Finite Group Databasebeta

← #16786799

Subgroups — #16786799

Order 3328.

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

normal subgroups only

This group has 454 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
1D13⋊#324C212yesmaximal
2#13129778C212yesmaximal, complemented
3#13129777C212yesmaximal, complemented
4#13117461C211yesmaximal, characteristic
5C2×#88146C411yescharacteristic
6C2×C4⋊C4×D13C2211yescharacteristic
7C2×#88126C411yescharacteristic
8D13⋊(C22⋊C8)—22no—
9C13×#382C411yescharacteristic
10#11718638C2211yescharacteristic
11#11718637C411yescharacteristic
12#11718596C2211yescharacteristic
13#11718329—22no—
14#11718308—22no—
15#11718286—22no—
16#11718285C2214yes—
17C22×C4×D13C2×C411yescharacteristic
18C22×C4×D13D412yes—
19C2×D13⋊C8—42no—
20C2×C13×C4⋊C4C2×C411yescharacteristic
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—21no—
24C2×#6103—21no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13C2×C411yescharacteristic
27C2×C4⋊Dic13C2311yescharacteristic
28C2×#6101—21no—
29C2×#6101—22no—
30C2×#6101D412yes—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33#88146—42no—
34C4⋊C4×D13—42no—
35#88126—22no—
36#88126C814yescomplemented
37C22⋊#1057—24no—
38#88111—42no—
39C13×#95—22no—
40#88071—22no—
41#11448—131nomaximal, Sylow
42C23×D13C22⋊C411yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13C22⋊C412yes—
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—21no—
48C22×Dic13—21no—
49C22×Dic13C22⋊C411yescharacteristic
50C22×Dic13C2×D412yes—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—82no—
56C2×C4×D13C2×C812yes—
57C2×C4×D13M1612yes—
58C2×#1057—44no—
59D13⋊C8—84no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C42×C13—21no—
63C42×C13C2×C812yescomplemented
64#6103—24no—
65#6103—42no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68C4⋊Dic13—82no—
69#6101—24no—
70#6101—42no—
71#6101—82no—
72C4×Dic13—21no—
73C4×Dic13—42no—
74C4×Dic13C2×C812yescomplemented
75#2317—131no—
76C2×#324—132no—
77#1325—132no—
78#1324—132no—
79C23×C13C2×C22⋊C411yescharacteristic
80C22×D13—41no—
81C22×D13—41no—
82C22×D13C22⋊C812yes—
83C22×D13#9912yes—
84C22×D13#10112yes—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13C22×C811yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—41no—
105C2×Dic13C22⋊C812yes—
106C4×D13—24no—
107C4×D13—24no—
108C4×D13—44no—
109C4×D13—82no—
110#1057—84no—
111C2×#117—131no—
112C2×#117—131no—
113C22×C4⋊C4—131no—
114C2×C22⋊C8—262no—
115#389—262no—
116#385—262no—
117#384—131no—
118#384—131no—
119#382—131no—
120#382#26111yescharacteristic
121#324—134no—
122#324—262no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13C2×C22⋊C811yescharacteristic
126C22×C13C2×#9911yescharacteristic
127C22×C13C2×#10111yescharacteristic
128C2×D13—22no—
129C2×D13—22no—
130C2×D13—42no—
131C2×D13—42no—
132C2×D13#32414yes—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—42no—
136C4×C13—42no—
137C4×C13—81no—
138Dic13—22no—
139Dic13—42no—
140Dic13—42no—
141Dic13—81no—
142C23×C4—131no—
143C23×C4—132no—
144C22×C8—522no—
145#117—134no—
146#117—262no—
147#117—522no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—262no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—522no—
155C2×C4⋊C4C2×#26111yescharacteristic
156C2×C4⋊C4C2×#26111yescharacteristic
157C2×C22⋊C4—261no—
158C2×C22⋊C4—261no—
159C2×C42—131no—
160C2×C42—261no—
161C2×C42C2×#26111yescharacteristic
162C22⋊C8—264no—
163C22⋊C8—522no—
164#95—22no—
165#95—262no—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13C2×#32411yescharacteristic
169C2×C13#212711yescharacteristic
170C2×C13#213311yescharacteristic
171D13—24no—
172C24—131no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—131no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4—262no—
182C22×C4—262no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4—1042no—
186C22×C4C22⋊#26112yes—
187C22×C4C22×#26111yescharacteristic
188C2×C8—524no—
189C2×C8—1044no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—264no—
193C4⋊C4—522no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4—1042no—
197C4⋊C4—1042no—
198C22⋊C4—264no—
199C22⋊C4—522no—
200C42—21no—
201C42—132no—
202C42—261no—
203C42—522no—
204C42D13⋊C812yescomplemented
205C13#1144811yescharacteristic, complemented, Sylow
206C23—132no—
207C23—132no—
208C23—132no—
209C23—521no—
210C23—521no—
211C23C2×C22⋊#26111yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—132no—
222C2×C4—264no—
223C2×C4—264no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—524no—
229C2×C4—521no—
230C2×C4—521no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4—521no—
234C2×C4—1042no—
235C2×C4C2×D13⋊C811yescharacteristic
236C2×C4D13⋊M1611yescharacteristic
237C8—1044no—
238C22—21no—
239C22—21no—
240C22—134no—
241C22—262no—
242C22—262no—
243C22—522no—
244C22—522no—
245C22D13⋊(C22⋊C8)11yescharacteristic
246C22D13⋊#9911yescharacteristic
247C22D13⋊#10111yescharacteristic
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—81no—
253C4—262no—
254C4—522no—
255C4—522no—
256C4—1041no—
257C2—21no—
258C2—21no—
259C2—264no—
260C2D13⋊#32411yescharacteristic
261C2#1313111411yescharacteristic
262C2#1313113211yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenter#382#261
hypocenterC13#11448
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #13129778C2semidirect
3. #13129777C2semidirect
36. #88126C8semidirect
63. C42×C13C2×C8semidirect
74. C4×Dic13C2×C8semidirect
204. C42D13⋊C8semidirect
205. C13#11448semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3242
#131297782
#131297772
#131174612
#1144813