Finite Group Databasebeta

← #16787049

Subgroups — #16787049

Order 3328.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#13130087C211yesmaximal, characteristic
2#13130087C211yesmaximal, characteristic
3#13129781C214yesmaximal
4#13117460C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C2×#88180C411yescharacteristic
7C2×#88180C2211yescharacteristic
8#11719128—21no—
9#11719128—21no—
10#11718871C412yes—
11#11718871C2212yes—
12#11718638—21no—
13#11718637—21no—
14#11718634—21no—
15#11718634—21no—
16#11718305C2212yes—
17#11718305C2212yes—
18#11718285—21no—
19#11718285—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—41no—
25C2×C13×C4⋊C4—41no—
26C2×C22⋊Dic13C2×C412yes—
27C2×C22⋊Dic13C2×C411yescharacteristic
28C2×C22⋊Dic13C2311yescharacteristic
29#88180—24no—
30#88180—41no—
31#88180—41no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D411yescharacteristic
34C2×C4⋊Dic13D411yescharacteristic
35C2×#6101—22no—
36C2×#6101—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C22⋊#1057—22no—
41C22⋊#1057—22no—
42#88112—41no—
43#88112—41no—
44#88110—41no—
45#88110—41no—
46#88071—22no—
47#88071—22no—
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—42no—
56C22×C4×C13—82no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×#1057—42no—
65C2×#1057—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C22⋊Dic13—22no—
70C22⋊Dic13—41no—
71C22⋊Dic13—41no—
72C22⋊Dic13M1614yes—
73C4⋊Dic13—24no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76#6101—82no—
77#6101—82no—
78C4×Dic13—24no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—21no—
83#2317—131no—
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—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—84no—
103C2×C4×C13#9911yescharacteristic
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#10112yes—
106C2×Dic13—24no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117#1057—82no—
118#1057—82no—
119C2×#117—131no—
120C2×#117—131no—
121C22×C4⋊C4#26111yescharacteristic
122#432—261no—
123#432—261no—
124#389—261no—
125#389—261no—
126#385—132no—
127#385—132no—
128#384—261no—
129#382—261no—
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—82no—
148Dic13—44no—
149Dic13—41no—
150Dic13—41no—
151Dic13—41no—
152Dic13—41no—
153C23×C4C2×#26112yes—
154C23×C4C2×#26111yescharacteristic
155#117—264no—
156#117—521no—
157#117—521no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—261no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4—262no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—131no—
169C2×C22⋊C4—131no—
170C2×C42—131no—
171C2×C42—131no—
172C2×C42—261no—
173C4⋊C8—521no—
174C4⋊C8—521no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177#97—521no—
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
187C24C22×#26111yescharacteristic
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—42no—
194C22×C4—82no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—262no—
200C22×C4C22⋊#26111yescharacteristic
201C22×C4C22⋊#26111yescharacteristic
202C2×C8—522no—
203C2×C8—522no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—264no—
208C4⋊C4—521no—
209C4⋊C4—521no—
210C4⋊C4—1042no—
211C4⋊C4—1042no—
212C22⋊C4—134no—
213C22⋊C4—262no—
214C22⋊C4—521no—
215C22⋊C4—521no—
216C42—264no—
217C42—261no—
218C42—261no—
219C42—261no—
220C42—261no—
221C13#1152011yescharacteristic, complemented, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23D13⋊M1612yes—
227C23C2×C22⋊#26111yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—84no—
238C2×C4—264no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4#8811312yes—
250C2×C4#8811911yescharacteristic
251C2×C4#8811911yescharacteristic
252C8—1042no—
253C8—1042no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1171912611yescharacteristic
262C22C2×#8811311yescharacteristic
263C22C2×#8811911yescharacteristic
264C4—22no—
265C4—21no—
266C4—21no—
267C4—82no—
268C4—524no—
269C4—521no—
270C4—521no—
271C4—521no—
272C4—521no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1313008611yescharacteristic
277C2#1313109511yescharacteristic
278C2#1313109811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
cosocleC2×C22⋊Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11520
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

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
#131300872
#131297812
#131174602
#1152013