Finite Group Databasebeta

← D13⋊#352 #13131085

Subgroups — D13⋊#352 #13131085

Order 1664.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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×#123C211yesmaximal, characteristic
2D13⋊#100C211yesmaximal, characteristic
3D13⋊#99C211yesmaximal, characteristic
4#11718288C212yesmaximal, complemented
5#11718237C212yesmaximal, complemented
6C2×D4×D13C2211yescharacteristic
7C22×C4×D13C411yescharacteristic, complemented
8C2×C22⋊#261—21no—
9D13⋊M16—21no—
10C13×#123C411yescharacteristic, complemented
11#88189C411yescharacteristic, complemented
12#88183C2211yescharacteristic
13#88148—21no—
14C4⋊C4×D13—21no—
15#88140C2211yescharacteristic
16#88137—21no—
17C22⋊C4×D13—21no—
18C22⋊C4×D13C411yescharacteristic, complemented
19#88121—21no—
20#88121C2212yes—
21#88119C2212yes—
22#88107—21no—
23C23×D13C2×C411yescharacteristic
24C23×D13D411yescharacteristic
25C22×#261—41no—
26C2×D4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic, complemented
28C2×C22⋊D13D411yescharacteristic
29C2×C22⋊D13C2311yescharacteristic
30C22×Dic13C2×C411yescharacteristic, complemented
31D4×D13—41no—
32D4×D13—41no—
33C2×D52D411yescharacteristic
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13—21no—
37C2×C4×D13—41no—
38C2×C4×D13—41no—
39C2×C4×D13D411yescharacteristic
40C22⋊#261—22no—
41C22⋊#261—41no—
42#6122—22no—
43#6118—41no—
44D13⋊C8—41no—
45C13×C4⋊C4—21no—
46C13×C22⋊C4—21no—
47C13×C22⋊C4C2×C411yescharacteristic, complemented
48C22⋊Dic13—21no—
49C22⋊Dic13C2×C411yescharacteristic, complemented
50#6103—21no—
51#6103—21no—
52#6103—21no—
53C4⋊Dic13—21no—
54#6101—21no—
55#6101—21no—
56C2×#352—131nomaximal, Sylow
57C23×C13C22⋊C411yescharacteristic
58C23×C13C22×C411yescharacteristic
59C22×D13—21no—
60C22×D13—21no—
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—42no—
64C22×D13—42no—
65C22×D13C22⋊C411yescharacteristic
66C22×D13C22⋊C411yescharacteristic
67C22×D13C2×D411yescharacteristic
68C2×#261—42no—
69C2×#261—82no—
70D4×C13—41no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—41no—
74C2×C4×C13C22⋊C411yescharacteristic
75C22⋊D13—41no—
76C22⋊D13—41no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—41no—
80C2×Dic13C2×D411yescharacteristic
81D52—41no—
82C4×D13—21no—
83C4×D13—21no—
84C4×D13—42no—
85C4×D13—42no—
86C4×D13—41no—
87C4×D13—41no—
88#1057—42no—
89C2×#123—131no—
90C2×#100—131no—
91C2×#99—131no—
92#352—132no—
93#352—132no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13C2×C22⋊C411yescharacteristic
99C2×D13—22no—
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—41no—
106C2×D13—41no—
107C2×D13—81no—
108C2×D13#9911yescharacteristic
109C2×D13#9911yescharacteristic
110#261—82no—
111C4×C13—21no—
112C4×C13—41no—
113C4×C13—41no—
114Dic13—21no—
115Dic13—41no—
116Dic13—41no—
117C22×D4—131no—
118C23×C4—131no—
119C2×M16—261no—
120#123—131no—
121#123—131no—
122#123—131no—
123#123—261no—
124#123—261no—
125#123#26111yescharacteristic, complemented
126C2×C4⋊C4—261no—
127C2×C22⋊C4—131no—
128C2×C22⋊C4—261no—
129C2×C22⋊C4—261no—
130#100—132no—
131#100—261no—
132#99—132no—
133#99—261no—
134C2×C13—21no—
135C2×C13—41no—
136C2×C13—41no—
137C2×C13C2×#9911yescharacteristic
138D13—21no—
139D13—41no—
140D13—41no—
141D13#35212yescomplemented
142C24—131no—
143C24—131no—
144C2×D4—131no—
145C2×D4—131no—
146C2×D4—131no—
147C2×D4—521no—
148C2×D4—521no—
149C2×D4C2×#26111yescharacteristic
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—261no—
153C22×C4—261no—
154C22×C4—261no—
155C22×C4—521no—
156C22×C4—521no—
157C22×C4—521no—
158C22×C4C2×#26111yescharacteristic, complemented
159M16—262no—
160M16—521no—
161C2×C8—521no—
162C4⋊C4—21no—
163C4⋊C4—261no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C22⋊C4—21no—
167C22⋊C4—131no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C22⋊C4—262no—
173C22⋊C4—521no—
174C22⋊C4C2×#26111yescharacteristic, complemented
175C13C2×#35211yescharacteristic, complemented, Sylow
176C23—131no—
177C23—131no—
178C23—131no—
179C23—261no—
180C23—261no—
181C23—261no—
182C23—261no—
183C23—522no—
184C23—522no—
185C23C22⋊#26111yescharacteristic
186C23C22×#26111yescharacteristic
187D4—41no—
188D4—521no—
189D4—521no—
190D4—521no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—131no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—521no—
200C2×C4—521no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—521no—
204C2×C4—522no—
205C2×C4—1042no—
206C2×C4C22⋊#26111yescharacteristic
207C8—522no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—131no—
213C22—131no—
214C22—262no—
215C22—261no—
216C22—261no—
217C22—521no—
218C22—521no—
219C22—522no—
220C22—522no—
221C22—522no—
222C22—1041no—
223C22C2×C22⋊#26111yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—261no—
228C4—521no—
229C4—521no—
230C4—1042no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—132no—
235C2—261no—
236C2—521no—
237C2—521no—
238C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#123C4
socleC2×C13C2×#99
prime radicalC2×D4×D13C22
cosocleC2×C22⋊D13C23
hypercenter#123#261
hypocenterC13C2×#352
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11718288C2semidirect
5. #11718237C2semidirect
7. C22×C4×D13C4semidirect
10. C13×#123C4semidirect
11. #88189C4semidirect
18. C22⋊C4×D13C4semidirect
27. C22×C4×C13C2×C4semidirect
30. C22×Dic13C2×C4semidirect
47. C13×C22⋊C4C2×C4semidirect
49. C22⋊Dic13C2×C4semidirect
125. #123#261semidirect
141. D13#352semidirect
158. C22×C4C2×#261semidirect
174. C22⋊C4C2×#261semidirect
175. C13C2×#352semidirect

Maximal subgroups

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

subgroupindex
D13×#1232
D13⋊#1002
D13⋊#992
#117182882
#117182372
C2×#35213