Finite Group Databasebeta

← #15772086

Subgroups — #15772086

Order 3328.

434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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#13113150C211yesmaximal, characteristic
3#13112781C214yesmaximal, complemented
4C13×#1458C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C13×#431—21no—
9#11718638C412yes—
10#11718637C2212yes—
11#11718607—21no—
12#11718607—21no—
13#11718589—21no—
14#11718589—21no—
15#11718586—21no—
16C13×#324C2212yes—
17C13×#323—21no—
18#11718120C2212yes—
19#11718117—21no—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13—21no—
22C13×#117—41no—
23C13×#117—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C13×C22⋊C4D411yescharacteristic
27C2×C13×C22⋊C4D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—21no—
31#88180—22no—
32#88180C814yescomplemented
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—41no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13C2×C412yes—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×C4×Dic13C2×C412yes—
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C4×C8×C13—41no—
44#88071—22no—
45#88071—22no—
46C22⋊#1055—22no—
47C4⋊#1055—41no—
48C4×#1055—41no—
49#11450—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
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×C13C2×C812yes—
58C22×C4×C13M1612yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—42no—
65C22×Dic13—82no—
66C2×C8×C13—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C22⋊C4—41no—
70C13×C22⋊C4—41no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C22⋊Dic13—24no—
76C4⋊Dic13—24no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79C4⋊Dic13—42no—
80#6101—82no—
81#6101—82no—
82C4×Dic13—22no—
83C4×Dic13C2×C814yes—
84C2×#1055—42no—
85#2317—131no—
86#1458—131no—
87#1458D1311yescharacteristic
88#1325—134no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13C22⋊C812yes—
94C23×C13C2×C22⋊C411yescharacteristic
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13C22⋊C812yes—
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#9911yescharacteristic
112C2×C4×C13#10112yes—
113C2×C4×C13C22×C811yescharacteristic
114C2×C4×C13C2×M1611yescharacteristic
115C2×Dic13—24no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—84no—
122C8×C13—82no—
123#1055—82no—
124C2×#117—131no—
125C2×#117C2×D1311yescharacteristic
126C22×C4⋊C4—131no—
127#431—21no—
128#431—261no—
129#389—261no—
130#389—261no—
131#385—261no—
132#385—261no—
133#384—132no—
134#382—132no—
135#324—132no—
136#324C2×D1312yes—
137#323—21no—
138#323—261no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—42no—
143C22×C13—42no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13C2×C22⋊C811yescharacteristic
147C22×C13C2×#9911yescharacteristic
148C22×C13C2×#10111yescharacteristic
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13#32412yes—
156C4×C13#32412yes—
157Dic13—44no—
158Dic13—82no—
159C23×C4—261no—
160C23×C4C4×D1311yescharacteristic
161#117—41no—
162#117—41no—
163#117—134no—
164#117—262no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—261no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—262no—
169C2×C4⋊C4—262no—
170C2×C4⋊C4—521no—
171C2×C4⋊C4—521no—
172C2×C4⋊C4C4×D1311yescharacteristic
173C2×C4⋊C4C22×D1311yescharacteristic
174C2×C22⋊C4—261no—
175C2×C22⋊C4D5211yescharacteristic
176C2×C22⋊C4C22⋊D1311yescharacteristic
177C2×C42—132no—
178C2×C42D5211yescharacteristic
179C2×C42C22⋊D1311yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—521no—
182C22⋊C8—22no—
183C22⋊C8—262no—
184C4×C8—41no—
185C4×C8—521no—
186#95—262no—
187#95—262no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13C2×#32411yescharacteristic
192C2×C13#212811yescharacteristic
193C2×C13#213511yescharacteristic
194C24#610311yescharacteristic
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—522no—
201C22×C4—1042no—
202C22×C4C8×D1312yes—
203C22×C4#609412yes—
204C22×C4#610311yescharacteristic
205C22×C4#610311yescharacteristic
206C22×C4#610311yescharacteristic
207C22×C4C2×C4×D1311yescharacteristic
208C22×C4C2×D5211yescharacteristic
209C22×C4C2×C22⋊D1311yescharacteristic
210C2×C8—42no—
211C2×C8—522no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—264no—
215C4⋊C4—522no—
216C4⋊C4—521no—
217C4⋊C4—521no—
218C4⋊C4—1042no—
219C4⋊C4—1042no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—264no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—134no—
228C42—262no—
229C13#1145011yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—41no—
233C23—41no—
234C23#8806012yes—
235C23C2×#610311yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—264no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—1044no—
257C2×C4#8804611yescharacteristic
258C2×C4#8804611yescharacteristic
259C2×C4#8806012yes—
260C2×C4#8806412yes—
261C2×C4C2×C8×D1311yescharacteristic
262C2×C4C2×#609411yescharacteristic
263C8—82no—
264C8—1042no—
265C22—21no—
266C22—21no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22C2×#8804611yescharacteristic
273C22C2×#8806011yescharacteristic
274C22C2×#8806411yescharacteristic
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—524no—
282C4—1042no—
283C4#1171806112yes—
284C4#1171806112yes—
285C2—21no—
286C2—21no—
287C2—42no—
288C2C2×#1171806111yescharacteristic
289C2#1311650711yescharacteristic
290C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1458D13
hypocenterC13#11450
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
32. #88180C8semidirect
229. C13#11450semidirect

Maximal subgroups

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

subgroupindex
#131174562
#131131502
#131127812
C13×#14582
#1145013