Finite Group Databasebeta

← D13⋊#2916 #16808159

Subgroups — D13⋊#2916 #16808159

Order 3328.

2586 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#568C212yesmaximal
2#13131498C218yesmaximal, complemented
3#13131497C218yesmaximal, complemented
4D13⋊#430C216yesmaximal, complemented
5C2×D13⋊#108C216yesmaximal, complemented
6C2×D13×#131C211yesmaximal, characteristic
7C2×#41×D13C2211yescharacteristic
8#11719629C22116yes—
9D13⋊#131—28no—
10#11719625—22no—
11#11719621—26no—
12C2×D13⋊M16C22112yes—
13C2×C13×#131C411yescharacteristic
14C2×#88202C411yescharacteristic
15D13×#131C414yes—
16D13×#131C414yes—
17D13×#131C2214yes—
18D13×#131C2214yes—
19C2×#88161C413yes—
20C2×M16×D13C2213yes—
21C2×#88155C413yes—
22C22×C8×D13C2213yes—
23#11719100C22148yescomplemented
24D13⋊#108C2214yes—
25D13⋊#108C22112yes—
26D13⋊#108C22112yescomplemented
27D13⋊#108C22112yescomplemented
28C2×#88104C22112yescomplemented
29C2×#88103C22112yescomplemented
30C2×C13×#41C2×C411yescharacteristic
31#41×D13C2×C414yes—
32#41×D13D414yes—
33#41×D13Q814yes—
34#41×D13C2314yes—
35C2×#6131D411yescharacteristic
36C2×Q8×D13Q811yescharacteristic
37C2×#6129D413yes—
38C2×D4×D13Q813yes—
39C2×#6127C2×C413yes—
40C22×C4×D13C2313yes—
41C2×#6122—212no—
42#88240—216no—
43#88238—248no—
44D13⋊M16—212no—
45D13⋊M16—212no—
46D13⋊M16C2318yes—
47D13⋊M16C23124yes—
48C2×#6118C23124yes—
49C2×D13⋊C8—212no—
50C13×#131C2×C414yes—
51C13×#131C2×C414yes—
52C2×C13×M16C2×C413yes—
53C22×C8×C13C2×C413yes—
54#88202C2×C414yes—
55#88202C2×C414yes—
56C2×#6099C2×C413yes—
57C22×#1055C2×C413yes—
58#88161C2×C4112yes—
59#88161C2×C4112yes—
60M16×D13C2×C4112yes—
61M16×D13C23112yes—
62#88155C2×C4112yes—
63#88155C2×C4112yes—
64C2×#6094C2×C416yes—
65C2×C8×D13C2×C413yes—
66C2×C8×D13C2×C413yes—
67C2×C8×D13C2×C416yes—
68C2×C8×D13C2×C416yes—
69C2×C8×D13C2311yescharacteristic
70C2×C8×D13C2313yes—
71C2×C8×D13C2316yes—
72C2×C8×D13C2316yes—
73#88104C2318yes—
74#88104C23124yes—
75#88103C2318yes—
76#88103C23124yes—
77C2×#2916—131nomaximal, Sylow
78C23×D13C2×Q813yes—
79C13×#41C4⋊C414yes—
80C13×#41C22×C414yes—
81C2×Q8×C13C4⋊C411yescharacteristic
82C2×D4×C13C4⋊C413yes—
83C22×C4×C13C22×C413yes—
84C2×C22⋊D13C4⋊C416yes—
85C22×Dic13C2×D413yes—
86#6131C4⋊C414yes—
87#6131C2×D414yes—
88Q8×D13C4⋊C414yes—
89Q8×D13C2×Q814yes—
90#6129C4⋊C4112yes—
91#6129C2×D4112yes—
92D4×D13C4⋊C4112yes—
93D4×D13C2×Q8112yes—
94#6127C4⋊C4112yes—
95#6127C22×C4112yes—
96C2×D52C4⋊C413yes—
97C2×C4×D13C22×C413yes—
98C2×C4×D13C22×C416yes—
99C2×C4×D13C2×D416yes—
100C2×C4×D13C2×D413yes—
101C2×C4×D13C2×Q813yes—
102C2×C4×D13C2×Q816yes—
103C2×C4×D13C2411yescharacteristic
104C2×C4×D13C2416yes—
105C2×Dic26C4⋊C413yes—
106#6122—28no—
107#6122—224no—
108C2×#1057—224no—
109#6118—224no—
110#6118C24116yes—
111D13⋊C8—28no—
112D13⋊C8—224no—
113C13×M16C22×C4112yes—
114C2×C8×C13C22×C411yescharacteristic
115C2×C8×C13C22×C413yes—
116C2×C8×C13C22×C416yes—
117C2×C8×C13C22×C416yes—
118#6099C22×C4112yes—
119C2×#1055C22×C411yescharacteristic
120C2×#1055C22×C413yes—
121C2×#1055C22×C416yes—
122C2×#1055C22×C416yes—
