Finite Group Databasebeta

← #16779578

Subgroups — #16779578

Order 3328.

546 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 152 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⋊#432C212yesmaximal
2#13129701C214yesmaximal, complemented
3C2×#11718346C211yesmaximal, characteristic
4C2×C42×D13C2211yescharacteristic
5#11719130C2214yes—
6#11719128—22no—
7D13⋊(C22⋊C8)—22no—
8#11719055C414yes—
9#11719054—22no—
10D13⋊(C4⋊C8)—22no—
11#11719047C414yes—
12C2×C4×C8×C13C411yescharacteristic
13C2×#88060C412yes—
14C2×#88054C2212yes—
15C2×C4×#1055C411yescharacteristic
16#11718346—22no—
17#11718346—22no—
18C22×C4×D13C2×C411yescharacteristic
19C22×C4×D13D411yescharacteristic
20C22×C4×D13Q811yescharacteristic
21C2×D13⋊C8—24no—
22C22×C8×C13C2×C412yes—
23C2×C42×C13C2×C411yescharacteristic
24C2×C4×Dic13D411yescharacteristic
25C2×C4×Dic13Q811yescharacteristic
26C2×C4×Dic13C2311yescharacteristic
27C22×#1055C2×C412yes—
28C42×D13C2×C412yes—
29C42×D13C2×C412yes—
30C42×D13D412yes—
31C42×D13D412yes—
32C22⋊#1057—24no—
33#88112—24no—
34#88111—24no—
35#88110—24no—
36#88110C2×C418yes—
37C4⋊#1057—24no—
38C4×C8×C13—21no—
39C4×C8×C13—21no—
40#88060—24no—
41#88054—24no—
42C4×#1055—21no—
43C4×#1055—21no—
44#7986—131nomaximal, Sylow
45C23×D13C4⋊C411yescharacteristic
46C22×C4×C13C4⋊C411yescharacteristic
47C22×C4×C13C4⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C4⋊C411yescharacteristic
50C22×Dic13C2×D411yescharacteristic
51C22×Dic13C2×Q811yescharacteristic
52C2×C4×D13—24no—
53C2×C4×D13—42no—
54C2×C4×D13—42no—
55C2×C4×D13C4212yes—
56C2×C4×D13C22⋊C412yes—
57C2×C4×D13C22⋊C412yes—
58C2×C4×D13C22⋊C412yes—
59C2×C4×D13C4⋊C412yes—
60C2×C4×D13C4⋊C412yes—
61C2×#1057—28no—
62D13⋊C8—48no—
63C2×C8×C13—22no—
64C2×C8×C13—42no—
65C42×C13C4211yescharacteristic
66C42×C13C4211yescharacteristic
67C42×C13C22⋊C411yescharacteristic
68C42×C13C22⋊C411yescharacteristic
69C4×Dic13C22⋊C412yes—
70C4×Dic13C22⋊C412yes—
71C4×Dic13C4⋊C412yes—
72C4×Dic13C4⋊C412yes—
73C4×Dic13C22×C412yes—
74C4×Dic13C2×D412yes—
75C2×#1055—22no—
76C2×#1055—42no—
77C2×#432—132no—
78C2×#431—131no—
79#1290—134no—
80C23×C13C2×C4⋊C411yescharacteristic
81C22×D13—41no—
82C22×D13—41no—
83C22×D13#9512yes—
84C22×D13#10814yes—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13#9511yescharacteristic
89C2×C4×C13#9511yescharacteristic
90C2×C4×C13#9511yescharacteristic
91C2×C4×C13#9511yescharacteristic
92C2×C4×C13C2×C4211yescharacteristic
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×Dic13—22no—
95C2×Dic13—41no—
96C2×Dic13—41no—
97C2×Dic13#9512yes—
98C2×Dic13C2×C22⋊C412yes—
99C2×Dic13C2×C4⋊C412yes—
100C4×D13—24no—
101C4×D13—24no—
102C4×D13—24no—
103C4×D13—24no—
104C4×D13—42no—
105C4×D13—42no—
106#1057—48no—
107C8×C13—42no—
108#1055—42no—
109C22×C42—131no—
110#432—134no—
111#432—134no—
112#432—262no—
113#432—262no—
114#431—262no—
115#431—262no—
116C2×C4⋊C8—132no—
117C2×C4⋊C8—262no—
118C2×C22⋊C8—132no—
119C2×C22⋊C8—262no—
120C2×#97—134no—
121C2×C4×C8—131no—
