Finite Group Databasebeta

← #15760643

Subgroups — #15760643

Order 3328.

512 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 103 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#13119317C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13113368C212yesmaximal
4#13112688C212yesmaximal
5C13×#2313C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C13×#387—24no—
9C13×#381C2212yes—
10C13×#380—21no—
11C4×C13×C22⋊C4—21no—
12#11718872—21no—
13#11718872—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16#11718643—22no—
17#11718638C412yescomplemented
18#11718635C412yescomplemented
19#11718122—22no—
20#11718044—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35#88178—22no—
36#88178—22no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C412yes—
39C2×#6099—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95D414yes—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9460—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—24no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4112yes—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×Dic26—22no—
71C2×Dic26—42no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—44no—
76C42×C13—82no—
77C22⋊Dic13—42no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C4⋊Dic13—22no—
81#6101—42no—
82C4×Dic13—42no—
83#6099—44no—
84C2×#1055—42no—
85#2503—131no—
86#2313D1311yescharacteristic
87#1821—131no—
88#1511—132no—
89#1284—132no—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—41no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13#12011yescharacteristic
95C23×C13#12311yescharacteristic
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—44no—
107C2×C4×C13—44no—
108C2×C4×C13—44no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13C4×D412yes—
112C2×C4×C13#12112yes—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120Dic26—82no—
121#1055—82no—
122C2×C22⋊Q8—131no—
123C22×C4⋊C4C2×D1311yescharacteristic
124#407—132no—
125#400—262no—
126#391—132no—
127#387—24no—
128#382—132no—
129#381—261no—
130#381—261no—
131#381C2×D1312yes—
132#380—21no—
133C4×C22⋊C4—21no—
134C4×C22⋊C4—131no—
135#343—262no—
136#328—264no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—44no—
145C22×C13#38611yescharacteristic
146C22×C13#41012yes—
147C22×C13#45512yes—
148C4×C13—22no—
149C4×C13—22no—
150C4×C13—42no—
151C4×C13—42no—
152C4×C13—84no—
153Dic13—82no—
154Dic13—81no—
155Dic13—81no—
156C22×Q8—131no—
157C23×C4C22⋊D1311yescharacteristic
158C23×C4C22⋊D1311yescharacteristic
159C23×C4C22×D1311yescharacteristic
160C2×M16—262no—
161C22⋊Q8—262no—
162C22⋊Q8—262no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4C4×D1312yes—
169C2×C4⋊C4D5212yes—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—261no—
172C2×C22⋊C4—261no—
173C2×C42—22no—
174C2×C42—132no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—262no—
181#95—262no—
182#95—262no—
183#95—262no—
184#95—261no—
185#95C22⋊D1314yes—
186C2×C13—22no—
187C2×C13—22no—
188C2×C13—41no—
189C2×C13#188511yescharacteristic
190C2×C13#189911yescharacteristic
191C2×C13#191211yescharacteristic
192C24C2×C22⋊D1311yescharacteristic
193C2×Q8—262no—
194C2×Q8—522no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—24no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—262no—
204C22×C4—261no—
205C22×C4—261no—
206C22×C4#610312yes—
207C22×C4#610312yes—
208C22×C4C2×C4×D1311yescharacteristic
209C22×C4C2×D5211yescharacteristic
210C22×C4#612712yes—
211C22×C4C2×C22⋊D1312yes—
212M16—524no—
213C2×C8—522no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—82no—
217C4⋊C4—262no—
218C4⋊C4—522no—
219C22⋊C4—44no—
220C22⋊C4—522no—
221C22⋊C4—521no—
222C22⋊C4—521no—
223C42—82no—
224C42—522no—
225C13#946011yescharacteristic, complemented, Sylow
226C23—22no—
227C23—22no—
228C23—41no—
229C23C2×#610311yescharacteristic
230C23#8818311yescharacteristic
231C23#8820711yescharacteristic
232Q8—1042no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4C4×C22⋊D1312yes—
256C2×C4#8818412yes—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22#1171866712yes—
267C22#1171887411yescharacteristic
268C22#1171890312yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—1042no—
275C4—1041no—
276C4—1041no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2#1311522411yescharacteristic
281C2#1311529411yescharacteristic
282C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9460
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
17. #11718638C4semidirect
18. #11718635C4semidirect
225. C13#9460semidirect

Maximal subgroups

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

subgroupindex
#131193172
#131149162
#131133682
#131126882
C13×#23132
#946013