Finite Group Databasebeta

← #15774087

Subgroups — #15774087

Order 3328.

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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#13120041C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13112867C214yesmaximal
4C13×#1461C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88123C411yescharacteristic
7C13×#431—21no—
8#11718891—21no—
9C2×#88076—21no—
10#11718640C412yes—
11#11718640C2212yes—
12#11718637—21no—
13C4×C4⋊Dic13C411yescharacteristic
14#11718589—21no—
15#11718589—21no—
16#11718585—21no—
17C13×#324—21no—
18C13×#324C2212yes—
19#11718122C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×C4×Dic13—21no—
36C2×#6099—22no—
37#88123—41no—
38#88123—41no—
39C13×C4⋊C8—41no—
40C13×C22⋊C8—22no—
41C4×C8×C13—41no—
42#88076—42no—
43#88071—22no—
44#88071—22no—
45#88071C2×C412yes—
46C4⋊#1055—41no—
47C4⋊#1055—41no—
48#11908—131nomaximal, Sylow
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13SD1612yes—
52C2×Q8×C13Q1612yes—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C2×Dic26—42no—
63C2×Dic26—82no—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C4⋊Dic13—24no—
75C4⋊Dic13—42no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78#6101—82no—
79#6101—82no—
80C4×Dic13—42no—
81#6099—42no—
82#6099—42no—
83C2×#1055—42no—
84#2567—131no—
85#1801—131no—
86#1461D1311yescharacteristic
87#1354—134no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—42no—
90Q8×C13—42no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#9911yescharacteristic
106C2×C4×C13#10312yes—
107C2×C4×C13#10312yes—
108C2×C4×C13C2×SD1611yescharacteristic
109C2×C4×C13C2×Q1611yescharacteristic
110C2×Dic13—24no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116Dic26—84no—
117C8×C13—82no—
118#1055—82no—
119C2×C4⋊Q8—131no—
120C2×C4×Q8C2×D1311yescharacteristic
121#431—21no—
122#423—261no—
123C2×#101—261no—
124#395—132no—
125#395—132no—
126#391—261no—
127#389—261no—
128#389—261no—
129#384—261no—
130C4×C4⋊C4—131no—
131#343—132no—
132#324—21no—
133#324C2×D1312yes—
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—41no—
145C4×C13—41no—
146C4×C13—41no—
147C4×C13#35612yes—
148Dic13—44no—
149Dic13—82no—
150C22×Q8—132no—
151C22×Q8D5211yescharacteristic
152C2×M16—262no—
153C4⋊Q8—521no—
154C4⋊Q8—521no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—262no—
161C2×C4⋊C4—262no—
162C2×C4⋊C4C4×D1311yescharacteristic
163C2×C4⋊C4C22⋊D1311yescharacteristic
164C2×C4⋊C4C22×D1311yescharacteristic
165C2×C42—261no—
166C2×C42C4×D1311yescharacteristic
167C2×C42D5211yescharacteristic
168C2×C42C22⋊D1311yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—521no—
171C4⋊C8—521no—
172#101—522no—
173C22⋊C8—22no—
174C4×C8—41no—
175#95—132no—
176#95—262no—
177#95—262no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#152011yescharacteristic
181C2×C13#212211yescharacteristic
182C2×C13C2×#35611yescharacteristic
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—522no—
186C2×Q8—1042no—
187C2×Q8#609512yes—
188C2×Q8Dic5212yes—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4#610311yescharacteristic
192C22×C4#610311yescharacteristic
193C22×C4#610311yescharacteristic
194C22×C4#610311yescharacteristic
195C22×C4C2×C4×D1311yescharacteristic
196C22×C4C2×D5211yescharacteristic
197C22×C4C2×C22⋊D1311yescharacteristic
198M16—522no—
199M16—522no—
200C2×C8—42no—
201C2×C8—522no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—264no—
206C4⋊C4—522no—
207C4⋊C4—521no—
208C4⋊C4—521no—
209C4⋊C4—1042no—
210C4⋊C4—1042no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—522no—
218C13#1190811yescharacteristic, complemented, Sylow
219C23C2×#610311yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—1044no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—264no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4#8804611yescharacteristic
243C2×C4#8804611yescharacteristic
244C2×C4#8805612yes—
245C2×C4#8805612yes—
246C2×C4C2×#609511yescharacteristic
247C2×C4C2×Dic5211yescharacteristic
248C8—82no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22C2×#8804611yescharacteristic
253C22C2×#8805611yescharacteristic
254C22#1171880011yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—524no—
264C4—1042no—
265C4#1171807012yes—
266C2—21no—
267C2—21no—
268C2#1311340911yescharacteristic
269C2#1311648511yescharacteristic
270C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11908
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

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
#131200412
#131148322
#131128672
C13×#14612
#1190813