122C2×C4×C8#26111yescharacteristic
123C22×C13—21no—
124C22×C13—21no—
125C22×C13C2×#9511yescharacteristic
126C22×C13C2×#10812yes—
127C2×D13—22no—
128C2×D13—22no—
129C2×D13—44no—
130C2×D13#34114yes—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13H(3,ℤ/4)12yes—
136C4×C13#41312yes—
137Dic13—22no—
138Dic13—22no—
139Dic13—22no—
140C23×C4—131no—
141C23×C4—131no—
142C23×C4—131no—
143C22×C8—132no—
144C22×C8—264no—
145C22×C8C2×#26112yes—
146C2×C42—131no—
147C2×C42—131no—
148C2×C42—131no—
149C2×C42—132no—
150C2×C42—132no—
151C2×C42—132no—
152C2×C42—132no—
153C2×C42C2×#26111yescharacteristic
154C4⋊C8—264no—
155C4⋊C8—264no—
156C4⋊C8—264no—
157C22⋊C8—264no—
158C22⋊C8—264no—
159C22⋊C8—264no—
160#97—138no—
161#97—264no—
162C4×C8—21no—
163C4×C8—21no—
164C4×C8—261no—
165C4×C8—261no—
166C2×C13—22no—
167C2×C13C2×H(3,ℤ/4)11yescharacteristic
168C2×C13C2×#34111yescharacteristic
169C2×C13#174211yescharacteristic
170D13—24no—
171C24—131no—
172C22×C4—131no—
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—132no—
180C22×C4—132no—
181C22×C4—264no—
182C22×C4—522no—
183C22×C4—522no—
184C22×C4C4⋊#26111yescharacteristic
185C22×C4C4⋊#26111yescharacteristic
186C22×C4C22×#26111yescharacteristic
187C2×C8—22no—
188C2×C8—42no—
189C2×C8—268no—
190C2×C8—262no—
191C2×C8—528no—
192C2×C8—522no—
193C42—132no—
194C42—132no—
195C42—132no—
196C42—132no—
197C42—132no—
198C42—132no—
199C42C4×#26111yescharacteristic
200C42C4×#26111yescharacteristic
201C42C22⋊#26111yescharacteristic
202C42C22⋊#26111yescharacteristic
203C13#798611yescharacteristic, complemented, Sylow
204C23—132no—
205C23—134no—
206C23—521no—
207C23—521no—
208C23C2×C4⋊#26111yescharacteristic
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—132no—
213C2×C4—132no—
214C2×C4—132no—
215C2×C4—264no—
216C2×C4—264no—
217C2×C4—262no—
218C2×C4—264no—
219C2×C4—264no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4(C2×#261)⋊C411yescharacteristic
225C2×C4(C2×#261)⋊C411yescharacteristic
226C2×C4(C2×#261)⋊C411yescharacteristic
227C2×C4(C2×#261)⋊C411yescharacteristic
228C2×C4C2×C4×#26111yescharacteristic
229C2×C4C2×C22⋊#26111yescharacteristic
230C8—42no—
231C8—528no—
232C8—522no—
233C22—21no—
234C22—21no—
235C22—134no—
236C22—262no—
237C22—262no—
238C22—524no—
239C22D13⋊#10812yes—
240C22C2×(C2×#261)⋊C411yescharacteristic
241C4—21no—
242C4—21no—
243C4—21no—
244C4—21no—
245C4—262no—
246C4—262no—
247C4—262no—
248C4#1171826712yes—
249C4#1171913212yes—
250C2—22no—
251C2—264no—
252C2C2×#1171826711yescharacteristic
253C2#1313052811yescharacteristic
254C2#1313054111yescharacteristic
subgroupG/H
centerC2×C4(C2×#261)⋊C4
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13C2×#95
prime radicalC23×D13C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×C8#261
hypocenterC13#7986
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #13129701C2semidirect
203. C13#7986semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4322
#131297012
C2×#117183462
#798613