Finite Group Databasebeta

← #15772080

Subgroups — #15772080

Order 3328.

454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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#13117457C211yesmaximal, characteristic
2D13×#324C212yesmaximal
3#13112782C211yesmaximal, characteristic, complemented
4#13112779C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C2×#88146C411yescharacteristic
7C2×C4⋊C4×D13C2211yescharacteristic
8C2×#88126C411yescharacteristic
9C13×#384C2211yescharacteristic
10#11718650—22no—
11#11718638C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718633—22no—
14#11718597C411yescharacteristic
15D13×C22⋊C8—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×C4×D13C2×C411yescharacteristic
20C22×C4×D13D412yes—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C4⋊C4C2311yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6103—21no—
26C2×#6103—21no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×#6101—21no—
30C2×#6101—22no—
31C2×#6101D412yes—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C8×D13—42no—
35#88146—42no—
36C4⋊C4×D13—42no—
37#88126—22no—
38#88126C814yescomplemented
39C13×C22⋊C8—22no—
40#88071—22no—
41#88071—22no—
42C22⋊#1055—22no—
43#88060—42no—
44#11448—131nomaximal, Sylow
45C23×D13C22⋊C411yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22×C411yescharacteristic
49C22×C4×C13C2×D412yes—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C412yes—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—82no—
59C2×C4×D13C2×C812yes—
60C2×C4×D13M1612yes—
61C2×C8×C13—42no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—82no—
65C42×C13—21no—
66C42×C13C2×C812yescomplemented
67#6103—24no—
68#6103—42no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71#6101—24no—
72#6101—42no—
73#6101—82no—
74C4×Dic13—21no—
75C4×Dic13—42no—
76C4×Dic13C2×C812yescomplemented
77C2×#1055—42no—
78C8×D13—84no—
79#2317—131no—
80C2×#324—132no—
81#1325—131no—
82#1325D1311yescharacteristic, complemented
83#1324—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—41no—
86C22×D13—41no—
87C22×D13C22⋊C812yes—
88C22×D13#9912yes—
89C22×D13#10112yes—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13C22×C811yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C2×Dic13C22⋊C812yes—
111C4×D13—24no—
112C4×D13—24no—
113C4×D13—44no—
114C4×D13—82no—
115C8×C13—82no—
116#1055—82no—
117C2×#117—131no—
118C2×#117—131no—
119C22×C4⋊C4—131no—
120C2×C22⋊C8—262no—
121#389—262no—
122#385—262no—
123#384—131no—
124#384C2×D1311yescharacteristic
125#382—131no—
126#382—131no—
127#324—132no—
128#324—262no—
129#324C2×D1312yes—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13C2×C22⋊C811yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13C2×#10111yescharacteristic
135C2×D13—22no—
136C2×D13—22no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13#32414yes—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13—42no—
144C4×C13—81no—
145Dic13—22no—
146Dic13—42no—
147Dic13—42no—
148Dic13—81no—
149C23×C4—131no—
150C23×C4—132no—
151C22×C8—522no—
152#117—134no—
153#117—262no—
154#117—522no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—262no—
161C2×C4⋊C4—522no—
162C2×C4⋊C4C4×D1311yescharacteristic
163C2×C4⋊C4C22×D1311yescharacteristic
164C2×C22⋊C4—261no—
165C2×C22⋊C4—261no—
166C2×C42—131no—
167C2×C42—261no—
168C2×C42C4×D1311yescharacteristic
169C22⋊C8—22no—
170C22⋊C8—262no—
171C22⋊C8—522no—
172#95—262no—
173#95—262no—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13C2×#32411yescharacteristic
177C2×C13#212711yescharacteristic
178C2×C13#213311yescharacteristic
179D13—24no—
180C24—131no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—131no—
184C22×C4—132no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4—262no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—261no—
192C22×C4—261no—
193C22×C4—1042no—
194C22×C4C2×C4×D1311yescharacteristic
195C22×C4D4×D1312yes—
196C2×C8—42no—
197C2×C8—522no—
198C2×C8—1044no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—82no—
202C4⋊C4—264no—
203C4⋊C4—522no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C4⋊C4—1042no—
207C22⋊C4—264no—
208C22⋊C4—522no—
209C42—21no—
210C42—132no—
211C42—261no—
212C42—522no—
213C42C8×D1312yescomplemented
214C13#1144811yescharacteristic, complemented, Sylow
215C23—132no—
216C23—132no—
217C23—132no—
218C23—521no—
219C23—521no—
220C23C22⋊C4×D1311yescharacteristic
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—132no—
231C2×C4—264no—
232C2×C4—264no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—524no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—521no—
243C2×C4—1042no—
244C2×C4C2×C8×D1311yescharacteristic
245C2×C4M16×D1311yescharacteristic
246C8—82no—
247C8—1042no—
248C22—21no—
249C22—21no—
250C22—134no—
251C22—262no—
252C22—262no—
253C22—522no—
254C22—522no—
255C22D13×C22⋊C811yescharacteristic
256C22D13×#9911yescharacteristic
257C22D13×#10111yescharacteristic
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—81no—
263C4—262no—
264C4—522no—
265C4—522no—
266C4—1041no—
267C2—21no—
268C2—21no—
269C2—264no—
270C2D13×#32411yescharacteristic
271C2#1311650211yescharacteristic
272C2#1311652411yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1325C2
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1325D13
hypocenterC13#11448
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
4. #13112779C2semidirect
5. C13×#1325C2semidirect
38. #88126C8semidirect
66. C42×C13C2×C8semidirect
76. C4×Dic13C2×C8semidirect
82. #1325D13semidirect
213. C42C8×D13semidirect
214. C13#11448semidirect

Maximal subgroups

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

subgroupindex
#131174572
D13×#3242
#131127822
#131127792
C13×#13252
#1144813