Finite Group Databasebeta

← #15774086

Subgroups — #15774086

Order 3328.

388 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112866C214yesmaximal
4C13×#2567C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#395C412yes—
8C13×#395C2212yes—
9C13×#391—21no—
10C13×#389—21no—
11C13×#389—21no—
12C13×#384—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718586—21no—
16#11718585—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95C2×C412yes—
42#88076—42no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45C4⋊#1055—41no—
46C4⋊#1055—41no—
47C4×#1055—41no—
48#11908—131nomaximal, Sylow
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—42no—
52C2×Q8×C13—82no—
53C2×Q8×C13SD1612yes—
54C2×Q8×C13Q1612yes—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C13×C4⋊C4—24no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—82no—
72C13×C4⋊C4—82no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—42no—
80#6099—42no—
81#6099—42no—
82C2×#1055—42no—
83C2×#1055—42no—
84#2567D1311yescharacteristic
85#1801—131no—
86#1461—131no—
87#1354—134no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—42no—
90Q8×C13—42no—
91Q8×C13—84no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—24no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13#9911yescharacteristic
112C2×C4×C13#9911yescharacteristic
113C2×C4×C13#10312yes—
114C2×C4×C13#10312yes—
115C2×C4×C13C2×SD1611yescharacteristic
116C2×C4×C13C2×Q1611yescharacteristic
117#1055—82no—
118#1055—82no—
119C2×C4⋊Q8Dic1311yescharacteristic
120C2×C4×Q8C2×D1311yescharacteristic
121#431—261no—
122#423—261no—
123C2×#101—261no—
124#395Dic1312yes—
125#395C2×D1312yes—
126#391—21no—
127#389—21no—
128#389—21no—
129#384—21no—
130C4×C4⋊C4Dic1311yescharacteristic
131#343—132no—
132#324—132no—
133#324—261no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#10311yescharacteristic
138C22×C13#42111yescharacteristic
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—21no—
144C4×C13—44no—
145C4×C13—41no—
146C4×C13—41no—
147C4×C13—41no—
148C4×C13—82no—
149C4×C13#35612yes—
150C22×Q8C2×Dic1312yes—
151C22×Q8C22⋊D1311yescharacteristic
152C2×M16—262no—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C2×Dic1311yescharacteristic
163C2×C4⋊C4C22⋊D1311yescharacteristic
164C2×C4⋊C4C22×D1311yescharacteristic
165C2×C42—21no—
166C2×C42C2×Dic1311yescharacteristic
167C2×C42C22⋊D1311yescharacteristic
168C2×C42C22⋊D1311yescharacteristic
169C4⋊C8—521no—
170C4⋊C8—521no—
171C4⋊C8—521no—
172#101—522no—
173C22⋊C8—262no—
174C4×C8—521no—
175#95—22no—
176#95—22no—
177#95C2×Dic1312yes—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#152011yescharacteristic
181C2×C13#212211yescharacteristic
182C2×C13C2×#35611yescharacteristic
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—42no—
186C2×Q8—82no—
187C2×Q8#610612yes—
188C2×Q8#610712yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊Dic1311yescharacteristic
192C22×C4C22⋊Dic1311yescharacteristic
193C22×C4C22⋊Dic1311yescharacteristic
194C22×C4C22⋊Dic1311yescharacteristic
195C22×C4C22×Dic1311yescharacteristic
196C22×C4C2×C22⋊D1311yescharacteristic
197C22×C4C2×C22⋊D1311yescharacteristic
198M16—522no—
199M16—522no—
200C2×C8—522no—
201C2×C8—522no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C13#1190811yescharacteristic, complemented, Sylow
219C23C2×C22⋊Dic1311yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—84no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4#8807411yescharacteristic
243C2×C4#8807411yescharacteristic
244C2×C4#8807512yes—
245C2×C4#8807512yes—
246C2×C4C2×#610611yescharacteristic
247C2×C4C2×#610711yescharacteristic
248C8—1042no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22C2×#8807411yescharacteristic
253C22C2×#8807511yescharacteristic
254C22#1171889711yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#1171814012yes—
266C2—21no—
267C2—21no—
268C2#1311340811yescharacteristic
269C2#1311648611yescharacteristic
270C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2567C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2567D13
hypocenterC13#11908
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
218. C13#11908semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131128662
C13×#25672
#1190813