Finite Group Databasebeta

← D13⋊#1348 #16787676

Subgroups — D13⋊#1348 #16787676

Order 3328.

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

normal subgroups only

This group has 506 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⋊(C22⋊C16)C211yesmaximal, characteristic
2C2×#11718265C211yesmaximal, characteristic
3#13129825C212yesmaximal, complemented
4#13129824C212yesmaximal, complemented
5D13×#467C211yesmaximal, characteristic
6C22×C4⋊#261—21no—
7C2×Q16×D13C411yescharacteristic, complemented
8C22×C8×D13C2211yescharacteristic
9D13×C22⋊Q8—21no—
10C2×D13⋊C16—21no—
11C13×#467C411yescharacteristic, complemented
12#11718849C2211yescharacteristic
13#11718777C411yescharacteristic, complemented
14#11718712—21no—
15#11718548C2211yescharacteristic
16D13×#107C411yescharacteristic, complemented
17#11718474—21no—
18D13×#103—21no—
19C22⋊#6092—21no—
20#11718265—21no—
21#11718265C2212yes—
22#11718259C2212yes—
23C23×#261—41no—
24C2×Q8×D13—21no—
25C22×C4×D13D411yescharacteristic
26C2×C4⋊#261—24no—
27C2×C4⋊#261—22no—
28C2×C4⋊#261—42no—
29C2×C4⋊#261—41no—
30C2×C13×Q16C2×C411yescharacteristic, complemented
31C22×C8×C13C2×C411yescharacteristic
32C13×C22⋊Q8—21no—
33#88200—21no—
34C2×#6107—21no—
35#88178—21no—
36C22×#1055D411yescharacteristic
37Q16×D13—42no—
38C2×Dic52C2×C411yescharacteristic, complemented
39C2×C8×D13—42no—
40C2×C8×D13C2×C411yescharacteristic
41C2×C8×D13D411yescharacteristic
42C2×C8×D13D411yescharacteristic
43C2×C8×D13C2311yescharacteristic
44#88151—21no—
45#88150—41no—
46C4⋊C4×D13—21no—
47C4⋊C4×D13—41no—
48C22⋊C4×D13—41no—
49#88132—41no—
50C2×#6092—22no—
51D13⋊C16—42no—
52C13×#107C2×C411yescharacteristic, complemented
53C13×#103—21no—
54#88075—21no—
55#88058C2×C411yescharacteristic, complemented
56#88056—21no—
57#88050—21no—
58#88047—21no—
59C2×#1348—131nomaximal, Sylow
60C23×D13D811yescharacteristic
61C22×#261—44no—
62C22×#261—42no—
63C22×#261—82no—
64C22×#261—82no—
65C2×Q8×C13—21no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×Dic13SD1611yescharacteristic
68Q8×D13—42no—
69Q8×D13—42no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13C22⋊C411yescharacteristic
75C2×C4×D13D811yescharacteristic
76C2×C4×D13SD1611yescharacteristic
77C2×C4×D13C2×D411yescharacteristic
78C2×Dic26—21no—
79C2×Dic26—41no—
80C4⋊#261—24no—
81C4⋊#261—42no—
82C4⋊#261—44no—
83C13×Q16—41no—
84C2×C8×C13—41no—
85C2×C8×C13C22⋊C411yescharacteristic
86C2×C8×C13C22×C411yescharacteristic
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—41no—
91#6107—42no—
92#6103—41no—
93#6103—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13—41no—
96#6101—41no—
97#6101—41no—
98#6101—41no—
99C2×#1055—41no—
100C2×#1055C22⋊C411yescharacteristic
101C2×#1055C2×D411yescharacteristic
102Dic52—41no—
103C8×D13—22no—
104C8×D13—22no—
105C8×D13—41no—
106C8×D13—41no—
107#6092—42no—
108C2×#467—131no—
109C2×C22⋊C16—131no—
110C2×#340—131no—
111#1348—132no—
112#1348—132no—
113C23×C13#10211yescharacteristic
114C22×D13—22no—
115C22×D13—22no—
116C22×D13#10211yescharacteristic
117C22×D13SD3212yes—
118C22×D13Q3212yes—
119C22×D13C2×D811yescharacteristic
120C2×#261—44no—
121C2×#261—82no—
122C2×#261—88no—
123C2×#261—82no—
124Q8×C13—41no—
125Q8×C13—41no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#10211yescharacteristic
131C2×C4×C13C2×C22⋊C411yescharacteristic
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13#10211yescharacteristic
136C2×Dic13C2×SD1611yescharacteristic
137C4×D13—22no—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—22no—
141C4×D13—82no—
142C4×D13—82no—
143C4×D13#9912yes—
144C4×D13#10412yes—
145Dic26—41no—
146Dic26—41no—
147Dic26—82no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152C22×Q16—131no—
153C23×C8—131no—
154C2×C22⋊Q8—261no—
155C22×C4⋊C4—261no—
156C22×C16—261no—
157#467—131no—
158#467—131no—
159#467—131no—
160#467—261no—
161#467—261no—
162#467#26111yescharacteristic, complemented
163C2×#107—131no—
164C2×#103—261no—
165C22⋊C16—132no—
166C22⋊C16—261no—
167#340—132no—
168#340—261no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#35812yes—
