Finite Group Databasebeta

← #15772346

Subgroups — #15772346

Order 3328.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#13113170C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112784C214yesmaximal
4C13×#2317C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C13×#389—21no—
9C13×#389—21no—
10C13×#385C412yes—
11C13×#385C2212yes—
12C13×#384—21no—
13C13×#382—21no—
14#11718587—21no—
15#11718587—21no—
16#11718120—21no—
17#11718120—21no—
18#11718117C2212yes—
19#11718117C2212yes—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C412yes—
22C13×#117—24no—
23C13×#117—41no—
24C13×#117—41no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2×C412yes—
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4C2311yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C13×#95—22no—
41C13×#95—22no—
42C22⋊#1055—22no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45C4⋊#1055—41no—
46#88043—41no—
47#88043—41no—
48#11520—131nomaximal, Sylow
49C24×C13C22×C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—82no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C13×C4⋊C4—24no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—82no—
71C13×C4⋊C4—82no—
72C13×C22⋊C4—22no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4M1614yes—
76C42×C13—24no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C2×#1055—42no—
82C2×#1055—42no—
83#2317D1311yescharacteristic
84#1464—131no—
85#1464—131no—
86#1326—134no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—41no—
90C23×C13—41no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13C2×M1612yes—
93C2×C4×C13—24no—
94C2×C4×C13—24no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—24no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—84no—
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#10112yes—
117#1055—82no—
118#1055—82no—
119C2×#117Dic1311yescharacteristic
120C2×#117C2×D1311yescharacteristic
121C22×C4⋊C4Dic1311yescharacteristic
122#432—261no—
123#432—261no—
124#389—21no—
125#389—21no—
126#385Dic1312yes—
127#385C2×D1312yes—
128#384—21no—
129#382—21no—
130#324—261no—
131#324—261no—
132#323—132no—
133#323—132no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—22no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13#40711yescharacteristic
142C22×C13C2×#9911yescharacteristic
143C22×C13C2×#10111yescharacteristic
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—22no—
147C4×C13—44no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—82no—
153C23×C4C2×Dic1311yescharacteristic
154C23×C4C2×Dic1312yes—
155#117—24no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4C22⋊D1311yescharacteristic
166C2×C4⋊C4C22⋊D1311yescharacteristic
167C2×C22⋊C4C2×Dic1312yes—
168C2×C22⋊C4C2×Dic1311yescharacteristic
169C2×C22⋊C4C22×D1311yescharacteristic
170C2×C42—21no—
171C2×C42C22⋊D1311yescharacteristic
172C2×C42C22⋊D1311yescharacteristic
173C4⋊C8—521no—
174C4⋊C8—521no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177#97—521no—
178#97—521no—
179#95—22no—
180#95—22no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13—42no—
184C2×C13#146311yescharacteristic
185C2×C13#212211yescharacteristic
186C2×C13#212311yescharacteristic
187C24C22×Dic1311yescharacteristic
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—82no—
196C22×C4C22⋊Dic1311yescharacteristic
197C22×C4C22⋊Dic1311yescharacteristic
198C22×C4C22⋊Dic1311yescharacteristic
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C2×C22⋊D1311yescharacteristic
201C22×C4C2×C22⋊D1311yescharacteristic
202C2×C8—522no—
203C2×C8—522no—
204C4⋊C4—24no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C22⋊C4—22no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4#609914yes—
216C42—24no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C13#1152011yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×#609912yes—
227C23C2×C22⋊Dic1311yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4#8807411yescharacteristic
250C2×C4#8807411yescharacteristic
251C2×C4#8807612yes—
252C8—1042no—
253C8—1042no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1171886811yescharacteristic
262C22C2×#8807411yescharacteristic
263C22C2×#8807611yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1311316611yescharacteristic
277C2#1311648611yescharacteristic
278C2#1311649011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutator, prime radicalC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2317C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2317D13
hypocenterC13#11520
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
221. C13#11520semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131127842
C13×#23172
#1152013