Finite Group Databasebeta

← #16778385

Subgroups — #16778385

Order 3328.

492 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 106 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#13130752C212yesmaximal, complemented
2#13129656C212yesmaximal, complemented
3#13129653C212yesmaximal
4C4×#88201C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88201C411yescharacteristic
7C2×C4×D52C411yescharacteristic
8C2×#88112—22no—
9#11718891C2211yescharacteristic
10#11718651—22no—
11#11718649C2211yescharacteristic
12#11718638C411yescharacteristic
13C4×#6103—22no—
14C42×Dic13C2211yescharacteristic
15#11718290—22no—
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#88201C814yescomplemented
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#88112—44no—
38#88071—22no—
39#88071—22no—
40#7601—131nomaximal, Sylow
41C23×D13—21no—
42C2×Q8×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—41no—
45C2×Q8×C13C2×C812yes—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—21no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C2×D52—21no—
55C2×D52—41no—
56C2×D52—41no—
57C2×D52C2×C812yes—
58C2×C4×D13—44no—
59C2×C4×D13—42no—
60C2×#1057—44no—
61C2×#1057—44no—
62C2×#1057—44no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C42×C13—22no—
66C42×C13—42no—
67#6103—28no—
68#6103—42no—
69#6103—42no—
70#6103—42no—
71C4⋊Dic13—41no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—42no—
75C4×Dic13—41no—
76C4×Dic13C2×C812yes—
77C4×Dic13M1612yes—
78C4×#124—131no—
79#1831—132no—
80#1272—132no—
81#1270—132no—
82C23×C13C2×C22⋊C411yescharacteristic
83C22×D13—22no—
84C22×D13—41no—
85C22×D13—41no—
86C22×D13—42no—
87C22×D13—42no—
88Q8×C13—42no—
89Q8×C13—42no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
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×C13C22×C811yescharacteristic
102C2×C4×C13C2×M1611yescharacteristic
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—41no—
108C2×Dic13—42no—
109C2×Dic13C22⋊C814yes—
110C2×Dic13AGL(1,ℤ/8)12yes—
111C2×Dic13#13712yes—
112D52—42no—
113D52—42no—
114C4×D13—84no—
115#1057—84no—
116C2×#124—131no—
117C2×C4×Q8#26111yescharacteristic
118C2×C4×D4—131no—
119C2×C4⋊C8—262no—
120#391—131no—
121#390—131no—
122#388—262no—
123#382—131no—
124C4×C22⋊C4—262no—
125C43—131no—
126#336—134no—
127#336—262no—
128C22×C13C2×C22⋊C811yescharacteristic
129C22×C13#41011yescharacteristic
130C22×C13C2×#10011yescharacteristic
131C22×C13#41712yes—
132C22×C13#42112yes—
133C2×D13—42no—
134C2×D13—44no—
135C2×D13—81no—
136C2×D13—82no—
137C2×D13—81no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—22no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13—81no—
144Dic13—24no—
145Dic13—22no—
146Dic13—22no—
147Dic13—81no—
148C22×Q8C2×#26111yescharacteristic
149C22×D4—131no—
150C23×C4—261no—
151C22×C8—264no—
152#124—134no—
153#124—262no—
154C4×Q8—42no—
155C4×D4—522no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4C2×#26111yescharacteristic
159C2×C22⋊C4—262no—
160C2×C22⋊C4—262no—
161C2×C22⋊C4—261no—
162C2×C42—21no—
163C2×C42—131no—
164C2×C42—132no—
165C2×C42—132no—
166C2×C42—131no—
167C2×C42C2×#26111yescharacteristic
168C4⋊C8—524no—
169#95—262no—
170#95—262no—
171C2×C13#146011yescharacteristic
172C2×C13#147712yes—
173C2×C13#151212yes—
174C2×C13#153311yescharacteristic
175C2×C13#156011yescharacteristic
176D13—82no—
177C24—261no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8D13⋊C812yes—
182C2×D4—132no—
183C2×D4—261no—
184C2×D4—521no—
185C2×D4—521no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—261no—
191C22×C4—524no—
192C22×C4—522no—
193C22×C4C22⋊#26111yescharacteristic
194C22×C4C22⋊#26111yescharacteristic
195C22×C4C22×#26111yescharacteristic
196C2×C8—524no—
197C2×C8—524no—
198C2×C8—524no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—521no—
202C22⋊C4—268no—
203C22⋊C4—522no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42—22no—
207C42—42no—
208C42—132no—
209C42—132no—
210C42—262no—
211C42—262no—
212C42—521no—
213C42—522no—
214C13#760111yescharacteristic, complemented, Sylow
215C23—262no—
216C23—521no—
217C23—521no—
218C23—522no—
219C23—522no—
220C23C2×C22⋊#26111yescharacteristic
221Q8—42no—
222Q8—42no—
223D4—522no—
224D4—522no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—134no—
236C2×C4—132no—
237C2×C4—132no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—521no—
243C2×C4—522no—
244C2×C4—1044no—
245C2×C4#8812112yes—
246C2×C4C2×D13⋊C811yescharacteristic
247C2×C4D13⋊M1611yescharacteristic
248C8—1044no—
249C22—522no—
250C22—524no—
251C22—1042no—
252C22—1041no—
253C22—1041no—
254C22#1171911611yescharacteristic
255C22D13⋊(C22⋊C8)11yescharacteristic
256C22#1171915512yes—
257C22#1171916412yes—
258C22C2×#8812111yescharacteristic
259C4—22no—
260C4—21no—
261C4—21no—
262C4—42no—
263C4—41no—
264C4—81no—
265C4—262no—
266C4—262no—
267C4—264no—
268C4—1041no—
269C2—1042no—
270C2#1313007511yescharacteristic
271C2#1313013412yes—
272C2#1313024912yes—
273C2#1313031711yescharacteristic
274C2#1313037311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7601
LCSG ▷ C2×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. #13130752C2semidirect
2. #13129656C2semidirect
27. #88201C8semidirect
214. C13#7601semidirect

Maximal subgroups

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

subgroupindex
#131307522
#131296562
#131296532
C4×#882012
#760113