Finite Group Databasebeta

← Dic13×#360 #15778169

Subgroups — Dic13×#360 #15778169

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#135×Dic13C211yesmaximal, characteristic
2C2×#11718158C211yesmaximal, characteristic
3M32×Dic13C211yesmaximal, characteristic, complemented
4#106×Dic13C211yesmaximal, characteristic, complemented
5#13112943C211yesmaximal, characteristic, complemented
6#13112942C211yesmaximal, characteristic, complemented
7C2×C13×#360C211yesmaximal, characteristic
8C2×C13×#135C2211yescharacteristic
9#41×Dic13—21no—
10C2×C13×M32C2211yescharacteristic
11C2×C13×#106C2211yescharacteristic
12#11718894—21no—
13Q16×Dic13C411yescharacteristic, complemented
14Q16×Dic13C411yescharacteristic, complemented
15SD16×Dic13—21no—
16SD16×Dic13—21no—
17D8×Dic13C411yescharacteristic, complemented
18D8×Dic13C411yescharacteristic, complemented
19#11718767C2211yescharacteristic
20C2×#88057C2211yescharacteristic
21C2×C8×Dic13C2211yescharacteristic
22C2×#88052C2211yescharacteristic
23C4⋊C4×Dic13—21no—
24C13×#360C414yescomplemented
25#11718158C414yescomplemented
26#11718121—21no—
27#11718094—21no—
28C16×Dic13—21no—
29C2×C13×#41—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135C2×C412yes—
33C13×#135C2×C412yes—
34C2×C13×Q16C2×C411yescharacteristic
35C2×C13×SD16—21no—
36C2×C13×D8C2×C411yescharacteristic
37C22×C8×C13C2311yescharacteristic
38C2×C13×C4⋊C4—21no—
39Q8×Dic13—21no—
40Q8×Dic13—21no—
41D4×Dic13—21no—
42D4×Dic13—21no—
43D4×Dic13—41no—
44D4×Dic13—41no—
45#88180—21no—
46#88180—41no—
47C2×C4⋊Dic13—21no—
48C2×C4×Dic13—41no—
49C2×C4×Dic13—41no—
50C2×C4×Dic13D411yescharacteristic
51C22×#1055D411yescharacteristic
52C13×M32—21no—
53C13×M32C2×C412yescomplemented
54C2×C13×C16—21no—
55C13×#106—21no—
56C13×#106C2×C412yescomplemented
57#88075—21no—
58#88075—21no—
59#88072—21no—
60#88072—21no—
61#88071—41no—
62#88058C2×C411yescharacteristic
63#88058C2×C411yescharacteristic
64#88057—21no—
65#88057—21no—
66#88057C2×C412yescomplemented
67C8×Dic13C2×C411yescharacteristic
68C8×Dic13C2×C411yescharacteristic
69C8×Dic13D411yescharacteristic
70C8×Dic13D411yescharacteristic
71#88052—21no—
72#88052C2×C412yescomplemented
73C2×#6090—21no—
74C4×#360—131nomaximal, Sylow
75C13×#41—22no—
76C13×#41—22no—
77C13×#41—41no—
78C13×#41—41no—
79C2×Q8×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13D811yescharacteristic
89C22×Dic13D811yescharacteristic
90C13×Q16—21no—
91C13×Q16C4212yescomplemented
92C13×SD16—22no—
93C13×SD16—22no—
94C13×D8—21no—
95C13×D8C4212yescomplemented
96C2×C8×C13C22×C411yescharacteristic
97C2×C8×C13C22×C411yescharacteristic
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C13×C4⋊C4—22no—
103C13×C4⋊C4—41no—
104C22⋊Dic13—41no—
105C22⋊Dic13—41no—
106C22⋊Dic13—41no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—22no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4×Dic13—41no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116C4×Dic13—82no—
117C4×Dic13C22⋊C411yescharacteristic
118C4×Dic13C22⋊C411yescharacteristic
119C4×Dic13SD1611yescharacteristic
