Finite Group Databasebeta

← Dic13×#361 #15778174

Subgroups — Dic13×#361 #15778174

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic13C211yesmaximal, characteristic
2C2×#11718155C211yesmaximal, characteristic
3M32×Dic13C211yesmaximal, characteristic, complemented
4#108×Dic13C211yesmaximal, characteristic, complemented
5#13112946C211yesmaximal, characteristic, complemented
6#13112945C211yesmaximal, characteristic, complemented
7C2×C13×#361C211yesmaximal, characteristic
8C22×C13×D8C2211yescharacteristic
9C2×D4×Dic13—21no—
10C2×C13×M32C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×#88072—21no—
13D8×Dic13—21no—
14D8×Dic13—21no—
15D8×Dic13C412yes—
16D8×Dic13C412yes—
17M16×Dic13—21no—
18C2×#88059C2211yescharacteristic
19C2×#88058C2211yescharacteristic
20C2×C8×Dic13C2211yescharacteristic
21C2×#88052C2211yescharacteristic
22C13×#361C414yescomplemented
23#11718155C414yescomplemented
24#11718150—21no—
25#11718094—21no—
26C16×Dic13—21no—
27C22×D4×C13—21no—
28C23×Dic13—41no—
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8C2×C412yes—
33C2×C13×D8C2×C412yes—
34C2×C13×D8C2×C412yes—
35C2×C13×M16—21no—
36C22×C8×C13C2311yescharacteristic
37C2×C22⋊Dic13—41no—
38D4×Dic13—22no—
39D4×Dic13—22no—
40D4×Dic13—41no—
41D4×Dic13—41no—
42C2×C4⋊Dic13—21no—
43C2×C4×Dic13D411yescharacteristic
44C2×#6099—21no—
45C22×#1055D411yescharacteristic
46C13×M32—21no—
47C13×M32C2×C412yescomplemented
48C2×C13×C16—21no—
49C13×#108—21no—
50C13×#108C2×C412yescomplemented
51#88072—22no—
52#88072—22no—
53#88059—21no—
54#88059C2×C412yescomplemented
55#88058—21no—
56#88058C2×C412yes—
57#88055—41no—
58C8×Dic13—41no—
59C8×Dic13C2×C411yescharacteristic
60C8×Dic13C2×C411yescharacteristic
61C8×Dic13D411yescharacteristic
62C8×Dic13D411yescharacteristic
63#88052—21no—
64#88052C2×C412yescomplemented
65C2×#6090—21no—
66C4×#361—131nomaximal, Sylow
67C24×C13—41no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—41no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13—84no—
79C22×Dic13SD1611yescharacteristic
80C22×Dic13SD1611yescharacteristic
81C13×D8—22no—
82C13×D8—22no—
83C13×D8—22no—
84C13×D8C4214yes—
85C13×M16—22no—
86C13×M16—41no—
87C2×C8×C13—41no—
88C2×C8×C13C22×C411yescharacteristic
89C2×C8×C13C22×C411yescharacteristic
90C2×C8×C13C22×C411yescharacteristic
91C2×C8×C13C2×D411yescharacteristic
92C2×C8×C13#4111yescharacteristic
93C2×C8×C13#4111yescharacteristic
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C4⋊Dic13—22no—
97C4⋊Dic13—41no—
98C4×Dic13C22⋊C411yescharacteristic
99C4×Dic13C22⋊C411yescharacteristic
100C4×Dic13D811yescharacteristic
101C4×Dic13D811yescharacteristic
102#6099—22no—
103#6099—41no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—41no—
107C2×#1055C22⋊C411yescharacteristic
108C2×#1055C22⋊C411yescharacteristic
109C13×C16—22no—
110#6090—22no—
111C2×C4×D8—131no—
112C2×#361—131no—
113C2×#361D1311yescharacteristic
114C4×M32—131no—
115C4×#108—131no—
116#1387—131no—
117#1387—131no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—82no—
122C23×C13—82no—
123C23×C13C2×SD1611yescharacteristic
124D4×C13—24no—
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—42no—
128C2×C4×C13C2×C22⋊C411yescharacteristic
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×Dic13—22no—
135C2×Dic13—41no—
136C2×Dic13—42no—
137C2×Dic13—84no—
138C2×Dic13—82no—
139C2×Dic13—84no—
140C2×Dic13#10211yescharacteristic
141C2×Dic13#10211yescharacteristic
142C2×Dic13#10211yescharacteristic
143C2×Dic13#10211yescharacteristic
144C8×C13—42no—
145C8×C13C2×C4211yescharacteristic
146C8×C13#11711yescharacteristic
147C8×C13C4×D411yescharacteristic
148C8×C13C4×D411yescharacteristic
149#1055—21no—
150#1055—21no—
151#1055—42no—
152C22×D8C2×D1311yescharacteristic
153C2×C4×D4—261no—
154C2×M32—131no—
155C2×M32C2×D1311yescharacteristic
156C4×D8—132no—
157C4×D8—132no—
158C4×D8—261no—
159C4×D8—261no—
160C2×#108—131no—
161C2×#108C2×D1311yescharacteristic
162C2×#107—131no—
163C2×#102—261no—
164C4×M16—261no—
165C2×C4×C8—131no—
166#361—134no—
167#361Dic1314yesdirect product factor
168#346—261no—
169C4×C16—261no—
