Finite Group Databasebeta

← D13⋊#1324 #16786787

Subgroups — D13⋊#1324 #16786787

Order 3328.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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#13129777C212yesmaximal, complemented
3#13129776C212yesmaximal, complemented
4D13×#382C211yesmaximal, characteristic
5C2×C4⋊C4×D13C411yescharacteristic
6C2×C4⋊C4×D13C2211yescharacteristic
7C2×C42×D13C411yescharacteristic
8D13⋊(C22⋊C8)—22no—
9C13×#382C411yescharacteristic
10#11718638C411yescharacteristic
11#11718638C2211yescharacteristic
12#11718597C2211yescharacteristic
13D13×#95—22no—
14#11718311—22no—
15#11718286—22no—
16#11718285C2214yes—
17C22×C4×D13—21no—
18C22×C4×D13—21no—
19C22×C4×D13C2×C411yescharacteristic
20C22×C4×D13D412yes—
21C2×D13⋊C8—42no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13C2311yescharacteristic
27C2×#6101—21no—
28C2×#6101D412yes—
29C2×C4×Dic13—21no—
30C2×C4×Dic13C2×C411yescharacteristic
31C4⋊C4×D13—41no—
32C4⋊C4×D13—41no—
33C4⋊C4×D13—41no—
34C4⋊C4×D13—41no—
35C42×D13—22no—
36C42×D13C814yescomplemented
37C22⋊#1057—24no—
38#88111—42no—
39C13×#95—22no—
40#88071—22no—
41#88071—22no—
42#88071—22no—
43C2×#1324—131nomaximal, Sylow
44C23×D13C22⋊C411yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C412yes—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13C22⋊C411yescharacteristic
52C22×Dic13C2×D412yes—
53C2×C4×D13—21no—
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×C4×D13—24no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—42no—
60C2×C4×D13—42no—
61C2×C4×D13—44no—
62C2×C4×D13—44no—
63C2×C4×D13—41no—
64C2×C4×D13—41no—
65C2×C4×D13C2×C812yes—
66C2×C4×D13M1612yes—
67C2×#1057—44no—
68D13⋊C8—84no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C42×C13—21no—
72C42×C13C2×C812yescomplemented
73C4⋊Dic13—41no—
74C4⋊Dic13—41no—
75#6101—42no—
76#6101—42no—
77C4×Dic13—21no—
78C4×Dic13—24no—
79C4×Dic13C2×C812yescomplemented
80C2×#382—131no—
81C2×#324—132no—
82#1324—132no—
83#1324—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—22no—
86C22×D13—22no—
87C22×D13C22⋊C812yes—
88C22×D13#9911yescharacteristic
89C22×D13#9911yescharacteristic
90C22×D13#10112yes—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13C22×C811yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13C22⋊C812yes—
112C4×D13—22no—
113C4×D13—22no—
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—48no—
117C4×D13—44no—
118C4×D13—82no—
119C4×D13—82no—
120C4×D13—82no—
121#1057—84no—
122C22×C4⋊C4—131no—
123C22×C4⋊C4—131no—
124C22×C42—131no—
125C2×C22⋊C8—262no—
126#382—131no—
127#382—131no—
128#382—131no—
129#382—262no—
130#382#26111yescharacteristic
131C2×#95—262no—
132#324—134no—
133#324—262no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13C2×C22⋊C811yescharacteristic
137C22×C13C2×#9911yescharacteristic
138C22×C13C2×#10111yescharacteristic
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—24no—
142C2×D13—24no—
143C2×D13#32412yes—
144C2×D13#32412yes—
145C2×D13#35412yes—
146C2×D13#35512yes—
147C4×C13—21no—
148C4×C13—21no—
149C4×C13—42no—
150C4×C13—42no—
151C4×C13—81no—
152Dic13—22no—
153Dic13—42no—
154Dic13—42no—
155Dic13—81no—
156C23×C4—131no—
157C23×C4—132no—
158C23×C4—261no—
159C23×C4—261no—
160C22×C8—522no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—261no—
165C2×C4⋊C4—521no—
166C2×C4⋊C4—521no—
167C2×C4⋊C4—521no—
168C2×C4⋊C4—521no—
169C2×C4⋊C4C2×#26111yescharacteristic
170C2×C4⋊C4C2×#26111yescharacteristic
171C2×C42—131no—
172C2×C42—134no—
173C2×C42—262no—
174C2×C42—261no—
175C2×C42C2×#26111yescharacteristic
176C22⋊C8—264no—
177C22⋊C8—522no—
178#95—22no—
179#95—262no—
180#95—262no—
181#95—262no—
182C2×C13—21no—
183C2×C13—21no—
184C2×C13C2×#32411yescharacteristic
185C2×C13C2×#35411yescharacteristic
186C2×C13C2×#35511yescharacteristic
187D13—22no—
188D13#132414yescomplemented
189C24—131no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—131no—
193C22×C4—132no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—262no—
199C22×C4—264no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—522no—
205C22×C4—522no—
206C22×C4—524no—
207C22×C4—521no—
208C22×C4—521no—
209C22×C4—524no—
210C22×C4C22⋊#26112yes—
211C22×C4C22×#26111yescharacteristic
212C2×C8—524no—
213C2×C8—1044no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—522no—
217C4⋊C4—521no—
218C4⋊C4—521no—
219C4⋊C4—522no—
220C42—21no—
221C42—132no—
222C42—264no—
223C42—261no—
224C42D13⋊C812yescomplemented
225C13C2×#132411yescharacteristic, complemented, Sylow
226C23—131no—
227C23—132no—
228C23—131no—
229C23—132no—
230C23—262no—
231C23—262no—
232C23C2×C22⋊#26111yescharacteristic
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—132no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—524no—
252C2×C4—528no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—521no—
258C2×C4—1042no—
259C2×C4—1042no—
260C2×C4—1042no—
261C2×C4C2×D13⋊C811yescharacteristic
262C2×C4D13⋊M1611yescharacteristic
263C8—1044no—
264C22—21no—
265C22—21no—
266C22—132no—
267C22—132no—
268C22—132no—
269C22—132no—
270C22—264no—
271C22—264no—
272C22—261no—
273C22—261no—
274C22D13⋊(C22⋊C8)11yescharacteristic
275C22D13⋊#9911yescharacteristic
276C22D13⋊#10111yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—262no—
283C4—522no—
284C4—522no—
285C4—1041no—
286C2—21no—
287C2—21no—
288C2—134no—
289C2—262no—
290C2D13⋊#32411yescharacteristic
291C2D13⋊#35411yescharacteristic
292C2D13⋊#35511yescharacteristic
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
hypocenterC13C2×#1324
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. #13129777C2semidirect
3. #13129776C2semidirect
36. C42×D13C8semidirect
72. C42×C13C2×C8semidirect
79. C4×Dic13C2×C8semidirect
188. D13#1324semidirect
224. C42D13⋊C8semidirect
225. C13C2×#1324semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3242
#131297772
#131297762
D13×#3822
C2×#132413