120C4×Dic13SD1611yescharacteristic
121C2×#1055—21no—
122C2×#1055—21no—
123C2×#1055C22⋊C411yescharacteristic
124C2×#1055C22⋊C411yescharacteristic
125C13×C16—22no—
126#6090—22no—
127C4×#135—131no—
128C2×#360—131no—
129C2×#360D1311yescharacteristic
130C4×M32—131no—
131C4×#106—131no—
132#1386—131no—
133#1386—131no—
134C23×C13—41no—
135C23×C13C2×D811yescharacteristic
136Q8×C13—22no—
137Q8×C13—41no—
138D4×C13—22no—
139D4×C13—42no—
140D4×C13—42no—
141D4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13C2×C22⋊C411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×Dic13—22no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—82no—
160C2×Dic13—81no—
161C2×Dic13—81no—
162C2×Dic13—82no—
163C2×Dic13#10211yescharacteristic
164C2×Dic13#10211yescharacteristic
165C2×Dic13#10211yescharacteristic
166C2×Dic13#10211yescharacteristic
167C8×C13C2×C4211yescharacteristic
168C8×C13#11711yescharacteristic
169C8×C13C4×D411yescharacteristic
170C8×C13C4×D411yescharacteristic
171#1055—21no—
172#1055—21no—
173C2×#135C2×D1311yescharacteristic
174C4×#41—261no—
175C2×M32—131no—
176C2×M32C2×D1311yescharacteristic
177C4×Q16—131no—
178C4×Q16—131no—
179C4×SD16—261no—
180C4×SD16—261no—
181C4×D8—131no—
182C4×D8—131no—
183#427—131no—
184C2×#106—131no—
185C2×#106C2×D1311yescharacteristic
186#416—261no—
187C2×C4×C8—131no—
188C4×C4⋊C4—261no—
189#360—134no—
190#360Dic1314yesdirect product factor
191#346—261no—
192C4×C16—261no—
193#340—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—42no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13C2×#10211yescharacteristic
200C22×C13C4×D811yescharacteristic
201C22×C13C4×D811yescharacteristic
202C4×C13—42no—
203C4×C13—82no—
204C4×C13C4×C22⋊C411yescharacteristic
205C4×C13#41611yescharacteristic
206C4×C13C4×SD1611yescharacteristic
207C4×C13C4×SD1611yescharacteristic
208Dic13—21no—
209Dic13—21no—
210Dic13—21no—
211Dic13—82no—
212Dic13—81no—
213Dic13—81no—
214Dic13#36012yesdirect product factor
215C2×#41—21no—
216#135—21no—
217#135—21no—
218#135C4×D1312yes—
219#135C2×Dic1312yes—
220C2×Q16C4×D1311yescharacteristic
221C2×SD16—21no—
222C2×D8C4×D1311yescharacteristic
223C22×C8—131no—
224C22×C8C22×D1311yescharacteristic
225C4×Q8—261no—
226C4×Q8—261no—
227C4×D4—261no—
228C4×D4—261no—
229C4×D4—521no—
230C4×D4—521no—
231#117—261no—
232#117—521no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—261no—
235C2×C42—131no—
236C2×C42—521no—
237C2×C42—521no—
238M32—21no—
239M32—132no—
240M32—261no—
241M32C2×Dic1312yescomplemented
242C2×C16—21no—
243C2×C16—261no—
244#107—131no—
245#107—131no—
246#106—21no—
247#106—132no—
248#106—261no—
249#106—261no—
250#106C2×Dic1312yescomplemented
251#103—261no—
252#103—261no—
253#102—261no—
254#102—261no—
255C4×C8—131no—
256C4×C8—131no—
257C4×C8—131no—
258C4×C8—131no—
259#95—521no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—82no—
263C2×C13C4×#10211yescharacteristic
264C2×C13C2×#36011yescharacteristic
265C2×C13#214511yescharacteristic
266#41—22no—