123#6094C22×C4124yes—
124C8×D13C22×C411yescharacteristic
125C8×D13C22×C411yescharacteristic
126C8×D13C22×C416yes—
127C8×D13C22×C416yes—
128C8×D13C22×C416yes—
129C8×D13C22×C416yes—
130C8×D13C22×C416yes—
131C8×D13C2411yescharacteristic
132C8×D13C2416yes—
133C8×D13C2411yescharacteristic
134C2×#568—132no—
135C22×#131—131no—
136#2916—138no—
137#2916—138no—
138C2×#430—136no—
139C22×#108—136no—
140C23×C13C2×C4⋊C413yes—
141C22×D13—46no—
142C22×D13C2×C4⋊C416yes—
143C22×D13C2×C4⋊C413yes—
144C22×D13C22×Q811yescharacteristic
145C22×D13C22×Q816yes—
146Q8×C13C2×C4⋊C414yes—
147D4×C13C2×C4⋊C4112yes—
148C2×C4×C13C2×C4⋊C413yes—
149C2×C4×C13C2×C4⋊C416yes—
150C2×C4×C13C23×C411yescharacteristic
151C2×C4×C13C23×C416yes—
152C22⋊D13C2×C4⋊C4124yes—
153C2×Dic13C2×C4⋊C413yes—
154C2×Dic13C2×C4⋊C416yes—
155C2×Dic13C22×D416yes—
156C2×Dic13C22×D411yescharacteristic
157D52C2×C4⋊C4112yes—
158C4×D13C2×C4⋊C416yes—
159C4×D13C2×C4⋊C416yes—
160C4×D13C2×C4⋊C416yes—
161C4×D13C23×C411yescharacteristic
162C4×D13C23×C416yes—
163C4×D13C22×D411yescharacteristic
164C4×D13C22×D416yes—
165C4×D13C22×Q811yescharacteristic
166C4×D13C22×Q816yes—
167C4×D13C2511yescharacteristic
168Dic26C2×C4⋊C4112yes—
169#1057—216no—
170C8×C13C23×C411yescharacteristic
171C8×C13C23×C411yescharacteristic
172C8×C13C23×C416yes—
173#1055C23×C411yescharacteristic
174#1055C23×C411yescharacteristic
175#1055C23×C416yes—
176C22×#41—131no—
177#568—1316no—
178#568—266no—
179#568—262no—
180C2×#131—131no—
181C2×#131—134no—
182C2×#131—134no—
183C2×#131—134no—
184C2×#131—134no—
185C2×#131—133no—
186C2×#131—133no—
187C2×#131—268no—
188C2×#131#26111yescharacteristic
189C22×M16—133no—
190C22×M16—1312no—
191C23×C8—133no—
192#430—1348no—
193C2×#108—134no—
194C2×#108—1312no—
195C2×#108—1312no—
196C2×#108—1312no—
197C2×#108—1312no—
198C2×#108—1312no—
199C22×C13—43no—
200C22×C13C22×C4⋊C411yescharacteristic
201C22×C13C22×C4⋊C416yes—
202C2×D13—22no—
203C2×D13—212no—
204C2×D13—43no—
205C2×D13—46no—
206C2×D13C22×C4⋊C416yes—
207C2×D13C22×C4⋊C411yescharacteristic
208C2×D13C23×Q811yescharacteristic
209C4×C13C22×C4⋊C416yes—
210C4×C13C22×C4⋊C411yescharacteristic
211C4×C13C24×C411yescharacteristic
212Dic13C22×C4⋊C416yes—
213Dic13C22×C4⋊C411yescharacteristic
214Dic13C23×D411yescharacteristic
215C2×#41—134no—
216C2×#41—134no—
217C2×#41—134no—
218C2×#41—134no—
219C2×#41—131no—
220C2×#41—133no—
221C2×#41—133no—
222C2×#41C2×#26111yescharacteristic
223C22×Q8—131no—
224C22×D4—133no—
225C23×C4—133no—
226#131—134no—
227#131—134no—
228#131—1312no—
229#131—1312no—
230#131—1312no—
231#131—1312no—
232#131—2648no—
233#131—2616no—
234#131C2×#26114yes—
235#131C2×#26114yes—
236C2×M16—133no—
237C2×M16—1312no—
238C2×M16—1312no—
239C2×M16—136no—
240C2×M16—138no—
241C2×M16—1324no—
242C2×M16—1324no—
243C2×M16—2612no—
244C2×M16—2612no—
245C2×M16—2612no—
246C2×M16C2×#26113yes—
247C22×C8—133no—
248C22×C8—131no—
249C22×C8—133no—
250C22×C8—133no—
251C22×C8—133no—
252C22×C8—136no—
253C22×C8—136no—
254C22×C8—136no—
255C22×C8—136no—
256C22×C8—2612no—
257C22×C8C2×#26113yes—
