Finite Group Databasebeta

← #16786901

Subgroups — #16786901

Order 3328.

460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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#13130079C212yesmaximal, complemented
2#13129777C212yesmaximal, complemented
3#13129765C212yesmaximal
4#13117379C211yesmaximal, characteristic
5C2×#88201C411yescharacteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88147C411yescharacteristic
8#11719119—22no—
9C13×#391C411yescharacteristic
10#11718638C2211yescharacteristic
11#11718600C2211yescharacteristic
12C42×Dic13C411yescharacteristic
13#11718331—22no—
14#11718327—22no—
15#11718285—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D52C2×C411yescharacteristic
19C22×C4×D13—21no—
20C2×C13×C4⋊C4C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22#88201—22no—
23#88201C814yescomplemented
24Q8×Dic13—41no—
25Q8×Dic13—41no—
26C2×#6103—22no—
27C2×#6103—21no—
28C2×#6103—22no—
29C2×C4⋊Dic13D412yes—
30C2×C4⋊Dic13C2311yescharacteristic
31C2×C4×Dic13—21no—
32C2×C4×Dic13—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D412yes—
36#88147—41no—
37#88147—41no—
38C22⋊#1057—24no—
39C4⋊#1057—42no—
40C4×#1057—42no—
41C13×#95—22no—
42#88071—22no—
43#11476—131nomaximal, Sylow
44C23×D13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13C2×C812yes—
48C2×Q8×C13M1612yes—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—21no—
54C22×Dic13C22⋊C411yescharacteristic
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C2×D412yes—
57C2×D52—21no—
58C2×D52—41no—
59C2×D52—41no—
60C2×D52C2×C812yes—
61C2×C4×D13—44no—
62C2×C4×D13—41no—
63C2×C4×D13—41no—
64C2×#1057—44no—
65C13×C4⋊C4—41no—
66C42×C13—41no—
67#6103—28no—
68#6103—42no—
69#6103—44no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13—42no—
78C4×Dic13—42no—
79C4×Dic13C2×C812yes—
80C4×#124—131no—
81#1461—132no—
82#1324—132no—
83#1318—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—42no—
88C22×D13—41no—
89C22×D13—41no—
90Q8×C13—42no—
91Q8×C13—42no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13C22⋊C814yes—
102C2×C4×C13C22×C811yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13#9911yescharacteristic
113C2×Dic13#9911yescharacteristic
114D52—42no—
115D52—42no—
116C4×D13—82no—
117C4×D13—82no—
118#1057—84no—
119C2×#124—131no—
120C2×C4×Q8—131no—
121C2×C4×D4—131no—
122#431—262no—
123#391#26111yescharacteristic
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×C13C2×C22⋊C811yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13#41311yescharacteristic
136C2×D13—44no—
137C2×D13—42no—
138C2×D13—82no—
139C2×D13—81no—
140C2×D13—81no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—24no—
144C4×C13—42no—
145C4×C13—81no—
146Dic13—21no—
147Dic13—42no—
148Dic13—42no—
149Dic13—41no—
150Dic13#35512yes—
151C22×Q8C2×#26111yescharacteristic
152C22×D4—131no—
153C23×C4—261no—
154#124—134no—
155#124—262no—
156C4×Q8—521no—
157C4×Q8—521no—
158C4×D4—521no—
159C4×D4—521no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4C2×#26111yescharacteristic
163C2×C22⋊C4—262no—
164C2×C22⋊C4—261no—
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—22no—
176#95—262no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13#145911yescharacteristic
180C2×C13#212611yescharacteristic
181C2×C13C2×#35511yescharacteristic
182D13—82no—
183C24—261no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8D13⋊C812yes—
187C2×Q8#611812yes—
188C2×D4—132no—
189C2×D4—261no—
190C2×D4—521no—
191C2×D4—521no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—131no—
195C22×C4—132no—
196C22×C4—131no—
197C22×C4—261no—
198C22×C4—521no—
199C22×C4—521no—
200C22×C4—524no—
201C22×C4C22⋊#26112yes—
202C22×C4C22×#26111yescharacteristic
203C2×C8—524no—
204C4⋊C4—41no—
205C4⋊C4—521no—
206C4⋊C4—522no—
207C22⋊C4—268no—
208C22⋊C4—524no—
209C22⋊C4—522no—
210C42—41no—
211C42—132no—
212C42—262no—
213C42—262no—
214C42—261no—
215C42—261no—
216C42—261no—
217C42—522no—
218C42—522no—
219C13#1147611yescharacteristic, complemented, Sylow
220C23—262no—
221C23—522no—
222C23—522no—
223C23—521no—
224C23—521no—
225C23C2×C22⋊#26111yescharacteristic
226Q8—42no—
227Q8—42no—
228D4—522no—
229D4—522no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—131no—
240C2×C4—131no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—522no—
249C2×C4—1042no—
250C2×C4—1042no—
251C2×C4#8811114yes—
252C2×C4C2×D13⋊C811yescharacteristic
253C2×C4C2×#611811yescharacteristic
254C8—1044no—
255C22—21no—
256C22—21no—
257C22—524no—
258C22—522no—
259C22—1042no—
260C22—1041no—
261C22—1041no—
262C22C2×#8811111yescharacteristic
263C22D13⋊#9911yescharacteristic
264C22#1171914811yescharacteristic
265C4—24no—
266C4—21no—
267C4—21no—
268C4—42no—
269C4—81no—
270C4—132no—
271C4—261no—
272C4—522no—
273C4—522no—
274C4—521no—
275C2—21no—
276C2—21no—
277C2—1042no—
278C2#1313007411yescharacteristic
279C2#1313111011yescharacteristic
280C2D13⋊#35511yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#391C4
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C4⋊Dic13C23
hypercenter#391#261
hypocenterC13#11476
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #13130079C2semidirect
2. #13129777C2semidirect
23. #88201C8semidirect
219. C13#11476semidirect

Maximal subgroups

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

subgroupindex
#131300792
#131297772
#131297652
#131173792
#1147613