Finite Group Databasebeta

← #16781912

Subgroups — #16781912

Order 3328.

486 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130716C212yesmaximal, complemented
2#13130093C212yesmaximal
3#13129708C212yesmaximal, complemented
4C2×#11718495C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8#11719127C2214yes—
9C2×#88104—22no—
10C2×C13×C4⋊C8C411yescharacteristic
11C2×#88060C411yescharacteristic
12C2×#88060C2211yescharacteristic
13C2×C4×#1055C411yescharacteristic
14#11718495—22no—
15#11718495—22no—
16#11718287—22no—
17#11718285—22no—
18#11718268—22no—
19C22×D52Q811yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13C2311yescharacteristic
22C2×#6118—24no—
23C22×C8×C13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×#6103D411yescharacteristic
27C2×#6103Q811yescharacteristic
28C2×C4⋊Dic13D411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C2×C8×D13—21no—
32C2×C8×D13—21no—
33C2×C8×D13—42no—
34C2×C8×D13—42no—
35C2×C8×D13D412yes—
36C2×C8×D13D412yes—
37C4×D52—22no—
38C4×D52—22no—
39C22⋊#1057—24no—
40#88111—24no—
41#88104—44no—
42C13×C4⋊C8—22no—
43#88060—22no—
44#88060—22no—
45C4×#1055—21no—
46C4×#1055—21no—
47#8611—131nomaximal, Sylow
48C23×D13C4⋊C411yescharacteristic
49C23×D13C2×Q811yescharacteristic
50C22×C4×C13C4⋊C411yescharacteristic
51C22×C4×C13C4⋊C411yescharacteristic
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13C4⋊C411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C2×D52—22no—
56C2×D52—22no—
57C2×D52—22no—
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13—41no—
61C2×C4×D13—41no—
62C2×C4×D13—41no—
63C2×C4×D13—41no—
64C2×C4×D13C2×D412yes—
65C2×C4×D13#4112yes—
66C2×#1057—44no—
67#6118—44no—
68#6118—44no—
69C2×C8×C13—21no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13C22⋊C412yes—
73C42×C13—21no—
74C42×C13—21no—
75#6103—22no—
76#6103—22no—
77C4⋊Dic13—22no—
78C2×#1055—22no—
79C2×#1055—21no—
80C2×#1055—41no—
81C2×#1055C22⋊C411yescharacteristic
82C2×#1055C22⋊C411yescharacteristic
83C8×D13—24no—
84C8×D13—42no—
85C8×D13—42no—
86C8×D13—42no—
87C2×C8×D4—131no—
88#1810—132no—
89#1465—132no—
90#1293—132no—
91C23×C13C2×C4⋊C411yescharacteristic
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13#10812yescomplemented
101C22×D13C22⋊Q812yes—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13#10812yescomplemented
109C2×C4×C13C2×C22⋊C411yescharacteristic
110C2×C4×C13#11711yescharacteristic
111C2×Dic13—21no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13#12112yes—
115D52—28no—
116C4×D13—22no—
117C4×D13—22no—
118C4×D13—42no—
119C4×D13—42no—
120C4×D13—41no—
121C4×D13—41no—
122#1057—84no—
123C8×C13—22no—
124C8×C13—41no—
125#1055—21no—
126#1055—41no—
127#1055#9912yes—
128C23×C8—131no—
129C23×C8—131no—
130C2×C4×D4—131no—
131C8×D4—262no—
132C8×D4—262no—
133C2×#108—262no—
134C2×C4⋊C8#26111yescharacteristic
135#407—134no—
136C2×C22⋊C8—131no—
137C2×C22⋊C8—131no—
138C2×C4×C8—131no—
139#341—262no—
140#324—262no—
141#323—262no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13#38011yescharacteristic
145C22×C13C2×#10811yescharacteristic
146C22×C13C2×#10811yescharacteristic
147C2×D13—22no—
148C2×D13—22no—
149C2×D13—22no—
150C2×D13—22no—
151C2×D13—42no—
152C2×D13—42no—
