Finite Group Databasebeta

← #16778563

Subgroups — #16778563

Order 3328.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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
1#13130752C211yesmaximal, characteristic
2#13130752C211yesmaximal, characteristic
3#13129655C214yesmaximal
4#13117403C211yesmaximal, characteristic
5C2×#88141—21no—
6C2×#88123C411yescharacteristic
7C2×#88112—21no—
8C2×#88112—21no—
9C13×#384C411yescharacteristic
10C4⋊C4×Dic13—21no—
11C4⋊C4×Dic13C412yes—
12#11718635—21no—
13#11718634—21no—
14#11718634C2212yes—
15C42×Dic13C2211yescharacteristic
16#11718290—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Dic26—21no—
21C22×#1057—22no—
22C22×#1057—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13C2×C412yes—
29C2×#6101—22no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88141—42no—
38#88141—42no—
39#88123—24no—
40#88112—42no—
41#88112—42no—
42#88071—22no—
43#88071—22no—
44#7652—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13C22⋊C411yescharacteristic
51C22×Dic13C22⋊C411yescharacteristic
52C22×Dic13C2×D411yescharacteristic
53C22×Dic13C2×D411yescharacteristic
54C2×Dic26—24no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C2×#1057—42no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C2×#1057—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C42×C13—22no—
67C4⋊Dic13—24no—
68C4⋊Dic13—22no—
69C4⋊Dic13M1614yes—
70#6101—42no—
71#6101—42no—
72C4×Dic13—22no—
73C4×Dic13—41no—
74C4×Dic13—41no—
75C4×Dic13—41no—
76C4×Dic13—44no—
77C4×Dic13D812yes—
78C4×Dic13SD1612yes—
79C4×Dic13SD1612yes—
80C4×Dic13Q1612yes—
81C4×C4⋊Q8—131no—
82#1831—131no—
83#1831—131no—
84#1271—134no—
85C23×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13#10212yes—
96C2×C4×C13#10312yes—
97C2×C4×C13C2×M1612yes—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—24no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13#10112yes—
109C2×Dic13#10212yes—
110C2×Dic13#10312yes—
111C2×Dic13C2×D811yescharacteristic
112C2×Dic13C2×SD1611yescharacteristic
113C2×Dic13C2×SD1611yescharacteristic
114C2×Dic13C2×Q1611yescharacteristic
115Dic26—48no—
116#1057—82no—
117#1057—82no—
118C2×C4⋊Q8—131no—
119C2×C4×Q8—261no—
120C2×C4⋊C8—261no—
121C2×C4⋊C8—261no—
122#391—261no—
123#389—132no—
124#389—261no—
125#384#26111yescharacteristic
126C4×C4⋊C4—132no—
127C4×C4⋊C4—261no—
128C43—131no—
129#336—132no—
130#336—132no—
131#336—261no—
132#336—261no—
133C22×C13#40711yescharacteristic
134C22×C13#41011yescharacteristic
135C22×C13C2×#10111yescharacteristic
136C22×C13C2×#10211yescharacteristic
137C22×C13C2×#10311yescharacteristic
138C22×C13#42111yescharacteristic
139C22×C13#42111yescharacteristic
140C4×C13—22no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—82no—
144Dic13—21no—
145Dic13—21no—
146Dic13—21no—
147Dic13—21no—
148Dic13—41no—
149Dic13—44no—
150Dic13#33214yes—
151C22×Q8—261no—
152C22×C8—262no—
153C22×C8—262no—
154C4⋊Q8—264no—
155C4×Q8—522no—
156C4×Q8—522no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4—262no—
162C2×C4⋊C4C2×#26112yes—
163C2×C42—131no—
164C2×C42—131no—
165C2×C42—131no—
166C2×C42—131no—
167C2×C42—131no—
168C2×C42—131no—
169C2×C42—262no—
170C2×C42C2×#26111yescharacteristic
171C4⋊C8—522no—
172C4⋊C8—522no—
173#95—262no—
174#95—262no—
175C2×C13#146711yescharacteristic
176C2×C13#148611yescharacteristic
177C2×C13#148711yescharacteristic
178C2×C13#151711yescharacteristic
179C2×C13#151811yescharacteristic
180C2×C13#153711yescharacteristic
181C2×C13C2×#33211yescharacteristic
182C2×Q8—264no—
183C2×Q8—522no—
184C2×Q8—522no—
185C22×C4—22no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—262no—
191C22×C4C22⋊#26111yescharacteristic
192C22×C4C22⋊#26111yescharacteristic
193C22×C4C22×#26111yescharacteristic
194C2×C8—522no—
195C2×C8—522no—
196C2×C8—522no—
197C2×C8—522no—
198C2×C8—522no—
199C2×C8—522no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—134no—
204C4⋊C4—264no—
205C4⋊C4—262no—
206C4⋊C4—522no—
207C4⋊C4—522no—
208C42—22no—
209C42—132no—
210C42—132no—
211C42—132no—
212C42—132no—
213C42—262no—
214C42—521no—
215C42—521no—
216C42—521no—
217C42—524no—
218C13#765211yescharacteristic, complemented, Sylow
219C23C2×C22⋊#26111yescharacteristic
220Q8—528no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—132no—
231C2×C4—132no—
232C2×C4—132no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—131no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—264no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4#8811512yes—
248C2×C4#8811712yes—
249C2×C4D13⋊M1612yes—
250C8—1042no—
251C8—1042no—
252C22#1171912611yescharacteristic
253C22C2×#8811511yescharacteristic
254C22#1171914011yescharacteristic
255C22#1171914211yescharacteristic
256C22C2×#8811711yescharacteristic
257C22#1171915511yescharacteristic
258C22D13⋊#10111yescharacteristic
259C4—22no—
260C4—22no—
261C4—22no—
262C4—82no—
263C4—134no—
264C4—261no—
265C4—261no—
266C4—261no—
267C4—261no—
268C4—521no—
269C4—524no—
270C2#1313010011yescharacteristic
271C2#1313016311yescharacteristic
272C2#1313016611yescharacteristic
273C2#1313026511yescharacteristic
274C2#1313027011yescharacteristic
275C2#1313032811yescharacteristic
276C2D13⋊#33211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7652
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
218. C13#7652semidirect

Maximal subgroups

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

subgroupindex
#131307522
#131296552
#131174032
#765213