Finite Group Databasebeta

← Dic13×#356 #15778103

Subgroups — Dic13×#356 #15778103

Order 3328.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4⋊Q8×Dic13C211yesmaximal, characteristic
2C2×#11718140C211yesmaximal, characteristic
3#101×Dic13C212yesmaximal
4#13112962C212yesmaximal
5C2×C13×#356C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9C2×C13×#101C2212yes—
10#11718891C411yescharacteristic
11#11718891C2211yescharacteristic
12C2×#88076C2212yes—
13M16×Dic13—22no—
14#11718646—22no—
15C4⋊C4×Dic13—22no—
16#11718596C411yescharacteristic
17C42×Dic13C411yescharacteristic
18C13×#356C414yescomplemented
19#11718146—22no—
20#11718140C414yescomplemented
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13C2311yescharacteristic
23C2×C13×M16—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8C2×C412yes—
26C13×C4⋊Q8C2×C412yes—
27C2×C13×C4⋊C4—22no—
28C2×C42×C13C2×C411yescharacteristic
29Q8×Dic13—41no—
30Q8×Dic13—41no—
31Q8×Dic13—41no—
32Q8×Dic13—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13D412yes—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D412yes—
44C2×#6099—22no—
45C13×#101—22no—
46C13×#101C2×C414yes—
47#88076—22no—
48#88076C2×C414yes—
49#88071—22no—
50#88071—22no—
51#88055—42no—
52C8×Dic13—42no—
53C4×#356—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×Q8×C13—41no—
59C2×Q8×C13C4212yes—
60C2×Q8×C13C22×C411yescharacteristic
61C2×Q8×C13C22×C411yescharacteristic
62C2×Q8×C13#4112yes—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C412yes—
71C22×Dic13C22⋊C411yescharacteristic
72C13×M16—24no—
73C13×M16—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—24no—
77C42×C13—21no—
78C42×C13C4212yes—
79C4⋊Dic13—41no—
80C4⋊Dic13—42no—
81C4⋊Dic13—42no—
82C4⋊Dic13—44no—
83C4⋊Dic13—41no—
84C4×Dic13—24no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—42no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#6099—24no—
94#6099—42no—
95C2×#1055—42no—
96C4×C4⋊Q8—131no—
97C2×#356—131no—
98C2×#356D1311yescharacteristic
99C4×#101—132no—
100#1394—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—41no—
103Q8×C13—41no—
104Q8×C13—42no—
105Q8×C13—42no—
106Q8×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13C2×C4211yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C2×C4×C13C4×D412yes—
120C2×C4×C13C4×D412yes—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—21no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13#9911yescharacteristic
132C2×Dic13#9911yescharacteristic
133C8×C13—44no—
134#1055—44no—
135C2×C4⋊Q8C2×D1311yescharacteristic
136C2×C4×Q8—131no—
137C2×C4×Q8—131no—
138C2×#101—132no—
139C2×#101C2×D1312yes—
140C4×M16—262no—
141#391—131no—
142#391—131no—
143#389—262no—
144#384—131no—
145C4×C4⋊C4—262no—
146C43—131no—
147#356—134no—
148#356Dic1314yesdirect product factor
149#343—262no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13C4×C22⋊C411yescharacteristic
153C22×C13C2×#9911yescharacteristic
154C22×C13#41011yescharacteristic
155C4×C13—24no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—42no—
161Dic13—21no—
162Dic13—42no—
163Dic13—41no—
164Dic13—42no—
165Dic13—81no—
166Dic13#35612yesdirect product factor
167C22×Q8C4×D1311yescharacteristic
168C22×Q8C22×D1311yescharacteristic
169C2×M16—22no—
170C2×M16—262no—
171C4⋊Q8—22no—
172C4⋊Q8C4×D1312yes—
173C4⋊Q8C2×Dic1312yes—
174C4×Q8—521no—
175C4×Q8—521no—
176C4×Q8—521no—
177C4×Q8—521no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—132no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—262no—
184C2×C42—131no—
185C2×C42—132no—
186C2×C42—131no—
187C2×C42—261no—
188C2×C42—261no—
189C2×C42—261no—
190C2×C42C4×D1311yescharacteristic
191#101—22no—
192#101—134no—
193#101—262no—
194#101C2×Dic1314yes—
195#97—522no—
196C4×C8—522no—
197#95—262no—
198#95—262no—
199C2×C13—21no—
200C2×C13—21no—
201C2×C13C4×#9911yescharacteristic
202C2×C13C2×#35611yescharacteristic
203C2×C13#213211yescharacteristic
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8C4×Dic1312yes—
210C2×Q8C2×C4×D1311yescharacteristic
211C2×Q8#612912yes—
212C2×Q8C22×Dic1311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—132no—
217C22×C4—131no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4D4×D1312yes—
222M16—24no—
223M16—42no—
224M16—264no—
225M16—522no—
226C2×C8—42no—
227C2×C8—522no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—521no—
231C4⋊C4—522no—
232C4⋊C4—521no—
233C4⋊C4—524no—
234C4⋊C4—522no—
235C42—21no—
236C42—262no—
237C42—262no—
238C42—261no—
239C42—261no—
240C42—264no—
241C42—521no—
242C42—522no—
243C42—521no—
244C42—521no—
245C42C4×Dic1312yes—
246C13C4×#35611yescharacteristic, complemented, Sylow
247C23C22⋊C4×D1311yescharacteristic
248Q8—41no—
249Q8—42no—
250Q8—41no—
251Q8—42no—
252Q8—42no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—262no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—521no—
275C2×C4#8813111yescharacteristic
276C2×C4#8813512yes—
277C2×C4C2×C4×Dic1311yescharacteristic
278C2×C4D4×Dic1312yes—
279C8—44no—
280C8—524no—
281C22—21no—
282C22—21no—
283C22#1171840111yescharacteristic
284C22D13×#9911yescharacteristic
285C22C22⋊C4×Dic1311yescharacteristic
286C4—24no—
287C4—22no—
288C4—22no—
289C4—21no—
290C4—21no—
291C4—42no—
292C4—132no—
293C4—261no—
294C4—522no—
295C4—521no—
296C4—522no—
297C4—1041no—
298C2—21no—
299C2—21no—
300C2#99×Dic1311yescharacteristic
301C2D13×#35611yescharacteristic
302C2#1311652011yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC2×C13×#356C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC2×#356D13
hypocenterC13C4×#356
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
18. C13×#356C4semidirect
20. #11718140C4semidirect
148. #356Dic13direct (N × H)
166. Dic13#356direct (N × H)
246. C13C4×#356semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×Dic132
C2×#117181402
#101×Dic132
#131129622
C2×C13×#3562
C4×#35613