Finite Group Databasebeta

← #16778505

Subgroups — #16778505

Order 3328.

520 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130622C212yesmaximal, complemented
2#13129656C212yesmaximal, complemented
3#13129653C212yesmaximal
4C4×#88201C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88201C411yescharacteristic
7C2×C4×D52C411yescharacteristic
8C2×#88110—22no—
9C2×C4⋊#1057—22no—
10#11718891C2211yescharacteristic
11#11718651—22no—
12#11718649C2211yescharacteristic
13#11718638C411yescharacteristic
14C4×#6103—22no—
15C42×Dic13C2211yescharacteristic
16#11718290C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D52C2×C411yescharacteristic
19C22×C4×D13—21no—
20C22×#1057—24no—
21C4×Q8×C13—42no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13—21no—
25C2×C42×C13C2×C411yescharacteristic
26#88201—22no—
27#88201—22no—
28C2×#6103—22no—
29C2×#6103—21no—
30C2×#6103—22no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4×D52—42no—
37#88110—44no—
38C4⋊#1057—28no—
39#88071—22no—
40#88071—22no—
41#7635—131nomaximal, Sylow
42C23×D13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13M1612yes—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—21no—
53C22×Dic13C22⋊C412yes—
54C22×Dic13C2×D412yes—
55C2×D52—21no—
56C2×D52—41no—
57C2×D52—41no—
58C2×D52M1612yes—
59C2×C4×D13—42no—
60C2×C4×D13—44no—
61C2×#1057—28no—
62C2×#1057—44no—
63C2×#1057—44no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C42×C13—22no—
67C42×C13—42no—
68#6103—28no—
69#6103—42no—
70#6103—42no—
71#6103—42no—
72C4⋊Dic13—41no—
73C4×Dic13—24no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—22no—
77C4×Dic13—22no—
78C4×Dic13—41no—
79C4×#124—131no—
80#1767—132no—
81#1272—132no—
82#1270—132no—
83C23×C13C2×C22⋊C411yescharacteristic
84C22×D13—22no—
85C22×D13—41no—
86C22×D13—41no—
87C22×D13—42no—
88C22×D13—42no—
89Q8×C13—42no—
90Q8×C13—42no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13#10012yes—
101C2×C4×C13#10414yes—
102C2×C4×C13C2×M1611yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—41no—
110C2×Dic13—42no—
111C2×Dic13AGL(1,ℤ/8)12yes—
112C2×Dic13#13712yes—
113D52—42no—
114D52—42no—
115C4×D13—84no—
116#1057—48no—
117C2×#124—131no—
118C2×C4×Q8#26111yescharacteristic
119C2×C4×D4—131no—
120C2×C4⋊C8—262no—
121C2×#97—262no—
122#391—131no—
123#390—131no—
124#388—262no—
125#382—131no—
126C4×C22⋊C4—262no—
127C43—131no—
128#336—134no—
129C22×C13#40711yescharacteristic
130C22×C13#41011yescharacteristic
131C22×C13C2×#10011yescharacteristic
132C22×C13#41712yes—
133C22×C13C2×#10412yes—
134C2×D13—42no—
135C2×D13—44no—
136C2×D13—81no—
137C2×D13—82no—
138C2×D13—81no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13—81no—
144C4×C13#32914yes—
145Dic13—22no—
146Dic13—22no—
147Dic13—42no—
148Dic13—81no—
149C22×Q8C2×#26111yescharacteristic
150C22×D4—131no—
151C23×C4—261no—
152C22×C8—264no—
153#124—262no—
154#124—262no—
155C4×Q8—42no—
156C4×D4—522no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4C2×#26111yescharacteristic
160C2×C22⋊C4—262no—
161C2×C22⋊C4—262no—
162C2×C22⋊C4—261no—
163C2×C42—21no—
164C2×C42—132no—
165C2×C42—132no—
166C2×C42—131no—
167C2×C42—131no—
168C2×C42C2×#26111yescharacteristic
169C4⋊C8—268no—
170#97—524no—
171#95—262no—
172#95—262no—
173C2×C13#146611yescharacteristic
174C2×C13#148912yes—
175C2×C13#150912yes—
176C2×C13C2×#32911yescharacteristic
177C2×C13#156011yescharacteristic
178D13—82no—
179C24—261no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8#611812yes—
184C2×D4—132no—
185C2×D4—261no—
186C2×D4—521no—
187C2×D4—521no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—132no—
191C22×C4—132no—
192C22×C4—261no—
193C22×C4—524no—
194C22×C4—522no—
195C22×C4C22⋊#26111yescharacteristic
196C22×C4C22⋊#26111yescharacteristic
197C22×C4C22×#26111yescharacteristic
198C2×C8—268no—
199C2×C8—524no—
200C2×C8—524no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—521no—
204C22⋊C4—268no—
205C22⋊C4—522no—
206C22⋊C4—522no—
207C22⋊C4—522no—
208C42—22no—
209C42—42no—
210C42—262no—
211C42—262no—
212C42—264no—
213C42—261no—
214C42—261no—
215C42—521no—
216C13#763511yescharacteristic, complemented, Sylow
217C23—262no—
218C23—521no—
219C23—521no—
220C23—522no—
221C23—522no—
222C23C2×C22⋊#26111yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—522no—
226D4—522no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—132no—
237C2×C4—132no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—521no—
244C2×C4—522no—
245C2×C4—1044no—
246C2×C4#8811814yes—
247C2×C4#8812112yes—
248C2×C4C2×#611811yescharacteristic
249C2×C4D13⋊M1611yescharacteristic
250C8—528no—
251C22—522no—
252C22—524no—
253C22—1042no—
254C22—1041no—
255C22—1041no—
256C22#1171911611yescharacteristic
257C22#1171912711yescharacteristic
258C22C2×#8811812yes—
259C22#1171916412yes—
260C22C2×#8812111yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—81no—
266C4—262no—
267C4—262no—
268C4—522no—
269C4—1041no—
270C4#1171829914yes—
271C2—1042no—
272C2#1313009511yescharacteristic
273C2#1313017412yes—
274C2#1313024012yes—
275C2C2×#1171829911yescharacteristic
276C2#1313037311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13130622C2semidirect
2. #13129656C2semidirect
216. C13#7635semidirect

Maximal subgroups

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

subgroupindex
#131306222
#131296562
#131296532
C4×#882012
#763513