Finite Group Databasebeta

← #16789445

Subgroups — #16789445

Order 3328.

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

normal subgroups only

This group has 564 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×#11718300C212yesmaximal
2C4×#88107C212yesmaximal
3#13129931C212yesmaximal
4#13117543C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic, complemented
6C2×#88201C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8C4×C22⋊#261—22no—
9C2×#88107C2214yes—
10#11718891C411yescharacteristic, complemented
11#11718650—22no—
12#11718649C2211yescharacteristic
13#11718637C411yescharacteristic, complemented
14#11718601—22no—
15#11718593C411yescharacteristic, complemented
16#11718300C418yescomplemented
17#11718289—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D52C2311yescharacteristic
20C22×C4×D13D412yes—
21C2×C22⋊#261—24no—
22C2×C4×#261—42no—
23C4×Q8×C13—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C42×C13—21no—
27C2×C42×C13C2×C411yescharacteristic
28#88201—22no—
29#88201C2×C414yes—
30C2×#6103—22no—
31C2×#6103—22no—
32C2×#6103D412yes—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—22no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C4×D52—42no—
38(C2×#261)⋊C4—42no—
39#88107—24no—
40#88107C2×C418yes—
41#88071—21no—
42#88071—21no—
43#88071—22no—
44#12627—131nomaximal, Sylow
45C23×D13C2×D412yes—
46C22×#261—44no—
47C2×Q8×C13—21no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C4212yescomplemented
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C412yes—
59C2×D52—41no—
60C2×D52—41no—
61C2×D52C22×C412yes—
62C2×D52#4112yes—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—82no—
66C22⋊#261—28no—
67C22⋊#261—44no—
68C4×#261—84no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C42×C13—22no—
72C42×C13—42no—
73#6103—28no—
74#6103—42no—
75#6103—82no—
76C4⋊Dic13—41no—
77#6101—82no—
78C4×Dic13—21no—
79C4×Dic13—41no—
80C4×Dic13C4212yescomplemented
81#2326—131no—
82C2×#354—132no—
83C4×#99—132no—
84#1393—132no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13C4×D414yes—
91C2×#261—48no—
92C2×#261—84no—
93C2×#261—84no—
94Q8×C13—42no—
95Q8×C13—42no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13#9912yes—
107C2×C4×C13C2×C4211yescharacteristic
108C2×C4×C13#11711yescharacteristic
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—42no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117D52—42no—
118D52—42no—
119C4×D13—44no—
120C4×D13—82no—
121C2×#124—131no—
122C2×C4×Q8#26111yescharacteristic, complemented
123C2×C4×D4—131no—
124C2×#99—134no—
125#391—131no—
126#390—131no—
127#388—262no—
128#385—262no—
129#384—131no—
130C4×C22⋊C4—262no—
131#376—131no—
132#354—138no—
133#342—262no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13C4×C22⋊C411yescharacteristic
137C22×C13C2×#9911yescharacteristic
138C22×C13#41011yescharacteristic
139C2×D13—24no—
140C2×D13—42no—
141C2×D13—42no—
142C2×D13—44no—
143C2×D13—82no—
144#261—88no—
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13—42no—
150C4×C13—81no—
151Dic13—42no—
152Dic13—42no—
153Dic13—81no—
154C22×Q8C2×#26111yescharacteristic
155C22×D4—131no—
156C23×C4—132no—
157#124—134no—
158#124—262no—
159C4×Q8—42no—
160C4×D4—522no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4C2×#26111yescharacteristic
165C2×C22⋊C4—132no—
166C2×C22⋊C4—262no—
167C2×C22⋊C4—264no—
168C2×C22⋊C4—262no—
169C2×C42—21no—
170C2×C42—131no—
171C2×C42—131no—
172C2×C42—522no—
173C2×C42C2×#26111yescharacteristic
174#99—138no—
175#99—264no—
176#95—262no—
177#95—261no—
178#95—261no—
179#95—522no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13C4×#9911yescharacteristic
183C2×C13#212711yescharacteristic
184C2×C13#212911yescharacteristic
185D13—44no—
186C24—132no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C4×#26112yescomplemented
191C2×D4—132no—
192C2×D4—132no—
193C2×D4—521no—
194C2×D4—521no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—132no—
198C22×C4—261no—
199C22×C4—262no—
200C22×C4—262no—
201C22×C4—261no—
202C22×C4—524no—
203C22×C4—1042no—
204C22×C4C22⋊#26111yescharacteristic
205C22×C4C22⋊#26111yescharacteristic
206C22×C4C22×#26111yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—521no—
210C4⋊C4—1042no—
211C22⋊C4—268no—
212C22⋊C4—268no—
213C22⋊C4—522no—
214C22⋊C4—524no—
215C22⋊C4—1042no—
216C42—22no—
217C42—42no—
218C42—132no—
219C42—261no—
220C42—521no—
221C42—1044no—
222C13#1262711yescharacteristic, complemented, Sylow
223C23—134no—
224C23—262no—
225C23—262no—
226C23—522no—
227C23—522no—
228C23C2×C22⋊#26111yescharacteristic
229Q8—42no—
230Q8—42no—
231D4—522no—
232D4—522no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—524no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—522no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4—528no—
252C2×C4—521no—
253C2×C4—1042no—
254C2×C4—1044no—
255C2×C4—1044no—
256C2×C4#8811912yes—
257C2×C4C2×C4×#26111yescharacteristic
258C2×C4#8823711yescharacteristic
259C22—21no—
260C22—21no—
261C22—264no—
262C22—524no—
263C22—522no—
264C22—522no—
265C22—1042no—
266C22#1171911611yescharacteristic
267C22C4×C22⋊#26111yescharacteristic
268C22C2×#8811911yescharacteristic
269C4—21no—
270C4—21no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—81no—
275C4—522no—
276C4—522no—
277C4—1041no—
278C4—1048no—
279C2—21no—
280C2—21no—
281C2—524no—
282C2C4×#8811911yescharacteristic
283C2#1313111111yescharacteristic
284C2#1313111811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radical, cosocleC22×D52C23
hypercenterC2×C4×Q8#261
hypocenterC13#12627
LCSG ▷ C2×C4×C13 ▷ C22×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
5. C2×C4×Q8×C13C4semidirect
10. #11718891C4semidirect
13. #11718637C4semidirect
15. #11718593C4semidirect
16. #11718300C4semidirect
50. C2×Q8×C13C42semidirect
80. C4×Dic13C42semidirect
122. C2×C4×Q8#261semidirect
190. C2×Q8C4×#261semidirect
222. C13#12627semidirect

Maximal subgroups

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

subgroupindex
C2×#117183002
C4×#881072
#131299312
#131175432
#1262713