172C22×C13C2×#10211yescharacteristic
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—24no—
176C2×D13—24no—
177C2×D13#32712yes—
178C2×D13#35812yes—
179C2×D13#36012yes—
180C2×D13C2×SD3211yescharacteristic
181C2×D13C2×Q3211yescharacteristic
182#261—84no—
183C4×C13—21no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13C2×#9911yescharacteristic
187C4×C13C2×#10411yescharacteristic
188Dic13—21no—
189Dic13—81no—
190Dic13—81no—
191Dic13#32712yes—
192C22×Q8—261no—
193C23×C4—131no—
194C23×C4—521no—
195C2×Q16—131no—
196C2×Q16—261no—
197C2×Q16—522no—
198C2×Q16C2×#26111yescharacteristic, complemented
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—522no—
205C22×C8C2×#26111yescharacteristic
206C22⋊Q8—21no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209C22⋊Q8—261no—
210C22⋊Q8—521no—
211C22⋊Q8—521no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—262no—
214C2×C4⋊C4—264no—
215C2×C4⋊C4—521no—
216C2×C4⋊C4—521no—
217C2×C4⋊C4—522no—
218C2×C22⋊C4—521no—
219C2×C16—262no—
220C2×C16—522no—
221#107—131no—
222#107—261no—
223#107C2×#26111yescharacteristic, complemented
224#103—21no—
225#103—261no—
226#103—261no—
227#103—261no—
228C2×C13—22no—
229C2×C13C2×#32711yescharacteristic
230C2×C13C2×#35811yescharacteristic
231C2×C13C2×#36011yescharacteristic
232D13—21no—
233D13—21no—
234D13#134814yescomplemented
235C24—131no—
236C2×Q8—21no—
237C2×Q8—261no—
238C2×Q8—521no—
239C2×Q8—522no—
240C2×Q8—522no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—521no—
249C22×C4—521no—
250C22×C4—522no—
251C22×C4—524no—
252C22×C4—1042no—
253C22×C4—1042no—
254C22×C4C22⋊#26111yescharacteristic
255Q16—41no—
256Q16—521no—
257Q16—522no—
258C2×C8—41no—
259C2×C8—131no—
260C2×C8—131no—
261C2×C8—262no—
262C2×C8—262no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8C22⋊#26111yescharacteristic
267C2×C8C22×#26111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—264no—
271C4⋊C4—261no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—524no—
276C4⋊C4—522no—
277C4⋊C4—521no—
278C22⋊C4—41no—
279C22⋊C4—521no—
280C22⋊C4—521no—
281C22⋊C4—521no—
282C16—522no—
283C13C2×#134811yescharacteristic, complemented, Sylow
284C23—131no—
285C23—132no—
286C23—132no—
287C23—131no—
288C23—262no—
289C23—262no—
290C23#8811511yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—521no—
294Q8—521no—
295Q8—1042no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—131no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—131no—
304C2×C4—262no—
305C2×C4—262no—
306C2×C4—262no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—524no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4—1042no—
315C2×C4—1048no—
316C2×C4—1042no—
317C2×C4#8811511yescharacteristic
318C2×C4C2×C22⋊#26111yescharacteristic
319C8—21no—
320C8—21no—
321C8—261no—
322C8—261no—
323C22—21no—
324C22—21no—
325C22—132no—
326C22—132no—
327C22—132no—
328C22—131no—
329C22—131no—
330C22—264no—
331C22—264no—
332C22—261no—
333C22—261no—
334C22#1171828012yes—
335C22C2×#8811511yescharacteristic
336C4—21no—
337C4—81no—
338C4—81no—
339C4—132no—
340C4—261no—
341C4—1044no—
342C4—1041no—
343C4—1041no—
344C4D13⋊#9911yescharacteristic
345C4D13⋊#10411yescharacteristic
346C2—22no—
347C2—134no—
348C2—261no—
349C2—261no—
350C2D13⋊#32711yescharacteristic
351C2C2×#1171828011yescharacteristic
352C2D13⋊#36011yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#467C4
socleC22×C13C2×#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenter#467#261
hypocenterC13C2×#1348
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #13129825C2semidirect
4. #13129824C2semidirect
7. C2×Q16×D13C4semidirect
11. C13×#467C4semidirect
13. #11718777C4semidirect
16. D13×#107C4semidirect
30. C2×C13×Q16C2×C4semidirect
38. C2×Dic52C2×C4semidirect
52. C13×#107C2×C4semidirect
55. #88058C2×C4semidirect
162. #467#261semidirect
198. C2×Q16C2×#261semidirect
223. #107C2×#261semidirect
234. D13#1348semidirect
283. C13C2×#1348semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C22⋊C16)2
C2×#117182652
#131298252
#131298242
D13×#4672
C2×#134813