Finite Group Databasebeta

← #16786898

Subgroups — #16786898

Order 3328.

460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130078C212yesmaximal, complemented
2#13129777C212yesmaximal, complemented
3#13129764C212yesmaximal
4C4×#88190C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88190C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8#11719125—22no—
9#11718882C2211yescharacteristic
10C4×C22⋊Dic13—22no—
11#11718638C2211yescharacteristic
12#11718635C411yescharacteristic
13#11718606—22no—
14C42×Dic13C411yescharacteristic
15#11718286—22no—
16#11718285C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×Dic26C2×C411yescharacteristic
20C4×D4×C13—41no—
21C4×D4×C13—41no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—21no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13—22no—
27#88190—22no—
28#88190C814yescomplemented
29C2×C4⋊Dic13C2311yescharacteristic
30C2×#6101D412yes—
31C2×C4×Dic13—21no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D412yes—
36C4×Dic26—41no—
37C4×Dic26—41no—
38C22⋊#1057—24no—
39#88112—42no—
40C4×#1057—42no—
41#88071—22no—
42#88071—22no—
43#11476—131nomaximal, Sylow
44C24×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13C2×C812yes—
49C22×C4×C13—21no—
50C22×C4×C13—44no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C412yes—
59C22×Dic13C2×D412yes—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C2×C812yes—
63C2×Dic26M1612yes—
64C2×#1057—44no—
65C13×C4⋊C4—41no—
66C13×C22⋊C4—42no—
67C42×C13—21no—
68C42×C13—21no—
69C22⋊Dic13—28no—
70C22⋊Dic13—44no—
71C4⋊Dic13—41no—
72#6101—42no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—21no—
76C4×Dic13—42no—
77C4×Dic13—42no—
78C4×Dic13—41no—
79C4×Dic13C2×C812yes—
80C4×#124—131no—
81#1461—132no—
82#1324—132no—
83#1318—132no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13C2×C22⋊C411yescharacteristic
90D4×C13—42no—
91D4×C13—42no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—82no—
100C2×C4×C13—82no—
101C2×C4×C13#9911yescharacteristic
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13C22⋊C814yes—
116Dic26—42no—
117Dic26—42no—
118#1057—84no—
119C2×#124—131no—
120C2×C4×Q8—131no—
121C2×C4×D4#26111yescharacteristic
122#431—262no—
123#391—131no—
124#390—131no—
125#388—262no—
126#382—131no—
127C4×C22⋊C4—262no—
128C43—131no—
129#324—134no—
130#324—262no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—44no—
134C22×C13—42no—
135C22×C13—82no—
136C22×C13—81no—
137C22×C13—81no—
138C22×C13C2×C22⋊C811yescharacteristic
139C22×C13C2×#9911yescharacteristic
140C22×C13#41311yescharacteristic
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—81no—
146C4×C13#35512yes—
147Dic13—24no—
148Dic13—42no—
149Dic13—42no—
150Dic13—42no—
151C22×Q8—131no—
152C22×D4C2×#26111yescharacteristic
153C23×C4—21no—
154#124—134no—
155#124—262no—
156C4×Q8—521no—
157C4×Q8—521no—
158C4×D4—41no—
159C4×D4—41no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4C2×#26111yescharacteristic
163C2×C22⋊C4—21no—
164C2×C22⋊C4—262no—
165C2×C22⋊C4—262no—
166C2×C42—131no—
167C2×C42—132no—
168C2×C42—131no—
169C2×C42—261no—
170C2×C42—261no—
171C2×C42C2×#26111yescharacteristic
172C4⋊C8—522no—
173C22⋊C8—264no—
174C4×C8—522no—
175#95—262no—
176#95—262no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13—82no—
180C2×C13#145911yescharacteristic
181C2×C13#212611yescharacteristic
182C2×C13C2×#35511yescharacteristic
183C24—21no—
184C2×Q8—132no—
185C2×Q8—132no—
186C2×Q8—521no—
187C2×Q8—521no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4D13⋊C812yes—
192C22×C4—21no—
193C22×C4—44no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—132no—
197C22×C4—132no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4C22⋊#26111yescharacteristic
201C22×C4C22⋊#26111yescharacteristic
202C22×C4C22×#26111yescharacteristic
203C2×C8—524no—
204C4⋊C4—41no—
205C4⋊C4—522no—
206C4⋊C4—521no—
207C22⋊C4—42no—
208C22⋊C4—268no—
209C22⋊C4—524no—
210C42—21no—
211C42—21no—
212C42—132no—
213C42—262no—
214C42—262no—
215C42—261no—
216C42—521no—
217C42—522no—
218C42—522no—
219C13#1147611yescharacteristic, complemented, Sylow
220C23—22no—
221C23—42no—
222C23—42no—
223C23—41no—
224C23—41no—
225C23C2×C22⋊#26111yescharacteristic
226Q8—522no—
227Q8—522no—
228D4—42no—
229D4—42no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—134no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—522no—
250C2×C4#8811911yescharacteristic
251C2×C4#8811911yescharacteristic
252C2×C4C2×D13⋊C811yescharacteristic
253C2×C4D13⋊M1611yescharacteristic
254C8—1044no—
255C22—21no—
256C22—21no—
257C22—44no—
258C22—42no—
259C22—82no—
260C22—81no—
261C22—81no—
262C22D13⋊(C22⋊C8)11yescharacteristic
263C22#1171913211yescharacteristic
264C22C2×#8811911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—81no—
270C4—264no—
271C4—522no—
272C4—522no—
273C4—522no—
274C4#1171829512yes—
275C2—21no—
276C2—21no—
277C2—82no—
278C2#1313007111yescharacteristic
279C2#1313110711yescharacteristic
280C2C2×#1171829511yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#11476
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130078C2semidirect
2. #13129777C2semidirect
28. #88190C8semidirect
219. C13#11476semidirect

Maximal subgroups

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

subgroupindex
#131300782
#131297772
#131297642
C4×#881902
#1147613