Finite Group Databasebeta

← #16786815

Subgroups — #16786815

Order 3328.

434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130067C211yesmaximal, characteristic
2#13130067C211yesmaximal, characteristic
3#13129780C214yesmaximal
4#13117459C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C2211yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8#11719119—21no—
9#11719119—21no—
10#11718646—21no—
11#11718646—21no—
12#11718611C412yes—
13#11718611C2212yes—
14#11718597—21no—
15#11718596—21no—
16#11718305C2212yes—
17#11718305C2212yes—
18#11718285—21no—
19#11718285—21no—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13C2×C412yes—
22C13×#117—22no—
23C13×#117C814yescomplemented
24C2×C13×C4⋊C4—21no—
25C2×C13×C22⋊C4C2×C412yes—
26C2×C42×C13—21no—
27C2×C22⋊Dic13C2×C411yescharacteristic
28C2×C22⋊Dic13C2311yescharacteristic
29#88180—41no—
30#88180—41no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—41no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C22⋊#1057—22no—
42C22⋊#1057—22no—
43C4⋊#1057—41no—
44C4⋊#1057—41no—
45C4×#1057—41no—
46C4×#1057—41no—
47#88071—22no—
48#88071—22no—
49#11454—131nomaximal, Sylow
50C24×C13C22×C411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C2×C812yes—
58C22×C4×C13M1612yes—
59C22×Dic13—22no—
60C22×Dic13—42no—
61C22×Dic13—82no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×#1057—42no—
67C2×#1057—42no—
68C13×C4⋊C4—24no—
69C13×C22⋊C4—22no—
70C13×C22⋊C4C2×C814yes—
71C42×C13—24no—
72C22⋊Dic13—41no—
73C22⋊Dic13—41no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—42no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79C4⋊Dic13—82no—
80C4⋊Dic13—82no—
81C4×Dic13—21no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85#2317—131no—
86#1458—131no—
87#1458—131no—
88#1326—134no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13C22×C811yescharacteristic
95C23×C13C2×M1611yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—24no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13C22⋊C812yes—
106C2×C4×C13C22⋊C812yes—
107C2×C4×C13#9911yescharacteristic
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#10112yes—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—84no—
122#1057—82no—
123#1057—82no—
124C2×#117—131no—
125C2×#117#26111yescharacteristic
126C22×C4⋊C4—131no—
127#431—261no—
128#431—261no—
129#389—261no—
130#389—261no—
131#385—132no—
132#385—132no—
133#384—261no—
134#382—261no—
135#324—261no—
136#324—261no—
137#323—132no—
138#323—132no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13—42no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13C2×C22⋊C811yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13C2×#10111yescharacteristic
151C4×C13—22no—
152C4×C13—44no—
153C4×C13#32412yes—
154C4×C13#32412yes—
155Dic13—41no—
156Dic13—41no—
157Dic13—41no—
158Dic13—41no—
159Dic13—82no—
160C23×C4—132no—
161C23×C4C2×#26111yescharacteristic
162#117—22no—
163#117—521no—
164#117—521no—
165#117#105714yescomplemented
166C2×C4⋊C4—21no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4—262no—
173C2×C4⋊C4—521no—
174C2×C4⋊C4—521no—
175C2×C22⋊C4—131no—
176C2×C22⋊C4—131no—
177C2×C22⋊C4C2×#26112yes—
178C2×C42—21no—
179C2×C42—131no—
180C2×C42—131no—
181C4⋊C8—521no—
182C4⋊C8—521no—
183C22⋊C8—262no—
184C22⋊C8—262no—
185C4×C8—521no—
186C4×C8—521no—
187#95—262no—
188#95—262no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13—41no—
192C2×C13—41no—
193C2×C13C2×#32411yescharacteristic
194C2×C13#212211yescharacteristic
195C2×C13#212311yescharacteristic
196C24C22×#26111yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—262no—
206C22×C4—522no—
207C22×C4—1042no—
208C22×C4C2×#105712yes—
209C22×C4#612212yes—
210C22×C4C22⋊#26111yescharacteristic
211C22×C4C22⋊#26111yescharacteristic
212C2×C8—522no—
213C2×C8—522no—
214C4⋊C4—24no—
215C4⋊C4—521no—
216C4⋊C4—521no—
217C4⋊C4—522no—
218C4⋊C4—521no—
219C4⋊C4—521no—
220C4⋊C4—1042no—
221C4⋊C4—1042no—
222C22⋊C4—22no—
223C22⋊C4—521no—
224C22⋊C4—521no—
225C22⋊C4C2×#105714yes—
226C42—24no—
227C42—261no—
228C42—261no—
229C42—261no—
230C42—261no—
231C13#1145411yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23C22×#105711yescharacteristic
237C23C2×#612211yescharacteristic
238C23C2×C22⋊#26111yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—1044no—
260C2×C4#8810711yescharacteristic
261C2×C4#8810711yescharacteristic
262C2×C4#8811312yes—
263C2×C4C22⋊#105712yes—
264C2×C4C22⋊#105712yes—
265C8—1042no—
266C8—1042no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22C2×#8810711yescharacteristic
277C22C2×#8811311yescharacteristic
278C22C2×C22⋊#105711yescharacteristic
279C4—22no—
280C4—44no—
281C4—521no—
282C4—521no—
283C4—521no—
284C4—521no—
285C4—1042no—
286C4#1171828512yes—
287C4#1171828512yes—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2C2×#1171828511yescharacteristic
293C2#1313109711yescharacteristic
294C2#1313110011yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22×C4
cosocleC2×C22⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11454
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
23. C13×#117C8semidirect
165. #117#1057semidirect
231. C13#11454semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297802
#131174592
#1145413