Finite Group Databasebeta

← #16787103

Subgroups — #16787103

Order 3328.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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#13130099C212yesmaximal, complemented
2#13129778C212yesmaximal, complemented
3#13129764C212yesmaximal
4#13117549C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8#11719128—22no—
9#11718891C411yescharacteristic
10#11718882C2211yescharacteristic
11#11718612—22no—
12#11718611—22no—
13#11718596C2211yescharacteristic
14#11718593C411yescharacteristic
15#11718285—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×Dic13—21no—
20C13×#124—22no—
21C13×#124—22no—
22C2×C13×C22⋊C4—22no—
23C2×C42×C13C2×C411yescharacteristic
24C2×C22⋊Dic13—21no—
25C2×C22⋊Dic13—22no—
26Q8×Dic13—42no—
27D4×Dic13—42no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×C4⋊Dic13D412yes—
31C2×C4⋊Dic13C2311yescharacteristic
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C22⋊#1057—24no—
36#88112—42no—
37#88110—42no—
38#88071—22no—
39#88071—21no—
40#88071—21no—
41#11534—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—21no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13M1612yes—
51C22×C4×C13—21no—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13—42no—
57C22×Dic13—82no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C2×D412yes—
61C2×#1057—44no—
62C13×C22⋊C4—28no—
63C42×C13—21no—
64C42×C13M1612yes—
65C22⋊Dic13—42no—
66C22⋊Dic13—82no—
67C4⋊Dic13—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70C4⋊Dic13—82no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—41no—
75#2326—131no—
76#1467—132no—
77#1325—132no—
78#1318—132no—
79C23×C13—22no—
80C23×C13—42no—
81C23×C13—42no—
82C23×C13—41no—
83C23×C13—41no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87D4×C13—42no—
88D4×C13—42no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13C2×M1611yescharacteristic
98C2×C4×C13C2×M1611yescharacteristic
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—41no—
102C2×Dic13—42no—
103C2×Dic13—41no—
104C2×Dic13—42no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—84no—
110C2×Dic13#9912yes—
111#1057—84no—
112C2×#124#26111yescharacteristic
113C2×C4×Q8—131no—
114C2×C4×D4—131no—
115#432—262no—
116#391—131no—
117#390—131no—
118#388—262no—
119#385—262no—
120#384—131no—
121#376—131no—
122#324—134no—
123#324—262no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13—44no—
127C22×C13—42no—
128C22×C13—82no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#40711yescharacteristic
132C22×C13C2×#9911yescharacteristic
133C22×C13#41311yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138Dic13—22no—
139Dic13—42no—
140Dic13—41no—
141Dic13—81no—
142Dic13—81no—
143C22×Q8C2×#26111yescharacteristic
144C22×D4C2×#26111yescharacteristic
145C23×C4—261no—
146#124—22no—
147#124—22no—
148C4×Q8—522no—
149C4×D4—522no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—262no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—261no—
156C2×C22⋊C4—262no—
157C2×C42—132no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42C2×#26111yescharacteristic
161C4⋊C8—522no—
162C22⋊C8—264no—
163#97—522no—
164#95—261no—
165#95—261no—
166#95—262no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—82no—
170C2×C13#146511yescharacteristic
171C2×C13#212811yescharacteristic
172C2×C13#213311yescharacteristic
173C24—21no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4#612212yes—
182C22×C4—21no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—132no—
186C22×C4—261no—
187C22×C4—261no—
188C22×C4—522no—
189C22×C4—1042no—
190C22×C4C22⋊#26112yes—
191C22×C4C22×#26111yescharacteristic
192C2×C8—524no—
193C4⋊C4—521no—
194C4⋊C4—522no—
195C4⋊C4—521no—
196C4⋊C4—1042no—
197C22⋊C4—28no—
198C22⋊C4—522no—
199C22⋊C4—1042no—
200C42—21no—
201C42—262no—
202C42—262no—
203C42—262no—
204C42—521no—
205C42#612212yes—
206C13#1153411yescharacteristic, complemented, Sylow
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23C2×C22⋊#26111yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—132no—
226C2×C4—262no—
227C2×C4—261no—
228C2×C4—521no—
229C2×C4—522no—
230C2×C4—521no—
231C2×C4—521no—
232C2×C4—522no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—1044no—
237C2×C4C2×#612211yescharacteristic
238C2×C4C2×#612211yescharacteristic
239C8—1044no—
240C22—21no—
241C22—21no—
242C22—44no—
243C22—42no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22D13⋊#9911yescharacteristic
248C22#1171914811yescharacteristic
249C22#1171916911yescharacteristic
250C4—21no—
251C4—21no—
252C4—42no—
253C4—42no—
254C4—262no—
255C4—522no—
256C4—521no—
257C4—1041no—
258C4—1041no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2#1313009211yescharacteristic
263C2#1313111611yescharacteristic
264C2#1313113211yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#124C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#124#261
hypocenterC13#11534
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #13130099C2semidirect
2. #13129778C2semidirect
206. C13#11534semidirect

Maximal subgroups

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

subgroupindex
#131300992
#131297782
#131297642
#131175492
#1153413