153C2×D13—42no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—42no—
157C4×C13—21no—
158C4×C13—22no—
159C4×C13—41no—
160C4×C13C2×#9911yescharacteristic
161C4×C13#41011yescharacteristic
162Dic13—22no—
163Dic13—41no—
164C22×D4—131no—
165C23×C4—131no—
166C23×C4—131no—
167C2×M16—264no—
168C22×C8—131no—
169C22×C8—132no—
170C22×C8—132no—
171C22×C8—131no—
172C22×C8—261no—
173C22×C8—261no—
174C22×C8—522no—
175C22×C8—522no—
176C22×C8C2×#26111yescharacteristic
177C22×C8C2×#26111yescharacteristic
178C4×D4—262no—
179C4×D4—262no—
180C2×C4⋊C4—131no—
181C2×C22⋊C4—131no—
182C2×C22⋊C4—131no—
183C2×C42C2×#26111yescharacteristic
184#108—524no—
185C4⋊C8—22no—
186C22⋊C8—262no—
187C22⋊C8—262no—
188C22⋊C8—264no—
189C22⋊C8—264no—
190C4×C8—261no—
191C4×C8—261no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13#179911yescharacteristic
195C2×C13#181011yescharacteristic
196C2×C13#181311yescharacteristic
197D13—42no—
198D13—42no—
199C24—131no—
200C24—131no—
201C2×D4—262no—
202C2×D4—262no—
203C2×D4—262no—
204C22×C4—131no—
205C22×C4—132no—
206C22×C4—132no—
207C22×C4—131no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—521no—
211C22×C4—521no—
212C22×C4—521no—
213C22×C4—521no—
214C22×C4C4⋊#26111yescharacteristic
215C22×C4C4⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217M16—524no—
218M16—524no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—131no—
223C2×C8—131no—
224C2×C8—264no—
225C2×C8—262no—
226C2×C8—261no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C2×C8—521no—
231C2×C8—524no—
232C2×C8C22⋊#26112yes—
233C4⋊C4—262no—
234C22⋊C4—262no—
235C22⋊C4—262no—
236C42—21no—
237C42—21no—
238C13#861111yescharacteristic, complemented, Sylow
239C23—132no—
240C23—132no—
241C23—261no—
242C23—261no—
243C23—261no—
244C23—261no—
245C23—521no—
246C23—521no—
247C23—521no—
248C23—521no—
249C23C2×C4⋊#26111yescharacteristic
250D4—268no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—132no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—261no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4#8810412yescomplemented
268C2×C4#8823711yescharacteristic
269C2×C4C2×C22⋊#26111yescharacteristic
270C8—22no—
271C8—41no—
272C8—132no—
273C8—261no—
274C8—521no—
275C8—1044no—
276C22—21no—
277C22—21no—
278C22—262no—
279C22—262no—
280C22—262no—
281C22—262no—
282C22—522no—
283C22—522no—
284C22—522no—
285C22—522no—
286C22—521no—
287C22—521no—
288C22C2×#8810411yescharacteristic
289C22D13⋊#10811yescharacteristic
290C22#1171913611yescharacteristic
291C4—21no—
292C4—22no—
293C4—41no—
294C4—262no—
295C4—521no—
296C4D13⋊#9911yescharacteristic
297C4#1171915611yescharacteristic
298C2—21no—
299C2—21no—
300C2—522no—
301C2—522no—
302C2#1313069911yescharacteristic
303C2#1313071611yescharacteristic
304C2#1313072111yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13#380
prime radicalC22×D52Q8
cosocleC22×C4×D13C23
hypercenterC2×C4⋊C8#261
hypocenterC13#8611
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #13130716C2semidirect
3. #13129708C2semidirect
100. C22×D13#108semidirect
108. C2×C4×C13#108semidirect
238. C13#8611semidirect
267. C2×C4#88104semidirect

Maximal subgroups

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

subgroupindex
#131307162
#131300932
#131297082
C2×#117184952
#861113