Finite Group Databasebeta

← D13⋊#1330 #16787287

Subgroups — D13⋊#1330 #16787287

Order 3328.

422 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 108 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⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
2#13131037C211yesmaximal, characteristic, complemented
3#13129789C212yesmaximal, complemented
4#13129788C212yesmaximal, complemented
5D13×#436C211yesmaximal, characteristic
6C2×M16×D13—21no—
7C4×D4×D13C411yescharacteristic
8C2×D13⋊C16—21no—
9C2×D13⋊C16—21no—
10C13×#436C411yescharacteristic
11#11718789—21no—
12#11718673C2211yescharacteristic
13#11718499C2211yescharacteristic
14D13×C4⋊C8C411yescharacteristic
15#11718390—21no—
16D13×C22⋊C8—21no—
17#11718349C411yescharacteristic
18C4×C8×D13C2211yescharacteristic
19#11718260—21no—
20#11718258—21no—
21#11718231C2212yescomplemented
22C4⋊#6092C2212yescomplemented
23C2×D4×D13C811yescharacteristic
24C22×C4×D13—21no—
25C2×C13×M16—21no—
26C4×D4×C13C2×C411yescharacteristic
27D4×Dic13C811yescharacteristic
28C4×C22⋊D13—21no—
29C2×#6099—21no—
30M16×D13—42no—
31M16×D13—42no—
32C2×#6094—21no—
33C2×#6094—21no—
34C2×C8×D13—21no—
35C2×C8×D13D411yescharacteristic
36C2×C8×D13D411yescharacteristic
37#88147C811yescharacteristic
38C4⋊C4×D13C811yescharacteristic
39#88135—21no—
40C22⋊C4×D13—21no—
41C4×D52C2×C411yescharacteristic
42C42×D13C2×C411yescharacteristic
43C2×#6092—22no—
44C2×#6092—22no—
45D13⋊C16—24no—
46D13⋊C16—42no—
47C13×C4⋊C8C2×C411yescharacteristic
48C13×C22⋊C8—21no—
49C4×C8×C13C2×C411yescharacteristic
50C22⋊#1055—21no—
51#88060—21no—
52#88060—21no—
53#88054—21no—
54C8×Dic13D411yescharacteristic
55C8×Dic13D411yescharacteristic
56C4⋊#1055C2×C411yescharacteristic
57C4×#1055C2311yescharacteristic
58C2×#1330—131nomaximal, Sylow
59C23×D13—21no—
60C2×D4×C13C2×C811yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64D4×D13—42no—
65C2×D52C2×C811yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×C4×D13C22⋊C411yescharacteristic
72C2×C4×D13C2×C811yescharacteristic
73C2×C4×D13M1611yescharacteristic
74C13×M16—42no—
75C2×C8×C13—21no—
76C2×C8×C13C22⋊C411yescharacteristic
77C2×C8×C13C22⋊C411yescharacteristic
78C13×C4⋊C4C2×C811yescharacteristic
79C13×C22⋊C4—21no—
80C42×C13C22×C411yescharacteristic
81C22⋊Dic13—21no—
82#6103—21no—
83#6103—21no—
84C4⋊Dic13C2×C811yescharacteristic
85#6101—21no—
86C4×Dic13C22⋊C411yescharacteristic
87C4×Dic13C2×C811yescharacteristic
88C4×Dic13M1611yescharacteristic
89#6099—41no—
90#6099—41no—
91C2×#1055—21no—
92C2×#1055C2×D411yescharacteristic
93C2×#1055C2×D411yescharacteristic
94#6094—42no—
95#6094—41no—
96#6094—41no—
97C8×D13—22no—
98C8×D13—42no—
99C8×D13D812yes—
100C8×D13SD1612yes—
101#6092—24no—
102#6092—42no—
103C2×#436—131no—
104C2×C4⋊C16—131no—
105C2×#346—131no—
106#1330—132no—
107#1330—132no—
108C23×C13—21no—
109C22×D13—21no—
110C22×D13—42no—
111C22×D13—42no—
112C22×D13—42no—
113C22×D13C22⋊C811yescharacteristic
114D4×C13—41no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13C22×C811yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C22⋊D13—42no—
122C2×Dic13—21no—
123C2×Dic13—42no—
124C2×Dic13C22⋊C811yescharacteristic
125C2×Dic13C22⋊C811yescharacteristic
126C2×Dic13C22⋊C811yescharacteristic
127D52—41no—
128C4×D13—22no—
129C4×D13—22no—
130C4×D13—42no—
131C4×D13—41no—
132C4×D13—41no—
133C4×D13—42no—
134C4×D13#10212yes—
135C4×D13#10412yes—
136C8×C13—21no—
137C8×C13—41no—
138C8×C13#10212yes—
139#1055—21no—
140#1055—41no—
141#1055C2×D811yescharacteristic
142#1055C2×SD1611yescharacteristic
143C22×M16—261no—
144C2×C4×D4—131no—
145C22×C16—261no—
146C22×C16—261no—
147#436—131no—
148#436—131no—
