Finite Group Databasebeta

← #16786794

Subgroups — #16786794

Order 3328.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130067C212yesmaximal
2#13129779C212yesmaximal, complemented
3#13129777C212yesmaximal, complemented
4#13117239C211yesmaximal, characteristic
5C2×C13×#117C411yescharacteristic
6C2×#88180C2211yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8#11719119—22no—
9#11718638C411yescharacteristic
10#11718638C2211yescharacteristic
11#11718637C411yescharacteristic
12#11718637C2211yescharacteristic
13#11718603—22no—
14C4×#6101—22no—
15#11718305—22no—
16#11718285C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13—21no—
19C13×#117—41no—
20C13×#117—41no—
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—21no—
24C2×C42×C13—21no—
25C2×C22⋊Dic13D412yes—
26#88180—41no—
27#88180—41no—
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×C4⋊Dic13C2311yescharacteristic
30C2×#6101—22no—
31C2×#6101—22no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13—22no—
34C2×C4×Dic13C814yescomplemented
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D412yes—
38C22⋊#1057—24no—
39C4⋊#1057—42no—
40C4×#1057—42no—
41#88071—22no—
42#88071—22no—
43#11447—131nomaximal, Sylow
44C24×C13C22⋊C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C2×C812yes—
52C22×C4×C13M1612yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—21no—
55C22×Dic13—24no—
56C22×Dic13—21no—
57C22×Dic13—42no—
58C22×Dic13—42no—
59C22×Dic13C22⋊C412yes—
60C22×Dic13C2×D412yes—
61C2×#1057—44no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C22⋊C4—42no—
65C42×C13—41no—
66C42×C13—41no—
67C22⋊Dic13—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70#6101—44no—
71#6101—44no—
72C4×Dic13—24no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13C2×C812yes—
78C4×Dic13C2×C812yes—
79#2285—131no—
80#1458—132no—
81#1325—132no—
82#1324—132no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13C22⋊C812yes—
88C23×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13C22⋊C812yes—
100C2×C4×C13#9911yescharacteristic
101C2×C4×C13#9911yescharacteristic
102C2×C4×C13#10112yes—
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—48no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116#1057—84no—
117C2×#117—131no—
118C2×#117#26111yescharacteristic
119C22×C42—131no—
120#431—262no—
121#384—131no—
122#384—131no—
123#382—131no—
124#382—131no—
125#380—262no—
126C4×C4⋊C4—262no—
127#324—134no—
128#323—262no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—22no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13C2×C22⋊C811yescharacteristic
137C22×C13C2×#9911yescharacteristic
138C22×C13C2×#10111yescharacteristic
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—81no—
142C4×C13—81no—
143C4×C13#32412yes—
144C4×C13#32412yes—
145Dic13—24no—
146Dic13—42no—
147Dic13—42no—
148Dic13—42no—
149C23×C4—261no—
150C23×C4C2×#26111yescharacteristic
151#117—41no—
152#117—41no—
153#117—521no—
154#117—521no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—262no—
158C2×C4⋊C4—262no—
159C2×C4⋊C4C2×#26111yescharacteristic
160C2×C4⋊C4C2×#26111yescharacteristic
161C2×C22⋊C4—21no—
162C2×C22⋊C4—132no—
163C2×C42—21no—
164C2×C42—134no—
165C2×C42—131no—
166C2×C42—131no—
167C2×C42—132no—
168C2×C42—262no—
169C2×C42—261no—
170C4⋊C8—522no—
171C22⋊C8—264no—
172C4×C8—522no—
173#95—262no—
174#95—262no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—42no—
178C2×C13C2×#32411yescharacteristic
179C2×C13#212611yescharacteristic
180C2×C13#213211yescharacteristic
181C24C22⋊#26111yescharacteristic
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—261no—
190C22×C4—264no—
191C22×C4—261no—
192C22×C4—522no—
193C22×C4—522no—
194C22×C4D13⋊C812yes—
195C22×C4#611812yes—
196C22×C4C22⋊#26111yescharacteristic
197C22×C4C22×#26111yescharacteristic
198C2×C8—524no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—521no—
202C4⋊C4—521no—
203C4⋊C4—524no—
204C4⋊C4—524no—
205C22⋊C4—42no—
206C22⋊C4—522no—
207C42—41no—
208C42—41no—
209C42—132no—
210C42—132no—
211C42—264no—
212C42—262no—
213C42—262no—
214C42—261no—
215C42—261no—
216C13#1144711yescharacteristic, complemented, Sylow
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23#8811112yes—
222C23C2×C22⋊#26111yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—528no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4#8811112yes—
245C2×C4#8811312yes—
246C2×C4#8811911yescharacteristic
247C2×C4#8811911yescharacteristic
248C2×C4C2×D13⋊C811yescharacteristic
249C2×C4C2×#611811yescharacteristic
250C8—1044no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×#8811111yescharacteristic
259C22C2×#8811311yescharacteristic
260C22C2×#8811911yescharacteristic
261C4—21no—
262C4—21no—
263C4—81no—
264C4—81no—
265C4—264no—
266C4—522no—
267C4—522no—
268C4—522no—
269C4#1171828612yes—
270C4#1171828612yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#1171828611yescharacteristic
275C2#1313110711yescharacteristic
276C2#1313112711yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11447
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129779C2semidirect
3. #13129777C2semidirect
34. C2×C4×Dic13C8semidirect
216. C13#11447semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297792
#131297772
#131172392
#1144713