Finite Group Databasebeta

← #15772210

Subgroups — #15772210

Order 3328.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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#13117550C211yesmaximal, characteristic
2#13113153C212yesmaximal
3#13112781C212yesmaximal, complemented
4#13112770C211yesmaximal, characteristic, complemented
5C13×#1319C211yesmaximal, characteristic, complemented
6C2×#88201C411yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×#88147C2211yescharacteristic
9C13×#391C2211yescharacteristic
10#11718637C2211yescharacteristic
11#11718600C411yescharacteristic
12#11718593C411yescharacteristic
13D13×C22⋊C8—22no—
14#11718330—22no—
15#11718329—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718060—22no—
19C22×Q8×C13C2×C411yescharacteristic
20C22×D52C2×C411yescharacteristic
21C22×C4×D13D412yes—
22C2×C13×C4⋊C4C2311yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24#88201—22no—
25#88201C814yescomplemented
26Q8×Dic13—42no—
27C2×#6103—22no—
28C2×#6103—22no—
29C2×#6103D412yes—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—22no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C8×D13—42no—
37#88147—42no—
38C13×C22⋊C8—22no—
39C13×#95—22no—
40#88071—21no—
41#88071—21no—
42C22⋊#1055—22no—
43#88060—42no—
44#11481—131nomaximal, Sylow
45C23×D13C22⋊C412yes—
46C2×Q8×C13—21no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13C2×C812yescomplemented
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C22×C411yescharacteristic
53C22×C4×C13C2×D412yes—
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C2×D52—41no—
59C2×D52—41no—
60C2×D52C2×C812yes—
61C2×D52M1612yes—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—82no—
65C2×C8×C13—42no—
66C13×C4⋊C4—41no—
67C42×C13—41no—
68#6103—28no—
69#6103—42no—
70#6103—82no—
71C4⋊Dic13—42no—
72C4⋊Dic13—41no—
73#6101—82no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13—42no—
77C4×Dic13C2×C812yescomplemented
78C2×#1055—42no—
79C8×D13—84no—
80#2326—131no—
81#1459—132no—
82#1325—132no—
83#1319—131no—
84#1319D1311yescharacteristic, complemented
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13C22⋊C814yes—
91Q8×C13—42no—
92Q8×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13—41no—
113C2×Dic13#9912yes—
114D52—42no—
115D52—42no—
116C4×D13—44no—
117C4×D13—82no—
118C8×C13—82no—
119#1055—82no—
120C2×#124—131no—
121C2×C4×Q8—131no—
122C2×C4×D4—131no—
123C2×C22⋊C8—262no—
124#391C2×D1311yescharacteristic
125#390—131no—
126#388—262no—
127#385—262no—
128#384—131no—
129#376—131no—
130#324—132no—
131#324C2×D1312yes—
132#323—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13C2×C22⋊C811yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13#41311yescharacteristic
138C2×D13—24no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13—44no—
142C2×D13—82no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—42no—
146C4×C13—42no—
147C4×C13—81no—
148Dic13—22no—
149Dic13—42no—
150Dic13—41no—
151Dic13—81no—
152C22×Q8C4×D1311yescharacteristic
153C22×D4—131no—
154C23×C4—132no—
155C22×C8—522no—
156#124—134no—
157#124—262no—
158C4×Q8—522no—
159C4×D4—522no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—261no—
162C2×C4⋊C4—262no—
163C2×C4⋊C4C22×D1311yescharacteristic
164C2×C22⋊C4—132no—
165C2×C22⋊C4—262no—
166C2×C22⋊C4—262no—
167C2×C42—131no—
168C2×C42—131no—
169C2×C42—261no—
170C2×C42C4×D1311yescharacteristic
171C22⋊C8—22no—
172C22⋊C8—262no—
173C22⋊C8—522no—
174#95—22no—
175#95—261no—
176#95—261no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13#145911yescharacteristic
180C2×C13#212711yescharacteristic
181C2×C13#213511yescharacteristic
182D13—44no—
183C24—132no—
184C2×Q8—21no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8C8×D1312yescomplemented
188C2×D4—132no—
189C2×D4—132no—
190C2×D4—521no—
191C2×D4—521no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—262no—
197C22×C4—262no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4—1042no—
201C22×C4C2×C4×D1311yescharacteristic
202C22×C4D4×D1312yes—
203C2×C8—42no—
204C2×C8—522no—
205C2×C8—1044no—
206C4⋊C4—41no—
207C4⋊C4—521no—
208C4⋊C4—522no—
209C4⋊C4—1042no—
210C22⋊C4—268no—
211C22⋊C4—522no—
212C22⋊C4—1042no—
213C42—41no—
214C42—132no—
215C42—262no—
216C42—261no—
217C42—522no—
218C13#1148111yescharacteristic, complemented, Sylow
219C23—134no—
220C23—262no—
221C23—262no—
222C23—522no—
223C23—522no—
224C23C22⋊C4×D1311yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—522no—
228D4—522no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—132no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—524no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—522no—
248C2×C4—521no—
249C2×C4—1042no—
250C2×C4C2×C8×D1311yescharacteristic
251C2×C4M16×D1311yescharacteristic
252C8—82no—
253C8—1042no—
254C22—21no—
255C22—21no—
256C22—264no—
257C22—524no—
258C22—522no—
259C22—522no—
260C22—1042no—
261C22D13×C22⋊C811yescharacteristic
262C22D13×#9911yescharacteristic
263C22#1171840611yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—42no—
268C4—81no—
269C4—262no—
270C4—522no—
271C4—521no—
272C4—1041no—
273C2—21no—
274C2—21no—
275C2—524no—
276C2#1311315111yescharacteristic
277C2#1311650411yescharacteristic
278C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1319C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1319D13
hypocenterC13#11481
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
4. #13112770C2semidirect
5. C13×#1319C2semidirect
25. #88201C8semidirect
49. C2×Q8×C13C2×C8semidirect
77. C4×Dic13C2×C8semidirect
84. #1319D13semidirect
187. C2×Q8C8×D13semidirect
218. C13#11481semidirect

Maximal subgroups

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

subgroupindex
#131175502
#131131532
#131127812
#131127702
C13×#13192
#1148113