Finite Group Databasebeta

← #16786734

Subgroups — #16786734

Order 3328.

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

normal subgroups only

This group has 526 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#13130068C212yesmaximal
2#13129763C212yesmaximal
3#13129762C212yesmaximal
4#13117421C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C2×#88131C411yescharacteristic
7C2×#88131C2211yescharacteristic
8#11719125—22no—
9C13×#381C411yescharacteristic
10#11718872C2211yescharacteristic
11#11718604C411yescharacteristic
12#11718604C2211yescharacteristic
13#11718307—22no—
14#11718307—22no—
15#11718305C2214yes—
16#11718286—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13C2×C411yescharacteristic
19C23×Dic13C2×C411yescharacteristic
20C22×Dic26—21no—
21C22×Dic26—21no—
22C22×Dic26—22no—
23C22×Dic26—42no—
24C22×Dic26—42no—
25C22×Dic26C814yescomplemented
26C2×C13×C22⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4C2×C411yescharacteristic
28C2×C22⋊Dic13C2×C411yescharacteristic
29C2×C22⋊Dic13C2311yescharacteristic
30C2×#6101—21no—
31C2×#6101D412yes—
32C2×C4×Dic13—21no—
33C2×C4×Dic13D412yes—
34#88131—42no—
35#88131—42no—
36C22⋊#1057—24no—
37#88112—42no—
38C4×#1057—42no—
39C13×#95—22no—
40#88071—22no—
41#88071—22no—
42#88071—22no—
43#11428—131nomaximal, Sylow
44C24×C13C22×C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C2×C812yes—
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13—21no—
57C22×Dic13—41no—
58C22×Dic13—41no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×C812yes—
62C22×Dic13C2×C812yes—
63C22×Dic13M1612yes—
64C22×Dic13C2×D412yes—
65C2×Dic26—24no—
66C2×Dic26—24no—
67C2×Dic26—42no—
68C2×Dic26—42no—
69C2×Dic26—48no—
70C2×Dic26—42no—
71C2×Dic26—42no—
72C2×Dic26—48no—
73C2×#1057—44no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C22⋊Dic13—41no—
77C22⋊Dic13—41no—
78#6101—42no—
79#6101—42no—
80C4×Dic13—22no—
81C4×Dic13—22no—
82C4×Dic13—42no—
83#2310—131no—
84#1458—132no—
85#1317—132no—
86#1317—132no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—42no—
90C23×C13C2×C22⋊C411yescharacteristic
91C23×C13C22×C811yescharacteristic
92C23×C13C2×M1611yescharacteristic
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—24no—
105C2×Dic13—24no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—41no—
115C2×Dic13C22⋊C812yes—
116C2×Dic13C22⋊C812yes—
117C2×Dic13#9912yes—
118C2×Dic13#10012yes—
119Dic26—48no—
120Dic26—48no—
121#1057—84no—
122C23×Q8—131no—
123C2×#117—131no—
124C2×#117—131no—
125#431—262no—
126#391—262no—
127#391—262no—
128#381—131no—
129#381—131no—
130#381—131no—
131#381#26111yescharacteristic
132#324—262no—
133#323—134no—
134C22×C13—22no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13C2×C22⋊C811yescharacteristic
142C22×C13C2×#9911yescharacteristic
143C22×C13C2×#10011yescharacteristic
144C4×C13—42no—
145C4×C13—42no—
146C4×C13—81no—
147Dic13—22no—
148Dic13—42no—
149Dic13—42no—
150Dic13—81no—
151Dic13#32314yes—
152C22×Q8—134no—
153C22×Q8—261no—
154C22×Q8—261no—
155C22×Q8—262no—
156C22×Q8—522no—
157C22×Q8—522no—
158C23×C4—131no—
159C23×C4—131no—
160C23×C4C2×#26111yescharacteristic
161#117—522no—
162#117—522no—
163C2×C4⋊C4—132no—
164C2×C4⋊C4—261no—
165C2×C22⋊C4—131no—
166C2×C22⋊C4—131no—
167C2×C22⋊C4C2×#26111yescharacteristic
168C2×C22⋊C4C2×#26111yescharacteristic
169C2×C42—132no—
170C2×C42—261no—
171C4⋊C8—522no—
172C22⋊C8—264no—
173C4×C8—522no—
174#95—22no—
175#95—262no—
176#95—262no—
177#95—262no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13—41no—
181C2×C13—41no—
182C2×C13C2×#32311yescharacteristic
183C2×C13#212312yes—
184C24C22×#26111yescharacteristic
185C2×Q8—264no—
186C2×Q8—264no—
187C2×Q8—522no—
188C2×Q8—522no—
189C2×Q8—528no—
190C2×Q8—528no—
191C2×Q8—522no—
192C2×Q8—522no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—131no—
199C22×C4—132no—
200C22×C4—132no—
201C22×C4—131no—
202C22×C4—132no—
203C22×C4—132no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4—521no—
210C22×C4—521no—
211C22×C4D13⋊C812yes—
212C22×C4C22⋊#26112yes—
213C2×C8—524no—
214C4⋊C4—522no—
215C4⋊C4—522no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—521no—
219C22⋊C4—521no—
220C42—262no—
221C42—262no—
222C42—522no—
223C13#1142811yescharacteristic, complemented, Sylow
224C23—21no—
225C23—21no—
226C23—42no—
227C23C2×D13⋊C811yescharacteristic
228C23D13⋊M1611yescharacteristic
229C23C2×C22⋊#26111yescharacteristic
230Q8—528no—
231Q8—528no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—132no—
242C2×C4—132no—
243C2×C4—132no—
244C2×C4—132no—
245C2×C4—264no—
246C2×C4—264no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—521no—
258C8—1044no—
259C22—22no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22D13⋊(C22⋊C8)11yescharacteristic
267C22D13⋊#9911yescharacteristic
268C22D13⋊#10011yescharacteristic
269C4—42no—
270C4—42no—
271C4—81no—
272C4—134no—
273C4—262no—
274C4—522no—
275C4—522no—
276C4—1041no—
277C2—21no—
278C2—21no—
279C2—41no—
280C2—41no—
281C2D13⋊#32311yescharacteristic
282C2#1313109912yes—
subgroupG/H
centerC22D13⋊#99
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC13×#381C4
socleC22×C13C2×#99
prime radicalC24×C13C22×C4
cosocleC2×C22⋊Dic13C23
hypercenter#381#261
hypocenterC13#11428
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
25. C22×Dic26C8semidirect
223. C13#11428semidirect

Maximal subgroups

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

subgroupindex
#131300682
#131297632
#131297622
#131174212
#1142813