258#108—138no—
259#108—1324no—
260#108—138no—
261#108—1324no—
262C2×C13—21no—
263C2×C13—26no—
264C2×C13C23×C4⋊C411yescharacteristic
265D13—21no—
266D13—26no—
267D13#291612yescomplemented
268C24—133no—
269#41—134no—
270#41—134no—
271#41—1312no—
272#41—1312no—
273#41—1312no—
274#41—1312no—
275#41C4⋊#26114yes—
276#41C22×#26114yes—
277C2×Q8—134no—
278C2×Q8—134no—
279C2×Q8—133no—
280C2×Q8C4⋊#26111yescharacteristic
281C2×D4—136no—
282C2×D4—1312no—
283C2×D4—1312no—
284C2×D4—133no—
285C2×D4C4⋊#26113yes—
286C22×C4—133no—
287C22×C4—136no—
288C22×C4—133no—
289C22×C4—133no—
290C22×C4—136no—
291C22×C4—131no—
292C22×C4—136no—
293C22×C4—133no—
294C22×C4—136no—
295C22×C4C22×#26113yes—
296M16—1312no—
297M16—1324no—
298M16—1316no—
299M16—268no—
300M16—2624no—
301M16—2624no—
302M16C22×#261112yes—
303C2×C8—131no—
304C2×C8—133no—
305C2×C8—136no—
306C2×C8—136no—
307C2×C8—131no—
308C2×C8—131no—
309C2×C8—136no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—136no—
313C2×C8—136no—
314C2×C8—136no—
315C2×C8—136no—
316C2×C8—136no—
317C2×C8—268no—
318C2×C8—2624no—
319C2×C8—2624no—
320C2×C8C22×#26111yescharacteristic
321C2×C8C22×#26113yes—
322C2×C8C22×#26116yes—
323C2×C8C22×#26116yes—
324C13C2×#291611yescharacteristic, complemented, Sylow
325C23—131no—
326C23—136no—
327C23—133no—
328C23—136no—
329C23—526no—
330C23C2×C4⋊#26113yes—
331Q8—1312no—
332Q8C2×C4⋊#26114yes—
333D4—1324no—
334D4—1312no—
335D4C2×C4⋊#261112yes—
336C2×C4—136no—
337C2×C4—131no—
338C2×C4—133no—
339C2×C4—136no—
340C2×C4—136no—
341C2×C4—136no—
342C2×C4—136no—
343C2×C4—136no—
344C2×C4—131no—
345C2×C4—136no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—136no—
350C2×C4C2×C4⋊#26113yes—
351C2×C4C2×C4⋊#26116yes—
352C2×C4C23×#26116yes—
353C2×C4C23×#26111yescharacteristic
354C8—131no—
355C8—131no—
356C8—136no—
357C8—2616no—
358C8C23×#26111yescharacteristic
359C8C23×#26111yescharacteristic
360C8C23×#26116yes—
361C22—43no—
362C22—131no—
363C22—136no—
364C22—131no—
365C22—2612no—
366C22—262no—
367C22—523no—
368C22—526no—
369C22C22×C4⋊#26111yescharacteristic
370C22C22×C4⋊#26116yes—
371C4—131no—
372C4—136no—
373C4—131no—
374C4C22×C4⋊#26116yes—
375C4C22×C4⋊#26111yescharacteristic
376C4C24×#26111yescharacteristic
377C2—21no—
378C2—26no—
379C2—132no—
380C2—261no—
381C2—266no—
382C2C23×C4⋊#26111yescharacteristic
subgroupG/H
centerC4C22×C4⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×#131C4
socleC2×C13C23×C4⋊C4
prime radicalC2×#41×D13C22
cosocleC4×D13C25
hypercenterC2×#131#261
hypocenterC13C2×#2916
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #13131498C2semidirect
3. #13131497C2semidirect
4. D13⋊#430C2semidirect
5. C2×D13⋊#108C2semidirect
23. #11719100C22semidirect
26. D13⋊#108C22semidirect
27. D13⋊#108C22semidirect
28. C2×#88104C22semidirect
29. C2×#88103C22semidirect
267. D13#2916semidirect
324. C13C2×#2916semidirect

Maximal subgroups

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

subgroupindex
D13⋊#5682
#131314982
#131314972
D13⋊#4302
C2×D13⋊#1082
C2×D13×#1312
C2×#291613