Finite Group Databasebeta

← #15772347

Subgroups — #15772347

Order 3328.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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#13117456C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112785C214yesmaximal
4C13×#1464C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C13×#432—21no—
9#11718638—21no—
10#11718637—21no—
11#11718607C412yes—
12#11718607C2212yes—
13#11718589—21no—
14#11718589—21no—
15#11718587—21no—
16C13×#324—21no—
17C13×#323C2212yes—
18#11718120—21no—
19#11718117C2212yes—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13C2×C412yes—
22C13×#117—41no—
23C13×#117—41no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C22⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4C2311yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13C2×C412yes—
31#88180—24no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—41no—
36C2×C4⋊Dic13—41no—
37C2×#6101—22no—
38C2×#6101—22no—
39C2×C4×Dic13—21no—
40C13×C4⋊C8—41no—
41C13×C22⋊C8—22no—
42C13×#97—41no—
43#88071—22no—
44#88071—22no—
45C22⋊#1055—22no—
46C4⋊#1055—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×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—42no—
63C22×Dic13—82no—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C22⋊C4—41no—
68C13×C22⋊C4—41no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C22⋊Dic13—22no—
74C22⋊Dic13M1614yes—
75C4⋊Dic13—24no—
76C4⋊Dic13—42no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—82no—
80#6101—82no—
81C4×Dic13—24no—
82C2×#1055—42no—
83#2317—131no—
84#1464—131no—
85#1464D1311yescharacteristic
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—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13#9911yescharacteristic
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#10112yes—
110C2×Dic13—24no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—84no—
117C8×C13—82no—
118#1055—82no—
119C2×#117—131no—
120C2×#117C2×D1311yescharacteristic
121C22×C4⋊C4—131no—
122#432—21no—
123#432—261no—
124#389—261no—
125#389—261no—
126#385—132no—
127#385—132no—
128#384—261no—
129#382—261no—
130#324—21no—
131#324—261no—
132#323—132no—
133#323C2×D1312yes—
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—41no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151Dic13—44no—
152Dic13—82no—
153C23×C4—132no—
154C23×C4C4×D1311yescharacteristic
155#117—41no—
156#117—41no—
157#117—264no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4—262no—
162C2×C4⋊C4—262no—
163C2×C4⋊C4—521no—
164C2×C4⋊C4—521no—
165C2×C4⋊C4D5211yescharacteristic
166C2×C4⋊C4C22⋊D1311yescharacteristic
167C2×C22⋊C4—132no—
168C2×C22⋊C4C4×D1311yescharacteristic
169C2×C22⋊C4C22×D1311yescharacteristic
170C2×C42—261no—
171C2×C42D5211yescharacteristic
172C2×C42C22⋊D1311yescharacteristic
173C4⋊C8—41no—
174C4⋊C8—521no—
175C22⋊C8—22no—
176C22⋊C8—262no—
177#97—41no—
178#97—521no—
179#95—262no—
180#95—262no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13—42no—
184C2×C13#146311yescharacteristic
185C2×C13#212211yescharacteristic
186C2×C13#212311yescharacteristic
187C24C2×C4×D1311yescharacteristic
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—262no—
193C22×C4—262no—
194C22×C4—522no—
195C22×C4—1042no—
196C22×C4#610311yescharacteristic
197C22×C4#610311yescharacteristic
198C22×C4#610311yescharacteristic
199C22×C4#610311yescharacteristic
200C22×C4C2×D5211yescharacteristic
201C22×C4C2×C22⋊D1311yescharacteristic
202C2×C8—42no—
203C2×C8—522no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—264no—
207C4⋊C4—522no—
208C4⋊C4—521no—
209C4⋊C4—521no—
210C4⋊C4—1042no—
211C4⋊C4—1042no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—134no—
215C22⋊C4—262no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—264no—
221C13#1152011yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23M16×D1312yes—
227C23C2×#610311yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—264no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—1044no—
249C2×C4#8804611yescharacteristic
250C2×C4#8804611yescharacteristic
251C2×C4#8806412yes—
252C8—82no—
253C8—1042no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C2×#8804611yescharacteristic
262C22#1171878711yescharacteristic
263C22C2×#8806411yescharacteristic
264C4—22no—
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—524no—
272C4—1042no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1311316511yescharacteristic
277C2#1311648711yescharacteristic
278C2#1311648911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutator, prime radicalC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#1464D13
hypocenterC13#11520
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

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
#131174562
#131131702
#131127852
C13×#14642
#1152013