Finite Group Databasebeta

← #16786804

Subgroups — #16786804

Order 3328.

434 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130070C212yesmaximal
2#13129779C212yesmaximal, complemented
3#13129778C212yesmaximal, complemented
4#13117461C211yesmaximal, characteristic
5C2×#88146C2211yescharacteristic
6C2×C4⋊C4×D13C411yescharacteristic
7C2×#88126C411yescharacteristic
8#11719125—22no—
9C13×#382C411yescharacteristic
10#11718638C411yescharacteristic
11#11718637C2211yescharacteristic
12#11718596C2211yescharacteristic
13#11718329—22no—
14#11718308—22no—
15#11718287—22no—
16#11718285C2214yes—
17C22×C4×D13—21no—
18C22×C4×D13C2×C411yescharacteristic
19C2×C13×C4⋊C4C2×C411yescharacteristic
20C2×C13×C4⋊C4C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22C2×#6103—21no—
23C2×#6103D412yes—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13C2311yescharacteristic
27C2×#6101—21no—
28C2×#6101—21no—
29C2×#6101—22no—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13D412yes—
32#88146—42no—
33C4⋊C4×D13—42no—
34#88126—22no—
35#88126C814yescomplemented
36C22⋊#1057—24no—
37#88112—42no—
38C4×#1057—42no—
39C13×#95—22no—
40#88071—22no—
41#11450—131nomaximal, Sylow
42C23×D13C22⋊C411yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13C22⋊C412yes—
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—21no—
48C22×Dic13—21no—
49C22×Dic13C22⋊C411yescharacteristic
50C22×Dic13C2×D412yes—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—42no—
54C2×C4×D13—82no—
55C2×C4×D13C2×C812yes—
56C2×C4×D13M1612yes—
57C2×#1057—44no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C42×C13—21no—
61C42×C13C2×C812yes—
62#6103—24no—
63#6103—42no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—82no—
67#6101—24no—
68#6101—42no—
69#6101—82no—
70C4×Dic13—21no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13C2×C812yes—
74#2317—131no—
75#1458—132no—
76#1325—132no—
77#1325—132no—
78C23×C13C2×C22⋊C411yescharacteristic
79C22×D13—21no—
80C22×D13—21no—
81C22×D13—41no—
82C22×D13—41no—
83C22×D13C22⋊C812yes—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—41no—
93C2×C4×C13C22×C811yescharacteristic
94C2×C4×C13C2×M1611yescharacteristic
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—41no—
102C2×Dic13C22⋊C812yes—
103C2×Dic13#9912yes—
104C2×Dic13#10112yes—
105C4×D13—24no—
106C4×D13—24no—
107C4×D13—84no—
108#1057—84no—
109C2×#117—131no—
110C2×#117—131no—
111C22×C4⋊C4—131no—
112#431—262no—
113#389—262no—
114#385—262no—
115#384—131no—
116#384—131no—
117#382—131no—
118#382#26111yescharacteristic
119#324—134no—
120#323—262no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13C2×C22⋊C811yescharacteristic
124C22×C13C2×#9911yescharacteristic
125C22×C13C2×#10111yescharacteristic
126C2×D13—22no—
127C2×D13—42no—
128C2×D13—41no—
129C2×D13—41no—
130C2×D13—42no—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—42no—
134C4×C13—42no—
135C4×C13—81no—
136Dic13—42no—
137Dic13—42no—
138Dic13—81no—
139Dic13#32414yes—
140C23×C4—131no—
141C23×C4—261no—
142#117—134no—
143#117—262no—
144#117—522no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—261no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—262no—
151C2×C4⋊C4—522no—
152C2×C4⋊C4C2×#26111yescharacteristic
153C2×C4⋊C4C2×#26111yescharacteristic
154C2×C22⋊C4—132no—
155C2×C22⋊C4—261no—
156C2×C42—131no—
157C2×C42—132no—
158C2×C42C2×#26111yescharacteristic
159C4⋊C8—522no—
160C22⋊C8—264no—
161C4×C8—522no—
162#95—22no—
163#95—262no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13C2×#32411yescharacteristic
167C2×C13#212811yescharacteristic
168C2×C13#213511yescharacteristic
169D13—42no—
170C24—131no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4—261no—
180C22×C4—261no—
181C22×C4—522no—
182C22×C4—1042no—
183C22×C4C22⋊#26112yes—
184C22×C4C22×#26111yescharacteristic
185C2×C8—524no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—264no—
189C4⋊C4—521no—
190C4⋊C4—521no—
191C4⋊C4—522no—
192C4⋊C4—1042no—
193C4⋊C4—1042no—
194C22⋊C4—264no—
195C22⋊C4—522no—
196C42—21no—
197C42—132no—
198C42—262no—
199C42—262no—
200C42—261no—
201C42D13⋊C812yes—
202C13#1145011yescharacteristic, complemented, Sylow
203C23—132no—
204C23—261no—
205C23—261no—
206C23—521no—
207C23—521no—
208C23C2×C22⋊#26111yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—132no—
219C2×C4—132no—
220C2×C4—132no—
221C2×C4—264no—
222C2×C4—264no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—521no—
230C2×C4—1044no—
231C2×C4C2×D13⋊C811yescharacteristic
232C2×C4D13⋊M1611yescharacteristic
233C8—1044no—
234C22—21no—
235C22—21no—
236C22—262no—
237C22—522no—
238C22—522no—
239C22—521no—
240C22—521no—
241C22D13⋊(C22⋊C8)11yescharacteristic
242C22D13⋊#9911yescharacteristic
243C22D13⋊#10111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—81no—
249C4—134no—
250C4—522no—
251C4—522no—
252C4—1041no—
253C2—21no—
254C2—21no—
255C2—522no—
256C2D13⋊#32411yescharacteristic
257C2#1313111611yescharacteristic
258C2#1313113911yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenter#382#261
hypocenterC13#11450
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #13129779C2semidirect
3. #13129778C2semidirect
35. #88126C8semidirect
202. C13#11450semidirect

Maximal subgroups

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

subgroupindex
#131300702
#131297792
#131297782
#131174612
#1145013