170#341—261no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—44no—
174C22×C13—84no—
175C22×C13—84no—
176C22×C13—82no—
177C22×C13—82no—
178C22×C13C2×#10211yescharacteristic
179C22×C13C4×SD1611yescharacteristic
180C22×C13C4×SD1611yescharacteristic
181C4×C13C4×C22⋊C411yescharacteristic
182C4×C13#41611yescharacteristic
183C4×C13C4×D811yescharacteristic
184C4×C13C4×D811yescharacteristic
185Dic13—21no—
186Dic13—21no—
187Dic13—21no—
188Dic13—82no—
189Dic13#36112yesdirect product factor
190C22×D4—21no—
191C23×C4—521no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8C4×D1312yes—
196C2×D8C4×D1312yes—
197C2×D8C2×Dic1312yes—
198C2×M16—21no—
199C2×M16—261no—
200C22×C8—131no—
201C22×C8C22×D1311yescharacteristic
202C4×D4—262no—
203C4×D4—262no—
204C4×D4—521no—
205C4×D4—521no—
206C2×C4⋊C4—261no—
207C2×C22⋊C4—521no—
208C2×C42—131no—
209M32—21no—
210M32—132no—
211M32—261no—
212M32C2×Dic1312yescomplemented
213C2×C16—21no—
214C2×C16—261no—
215#108—21no—
216#108—132no—
217#108—261no—
218#108C2×Dic1312yescomplemented
219#107—132no—
220#107—261no—
221#102—262no—
222#102—262no—
223#97—521no—
224C4×C8—131no—
225C4×C8—131no—
226C4×C8—131no—
227C4×C8—131no—
228C4×C8—521no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—84no—
232C2×C13C4×#10211yescharacteristic
233C2×C13C2×#36111yescharacteristic
234C2×C13#214811yescharacteristic
235C24—41no—
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4—521no—
247C22×C4—1044no—
248C22×C4D4×D1311yescharacteristic
249D8—22no—
250D8—22no—
251D8—22no—
252D8C4×Dic1314yes—
253M16—22no—
254M16—41no—
255M16—262no—
256M16—521no—
257C2×C8—41no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—261no—
261C2×C8—261no—
262C2×C8—521no—
263C2×C8C2×C4×D1311yescharacteristic
264C2×C8C2×C4×D1311yescharacteristic
265C2×C8D4×D1311yescharacteristic
266C2×C8#612911yescharacteristic
267C2×C8#612911yescharacteristic
268C2×C8C22×Dic1311yescharacteristic
269C4⋊C4—262no—
270C4⋊C4—521no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C42—131no—
274C42—131no—
275C42—131no—
276C42—131no—
277C16—22no—
278C16—262no—
279C13C4×#36111yescharacteristic, complemented, Sylow
280C23—42no—
281C23—42no—
282C23—42no—
283C23—82no—
284C23—82no—
285C23SD16×D1311yescharacteristic
286D4—24no—
287D4—42no—
288D4—42no—
289D4—42no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—262no—
295C2×C4—521no—
296C2×C4—522no—
297C2×C4—1044no—
298C2×C4—1044no—
299C2×C4—1042no—
300C2×C4C22⋊C4×D1311yescharacteristic
301C2×C4#8813511yescharacteristic
302C2×C4D8×D1311yescharacteristic
303C2×C4#8816611yescharacteristic
304C2×C4#8817011yescharacteristic
305C2×C4D4×Dic1311yescharacteristic
306C8—42no—
307C8—261no—
308C8—261no—
309C8—522no—
310C8#8813111yescharacteristic
311C8#8813511yescharacteristic
312C8C2×C4×Dic1311yescharacteristic
313C8D4×Dic1311yescharacteristic
314C22—21no—
315C22—21no—
316C22—44no—
317C22—84no—
318C22—84no—
319C22—82no—
320C22—82no—
321C22#1171841911yescharacteristic
322C22D13×#10211yescharacteristic
323C22SD16×Dic1311yescharacteristic
324C4—132no—
325C4—261no—
326C4—261no—
327C4—261no—
328C4—1042no—
329C4#1171841711yescharacteristic
330C4#1171843311yescharacteristic
331C4C22⋊C4×Dic1311yescharacteristic
332C4D8×Dic1311yescharacteristic
333C2—21no—
334C2—21no—
335C2—84no—
336C2#102×Dic1311yescharacteristic
337C2D13×#36111yescharacteristic
338C2#1311658211yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C13×#361C2
socleC22×C13C2×#102
prime radicalC22×C13×D8C22
cosocleC22×C8×C13C23
hypercenterC2×#361D13
hypocenterC13C4×#361
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
3. M32×Dic13C2semidirect
4. #108×Dic13C2semidirect
5. #13112946C2semidirect
6. #13112945C2semidirect
22. C13×#361C4semidirect
23. #11718155C4semidirect
47. C13×M32C2×C4semidirect
50. C13×#108C2×C4semidirect
54. #88059C2×C4semidirect
64. #88052C2×C4semidirect
167. #361Dic13direct (N × H)
189. Dic13#361direct (N × H)
212. M32C2×Dic13semidirect
218. #108C2×Dic13semidirect
279. C13C4×#361semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic132
C2×#117181552
M32×Dic132
#108×Dic132
#131129462
#131129452
C2×C13×#3612
C4×#36113