149#436—131no—
150#436—261no—
151#436—261no—
152#436#26111yescharacteristic
153C2×C4⋊C8—131no—
154C2×C22⋊C8—261no—
155C2×C4×C8—131no—
156C4⋊C16—132no—
157C4⋊C16—261no—
158#346—132no—
159#346—261no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C2×C22⋊C811yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—84no—
168C2×D13D4⋊C812yes—
169C2×D13#34912yes—
170C2×D13#35012yes—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13C2×#10211yescharacteristic
175C4×C13C2×#10411yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13D4⋊C812yes—
180C22×D4—131no—
181C23×C4—261no—
182C2×M16—21no—
183C2×M16—261no—
184C2×M16—261no—
185C2×M16—261no—
186C2×M16—522no—
187C2×M16—522no—
188C22×C8—131no—
189C22×C8—131no—
190C22×C8—261no—
191C4×D4—131no—
192C4×D4—131no—
193C4×D4—131no—
194C4×D4—261no—
195C4×D4—261no—
196C4×D4C2×#26111yescharacteristic
197C2×C4⋊C4—131no—
198C2×C22⋊C4—261no—
199C2×C42—131no—
200C2×C16—262no—
201C2×C16—264no—
202C2×C16—262no—
203C2×C16—522no—
204C4⋊C8—131no—
205C4⋊C8—261no—
206C4⋊C8C2×#26111yescharacteristic
207C22⋊C8—21no—
208C22⋊C8—261no—
209C22⋊C8—261no—
210C22⋊C8—261no—
211C4×C8—131no—
212C4×C8—131no—
213C4×C8—131no—
214C4×C8C2×#26111yescharacteristic
215C2×C13—81no—
216C2×C13C2×D4⋊C811yescharacteristic
217C2×C13C2×#34911yescharacteristic
218C2×C13C2×#35011yescharacteristic
219D13—81no—
220D13#133014yescomplemented
221C24—261no—
222C2×D4—131no—
223C2×D4—261no—
224C2×D4—522no—
225C2×D4D13⋊C811yescharacteristic
226C22×C4—21no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—522no—
235C22×C4—522no—
236M16—42no—
237M16—521no—
238M16—521no—
239M16—521no—
240M16—521no—
241M16—522no—
242C2×C8—21no—
243C2×C8—131no—
244C2×C8—132no—
245C2×C8—132no—
246C2×C8—131no—
247C2×C8—262no—
248C2×C8—261no—
249C2×C8—522no—
250C2×C8C22⋊#26111yescharacteristic
251C2×C8C22⋊#26111yescharacteristic
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4D13⋊C811yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C42—131no—
260C42—131no—
261C42—131no—
262C42C22×#26111yescharacteristic
263C16—264no—
264C16—522no—
265C13C2×#133011yescharacteristic, complemented, Sylow
266C23—21no—
267C23—131no—
268C23—261no—
269C23—522no—
270C23—522no—
271C23—522no—
272D4—41no—
273D4—521no—
274D4—522no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—131no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—261no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4C2×D13⋊C811yescharacteristic
292C2×C4D13⋊M1611yescharacteristic
293C2×C4C2×C22⋊#26111yescharacteristic
294C8—21no—
295C8—41no—
296C8—131no—
297C8—131no—
298C8—261no—
299C8—521no—
300C8#8811512yes—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—132no—
305C22—132no—
306C22—132no—
307C22—521no—
308C22—521no—
309C22—521no—
310C22—1044no—
311C22D13⋊(C22⋊C8)11yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—132no—
316C4—261no—
317C4—261no—
318C4—521no—
319C4C2×#8811511yescharacteristic
320C4D13⋊#10411yescharacteristic
321C2—81no—
322C2—134no—
323C2—1041no—
324C2D13⋊(D4⋊C8)11yescharacteristic
325C2D13⋊#34911yescharacteristic
326C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#436C4
socleC22×C13C2×C22⋊C8
prime radicalC2×D4×D13C8
cosocleC4×#1055C23
hypercenter#436#261
hypocenterC13C2×#1330
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. D13⋊(C4⋊C16)C2semidirect
2. #13131037C2semidirect
3. #13129789C2semidirect
4. #13129788C2semidirect
21. #11718231C22semidirect
22. C4⋊#6092C22semidirect
220. D13#1330semidirect
265. C13C2×#1330semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C4⋊C16)2
#131310372
#131297892
#131297882
D13×#4362
C2×#133013