Finite Group Databasebeta

← #13130864

Subgroups — #13130864

Order 1664.

338 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×D13⋊M16C211yesmaximal, characteristic
2C2×#88150C211yesmaximal, characteristic
3C2×#88113C212yesmaximal, complemented
4#11719126C211yesmaximal, characteristic
5#11718291C212yesmaximal, complemented
6C22×C4×D13C2211yescharacteristic
7C22×Dic26C2211yescharacteristic
8C2×#6122C2212yes—
9C2×#6122C2212yes—
10D13⋊M16—24no—
11C2×#6118—21no—
12C2×D13⋊C8—21no—
13C2×C13×C4⋊C4C411yescharacteristic
14C2×#6103C411yescharacteristic
15C2×#6103C411yescharacteristic
16C2×#6101C411yescharacteristic
17C2×#6101C2211yescharacteristic
18#88150—21no—
19#88150—21no—
20#88150—21no—
21#88150—21no—
22#88113—24no—
23#88111—21no—
24#88111—21no—
25C23×D13C2×C411yescharacteristic
26C22×C4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C22×Dic13C2×C411yescharacteristic
30C22×Dic13C2×C411yescharacteristic
31C22×Dic13C2311yescharacteristic
32C2×C4×D13—22no—
33C2×C4×D13—22no—
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×Dic26—22no—
39C2×Dic26—21no—
40C2×Dic26—21no—
41C2×Dic26—22no—
42#6122—22no—
43#6122—22no—
44#6122—22no—
45#6122D414yes—
46C2×#1057—22no—
47C2×#1057—22no—
48#6118—24no—
49D13⋊C8—24no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6103—21no—
56#6101—21no—
57#6101—21no—
58#6101—21no—
59#6101—21no—
60#1901—131nomaximal, Sylow
61C23×C13C22×C411yescharacteristic
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—41no—
65C22×D13C22⋊C411yescharacteristic
66C22×D13C22⋊C411yescharacteristic
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—41no—
72C2×C4×C13C22⋊C411yescharacteristic
73C2×C4×C13C22⋊C411yescharacteristic
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—41no—
78C2×Dic13C2×D412yes—
79C2×Dic13C2×D411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81C2×Dic13#4112yes—
82C4×D13—21no—
83C4×D13—21no—
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—21no—
87C4×D13—21no—
88Dic26—41no—
89Dic26—42no—
90Dic26—41no—
91#1057—24no—
92#1057—42no—
93C22×M16—131no—
94C2×C22⋊Q8—131no—
95C2×#101—132no—
96#407—131no—
97#343—132no—
98C22×C13—21no—
99C22×C13—21no—
100C22×C13C2×C22⋊C411yescharacteristic
101C22×C13C4×D412yes—
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—44no—
108C2×D13#10112yescomplemented
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—41no—
112C4×C13—41no—
113Dic13—41no—
114Dic13—41no—
115Dic13#12011yescharacteristic
116Dic13#12112yes—
117Dic13#12311yescharacteristic
118C22×Q8—131no—
119C23×C4—131no—
120C2×M16—132no—
121C2×M16—132no—
122C2×M16—264no—
123C2×M16—261no—
124C22×C8—261no—
125C22⋊Q8—261no—
126C22⋊Q8—261no—
127C22⋊Q8—261no—
128C22⋊Q8—261no—
129C2×C4⋊C4—131no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4#26111yescharacteristic
132C2×C22⋊C4—131no—
133C2×C22⋊C4—131no—
134#101—264no—
135C22⋊C8—261no—
136C22⋊C8—261no—
137C2×C13—22no—
138C2×C13#38611yescharacteristic
139C2×C13C2×#10111yescharacteristic
140C2×C13#41311yescharacteristic
141D13—22no—
142D13—41no—
143C24—131no—
144C2×Q8—262no—
145C2×Q8—261no—
146C2×Q8—261no—
147C2×Q8—262no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—262no—
156C22×C4—262no—
157C22×C4C2×#26111yescharacteristic
158C22×C4C2×#26111yescharacteristic
159C22×C4C2×#26111yescharacteristic
160M16—134no—
161M16—262no—
162M16—264no—
163M16—262no—
164M16—262no—
165C2×C8—262no—
166C2×C8—264no—
167C2×C8—262no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—261no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4—261no—
174C22⋊C4—261no—
175C22⋊C4—261no—
176C22⋊C4—261no—
177C22⋊C4—261no—
178C13#190111yescharacteristic, complemented, Sylow
179C23—131no—
180C23—131no—
181C23—262no—
182C23—262no—
183C23—521no—
184C23C22×#26111yescharacteristic
185Q8—521no—
186Q8—522no—
187Q8—521no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—261no—
202C2×C4—261no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—521no—
207C2×C4C22⋊#26111yescharacteristic
208C2×C4C22⋊#26111yescharacteristic
209C8—264no—
210C8—522no—
211C22—21no—
212C22—21no—
213C22—132no—
214C22—261no—
215C22—261no—
216C22—261no—
217C22—261no—
218C22—261no—
219C22—524no—
220C22D4×#26112yes—
221C22C2×C22⋊#26111yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—131no—
227C4—132no—
228C4—131no—
229C4—521no—
230C4—521no—
231C2—22no—
232C2—262no—
233C2—521no—
234C2#1171913211yescharacteristic
235C2#1171915011yescharacteristic
236C2D13⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13C2×C4
cosocleC22×Dic13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1901
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#88113C2semidirect
5. #11718291C2semidirect
108. C2×D13#101semidirect
178. C13#1901semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊M162
C2×#881502
C2×#881132
#117191262
#117182912
#190113