no—
163C23×C4—132no—
164#124—134no—
165#124—262no—
166C4×Q8—521no—
167C4×Q8—521no—
168C4×D4—521no—
169C4×D4—521no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4C2×#26111yescharacteristic
172C2×C4⋊C4C2×#26111yescharacteristic
173C2×C22⋊C4—132no—
174C2×C22⋊C4—262no—
175C2×C22⋊C4—264no—
176C2×C22⋊C4—262no—
177C2×C42—131no—
178C2×C42—131no—
179C2×C42—261no—
180C2×C42—261no—
181C2×C42—261no—
182C2×C42—522no—
183C2×C42C2×#26111yescharacteristic
184#99—138no—
185#99—264no—
186#95—22no—
187#95—262no—
188#95—522no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13C4×#9911yescharacteristic
192C2×C13C2×#35411yescharacteristic
193C2×C13#212611yescharacteristic
194D13—44no—
195C24—132no—
196C2×Q8—132no—
197C2×Q8—261no—
198C2×Q8—521no—
199C2×Q8—521no—
200C2×D4—132no—
201C2×D4—132no—
202C2×D4—521no—
203C2×D4—521no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—524no—
213C22×C4—524no—
214C22×C4C22⋊#26112yes—
215C22×C4C22×#26111yescharacteristic
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—522no—
219C22⋊C4—268no—
220C22⋊C4—268no—
221C22⋊C4—522no—
222C22⋊C4—524no—
223C22⋊C4—524no—
224C42—21no—
225C42—261no—
226C42—261no—
227C42—521no—
228C42—521no—
229C42—521no—
230C42—522no—
231C42—522no—
232C42—1044no—
233C42C4×#26112yescomplemented
234C13C4×#35411yescharacteristic, complemented, Sylow
235C23—134no—
236C23—262no—
237C23—262no—
238C23—522no—
239C23—522no—
240C23C2×C22⋊#26111yescharacteristic
241Q8—522no—
242Q8—522no—
243D4—522no—
244D4—522no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—131no—
255C2×C4—131no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—524no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—528no—
267C2×C4—1042no—
268C2×C4—1044no—
269C2×C4—1044no—
270C2×C4C2×C4×#26111yescharacteristic
271C2×C4#8823711yescharacteristic
272C22—21no—
273C22—21no—
274C22—264no—
275C22—524no—
276C22—522no—
277C22—522no—
278C22—1042no—
279C22C4×C22⋊#26111yescharacteristic
280C22D13⋊#9911yescharacteristic
281C22#1171915611yescharacteristic
282C4—21no—
283C4—21no—
284C4—42no—
285C4—42no—
286C4—81no—
287C4—132no—
288C4—261no—
289C4—522no—
290C4—522no—
291C4—521no—
292C4—1048no—
293C2—21no—
294C2—21no—
295C2—524no—
296C2#1313058111yescharacteristic
297C2D13⋊#35411yescharacteristic
298C2#1313110811yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC22×C13C2×#99
prime radical, cosocleC22×D52C23
hypercenter#382#261
hypocenterC13C4×#354
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
6. C2×#88141C4semidirect
10. C13×#382C4semidirect
12. #11718635C4semidirect
13. C42×Dic13C4semidirect
17. #11718226C4semidirect
67. C2×Dic26C42semidirect
74. C42×C13C42semidirect
134. #382#261semidirect
160. Dic13#354semidirect
233. C42C4×#261semidirect
234. C13C4×#354semidirect

Maximal subgroups

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

subgroupindex
C2×#117182262
#131305812
#131299312
#131173752
C4×#35413