267#41—22no—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—521no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4D4×D1311yescharacteristic
281Q16—21no—
282Q16C4×Dic1312yescomplemented
283SD16—22no—
284SD16—22no—
285D8—21no—
286D8C4×Dic1312yescomplemented
287C2×C8—131no—
288C2×C8—131no—
289C2×C8—261no—
290C2×C8—261no—
291C2×C8C2×C4×D1311yescharacteristic
292C2×C8C2×C4×D1311yescharacteristic
293C2×C8D4×D1311yescharacteristic
294C2×C8#612911yescharacteristic
295C2×C8#612911yescharacteristic
296C2×C8C22×Dic1311yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—262no—
302C4⋊C4—521no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—131no—
312C42—521no—
313C42—521no—
314C42—521no—
315C42—1042no—
316C16—22no—
317C16—262no—
318C13C4×#36011yescharacteristic, complemented, Sylow
319C23—41no—
320C23D8×D1311yescharacteristic
321Q8—22no—
322Q8—41no—
323D4—22no—
324D4—42no—
325D4—42no—
326D4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—131no—
334C2×C4—131no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—262no—
338C2×C4—521no—
339C2×C4—522no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—1042no—
343C2×C4—1042no—
344C2×C4—1041no—
345C2×C4—1041no—
346C2×C4C22⋊C4×D1311yescharacteristic
347C2×C4#8813511yescharacteristic
348C2×C4#8816611yescharacteristic
349C2×C4SD16×D1311yescharacteristic
350C2×C4#8817011yescharacteristic
351C2×C4D4×Dic1311yescharacteristic
352C8—261no—
353C8—261no—
354C8#8813111yescharacteristic
355C8#8813511yescharacteristic
356C8C2×C4×Dic1311yescharacteristic
357C8D4×Dic1311yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22#1171841711yescharacteristic
364C22D13×#10211yescharacteristic
365C22D8×Dic1311yescharacteristic
366C4—42no—
367C4—82no—
368C4—132no—
369C4—261no—
370C4—261no—
371C4—261no—
372C4—1042no—
373C4—1041no—
374C4—1041no—
375C4#1171841911yescharacteristic
376C4#1171843311yescharacteristic
377C4C22⋊C4×Dic1311yescharacteristic
378C4SD16×Dic1311yescharacteristic
379C2—21no—
380C2—21no—
381C2—82no—
382C2#102×Dic1311yescharacteristic
383C2D13×#36011yescharacteristic
384C2#1311657011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#360C2
socleC22×C13C2×#102
prime radicalC2×C13×#135C22
cosocleC22×C8×C13C23
hypercenterC2×#360D13
hypocenterC13C4×#360
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. M32×Dic13C2semidirect
4. #106×Dic13C2semidirect
5. #13112943C2semidirect
6. #13112942C2semidirect
13. Q16×Dic13C4semidirect
14. Q16×Dic13C4semidirect
17. D8×Dic13C4semidirect
18. D8×Dic13C4semidirect
24. C13×#360C4semidirect
25. #11718158C4semidirect
53. C13×M32C2×C4semidirect
56. C13×#106C2×C4semidirect
66. #88057C2×C4semidirect
72. #88052C2×C4semidirect
91. C13×Q16C42semidirect
95. C13×D8C42semidirect
190. #360Dic13direct (N × H)
214. Dic13#360direct (N × H)
241. M32C2×Dic13semidirect
250. #106C2×Dic13semidirect
282. Q16C4×Dic13semidirect
286. D8C4×Dic13semidirect
318. C13C4×#360semidirect

Maximal subgroups

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

subgroupindex
#135×Dic132
C2×#117181582
M32×Dic132
#106×Dic132
#131129432
#131129422
C2×C13×#3602
C4×#36013